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  22.    <div id="projectname">3DEX&#160;<span id="projectnumber">1.0</span></div>
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  23.    <div id="projectbrief">Three-dimensional Fourier-Bessel decomposition</div>
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  62. <div class="title">/Users/bl/Dropbox/3DEX/src/f90/external/quadrule.f90</div>  </div>
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  64. <div class="contents">
    65. 

  65. <a href="quadrule_8f90.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a><a class="code" href="quadrule_8f90.html#a5db7bba3aa7d37d932b3f545141b52d4">00001</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a5db7bba3aa7d37d932b3f545141b52d4">bashforth_set</a> ( norder, xtab, weight )
    66. 

  66. <a name="l00002"></a>00002 <span class="comment">!</span>
    67. 

  67. <a name="l00003"></a>00003 <span class="comment">!*******************************************************************************</span>
    68. 

  68. <a name="l00004"></a>00004 <span class="comment">!</span>
    69. 

  69. <a name="l00005"></a>00005 <span class="comment">!! BASHFORTH_SET sets abscissas and weights for Adams-Bashforth quadrature.</span>
    70. 

  70. <a name="l00006"></a>00006 <span class="comment">!</span>
    71. 

  71. <a name="l00007"></a>00007 <span class="comment">!</span>
    72. 

  72. <a name="l00008"></a>00008 <span class="comment">!  Definition:</span>
    73. 

  73. <a name="l00009"></a>00009 <span class="comment">!</span>
    74. 

  74. <a name="l00010"></a>00010 <span class="comment">!    Adams-Bashforth quadrature formulas are normally used in solving</span>
    75. 

  75. <a name="l00011"></a>00011 <span class="comment">!    ordinary differential equations, and are not really suitable for</span>
    76. 

  76. <a name="l00012"></a>00012 <span class="comment">!    general quadrature computations.  However, an Adams-Bashforth formula</span>
    77. 

  77. <a name="l00013"></a>00013 <span class="comment">!    is equivalent to approximating the integral of F(Y(X)) between X(M)</span>
    78. 

  78. <a name="l00014"></a>00014 <span class="comment">!    and X(M+1), using an explicit formula that relies only on known values</span>
    79. 

  79. <a name="l00015"></a>00015 <span class="comment">!    of F(Y(X)) at X(M-N+1) through X(M).  For this reason, the formulas</span>
    80. 

  80. <a name="l00016"></a>00016 <span class="comment">!    have been included here.</span>
    81. 

  81. <a name="l00017"></a>00017 <span class="comment">!</span>
    82. 

  82. <a name="l00018"></a>00018 <span class="comment">!    Suppose the unknown function is denoted by Y(X), with derivative</span>
    83. 

  83. <a name="l00019"></a>00019 <span class="comment">!    F(Y(X)), and that approximate values of the function are known at a</span>
    84. 

  84. <a name="l00020"></a>00020 <span class="comment">!    series of X values, which we write as X(1), X(2), ..., X(M).  We write</span>
    85. 

  85. <a name="l00021"></a>00021 <span class="comment">!    the value Y(X(1)) as Y(1) and so on.</span>
    86. 

  86. <a name="l00022"></a>00022 <span class="comment">!</span>
    87. 

  87. <a name="l00023"></a>00023 <span class="comment">!    Then the solution of the ODE Y&#39;=F(X,Y) at the next point X(M+1) is</span>
    88. 

  88. <a name="l00024"></a>00024 <span class="comment">!    computed by:</span>
    89. 

  89. <a name="l00025"></a>00025 <span class="comment">!</span>
    90. 

  90. <a name="l00026"></a>00026 <span class="comment">!      Y(M+1) = Y(M) + Integral ( X(M) &lt; X &lt; X(M+1) ) F(Y(X)) dX</span>
    91. 

  91. <a name="l00027"></a>00027 <span class="comment">!             = Y(M) + H * Sum ( 1 &lt;= I &lt;= N ) W(I) * F(Y(M+1-I)) approximately.</span>
    92. 

  92. <a name="l00028"></a>00028 <span class="comment">!</span>
    93. 

  93. <a name="l00029"></a>00029 <span class="comment">!    In the documentation that follows, we replace F(Y(X)) by F(X).</span>
    94. 

  94. <a name="l00030"></a>00030 <span class="comment">!</span>
    95. 

  95. <a name="l00031"></a>00031 <span class="comment">!  Integration interval:</span>
    96. 

  96. <a name="l00032"></a>00032 <span class="comment">!</span>
    97. 

  97. <a name="l00033"></a>00033 <span class="comment">!    [ 0, 1 ].</span>
    98. 

  98. <a name="l00034"></a>00034 <span class="comment">!</span>
    99. 

  99. <a name="l00035"></a>00035 <span class="comment">!  Weight function:</span>
    100. 

  100. <a name="l00036"></a>00036 <span class="comment">!</span>
    101. 

  101. <a name="l00037"></a>00037 <span class="comment">!    1.0D+00</span>
    102. 

  102. <a name="l00038"></a>00038 <span class="comment">!</span>
    103. 

  103. <a name="l00039"></a>00039 <span class="comment">!  Integral to approximate:</span>
    104. 

  104. <a name="l00040"></a>00040 <span class="comment">!</span>
    105. 

  105. <a name="l00041"></a>00041 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) F(X) dX.</span>
    106. 

  106. <a name="l00042"></a>00042 <span class="comment">!</span>
    107. 

  107. <a name="l00043"></a>00043 <span class="comment">!  Approximate integral:</span>
    108. 

  108. <a name="l00044"></a>00044 <span class="comment">!</span>
    109. 

  109. <a name="l00045"></a>00045 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( 1 - I ),</span>
    110. 

  110. <a name="l00046"></a>00046 <span class="comment">!</span>
    111. 

  111. <a name="l00047"></a>00047 <span class="comment">!  Note:</span>
    112. 

  112. <a name="l00048"></a>00048 <span class="comment">!</span>
    113. 

  113. <a name="l00049"></a>00049 <span class="comment">!    The Adams-Bashforth formulas require equally spaced data.</span>
    114. 

  114. <a name="l00050"></a>00050 <span class="comment">!</span>
    115. 

  115. <a name="l00051"></a>00051 <span class="comment">!    Here is how the formula is applied in the case with non-unit spacing:</span>
    116. 

  116. <a name="l00052"></a>00052 <span class="comment">!</span>
    117. 

  117. <a name="l00053"></a>00053 <span class="comment">!      Integral ( A &lt;= X &lt;= A+H ) F(X) dX =</span>
    118. 

  118. <a name="l00054"></a>00054 <span class="comment">!      H * Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( A - (I-1)*H ),</span>
    119. 

  119. <a name="l00055"></a>00055 <span class="comment">!      approximately.</span>
    120. 

  120. <a name="l00056"></a>00056 <span class="comment">!</span>
    121. 

  121. <a name="l00057"></a>00057 <span class="comment">!    The reference lists the second coefficient of the order 8 Adams-Bashforth</span>
    122. 

  122. <a name="l00058"></a>00058 <span class="comment">!    formula as</span>
    123. 

  123. <a name="l00059"></a>00059 <span class="comment">!      weight(2) =  -1162169.0D+00 / 120960.0D+00</span>
    124. 

  124. <a name="l00060"></a>00060 <span class="comment">!    but this should be</span>
    125. 

  125. <a name="l00061"></a>00061 <span class="comment">!      weight(2) =  -1152169.0D+00 / 120960.0D+00</span>
    126. 

  126. <a name="l00062"></a>00062 <span class="comment">!</span>
    127. 

  127. <a name="l00063"></a>00063 <span class="comment">!  Reference:</span>
    128. 

  128. <a name="l00064"></a>00064 <span class="comment">!</span>
    129. 

  129. <a name="l00065"></a>00065 <span class="comment">!    Abramowitz and Stegun,</span>
    130. 

  130. <a name="l00066"></a>00066 <span class="comment">!    Handbook of Mathematical Functions,</span>
    131. 

  131. <a name="l00067"></a>00067 <span class="comment">!    National Bureau of Standards, 1964.</span>
    132. 

  132. <a name="l00068"></a>00068 <span class="comment">!</span>
    133. 

  133. <a name="l00069"></a>00069 <span class="comment">!    Jean Lapidus and John Seinfeld,</span>
    134. 

  134. <a name="l00070"></a>00070 <span class="comment">!    Numerical Solution of Ordinary Differential Equations,</span>
    135. 

  135. <a name="l00071"></a>00071 <span class="comment">!    Academic Press, 1971.</span>
    136. 

  136. <a name="l00072"></a>00072 <span class="comment">!</span>
    137. 

  137. <a name="l00073"></a>00073 <span class="comment">!    Daniel Zwillinger, editor,</span>
    138. 

  138. <a name="l00074"></a>00074 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    139. 

  139. <a name="l00075"></a>00075 <span class="comment">!    30th Edition,</span>
    140. 

  140. <a name="l00076"></a>00076 <span class="comment">!    CRC Press, 1996.</span>
    141. 

  141. <a name="l00077"></a>00077 <span class="comment">!</span>
    142. 

  142. <a name="l00078"></a>00078 <span class="comment">!  Modified:</span>
    143. 

  143. <a name="l00079"></a>00079 <span class="comment">!</span>
    144. 

  144. <a name="l00080"></a>00080 <span class="comment">!    15 September 1998</span>
    145. 

  145. <a name="l00081"></a>00081 <span class="comment">!</span>
    146. 

  146. <a name="l00082"></a>00082 <span class="comment">!  Author:</span>
    147. 

  147. <a name="l00083"></a>00083 <span class="comment">!</span>
    148. 

  148. <a name="l00084"></a>00084 <span class="comment">!    John Burkardt</span>
    149. 

  149. <a name="l00085"></a>00085 <span class="comment">!</span>
    150. 

  150. <a name="l00086"></a>00086 <span class="comment">!  Parameters:</span>
    151. 

  151. <a name="l00087"></a>00087 <span class="comment">!</span>
    152. 

  152. <a name="l00088"></a>00088 <span class="comment">!    Input, integer NORDER, the order of the rule.  NORDER should be</span>
    153. 

  153. <a name="l00089"></a>00089 <span class="comment">!    between 1 and 8.</span>
    154. 

  154. <a name="l00090"></a>00090 <span class="comment">!</span>
    155. 

  155. <a name="l00091"></a>00091 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    156. 

  156. <a name="l00092"></a>00092 <span class="comment">!</span>
    157. 

  157. <a name="l00093"></a>00093 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    158. 

  158. <a name="l00094"></a>00094 <span class="comment">!    WEIGHT(1) is the weight at X = 0, WEIGHT(2) the weight at X = -1,</span>
    159. 

  159. <a name="l00095"></a>00095 <span class="comment">!    and so on.  The weights are rational, and should sum to 1.  Some</span>
    160. 

  160. <a name="l00096"></a>00096 <span class="comment">!    weights may be negative.</span>
    161. 

  161. <a name="l00097"></a>00097 <span class="comment">!</span>
    162. 

  162. <a name="l00098"></a>00098   <span class="keyword">implicit none</span>
    163. 

  163. <a name="l00099"></a>00099 <span class="comment">!</span>
    164. 

  164. <a name="l00100"></a>00100   <span class="keywordtype">integer</span> norder
    165. 

  165. <a name="l00101"></a>00101 <span class="comment">!</span>
    166. 

  166. <a name="l00102"></a>00102   <span class="keywordtype">double precision</span> d
    167. 

  167. <a name="l00103"></a>00103   <span class="keywordtype">integer</span> i
    168. 

  168. <a name="l00104"></a>00104   <span class="keywordtype">double precision</span> weight(norder)
    169. 

  169. <a name="l00105"></a>00105   <span class="keywordtype">double precision</span> xtab(norder)
    170. 

  170. <a name="l00106"></a>00106 <span class="comment">!</span>
    171. 

  171. <a name="l00107"></a>00107   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    172. 

  172. <a name="l00108"></a>00108 
    173. 

  173. <a name="l00109"></a>00109     weight(1) = 1.0D+00
    174. 

  174. <a name="l00110"></a>00110 
    175. 

  175. <a name="l00111"></a>00111   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    176. 

  176. <a name="l00112"></a>00112 
    177. 

  177. <a name="l00113"></a>00113     d = 2.0D+00
    178. 

  178. <a name="l00114"></a>00114 
    179. 

  179. <a name="l00115"></a>00115     weight(1) =   3.0D+00 / d
    180. 

  180. <a name="l00116"></a>00116     weight(2) = - 1.0D+00 / d
    181. 

  181. <a name="l00117"></a>00117 
    182. 

  182. <a name="l00118"></a>00118   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    183. 

  183. <a name="l00119"></a>00119 
    184. 

  184. <a name="l00120"></a>00120     d = 12.0D+00
    185. 

  185. <a name="l00121"></a>00121 
    186. 

  186. <a name="l00122"></a>00122     weight(1) =   23.0D+00 / d
    187. 

  187. <a name="l00123"></a>00123     weight(2) = - 16.0D+00 / d
    188. 

  188. <a name="l00124"></a>00124     weight(3) =    5.0D+00 / d
    189. 

  189. <a name="l00125"></a>00125 
    190. 

  190. <a name="l00126"></a>00126   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    191. 

  191. <a name="l00127"></a>00127 
    192. 

  192. <a name="l00128"></a>00128     d = 24.0D+00
    193. 

  193. <a name="l00129"></a>00129 
    194. 

  194. <a name="l00130"></a>00130     weight(1) =   55.0D+00 / d
    195. 

  195. <a name="l00131"></a>00131     weight(2) = - 59.0D+00 / d
    196. 

  196. <a name="l00132"></a>00132     weight(3) =   37.0D+00 / d
    197. 

  197. <a name="l00133"></a>00133     weight(4) =  - 9.0D+00 / d
    198. 

  198. <a name="l00134"></a>00134 
    199. 

  199. <a name="l00135"></a>00135   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    200. 

  200. <a name="l00136"></a>00136 
    201. 

  201. <a name="l00137"></a>00137     d = 720.0D+00
    202. 

  202. <a name="l00138"></a>00138 
    203. 

  203. <a name="l00139"></a>00139     weight(1) =   1901.0D+00 / d
    204. 

  204. <a name="l00140"></a>00140     weight(2) = - 2774.0D+00 / d
    205. 

  205. <a name="l00141"></a>00141     weight(3) =   2616.0D+00 / d
    206. 

  206. <a name="l00142"></a>00142     weight(4) = - 1274.0D+00 / d
    207. 

  207. <a name="l00143"></a>00143     weight(5) =    251.0D+00 / d
    208. 

  208. <a name="l00144"></a>00144 
    209. 

  209. <a name="l00145"></a>00145   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    210. 

  210. <a name="l00146"></a>00146 
    211. 

  211. <a name="l00147"></a>00147     d = 1440.0D+00
    212. 

  212. <a name="l00148"></a>00148 
    213. 

  213. <a name="l00149"></a>00149     weight(1) =   4277.0D+00 / d
    214. 

  214. <a name="l00150"></a>00150     weight(2) = - 7923.0D+00 / d
    215. 

  215. <a name="l00151"></a>00151     weight(3) =   9982.0D+00 / d
    216. 

  216. <a name="l00152"></a>00152     weight(4) = - 7298.0D+00 / d
    217. 

  217. <a name="l00153"></a>00153     weight(5) =   2877.0D+00 / d
    218. 

  218. <a name="l00154"></a>00154     weight(6) =  - 475.0D+00 / d
    219. 

  219. <a name="l00155"></a>00155 
    220. 

  220. <a name="l00156"></a>00156   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    221. 

  221. <a name="l00157"></a>00157 
    222. 

  222. <a name="l00158"></a>00158     d = 60480.0D+00
    223. 

  223. <a name="l00159"></a>00159 
    224. 

  224. <a name="l00160"></a>00160     weight(1) =    198721.0D+00 / d
    225. 

  225. <a name="l00161"></a>00161     weight(2) =  - 447288.0D+00 / d
    226. 

  226. <a name="l00162"></a>00162     weight(3) =    705549.0D+00 / d
    227. 

  227. <a name="l00163"></a>00163     weight(4) =  - 688256.0D+00 / d
    228. 

  228. <a name="l00164"></a>00164     weight(5) =    407139.0D+00 / d
    229. 

  229. <a name="l00165"></a>00165     weight(6) =  - 134472.0D+00 / d
    230. 

  230. <a name="l00166"></a>00166     weight(7) =     19087.0D+00 / d
    231. 

  231. <a name="l00167"></a>00167 
    232. 

  232. <a name="l00168"></a>00168   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    233. 

  233. <a name="l00169"></a>00169 
    234. 

  234. <a name="l00170"></a>00170     d = 120960.0D+00
    235. 

  235. <a name="l00171"></a>00171 
    236. 

  236. <a name="l00172"></a>00172     weight(1) =     434241.0D+00 / d
    237. 

  237. <a name="l00173"></a>00173     weight(2) =  - 1152169.0D+00 / d
    238. 

  238. <a name="l00174"></a>00174     weight(3) =    2183877.0D+00 / d
    239. 

  239. <a name="l00175"></a>00175     weight(4) =  - 2664477.0D+00 / d
    240. 

  240. <a name="l00176"></a>00176     weight(5) =    2102243.0D+00 / d
    241. 

  241. <a name="l00177"></a>00177     weight(6) =  - 1041723.0D+00 / d
    242. 

  242. <a name="l00178"></a>00178     weight(7) =     295767.0D+00 / d
    243. 

  243. <a name="l00179"></a>00179     weight(8) =    - 36799.0D+00 / d
    244. 

  244. <a name="l00180"></a>00180 
    245. 

  245. <a name="l00181"></a>00181   <span class="keyword">else</span>
    246. 

  246. <a name="l00182"></a>00182 
    247. 

  247. <a name="l00183"></a>00183     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    248. 

  248. <a name="l00184"></a>00184     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;BASHFORTH_SET - Fatal error!&#39;</span>
    249. 

  249. <a name="l00185"></a>00185     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    250. 

  250. <a name="l00186"></a>00186     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 1 through 8.&#39;</span>
    251. 

  251. <a name="l00187"></a>00187     stop
    252. 

  252. <a name="l00188"></a>00188 
    253. 

  253. <a name="l00189"></a>00189   <span class="keyword">end if</span>
    254. 

  254. <a name="l00190"></a>00190 
    255. 

  255. <a name="l00191"></a>00191   <span class="keyword">do</span> i = 1, norder
    256. 

  256. <a name="l00192"></a>00192     xtab(i) = dble ( 1 - i )
    257. 

  257. <a name="l00193"></a>00193   <span class="keyword">end do</span>
    258. 

  258. <a name="l00194"></a>00194 
    259. 

  259. <a name="l00195"></a>00195   return
    260. 

  260. <a name="l00196"></a>00196 <span class="keyword">end</span>
    261. 

  261. <a name="l00197"></a><a class="code" href="quadrule_8f90.html#a33c49c6fa2701ed35a7132dfa2ee7a90">00197</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a33c49c6fa2701ed35a7132dfa2ee7a90">bdf_set</a> ( norder, alpha, beta, gamma )
    262. 

  262. <a name="l00198"></a>00198 <span class="comment">!</span>
    263. 

  263. <a name="l00199"></a>00199 <span class="comment">!*******************************************************************************</span>
    264. 

  264. <a name="l00200"></a>00200 <span class="comment">!</span>
    265. 

  265. <a name="l00201"></a>00201 <span class="comment">!! BDF_SET sets weights for backward differentiation ODE weights.</span>
    266. 

  266. <a name="l00202"></a>00202 <span class="comment">!</span>
    267. 

  267. <a name="l00203"></a>00203 <span class="comment">!</span>
    268. 

  268. <a name="l00204"></a>00204 <span class="comment">!  Discussion:</span>
    269. 

  269. <a name="l00205"></a>00205 <span class="comment">!</span>
    270. 

  270. <a name="l00206"></a>00206 <span class="comment">!    GAMMA * Y(N+1) = Sum ( 1 &lt;= I &lt;= NORDER ) ALPHA(I) * Y(N+1-I)</span>
    271. 

  271. <a name="l00207"></a>00207 <span class="comment">!                     + dX * BETA * Y&#39;(X(N+1),Y(N+1))</span>
    272. 

  272. <a name="l00208"></a>00208 <span class="comment">!</span>
    273. 

  273. <a name="l00209"></a>00209 <span class="comment">!    This is equivalent to the backward differentiation corrector formulas.</span>
    274. 

  274. <a name="l00210"></a>00210 <span class="comment">!</span>
    275. 

  275. <a name="l00211"></a>00211 <span class="comment">!  Modified:</span>
    276. 

  276. <a name="l00212"></a>00212 <span class="comment">!</span>
    277. 

  277. <a name="l00213"></a>00213 <span class="comment">!    30 December 1999</span>
    278. 

  278. <a name="l00214"></a>00214 <span class="comment">!</span>
    279. 

  279. <a name="l00215"></a>00215 <span class="comment">!  Author:</span>
    280. 

  280. <a name="l00216"></a>00216 <span class="comment">!</span>
    281. 

  281. <a name="l00217"></a>00217 <span class="comment">!    John Burkardt</span>
    282. 

  282. <a name="l00218"></a>00218 <span class="comment">!</span>
    283. 

  283. <a name="l00219"></a>00219 <span class="comment">!  Parameters:</span>
    284. 

  284. <a name="l00220"></a>00220 <span class="comment">!</span>
    285. 

  285. <a name="l00221"></a>00221 <span class="comment">!    Input, integer NORDER, the order of the rule, between 1 and 6.</span>
    286. 

  286. <a name="l00222"></a>00222 <span class="comment">!</span>
    287. 

  287. <a name="l00223"></a>00223 <span class="comment">!    Output, double precision ALPHA(NORDER), BETA, GAMMA, the weights.</span>
    288. 

  288. <a name="l00224"></a>00224 <span class="comment">!</span>
    289. 

  289. <a name="l00225"></a>00225   <span class="keyword">implicit none</span>
    290. 

  290. <a name="l00226"></a>00226 <span class="comment">!</span>
    291. 

  291. <a name="l00227"></a>00227   <span class="keywordtype">integer</span> norder
    292. 

  292. <a name="l00228"></a>00228 <span class="comment">!</span>
    293. 

  293. <a name="l00229"></a>00229   <span class="keywordtype">double precision</span> alpha(norder)
    294. 

  294. <a name="l00230"></a>00230   <span class="keywordtype">double precision</span> beta
    295. 

  295. <a name="l00231"></a>00231   <span class="keywordtype">double precision</span> gamma
    296. 

  296. <a name="l00232"></a>00232 <span class="comment">!</span>
    297. 

  297. <a name="l00233"></a>00233   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    298. 

  298. <a name="l00234"></a>00234     beta =     1.0D+00
    299. 

  299. <a name="l00235"></a>00235     gamma =    1.0D+00
    300. 

  300. <a name="l00236"></a>00236     alpha(1) = 1.0D+00
    301. 

  301. <a name="l00237"></a>00237   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    302. 

  302. <a name="l00238"></a>00238     beta =       2.0D+00
    303. 

  303. <a name="l00239"></a>00239     gamma =      3.0D+00
    304. 

  304. <a name="l00240"></a>00240     alpha(1) =   4.0D+00
    305. 

  305. <a name="l00241"></a>00241     alpha(2) = - 1.0D+00
    306. 

  306. <a name="l00242"></a>00242   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    307. 

  307. <a name="l00243"></a>00243     beta =       6.0D+00
    308. 

  308. <a name="l00244"></a>00244     gamma =     11.0D+00
    309. 

  309. <a name="l00245"></a>00245     alpha(1) =  18.0D+00
    310. 

  310. <a name="l00246"></a>00246     alpha(2) = - 9.0D+00
    311. 

  311. <a name="l00247"></a>00247     alpha(3) =   2.0D+00
    312. 

  312. <a name="l00248"></a>00248   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    313. 

  313. <a name="l00249"></a>00249     beta =       12.0D+00
    314. 

  314. <a name="l00250"></a>00250     gamma =      25.0D+00
    315. 

  315. <a name="l00251"></a>00251     alpha(1) =   48.0D+00
    316. 

  316. <a name="l00252"></a>00252     alpha(2) = - 36.0D+00
    317. 

  317. <a name="l00253"></a>00253     alpha(3) =   16.0D+00
    318. 

  318. <a name="l00254"></a>00254     alpha(4) =  - 3.0D+00
    319. 

  319. <a name="l00255"></a>00255   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    320. 

  320. <a name="l00256"></a>00256     beta =        60.0D+00
    321. 

  321. <a name="l00257"></a>00257     gamma =      137.0D+00
    322. 

  322. <a name="l00258"></a>00258     alpha(1) =   300.0D+00
    323. 

  323. <a name="l00259"></a>00259     alpha(2) = - 300.0D+00
    324. 

  324. <a name="l00260"></a>00260     alpha(3) =   200.0D+00
    325. 

  325. <a name="l00261"></a>00261     alpha(4) =  - 75.0D+00
    326. 

  326. <a name="l00262"></a>00262     alpha(5) =    12.0D+00
    327. 

  327. <a name="l00263"></a>00263   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    328. 

  328. <a name="l00264"></a>00264     beta =        60.0D+00
    329. 

  329. <a name="l00265"></a>00265     gamma =      147.0D+00
    330. 

  330. <a name="l00266"></a>00266     alpha(1) =   360.0D+00
    331. 

  331. <a name="l00267"></a>00267     alpha(2) = - 450.0D+00
    332. 

  332. <a name="l00268"></a>00268     alpha(3) =   400.0D+00
    333. 

  333. <a name="l00269"></a>00269     alpha(4) = - 225.0D+00
    334. 

  334. <a name="l00270"></a>00270     alpha(5) =    72.0D+00
    335. 

  335. <a name="l00271"></a>00271     alpha(6) =  - 10.0D+00
    336. 

  336. <a name="l00272"></a>00272   <span class="keyword">else</span>
    337. 

  337. <a name="l00273"></a>00273     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    338. 

  338. <a name="l00274"></a>00274     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;BDF_SET - Fatal error!&#39;</span>
    339. 

  339. <a name="l00275"></a>00275     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal order requested = &#39;</span>, norder
    340. 

  340. <a name="l00276"></a>00276     stop
    341. 

  341. <a name="l00277"></a>00277   <span class="keyword">end if</span>
    342. 

  342. <a name="l00278"></a>00278 
    343. 

  343. <a name="l00279"></a>00279   return
    344. 

  344. <a name="l00280"></a>00280 <span class="keyword">end</span>
    345. 

  345. <a name="l00281"></a><a class="code" href="quadrule_8f90.html#a7888ddfbe8865b018471ece2f1ac169b">00281</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a7888ddfbe8865b018471ece2f1ac169b">bdfc_set</a> ( norder, weight, xtab )
    346. 

  346. <a name="l00282"></a>00282 <span class="comment">!</span>
    347. 

  347. <a name="l00283"></a>00283 <span class="comment">!*******************************************************************************</span>
    348. 

  348. <a name="l00284"></a>00284 <span class="comment">!</span>
    349. 

  349. <a name="l00285"></a>00285 <span class="comment">!! BDFC_SET sets weights for backward differentiation corrector quadrature.</span>
    350. 

  350. <a name="l00286"></a>00286 <span class="comment">!</span>
    351. 

  351. <a name="l00287"></a>00287 <span class="comment">!</span>
    352. 

  352. <a name="l00288"></a>00288 <span class="comment">!  Definition:</span>
    353. 

  353. <a name="l00289"></a>00289 <span class="comment">!</span>
    354. 

  354. <a name="l00290"></a>00290 <span class="comment">!    A backward differentiation corrector formula is defined for a set</span>
    355. 

  355. <a name="l00291"></a>00291 <span class="comment">!    of evenly spaced abscissas X(I) with X(1) = 1 and X(2) = 0.  Assuming</span>
    356. 

  356. <a name="l00292"></a>00292 <span class="comment">!    that the values of the function to be integrated are known at the</span>
    357. 

  357. <a name="l00293"></a>00293 <span class="comment">!    abscissas, the formula is written in terms of the function value at</span>
    358. 

  358. <a name="l00294"></a>00294 <span class="comment">!    X(1), and the backward differences at X(1) that approximate the</span>
    359. 

  359. <a name="l00295"></a>00295 <span class="comment">!    derivatives there.</span>
    360. 

  360. <a name="l00296"></a>00296 <span class="comment">!</span>
    361. 

  361. <a name="l00297"></a>00297 <span class="comment">!  Integration interval:</span>
    362. 

  362. <a name="l00298"></a>00298 <span class="comment">!</span>
    363. 

  363. <a name="l00299"></a>00299 <span class="comment">!    [ 0, 1 ]</span>
    364. 

  364. <a name="l00300"></a>00300 <span class="comment">!</span>
    365. 

  365. <a name="l00301"></a>00301 <span class="comment">!  Weight function:</span>
    366. 

  366. <a name="l00302"></a>00302 <span class="comment">!</span>
    367. 

  367. <a name="l00303"></a>00303 <span class="comment">!    1.0D+00</span>
    368. 

  368. <a name="l00304"></a>00304 <span class="comment">!</span>
    369. 

  369. <a name="l00305"></a>00305 <span class="comment">!  Integral to approximate:</span>
    370. 

  370. <a name="l00306"></a>00306 <span class="comment">!</span>
    371. 

  371. <a name="l00307"></a>00307 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) F(X) dX</span>
    372. 

  372. <a name="l00308"></a>00308 <span class="comment">!</span>
    373. 

  373. <a name="l00309"></a>00309 <span class="comment">!  Approximate integral:</span>
    374. 

  374. <a name="l00310"></a>00310 <span class="comment">!</span>
    375. 

  375. <a name="l00311"></a>00311 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * BD**(I-1) F ( 1 ).</span>
    376. 

  376. <a name="l00312"></a>00312 <span class="comment">!</span>
    377. 

  377. <a name="l00313"></a>00313 <span class="comment">!    Here, &quot;BD**(I-1) F ( 1 )&quot; denotes the (I-1)st backward difference</span>
    378. 

  378. <a name="l00314"></a>00314 <span class="comment">!    of F at X = 1, using a spacing of 1.  In particular,</span>
    379. 

  379. <a name="l00315"></a>00315 <span class="comment">!</span>
    380. 

  380. <a name="l00316"></a>00316 <span class="comment">!    BD**0 F(1) = F(1)</span>
    381. 

  381. <a name="l00317"></a>00317 <span class="comment">!    BD**1 F(1) = F(1) - F(0)</span>
    382. 

  382. <a name="l00318"></a>00318 <span class="comment">!    BD**2 F(1) = F(1) - 2 * F(0) + F(-1 )</span>
    383. 

  383. <a name="l00319"></a>00319 <span class="comment">!</span>
    384. 

  384. <a name="l00320"></a>00320 <span class="comment">!  Note:</span>
    385. 

  385. <a name="l00321"></a>00321 <span class="comment">!</span>
    386. 

  386. <a name="l00322"></a>00322 <span class="comment">!    The relationship between a backward difference corrector and the</span>
    387. 

  387. <a name="l00323"></a>00323 <span class="comment">!    corresponding Adams-Moulton formula may be illustrated for the</span>
    388. 

  388. <a name="l00324"></a>00324 <span class="comment">!    BDF corrector of order 4:</span>
    389. 

  389. <a name="l00325"></a>00325 <span class="comment">!</span>
    390. 

  390. <a name="l00326"></a>00326 <span class="comment">!      BD**0 F(1) - 1/2 * BD**1 F(1) - 1/12 * BD**2 F(1) - 1/24 * BDF**3 F(1)</span>
    391. 

  391. <a name="l00327"></a>00327 <span class="comment">!      =            F(1)</span>
    392. 

  392. <a name="l00328"></a>00328 <span class="comment">!        -  1/2 * ( F(1) -         F(0) )</span>
    393. 

  393. <a name="l00329"></a>00329 <span class="comment">!        - 1/12 * ( F(1) - 2     * F(0) +        F(-1) )</span>
    394. 

  394. <a name="l00330"></a>00330 <span class="comment">!        - 1/24 * ( F(1) - 3     * F(0) + 3    * F(-1) -        F(-2) )</span>
    395. 

  395. <a name="l00331"></a>00331 <span class="comment">!      =   9/24 *   F(1) + 19/24 * F(0) - 5/24 * F(-1) + 1/24 * F(-2)</span>
    396. 

  396. <a name="l00332"></a>00332 <span class="comment">!</span>
    397. 

  397. <a name="l00333"></a>00333 <span class="comment">!    which is the Adams-Moulton formula of order 4.</span>
    398. 

  398. <a name="l00334"></a>00334 <span class="comment">! </span>
    399. 

  399. <a name="l00335"></a>00335 <span class="comment">!  Reference:</span>
    400. 

  400. <a name="l00336"></a>00336 <span class="comment">!</span>
    401. 

  401. <a name="l00337"></a>00337 <span class="comment">!    Simeon Fatunla,</span>
    402. 

  402. <a name="l00338"></a>00338 <span class="comment">!    Numerical Methods for Initial Value Problems in Ordinary Differential</span>
    403. 

  403. <a name="l00339"></a>00339 <span class="comment">!      Equations,</span>
    404. 

  404. <a name="l00340"></a>00340 <span class="comment">!    Academic Press, 1988.</span>
    405. 

  405. <a name="l00341"></a>00341 <span class="comment">!</span>
    406. 

  406. <a name="l00342"></a>00342 <span class="comment">!  Modified:</span>
    407. 

  407. <a name="l00343"></a>00343 <span class="comment">!</span>
    408. 

  408. <a name="l00344"></a>00344 <span class="comment">!    28 February 2000</span>
    409. 

  409. <a name="l00345"></a>00345 <span class="comment">!</span>
    410. 

  410. <a name="l00346"></a>00346 <span class="comment">!  Author:</span>
    411. 

  411. <a name="l00347"></a>00347 <span class="comment">!</span>
    412. 

  412. <a name="l00348"></a>00348 <span class="comment">!    John Burkardt</span>
    413. 

  413. <a name="l00349"></a>00349 <span class="comment">!</span>
    414. 

  414. <a name="l00350"></a>00350 <span class="comment">!  Parameters:</span>
    415. 

  415. <a name="l00351"></a>00351 <span class="comment">!</span>
    416. 

  416. <a name="l00352"></a>00352 <span class="comment">!    Input, integer NORDER, the order of the rule, which can be</span>
    417. 

  417. <a name="l00353"></a>00353 <span class="comment">!    any value from 1 to 19.</span>
    418. 

  418. <a name="l00354"></a>00354 <span class="comment">!</span>
    419. 

  419. <a name="l00355"></a>00355 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    420. 

  420. <a name="l00356"></a>00356 <span class="comment">!</span>
    421. 

  421. <a name="l00357"></a>00357 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    422. 

  422. <a name="l00358"></a>00358 <span class="comment">!</span>
    423. 

  423. <a name="l00359"></a>00359   <span class="keyword">implicit none</span>
    424. 

  424. <a name="l00360"></a>00360 <span class="comment">!</span>
    425. 

  425. <a name="l00361"></a>00361   <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxord = 19
    426. 

  426. <a name="l00362"></a>00362 <span class="comment">!</span>
    427. 

  427. <a name="l00363"></a>00363   <span class="keywordtype">integer</span> norder
    428. 

  428. <a name="l00364"></a>00364 <span class="comment">!</span>
    429. 

  429. <a name="l00365"></a>00365   <span class="keywordtype">integer</span> i
    430. 

  430. <a name="l00366"></a>00366   <span class="keywordtype">double precision</span> w(maxord)
    431. 

  431. <a name="l00367"></a>00367   <span class="keywordtype">double precision</span> weight(norder)
    432. 

  432. <a name="l00368"></a>00368   <span class="keywordtype">double precision</span> xtab(norder)
    433. 

  433. <a name="l00369"></a>00369 <span class="comment">!</span>
    434. 

  434. <a name="l00370"></a>00370   w(1) =                 1.0D+00
    435. 

  435. <a name="l00371"></a>00371   w(2) =               - 1.0D+00 /               2.0D+00
    436. 

  436. <a name="l00372"></a>00372   w(3) =               - 1.0D+00 /              12.0D+00
    437. 

  437. <a name="l00373"></a>00373   w(4) =               - 1.0D+00 /              24.0D+00
    438. 

  438. <a name="l00374"></a>00374   w(5) =              - 19.0D+00 /             720.0D+00
    439. 

  439. <a name="l00375"></a>00375   w(6) =               - 3.0D+00 /             160.0D+00
    440. 

  440. <a name="l00376"></a>00376   w(7) =             - 863.0D+00 /           60480.0D+00
    441. 

  441. <a name="l00377"></a>00377   w(8) =             - 275.0D+00 /           24792.0D+00
    442. 

  442. <a name="l00378"></a>00378   w(9) =           - 33953.0D+00 /         3628800.0D+00
    443. 

  443. <a name="l00379"></a>00379   w(10) =           - 8183.0D+00 /         1036800.0D+00
    444. 

  444. <a name="l00380"></a>00380   w(11) =        - 3250433.0D+00 /       479001600.0D+00
    445. 

  445. <a name="l00381"></a>00381   w(12) =           - 4671.0D+00 /          788480.0D+00
    446. 

  446. <a name="l00382"></a>00382   w(13) =    - 13695779093.0D+00 /   2615348736000.0D+00
    447. 

  447. <a name="l00383"></a>00383   w(14) =     - 2224234463.0D+00 /    475517952000.0D+00
    448. 

  448. <a name="l00384"></a>00384   w(15) =   - 132282840127.0D+00 /  31384184832000.0D+00
    449. 

  449. <a name="l00385"></a>00385   w(16) =     - 2639651053.0D+00 /    689762304000.0D+00
    450. 

  450. <a name="l00386"></a>00386   w(17) =  111956703448001.0D+00 /   3201186852864.0D+00
    451. 

  451. <a name="l00387"></a>00387   w(18) =         50188465.0D+00 /     15613165568.0D+00
    452. 

  452. <a name="l00388"></a>00388   w(19) = 2334028946344463.0D+00 / 786014494949376.0D+00
    453. 

  453. <a name="l00389"></a>00389 
    454. 

  454. <a name="l00390"></a>00390   <span class="keyword">do</span> i = 1, min ( norder, maxord )
    455. 

  455. <a name="l00391"></a>00391     weight(i) = w(i)
    456. 

  456. <a name="l00392"></a>00392   <span class="keyword">end do</span>
    457. 

  457. <a name="l00393"></a>00393 
    458. 

  458. <a name="l00394"></a>00394   <span class="keyword">do</span> i = 1, norder
    459. 

  459. <a name="l00395"></a>00395     xtab(i) = dble ( 2 - i )
    460. 

  460. <a name="l00396"></a>00396   <span class="keyword">end do</span>
    461. 

  461. <a name="l00397"></a>00397 
    462. 

  462. <a name="l00398"></a>00398   return
    463. 

  463. <a name="l00399"></a>00399 <span class="keyword">end</span>
    464. 

  464. <a name="l00400"></a><a class="code" href="quadrule_8f90.html#ae1f2722140b0af5e1a2bf8e5877222aa">00400</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#ae1f2722140b0af5e1a2bf8e5877222aa">bdfp_set</a> ( norder, weight, xtab )
    465. 

  465. <a name="l00401"></a>00401 <span class="comment">!</span>
    466. 

  466. <a name="l00402"></a>00402 <span class="comment">!*******************************************************************************</span>
    467. 

  467. <a name="l00403"></a>00403 <span class="comment">!</span>
    468. 

  468. <a name="l00404"></a>00404 <span class="comment">!! BDFP_SET sets weights for backward differentiation predictor quadrature.</span>
    469. 

  469. <a name="l00405"></a>00405 <span class="comment">!</span>
    470. 

  470. <a name="l00406"></a>00406 <span class="comment">!</span>
    471. 

  471. <a name="l00407"></a>00407 <span class="comment">!  Definition:</span>
    472. 

  472. <a name="l00408"></a>00408 <span class="comment">!</span>
    473. 

  473. <a name="l00409"></a>00409 <span class="comment">!    A backward differentiation predictor formula is defined for a set</span>
    474. 

  474. <a name="l00410"></a>00410 <span class="comment">!    of evenly spaced abscissas X(I) with X(1) = 1 and X(2) = 0.  Assuming</span>
    475. 

  475. <a name="l00411"></a>00411 <span class="comment">!    that the values of the function to be integrated are known at the</span>
    476. 

  476. <a name="l00412"></a>00412 <span class="comment">!    abscissas, the formula is written in terms of the function value at</span>
    477. 

  477. <a name="l00413"></a>00413 <span class="comment">!    X(2), and the backward differences at X(2) that approximate the</span>
    478. 

  478. <a name="l00414"></a>00414 <span class="comment">!    derivatives there.  A backward differentiation predictor formula</span>
    479. 

  479. <a name="l00415"></a>00415 <span class="comment">!    is equivalent to an Adams-Bashforth formula of the same order.</span>
    480. 

  480. <a name="l00416"></a>00416 <span class="comment">!</span>
    481. 

  481. <a name="l00417"></a>00417 <span class="comment">!  Integration interval:</span>
    482. 

  482. <a name="l00418"></a>00418 <span class="comment">!</span>
    483. 

  483. <a name="l00419"></a>00419 <span class="comment">!    [ 0, 1 ]</span>
    484. 

  484. <a name="l00420"></a>00420 <span class="comment">!</span>
    485. 

  485. <a name="l00421"></a>00421 <span class="comment">!  Weight function:</span>
    486. 

  486. <a name="l00422"></a>00422 <span class="comment">!</span>
    487. 

  487. <a name="l00423"></a>00423 <span class="comment">!    1.0D+00</span>
    488. 

  488. <a name="l00424"></a>00424 <span class="comment">!</span>
    489. 

  489. <a name="l00425"></a>00425 <span class="comment">!  Integral to approximate:</span>
    490. 

  490. <a name="l00426"></a>00426 <span class="comment">!</span>
    491. 

  491. <a name="l00427"></a>00427 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) F(X) dX</span>
    492. 

  492. <a name="l00428"></a>00428 <span class="comment">!</span>
    493. 

  493. <a name="l00429"></a>00429 <span class="comment">!  Approximate integral:</span>
    494. 

  494. <a name="l00430"></a>00430 <span class="comment">!</span>
    495. 

  495. <a name="l00431"></a>00431 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * BD**(I-1) F ( 0 ),</span>
    496. 

  496. <a name="l00432"></a>00432 <span class="comment">!</span>
    497. 

  497. <a name="l00433"></a>00433 <span class="comment">!    Here, &quot;BD**(I-1) F ( 0 )&quot; denotes the (I-1)st backward difference</span>
    498. 

  498. <a name="l00434"></a>00434 <span class="comment">!    of F at X = 0, using a spacing of 1.  In particular,</span>
    499. 

  499. <a name="l00435"></a>00435 <span class="comment">!</span>
    500. 

  500. <a name="l00436"></a>00436 <span class="comment">!    BD**0 F(0) = F(0)</span>
    501. 

  501. <a name="l00437"></a>00437 <span class="comment">!    BD**1 F(0) = F(0) - F(-1)</span>
    502. 

  502. <a name="l00438"></a>00438 <span class="comment">!    BD**2 F(0) = F(0) - 2 * F(-1) + F(-2 )</span>
    503. 

  503. <a name="l00439"></a>00439 <span class="comment">!</span>
    504. 

  504. <a name="l00440"></a>00440 <span class="comment">!  Note:</span>
    505. 

  505. <a name="l00441"></a>00441 <span class="comment">!</span>
    506. 

  506. <a name="l00442"></a>00442 <span class="comment">!    The relationship between a backward difference predictor and the</span>
    507. 

  507. <a name="l00443"></a>00443 <span class="comment">!    corresponding Adams-Bashforth formula may be illustrated for the</span>
    508. 

  508. <a name="l00444"></a>00444 <span class="comment">!    BDF predictor of order 3:</span>
    509. 

  509. <a name="l00445"></a>00445 <span class="comment">!</span>
    510. 

  510. <a name="l00446"></a>00446 <span class="comment">!      BD**0 F(0) + 0.5 * BD**1 F(0) + 5/12 * BD**2 F(0)</span>
    511. 

  511. <a name="l00447"></a>00447 <span class="comment">!      =            F(0)</span>
    512. 

  512. <a name="l00448"></a>00448 <span class="comment">!        + 1/2  * ( F(0) -         F(1) )</span>
    513. 

  513. <a name="l00449"></a>00449 <span class="comment">!        + 5/12 * ( F(0) - 2     * F(-1) +      F(-2) )</span>
    514. 

  514. <a name="l00450"></a>00450 <span class="comment">!      =  23/12 *   F(0) - 16/12 * F(-1) + 5/12 F(-2)</span>
    515. 

  515. <a name="l00451"></a>00451 <span class="comment">!</span>
    516. 

  516. <a name="l00452"></a>00452 <span class="comment">!    which is the Adams-Bashforth formula of order 3.</span>
    517. 

  517. <a name="l00453"></a>00453 <span class="comment">! </span>
    518. 

  518. <a name="l00454"></a>00454 <span class="comment">!  Reference:</span>
    519. 

  519. <a name="l00455"></a>00455 <span class="comment">!</span>
    520. 

  520. <a name="l00456"></a>00456 <span class="comment">!    Simeon Fatunla,</span>
    521. 

  521. <a name="l00457"></a>00457 <span class="comment">!    Numerical Methods for Initial Value Problems in Ordinary Differential</span>
    522. 

  522. <a name="l00458"></a>00458 <span class="comment">!      Equations,</span>
    523. 

  523. <a name="l00459"></a>00459 <span class="comment">!    Academic Press, 1988.</span>
    524. 

  524. <a name="l00460"></a>00460 <span class="comment">!</span>
    525. 

  525. <a name="l00461"></a>00461 <span class="comment">!  Modified:</span>
    526. 

  526. <a name="l00462"></a>00462 <span class="comment">!</span>
    527. 

  527. <a name="l00463"></a>00463 <span class="comment">!    29 February 2000</span>
    528. 

  528. <a name="l00464"></a>00464 <span class="comment">!</span>
    529. 

  529. <a name="l00465"></a>00465 <span class="comment">!  Author:</span>
    530. 

  530. <a name="l00466"></a>00466 <span class="comment">!</span>
    531. 

  531. <a name="l00467"></a>00467 <span class="comment">!    John Burkardt</span>
    532. 

  532. <a name="l00468"></a>00468 <span class="comment">!</span>
    533. 

  533. <a name="l00469"></a>00469 <span class="comment">!  Parameters:</span>
    534. 

  534. <a name="l00470"></a>00470 <span class="comment">!</span>
    535. 

  535. <a name="l00471"></a>00471 <span class="comment">!    Input, integer NORDER, the order of the rule, which can be</span>
    536. 

  536. <a name="l00472"></a>00472 <span class="comment">!    any value from 1 to 19.</span>
    537. 

  537. <a name="l00473"></a>00473 <span class="comment">!</span>
    538. 

  538. <a name="l00474"></a>00474 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weight of the rule.</span>
    539. 

  539. <a name="l00475"></a>00475 <span class="comment">!</span>
    540. 

  540. <a name="l00476"></a>00476 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    541. 

  541. <a name="l00477"></a>00477 <span class="comment">!</span>
    542. 

  542. <a name="l00478"></a>00478   <span class="keyword">implicit none</span>
    543. 

  543. <a name="l00479"></a>00479 <span class="comment">!</span>
    544. 

  544. <a name="l00480"></a>00480   <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxord = 19
    545. 

  545. <a name="l00481"></a>00481 <span class="comment">!</span>
    546. 

  546. <a name="l00482"></a>00482   <span class="keywordtype">integer</span> norder
    547. 

  547. <a name="l00483"></a>00483 <span class="comment">!</span>
    548. 

  548. <a name="l00484"></a>00484   <span class="keywordtype">integer</span> i
    549. 

  549. <a name="l00485"></a>00485   <span class="keywordtype">double precision</span> w(maxord)
    550. 

  550. <a name="l00486"></a>00486   <span class="keywordtype">double precision</span> weight(norder)
    551. 

  551. <a name="l00487"></a>00487   <span class="keywordtype">double precision</span> xtab(norder)
    552. 

  552. <a name="l00488"></a>00488 <span class="comment">!</span>
    553. 

  553. <a name="l00489"></a>00489   w(1) =                       1.0D+00
    554. 

  554. <a name="l00490"></a>00490   w(2) =                       1.0D+00 /                2.0D+00
    555. 

  555. <a name="l00491"></a>00491   w(3) =                       5.0D+00 /               12.0D+00
    556. 

  556. <a name="l00492"></a>00492   w(4) =                       3.0D+00 /                8.0D+00
    557. 

  557. <a name="l00493"></a>00493   w(5) =                     251.0D+00 /              720.0D+00
    558. 

  558. <a name="l00494"></a>00494   w(6) =                      95.0D+00 /              288.0D+00
    559. 

  559. <a name="l00495"></a>00495   w(7) =                   19087.0D+00 /            60480.0D+00
    560. 

  560. <a name="l00496"></a>00496   w(8) =                    5257.0D+00 /            17280.0D+00
    561. 

  561. <a name="l00497"></a>00497   w(9) =                 1070017.0D+00 /          3628800.0D+00
    562. 

  562. <a name="l00498"></a>00498   w(10) =                  25713.0D+00 /            89600.0D+00
    563. 

  563. <a name="l00499"></a>00499   w(11) =               26842253.0D+00 /         95800320.0D+00
    564. 

  564. <a name="l00500"></a>00500   w(12) =                4777223.0D+00 /         17418240.0D+00
    565. 

  565. <a name="l00501"></a>00501   w(13) =           703604254357.0D+00 /    2615348736000.0D+00
    566. 

  566. <a name="l00502"></a>00502   w(14) =           106364763817.0D+00 /     402361344000.0D+00
    567. 

  567. <a name="l00503"></a>00503   w(15) =          1166309819657.0D+00 /    4483454976000.0D+00
    568. 

  568. <a name="l00504"></a>00504   w(16) =               25221445.0D+00 /         98402304.0D+00
    569. 

  569. <a name="l00505"></a>00505   w(17) =       8092989203533249.0D+00 /    3201186852864.0D+00
    570. 

  570. <a name="l00506"></a>00506   w(18) =         85455477715379.0D+00 /      34237292544.0D+00
    571. 

  571. <a name="l00507"></a>00507   w(19) =   12600467236042756559.0D+00 / 5109094217170944.0D+00
    572. 

  572. <a name="l00508"></a>00508 
    573. 

  573. <a name="l00509"></a>00509   <span class="keyword">do</span> i = 1, min ( norder, maxord )
    574. 

  574. <a name="l00510"></a>00510     weight(i) = w(i)
    575. 

  575. <a name="l00511"></a>00511   <span class="keyword">end do</span>
    576. 

  576. <a name="l00512"></a>00512 
    577. 

  577. <a name="l00513"></a>00513   <span class="keyword">do</span> i = 1, norder
    578. 

  578. <a name="l00514"></a>00514     xtab(i) = dble ( 1 - i )
    579. 

  579. <a name="l00515"></a>00515   <span class="keyword">end do</span>
    580. 

  580. <a name="l00516"></a>00516 
    581. 

  581. <a name="l00517"></a>00517   return
    582. 

  582. <a name="l00518"></a>00518 <span class="keyword">end</span>
    583. 

  583. <a name="l00519"></a><a class="code" href="quadrule_8f90.html#aed98218103418a57a42bce561d3f221a">00519</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#aed98218103418a57a42bce561d3f221a">bdf_sum</a> ( func, norder, weight, xtab, diftab, result )
    584. 

  584. <a name="l00520"></a>00520 <span class="comment">!</span>
    585. 

  585. <a name="l00521"></a>00521 <span class="comment">!*******************************************************************************</span>
    586. 

  586. <a name="l00522"></a>00522 <span class="comment">!</span>
    587. 

  587. <a name="l00523"></a>00523 <span class="comment">!! BDF_SUM carries out an explicit backward difference quadrature rule for [0,1].</span>
    588. 

  588. <a name="l00524"></a>00524 <span class="comment">!</span>
    589. 

  589. <a name="l00525"></a>00525 <span class="comment">!</span>
    590. 

  590. <a name="l00526"></a>00526 <span class="comment">!  Integral to approximate:</span>
    591. 

  591. <a name="l00527"></a>00527 <span class="comment">!</span>
    592. 

  592. <a name="l00528"></a>00528 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) F(X) dX</span>
    593. 

  593. <a name="l00529"></a>00529 <span class="comment">!</span>
    594. 

  594. <a name="l00530"></a>00530 <span class="comment">!  Formula:</span>
    595. 

  595. <a name="l00531"></a>00531 <span class="comment">!</span>
    596. 

  596. <a name="l00532"></a>00532 <span class="comment">!    RESULT = Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * BDF**(I-1) FUNC ( 0 )</span>
    597. 

  597. <a name="l00533"></a>00533 <span class="comment">!</span>
    598. 

  598. <a name="l00534"></a>00534 <span class="comment">!  Note:</span>
    599. 

  599. <a name="l00535"></a>00535 <span class="comment">!</span>
    600. 

  600. <a name="l00536"></a>00536 <span class="comment">!    The integral from 0 to 1 is approximated using data at X = 0,</span>
    601. 

  601. <a name="l00537"></a>00537 <span class="comment">!    -1, -2, ..., -NORDER+1.  This is a form of extrapolation, and</span>
    602. 

  602. <a name="l00538"></a>00538 <span class="comment">!    the approximation can become poor as NORDER increases.</span>
    603. 

  603. <a name="l00539"></a>00539 <span class="comment">!</span>
    604. 

  604. <a name="l00540"></a>00540 <span class="comment">!  Modified:</span>
    605. 

  605. <a name="l00541"></a>00541 <span class="comment">!</span>
    606. 

  606. <a name="l00542"></a>00542 <span class="comment">!    26 October 2000</span>
    607. 

  607. <a name="l00543"></a>00543 <span class="comment">!</span>
    608. 

  608. <a name="l00544"></a>00544 <span class="comment">!  Author:</span>
    609. 

  609. <a name="l00545"></a>00545 <span class="comment">!</span>
    610. 

  610. <a name="l00546"></a>00546 <span class="comment">!    John Burkardt</span>
    611. 

  611. <a name="l00547"></a>00547 <span class="comment">!</span>
    612. 

  612. <a name="l00548"></a>00548 <span class="comment">!  Parameters:</span>
    613. 

  613. <a name="l00549"></a>00549 <span class="comment">!</span>
    614. 

  614. <a name="l00550"></a>00550 <span class="comment">!    Input, external FUNC, the name of the FORTRAN function which evaluates</span>
    615. 

  615. <a name="l00551"></a>00551 <span class="comment">!    the integrand.  The function must have the form</span>
    616. 

  616. <a name="l00552"></a>00552 <span class="comment">!      double precision func ( x ).</span>
    617. 

  617. <a name="l00553"></a>00553 <span class="comment">!</span>
    618. 

  618. <a name="l00554"></a>00554 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    619. 

  619. <a name="l00555"></a>00555 <span class="comment">!</span>
    620. 

  620. <a name="l00556"></a>00556 <span class="comment">!    Input, double precision WEIGHT(NORDER), the weights of the rule.</span>
    621. 

  621. <a name="l00557"></a>00557 <span class="comment">!</span>
    622. 

  622. <a name="l00558"></a>00558 <span class="comment">!    Input, double precision XTAB(NORDER), the abscissas of the rule.</span>
    623. 

  623. <a name="l00559"></a>00559 <span class="comment">!</span>
    624. 

  624. <a name="l00560"></a>00560 <span class="comment">!    Workspace, double precision DIFTAB(NORDER).</span>
    625. 

  625. <a name="l00561"></a>00561 <span class="comment">!</span>
    626. 

  626. <a name="l00562"></a>00562 <span class="comment">!    Output, double precision RESULT, the approximate value of the integral.</span>
    627. 

  627. <a name="l00563"></a>00563 <span class="comment">!</span>
    628. 

  628. <a name="l00564"></a>00564   <span class="keyword">implicit none</span>
    629. 

  629. <a name="l00565"></a>00565 <span class="comment">!</span>
    630. 

  630. <a name="l00566"></a>00566   <span class="keywordtype">integer</span> norder
    631. 

  631. <a name="l00567"></a>00567 <span class="comment">!</span>
    632. 

  632. <a name="l00568"></a>00568   <span class="keywordtype">double precision</span> diftab(norder)
    633. 

  633. <a name="l00569"></a>00569   <span class="keywordtype">double precision</span>, <span class="keywordtype">external</span> :: func
    634. 

  634. <a name="l00570"></a>00570   <span class="keywordtype">integer</span> i
    635. 

  635. <a name="l00571"></a>00571   <span class="keywordtype">integer</span> j
    636. 

  636. <a name="l00572"></a>00572   <span class="keywordtype">double precision</span> result
    637. 

  637. <a name="l00573"></a>00573   <span class="keywordtype">double precision</span> weight(norder)
    638. 

  638. <a name="l00574"></a>00574   <span class="keywordtype">double precision</span> xtab(norder)
    639. 

  639. <a name="l00575"></a>00575 <span class="comment">!</span>
    640. 

  640. <a name="l00576"></a>00576   <span class="keyword">do</span> i = 1, norder
    641. 

  641. <a name="l00577"></a>00577     diftab(i) = func ( xtab(i) )
    642. 

  642. <a name="l00578"></a>00578   <span class="keyword">end do</span>
    643. 

  643. <a name="l00579"></a>00579 
    644. 

  644. <a name="l00580"></a>00580   <span class="keyword">do</span> i = 2, norder
    645. 

  645. <a name="l00581"></a>00581     <span class="keyword">do</span> j = i, norder
    646. 

  646. <a name="l00582"></a>00582       diftab(norder+i-j) = ( diftab(norder+i-j-1) - diftab(norder+i-j) )
    647. 

  647. <a name="l00583"></a>00583     <span class="keyword">end do</span>
    648. 

  648. <a name="l00584"></a>00584   <span class="keyword">end do</span>
    649. 

  649. <a name="l00585"></a>00585 
    650. 

  650. <a name="l00586"></a>00586   result = dot_product ( weight(1:norder), diftab(1:norder) )
    651. 

  651. <a name="l00587"></a>00587 
    652. 

  652. <a name="l00588"></a>00588   return
    653. 

  653. <a name="l00589"></a>00589 <span class="keyword">end</span>
    654. 

  654. <a name="l00590"></a><a class="code" href="quadrule_8f90.html#ade9f4e674221ccedd6251da05db6bbba">00590</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#ade9f4e674221ccedd6251da05db6bbba">cheb_set</a> ( norder, xtab, weight )
    655. 

  655. <a name="l00591"></a>00591 <span class="comment">!</span>
    656. 

  656. <a name="l00592"></a>00592 <span class="comment">!*******************************************************************************</span>
    657. 

  657. <a name="l00593"></a>00593 <span class="comment">!</span>
    658. 

  658. <a name="l00594"></a>00594 <span class="comment">!! CHEB_SET sets abscissas and weights for Chebyshev quadrature.</span>
    659. 

  659. <a name="l00595"></a>00595 <span class="comment">!</span>
    660. 

  660. <a name="l00596"></a>00596 <span class="comment">!</span>
    661. 

  661. <a name="l00597"></a>00597 <span class="comment">!  Integration interval:</span>
    662. 

  662. <a name="l00598"></a>00598 <span class="comment">!</span>
    663. 

  663. <a name="l00599"></a>00599 <span class="comment">!    [ -1, 1 ]</span>
    664. 

  664. <a name="l00600"></a>00600 <span class="comment">!</span>
    665. 

  665. <a name="l00601"></a>00601 <span class="comment">!  Weight function:</span>
    666. 

  666. <a name="l00602"></a>00602 <span class="comment">!</span>
    667. 

  667. <a name="l00603"></a>00603 <span class="comment">!    1.0D+00</span>
    668. 

  668. <a name="l00604"></a>00604 <span class="comment">!</span>
    669. 

  669. <a name="l00605"></a>00605 <span class="comment">!  Integral to approximate:</span>
    670. 

  670. <a name="l00606"></a>00606 <span class="comment">!</span>
    671. 

  671. <a name="l00607"></a>00607 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    672. 

  672. <a name="l00608"></a>00608 <span class="comment">!</span>
    673. 

  673. <a name="l00609"></a>00609 <span class="comment">!  Approximate integral:</span>
    674. 

  674. <a name="l00610"></a>00610 <span class="comment">!</span>
    675. 

  675. <a name="l00611"></a>00611 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    676. 

  676. <a name="l00612"></a>00612 <span class="comment">!</span>
    677. 

  677. <a name="l00613"></a>00613 <span class="comment">!  Note:</span>
    678. 

  678. <a name="l00614"></a>00614 <span class="comment">!</span>
    679. 

  679. <a name="l00615"></a>00615 <span class="comment">!    The Chebyshev rule is distinguished by using equal weights.</span>
    680. 

  680. <a name="l00616"></a>00616 <span class="comment">!</span>
    681. 

  681. <a name="l00617"></a>00617 <span class="comment">!  Reference:</span>
    682. 

  682. <a name="l00618"></a>00618 <span class="comment">!</span>
    683. 

  683. <a name="l00619"></a>00619 <span class="comment">!    Abramowitz and Stegun,</span>
    684. 

  684. <a name="l00620"></a>00620 <span class="comment">!    Handbook of Mathematical Functions,</span>
    685. 

  685. <a name="l00621"></a>00621 <span class="comment">!    National Bureau of Standards, 1964.</span>
    686. 

  686. <a name="l00622"></a>00622 <span class="comment">!</span>
    687. 

  687. <a name="l00623"></a>00623 <span class="comment">!    H Engels,</span>
    688. 

  688. <a name="l00624"></a>00624 <span class="comment">!    Numerical Quadrature and Cubature,</span>
    689. 

  689. <a name="l00625"></a>00625 <span class="comment">!    Academic Press, 1980.</span>
    690. 

  690. <a name="l00626"></a>00626 <span class="comment">!</span>
    691. 

  691. <a name="l00627"></a>00627 <span class="comment">!    Zdenek Kopal,</span>
    692. 

  692. <a name="l00628"></a>00628 <span class="comment">!    Numerical Analysis,</span>
    693. 

  693. <a name="l00629"></a>00629 <span class="comment">!    John Wiley, 1955.</span>
    694. 

  694. <a name="l00630"></a>00630 <span class="comment">!</span>
    695. 

  695. <a name="l00631"></a>00631 <span class="comment">!    Daniel Zwillinger, editor,</span>
    696. 

  696. <a name="l00632"></a>00632 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    697. 

  697. <a name="l00633"></a>00633 <span class="comment">!    30th Edition,</span>
    698. 

  698. <a name="l00634"></a>00634 <span class="comment">!    CRC Press, 1996.</span>
    699. 

  699. <a name="l00635"></a>00635 <span class="comment">!</span>
    700. 

  700. <a name="l00636"></a>00636 <span class="comment">!  Modified:</span>
    701. 

  701. <a name="l00637"></a>00637 <span class="comment">!</span>
    702. 

  702. <a name="l00638"></a>00638 <span class="comment">!    27 October 2000</span>
    703. 

  703. <a name="l00639"></a>00639 <span class="comment">!</span>
    704. 

  704. <a name="l00640"></a>00640 <span class="comment">!  Author:</span>
    705. 

  705. <a name="l00641"></a>00641 <span class="comment">!</span>
    706. 

  706. <a name="l00642"></a>00642 <span class="comment">!    John Burkardt</span>
    707. 

  707. <a name="l00643"></a>00643 <span class="comment">!</span>
    708. 

  708. <a name="l00644"></a>00644 <span class="comment">!  Parameters:</span>
    709. 

  709. <a name="l00645"></a>00645 <span class="comment">!</span>
    710. 

  710. <a name="l00646"></a>00646 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    711. 

  711. <a name="l00647"></a>00647 <span class="comment">!    NORDER may only have the values 1, 2, 3, 4, 5, 6, 7 or 9.</span>
    712. 

  712. <a name="l00648"></a>00648 <span class="comment">!    There are NO other Chebyshev rules with real abscissas.</span>
    713. 

  713. <a name="l00649"></a>00649 <span class="comment">!</span>
    714. 

  714. <a name="l00650"></a>00650 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule,</span>
    715. 

  715. <a name="l00651"></a>00651 <span class="comment">!    which are symmetric in [-1,1].</span>
    716. 

  716. <a name="l00652"></a>00652 <span class="comment">!</span>
    717. 

  717. <a name="l00653"></a>00653 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule,</span>
    718. 

  718. <a name="l00654"></a>00654 <span class="comment">!    which should each equal 2 / NORDER.</span>
    719. 

  719. <a name="l00655"></a>00655 <span class="comment">!</span>
    720. 

  720. <a name="l00656"></a>00656   <span class="keyword">implicit none</span>
    721. 

  721. <a name="l00657"></a>00657 <span class="comment">!</span>
    722. 

  722. <a name="l00658"></a>00658   <span class="keywordtype">integer</span> norder
    723. 

  723. <a name="l00659"></a>00659 <span class="comment">!</span>
    724. 

  724. <a name="l00660"></a>00660   <span class="keywordtype">integer</span> i
    725. 

  725. <a name="l00661"></a>00661   <span class="keywordtype">double precision</span> weight(norder)
    726. 

  726. <a name="l00662"></a>00662   <span class="keywordtype">double precision</span> xtab(norder)
    727. 

  727. <a name="l00663"></a>00663 <span class="comment">!</span>
    728. 

  728. <a name="l00664"></a>00664   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    729. 

  729. <a name="l00665"></a>00665 
    730. 

  730. <a name="l00666"></a>00666     xtab(1) = 0.0D+00
    731. 

  731. <a name="l00667"></a>00667 
    732. 

  732. <a name="l00668"></a>00668   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    733. 

  733. <a name="l00669"></a>00669 
    734. 

  734. <a name="l00670"></a>00670     xtab(1) = - 1.0D+00 / sqrt ( 3.0D+00 )
    735. 

  735. <a name="l00671"></a>00671     xtab(2) =   1.0D+00 / sqrt ( 3.0D+00 )
    736. 

  736. <a name="l00672"></a>00672 
    737. 

  737. <a name="l00673"></a>00673   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    738. 

  738. <a name="l00674"></a>00674 
    739. 

  739. <a name="l00675"></a>00675     xtab(1) = - 1.0D+00 / sqrt ( 2.0D+00 )
    740. 

  740. <a name="l00676"></a>00676     xtab(2) =   0.0D+00
    741. 

  741. <a name="l00677"></a>00677     xtab(3) =   1.0D+00 / sqrt ( 2.0D+00 )
    742. 

  742. <a name="l00678"></a>00678 
    743. 

  743. <a name="l00679"></a>00679   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    744. 

  744. <a name="l00680"></a>00680 
    745. 

  745. <a name="l00681"></a>00681     xtab(1) =   - sqrt ( ( 1.0D+00 + 2.0D+00/ sqrt ( 5.0D+00 ) ) / 3.0D+00 )
    746. 

  746. <a name="l00682"></a>00682     xtab(2) =   - sqrt ( ( 1.0D+00 - 2.0D+00/ sqrt ( 5.0D+00 ) ) / 3.0D+00 )
    747. 

  747. <a name="l00683"></a>00683     xtab(3) =     sqrt ( ( 1.0D+00 - 2.0D+00/ sqrt ( 5.0D+00 ) ) / 3.0D+00 )
    748. 

  748. <a name="l00684"></a>00684     xtab(4) =     sqrt ( ( 1.0D+00 + 2.0D+00/ sqrt ( 5.0D+00 ) ) / 3.0D+00 )
    749. 

  749. <a name="l00685"></a>00685 
    750. 

  750. <a name="l00686"></a>00686   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    751. 

  751. <a name="l00687"></a>00687 
    752. 

  752. <a name="l00688"></a>00688     xtab(1) = - sqrt ( ( 5.0D+00 + sqrt ( 11.0D+00) ) / 12.0D+00 )
    753. 

  753. <a name="l00689"></a>00689     xtab(2) = - sqrt ( ( 5.0D+00 - sqrt ( 11.0D+00) ) / 12.0D+00 )
    754. 

  754. <a name="l00690"></a>00690     xtab(3) =   0.0D+00
    755. 

  755. <a name="l00691"></a>00691     xtab(4) =   sqrt ( ( 5.0D+00 - sqrt ( 11.0D+00) ) / 12.0D+00 )
    756. 

  756. <a name="l00692"></a>00692     xtab(5) =   sqrt ( ( 5.0D+00 + sqrt ( 11.0D+00) ) / 12.0D+00 )
    757. 

  757. <a name="l00693"></a>00693 
    758. 

  758. <a name="l00694"></a>00694   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    759. 

  759. <a name="l00695"></a>00695 
    760. 

  760. <a name="l00696"></a>00696     xtab(1) = - 0.866246818107820591383598D+00
    761. 

  761. <a name="l00697"></a>00697     xtab(2) = - 0.422518653761111529118546D+00
    762. 

  762. <a name="l00698"></a>00698     xtab(3) = - 0.266635401516704720331534D+00
    763. 

  763. <a name="l00699"></a>00699     xtab(4) =   0.266635401516704720331534D+00
    764. 

  764. <a name="l00700"></a>00700     xtab(5) =   0.422518653761111529118546D+00
    765. 

  765. <a name="l00701"></a>00701     xtab(6) =   0.866246818107820591383598D+00
    766. 

  766. <a name="l00702"></a>00702 
    767. 

  767. <a name="l00703"></a>00703   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    768. 

  768. <a name="l00704"></a>00704 
    769. 

  769. <a name="l00705"></a>00705     xtab(1) = - 0.883861700758049035704224D+00
    770. 

  770. <a name="l00706"></a>00706     xtab(2) = - 0.529656775285156811385048D+00
    771. 

  771. <a name="l00707"></a>00707     xtab(3) = - 0.323911810519907637519673D+00
    772. 

  772. <a name="l00708"></a>00708     xtab(4) =   0.0D+00
    773. 

  773. <a name="l00709"></a>00709     xtab(5) =   0.323911810519907637519673D+00
    774. 

  774. <a name="l00710"></a>00710     xtab(6) =   0.529656775285156811385048D+00
    775. 

  775. <a name="l00711"></a>00711     xtab(7) =   0.883861700758049035704224D+00
    776. 

  776. <a name="l00712"></a>00712 
    777. 

  777. <a name="l00713"></a>00713   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    778. 

  778. <a name="l00714"></a>00714 
    779. 

  779. <a name="l00715"></a>00715     xtab(1) = - 0.911589307728434473664949D+00
    780. 

  780. <a name="l00716"></a>00716     xtab(2) = - 0.601018655380238071428128D+00
    781. 

  781. <a name="l00717"></a>00717     xtab(3) = - 0.528761783057879993260181D+00
    782. 

  782. <a name="l00718"></a>00718     xtab(4) = - 0.167906184214803943068031D+00
    783. 

  783. <a name="l00719"></a>00719     xtab(5) =   0.0D+00
    784. 

  784. <a name="l00720"></a>00720     xtab(6) =   0.167906184214803943068031D+00
    785. 

  785. <a name="l00721"></a>00721     xtab(7) =   0.528761783057879993260181D+00
    786. 

  786. <a name="l00722"></a>00722     xtab(8) =   0.601018655380238071428128D+00
    787. 

  787. <a name="l00723"></a>00723     xtab(9) =   0.911589307728434473664949D+00
    788. 

  788. <a name="l00724"></a>00724 
    789. 

  789. <a name="l00725"></a>00725   <span class="keyword">else</span>
    790. 

  790. <a name="l00726"></a>00726 
    791. 

  791. <a name="l00727"></a>00727     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    792. 

  792. <a name="l00728"></a>00728     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;CHEB_SET - Fatal error!&#39;</span>
    793. 

  793. <a name="l00729"></a>00729     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    794. 

  794. <a name="l00730"></a>00730     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 1 through 7, and 9.&#39;</span>
    795. 

  795. <a name="l00731"></a>00731     stop
    796. 

  796. <a name="l00732"></a>00732 
    797. 

  797. <a name="l00733"></a>00733   <span class="keyword">end if</span>
    798. 

  798. <a name="l00734"></a>00734 
    799. 

  799. <a name="l00735"></a>00735   weight(1:norder) = 2.0D+00 / dble ( norder )
    800. 

  800. <a name="l00736"></a>00736 
    801. 

  801. <a name="l00737"></a>00737   return
    802. 

  802. <a name="l00738"></a>00738 <span class="keyword">end</span>
    803. 

  803. <a name="l00739"></a><a class="code" href="quadrule_8f90.html#a54208a5fdf9d1d82565b1aa741c51811">00739</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a54208a5fdf9d1d82565b1aa741c51811">cheb_to_set</a> ( norder, xtab, weight )
    804. 

  804. <a name="l00740"></a>00740 <span class="comment">!</span>
    805. 

  805. <a name="l00741"></a>00741 <span class="comment">!*******************************************************************************</span>
    806. 

  806. <a name="l00742"></a>00742 <span class="comment">!</span>
    807. 

  807. <a name="l00743"></a>00743 <span class="comment">!! CHEB_TO_SET sets up open Gauss-Chebyshev (first kind) quadrature.</span>
    808. 

  808. <a name="l00744"></a>00744 <span class="comment">!</span>
    809. 

  809. <a name="l00745"></a>00745 <span class="comment">!</span>
    810. 

  810. <a name="l00746"></a>00746 <span class="comment">!  Integration interval:</span>
    811. 

  811. <a name="l00747"></a>00747 <span class="comment">!</span>
    812. 

  812. <a name="l00748"></a>00748 <span class="comment">!    [ -1, 1 ]</span>
    813. 

  813. <a name="l00749"></a>00749 <span class="comment">!</span>
    814. 

  814. <a name="l00750"></a>00750 <span class="comment">!  Weight function:</span>
    815. 

  815. <a name="l00751"></a>00751 <span class="comment">!</span>
    816. 

  816. <a name="l00752"></a>00752 <span class="comment">!    1 / SQRT ( 1 - X**2 )</span>
    817. 

  817. <a name="l00753"></a>00753 <span class="comment">!</span>
    818. 

  818. <a name="l00754"></a>00754 <span class="comment">!  Integral to approximate:</span>
    819. 

  819. <a name="l00755"></a>00755 <span class="comment">!</span>
    820. 

  820. <a name="l00756"></a>00756 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) / SQRT ( 1 - X**2 ) dX</span>
    821. 

  821. <a name="l00757"></a>00757 <span class="comment">!</span>
    822. 

  822. <a name="l00758"></a>00758 <span class="comment">!  Approximate integral:</span>
    823. 

  823. <a name="l00759"></a>00759 <span class="comment">!</span>
    824. 

  824. <a name="l00760"></a>00760 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    825. 

  825. <a name="l00761"></a>00761 <span class="comment">!</span>
    826. 

  826. <a name="l00762"></a>00762 <span class="comment">!  Precision:</span>
    827. 

  827. <a name="l00763"></a>00763 <span class="comment">!</span>
    828. 

  828. <a name="l00764"></a>00764 <span class="comment">!    If NORDER points are used, then Gauss-Chebyshev quadrature</span>
    829. 

  829. <a name="l00765"></a>00765 <span class="comment">!    will compute the integral exactly, whenever F(X) is a polynomial</span>
    830. 

  830. <a name="l00766"></a>00766 <span class="comment">!    of degree 2*NORDER-1 or less.</span>
    831. 

  831. <a name="l00767"></a>00767 <span class="comment">!</span>
    832. 

  832. <a name="l00768"></a>00768 <span class="comment">!  Note:</span>
    833. 

  833. <a name="l00769"></a>00769 <span class="comment">!</span>
    834. 

  834. <a name="l00770"></a>00770 <span class="comment">!    The abscissas of the rule are zeroes of the Chebyshev polynomials</span>
    835. 

  835. <a name="l00771"></a>00771 <span class="comment">!    of the first kind, T(NORDER)(X).</span>
    836. 

  836. <a name="l00772"></a>00772 <span class="comment">!</span>
    837. 

  837. <a name="l00773"></a>00773 <span class="comment">!  Reference:</span>
    838. 

  838. <a name="l00774"></a>00774 <span class="comment">!</span>
    839. 

  839. <a name="l00775"></a>00775 <span class="comment">!    Daniel Zwillinger, editor,</span>
    840. 

  840. <a name="l00776"></a>00776 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    841. 

  841. <a name="l00777"></a>00777 <span class="comment">!    30th Edition,</span>
    842. 

  842. <a name="l00778"></a>00778 <span class="comment">!    CRC Press, 1996.</span>
    843. 

  843. <a name="l00779"></a>00779 <span class="comment">!</span>
    844. 

  844. <a name="l00780"></a>00780 <span class="comment">!  Modified:</span>
    845. 

  845. <a name="l00781"></a>00781 <span class="comment">!</span>
    846. 

  846. <a name="l00782"></a>00782 <span class="comment">!    15 September 1998</span>
    847. 

  847. <a name="l00783"></a>00783 <span class="comment">!</span>
    848. 

  848. <a name="l00784"></a>00784 <span class="comment">!  Author:</span>
    849. 

  849. <a name="l00785"></a>00785 <span class="comment">!</span>
    850. 

  850. <a name="l00786"></a>00786 <span class="comment">!    John Burkardt</span>
    851. 

  851. <a name="l00787"></a>00787 <span class="comment">!</span>
    852. 

  852. <a name="l00788"></a>00788 <span class="comment">!  Parameters:</span>
    853. 

  853. <a name="l00789"></a>00789 <span class="comment">!</span>
    854. 

  854. <a name="l00790"></a>00790 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    855. 

  855. <a name="l00791"></a>00791 <span class="comment">!</span>
    856. 

  856. <a name="l00792"></a>00792 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    857. 

  857. <a name="l00793"></a>00793 <span class="comment">!</span>
    858. 

  858. <a name="l00794"></a>00794 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule,</span>
    859. 

  859. <a name="l00795"></a>00795 <span class="comment">!    which are all equal to PI / NORDER.</span>
    860. 

  860. <a name="l00796"></a>00796 <span class="comment">!</span>
    861. 

  861. <a name="l00797"></a>00797   <span class="keyword">implicit none</span>
    862. 

  862. <a name="l00798"></a>00798 <span class="comment">!</span>
    863. 

  863. <a name="l00799"></a>00799   <span class="keywordtype">integer</span> norder
    864. 

  864. <a name="l00800"></a>00800 <span class="comment">!</span>
    865. 

  865. <a name="l00801"></a>00801   <span class="keywordtype">double precision</span> angle
    866. 

  866. <a name="l00802"></a>00802   <span class="keywordtype">double precision</span> d_pi
    867. 

  867. <a name="l00803"></a>00803   <span class="keywordtype">integer</span> i
    868. 

  868. <a name="l00804"></a>00804   <span class="keywordtype">double precision</span> weight(norder)
    869. 

  869. <a name="l00805"></a>00805   <span class="keywordtype">double precision</span> xtab(norder)
    870. 

  870. <a name="l00806"></a>00806 <span class="comment">!</span>
    871. 

  871. <a name="l00807"></a>00807   <span class="keyword">do</span> i = 1, norder
    872. 

  872. <a name="l00808"></a>00808     angle = dble ( 2 * i - 1 ) * d_pi ( ) / dble ( 2 * norder )
    873. 

  873. <a name="l00809"></a>00809     xtab(i) = cos ( angle )
    874. 

  874. <a name="l00810"></a>00810   <span class="keyword">end do</span>
    875. 

  875. <a name="l00811"></a>00811 
    876. 

  876. <a name="l00812"></a>00812   weight(1:norder) = d_pi ( ) / dble ( norder )
    877. 

  877. <a name="l00813"></a>00813 
    878. 

  878. <a name="l00814"></a>00814   return
    879. 

  879. <a name="l00815"></a>00815 <span class="keyword">end</span>
    880. 

  880. <a name="l00816"></a><a class="code" href="quadrule_8f90.html#aa1f1a725b4cc2ef2f039255e99227f0d">00816</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#aa1f1a725b4cc2ef2f039255e99227f0d">cheb_tc_set</a> ( norder, xtab, weight )
    881. 

  881. <a name="l00817"></a>00817 <span class="comment">!</span>
    882. 

  882. <a name="l00818"></a>00818 <span class="comment">!*******************************************************************************</span>
    883. 

  883. <a name="l00819"></a>00819 <span class="comment">!</span>
    884. 

  884. <a name="l00820"></a>00820 <span class="comment">!! CHEB_TC_SET sets up closed Gauss-Chebyshev (first kind) quadrature.</span>
    885. 

  885. <a name="l00821"></a>00821 <span class="comment">!</span>
    886. 

  886. <a name="l00822"></a>00822 <span class="comment">!</span>
    887. 

  887. <a name="l00823"></a>00823 <span class="comment">!  Integration interval:</span>
    888. 

  888. <a name="l00824"></a>00824 <span class="comment">!</span>
    889. 

  889. <a name="l00825"></a>00825 <span class="comment">!    [ -1, 1 ]</span>
    890. 

  890. <a name="l00826"></a>00826 <span class="comment">!</span>
    891. 

  891. <a name="l00827"></a>00827 <span class="comment">!  Weight function:</span>
    892. 

  892. <a name="l00828"></a>00828 <span class="comment">!</span>
    893. 

  893. <a name="l00829"></a>00829 <span class="comment">!    1 / SQRT ( 1 - X**2 )</span>
    894. 

  894. <a name="l00830"></a>00830 <span class="comment">!</span>
    895. 

  895. <a name="l00831"></a>00831 <span class="comment">!  Integral to approximate:</span>
    896. 

  896. <a name="l00832"></a>00832 <span class="comment">!</span>
    897. 

  897. <a name="l00833"></a>00833 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) / SQRT ( 1 - X**2 ) dX</span>
    898. 

  898. <a name="l00834"></a>00834 <span class="comment">!</span>
    899. 

  899. <a name="l00835"></a>00835 <span class="comment">!  Approximate integral:</span>
    900. 

  900. <a name="l00836"></a>00836 <span class="comment">!</span>
    901. 

  901. <a name="l00837"></a>00837 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    902. 

  902. <a name="l00838"></a>00838 <span class="comment">!</span>
    903. 

  903. <a name="l00839"></a>00839 <span class="comment">!  Precision:</span>
    904. 

  904. <a name="l00840"></a>00840 <span class="comment">!</span>
    905. 

  905. <a name="l00841"></a>00841 <span class="comment">!    If NORDER points are used, then Gauss-Chebyshev quadrature</span>
    906. 

  906. <a name="l00842"></a>00842 <span class="comment">!    will compute the integral exactly, whenever F(X) is a polynomial</span>
    907. 

  907. <a name="l00843"></a>00843 <span class="comment">!    of degree 2*NORDER-3 or less.</span>
    908. 

  908. <a name="l00844"></a>00844 <span class="comment">!</span>
    909. 

  909. <a name="l00845"></a>00845 <span class="comment">!  Note:</span>
    910. 

  910. <a name="l00846"></a>00846 <span class="comment">!</span>
    911. 

  911. <a name="l00847"></a>00847 <span class="comment">!    The abscissas include -1 and 1.</span>
    912. 

  912. <a name="l00848"></a>00848 <span class="comment">!</span>
    913. 

  913. <a name="l00849"></a>00849 <span class="comment">!    If the order is doubled, the abscissas of the new rule include</span>
    914. 

  914. <a name="l00850"></a>00850 <span class="comment">!    all the points of the old rule.  This fact can be used to</span>
    915. 

  915. <a name="l00851"></a>00851 <span class="comment">!    efficiently implement error estimation.</span>
    916. 

  916. <a name="l00852"></a>00852 <span class="comment">!</span>
    917. 

  917. <a name="l00853"></a>00853 <span class="comment">!  Reference:</span>
    918. 

  918. <a name="l00854"></a>00854 <span class="comment">!</span>
    919. 

  919. <a name="l00855"></a>00855 <span class="comment">!    Daniel Zwillinger, editor,</span>
    920. 

  920. <a name="l00856"></a>00856 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    921. 

  921. <a name="l00857"></a>00857 <span class="comment">!    30th Edition,</span>
    922. 

  922. <a name="l00858"></a>00858 <span class="comment">!    CRC Press, 1996.</span>
    923. 

  923. <a name="l00859"></a>00859 <span class="comment">!</span>
    924. 

  924. <a name="l00860"></a>00860 <span class="comment">!  Modified:</span>
    925. 

  925. <a name="l00861"></a>00861 <span class="comment">!</span>
    926. 

  926. <a name="l00862"></a>00862 <span class="comment">!    15 September 1998</span>
    927. 

  927. <a name="l00863"></a>00863 <span class="comment">!</span>
    928. 

  928. <a name="l00864"></a>00864 <span class="comment">!  Author:</span>
    929. 

  929. <a name="l00865"></a>00865 <span class="comment">!</span>
    930. 

  930. <a name="l00866"></a>00866 <span class="comment">!    John Burkardt</span>
    931. 

  931. <a name="l00867"></a>00867 <span class="comment">!</span>
    932. 

  932. <a name="l00868"></a>00868 <span class="comment">!  Parameters:</span>
    933. 

  933. <a name="l00869"></a>00869 <span class="comment">!</span>
    934. 

  934. <a name="l00870"></a>00870 <span class="comment">!    Input, integer NORDER, the order of the rule, which must be at least 2.</span>
    935. 

  935. <a name="l00871"></a>00871 <span class="comment">!</span>
    936. 

  936. <a name="l00872"></a>00872 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    937. 

  937. <a name="l00873"></a>00873 <span class="comment">!</span>
    938. 

  938. <a name="l00874"></a>00874 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    939. 

  939. <a name="l00875"></a>00875 <span class="comment">!    The first and last weights are 0.5 * PI / ( NORDER - 1),</span>
    940. 

  940. <a name="l00876"></a>00876 <span class="comment">!    and all other weights are PI / ( NORDER - 1 ).</span>
    941. 

  941. <a name="l00877"></a>00877 <span class="comment">!</span>
    942. 

  942. <a name="l00878"></a>00878   <span class="keyword">implicit none</span>
    943. 

  943. <a name="l00879"></a>00879 <span class="comment">!</span>
    944. 

  944. <a name="l00880"></a>00880   <span class="keywordtype">integer</span> norder
    945. 

  945. <a name="l00881"></a>00881 <span class="comment">!</span>
    946. 

  946. <a name="l00882"></a>00882   <span class="keywordtype">double precision</span> angle
    947. 

  947. <a name="l00883"></a>00883   <span class="keywordtype">double precision</span> d_pi
    948. 

  948. <a name="l00884"></a>00884   <span class="keywordtype">integer</span> i
    949. 

  949. <a name="l00885"></a>00885   <span class="keywordtype">double precision</span> weight(norder)
    950. 

  950. <a name="l00886"></a>00886   <span class="keywordtype">double precision</span> xtab(norder)
    951. 

  951. <a name="l00887"></a>00887 <span class="comment">!</span>
    952. 

  952. <a name="l00888"></a>00888   <span class="keyword">if</span> ( norder &lt; 2 ) <span class="keyword">then</span>
    953. 

  953. <a name="l00889"></a>00889     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    954. 

  954. <a name="l00890"></a>00890     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;CHEB_TC_SET - Fatal error!&#39;</span>
    955. 

  955. <a name="l00891"></a>00891     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  NORDER must be at least 2.&#39;</span>
    956. 

  956. <a name="l00892"></a>00892     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  The input value was NORDER = &#39;</span>, norder
    957. 

  957. <a name="l00893"></a>00893     stop
    958. 

  958. <a name="l00894"></a>00894   <span class="keyword">end if</span>
    959. 

  959. <a name="l00895"></a>00895 
    960. 

  960. <a name="l00896"></a>00896   <span class="keyword">do</span> i = 1, norder
    961. 

  961. <a name="l00897"></a>00897 
    962. 

  962. <a name="l00898"></a>00898     angle = dble ( i - 1 ) * d_pi ( ) / dble ( norder - 1 )
    963. 

  963. <a name="l00899"></a>00899     xtab(i) = cos ( angle )
    964. 

  964. <a name="l00900"></a>00900 
    965. 

  965. <a name="l00901"></a>00901   <span class="keyword">end do</span>
    966. 

  966. <a name="l00902"></a>00902 
    967. 

  967. <a name="l00903"></a>00903   weight(1) = d_pi ( ) / dble ( 2 * ( norder - 1 ) )
    968. 

  968. <a name="l00904"></a>00904   weight(2:norder-1) = d_pi ( ) / dble ( norder - 1 )
    969. 

  969. <a name="l00905"></a>00905   weight(norder) = d_pi ( ) / dble ( 2 * ( norder - 1 ) )
    970. 

  970. <a name="l00906"></a>00906 
    971. 

  971. <a name="l00907"></a>00907   return
    972. 

  972. <a name="l00908"></a>00908 <span class="keyword">end</span>
    973. 

  973. <a name="l00909"></a><a class="code" href="quadrule_8f90.html#ac7f04c61f2321ddc4bbf90358305d11e">00909</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#ac7f04c61f2321ddc4bbf90358305d11e">cheb_u_set</a> ( norder, xtab, weight )
    974. 

  974. <a name="l00910"></a>00910 <span class="comment">!</span>
    975. 

  975. <a name="l00911"></a>00911 <span class="comment">!*******************************************************************************</span>
    976. 

  976. <a name="l00912"></a>00912 <span class="comment">!</span>
    977. 

  977. <a name="l00913"></a>00913 <span class="comment">!! CHEB_U_SET sets abscissas and weights for Gauss-Chebyshev quadrature.</span>
    978. 

  978. <a name="l00914"></a>00914 <span class="comment">!</span>
    979. 

  979. <a name="l00915"></a>00915 <span class="comment">!</span>
    980. 

  980. <a name="l00916"></a>00916 <span class="comment">!  Integration interval:</span>
    981. 

  981. <a name="l00917"></a>00917 <span class="comment">!</span>
    982. 

  982. <a name="l00918"></a>00918 <span class="comment">!    [ -1, 1 ]</span>
    983. 

  983. <a name="l00919"></a>00919 <span class="comment">!</span>
    984. 

  984. <a name="l00920"></a>00920 <span class="comment">!  Weight function:</span>
    985. 

  985. <a name="l00921"></a>00921 <span class="comment">!</span>
    986. 

  986. <a name="l00922"></a>00922 <span class="comment">!    SQRT ( 1 - X**2 )</span>
    987. 

  987. <a name="l00923"></a>00923 <span class="comment">!</span>
    988. 

  988. <a name="l00924"></a>00924 <span class="comment">!  Integral to approximate:</span>
    989. 

  989. <a name="l00925"></a>00925 <span class="comment">!</span>
    990. 

  990. <a name="l00926"></a>00926 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) SQRT ( 1 - X**2 ) * F(X) dX</span>
    991. 

  991. <a name="l00927"></a>00927 <span class="comment">!</span>
    992. 

  992. <a name="l00928"></a>00928 <span class="comment">!  Approximate integral:</span>
    993. 

  993. <a name="l00929"></a>00929 <span class="comment">!</span>
    994. 

  994. <a name="l00930"></a>00930 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    995. 

  995. <a name="l00931"></a>00931 <span class="comment">!</span>
    996. 

  996. <a name="l00932"></a>00932 <span class="comment">!  Precision:</span>
    997. 

  997. <a name="l00933"></a>00933 <span class="comment">!</span>
    998. 

  998. <a name="l00934"></a>00934 <span class="comment">!    If NORDER points are used, then Gauss-Chebyshev quadrature</span>
    999. 

  999. <a name="l00935"></a>00935 <span class="comment">!    will compute the integral exactly, whenever F(X) is a polynomial</span>
    1000. 

  1000. <a name="l00936"></a>00936 <span class="comment">!    of degree 2*NORDER-1 or less.</span>
    1001. 

  1001. <a name="l00937"></a>00937 <span class="comment">!</span>
    1002. 

  1002. <a name="l00938"></a>00938 <span class="comment">!  Note:</span>
    1003. 

  1003. <a name="l00939"></a>00939 <span class="comment">!</span>
    1004. 

  1004. <a name="l00940"></a>00940 <span class="comment">!    The abscissas are zeroes of the Chebyshev polynomials</span>
    1005. 

  1005. <a name="l00941"></a>00941 <span class="comment">!    of the second kind, U(NORDER)(X).</span>
    1006. 

  1006. <a name="l00942"></a>00942 <span class="comment">!</span>
    1007. 

  1007. <a name="l00943"></a>00943 <span class="comment">!  Reference:</span>
    1008. 

  1008. <a name="l00944"></a>00944 <span class="comment">!</span>
    1009. 

  1009. <a name="l00945"></a>00945 <span class="comment">!    Daniel Zwillinger, editor,</span>
    1010. 

  1010. <a name="l00946"></a>00946 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    1011. 

  1011. <a name="l00947"></a>00947 <span class="comment">!    30th Edition,</span>
    1012. 

  1012. <a name="l00948"></a>00948 <span class="comment">!    CRC Press, 1996.</span>
    1013. 

  1013. <a name="l00949"></a>00949 <span class="comment">!</span>
    1014. 

  1014. <a name="l00950"></a>00950 <span class="comment">!  Modified:</span>
    1015. 

  1015. <a name="l00951"></a>00951 <span class="comment">!</span>
    1016. 

  1016. <a name="l00952"></a>00952 <span class="comment">!    15 September 1998</span>
    1017. 

  1017. <a name="l00953"></a>00953 <span class="comment">!</span>
    1018. 

  1018. <a name="l00954"></a>00954 <span class="comment">!  Author:</span>
    1019. 

  1019. <a name="l00955"></a>00955 <span class="comment">!</span>
    1020. 

  1020. <a name="l00956"></a>00956 <span class="comment">!    John Burkardt</span>
    1021. 

  1021. <a name="l00957"></a>00957 <span class="comment">!</span>
    1022. 

  1022. <a name="l00958"></a>00958 <span class="comment">!  Parameters:</span>
    1023. 

  1023. <a name="l00959"></a>00959 <span class="comment">!</span>
    1024. 

  1024. <a name="l00960"></a>00960 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    1025. 

  1025. <a name="l00961"></a>00961 <span class="comment">!</span>
    1026. 

  1026. <a name="l00962"></a>00962 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    1027. 

  1027. <a name="l00963"></a>00963 <span class="comment">!</span>
    1028. 

  1028. <a name="l00964"></a>00964 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule,</span>
    1029. 

  1029. <a name="l00965"></a>00965 <span class="comment">!    which are all equal to PI / NORDER.</span>
    1030. 

  1030. <a name="l00966"></a>00966 <span class="comment">!</span>
    1031. 

  1031. <a name="l00967"></a>00967   <span class="keyword">implicit none</span>
    1032. 

  1032. <a name="l00968"></a>00968 <span class="comment">!</span>
    1033. 

  1033. <a name="l00969"></a>00969   <span class="keywordtype">integer</span> norder
    1034. 

  1034. <a name="l00970"></a>00970 <span class="comment">!</span>
    1035. 

  1035. <a name="l00971"></a>00971   <span class="keywordtype">double precision</span> angle
    1036. 

  1036. <a name="l00972"></a>00972   <span class="keywordtype">double precision</span> d_pi
    1037. 

  1037. <a name="l00973"></a>00973   <span class="keywordtype">integer</span> i
    1038. 

  1038. <a name="l00974"></a>00974   <span class="keywordtype">double precision</span> weight(norder)
    1039. 

  1039. <a name="l00975"></a>00975   <span class="keywordtype">double precision</span> xtab(norder)
    1040. 

  1040. <a name="l00976"></a>00976 <span class="comment">!</span>
    1041. 

  1041. <a name="l00977"></a>00977   <span class="keyword">do</span> i = 1, norder
    1042. 

  1042. <a name="l00978"></a>00978     angle = dble ( i ) * d_pi ( ) / dble ( norder + 1 )
    1043. 

  1043. <a name="l00979"></a>00979     xtab(i) = cos ( angle )
    1044. 

  1044. <a name="l00980"></a>00980     weight(i) = d_pi ( ) * ( sin ( angle ) )**2 / dble ( norder + 1 )
    1045. 

  1045. <a name="l00981"></a>00981   <span class="keyword">end do</span>
    1046. 

  1046. <a name="l00982"></a>00982 
    1047. 

  1047. <a name="l00983"></a>00983   return
    1048. 

  1048. <a name="l00984"></a>00984 <span class="keyword">end</span>
    1049. 

  1049. <a name="l00985"></a><a class="code" href="quadrule_8f90.html#ab73cf601dce50b6fc79d82a6ee87bb67">00985</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#ab73cf601dce50b6fc79d82a6ee87bb67">d_swap</a> ( x, y )
    1050. 

  1050. <a name="l00986"></a>00986 <span class="comment">!</span>
    1051. 

  1051. <a name="l00987"></a>00987 <span class="comment">!*******************************************************************************</span>
    1052. 

  1052. <a name="l00988"></a>00988 <span class="comment">!</span>
    1053. 

  1053. <a name="l00989"></a>00989 <span class="comment">!! D_SWAP switches two double precision values.</span>
    1054. 

  1054. <a name="l00990"></a>00990 <span class="comment">!</span>
    1055. 

  1055. <a name="l00991"></a>00991 <span class="comment">!</span>
    1056. 

  1056. <a name="l00992"></a>00992 <span class="comment">!  Modified:</span>
    1057. 

  1057. <a name="l00993"></a>00993 <span class="comment">!</span>
    1058. 

  1058. <a name="l00994"></a>00994 <span class="comment">!    01 May 2000</span>
    1059. 

  1059. <a name="l00995"></a>00995 <span class="comment">!</span>
    1060. 

  1060. <a name="l00996"></a>00996 <span class="comment">!  Author:</span>
    1061. 

  1061. <a name="l00997"></a>00997 <span class="comment">!</span>
    1062. 

  1062. <a name="l00998"></a>00998 <span class="comment">!    John Burkardt</span>
    1063. 

  1063. <a name="l00999"></a>00999 <span class="comment">!</span>
    1064. 

  1064. <a name="l01000"></a>01000 <span class="comment">!  Parameters:</span>
    1065. 

  1065. <a name="l01001"></a>01001 <span class="comment">!</span>
    1066. 

  1066. <a name="l01002"></a>01002 <span class="comment">!    Input/output, double precision X, Y.  On output, the values of X and</span>
    1067. 

  1067. <a name="l01003"></a>01003 <span class="comment">!    Y have been interchanged.</span>
    1068. 

  1068. <a name="l01004"></a>01004 <span class="comment">!</span>
    1069. 

  1069. <a name="l01005"></a>01005   <span class="keyword">implicit none</span>
    1070. 

  1070. <a name="l01006"></a>01006 <span class="comment">!</span>
    1071. 

  1071. <a name="l01007"></a>01007   <span class="keywordtype">double precision</span> x
    1072. 

  1072. <a name="l01008"></a>01008   <span class="keywordtype">double precision</span> y
    1073. 

  1073. <a name="l01009"></a>01009   <span class="keywordtype">double precision</span> z
    1074. 

  1074. <a name="l01010"></a>01010 <span class="comment">!</span>
    1075. 

  1075. <a name="l01011"></a>01011   z = x
    1076. 

  1076. <a name="l01012"></a>01012   x = y
    1077. 

  1077. <a name="l01013"></a>01013   y = z
    1078. 

  1078. <a name="l01014"></a>01014 
    1079. 

  1079. <a name="l01015"></a>01015   return
    1080. 

  1080. <a name="l01016"></a>01016 <span class="keyword">end</span>
    1081. 

  1081. <a name="l01017"></a><a class="code" href="quadrule_8f90.html#a1196e8a1c04167d129db7f177728d7fc">01017</a> <span class="keyword">function </span>d_pi ( )
    1082. 

  1082. <a name="l01018"></a>01018 <span class="comment">!</span>
    1083. 

  1083. <a name="l01019"></a>01019 <span class="comment">!*******************************************************************************</span>
    1084. 

  1084. <a name="l01020"></a>01020 <span class="comment">!</span>
    1085. 

  1085. <a name="l01021"></a>01021 <span class="comment">!! DPI returns the value of pi as a double precision quantity.</span>
    1086. 

  1086. <a name="l01022"></a>01022 <span class="comment">!</span>
    1087. 

  1087. <a name="l01023"></a>01023 <span class="comment">!</span>
    1088. 

  1088. <a name="l01024"></a>01024 <span class="comment">!  Modified:</span>
    1089. 

  1089. <a name="l01025"></a>01025 <span class="comment">!</span>
    1090. 

  1090. <a name="l01026"></a>01026 <span class="comment">!    28 April 2000</span>
    1091. 

  1091. <a name="l01027"></a>01027 <span class="comment">!</span>
    1092. 

  1092. <a name="l01028"></a>01028 <span class="comment">!  Author:</span>
    1093. 

  1093. <a name="l01029"></a>01029 <span class="comment">!</span>
    1094. 

  1094. <a name="l01030"></a>01030 <span class="comment">!    John Burkardt</span>
    1095. 

  1095. <a name="l01031"></a>01031 <span class="comment">!</span>
    1096. 

  1096. <a name="l01032"></a>01032 <span class="comment">!  Parameters:</span>
    1097. 

  1097. <a name="l01033"></a>01033 <span class="comment">!</span>
    1098. 

  1098. <a name="l01034"></a>01034 <span class="comment">!    Output, double precision D_PI, the value of pi.</span>
    1099. 

  1099. <a name="l01035"></a>01035 <span class="comment">!</span>
    1100. 

  1100. <a name="l01036"></a>01036   <span class="keyword">implicit none</span>
    1101. 

  1101. <a name="l01037"></a>01037 <span class="comment">!</span>
    1102. 

  1102. <a name="l01038"></a>01038   <span class="keywordtype">double precision</span> d_pi
    1103. 

  1103. <a name="l01039"></a>01039 <span class="comment">!</span>
    1104. 

  1104. <a name="l01040"></a>01040   d_pi = 3.14159265358979323846264338327950288419716939937510D+00
    1105. 

  1105. <a name="l01041"></a>01041 
    1106. 

  1106. <a name="l01042"></a>01042   return
    1107. 

  1107. <a name="l01043"></a>01043 <span class="keyword">end</span>
    1108. 

  1108. <a name="l01044"></a><a class="code" href="quadrule_8f90.html#a7841cf442902dd98d08b6a4d89a9a7bf">01044</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a7841cf442902dd98d08b6a4d89a9a7bf">dvec_reverse</a> ( n, a )
    1109. 

  1109. <a name="l01045"></a>01045 <span class="comment">!</span>
    1110. 

  1110. <a name="l01046"></a>01046 <span class="comment">!*******************************************************************************</span>
    1111. 

  1111. <a name="l01047"></a>01047 <span class="comment">!</span>
    1112. 

  1112. <a name="l01048"></a>01048 <span class="comment">!! DVEC_REVERSE reverses the elements of a double precision vector.</span>
    1113. 

  1113. <a name="l01049"></a>01049 <span class="comment">!</span>
    1114. 

  1114. <a name="l01050"></a>01050 <span class="comment">!</span>
    1115. 

  1115. <a name="l01051"></a>01051 <span class="comment">!  Example:</span>
    1116. 

  1116. <a name="l01052"></a>01052 <span class="comment">!</span>
    1117. 

  1117. <a name="l01053"></a>01053 <span class="comment">!    Input:</span>
    1118. 

  1118. <a name="l01054"></a>01054 <span class="comment">!</span>
    1119. 

  1119. <a name="l01055"></a>01055 <span class="comment">!      N = 5, A = ( 11.0, 12.0, 13.0, 14.0, 15.0D+00 )</span>
    1120. 

  1120. <a name="l01056"></a>01056 <span class="comment">!</span>
    1121. 

  1121. <a name="l01057"></a>01057 <span class="comment">!    Output:</span>
    1122. 

  1122. <a name="l01058"></a>01058 <span class="comment">!</span>
    1123. 

  1123. <a name="l01059"></a>01059 <span class="comment">!      A = ( 15.0, 14.0, 13.0, 12.0, 11.0D+00 )</span>
    1124. 

  1124. <a name="l01060"></a>01060 <span class="comment">!</span>
    1125. 

  1125. <a name="l01061"></a>01061 <span class="comment">!  Modified:</span>
    1126. 

  1126. <a name="l01062"></a>01062 <span class="comment">!</span>
    1127. 

  1127. <a name="l01063"></a>01063 <span class="comment">!    06 October 1998</span>
    1128. 

  1128. <a name="l01064"></a>01064 <span class="comment">!</span>
    1129. 

  1129. <a name="l01065"></a>01065 <span class="comment">!  Author:</span>
    1130. 

  1130. <a name="l01066"></a>01066 <span class="comment">!</span>
    1131. 

  1131. <a name="l01067"></a>01067 <span class="comment">!    John Burkardt</span>
    1132. 

  1132. <a name="l01068"></a>01068 <span class="comment">!</span>
    1133. 

  1133. <a name="l01069"></a>01069 <span class="comment">!  Parameters:</span>
    1134. 

  1134. <a name="l01070"></a>01070 <span class="comment">!</span>
    1135. 

  1135. <a name="l01071"></a>01071 <span class="comment">!    Input, integer N, the number of entries in the array.</span>
    1136. 

  1136. <a name="l01072"></a>01072 <span class="comment">!</span>
    1137. 

  1137. <a name="l01073"></a>01073 <span class="comment">!    Input/output, double precision A(N), the array to be reversed.</span>
    1138. 

  1138. <a name="l01074"></a>01074 <span class="comment">!</span>
    1139. 

  1139. <a name="l01075"></a>01075   <span class="keyword">implicit none</span>
    1140. 

  1140. <a name="l01076"></a>01076 <span class="comment">!</span>
    1141. 

  1141. <a name="l01077"></a>01077   <span class="keywordtype">integer</span> n
    1142. 

  1142. <a name="l01078"></a>01078 <span class="comment">!</span>
    1143. 

  1143. <a name="l01079"></a>01079   <span class="keywordtype">double precision</span> a(n)
    1144. 

  1144. <a name="l01080"></a>01080   <span class="keywordtype">integer</span> i
    1145. 

  1145. <a name="l01081"></a>01081 <span class="comment">!</span>
    1146. 

  1146. <a name="l01082"></a>01082   <span class="keyword">do</span> i = 1, n/2
    1147. 

  1147. <a name="l01083"></a>01083     call <a class="code" href="quadrule_8f90.html#ab73cf601dce50b6fc79d82a6ee87bb67">d_swap </a>( a(i), a(n+1-i) )
    1148. 

  1148. <a name="l01084"></a>01084   <span class="keyword">end do</span>
    1149. 

  1149. <a name="l01085"></a>01085 
    1150. 

  1150. <a name="l01086"></a>01086   return
    1151. 

  1151. <a name="l01087"></a>01087 <span class="keyword">end</span>
    1152. 

  1152. <a name="l01088"></a><a class="code" href="quadrule_8f90.html#a688af4295664e9e84424169e79729a11">01088</a> <span class="keyword">function </span>gamma ( x )
    1153. 

  1153. <a name="l01089"></a>01089 <span class="comment">!</span>
    1154. 

  1154. <a name="l01090"></a>01090 <span class="comment">!*******************************************************************************</span>
    1155. 

  1155. <a name="l01091"></a>01091 <span class="comment">!</span>
    1156. 

  1156. <a name="l01092"></a>01092 <span class="comment">!! GAMMA computes the gamma function using Hastings&#39;s approximation.</span>
    1157. 

  1157. <a name="l01093"></a>01093 <span class="comment">!</span>
    1158. 

  1158. <a name="l01094"></a>01094 <span class="comment">!</span>
    1159. 

  1159. <a name="l01095"></a>01095 <span class="comment">!  Reference:</span>
    1160. 

  1160. <a name="l01096"></a>01096 <span class="comment">!</span>
    1161. 

  1161. <a name="l01097"></a>01097 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    1162. 

  1162. <a name="l01098"></a>01098 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    1163. 

  1163. <a name="l01099"></a>01099 <span class="comment">!    Prentice Hall, 1966.</span>
    1164. 

  1164. <a name="l01100"></a>01100 <span class="comment">!</span>
    1165. 

  1165. <a name="l01101"></a>01101 <span class="comment">!  Modified:</span>
    1166. 

  1166. <a name="l01102"></a>01102 <span class="comment">!</span>
    1167. 

  1167. <a name="l01103"></a>01103 <span class="comment">!    19 September 1998</span>
    1168. 

  1168. <a name="l01104"></a>01104 <span class="comment">!</span>
    1169. 

  1169. <a name="l01105"></a>01105 <span class="comment">!  Parameters:</span>
    1170. 

  1170. <a name="l01106"></a>01106 <span class="comment">!</span>
    1171. 

  1171. <a name="l01107"></a>01107 <span class="comment">!    Input, double precision X, the argument at which the gamma function</span>
    1172. 

  1172. <a name="l01108"></a>01108 <span class="comment">!    is to be evaluated.  X must be greater than 0, and less than 70.</span>
    1173. 

  1173. <a name="l01109"></a>01109 <span class="comment">!</span>
    1174. 

  1174. <a name="l01110"></a>01110 <span class="comment">!    Output, double precision GAMMA, the gamma function at X.</span>
    1175. 

  1175. <a name="l01111"></a>01111 <span class="comment">!</span>
    1176. 

  1176. <a name="l01112"></a>01112   <span class="keyword">implicit none</span>
    1177. 

  1177. <a name="l01113"></a>01113 <span class="comment">!</span>
    1178. 

  1178. <a name="l01114"></a>01114   <span class="keywordtype">double precision</span> gam
    1179. 

  1179. <a name="l01115"></a>01115   <span class="keywordtype">double precision</span> gamma
    1180. 

  1180. <a name="l01116"></a>01116   <span class="keywordtype">double precision</span> x
    1181. 

  1181. <a name="l01117"></a>01117   <span class="keywordtype">double precision</span> y
    1182. 

  1182. <a name="l01118"></a>01118   <span class="keywordtype">double precision</span> z
    1183. 

  1183. <a name="l01119"></a>01119   <span class="keywordtype">double precision</span> za
    1184. 

  1184. <a name="l01120"></a>01120 <span class="comment">!</span>
    1185. 

  1185. <a name="l01121"></a>01121   gam ( y ) = ((((((( &amp;
    1186. 

  1186. <a name="l01122"></a>01122           0.035868343D+00   * y &amp;
    1187. 

  1187. <a name="l01123"></a>01123         - 0.193527818D+00 ) * y &amp;
    1188. 

  1188. <a name="l01124"></a>01124         + 0.482199394D+00 ) * y &amp;
    1189. 

  1189. <a name="l01125"></a>01125         - 0.756704078D+00 ) * y &amp;
    1190. 

  1190. <a name="l01126"></a>01126         + 0.918206857D+00 ) * y &amp;
    1191. 

  1191. <a name="l01127"></a>01127         - 0.897056937D+00 ) * y &amp;
    1192. 

  1192. <a name="l01128"></a>01128         + 0.988205891D+00 ) * y &amp;
    1193. 

  1193. <a name="l01129"></a>01129         - 0.577191652D+00 ) * y + 1.0D+00
    1194. 

  1194. <a name="l01130"></a>01130 
    1195. 

  1195. <a name="l01131"></a>01131   <span class="keyword">if</span> ( x &lt;= 0.0D+00 ) <span class="keyword">then</span>
    1196. 

  1196. <a name="l01132"></a>01132     gamma = 0.0D+00
    1197. 

  1197. <a name="l01133"></a>01133     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    1198. 

  1198. <a name="l01134"></a>01134     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;GAMMA - Fatal error!&#39;</span>
    1199. 

  1199. <a name="l01135"></a>01135     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Input argument X &lt;= 0.&#39;</span>
    1200. 

  1200. <a name="l01136"></a>01136     stop
    1201. 

  1201. <a name="l01137"></a>01137   <span class="keyword">end if</span>
    1202. 

  1202. <a name="l01138"></a>01138 
    1203. 

  1203. <a name="l01139"></a>01139   <span class="keyword">if</span> ( x &gt;= 70.0D+00 ) <span class="keyword">then</span>
    1204. 

  1204. <a name="l01140"></a>01140     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    1205. 

  1205. <a name="l01141"></a>01141     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;GAMMA - Fatal error!&#39;</span>
    1206. 

  1206. <a name="l01142"></a>01142     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Input argument X &gt;= 70.&#39;</span>
    1207. 

  1207. <a name="l01143"></a>01143     stop
    1208. 

  1208. <a name="l01144"></a>01144   <span class="keyword">end if</span>
    1209. 

  1209. <a name="l01145"></a>01145 
    1210. 

  1210. <a name="l01146"></a>01146   <span class="keyword">if</span> ( x == 1.0D+00 ) <span class="keyword">then</span>
    1211. 

  1211. <a name="l01147"></a>01147     gamma = 1.0D+00
    1212. 

  1212. <a name="l01148"></a>01148     return
    1213. 

  1213. <a name="l01149"></a>01149   <span class="keyword">end if</span>
    1214. 

  1214. <a name="l01150"></a>01150 
    1215. 

  1215. <a name="l01151"></a>01151   <span class="keyword">if</span> ( x &lt;= 1.0D+00 ) <span class="keyword">then</span>
    1216. 

  1216. <a name="l01152"></a>01152     gamma = gam ( x ) / x
    1217. 

  1217. <a name="l01153"></a>01153     return
    1218. 

  1218. <a name="l01154"></a>01154   <span class="keyword">end if</span>
    1219. 

  1219. <a name="l01155"></a>01155 
    1220. 

  1220. <a name="l01156"></a>01156   z = x
    1221. 

  1221. <a name="l01157"></a>01157 
    1222. 

  1222. <a name="l01158"></a>01158   za = 1.0D+00
    1223. 

  1223. <a name="l01159"></a>01159 
    1224. 

  1224. <a name="l01160"></a>01160   <span class="keyword">do</span>
    1225. 

  1225. <a name="l01161"></a>01161 
    1226. 

  1226. <a name="l01162"></a>01162     z = z - 1.0D+00
    1227. 

  1227. <a name="l01163"></a>01163 
    1228. 

  1228. <a name="l01164"></a>01164     <span class="keyword">if</span> ( z &lt; 1.0D+00 ) <span class="keyword">then</span>
    1229. 

  1229. <a name="l01165"></a>01165       gamma = za * gam ( z )
    1230. 

  1230. <a name="l01166"></a>01166       exit
    1231. 

  1231. <a name="l01167"></a>01167     <span class="keyword">else</span> <span class="keyword">if</span> ( z == 1.0D+00 ) <span class="keyword">then</span>
    1232. 

  1232. <a name="l01168"></a>01168       gamma = za
    1233. 

  1233. <a name="l01169"></a>01169       exit
    1234. 

  1234. <a name="l01170"></a>01170     <span class="keyword">end if</span>
    1235. 

  1235. <a name="l01171"></a>01171 
    1236. 

  1236. <a name="l01172"></a>01172     za = za * z
    1237. 

  1237. <a name="l01173"></a>01173 
    1238. 

  1238. <a name="l01174"></a>01174   <span class="keyword">end do</span>
    1239. 

  1239. <a name="l01175"></a>01175 
    1240. 

  1240. <a name="l01176"></a>01176   return
    1241. 

  1241. <a name="l01177"></a>01177 <span class="keyword">end</span>
    1242. 

  1242. <a name="l01178"></a><a class="code" href="quadrule_8f90.html#a85e94b692189c91a3f77d8f4c210f70f">01178</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a85e94b692189c91a3f77d8f4c210f70f">hermite_com</a> ( norder, xtab, weight )
    1243. 

  1243. <a name="l01179"></a>01179 <span class="comment">!</span>
    1244. 

  1244. <a name="l01180"></a>01180 <span class="comment">!*******************************************************************************</span>
    1245. 

  1245. <a name="l01181"></a>01181 <span class="comment">!</span>
    1246. 

  1246. <a name="l01182"></a>01182 <span class="comment">!! HERMITE_COM computes the abscissa and weights for Gauss-Hermite quadrature.</span>
    1247. 

  1247. <a name="l01183"></a>01183 <span class="comment">!</span>
    1248. 

  1248. <a name="l01184"></a>01184 <span class="comment">!</span>
    1249. 

  1249. <a name="l01185"></a>01185 <span class="comment">!  Discussion:</span>
    1250. 

  1250. <a name="l01186"></a>01186 <span class="comment">!</span>
    1251. 

  1251. <a name="l01187"></a>01187 <span class="comment">!    The abscissas are the zeros of the N-th order Hermite polynomial.</span>
    1252. 

  1252. <a name="l01188"></a>01188 <span class="comment">!</span>
    1253. 

  1253. <a name="l01189"></a>01189 <span class="comment">!  Integration interval:</span>
    1254. 

  1254. <a name="l01190"></a>01190 <span class="comment">!</span>
    1255. 

  1255. <a name="l01191"></a>01191 <span class="comment">!    ( -Infinity, +Infinity )</span>
    1256. 

  1256. <a name="l01192"></a>01192 <span class="comment">!</span>
    1257. 

  1257. <a name="l01193"></a>01193 <span class="comment">!  Weight function:</span>
    1258. 

  1258. <a name="l01194"></a>01194 <span class="comment">!</span>
    1259. 

  1259. <a name="l01195"></a>01195 <span class="comment">!    EXP ( - X**2 )</span>
    1260. 

  1260. <a name="l01196"></a>01196 <span class="comment">!</span>
    1261. 

  1261. <a name="l01197"></a>01197 <span class="comment">!  Integral to approximate:</span>
    1262. 

  1262. <a name="l01198"></a>01198 <span class="comment">!</span>
    1263. 

  1263. <a name="l01199"></a>01199 <span class="comment">!    Integral ( -INFINITY &lt; X &lt; +INFINITY ) EXP ( - X**2 ) * F(X) dX</span>
    1264. 

  1264. <a name="l01200"></a>01200 <span class="comment">!</span>
    1265. 

  1265. <a name="l01201"></a>01201 <span class="comment">!  Approximate integral:</span>
    1266. 

  1266. <a name="l01202"></a>01202 <span class="comment">!</span>
    1267. 

  1267. <a name="l01203"></a>01203 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    1268. 

  1268. <a name="l01204"></a>01204 <span class="comment">!</span>
    1269. 

  1269. <a name="l01205"></a>01205 <span class="comment">!  Reference:</span>
    1270. 

  1270. <a name="l01206"></a>01206 <span class="comment">!</span>
    1271. 

  1271. <a name="l01207"></a>01207 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    1272. 

  1272. <a name="l01208"></a>01208 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    1273. 

  1273. <a name="l01209"></a>01209 <span class="comment">!    Prentice Hall, 1966.</span>
    1274. 

  1274. <a name="l01210"></a>01210 <span class="comment">!</span>
    1275. 

  1275. <a name="l01211"></a>01211 <span class="comment">!  Modified:</span>
    1276. 

  1276. <a name="l01212"></a>01212 <span class="comment">!</span>
    1277. 

  1277. <a name="l01213"></a>01213 <span class="comment">!    19 September 1998</span>
    1278. 

  1278. <a name="l01214"></a>01214 <span class="comment">!</span>
    1279. 

  1279. <a name="l01215"></a>01215 <span class="comment">!  Author:</span>
    1280. 

  1280. <a name="l01216"></a>01216 <span class="comment">!</span>
    1281. 

  1281. <a name="l01217"></a>01217 <span class="comment">!    John Burkardt</span>
    1282. 

  1282. <a name="l01218"></a>01218 <span class="comment">!</span>
    1283. 

  1283. <a name="l01219"></a>01219 <span class="comment">!  Parameters:</span>
    1284. 

  1284. <a name="l01220"></a>01220 <span class="comment">!</span>
    1285. 

  1285. <a name="l01221"></a>01221 <span class="comment">!    Input, integer NORDER, the order of the formula to be computed.</span>
    1286. 

  1286. <a name="l01222"></a>01222 <span class="comment">!</span>
    1287. 

  1287. <a name="l01223"></a>01223 <span class="comment">!    Output, double precision XTAB(NORDER), the Gauss-Hermite abscissas.</span>
    1288. 

  1288. <a name="l01224"></a>01224 <span class="comment">!</span>
    1289. 

  1289. <a name="l01225"></a>01225 <span class="comment">!    Output, double precision WEIGHT(NORDER), the Gauss-Hermite weights.</span>
    1290. 

  1290. <a name="l01226"></a>01226 <span class="comment">!</span>
    1291. 

  1291. <a name="l01227"></a>01227   <span class="keyword">implicit none</span>
    1292. 

  1292. <a name="l01228"></a>01228 <span class="comment">!</span>
    1293. 

  1293. <a name="l01229"></a>01229   <span class="keywordtype">integer</span> norder
    1294. 

  1294. <a name="l01230"></a>01230 <span class="comment">!</span>
    1295. 

  1295. <a name="l01231"></a>01231   <span class="keywordtype">double precision</span> cc
    1296. 

  1296. <a name="l01232"></a>01232   <span class="keywordtype">double precision</span> dp2
    1297. 

  1297. <a name="l01233"></a>01233   <span class="keywordtype">double precision</span> gamma
    1298. 

  1298. <a name="l01234"></a>01234   <span class="keywordtype">integer</span> i
    1299. 

  1299. <a name="l01235"></a>01235   <span class="keywordtype">double precision</span> p1
    1300. 

  1300. <a name="l01236"></a>01236   <span class="keywordtype">double precision</span> s
    1301. 

  1301. <a name="l01237"></a>01237   <span class="keywordtype">double precision</span> temp
    1302. 

  1302. <a name="l01238"></a>01238   <span class="keywordtype">double precision</span> weight(norder)
    1303. 

  1303. <a name="l01239"></a>01239   <span class="keywordtype">double precision</span> x
    1304. 

  1304. <a name="l01240"></a>01240   <span class="keywordtype">double precision</span> xtab(norder)
    1305. 

  1305. <a name="l01241"></a>01241 <span class="comment">!</span>
    1306. 

  1306. <a name="l01242"></a>01242   cc = 1.7724538509D+00 * gamma ( dble ( norder ) ) / ( 2.0D+00**( norder - 1 ) )
    1307. 

  1307. <a name="l01243"></a>01243 
    1308. 

  1308. <a name="l01244"></a>01244   s = ( 2.0D+00 * dble ( norder ) + 1.0D+00 )**( 1.0D+00 / 6.0D+00 )
    1309. 

  1309. <a name="l01245"></a>01245 
    1310. 

  1310. <a name="l01246"></a>01246   <span class="keyword">do</span> i = 1, ( norder + 1 ) / 2
    1311. 

  1311. <a name="l01247"></a>01247 
    1312. 

  1312. <a name="l01248"></a>01248     <span class="keyword">if</span> ( i == 1 ) <span class="keyword">then</span>
    1313. 

  1313. <a name="l01249"></a>01249 
    1314. 

  1314. <a name="l01250"></a>01250       x = s**3 - 1.85575D+00 / s
    1315. 

  1315. <a name="l01251"></a>01251 
    1316. 

  1316. <a name="l01252"></a>01252     <span class="keyword">else</span> <span class="keyword">if</span> ( i == 2 ) <span class="keyword">then</span>
    1317. 

  1317. <a name="l01253"></a>01253 
    1318. 

  1318. <a name="l01254"></a>01254       x = x - 1.14D+00 * ( ( dble ( norder ) )**0.426D+00 ) / x
    1319. 

  1319. <a name="l01255"></a>01255 
    1320. 

  1320. <a name="l01256"></a>01256     <span class="keyword">else</span> <span class="keyword">if</span> ( i == 3 ) <span class="keyword">then</span>
    1321. 

  1321. <a name="l01257"></a>01257 
    1322. 

  1322. <a name="l01258"></a>01258       x = 1.86D+00 * x - 0.86D+00 * xtab(1)
    1323. 

  1323. <a name="l01259"></a>01259 
    1324. 

  1324. <a name="l01260"></a>01260     <span class="keyword">else</span> <span class="keyword">if</span> ( i == 4 ) <span class="keyword">then</span>
    1325. 

  1325. <a name="l01261"></a>01261 
    1326. 

  1326. <a name="l01262"></a>01262       x = 1.91D+00 * x - 0.91D+00 * xtab(2)
    1327. 

  1327. <a name="l01263"></a>01263 
    1328. 

  1328. <a name="l01264"></a>01264     <span class="keyword">else</span>
    1329. 

  1329. <a name="l01265"></a>01265 
    1330. 

  1330. <a name="l01266"></a>01266       x = 2.0D+00 * x - xtab(i-2)
    1331. 

  1331. <a name="l01267"></a>01267 
    1332. 

  1332. <a name="l01268"></a>01268     <span class="keyword">end if</span>
    1333. 

  1333. <a name="l01269"></a>01269 
    1334. 

  1334. <a name="l01270"></a>01270     call <a class="code" href="quadrule_8f90.html#ae9c37528989dee8bb6c51ff8a4626c05">hermite_root </a>( x, norder, dp2, p1 )
    1335. 

  1335. <a name="l01271"></a>01271 
    1336. 

  1336. <a name="l01272"></a>01272     xtab(i) = x
    1337. 

  1337. <a name="l01273"></a>01273     weight(i) = ( cc / dp2 ) / p1
    1338. 

  1338. <a name="l01274"></a>01274 
    1339. 

  1339. <a name="l01275"></a>01275     xtab(norder-i+1) = - x
    1340. 

  1340. <a name="l01276"></a>01276     weight(norder-i+1) = weight(i)
    1341. 

  1341. <a name="l01277"></a>01277 
    1342. 

  1342. <a name="l01278"></a>01278   <span class="keyword">end do</span>
    1343. 

  1343. <a name="l01279"></a>01279 <span class="comment">!</span>
    1344. 

  1344. <a name="l01280"></a>01280 <span class="comment">!  Reverse the order of the XTAB values.</span>
    1345. 

  1345. <a name="l01281"></a>01281 <span class="comment">!</span>
    1346. 

  1346. <a name="l01282"></a>01282   call <a class="code" href="quadrule_8f90.html#a7841cf442902dd98d08b6a4d89a9a7bf">dvec_reverse </a>( norder, xtab )
    1347. 

  1347. <a name="l01283"></a>01283 
    1348. 

  1348. <a name="l01284"></a>01284   return
    1349. 

  1349. <a name="l01285"></a>01285 <span class="keyword">end</span>
    1350. 

  1350. <a name="l01286"></a><a class="code" href="quadrule_8f90.html#a837c192f4116548551a6c0b69465adbb">01286</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a837c192f4116548551a6c0b69465adbb">hermite_recur</a> ( p2, dp2, p1, x, norder )
    1351. 

  1351. <a name="l01287"></a>01287 <span class="comment">!</span>
    1352. 

  1352. <a name="l01288"></a>01288 <span class="comment">!*******************************************************************************</span>
    1353. 

  1353. <a name="l01289"></a>01289 <span class="comment">!</span>
    1354. 

  1354. <a name="l01290"></a>01290 <span class="comment">!! HERMITE_RECUR finds the value and derivative of a Hermite polynomial.</span>
    1355. 

  1355. <a name="l01291"></a>01291 <span class="comment">!</span>
    1356. 

  1356. <a name="l01292"></a>01292 <span class="comment">!</span>
    1357. 

  1357. <a name="l01293"></a>01293 <span class="comment">!  Reference:</span>
    1358. 

  1358. <a name="l01294"></a>01294 <span class="comment">!</span>
    1359. 

  1359. <a name="l01295"></a>01295 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    1360. 

  1360. <a name="l01296"></a>01296 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    1361. 

  1361. <a name="l01297"></a>01297 <span class="comment">!    Prentice Hall, 1966.</span>
    1362. 

  1362. <a name="l01298"></a>01298 <span class="comment">!</span>
    1363. 

  1363. <a name="l01299"></a>01299 <span class="comment">!  Modified:</span>
    1364. 

  1364. <a name="l01300"></a>01300 <span class="comment">!</span>
    1365. 

  1365. <a name="l01301"></a>01301 <span class="comment">!    19 September 1998</span>
    1366. 

  1366. <a name="l01302"></a>01302 <span class="comment">!</span>
    1367. 

  1367. <a name="l01303"></a>01303 <span class="comment">!  Parameters:</span>
    1368. 

  1368. <a name="l01304"></a>01304 <span class="comment">!</span>
    1369. 

  1369. <a name="l01305"></a>01305 <span class="comment">!    Output, double precision P2, the value of H(NORDER)(X).</span>
    1370. 

  1370. <a name="l01306"></a>01306 <span class="comment">!</span>
    1371. 

  1371. <a name="l01307"></a>01307 <span class="comment">!    Output, double precision DP2, the value of H&#39;(NORDER)(X).</span>
    1372. 

  1372. <a name="l01308"></a>01308 <span class="comment">!</span>
    1373. 

  1373. <a name="l01309"></a>01309 <span class="comment">!    Output, double precision P1, the value of H(NORDER-1)(X).</span>
    1374. 

  1374. <a name="l01310"></a>01310 <span class="comment">!</span>
    1375. 

  1375. <a name="l01311"></a>01311 <span class="comment">!    Input, double precision X, the point at which polynomials are evaluated.</span>
    1376. 

  1376. <a name="l01312"></a>01312 <span class="comment">!</span>
    1377. 

  1377. <a name="l01313"></a>01313 <span class="comment">!    Input, integer NORDER, the order of the polynomial to be computed.</span>
    1378. 

  1378. <a name="l01314"></a>01314 <span class="comment">!</span>
    1379. 

  1379. <a name="l01315"></a>01315   <span class="keyword">implicit none</span>
    1380. 

  1380. <a name="l01316"></a>01316 <span class="comment">!</span>
    1381. 

  1381. <a name="l01317"></a>01317   <span class="keywordtype">integer</span> i
    1382. 

  1382. <a name="l01318"></a>01318   <span class="keywordtype">double precision</span> dp0
    1383. 

  1383. <a name="l01319"></a>01319   <span class="keywordtype">double precision</span> dp1
    1384. 

  1384. <a name="l01320"></a>01320   <span class="keywordtype">double precision</span> dp2
    1385. 

  1385. <a name="l01321"></a>01321   <span class="keywordtype">integer</span> norder
    1386. 

  1386. <a name="l01322"></a>01322   <span class="keywordtype">double precision</span> p0
    1387. 

  1387. <a name="l01323"></a>01323   <span class="keywordtype">double precision</span> p1
    1388. 

  1388. <a name="l01324"></a>01324   <span class="keywordtype">double precision</span> p2
    1389. 

  1389. <a name="l01325"></a>01325   <span class="keywordtype">double precision</span> x
    1390. 

  1390. <a name="l01326"></a>01326 <span class="comment">!</span>
    1391. 

  1391. <a name="l01327"></a>01327   p1 = 1.0D+00
    1392. 

  1392. <a name="l01328"></a>01328   dp1 = 0.0D+00
    1393. 

  1393. <a name="l01329"></a>01329 
    1394. 

  1394. <a name="l01330"></a>01330   p2 = x
    1395. 

  1395. <a name="l01331"></a>01331   dp2 = 1.0D+00
    1396. 

  1396. <a name="l01332"></a>01332 
    1397. 

  1397. <a name="l01333"></a>01333   <span class="keyword">do</span> i = 2, norder
    1398. 

  1398. <a name="l01334"></a>01334 
    1399. 

  1399. <a name="l01335"></a>01335     p0 = p1
    1400. 

  1400. <a name="l01336"></a>01336     dp0 = dp1
    1401. 

  1401. <a name="l01337"></a>01337 
    1402. 

  1402. <a name="l01338"></a>01338     p1 = p2
    1403. 

  1403. <a name="l01339"></a>01339     dp1 = dp2
    1404. 

  1404. <a name="l01340"></a>01340 
    1405. 

  1405. <a name="l01341"></a>01341     p2  = x * p1 - 0.5D+00 * ( dble ( i ) - 1.0D+00 ) * p0
    1406. 

  1406. <a name="l01342"></a>01342     dp2 = x * dp1 + p1 - 0.5D+00 * ( dble ( i ) - 1.0D+00 ) * dp0
    1407. 

  1407. <a name="l01343"></a>01343 
    1408. 

  1408. <a name="l01344"></a>01344   <span class="keyword">end do</span>
    1409. 

  1409. <a name="l01345"></a>01345 
    1410. 

  1410. <a name="l01346"></a>01346   return
    1411. 

  1411. <a name="l01347"></a>01347 <span class="keyword">end</span>
    1412. 

  1412. <a name="l01348"></a><a class="code" href="quadrule_8f90.html#ae9c37528989dee8bb6c51ff8a4626c05">01348</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#ae9c37528989dee8bb6c51ff8a4626c05">hermite_root</a> ( x, norder, dp2, p1 )
    1413. 

  1413. <a name="l01349"></a>01349 <span class="comment">!</span>
    1414. 

  1414. <a name="l01350"></a>01350 <span class="comment">!*******************************************************************************</span>
    1415. 

  1415. <a name="l01351"></a>01351 <span class="comment">!</span>
    1416. 

  1416. <a name="l01352"></a>01352 <span class="comment">!! HERMITE_ROOT improves an approximate root of a Hermite polynomial.</span>
    1417. 

  1417. <a name="l01353"></a>01353 <span class="comment">!</span>
    1418. 

  1418. <a name="l01354"></a>01354 <span class="comment">!</span>
    1419. 

  1419. <a name="l01355"></a>01355 <span class="comment">!  Reference:</span>
    1420. 

  1420. <a name="l01356"></a>01356 <span class="comment">!</span>
    1421. 

  1421. <a name="l01357"></a>01357 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    1422. 

  1422. <a name="l01358"></a>01358 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    1423. 

  1423. <a name="l01359"></a>01359 <span class="comment">!    Prentice Hall, 1966.</span>
    1424. 

  1424. <a name="l01360"></a>01360 <span class="comment">!</span>
    1425. 

  1425. <a name="l01361"></a>01361 <span class="comment">!  Modified:</span>
    1426. 

  1426. <a name="l01362"></a>01362 <span class="comment">!</span>
    1427. 

  1427. <a name="l01363"></a>01363 <span class="comment">!    19 September 1998</span>
    1428. 

  1428. <a name="l01364"></a>01364 <span class="comment">!</span>
    1429. 

  1429. <a name="l01365"></a>01365 <span class="comment">!  Parameters:</span>
    1430. 

  1430. <a name="l01366"></a>01366 <span class="comment">!</span>
    1431. 

  1431. <a name="l01367"></a>01367 <span class="comment">!    Input/output, double precision X, the approximate root, which</span>
    1432. 

  1432. <a name="l01368"></a>01368 <span class="comment">!    should be improved on output.</span>
    1433. 

  1433. <a name="l01369"></a>01369 <span class="comment">!</span>
    1434. 

  1434. <a name="l01370"></a>01370 <span class="comment">!    Input, integer NORDER, the order of the Hermite polynomial.</span>
    1435. 

  1435. <a name="l01371"></a>01371 <span class="comment">!</span>
    1436. 

  1436. <a name="l01372"></a>01372 <span class="comment">!    Output, double precision DP2, the value of H&#39;(NORDER)(X).</span>
    1437. 

  1437. <a name="l01373"></a>01373 <span class="comment">!</span>
    1438. 

  1438. <a name="l01374"></a>01374 <span class="comment">!    Output, double precision P1, the value of H(NORDER-1)(X).</span>
    1439. 

  1439. <a name="l01375"></a>01375 <span class="comment">!</span>
    1440. 

  1440. <a name="l01376"></a>01376   <span class="keyword">implicit none</span>
    1441. 

  1441. <a name="l01377"></a>01377 <span class="comment">!</span>
    1442. 

  1442. <a name="l01378"></a>01378   <span class="keywordtype">double precision</span> d
    1443. 

  1443. <a name="l01379"></a>01379   <span class="keywordtype">double precision</span> dp2
    1444. 

  1444. <a name="l01380"></a>01380   <span class="keywordtype">double precision</span>, <span class="keywordtype">parameter</span> :: eps = 1.0D-12
    1445. 

  1445. <a name="l01381"></a>01381   <span class="keywordtype">integer</span> i
    1446. 

  1446. <a name="l01382"></a>01382   <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxstep = 10
    1447. 

  1447. <a name="l01383"></a>01383   <span class="keywordtype">integer</span> norder
    1448. 

  1448. <a name="l01384"></a>01384   <span class="keywordtype">double precision</span> p1
    1449. 

  1449. <a name="l01385"></a>01385   <span class="keywordtype">double precision</span> p2
    1450. 

  1450. <a name="l01386"></a>01386   <span class="keywordtype">double precision</span> x
    1451. 

  1451. <a name="l01387"></a>01387 <span class="comment">!</span>
    1452. 

  1452. <a name="l01388"></a>01388   <span class="keyword">do</span> i = 1, maxstep
    1453. 

  1453. <a name="l01389"></a>01389 
    1454. 

  1454. <a name="l01390"></a>01390     call <a class="code" href="quadrule_8f90.html#a837c192f4116548551a6c0b69465adbb">hermite_recur </a>( p2, dp2, p1, x, norder )
    1455. 

  1455. <a name="l01391"></a>01391 
    1456. 

  1456. <a name="l01392"></a>01392     d = p2 / dp2
    1457. 

  1457. <a name="l01393"></a>01393     x = x - d
    1458. 

  1458. <a name="l01394"></a>01394 
    1459. 

  1459. <a name="l01395"></a>01395     <span class="keyword">if</span> ( abs ( d ) &lt;= eps * ( abs ( x ) + 1.0D+00 ) ) <span class="keyword">then</span>
    1460. 

  1460. <a name="l01396"></a>01396       return
    1461. 

  1461. <a name="l01397"></a>01397     <span class="keyword">end if</span>
    1462. 

  1462. <a name="l01398"></a>01398 
    1463. 

  1463. <a name="l01399"></a>01399   <span class="keyword">end do</span>
    1464. 

  1464. <a name="l01400"></a>01400 
    1465. 

  1465. <a name="l01401"></a>01401   return
    1466. 

  1466. <a name="l01402"></a>01402 <span class="keyword">end</span>
    1467. 

  1467. <a name="l01403"></a><a class="code" href="quadrule_8f90.html#aef932141d0758eb99a63c743dbb0e893">01403</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#aef932141d0758eb99a63c743dbb0e893">hermite_set</a> ( norder, xtab, weight )
    1468. 

  1468. <a name="l01404"></a>01404 <span class="comment">!</span>
    1469. 

  1469. <a name="l01405"></a>01405 <span class="comment">!*******************************************************************************</span>
    1470. 

  1470. <a name="l01406"></a>01406 <span class="comment">!</span>
    1471. 

  1471. <a name="l01407"></a>01407 <span class="comment">!! HERMITE_SET sets abscissas and weights for Hermite quadrature.</span>
    1472. 

  1472. <a name="l01408"></a>01408 <span class="comment">!</span>
    1473. 

  1473. <a name="l01409"></a>01409 <span class="comment">!</span>
    1474. 

  1474. <a name="l01410"></a>01410 <span class="comment">!  Integration interval:</span>
    1475. 

  1475. <a name="l01411"></a>01411 <span class="comment">!</span>
    1476. 

  1476. <a name="l01412"></a>01412 <span class="comment">!    ( -Infinity, +Infinity )</span>
    1477. 

  1477. <a name="l01413"></a>01413 <span class="comment">!</span>
    1478. 

  1478. <a name="l01414"></a>01414 <span class="comment">!  Weight function:</span>
    1479. 

  1479. <a name="l01415"></a>01415 <span class="comment">!</span>
    1480. 

  1480. <a name="l01416"></a>01416 <span class="comment">!    EXP ( - X**2 )</span>
    1481. 

  1481. <a name="l01417"></a>01417 <span class="comment">!</span>
    1482. 

  1482. <a name="l01418"></a>01418 <span class="comment">!  Integral to approximate:</span>
    1483. 

  1483. <a name="l01419"></a>01419 <span class="comment">!</span>
    1484. 

  1484. <a name="l01420"></a>01420 <span class="comment">!    Integral ( -INFINITY &lt; X &lt; +INFINITY ) EXP ( - X**2 ) * F(X) dX</span>
    1485. 

  1485. <a name="l01421"></a>01421 <span class="comment">!</span>
    1486. 

  1486. <a name="l01422"></a>01422 <span class="comment">!  Approximate integral:</span>
    1487. 

  1487. <a name="l01423"></a>01423 <span class="comment">!</span>
    1488. 

  1488. <a name="l01424"></a>01424 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) ).</span>
    1489. 

  1489. <a name="l01425"></a>01425 <span class="comment">!</span>
    1490. 

  1490. <a name="l01426"></a>01426 <span class="comment">!  Reference:</span>
    1491. 

  1491. <a name="l01427"></a>01427 <span class="comment">!</span>
    1492. 

  1492. <a name="l01428"></a>01428 <span class="comment">!    Abramowitz and Stegun,</span>
    1493. 

  1493. <a name="l01429"></a>01429 <span class="comment">!    Handbook of Mathematical Functions,</span>
    1494. 

  1494. <a name="l01430"></a>01430 <span class="comment">!    National Bureau of Standards, 1964.</span>
    1495. 

  1495. <a name="l01431"></a>01431 <span class="comment">!</span>
    1496. 

  1496. <a name="l01432"></a>01432 <span class="comment">!    Vladimir Krylov,</span>
    1497. 

  1497. <a name="l01433"></a>01433 <span class="comment">!    Approximate Calculation of Integrals,</span>
    1498. 

  1498. <a name="l01434"></a>01434 <span class="comment">!    MacMillan, 1962.</span>
    1499. 

  1499. <a name="l01435"></a>01435 <span class="comment">!</span>
    1500. 

  1500. <a name="l01436"></a>01436 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    1501. 

  1501. <a name="l01437"></a>01437 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    1502. 

  1502. <a name="l01438"></a>01438 <span class="comment">!    Prentice Hall, 1966.</span>
    1503. 

  1503. <a name="l01439"></a>01439 <span class="comment">!</span>
    1504. 

  1504. <a name="l01440"></a>01440 <span class="comment">!    Daniel Zwillinger, editor,</span>
    1505. 

  1505. <a name="l01441"></a>01441 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    1506. 

  1506. <a name="l01442"></a>01442 <span class="comment">!    30th Edition,</span>
    1507. 

  1507. <a name="l01443"></a>01443 <span class="comment">!    CRC Press, 1996.</span>
    1508. 

  1508. <a name="l01444"></a>01444 <span class="comment">!</span>
    1509. 

  1509. <a name="l01445"></a>01445 <span class="comment">!  Modified:</span>
    1510. 

  1510. <a name="l01446"></a>01446 <span class="comment">!</span>
    1511. 

  1511. <a name="l01447"></a>01447 <span class="comment">!    06 December 2000</span>
    1512. 

  1512. <a name="l01448"></a>01448 <span class="comment">!</span>
    1513. 

  1513. <a name="l01449"></a>01449 <span class="comment">!  Author:</span>
    1514. 

  1514. <a name="l01450"></a>01450 <span class="comment">!</span>
    1515. 

  1515. <a name="l01451"></a>01451 <span class="comment">!    John Burkardt</span>
    1516. 

  1516. <a name="l01452"></a>01452 <span class="comment">!</span>
    1517. 

  1517. <a name="l01453"></a>01453 <span class="comment">!  Parameters:</span>
    1518. 

  1518. <a name="l01454"></a>01454 <span class="comment">!</span>
    1519. 

  1519. <a name="l01455"></a>01455 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    1520. 

  1520. <a name="l01456"></a>01456 <span class="comment">!    NORDER must be between 1 and 20, or one of the values</span>
    1521. 

  1521. <a name="l01457"></a>01457 <span class="comment">!    30, 32, 40, 50, 60 or 64.</span>
    1522. 

  1522. <a name="l01458"></a>01458 <span class="comment">!</span>
    1523. 

  1523. <a name="l01459"></a>01459 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule,</span>
    1524. 

  1524. <a name="l01460"></a>01460 <span class="comment">!    which are symmetrically placed around 0.</span>
    1525. 

  1525. <a name="l01461"></a>01461 <span class="comment">!</span>
    1526. 

  1526. <a name="l01462"></a>01462 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    1527. 

  1527. <a name="l01463"></a>01463 <span class="comment">!    The weights are positive and symmetric, and should sum</span>
    1528. 

  1528. <a name="l01464"></a>01464 <span class="comment">!    to SQRT(PI).</span>
    1529. 

  1529. <a name="l01465"></a>01465 <span class="comment">!</span>
    1530. 

  1530. <a name="l01466"></a>01466   <span class="keyword">implicit none</span>
    1531. 

  1531. <a name="l01467"></a>01467 <span class="comment">!</span>
    1532. 

  1532. <a name="l01468"></a>01468   <span class="keywordtype">integer</span> norder
    1533. 

  1533. <a name="l01469"></a>01469 <span class="comment">!</span>
    1534. 

  1534. <a name="l01470"></a>01470   <span class="keywordtype">double precision</span> d_pi
    1535. 

  1535. <a name="l01471"></a>01471   <span class="keywordtype">double precision</span> xtab(norder)
    1536. 

  1536. <a name="l01472"></a>01472   <span class="keywordtype">double precision</span> weight(norder)
    1537. 

  1537. <a name="l01473"></a>01473 <span class="comment">!</span>
    1538. 

  1538. <a name="l01474"></a>01474   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    1539. 

  1539. <a name="l01475"></a>01475 
    1540. 

  1540. <a name="l01476"></a>01476     xtab(1) = 0.0D+00
    1541. 

  1541. <a name="l01477"></a>01477 
    1542. 

  1542. <a name="l01478"></a>01478     weight(1) = sqrt ( d_pi ( ) )
    1543. 

  1543. <a name="l01479"></a>01479 
    1544. 

  1544. <a name="l01480"></a>01480   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 )<span class="keyword">then</span>
    1545. 

  1545. <a name="l01481"></a>01481 
    1546. 

  1546. <a name="l01482"></a>01482     xtab(1) = - 0.707106781186547524400844362105D+00
    1547. 

  1547. <a name="l01483"></a>01483     xtab(2) =   0.707106781186547524400844362105D+00
    1548. 

  1548. <a name="l01484"></a>01484 
    1549. 

  1549. <a name="l01485"></a>01485     weight(1) = 0.886226925452758013649083741671D+00
    1550. 

  1550. <a name="l01486"></a>01486     weight(2) = 0.886226925452758013649083741671D+00
    1551. 

  1551. <a name="l01487"></a>01487 
    1552. 

  1552. <a name="l01488"></a>01488   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    1553. 

  1553. <a name="l01489"></a>01489 
    1554. 

  1554. <a name="l01490"></a>01490     xtab(1) = - 0.122474487139158904909864203735D+01
    1555. 

  1555. <a name="l01491"></a>01491     xtab(2) =   0.0D+00
    1556. 

  1556. <a name="l01492"></a>01492     xtab(3) =   0.122474487139158904909864203735D+01
    1557. 

  1557. <a name="l01493"></a>01493 
    1558. 

  1558. <a name="l01494"></a>01494     weight(1) = 0.295408975150919337883027913890D+00
    1559. 

  1559. <a name="l01495"></a>01495     weight(2) = 0.118163590060367735153211165556D+01
    1560. 

  1560. <a name="l01496"></a>01496     weight(3) = 0.295408975150919337883027913890D+00
    1561. 

  1561. <a name="l01497"></a>01497 
    1562. 

  1562. <a name="l01498"></a>01498   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    1563. 

  1563. <a name="l01499"></a>01499 
    1564. 

  1564. <a name="l01500"></a>01500     xtab(1) = - 0.165068012388578455588334111112D+01
    1565. 

  1565. <a name="l01501"></a>01501     xtab(2) = - 0.524647623275290317884060253835D+00
    1566. 

  1566. <a name="l01502"></a>01502     xtab(3) =   0.524647623275290317884060253835D+00
    1567. 

  1567. <a name="l01503"></a>01503     xtab(4) =   0.165068012388578455588334111112D+01
    1568. 

  1568. <a name="l01504"></a>01504 
    1569. 

  1569. <a name="l01505"></a>01505     weight(1) = 0.813128354472451771430345571899D-01
    1570. 

  1570. <a name="l01506"></a>01506     weight(2) = 0.804914090005512836506049184481D+00
    1571. 

  1571. <a name="l01507"></a>01507     weight(3) = 0.804914090005512836506049184481D+00
    1572. 

  1572. <a name="l01508"></a>01508     weight(4) = 0.813128354472451771430345571899D-01
    1573. 

  1573. <a name="l01509"></a>01509 
    1574. 

  1574. <a name="l01510"></a>01510   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    1575. 

  1575. <a name="l01511"></a>01511 
    1576. 

  1576. <a name="l01512"></a>01512     xtab(1) = - 0.202018287045608563292872408814D+01
    1577. 

  1577. <a name="l01513"></a>01513     xtab(2) = - 0.958572464613818507112770593893D+00
    1578. 

  1578. <a name="l01514"></a>01514     xtab(3) =   0.0D+00
    1579. 

  1579. <a name="l01515"></a>01515     xtab(4) =   0.958572464613818507112770593893D+00
    1580. 

  1580. <a name="l01516"></a>01516     xtab(5) =   0.202018287045608563292872408814D+01
    1581. 

  1581. <a name="l01517"></a>01517 
    1582. 

  1582. <a name="l01518"></a>01518     weight(1) = 0.199532420590459132077434585942D-01
    1583. 

  1583. <a name="l01519"></a>01519     weight(2) = 0.393619323152241159828495620852D+00
    1584. 

  1584. <a name="l01520"></a>01520     weight(3) = 0.945308720482941881225689324449D+00
    1585. 

  1585. <a name="l01521"></a>01521     weight(4) = 0.393619323152241159828495620852D+00
    1586. 

  1586. <a name="l01522"></a>01522     weight(5) = 0.199532420590459132077434585942D-01
    1587. 

  1587. <a name="l01523"></a>01523 
    1588. 

  1588. <a name="l01524"></a>01524   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    1589. 

  1589. <a name="l01525"></a>01525 
    1590. 

  1590. <a name="l01526"></a>01526     xtab(1) = - 0.235060497367449222283392198706D+01
    1591. 

  1591. <a name="l01527"></a>01527     xtab(2) = - 0.133584907401369694971489528297D+01
    1592. 

  1592. <a name="l01528"></a>01528     xtab(3) = - 0.436077411927616508679215948251D+00
    1593. 

  1593. <a name="l01529"></a>01529     xtab(4) =   0.436077411927616508679215948251D+00
    1594. 

  1594. <a name="l01530"></a>01530     xtab(5) =   0.133584907401369694971489528297D+01
    1595. 

  1595. <a name="l01531"></a>01531     xtab(6) =   0.235060497367449222283392198706D+01
    1596. 

  1596. <a name="l01532"></a>01532 
    1597. 

  1597. <a name="l01533"></a>01533     weight(1) = 0.453000990550884564085747256463D-02
    1598. 

  1598. <a name="l01534"></a>01534     weight(2) = 0.157067320322856643916311563508D+00
    1599. 

  1599. <a name="l01535"></a>01535     weight(3) = 0.724629595224392524091914705598D+00
    1600. 

  1600. <a name="l01536"></a>01536     weight(4) = 0.724629595224392524091914705598D+00
    1601. 

  1601. <a name="l01537"></a>01537     weight(5) = 0.157067320322856643916311563508D+00
    1602. 

  1602. <a name="l01538"></a>01538     weight(6) = 0.453000990550884564085747256463D-02
    1603. 

  1603. <a name="l01539"></a>01539 
    1604. 

  1604. <a name="l01540"></a>01540   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    1605. 

  1605. <a name="l01541"></a>01541 
    1606. 

  1606. <a name="l01542"></a>01542     xtab(1) = - 0.265196135683523349244708200652D+01
    1607. 

  1607. <a name="l01543"></a>01543     xtab(2) = - 0.167355162876747144503180139830D+01
    1608. 

  1608. <a name="l01544"></a>01544     xtab(3) = - 0.816287882858964663038710959027D+00
    1609. 

  1609. <a name="l01545"></a>01545     xtab(4) =   0.0D+00
    1610. 

  1610. <a name="l01546"></a>01546     xtab(5) =   0.816287882858964663038710959027D+00
    1611. 

  1611. <a name="l01547"></a>01547     xtab(6) =   0.167355162876747144503180139830D+01
    1612. 

  1612. <a name="l01548"></a>01548     xtab(7) =   0.265196135683523349244708200652D+01
    1613. 

  1613. <a name="l01549"></a>01549 
    1614. 

  1614. <a name="l01550"></a>01550     weight(1) = 0.971781245099519154149424255939D-03
    1615. 

  1615. <a name="l01551"></a>01551     weight(2) = 0.545155828191270305921785688417D-01
    1616. 

  1616. <a name="l01552"></a>01552     weight(3) = 0.425607252610127800520317466666D+00
    1617. 

  1617. <a name="l01553"></a>01553     weight(4) = 0.810264617556807326764876563813D+00
    1618. 

  1618. <a name="l01554"></a>01554     weight(5) = 0.425607252610127800520317466666D+00
    1619. 

  1619. <a name="l01555"></a>01555     weight(6) = 0.545155828191270305921785688417D-01
    1620. 

  1620. <a name="l01556"></a>01556     weight(7) = 0.971781245099519154149424255939D-03
    1621. 

  1621. <a name="l01557"></a>01557 
    1622. 

  1622. <a name="l01558"></a>01558   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    1623. 

  1623. <a name="l01559"></a>01559 
    1624. 

  1624. <a name="l01560"></a>01560     xtab(1) = - 0.293063742025724401922350270524D+01
    1625. 

  1625. <a name="l01561"></a>01561     xtab(2) = - 0.198165675669584292585463063977D+01
    1626. 

  1626. <a name="l01562"></a>01562     xtab(3) = - 0.115719371244678019472076577906D+01
    1627. 

  1627. <a name="l01563"></a>01563     xtab(4) = - 0.381186990207322116854718885584D+00
    1628. 

  1628. <a name="l01564"></a>01564     xtab(5) =   0.381186990207322116854718885584D+00
    1629. 

  1629. <a name="l01565"></a>01565     xtab(6) =   0.115719371244678019472076577906D+01
    1630. 

  1630. <a name="l01566"></a>01566     xtab(7) =   0.198165675669584292585463063977D+01
    1631. 

  1631. <a name="l01567"></a>01567     xtab(8) =   0.293063742025724401922350270524D+01
    1632. 

  1632. <a name="l01568"></a>01568 
    1633. 

  1633. <a name="l01569"></a>01569     weight(1) = 0.199604072211367619206090452544D-03
    1634. 

  1634. <a name="l01570"></a>01570     weight(2) = 0.170779830074134754562030564364D-01
    1635. 

  1635. <a name="l01571"></a>01571     weight(3) = 0.207802325814891879543258620286D+00
    1636. 

  1636. <a name="l01572"></a>01572     weight(4) = 0.661147012558241291030415974496D+00
    1637. 

  1637. <a name="l01573"></a>01573     weight(5) = 0.661147012558241291030415974496D+00
    1638. 

  1638. <a name="l01574"></a>01574     weight(6) = 0.207802325814891879543258620286D+00
    1639. 

  1639. <a name="l01575"></a>01575     weight(7) = 0.170779830074134754562030564364D-01
    1640. 

  1640. <a name="l01576"></a>01576     weight(8) = 0.199604072211367619206090452544D-03
    1641. 

  1641. <a name="l01577"></a>01577 
    1642. 

  1642. <a name="l01578"></a>01578   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    1643. 

  1643. <a name="l01579"></a>01579 
    1644. 

  1644. <a name="l01580"></a>01580     xtab(1) = - 0.319099320178152760723004779538D+01
    1645. 

  1645. <a name="l01581"></a>01581     xtab(2) = - 0.226658058453184311180209693284D+01
    1646. 

  1646. <a name="l01582"></a>01582     xtab(3) = - 0.146855328921666793166701573925D+01
    1647. 

  1647. <a name="l01583"></a>01583     xtab(4) = - 0.723551018752837573322639864579D+00
    1648. 

  1648. <a name="l01584"></a>01584     xtab(5) =   0.0D+00
    1649. 

  1649. <a name="l01585"></a>01585     xtab(6) =   0.723551018752837573322639864579D+00
    1650. 

  1650. <a name="l01586"></a>01586     xtab(7) =   0.146855328921666793166701573925D+01
    1651. 

  1651. <a name="l01587"></a>01587     xtab(8) =   0.226658058453184311180209693284D+01
    1652. 

  1652. <a name="l01588"></a>01588     xtab(9) =   0.319099320178152760723004779538D+01
    1653. 

  1653. <a name="l01589"></a>01589 
    1654. 

  1654. <a name="l01590"></a>01590     weight(1) = 0.396069772632643819045862946425D-04
    1655. 

  1655. <a name="l01591"></a>01591     weight(2) = 0.494362427553694721722456597763D-02
    1656. 

  1656. <a name="l01592"></a>01592     weight(3) = 0.884745273943765732879751147476D-01
    1657. 

  1657. <a name="l01593"></a>01593     weight(4) = 0.432651559002555750199812112956D+00
    1658. 

  1658. <a name="l01594"></a>01594     weight(5) = 0.720235215606050957124334723389D+00
    1659. 

  1659. <a name="l01595"></a>01595     weight(6) = 0.432651559002555750199812112956D+00
    1660. 

  1660. <a name="l01596"></a>01596     weight(7) = 0.884745273943765732879751147476D-01
    1661. 

  1661. <a name="l01597"></a>01597     weight(8) = 0.494362427553694721722456597763D-02
    1662. 

  1662. <a name="l01598"></a>01598     weight(9) = 0.396069772632643819045862946425D-04
    1663. 

  1663. <a name="l01599"></a>01599 
    1664. 

  1664. <a name="l01600"></a>01600   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
    1665. 

  1665. <a name="l01601"></a>01601 
    1666. 

  1666. <a name="l01602"></a>01602     xtab(1) =  - 0.343615911883773760332672549432D+01
    1667. 

  1667. <a name="l01603"></a>01603     xtab(2) =  - 0.253273167423278979640896079775D+01
    1668. 

  1668. <a name="l01604"></a>01604     xtab(3) =  - 0.175668364929988177345140122011D+01
    1669. 

  1669. <a name="l01605"></a>01605     xtab(4) =  - 0.103661082978951365417749191676D+01
    1670. 

  1670. <a name="l01606"></a>01606     xtab(5) =  - 0.342901327223704608789165025557D+00
    1671. 

  1671. <a name="l01607"></a>01607     xtab(6) =    0.342901327223704608789165025557D+00
    1672. 

  1672. <a name="l01608"></a>01608     xtab(7) =    0.103661082978951365417749191676D+01
    1673. 

  1673. <a name="l01609"></a>01609     xtab(8) =    0.175668364929988177345140122011D+01
    1674. 

  1674. <a name="l01610"></a>01610     xtab(9) =    0.253273167423278979640896079775D+01
    1675. 

  1675. <a name="l01611"></a>01611     xtab(10) =   0.343615911883773760332672549432D+01
    1676. 

  1676. <a name="l01612"></a>01612 
    1677. 

  1677. <a name="l01613"></a>01613     weight(1) =  0.764043285523262062915936785960D-05
    1678. 

  1678. <a name="l01614"></a>01614     weight(2) =  0.134364574678123269220156558585D-02
    1679. 

  1679. <a name="l01615"></a>01615     weight(3) =  0.338743944554810631361647312776D-01
    1680. 

  1680. <a name="l01616"></a>01616     weight(4) =  0.240138611082314686416523295006D+00
    1681. 

  1681. <a name="l01617"></a>01617     weight(5) =  0.610862633735325798783564990433D+00
    1682. 

  1682. <a name="l01618"></a>01618     weight(6) =  0.610862633735325798783564990433D+00
    1683. 

  1683. <a name="l01619"></a>01619     weight(7) =  0.240138611082314686416523295006D+00
    1684. 

  1684. <a name="l01620"></a>01620     weight(8) =  0.338743944554810631361647312776D-01
    1685. 

  1685. <a name="l01621"></a>01621     weight(9) =  0.134364574678123269220156558585D-02
    1686. 

  1686. <a name="l01622"></a>01622     weight(10) = 0.764043285523262062915936785960D-05
    1687. 

  1687. <a name="l01623"></a>01623 
    1688. 

  1688. <a name="l01624"></a>01624   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 11 ) <span class="keyword">then</span>
    1689. 

  1689. <a name="l01625"></a>01625 
    1690. 

  1690. <a name="l01626"></a>01626     xtab(1) =  - 0.366847084655958251845837146485D+01
    1691. 

  1691. <a name="l01627"></a>01627     xtab(2) =  - 0.278329009978165177083671870152D+01
    1692. 

  1692. <a name="l01628"></a>01628     xtab(3) =  - 0.202594801582575533516591283121D+01
    1693. 

  1693. <a name="l01629"></a>01629     xtab(4) =  - 0.132655708449493285594973473558D+01
    1694. 

  1694. <a name="l01630"></a>01630     xtab(5) =  - 0.656809566882099765024611575383D+00
    1695. 

  1695. <a name="l01631"></a>01631     xtab(6) =    0.0D+00
    1696. 

  1696. <a name="l01632"></a>01632     xtab(7) =    0.656809566882099765024611575383D+00
    1697. 

  1697. <a name="l01633"></a>01633     xtab(8) =    0.132655708449493285594973473558D+01
    1698. 

  1698. <a name="l01634"></a>01634     xtab(9) =    0.202594801582575533516591283121D+01
    1699. 

  1699. <a name="l01635"></a>01635     xtab(10) =   0.278329009978165177083671870152D+01
    1700. 

  1700. <a name="l01636"></a>01636     xtab(11) =   0.366847084655958251845837146485D+01
    1701. 

  1701. <a name="l01637"></a>01637 
    1702. 

  1702. <a name="l01638"></a>01638     weight(1) =  0.143956039371425822033088366032D-05
    1703. 

  1703. <a name="l01639"></a>01639     weight(2) =  0.346819466323345510643413772940D-03
    1704. 

  1704. <a name="l01640"></a>01640     weight(3) =  0.119113954449115324503874202916D-01
    1705. 

  1705. <a name="l01641"></a>01641     weight(4) =  0.117227875167708503381788649308D+00
    1706. 

  1706. <a name="l01642"></a>01642     weight(5) =  0.429359752356125028446073598601D+00
    1707. 

  1707. <a name="l01643"></a>01643     weight(6) =  0.654759286914591779203940657627D+00
    1708. 

  1708. <a name="l01644"></a>01644     weight(7) =  0.429359752356125028446073598601D+00
    1709. 

  1709. <a name="l01645"></a>01645     weight(8) =  0.117227875167708503381788649308D+00
    1710. 

  1710. <a name="l01646"></a>01646     weight(9) =  0.119113954449115324503874202916D-01
    1711. 

  1711. <a name="l01647"></a>01647     weight(10) = 0.346819466323345510643413772940D-03
    1712. 

  1712. <a name="l01648"></a>01648     weight(11) = 0.143956039371425822033088366032D-05
    1713. 

  1713. <a name="l01649"></a>01649 
    1714. 

  1714. <a name="l01650"></a>01650   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 12 ) <span class="keyword">then</span>
    1715. 

  1715. <a name="l01651"></a>01651 
    1716. 

  1716. <a name="l01652"></a>01652     xtab(1) =  - 0.388972489786978191927164274724D+01
    1717. 

  1717. <a name="l01653"></a>01653     xtab(2) =  - 0.302063702512088977171067937518D+01
    1718. 

  1718. <a name="l01654"></a>01654     xtab(3) =  - 0.227950708050105990018772856942D+01
    1719. 

  1719. <a name="l01655"></a>01655     xtab(4) =  - 0.159768263515260479670966277090D+01
    1720. 

  1720. <a name="l01656"></a>01656     xtab(5) =  - 0.947788391240163743704578131060D+00
    1721. 

  1721. <a name="l01657"></a>01657     xtab(6) =  - 0.314240376254359111276611634095D+00
    1722. 

  1722. <a name="l01658"></a>01658     xtab(7) =    0.314240376254359111276611634095D+00
    1723. 

  1723. <a name="l01659"></a>01659     xtab(8) =    0.947788391240163743704578131060D+00
    1724. 

  1724. <a name="l01660"></a>01660     xtab(9) =    0.159768263515260479670966277090D+01
    1725. 

  1725. <a name="l01661"></a>01661     xtab(10) =   0.227950708050105990018772856942D+01
    1726. 

  1726. <a name="l01662"></a>01662     xtab(11) =   0.302063702512088977171067937518D+01
    1727. 

  1727. <a name="l01663"></a>01663     xtab(12) =   0.388972489786978191927164274724D+01
    1728. 

  1728. <a name="l01664"></a>01664 
    1729. 

  1729. <a name="l01665"></a>01665     weight(1) =  0.265855168435630160602311400877D-06
    1730. 

  1730. <a name="l01666"></a>01666     weight(2) =  0.857368704358785865456906323153D-04
    1731. 

  1731. <a name="l01667"></a>01667     weight(3) =  0.390539058462906185999438432620D-02
    1732. 

  1732. <a name="l01668"></a>01668     weight(4) =  0.516079856158839299918734423606D-01
    1733. 

  1733. <a name="l01669"></a>01669     weight(5) =  0.260492310264161129233396139765D+00
    1734. 

  1734. <a name="l01670"></a>01670     weight(6) =  0.570135236262479578347113482275D+00
    1735. 

  1735. <a name="l01671"></a>01671     weight(7) =  0.570135236262479578347113482275D+00
    1736. 

  1736. <a name="l01672"></a>01672     weight(8) =  0.260492310264161129233396139765D+00
    1737. 

  1737. <a name="l01673"></a>01673     weight(9) =  0.516079856158839299918734423606D-01
    1738. 

  1738. <a name="l01674"></a>01674     weight(10) = 0.390539058462906185999438432620D-02
    1739. 

  1739. <a name="l01675"></a>01675     weight(11) = 0.857368704358785865456906323153D-04
    1740. 

  1740. <a name="l01676"></a>01676     weight(12) = 0.265855168435630160602311400877D-06
    1741. 

  1741. <a name="l01677"></a>01677 
    1742. 

  1742. <a name="l01678"></a>01678   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 13 ) <span class="keyword">then</span>
    1743. 

  1743. <a name="l01679"></a>01679 
    1744. 

  1744. <a name="l01680"></a>01680     xtab(1) =  - 0.410133759617863964117891508007D+01
    1745. 

  1745. <a name="l01681"></a>01681     xtab(2) =  - 0.324660897837240998812205115236D+01
    1746. 

  1746. <a name="l01682"></a>01682     xtab(3) =  - 0.251973568567823788343040913628D+01
    1747. 

  1747. <a name="l01683"></a>01683     xtab(4) =  - 0.185310765160151214200350644316D+01
    1748. 

  1748. <a name="l01684"></a>01684     xtab(5) =  - 0.122005503659074842622205526637D+01
    1749. 

  1749. <a name="l01685"></a>01685     xtab(6) =  - 0.605763879171060113080537108602D+00
    1750. 

  1750. <a name="l01686"></a>01686     xtab(7) =    0.0D+00
    1751. 

  1751. <a name="l01687"></a>01687     xtab(8) =    0.605763879171060113080537108602D+00
    1752. 

  1752. <a name="l01688"></a>01688     xtab(9) =    0.122005503659074842622205526637D+01
    1753. 

  1753. <a name="l01689"></a>01689     xtab(10) =   0.185310765160151214200350644316D+01
    1754. 

  1754. <a name="l01690"></a>01690     xtab(11) =   0.251973568567823788343040913628D+01
    1755. 

  1755. <a name="l01691"></a>01691     xtab(12) =   0.324660897837240998812205115236D+01
    1756. 

  1756. <a name="l01692"></a>01692     xtab(13) =   0.410133759617863964117891508007D+01
    1757. 

  1757. <a name="l01693"></a>01693 
    1758. 

  1758. <a name="l01694"></a>01694     weight(1) =  0.482573185007313108834997332342D-07
    1759. 

  1759. <a name="l01695"></a>01695     weight(2) =  0.204303604027070731248669432937D-04
    1760. 

  1760. <a name="l01696"></a>01696     weight(3) =  0.120745999271938594730924899224D-02
    1761. 

  1761. <a name="l01697"></a>01697     weight(4) =  0.208627752961699392166033805050D-01
    1762. 

  1762. <a name="l01698"></a>01698     weight(5) =  0.140323320687023437762792268873D+00
    1763. 

  1763. <a name="l01699"></a>01699     weight(6) =  0.421616296898543221746893558568D+00
    1764. 

  1764. <a name="l01700"></a>01700     weight(7) =  0.604393187921161642342099068579D+00
    1765. 

  1765. <a name="l01701"></a>01701     weight(8) =  0.421616296898543221746893558568D+00
    1766. 

  1766. <a name="l01702"></a>01702     weight(9) =  0.140323320687023437762792268873D+00
    1767. 

  1767. <a name="l01703"></a>01703     weight(10) = 0.208627752961699392166033805050D-01
    1768. 

  1768. <a name="l01704"></a>01704     weight(11) = 0.120745999271938594730924899224D-02
    1769. 

  1769. <a name="l01705"></a>01705     weight(12) = 0.204303604027070731248669432937D-04
    1770. 

  1770. <a name="l01706"></a>01706     weight(13) = 0.482573185007313108834997332342D-07
    1771. 

  1771. <a name="l01707"></a>01707 
    1772. 

  1772. <a name="l01708"></a>01708   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 14 ) <span class="keyword">then</span>
    1773. 

  1773. <a name="l01709"></a>01709 
    1774. 

  1774. <a name="l01710"></a>01710     xtab(1) =  - 0.430444857047363181262129810037D+01
    1775. 

  1775. <a name="l01711"></a>01711     xtab(2) =  - 0.346265693360227055020891736115D+01
    1776. 

  1776. <a name="l01712"></a>01712     xtab(3) =  - 0.274847072498540256862499852415D+01
    1777. 

  1777. <a name="l01713"></a>01713     xtab(4) =  - 0.209518325850771681573497272630D+01
    1778. 

  1778. <a name="l01714"></a>01714     xtab(5) =  - 0.147668273114114087058350654421D+01
    1779. 

  1779. <a name="l01715"></a>01715     xtab(6) =  - 0.878713787329399416114679311861D+00
    1780. 

  1780. <a name="l01716"></a>01716     xtab(7) =  - 0.291745510672562078446113075799D+00
    1781. 

  1781. <a name="l01717"></a>01717     xtab(8) =    0.291745510672562078446113075799D+00
    1782. 

  1782. <a name="l01718"></a>01718     xtab(9) =    0.878713787329399416114679311861D+00
    1783. 

  1783. <a name="l01719"></a>01719     xtab(10) =   0.147668273114114087058350654421D+01
    1784. 

  1784. <a name="l01720"></a>01720     xtab(11) =   0.209518325850771681573497272630D+01
    1785. 

  1785. <a name="l01721"></a>01721     xtab(12) =   0.274847072498540256862499852415D+01
    1786. 

  1786. <a name="l01722"></a>01722     xtab(13) =   0.346265693360227055020891736115D+01
    1787. 

  1787. <a name="l01723"></a>01723     xtab(14) =   0.430444857047363181262129810037D+01
    1788. 

  1788. <a name="l01724"></a>01724 
    1789. 

  1789. <a name="l01725"></a>01725     weight(1) =  0.862859116812515794532041783429D-08
    1790. 

  1790. <a name="l01726"></a>01726     weight(2) =  0.471648435501891674887688950105D-05
    1791. 

  1791. <a name="l01727"></a>01727     weight(3) =  0.355092613551923610483661076691D-03
    1792. 

  1792. <a name="l01728"></a>01728     weight(4) =  0.785005472645794431048644334608D-02
    1793. 

  1793. <a name="l01729"></a>01729     weight(5) =  0.685055342234652055387163312367D-01
    1794. 

  1794. <a name="l01730"></a>01730     weight(6) =  0.273105609064246603352569187026D+00
    1795. 

  1795. <a name="l01731"></a>01731     weight(7) =  0.536405909712090149794921296776D+00
    1796. 

  1796. <a name="l01732"></a>01732     weight(8) =  0.536405909712090149794921296776D+00
    1797. 

  1797. <a name="l01733"></a>01733     weight(9) =  0.273105609064246603352569187026D+00
    1798. 

  1798. <a name="l01734"></a>01734     weight(10) = 0.685055342234652055387163312367D-01
    1799. 

  1799. <a name="l01735"></a>01735     weight(11) = 0.785005472645794431048644334608D-02
    1800. 

  1800. <a name="l01736"></a>01736     weight(12) = 0.355092613551923610483661076691D-03
    1801. 

  1801. <a name="l01737"></a>01737     weight(13) = 0.471648435501891674887688950105D-05
    1802. 

  1802. <a name="l01738"></a>01738     weight(14) = 0.862859116812515794532041783429D-08
    1803. 

  1803. <a name="l01739"></a>01739 
    1804. 

  1804. <a name="l01740"></a>01740   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
    1805. 

  1805. <a name="l01741"></a>01741 
    1806. 

  1806. <a name="l01742"></a>01742     xtab(1) =  - 0.449999070730939155366438053053D+01
    1807. 

  1807. <a name="l01743"></a>01743     xtab(2) =  - 0.366995037340445253472922383312D+01
    1808. 

  1808. <a name="l01744"></a>01744     xtab(3) =  - 0.296716692790560324848896036355D+01
    1809. 

  1809. <a name="l01745"></a>01745     xtab(4) =  - 0.232573248617385774545404479449D+01
    1810. 

  1810. <a name="l01746"></a>01746     xtab(5) =  - 0.171999257518648893241583152515D+01
    1811. 

  1811. <a name="l01747"></a>01747     xtab(6) =  - 0.113611558521092066631913490556D+01
    1812. 

  1812. <a name="l01748"></a>01748     xtab(7) =  - 0.565069583255575748526020337198D+00
    1813. 

  1813. <a name="l01749"></a>01749     xtab(8) =    0.0D+00
    1814. 

  1814. <a name="l01750"></a>01750     xtab(9) =    0.565069583255575748526020337198D+00
    1815. 

  1815. <a name="l01751"></a>01751     xtab(10) =   0.113611558521092066631913490556D+01
    1816. 

  1816. <a name="l01752"></a>01752     xtab(11) =   0.171999257518648893241583152515D+01
    1817. 

  1817. <a name="l01753"></a>01753     xtab(12) =   0.232573248617385774545404479449D+01
    1818. 

  1818. <a name="l01754"></a>01754     xtab(13) =   0.296716692790560324848896036355D+01
    1819. 

  1819. <a name="l01755"></a>01755     xtab(14) =   0.366995037340445253472922383312D+01
    1820. 

  1820. <a name="l01756"></a>01756     xtab(15) =   0.449999070730939155366438053053D+01
    1821. 

  1821. <a name="l01757"></a>01757 
    1822. 

  1822. <a name="l01758"></a>01758     weight(1) =  0.152247580425351702016062666965D-08
    1823. 

  1823. <a name="l01759"></a>01759     weight(2) =  0.105911554771106663577520791055D-05
    1824. 

  1824. <a name="l01760"></a>01760     weight(3) =  0.100004441232499868127296736177D-03
    1825. 

  1825. <a name="l01761"></a>01761     weight(4) =  0.277806884291277589607887049229D-02
    1826. 

  1826. <a name="l01762"></a>01762     weight(5) =  0.307800338725460822286814158758D-01
    1827. 

  1827. <a name="l01763"></a>01763     weight(6) =  0.158488915795935746883839384960D+00
    1828. 

  1828. <a name="l01764"></a>01764     weight(7) =  0.412028687498898627025891079568D+00
    1829. 

  1829. <a name="l01765"></a>01765     weight(8) =  0.564100308726417532852625797340D+00
    1830. 

  1830. <a name="l01766"></a>01766     weight(9) =  0.412028687498898627025891079568D+00
    1831. 

  1831. <a name="l01767"></a>01767     weight(10) = 0.158488915795935746883839384960D+00
    1832. 

  1832. <a name="l01768"></a>01768     weight(11) = 0.307800338725460822286814158758D-01
    1833. 

  1833. <a name="l01769"></a>01769     weight(12) = 0.277806884291277589607887049229D-02
    1834. 

  1834. <a name="l01770"></a>01770     weight(13) = 0.100004441232499868127296736177D-03
    1835. 

  1835. <a name="l01771"></a>01771     weight(14) = 0.105911554771106663577520791055D-05
    1836. 

  1836. <a name="l01772"></a>01772     weight(15) = 0.152247580425351702016062666965D-08
    1837. 

  1837. <a name="l01773"></a>01773 
    1838. 

  1838. <a name="l01774"></a>01774   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
    1839. 

  1839. <a name="l01775"></a>01775 
    1840. 

  1840. <a name="l01776"></a>01776     xtab(1) =  - 0.468873893930581836468849864875D+01
    1841. 

  1841. <a name="l01777"></a>01777     xtab(2) =  - 0.386944790486012269871942409801D+01
    1842. 

  1842. <a name="l01778"></a>01778     xtab(3) =  - 0.317699916197995602681399455926D+01
    1843. 

  1843. <a name="l01779"></a>01779     xtab(4) =  - 0.254620215784748136215932870545D+01
    1844. 

  1844. <a name="l01780"></a>01780     xtab(5) =  - 0.195178799091625397743465541496D+01
    1845. 

  1845. <a name="l01781"></a>01781     xtab(6) =  - 0.138025853919888079637208966969D+01
    1846. 

  1846. <a name="l01782"></a>01782     xtab(7) =  - 0.822951449144655892582454496734D+00
    1847. 

  1847. <a name="l01783"></a>01783     xtab(8) =  - 0.273481046138152452158280401965D+00
    1848. 

  1848. <a name="l01784"></a>01784     xtab(9) =    0.273481046138152452158280401965D+00
    1849. 

  1849. <a name="l01785"></a>01785     xtab(10) =   0.822951449144655892582454496734D+00
    1850. 

  1850. <a name="l01786"></a>01786     xtab(11) =   0.138025853919888079637208966969D+01
    1851. 

  1851. <a name="l01787"></a>01787     xtab(12) =   0.195178799091625397743465541496D+01
    1852. 

  1852. <a name="l01788"></a>01788     xtab(13) =   0.254620215784748136215932870545D+01
    1853. 

  1853. <a name="l01789"></a>01789     xtab(14) =   0.317699916197995602681399455926D+01
    1854. 

  1854. <a name="l01790"></a>01790     xtab(15) =   0.386944790486012269871942409801D+01
    1855. 

  1855. <a name="l01791"></a>01791     xtab(16) =   0.468873893930581836468849864875D+01
    1856. 

  1856. <a name="l01792"></a>01792 
    1857. 

  1857. <a name="l01793"></a>01793     weight(1) =  0.265480747401118224470926366050D-09
    1858. 

  1858. <a name="l01794"></a>01794     weight(2) =  0.232098084486521065338749423185D-06
    1859. 

  1859. <a name="l01795"></a>01795     weight(3) =  0.271186009253788151201891432244D-04
    1860. 

  1860. <a name="l01796"></a>01796     weight(4) =  0.932284008624180529914277305537D-03
    1861. 

  1861. <a name="l01797"></a>01797     weight(5) =  0.128803115355099736834642999312D-01
    1862. 

  1862. <a name="l01798"></a>01798     weight(6) =  0.838100413989858294154207349001D-01
    1863. 

  1863. <a name="l01799"></a>01799     weight(7) =  0.280647458528533675369463335380D+00
    1864. 

  1864. <a name="l01800"></a>01800     weight(8) =  0.507929479016613741913517341791D+00
    1865. 

  1865. <a name="l01801"></a>01801     weight(9) =  0.507929479016613741913517341791D+00
    1866. 

  1866. <a name="l01802"></a>01802     weight(10) = 0.280647458528533675369463335380D+00
    1867. 

  1867. <a name="l01803"></a>01803     weight(11) = 0.838100413989858294154207349001D-01
    1868. 

  1868. <a name="l01804"></a>01804     weight(12) = 0.128803115355099736834642999312D-01
    1869. 

  1869. <a name="l01805"></a>01805     weight(13) = 0.932284008624180529914277305537D-03
    1870. 

  1870. <a name="l01806"></a>01806     weight(14) = 0.271186009253788151201891432244D-04
    1871. 

  1871. <a name="l01807"></a>01807     weight(15) = 0.232098084486521065338749423185D-06
    1872. 

  1872. <a name="l01808"></a>01808     weight(16) = 0.265480747401118224470926366050D-09
    1873. 

  1873. <a name="l01809"></a>01809 
    1874. 

  1874. <a name="l01810"></a>01810   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 17 ) <span class="keyword">then</span>
    1875. 

  1875. <a name="l01811"></a>01811 
    1876. 

  1876. <a name="l01812"></a>01812     xtab(1) =  - 0.487134519367440308834927655662D+01
    1877. 

  1877. <a name="l01813"></a>01813     xtab(2) =  - 0.406194667587547430689245559698D+01
    1878. 

  1878. <a name="l01814"></a>01814     xtab(3) =  - 0.337893209114149408338327069289D+01
    1879. 

  1879. <a name="l01815"></a>01815     xtab(4) =  - 0.275776291570388873092640349574D+01
    1880. 

  1880. <a name="l01816"></a>01816     xtab(5) =  - 0.217350282666662081927537907149D+01
    1881. 

  1881. <a name="l01817"></a>01817     xtab(6) =  - 0.161292431422123133311288254454D+01
    1882. 

  1882. <a name="l01818"></a>01818     xtab(7) =  - 0.106764872574345055363045773799D+01
    1883. 

  1883. <a name="l01819"></a>01819     xtab(8) =  - 0.531633001342654731349086553718D+00
    1884. 

  1884. <a name="l01820"></a>01820     xtab(9) =    0.0D+00
    1885. 

  1885. <a name="l01821"></a>01821     xtab(10) =   0.531633001342654731349086553718D+00
    1886. 

  1886. <a name="l01822"></a>01822     xtab(11) =   0.106764872574345055363045773799D+01
    1887. 

  1887. <a name="l01823"></a>01823     xtab(12) =   0.161292431422123133311288254454D+01
    1888. 

  1888. <a name="l01824"></a>01824     xtab(13) =   0.217350282666662081927537907149D+01
    1889. 

  1889. <a name="l01825"></a>01825     xtab(14) =   0.275776291570388873092640349574D+01
    1890. 

  1890. <a name="l01826"></a>01826     xtab(15) =   0.337893209114149408338327069289D+01
    1891. 

  1891. <a name="l01827"></a>01827     xtab(16) =   0.406194667587547430689245559698D+01
    1892. 

  1892. <a name="l01828"></a>01828     xtab(17) =   0.487134519367440308834927655662D+01
    1893. 

  1893. <a name="l01829"></a>01829 
    1894. 

  1894. <a name="l01830"></a>01830     weight(1) =  0.458057893079863330580889281222D-10
    1895. 

  1895. <a name="l01831"></a>01831     weight(2) =  0.497707898163079405227863353715D-07
    1896. 

  1896. <a name="l01832"></a>01832     weight(3) =  0.711228914002130958353327376218D-05
    1897. 

  1897. <a name="l01833"></a>01833     weight(4) =  0.298643286697753041151336643059D-03
    1898. 

  1898. <a name="l01834"></a>01834     weight(5) =  0.506734995762753791170069495879D-02
    1899. 

  1899. <a name="l01835"></a>01835     weight(6) =  0.409200341495762798094994877854D-01
    1900. 

  1900. <a name="l01836"></a>01836     weight(7) =  0.172648297670097079217645196219D+00
    1901. 

  1901. <a name="l01837"></a>01837     weight(8) =  0.401826469470411956577635085257D+00
    1902. 

  1902. <a name="l01838"></a>01838     weight(9) =  0.530917937624863560331883103379D+00
    1903. 

  1903. <a name="l01839"></a>01839     weight(10) = 0.401826469470411956577635085257D+00
    1904. 

  1904. <a name="l01840"></a>01840     weight(11) = 0.172648297670097079217645196219D+00
    1905. 

  1905. <a name="l01841"></a>01841     weight(12) = 0.409200341495762798094994877854D-01
    1906. 

  1906. <a name="l01842"></a>01842     weight(13) = 0.506734995762753791170069495879D-02
    1907. 

  1907. <a name="l01843"></a>01843     weight(14) = 0.298643286697753041151336643059D-03
    1908. 

  1908. <a name="l01844"></a>01844     weight(15) = 0.711228914002130958353327376218D-05
    1909. 

  1909. <a name="l01845"></a>01845     weight(16) = 0.497707898163079405227863353715D-07
    1910. 

  1910. <a name="l01846"></a>01846     weight(17) = 0.458057893079863330580889281222D-10
    1911. 

  1911. <a name="l01847"></a>01847 
    1912. 

  1912. <a name="l01848"></a>01848   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 18 ) <span class="keyword">then</span>
    1913. 

  1913. <a name="l01849"></a>01849 
    1914. 

  1914. <a name="l01850"></a>01850     xtab(1) =  - 0.504836400887446676837203757885D+01
    1915. 

  1915. <a name="l01851"></a>01851     xtab(2) =  - 0.424811787356812646302342016090D+01
    1916. 

  1916. <a name="l01852"></a>01852     xtab(3) =  - 0.357376906848626607950067599377D+01
    1917. 

  1917. <a name="l01853"></a>01853     xtab(4) =  - 0.296137750553160684477863254906D+01
    1918. 

  1918. <a name="l01854"></a>01854     xtab(5) =  - 0.238629908916668600026459301424D+01
    1919. 

  1919. <a name="l01855"></a>01855     xtab(6) =  - 0.183553160426162889225383944409D+01
    1920. 

  1920. <a name="l01856"></a>01856     xtab(7) =  - 0.130092085838961736566626555439D+01
    1921. 

  1921. <a name="l01857"></a>01857     xtab(8) =  - 0.776682919267411661316659462284D+00
    1922. 

  1922. <a name="l01858"></a>01858     xtab(9) =  - 0.258267750519096759258116098711D+00
    1923. 

  1923. <a name="l01859"></a>01859     xtab(10) =   0.258267750519096759258116098711D+00
    1924. 

  1924. <a name="l01860"></a>01860     xtab(11) =   0.776682919267411661316659462284D+00
    1925. 

  1925. <a name="l01861"></a>01861     xtab(12) =   0.130092085838961736566626555439D+01
    1926. 

  1926. <a name="l01862"></a>01862     xtab(13) =   0.183553160426162889225383944409D+01
    1927. 

  1927. <a name="l01863"></a>01863     xtab(14) =   0.238629908916668600026459301424D+01
    1928. 

  1928. <a name="l01864"></a>01864     xtab(15) =   0.296137750553160684477863254906D+01
    1929. 

  1929. <a name="l01865"></a>01865     xtab(16) =   0.357376906848626607950067599377D+01
    1930. 

  1930. <a name="l01866"></a>01866     xtab(17) =   0.424811787356812646302342016090D+01
    1931. 

  1931. <a name="l01867"></a>01867     xtab(18) =   0.504836400887446676837203757885D+01
    1932. 

  1932. <a name="l01868"></a>01868 
    1933. 

  1933. <a name="l01869"></a>01869     weight(1) =  0.782819977211589102925147471012D-11
    1934. 

  1934. <a name="l01870"></a>01870     weight(2) =  0.104672057957920824443559608435D-07
    1935. 

  1935. <a name="l01871"></a>01871     weight(3) =  0.181065448109343040959702385911D-05
    1936. 

  1936. <a name="l01872"></a>01872     weight(4) =  0.918112686792940352914675407371D-04
    1937. 

  1937. <a name="l01873"></a>01873     weight(5) =  0.188852263026841789438175325426D-02
    1938. 

  1938. <a name="l01874"></a>01874     weight(6) =  0.186400423875446519219315221973D-01
    1939. 

  1939. <a name="l01875"></a>01875     weight(7) =  0.973017476413154293308537234155D-01
    1940. 

  1940. <a name="l01876"></a>01876     weight(8) =  0.284807285669979578595606820713D+00
    1941. 

  1941. <a name="l01877"></a>01877     weight(9) =  0.483495694725455552876410522141D+00
    1942. 

  1942. <a name="l01878"></a>01878     weight(10) = 0.483495694725455552876410522141D+00
    1943. 

  1943. <a name="l01879"></a>01879     weight(11) = 0.284807285669979578595606820713D+00
    1944. 

  1944. <a name="l01880"></a>01880     weight(12) = 0.973017476413154293308537234155D-01
    1945. 

  1945. <a name="l01881"></a>01881     weight(13) = 0.186400423875446519219315221973D-01
    1946. 

  1946. <a name="l01882"></a>01882     weight(14) = 0.188852263026841789438175325426D-02
    1947. 

  1947. <a name="l01883"></a>01883     weight(15) = 0.918112686792940352914675407371D-04
    1948. 

  1948. <a name="l01884"></a>01884     weight(16) = 0.181065448109343040959702385911D-05
    1949. 

  1949. <a name="l01885"></a>01885     weight(17) = 0.104672057957920824443559608435D-07
    1950. 

  1950. <a name="l01886"></a>01886     weight(18) = 0.782819977211589102925147471012D-11
    1951. 

  1951. <a name="l01887"></a>01887 
    1952. 

  1952. <a name="l01888"></a>01888   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 19 ) <span class="keyword">then</span>
    1953. 

  1953. <a name="l01889"></a>01889 
    1954. 

  1954. <a name="l01890"></a>01890     xtab(1) =  - 0.522027169053748216460967142500D+01
    1955. 

  1955. <a name="l01891"></a>01891     xtab(2) =  - 0.442853280660377943723498532226D+01
    1956. 

  1956. <a name="l01892"></a>01892     xtab(3) =  - 0.376218735196402009751489394104D+01
    1957. 

  1957. <a name="l01893"></a>01893     xtab(4) =  - 0.315784881834760228184318034120D+01
    1958. 

  1958. <a name="l01894"></a>01894     xtab(5) =  - 0.259113378979454256492128084112D+01
    1959. 

  1959. <a name="l01895"></a>01895     xtab(6) =  - 0.204923170985061937575050838669D+01
    1960. 

  1960. <a name="l01896"></a>01896     xtab(7) =  - 0.152417061939353303183354859367D+01
    1961. 

  1961. <a name="l01897"></a>01897     xtab(8) =  - 0.101036838713431135136859873726D+01
    1962. 

  1962. <a name="l01898"></a>01898     xtab(9) =  - 0.503520163423888209373811765050D+00
    1963. 

  1963. <a name="l01899"></a>01899     xtab(10) =   0.0D+00
    1964. 

  1964. <a name="l01900"></a>01900     xtab(11) =   0.503520163423888209373811765050D+00
    1965. 

  1965. <a name="l01901"></a>01901     xtab(12) =   0.101036838713431135136859873726D+01
    1966. 

  1966. <a name="l01902"></a>01902     xtab(13) =   0.152417061939353303183354859367D+01
    1967. 

  1967. <a name="l01903"></a>01903     xtab(14) =   0.204923170985061937575050838669D+01
    1968. 

  1968. <a name="l01904"></a>01904     xtab(15) =   0.259113378979454256492128084112D+01
    1969. 

  1969. <a name="l01905"></a>01905     xtab(16) =   0.315784881834760228184318034120D+01
    1970. 

  1970. <a name="l01906"></a>01906     xtab(17) =   0.376218735196402009751489394104D+01
    1971. 

  1971. <a name="l01907"></a>01907     xtab(18) =   0.442853280660377943723498532226D+01
    1972. 

  1972. <a name="l01908"></a>01908     xtab(19) =   0.522027169053748216460967142500D+01
    1973. 

  1973. <a name="l01909"></a>01909 
    1974. 

  1974. <a name="l01910"></a>01910     weight(1) =  0.132629709449851575185289154385D-11
    1975. 

  1975. <a name="l01911"></a>01911     weight(2) =  0.216305100986355475019693077221D-08
    1976. 

  1976. <a name="l01912"></a>01912     weight(3) =  0.448824314722312295179447915594D-06
    1977. 

  1977. <a name="l01913"></a>01913     weight(4) =  0.272091977631616257711941025214D-04
    1978. 

  1978. <a name="l01914"></a>01914     weight(5) =  0.670877521407181106194696282100D-03
    1979. 

  1979. <a name="l01915"></a>01915     weight(6) =  0.798886677772299020922211491861D-02
    1980. 

  1980. <a name="l01916"></a>01916     weight(7) =  0.508103869090520673569908110358D-01
    1981. 

  1981. <a name="l01917"></a>01917     weight(8) =  0.183632701306997074156148485766D+00
    1982. 

  1982. <a name="l01918"></a>01918     weight(9) =  0.391608988613030244504042313621D+00
    1983. 

  1983. <a name="l01919"></a>01919     weight(10) = 0.502974888276186530840731361096D+00
    1984. 

  1984. <a name="l01920"></a>01920     weight(11) = 0.391608988613030244504042313621D+00
    1985. 

  1985. <a name="l01921"></a>01921     weight(12) = 0.183632701306997074156148485766D+00
    1986. 

  1986. <a name="l01922"></a>01922     weight(13) = 0.508103869090520673569908110358D-01
    1987. 

  1987. <a name="l01923"></a>01923     weight(14) = 0.798886677772299020922211491861D-02
    1988. 

  1988. <a name="l01924"></a>01924     weight(15) = 0.670877521407181106194696282100D-03
    1989. 

  1989. <a name="l01925"></a>01925     weight(16) = 0.272091977631616257711941025214D-04
    1990. 

  1990. <a name="l01926"></a>01926     weight(17) = 0.448824314722312295179447915594D-06
    1991. 

  1991. <a name="l01927"></a>01927     weight(18) = 0.216305100986355475019693077221D-08
    1992. 

  1992. <a name="l01928"></a>01928     weight(19) = 0.132629709449851575185289154385D-11
    1993. 

  1993. <a name="l01929"></a>01929 
    1994. 

  1994. <a name="l01930"></a>01930   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 20 ) <span class="keyword">then</span>
    1995. 

  1995. <a name="l01931"></a>01931 
    1996. 

  1996. <a name="l01932"></a>01932     xtab(1) =  - 0.538748089001123286201690041068D+01
    1997. 

  1997. <a name="l01933"></a>01933     xtab(2) =  - 0.460368244955074427307767524898D+01
    1998. 

  1998. <a name="l01934"></a>01934     xtab(3) =  - 0.394476404011562521037562880052D+01
    1999. 

  1999. <a name="l01935"></a>01935     xtab(4) =  - 0.334785456738321632691492452300D+01
    2000. 

  2000. <a name="l01936"></a>01936     xtab(5) =  - 0.278880605842813048052503375640D+01
    2001. 

  2001. <a name="l01937"></a>01937     xtab(6) =  - 0.225497400208927552308233334473D+01
    2002. 

  2002. <a name="l01938"></a>01938     xtab(7) =  - 0.173853771211658620678086566214D+01
    2003. 

  2003. <a name="l01939"></a>01939     xtab(8) =  - 0.123407621539532300788581834696D+01
    2004. 

  2004. <a name="l01940"></a>01940     xtab(9) =  - 0.737473728545394358705605144252D+00
    2005. 

  2005. <a name="l01941"></a>01941     xtab(10) = - 0.245340708300901249903836530634D+00
    2006. 

  2006. <a name="l01942"></a>01942     xtab(11) =   0.245340708300901249903836530634D+00
    2007. 

  2007. <a name="l01943"></a>01943     xtab(12) =   0.737473728545394358705605144252D+00
    2008. 

  2008. <a name="l01944"></a>01944     xtab(13) =   0.123407621539532300788581834696D+01
    2009. 

  2009. <a name="l01945"></a>01945     xtab(14) =   0.173853771211658620678086566214D+01
    2010. 

  2010. <a name="l01946"></a>01946     xtab(15) =   0.225497400208927552308233334473D+01
    2011. 

  2011. <a name="l01947"></a>01947     xtab(16) =   0.278880605842813048052503375640D+01
    2012. 

  2012. <a name="l01948"></a>01948     xtab(17) =   0.334785456738321632691492452300D+01
    2013. 

  2013. <a name="l01949"></a>01949     xtab(18) =   0.394476404011562521037562880052D+01
    2014. 

  2014. <a name="l01950"></a>01950     xtab(19) =   0.460368244955074427307767524898D+01
    2015. 

  2015. <a name="l01951"></a>01951     xtab(20) =   0.538748089001123286201690041068D+01
    2016. 

  2016. <a name="l01952"></a>01952 
    2017. 

  2017. <a name="l01953"></a>01953     weight(1) =  0.222939364553415129252250061603D-12
    2018. 

  2018. <a name="l01954"></a>01954     weight(2) =  0.439934099227318055362885145547D-09
    2019. 

  2019. <a name="l01955"></a>01955     weight(3) =  0.108606937076928169399952456345D-06
    2020. 

  2020. <a name="l01956"></a>01956     weight(4) =  0.780255647853206369414599199965D-05
    2021. 

  2021. <a name="l01957"></a>01957     weight(5) =  0.228338636016353967257145917963D-03
    2022. 

  2022. <a name="l01958"></a>01958     weight(6) =  0.324377334223786183218324713235D-02
    2023. 

  2023. <a name="l01959"></a>01959     weight(7) =  0.248105208874636108821649525589D-01
    2024. 

  2024. <a name="l01960"></a>01960     weight(8) =  0.109017206020023320013755033535D+00
    2025. 

  2025. <a name="l01961"></a>01961     weight(9) =  0.286675505362834129719659706228D+00
    2026. 

  2026. <a name="l01962"></a>01962     weight(10) = 0.462243669600610089650328639861D+00
    2027. 

  2027. <a name="l01963"></a>01963     weight(11) = 0.462243669600610089650328639861D+00
    2028. 

  2028. <a name="l01964"></a>01964     weight(12) = 0.286675505362834129719659706228D+00
    2029. 

  2029. <a name="l01965"></a>01965     weight(13) = 0.109017206020023320013755033535D+00
    2030. 

  2030. <a name="l01966"></a>01966     weight(14) = 0.248105208874636108821649525589D-01
    2031. 

  2031. <a name="l01967"></a>01967     weight(15) = 0.324377334223786183218324713235D-02
    2032. 

  2032. <a name="l01968"></a>01968     weight(16) = 0.228338636016353967257145917963D-03
    2033. 

  2033. <a name="l01969"></a>01969     weight(17) = 0.780255647853206369414599199965D-05
    2034. 

  2034. <a name="l01970"></a>01970     weight(18) = 0.108606937076928169399952456345D-06
    2035. 

  2035. <a name="l01971"></a>01971     weight(19) = 0.439934099227318055362885145547D-09
    2036. 

  2036. <a name="l01972"></a>01972     weight(20) = 0.222939364553415129252250061603D-12
    2037. 

  2037. <a name="l01973"></a>01973 
    2038. 

  2038. <a name="l01974"></a>01974   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 30 ) <span class="keyword">then</span>
    2039. 

  2039. <a name="l01975"></a>01975 
    2040. 

  2040. <a name="l01976"></a>01976     xtab( 1) =   -6.86334529352989158106110835756D+00
    2041. 

  2041. <a name="l01977"></a>01977     xtab( 2) =   -6.13827922012393462039499237854D+00
    2042. 

  2042. <a name="l01978"></a>01978     xtab( 3) =   -5.53314715156749572511833355558D+00
    2043. 

  2043. <a name="l01979"></a>01979     xtab( 4) =   -4.98891896858994394448649710633D+00
    2044. 

  2044. <a name="l01980"></a>01980     xtab( 5) =   -4.48305535709251834188703761971D+00
    2045. 

  2045. <a name="l01981"></a>01981     xtab( 6) =   -4.00390860386122881522787601332D+00
    2046. 

  2046. <a name="l01982"></a>01982     xtab( 7) =   -3.54444387315534988692540090217D+00
    2047. 

  2047. <a name="l01983"></a>01983     xtab( 8) =   -3.09997052958644174868873332237D+00
    2048. 

  2048. <a name="l01984"></a>01984     xtab( 9) =   -2.66713212453561720057110646422D+00
    2049. 

  2049. <a name="l01985"></a>01985     xtab(10) =   -2.24339146776150407247297999483D+00
    2050. 

  2050. <a name="l01986"></a>01986     xtab(11) =   -1.82674114360368803883588048351D+00
    2051. 

  2051. <a name="l01987"></a>01987     xtab(12) =   -1.41552780019818851194072510555D+00
    2052. 

  2052. <a name="l01988"></a>01988     xtab(13) =   -1.00833827104672346180498960870D+00
    2053. 

  2053. <a name="l01989"></a>01989     xtab(14) =   -0.603921058625552307778155678757D+00
    2054. 

  2054. <a name="l01990"></a>01990     xtab(15) =   -0.201128576548871485545763013244D+00
    2055. 

  2055. <a name="l01991"></a>01991     xtab(16) =    0.201128576548871485545763013244D+00
    2056. 

  2056. <a name="l01992"></a>01992     xtab(17) =    0.603921058625552307778155678757D+00
    2057. 

  2057. <a name="l01993"></a>01993     xtab(18) =    1.00833827104672346180498960870D+00
    2058. 

  2058. <a name="l01994"></a>01994     xtab(19) =    1.41552780019818851194072510555D+00
    2059. 

  2059. <a name="l01995"></a>01995     xtab(20) =    1.82674114360368803883588048351D+00
    2060. 

  2060. <a name="l01996"></a>01996     xtab(21) =    2.24339146776150407247297999483D+00
    2061. 

  2061. <a name="l01997"></a>01997     xtab(22) =    2.66713212453561720057110646422D+00
    2062. 

  2062. <a name="l01998"></a>01998     xtab(23) =    3.09997052958644174868873332237D+00
    2063. 

  2063. <a name="l01999"></a>01999     xtab(24) =    3.54444387315534988692540090217D+00
    2064. 

  2064. <a name="l02000"></a>02000     xtab(25) =    4.00390860386122881522787601332D+00
    2065. 

  2065. <a name="l02001"></a>02001     xtab(26) =    4.48305535709251834188703761971D+00
    2066. 

  2066. <a name="l02002"></a>02002     xtab(27) =    4.98891896858994394448649710633D+00
    2067. 

  2067. <a name="l02003"></a>02003     xtab(28) =    5.53314715156749572511833355558D+00
    2068. 

  2068. <a name="l02004"></a>02004     xtab(29) =    6.13827922012393462039499237854D+00
    2069. 

  2069. <a name="l02005"></a>02005     xtab(30) =    6.86334529352989158106110835756D+00
    2070. 

  2070. <a name="l02006"></a>02006 
    2071. 

  2071. <a name="l02007"></a>02007     weight( 1) =   0.290825470013122622941102747365D-20
    2072. 

  2072. <a name="l02008"></a>02008     weight( 2) =   0.281033360275090370876277491534D-16
    2073. 

  2073. <a name="l02009"></a>02009     weight( 3) =   0.287860708054870606219239791142D-13
    2074. 

  2074. <a name="l02010"></a>02010     weight( 4) =   0.810618629746304420399344796173D-11
    2075. 

  2075. <a name="l02011"></a>02011     weight( 5) =   0.917858042437852820850075742492D-09
    2076. 

  2076. <a name="l02012"></a>02012     weight( 6) =   0.510852245077594627738963204403D-07
    2077. 

  2077. <a name="l02013"></a>02013     weight( 7) =   0.157909488732471028834638794022D-05
    2078. 

  2078. <a name="l02014"></a>02014     weight( 8) =   0.293872522892298764150118423412D-04
    2079. 

  2079. <a name="l02015"></a>02015     weight( 9) =   0.348310124318685523420995323183D-03
    2080. 

  2080. <a name="l02016"></a>02016     weight(10) =   0.273792247306765846298942568953D-02
    2081. 

  2081. <a name="l02017"></a>02017     weight(11) =   0.147038297048266835152773557787D-01
    2082. 

  2082. <a name="l02018"></a>02018     weight(12) =   0.551441768702342511680754948183D-01
    2083. 

  2083. <a name="l02019"></a>02019     weight(13) =   0.146735847540890099751693643152D+00
    2084. 

  2084. <a name="l02020"></a>02020     weight(14) =   0.280130930839212667413493211293D+00
    2085. 

  2085. <a name="l02021"></a>02021     weight(15) =   0.386394889541813862555601849165D+00
    2086. 

  2086. <a name="l02022"></a>02022     weight(16) =   0.386394889541813862555601849165D+00
    2087. 

  2087. <a name="l02023"></a>02023     weight(17) =   0.280130930839212667413493211293D+00
    2088. 

  2088. <a name="l02024"></a>02024     weight(18) =   0.146735847540890099751693643152D+00
    2089. 

  2089. <a name="l02025"></a>02025     weight(19) =   0.551441768702342511680754948183D-01
    2090. 

  2090. <a name="l02026"></a>02026     weight(20) =   0.147038297048266835152773557787D-01
    2091. 

  2091. <a name="l02027"></a>02027     weight(21) =   0.273792247306765846298942568953D-02
    2092. 

  2092. <a name="l02028"></a>02028     weight(22) =   0.348310124318685523420995323183D-03
    2093. 

  2093. <a name="l02029"></a>02029     weight(23) =   0.293872522892298764150118423412D-04
    2094. 

  2094. <a name="l02030"></a>02030     weight(24) =   0.157909488732471028834638794022D-05
    2095. 

  2095. <a name="l02031"></a>02031     weight(25) =   0.510852245077594627738963204403D-07
    2096. 

  2096. <a name="l02032"></a>02032     weight(26) =   0.917858042437852820850075742492D-09
    2097. 

  2097. <a name="l02033"></a>02033     weight(27) =   0.810618629746304420399344796173D-11
    2098. 

  2098. <a name="l02034"></a>02034     weight(28) =   0.287860708054870606219239791142D-13
    2099. 

  2099. <a name="l02035"></a>02035     weight(29) =   0.281033360275090370876277491534D-16
    2100. 

  2100. <a name="l02036"></a>02036     weight(30) =   0.290825470013122622941102747365D-20
    2101. 

  2101. <a name="l02037"></a>02037 
    2102. 

  2102. <a name="l02038"></a>02038   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 32 ) <span class="keyword">then</span>
    2103. 

  2103. <a name="l02039"></a>02039 
    2104. 

  2104. <a name="l02040"></a>02040     xtab( 1) =   -7.12581390983D+00
    2105. 

  2105. <a name="l02041"></a>02041     xtab( 2) =   -6.40949814927D+00
    2106. 

  2106. <a name="l02042"></a>02042     xtab( 3) =   -5.81222594952D+00
    2107. 

  2107. <a name="l02043"></a>02043     xtab( 4) =   -5.27555098652D+00
    2108. 

  2108. <a name="l02044"></a>02044     xtab( 5) =   -4.77716450350D+00
    2109. 

  2109. <a name="l02045"></a>02045     xtab( 6) =   -4.30554795335D+00
    2110. 

  2110. <a name="l02046"></a>02046     xtab( 7) =   -3.85375548547D+00
    2111. 

  2111. <a name="l02047"></a>02047     xtab( 8) =   -3.41716749282D+00
    2112. 

  2112. <a name="l02048"></a>02048     xtab( 9) =   -2.99249082500D+00
    2113. 

  2113. <a name="l02049"></a>02049     xtab(10) =   -2.57724953773D+00
    2114. 

  2114. <a name="l02050"></a>02050     xtab(11) =   -2.16949918361D+00
    2115. 

  2115. <a name="l02051"></a>02051     xtab(12) =   -1.76765410946D+00
    2116. 

  2116. <a name="l02052"></a>02052     xtab(13) =   -1.37037641095D+00
    2117. 

  2117. <a name="l02053"></a>02053     xtab(14) =  -0.976500463590D+00
    2118. 

  2118. <a name="l02054"></a>02054     xtab(15) =  -0.584978765436D+00
    2119. 

  2119. <a name="l02055"></a>02055     xtab(16) =  -0.194840741569D+00
    2120. 

  2120. <a name="l02056"></a>02056     xtab(17) =   0.194840741569D+00
    2121. 

  2121. <a name="l02057"></a>02057     xtab(18) =   0.584978765436D+00
    2122. 

  2122. <a name="l02058"></a>02058     xtab(19) =   0.976500463590D+00
    2123. 

  2123. <a name="l02059"></a>02059     xtab(20) =    1.37037641095D+00
    2124. 

  2124. <a name="l02060"></a>02060     xtab(21) =    1.76765410946D+00
    2125. 

  2125. <a name="l02061"></a>02061     xtab(22) =    2.16949918361D+00
    2126. 

  2126. <a name="l02062"></a>02062     xtab(23) =    2.57724953773D+00
    2127. 

  2127. <a name="l02063"></a>02063     xtab(24) =    2.99249082500D+00
    2128. 

  2128. <a name="l02064"></a>02064     xtab(25) =    3.41716749282D+00
    2129. 

  2129. <a name="l02065"></a>02065     xtab(26) =    3.85375548547D+00
    2130. 

  2130. <a name="l02066"></a>02066     xtab(27) =    4.30554795335D+00
    2131. 

  2131. <a name="l02067"></a>02067     xtab(28) =    4.77716450350D+00
    2132. 

  2132. <a name="l02068"></a>02068     xtab(29) =    5.27555098652D+00
    2133. 

  2133. <a name="l02069"></a>02069     xtab(30) =    5.81222594952D+00
    2134. 

  2134. <a name="l02070"></a>02070     xtab(31) =    6.40949814927D+00
    2135. 

  2135. <a name="l02071"></a>02071     xtab(32) =    7.12581390983D+00
    2136. 

  2136. <a name="l02072"></a>02072 
    2137. 

  2137. <a name="l02073"></a>02073     weight( 1) =   0.731067642736D-22
    2138. 

  2138. <a name="l02074"></a>02074     weight( 2) =   0.923173653649D-18
    2139. 

  2139. <a name="l02075"></a>02075     weight( 3) =   0.119734401709D-14
    2140. 

  2140. <a name="l02076"></a>02076     weight( 4) =   0.421501021125D-12
    2141. 

  2141. <a name="l02077"></a>02077     weight( 5) =   0.593329146300D-10
    2142. 

  2142. <a name="l02078"></a>02078     weight( 6) =   0.409883216476D-08
    2143. 

  2143. <a name="l02079"></a>02079     weight( 7) =   0.157416779254D-06
    2144. 

  2144. <a name="l02080"></a>02080     weight( 8) =   0.365058512955D-05
    2145. 

  2145. <a name="l02081"></a>02081     weight( 9) =   0.541658406172D-04
    2146. 

  2146. <a name="l02082"></a>02082     weight(10) =   0.536268365526D-03
    2147. 

  2147. <a name="l02083"></a>02083     weight(11) =   0.365489032664D-02
    2148. 

  2148. <a name="l02084"></a>02084     weight(12) =   0.175534288315D-01
    2149. 

  2149. <a name="l02085"></a>02085     weight(13) =   0.604581309557D-01
    2150. 

  2150. <a name="l02086"></a>02086     weight(14) =   0.151269734076D+00
    2151. 

  2151. <a name="l02087"></a>02087     weight(15) =   0.277458142302D+00
    2152. 

  2152. <a name="l02088"></a>02088     weight(16) =   0.375238352592D+00
    2153. 

  2153. <a name="l02089"></a>02089     weight(17) =   0.375238352592D+00
    2154. 

  2154. <a name="l02090"></a>02090     weight(18) =   0.277458142302D+00
    2155. 

  2155. <a name="l02091"></a>02091     weight(19) =   0.151269734076D+00
    2156. 

  2156. <a name="l02092"></a>02092     weight(20) =   0.604581309557D-01
    2157. 

  2157. <a name="l02093"></a>02093     weight(21) =   0.175534288315D-01
    2158. 

  2158. <a name="l02094"></a>02094     weight(22) =   0.365489032664D-02
    2159. 

  2159. <a name="l02095"></a>02095     weight(23) =   0.536268365526D-03
    2160. 

  2160. <a name="l02096"></a>02096     weight(24) =   0.541658406172D-04
    2161. 

  2161. <a name="l02097"></a>02097     weight(25) =   0.365058512955D-05
    2162. 

  2162. <a name="l02098"></a>02098     weight(26) =   0.157416779254D-06
    2163. 

  2163. <a name="l02099"></a>02099     weight(27) =   0.409883216476D-08
    2164. 

  2164. <a name="l02100"></a>02100     weight(28) =   0.593329146300D-10
    2165. 

  2165. <a name="l02101"></a>02101     weight(29) =   0.421501021125D-12
    2166. 

  2166. <a name="l02102"></a>02102     weight(30) =   0.119734401709D-14
    2167. 

  2167. <a name="l02103"></a>02103     weight(31) =   0.923173653649D-18
    2168. 

  2168. <a name="l02104"></a>02104     weight(32) =   0.731067642736D-22
    2169. 

  2169. <a name="l02105"></a>02105 
    2170. 

  2170. <a name="l02106"></a>02106   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 40 ) <span class="keyword">then</span>
    2171. 

  2171. <a name="l02107"></a>02107 
    2172. 

  2172. <a name="l02108"></a>02108     xtab( 1) =   -8.09876113925D+00
    2173. 

  2173. <a name="l02109"></a>02109     xtab( 2) =   -7.41158253149D+00
    2174. 

  2174. <a name="l02110"></a>02110     xtab( 3) =   -6.84023730525D+00
    2175. 

  2175. <a name="l02111"></a>02111     xtab( 4) =   -6.32825535122D+00
    2176. 

  2176. <a name="l02112"></a>02112     xtab( 5) =   -5.85409505603D+00
    2177. 

  2177. <a name="l02113"></a>02113     xtab( 6) =   -5.40665424797D+00
    2178. 

  2178. <a name="l02114"></a>02114     xtab( 7) =   -4.97926097855D+00
    2179. 

  2179. <a name="l02115"></a>02115     xtab( 8) =   -4.56750207284D+00
    2180. 

  2180. <a name="l02116"></a>02116     xtab( 9) =   -4.16825706683D+00
    2181. 

  2181. <a name="l02117"></a>02117     xtab(10) =   -3.77920675344D+00
    2182. 

  2182. <a name="l02118"></a>02118     xtab(11) =   -3.39855826586D+00
    2183. 

  2183. <a name="l02119"></a>02119     xtab(12) =   -3.02487988390D+00
    2184. 

  2184. <a name="l02120"></a>02120     xtab(13) =   -2.65699599844D+00
    2185. 

  2185. <a name="l02121"></a>02121     xtab(14) =   -2.29391714188D+00
    2186. 

  2186. <a name="l02122"></a>02122     xtab(15) =   -1.93479147228D+00
    2187. 

  2187. <a name="l02123"></a>02123     xtab(16) =   -1.57886989493D+00
    2188. 

  2188. <a name="l02124"></a>02124     xtab(17) =   -1.22548010905D+00
    2189. 

  2189. <a name="l02125"></a>02125     xtab(18) =  -0.874006612357D+00
    2190. 

  2190. <a name="l02126"></a>02126     xtab(19) =  -0.523874713832D+00
    2191. 

  2191. <a name="l02127"></a>02127     xtab(20) =  -0.174537214598D+00
    2192. 

  2192. <a name="l02128"></a>02128     xtab(21) =   0.174537214598D+00
    2193. 

  2193. <a name="l02129"></a>02129     xtab(22) =   0.523874713832D+00
    2194. 

  2194. <a name="l02130"></a>02130     xtab(23) =   0.874006612357D+00
    2195. 

  2195. <a name="l02131"></a>02131     xtab(24) =    1.22548010905D+00
    2196. 

  2196. <a name="l02132"></a>02132     xtab(25) =    1.57886989493D+00
    2197. 

  2197. <a name="l02133"></a>02133     xtab(26) =    1.93479147228D+00
    2198. 

  2198. <a name="l02134"></a>02134     xtab(27) =    2.29391714188D+00
    2199. 

  2199. <a name="l02135"></a>02135     xtab(28) =    2.65699599844D+00
    2200. 

  2200. <a name="l02136"></a>02136     xtab(29) =    3.02487988390D+00
    2201. 

  2201. <a name="l02137"></a>02137     xtab(30) =    3.39855826586D+00
    2202. 

  2202. <a name="l02138"></a>02138     xtab(31) =    3.77920675344D+00
    2203. 

  2203. <a name="l02139"></a>02139     xtab(32) =    4.16825706683D+00
    2204. 

  2204. <a name="l02140"></a>02140     xtab(33) =    4.56750207284D+00
    2205. 

  2205. <a name="l02141"></a>02141     xtab(34) =    4.97926097855D+00
    2206. 

  2206. <a name="l02142"></a>02142     xtab(35) =    5.40665424797D+00
    2207. 

  2207. <a name="l02143"></a>02143     xtab(36) =    5.85409505603D+00
    2208. 

  2208. <a name="l02144"></a>02144     xtab(37) =    6.32825535122D+00
    2209. 

  2209. <a name="l02145"></a>02145     xtab(38) =    6.84023730525D+00
    2210. 

  2210. <a name="l02146"></a>02146     xtab(39) =    7.41158253149D+00
    2211. 

  2211. <a name="l02147"></a>02147     xtab(40) =    8.09876113925D+00
    2212. 

  2212. <a name="l02148"></a>02148 
    2213. 

  2213. <a name="l02149"></a>02149     weight( 1) =   0.259104371384D-28
    2214. 

  2214. <a name="l02150"></a>02150     weight( 2) =   0.854405696375D-24
    2215. 

  2215. <a name="l02151"></a>02151     weight( 3) =   0.256759336540D-20
    2216. 

  2216. <a name="l02152"></a>02152     weight( 4) =   0.198918101211D-17
    2217. 

  2217. <a name="l02153"></a>02153     weight( 5) =   0.600835878947D-15
    2218. 

  2218. <a name="l02154"></a>02154     weight( 6) =   0.880570764518D-13
    2219. 

  2219. <a name="l02155"></a>02155     weight( 7) =   0.715652805267D-11
    2220. 

  2220. <a name="l02156"></a>02156     weight( 8) =   0.352562079135D-09
    2221. 

  2221. <a name="l02157"></a>02157     weight( 9) =   0.112123608322D-07
    2222. 

  2222. <a name="l02158"></a>02158     weight(10) =   0.241114416359D-06
    2223. 

  2223. <a name="l02159"></a>02159     weight(11) =   0.363157615067D-05
    2224. 

  2224. <a name="l02160"></a>02160     weight(12) =   0.393693398108D-04
    2225. 

  2225. <a name="l02161"></a>02161     weight(13) =   0.313853594540D-03
    2226. 

  2226. <a name="l02162"></a>02162     weight(14) =   0.187149682959D-02
    2227. 

  2227. <a name="l02163"></a>02163     weight(15) =   0.846088800823D-02
    2228. 

  2228. <a name="l02164"></a>02164     weight(16) =   0.293125655361D-01
    2229. 

  2229. <a name="l02165"></a>02165     weight(17) =   0.784746058652D-01
    2230. 

  2230. <a name="l02166"></a>02166     weight(18) =   0.163378732713D+00
    2231. 

  2231. <a name="l02167"></a>02167     weight(19) =   0.265728251876D+00
    2232. 

  2232. <a name="l02168"></a>02168     weight(20) =   0.338643277425D+00
    2233. 

  2233. <a name="l02169"></a>02169     weight(21) =   0.338643277425D+00
    2234. 

  2234. <a name="l02170"></a>02170     weight(22) =   0.265728251876D+00
    2235. 

  2235. <a name="l02171"></a>02171     weight(23) =   0.163378732713D+00
    2236. 

  2236. <a name="l02172"></a>02172     weight(24) =   0.784746058652D-01
    2237. 

  2237. <a name="l02173"></a>02173     weight(25) =   0.293125655361D-01
    2238. 

  2238. <a name="l02174"></a>02174     weight(26) =   0.846088800823D-02
    2239. 

  2239. <a name="l02175"></a>02175     weight(27) =   0.187149682959D-02
    2240. 

  2240. <a name="l02176"></a>02176     weight(28) =   0.313853594540D-03
    2241. 

  2241. <a name="l02177"></a>02177     weight(29) =   0.393693398108D-04
    2242. 

  2242. <a name="l02178"></a>02178     weight(30) =   0.363157615067D-05
    2243. 

  2243. <a name="l02179"></a>02179     weight(31) =   0.241114416359D-06
    2244. 

  2244. <a name="l02180"></a>02180     weight(32) =   0.112123608322D-07
    2245. 

  2245. <a name="l02181"></a>02181     weight(33) =   0.352562079135D-09
    2246. 

  2246. <a name="l02182"></a>02182     weight(34) =   0.715652805267D-11
    2247. 

  2247. <a name="l02183"></a>02183     weight(35) =   0.880570764518D-13
    2248. 

  2248. <a name="l02184"></a>02184     weight(36) =   0.600835878947D-15
    2249. 

  2249. <a name="l02185"></a>02185     weight(37) =   0.198918101211D-17
    2250. 

  2250. <a name="l02186"></a>02186     weight(38) =   0.256759336540D-20
    2251. 

  2251. <a name="l02187"></a>02187     weight(39) =   0.854405696375D-24
    2252. 

  2252. <a name="l02188"></a>02188     weight(40) =   0.259104371384D-28
    2253. 

  2253. <a name="l02189"></a>02189 
    2254. 

  2254. <a name="l02190"></a>02190   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 50 ) <span class="keyword">then</span>
    2255. 

  2255. <a name="l02191"></a>02191 
    2256. 

  2256. <a name="l02192"></a>02192     xtab( 1) =   -9.18240695813D+00
    2257. 

  2257. <a name="l02193"></a>02193     xtab( 2) =   -8.52277103092D+00
    2258. 

  2258. <a name="l02194"></a>02194     xtab( 3) =   -7.97562236821D+00
    2259. 

  2259. <a name="l02195"></a>02195     xtab( 4) =   -7.48640942986D+00
    2260. 

  2260. <a name="l02196"></a>02196     xtab( 5) =   -7.03432350977D+00
    2261. 

  2261. <a name="l02197"></a>02197     xtab( 6) =   -6.60864797386D+00
    2262. 

  2262. <a name="l02198"></a>02198     xtab( 7) =   -6.20295251927D+00
    2263. 

  2263. <a name="l02199"></a>02199     xtab( 8) =   -5.81299467542D+00
    2264. 

  2264. <a name="l02200"></a>02200     xtab( 9) =   -5.43578608722D+00
    2265. 

  2265. <a name="l02201"></a>02201     xtab(10) =   -5.06911758492D+00
    2266. 

  2266. <a name="l02202"></a>02202     xtab(11) =   -4.71129366617D+00
    2267. 

  2267. <a name="l02203"></a>02203     xtab(12) =   -4.36097316045D+00
    2268. 

  2268. <a name="l02204"></a>02204     xtab(13) =   -4.01706817286D+00
    2269. 

  2269. <a name="l02205"></a>02205     xtab(14) =   -3.67867706252D+00
    2270. 

  2270. <a name="l02206"></a>02206     xtab(15) =   -3.34503831394D+00
    2271. 

  2271. <a name="l02207"></a>02207     xtab(16) =   -3.01549776957D+00
    2272. 

  2272. <a name="l02208"></a>02208     xtab(17) =   -2.68948470227D+00
    2273. 

  2273. <a name="l02209"></a>02209     xtab(18) =   -2.36649390430D+00
    2274. 

  2274. <a name="l02210"></a>02210     xtab(19) =   -2.04607196869D+00
    2275. 

  2275. <a name="l02211"></a>02211     xtab(20) =   -1.72780654752D+00
    2276. 

  2276. <a name="l02212"></a>02212     xtab(21) =   -1.41131775490D+00
    2277. 

  2277. <a name="l02213"></a>02213     xtab(22) =   -1.09625112896D+00
    2278. 

  2278. <a name="l02214"></a>02214     xtab(23) =  -0.782271729555D+00
    2279. 

  2279. <a name="l02215"></a>02215     xtab(24) =  -0.469059056678D+00
    2280. 

  2280. <a name="l02216"></a>02216     xtab(25) =  -0.156302546889D+00
    2281. 

  2281. <a name="l02217"></a>02217     xtab(26) =   0.156302546889D+00
    2282. 

  2282. <a name="l02218"></a>02218     xtab(27) =   0.469059056678D+00
    2283. 

  2283. <a name="l02219"></a>02219     xtab(28) =   0.782271729555D+00
    2284. 

  2284. <a name="l02220"></a>02220     xtab(29) =    1.09625112896D+00
    2285. 

  2285. <a name="l02221"></a>02221     xtab(30) =    1.41131775490D+00
    2286. 

  2286. <a name="l02222"></a>02222     xtab(31) =    1.72780654752D+00
    2287. 

  2287. <a name="l02223"></a>02223     xtab(32) =    2.04607196869D+00
    2288. 

  2288. <a name="l02224"></a>02224     xtab(33) =    2.36649390430D+00
    2289. 

  2289. <a name="l02225"></a>02225     xtab(34) =    2.68948470227D+00
    2290. 

  2290. <a name="l02226"></a>02226     xtab(35) =    3.01549776957D+00
    2291. 

  2291. <a name="l02227"></a>02227     xtab(36) =    3.34503831394D+00
    2292. 

  2292. <a name="l02228"></a>02228     xtab(37) =    3.67867706252D+00
    2293. 

  2293. <a name="l02229"></a>02229     xtab(38) =    4.01706817286D+00
    2294. 

  2294. <a name="l02230"></a>02230     xtab(39) =    4.36097316045D+00
    2295. 

  2295. <a name="l02231"></a>02231     xtab(40) =    4.71129366617D+00
    2296. 

  2296. <a name="l02232"></a>02232     xtab(41) =    5.06911758492D+00
    2297. 

  2297. <a name="l02233"></a>02233     xtab(42) =    5.43578608722D+00
    2298. 

  2298. <a name="l02234"></a>02234     xtab(43) =    5.81299467542D+00
    2299. 

  2299. <a name="l02235"></a>02235     xtab(44) =    6.20295251927D+00
    2300. 

  2300. <a name="l02236"></a>02236     xtab(45) =    6.60864797386D+00
    2301. 

  2301. <a name="l02237"></a>02237     xtab(46) =    7.03432350977D+00
    2302. 

  2302. <a name="l02238"></a>02238     xtab(47) =    7.48640942986D+00
    2303. 

  2303. <a name="l02239"></a>02239     xtab(48) =    7.97562236821D+00
    2304. 

  2304. <a name="l02240"></a>02240     xtab(49) =    8.52277103092D+00
    2305. 

  2305. <a name="l02241"></a>02241     xtab(50) =    9.18240695813D+00
    2306. 

  2306. <a name="l02242"></a>02242 
    2307. 

  2307. <a name="l02243"></a>02243     weight( 1) =   0.183379404857D-36
    2308. 

  2308. <a name="l02244"></a>02244     weight( 2) =   0.167380166790D-31
    2309. 

  2309. <a name="l02245"></a>02245     weight( 3) =   0.121524412340D-27
    2310. 

  2310. <a name="l02246"></a>02246     weight( 4) =   0.213765830835D-24
    2311. 

  2311. <a name="l02247"></a>02247     weight( 5) =   0.141709359957D-21
    2312. 

  2312. <a name="l02248"></a>02248     weight( 6) =   0.447098436530D-19
    2313. 

  2313. <a name="l02249"></a>02249     weight( 7) =   0.774238295702D-17
    2314. 

  2314. <a name="l02250"></a>02250     weight( 8) =   0.809426189344D-15
    2315. 

  2315. <a name="l02251"></a>02251     weight( 9) =   0.546594403180D-13
    2316. 

  2316. <a name="l02252"></a>02252     weight(10) =   0.250665552389D-11
    2317. 

  2317. <a name="l02253"></a>02253     weight(11) =   0.811187736448D-10
    2318. 

  2318. <a name="l02254"></a>02254     weight(12) =   0.190904054379D-08
    2319. 

  2319. <a name="l02255"></a>02255     weight(13) =   0.334679340401D-07
    2320. 

  2320. <a name="l02256"></a>02256     weight(14) =   0.445702996680D-06
    2321. 

  2321. <a name="l02257"></a>02257     weight(15) =   0.458168270794D-05
    2322. 

  2322. <a name="l02258"></a>02258     weight(16) =   0.368401905377D-04
    2323. 

  2323. <a name="l02259"></a>02259     weight(17) =   0.234269892109D-03
    2324. 

  2324. <a name="l02260"></a>02260     weight(18) =   0.118901178175D-02
    2325. 

  2325. <a name="l02261"></a>02261     weight(19) =   0.485326382616D-02
    2326. 

  2326. <a name="l02262"></a>02262     weight(20) =   0.160319410684D-01
    2327. 

  2327. <a name="l02263"></a>02263     weight(21) =   0.430791591566D-01
    2328. 

  2328. <a name="l02264"></a>02264     weight(22) =   0.945489354768D-01
    2329. 

  2329. <a name="l02265"></a>02265     weight(23) =   0.170032455676D+00
    2330. 

  2330. <a name="l02266"></a>02266     weight(24) =   0.251130856331D+00
    2331. 

  2331. <a name="l02267"></a>02267     weight(25) =   0.305085129203D+00
    2332. 

  2332. <a name="l02268"></a>02268     weight(26) =   0.305085129203D+00
    2333. 

  2333. <a name="l02269"></a>02269     weight(27) =   0.251130856331D+00
    2334. 

  2334. <a name="l02270"></a>02270     weight(28) =   0.170032455676D+00
    2335. 

  2335. <a name="l02271"></a>02271     weight(29) =   0.945489354768D-01
    2336. 

  2336. <a name="l02272"></a>02272     weight(30) =   0.430791591566D-01
    2337. 

  2337. <a name="l02273"></a>02273     weight(31) =   0.160319410684D-01
    2338. 

  2338. <a name="l02274"></a>02274     weight(32) =   0.485326382616D-02
    2339. 

  2339. <a name="l02275"></a>02275     weight(33) =   0.118901178175D-02
    2340. 

  2340. <a name="l02276"></a>02276     weight(34) =   0.234269892109D-03
    2341. 

  2341. <a name="l02277"></a>02277     weight(35) =   0.368401905377D-04
    2342. 

  2342. <a name="l02278"></a>02278     weight(36) =   0.458168270794D-05
    2343. 

  2343. <a name="l02279"></a>02279     weight(37) =   0.445702996680D-06
    2344. 

  2344. <a name="l02280"></a>02280     weight(38) =   0.334679340401D-07
    2345. 

  2345. <a name="l02281"></a>02281     weight(39) =   0.190904054379D-08
    2346. 

  2346. <a name="l02282"></a>02282     weight(40) =   0.811187736448D-10
    2347. 

  2347. <a name="l02283"></a>02283     weight(41) =   0.250665552389D-11
    2348. 

  2348. <a name="l02284"></a>02284     weight(42) =   0.546594403180D-13
    2349. 

  2349. <a name="l02285"></a>02285     weight(43) =   0.809426189344D-15
    2350. 

  2350. <a name="l02286"></a>02286     weight(44) =   0.774238295702D-17
    2351. 

  2351. <a name="l02287"></a>02287     weight(45) =   0.447098436530D-19
    2352. 

  2352. <a name="l02288"></a>02288     weight(46) =   0.141709359957D-21
    2353. 

  2353. <a name="l02289"></a>02289     weight(47) =   0.213765830835D-24
    2354. 

  2354. <a name="l02290"></a>02290     weight(48) =   0.121524412340D-27
    2355. 

  2355. <a name="l02291"></a>02291     weight(49) =   0.167380166790D-31
    2356. 

  2356. <a name="l02292"></a>02292     weight(50) =   0.183379404857D-36
    2357. 

  2357. <a name="l02293"></a>02293 
    2358. 

  2358. <a name="l02294"></a>02294   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 60 ) <span class="keyword">then</span>
    2359. 

  2359. <a name="l02295"></a>02295 
    2360. 

  2360. <a name="l02296"></a>02296     xtab( 1) =   -10.1591092462D+00
    2361. 

  2361. <a name="l02297"></a>02297     xtab( 2) =   -9.52090367701D+00
    2362. 

  2362. <a name="l02298"></a>02298     xtab( 3) =   -8.99239800140D+00
    2363. 

  2363. <a name="l02299"></a>02299     xtab( 4) =   -8.52056928412D+00
    2364. 

  2364. <a name="l02300"></a>02300     xtab( 5) =   -8.08518865425D+00
    2365. 

  2365. <a name="l02301"></a>02301     xtab( 6) =   -7.67583993750D+00
    2366. 

  2366. <a name="l02302"></a>02302     xtab( 7) =   -7.28627659440D+00
    2367. 

  2367. <a name="l02303"></a>02303     xtab( 8) =   -6.91238153219D+00
    2368. 

  2368. <a name="l02304"></a>02304     xtab( 9) =   -6.55125916706D+00
    2369. 

  2369. <a name="l02305"></a>02305     xtab(10) =   -6.20077355799D+00
    2370. 

  2370. <a name="l02306"></a>02306     xtab(11) =   -5.85929019639D+00
    2371. 

  2371. <a name="l02307"></a>02307     xtab(12) =   -5.52552108614D+00
    2372. 

  2372. <a name="l02308"></a>02308     xtab(13) =   -5.19842653458D+00
    2373. 

  2373. <a name="l02309"></a>02309     xtab(14) =   -4.87715007747D+00
    2374. 

  2374. <a name="l02310"></a>02310     xtab(15) =   -4.56097375794D+00
    2375. 

  2375. <a name="l02311"></a>02311     xtab(16) =   -4.24928643596D+00
    2376. 

  2376. <a name="l02312"></a>02312     xtab(17) =   -3.94156073393D+00
    2377. 

  2377. <a name="l02313"></a>02313     xtab(18) =   -3.63733587617D+00
    2378. 

  2378. <a name="l02314"></a>02314     xtab(19) =   -3.33620465355D+00
    2379. 

  2379. <a name="l02315"></a>02315     xtab(20) =   -3.03780333823D+00
    2380. 

  2380. <a name="l02316"></a>02316     xtab(21) =   -2.74180374807D+00
    2381. 

  2381. <a name="l02317"></a>02317     xtab(22) =   -2.44790690231D+00
    2382. 

  2382. <a name="l02318"></a>02318     xtab(23) =   -2.15583787123D+00
    2383. 

  2383. <a name="l02319"></a>02319     xtab(24) =   -1.86534153123D+00
    2384. 

  2384. <a name="l02320"></a>02320     xtab(25) =   -1.57617901198D+00
    2385. 

  2385. <a name="l02321"></a>02321     xtab(26) =   -1.28812467487D+00
    2386. 

  2386. <a name="l02322"></a>02322     xtab(27) =   -1.00096349956D+00
    2387. 

  2387. <a name="l02323"></a>02323     xtab(28) =  -0.714488781673D+00
    2388. 

  2388. <a name="l02324"></a>02324     xtab(29) =  -0.428500064221D+00
    2389. 

  2389. <a name="l02325"></a>02325     xtab(30) =  -0.142801238703D+00
    2390. 

  2390. <a name="l02326"></a>02326     xtab(31) =   0.142801238703D+00
    2391. 

  2391. <a name="l02327"></a>02327     xtab(32) =   0.428500064221D+00
    2392. 

  2392. <a name="l02328"></a>02328     xtab(33) =   0.714488781673D+00
    2393. 

  2393. <a name="l02329"></a>02329     xtab(34) =    1.00096349956D+00
    2394. 

  2394. <a name="l02330"></a>02330     xtab(35) =    1.28812467487D+00
    2395. 

  2395. <a name="l02331"></a>02331     xtab(36) =    1.57617901198D+00
    2396. 

  2396. <a name="l02332"></a>02332     xtab(37) =    1.86534153123D+00
    2397. 

  2397. <a name="l02333"></a>02333     xtab(38) =    2.15583787123D+00
    2398. 

  2398. <a name="l02334"></a>02334     xtab(39) =    2.44790690231D+00
    2399. 

  2399. <a name="l02335"></a>02335     xtab(40) =    2.74180374807D+00
    2400. 

  2400. <a name="l02336"></a>02336     xtab(41) =    3.03780333823D+00
    2401. 

  2401. <a name="l02337"></a>02337     xtab(42) =    3.33620465355D+00
    2402. 

  2402. <a name="l02338"></a>02338     xtab(43) =    3.63733587617D+00
    2403. 

  2403. <a name="l02339"></a>02339     xtab(44) =    3.94156073393D+00
    2404. 

  2404. <a name="l02340"></a>02340     xtab(45) =    4.24928643596D+00
    2405. 

  2405. <a name="l02341"></a>02341     xtab(46) =    4.56097375794D+00
    2406. 

  2406. <a name="l02342"></a>02342     xtab(47) =    4.87715007747D+00
    2407. 

  2407. <a name="l02343"></a>02343     xtab(48) =    5.19842653458D+00
    2408. 

  2408. <a name="l02344"></a>02344     xtab(49) =    5.52552108614D+00
    2409. 

  2409. <a name="l02345"></a>02345     xtab(50) =    5.85929019639D+00
    2410. 

  2410. <a name="l02346"></a>02346     xtab(51) =    6.20077355799D+00
    2411. 

  2411. <a name="l02347"></a>02347     xtab(52) =    6.55125916706D+00
    2412. 

  2412. <a name="l02348"></a>02348     xtab(53) =    6.91238153219D+00
    2413. 

  2413. <a name="l02349"></a>02349     xtab(54) =    7.28627659440D+00
    2414. 

  2414. <a name="l02350"></a>02350     xtab(55) =    7.67583993750D+00
    2415. 

  2415. <a name="l02351"></a>02351     xtab(56) =    8.08518865425D+00
    2416. 

  2416. <a name="l02352"></a>02352     xtab(57) =    8.52056928412D+00
    2417. 

  2417. <a name="l02353"></a>02353     xtab(58) =    8.99239800140D+00
    2418. 

  2418. <a name="l02354"></a>02354     xtab(59) =    9.52090367701D+00
    2419. 

  2419. <a name="l02355"></a>02355     xtab(60) =    10.1591092462D+00
    2420. 

  2420. <a name="l02356"></a>02356 
    2421. 

  2421. <a name="l02357"></a>02357     weight( 1) =   0.110958724796D-44
    2422. 

  2422. <a name="l02358"></a>02358     weight( 2) =   0.243974758810D-39
    2423. 

  2423. <a name="l02359"></a>02359     weight( 3) =   0.377162672698D-35
    2424. 

  2424. <a name="l02360"></a>02360     weight( 4) =   0.133255961176D-31
    2425. 

  2425. <a name="l02361"></a>02361     weight( 5) =   0.171557314767D-28
    2426. 

  2426. <a name="l02362"></a>02362     weight( 6) =   0.102940599693D-25
    2427. 

  2427. <a name="l02363"></a>02363     weight( 7) =   0.334575695574D-23
    2428. 

  2428. <a name="l02364"></a>02364     weight( 8) =   0.651256725748D-21
    2429. 

  2429. <a name="l02365"></a>02365     weight( 9) =   0.815364047300D-19
    2430. 

  2430. <a name="l02366"></a>02366     weight(10) =   0.692324790956D-17
    2431. 

  2431. <a name="l02367"></a>02367     weight(11) =   0.415244410968D-15
    2432. 

  2432. <a name="l02368"></a>02368     weight(12) =   0.181662457614D-13
    2433. 

  2433. <a name="l02369"></a>02369     weight(13) =   0.594843051597D-12
    2434. 

  2434. <a name="l02370"></a>02370     weight(14) =   0.148895734905D-10
    2435. 

  2435. <a name="l02371"></a>02371     weight(15) =   0.289935901280D-09
    2436. 

  2436. <a name="l02372"></a>02372     weight(16) =   0.445682277521D-08
    2437. 

  2437. <a name="l02373"></a>02373     weight(17) =   0.547555461926D-07
    2438. 

  2438. <a name="l02374"></a>02374     weight(18) =   0.543351613419D-06
    2439. 

  2439. <a name="l02375"></a>02375     weight(19) =   0.439428693625D-05
    2440. 

  2440. <a name="l02376"></a>02376     weight(20) =   0.291874190415D-04
    2441. 

  2441. <a name="l02377"></a>02377     weight(21) =   0.160277334681D-03
    2442. 

  2442. <a name="l02378"></a>02378     weight(22) =   0.731773556963D-03
    2443. 

  2443. <a name="l02379"></a>02379     weight(23) =   0.279132482894D-02
    2444. 

  2444. <a name="l02380"></a>02380     weight(24) =   0.893217836028D-02
    2445. 

  2445. <a name="l02381"></a>02381     weight(25) =   0.240612727660D-01
    2446. 

  2446. <a name="l02382"></a>02382     weight(26) =   0.547189709320D-01
    2447. 

  2447. <a name="l02383"></a>02383     weight(27) =   0.105298763697D+00
    2448. 

  2448. <a name="l02384"></a>02384     weight(28) =   0.171776156918D+00
    2449. 

  2449. <a name="l02385"></a>02385     weight(29) =   0.237868904958D+00
    2450. 

  2450. <a name="l02386"></a>02386     weight(30) =   0.279853117522D+00
    2451. 

  2451. <a name="l02387"></a>02387     weight(31) =   0.279853117522D+00
    2452. 

  2452. <a name="l02388"></a>02388     weight(32) =   0.237868904958D+00
    2453. 

  2453. <a name="l02389"></a>02389     weight(33) =   0.171776156918D+00
    2454. 

  2454. <a name="l02390"></a>02390     weight(34) =   0.105298763697D+00
    2455. 

  2455. <a name="l02391"></a>02391     weight(35) =   0.547189709320D-01
    2456. 

  2456. <a name="l02392"></a>02392     weight(36) =   0.240612727660D-01
    2457. 

  2457. <a name="l02393"></a>02393     weight(37) =   0.893217836028D-02
    2458. 

  2458. <a name="l02394"></a>02394     weight(38) =   0.279132482894D-02
    2459. 

  2459. <a name="l02395"></a>02395     weight(39) =   0.731773556963D-03
    2460. 

  2460. <a name="l02396"></a>02396     weight(40) =   0.160277334681D-03
    2461. 

  2461. <a name="l02397"></a>02397     weight(41) =   0.291874190415D-04
    2462. 

  2462. <a name="l02398"></a>02398     weight(42) =   0.439428693625D-05
    2463. 

  2463. <a name="l02399"></a>02399     weight(43) =   0.543351613419D-06
    2464. 

  2464. <a name="l02400"></a>02400     weight(44) =   0.547555461926D-07
    2465. 

  2465. <a name="l02401"></a>02401     weight(45) =   0.445682277521D-08
    2466. 

  2466. <a name="l02402"></a>02402     weight(46) =   0.289935901280D-09
    2467. 

  2467. <a name="l02403"></a>02403     weight(47) =   0.148895734905D-10
    2468. 

  2468. <a name="l02404"></a>02404     weight(48) =   0.594843051597D-12
    2469. 

  2469. <a name="l02405"></a>02405     weight(49) =   0.181662457614D-13
    2470. 

  2470. <a name="l02406"></a>02406     weight(50) =   0.415244410968D-15
    2471. 

  2471. <a name="l02407"></a>02407     weight(51) =   0.692324790956D-17
    2472. 

  2472. <a name="l02408"></a>02408     weight(52) =   0.815364047300D-19
    2473. 

  2473. <a name="l02409"></a>02409     weight(53) =   0.651256725748D-21
    2474. 

  2474. <a name="l02410"></a>02410     weight(54) =   0.334575695574D-23
    2475. 

  2475. <a name="l02411"></a>02411     weight(55) =   0.102940599693D-25
    2476. 

  2476. <a name="l02412"></a>02412     weight(56) =   0.171557314767D-28
    2477. 

  2477. <a name="l02413"></a>02413     weight(57) =   0.133255961176D-31
    2478. 

  2478. <a name="l02414"></a>02414     weight(58) =   0.377162672698D-35
    2479. 

  2479. <a name="l02415"></a>02415     weight(59) =   0.243974758810D-39
    2480. 

  2480. <a name="l02416"></a>02416     weight(60) =   0.110958724796D-44
    2481. 

  2481. <a name="l02417"></a>02417 
    2482. 

  2482. <a name="l02418"></a>02418   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 64 ) <span class="keyword">then</span>
    2483. 

  2483. <a name="l02419"></a>02419 
    2484. 

  2484. <a name="l02420"></a>02420     xtab( 1) =   -10.5261231680D+00
    2485. 

  2485. <a name="l02421"></a>02421     xtab( 2) =   -9.89528758683D+00
    2486. 

  2486. <a name="l02422"></a>02422     xtab( 3) =   -9.37315954965D+00
    2487. 

  2487. <a name="l02423"></a>02423     xtab( 4) =   -8.90724909996D+00
    2488. 

  2488. <a name="l02424"></a>02424     xtab( 5) =   -8.47752908338D+00
    2489. 

  2489. <a name="l02425"></a>02425     xtab( 6) =   -8.07368728501D+00
    2490. 

  2490. <a name="l02426"></a>02426     xtab( 7) =   -7.68954016404D+00
    2491. 

  2491. <a name="l02427"></a>02427     xtab( 8) =   -7.32101303278D+00
    2492. 

  2492. <a name="l02428"></a>02428     xtab( 9) =   -6.96524112055D+00
    2493. 

  2493. <a name="l02429"></a>02429     xtab(10) =   -6.62011226264D+00
    2494. 

  2494. <a name="l02430"></a>02430     xtab(11) =   -6.28401122877D+00
    2495. 

  2495. <a name="l02431"></a>02431     xtab(12) =   -5.95566632680D+00
    2496. 

  2496. <a name="l02432"></a>02432     xtab(13) =   -5.63405216435D+00
    2497. 

  2497. <a name="l02433"></a>02433     xtab(14) =   -5.31832522463D+00
    2498. 

  2498. <a name="l02434"></a>02434     xtab(15) =   -5.00777960220D+00
    2499. 

  2499. <a name="l02435"></a>02435     xtab(16) =   -4.70181564741D+00
    2500. 

  2500. <a name="l02436"></a>02436     xtab(17) =   -4.39991716823D+00
    2501. 

  2501. <a name="l02437"></a>02437     xtab(18) =   -4.10163447457D+00
    2502. 

  2502. <a name="l02438"></a>02438     xtab(19) =   -3.80657151395D+00
    2503. 

  2503. <a name="l02439"></a>02439     xtab(20) =   -3.51437593574D+00
    2504. 

  2504. <a name="l02440"></a>02440     xtab(21) =   -3.22473129199D+00
    2505. 

  2505. <a name="l02441"></a>02441     xtab(22) =   -2.93735082300D+00
    2506. 

  2506. <a name="l02442"></a>02442     xtab(23) =   -2.65197243543D+00
    2507. 

  2507. <a name="l02443"></a>02443     xtab(24) =   -2.36835458863D+00
    2508. 

  2508. <a name="l02444"></a>02444     xtab(25) =   -2.08627287988D+00
    2509. 

  2509. <a name="l02445"></a>02445     xtab(26) =   -1.80551717147D+00
    2510. 

  2510. <a name="l02446"></a>02446     xtab(27) =   -1.52588914021D+00
    2511. 

  2511. <a name="l02447"></a>02447     xtab(28) =   -1.24720015694D+00
    2512. 

  2512. <a name="l02448"></a>02448     xtab(29) =  -0.969269423071D+00
    2513. 

  2513. <a name="l02449"></a>02449     xtab(30) =  -0.691922305810D+00
    2514. 

  2514. <a name="l02450"></a>02450     xtab(31) =  -0.414988824121D+00
    2515. 

  2515. <a name="l02451"></a>02451     xtab(32) =  -0.138302244987D+00
    2516. 

  2516. <a name="l02452"></a>02452     xtab(33) =   0.138302244987D+00
    2517. 

  2517. <a name="l02453"></a>02453     xtab(34) =   0.414988824121D+00
    2518. 

  2518. <a name="l02454"></a>02454     xtab(35) =   0.691922305810D+00
    2519. 

  2519. <a name="l02455"></a>02455     xtab(36) =   0.969269423071D+00
    2520. 

  2520. <a name="l02456"></a>02456     xtab(37) =    1.24720015694D+00
    2521. 

  2521. <a name="l02457"></a>02457     xtab(38) =    1.52588914021D+00
    2522. 

  2522. <a name="l02458"></a>02458     xtab(39) =    1.80551717147D+00
    2523. 

  2523. <a name="l02459"></a>02459     xtab(40) =    2.08627287988D+00
    2524. 

  2524. <a name="l02460"></a>02460     xtab(41) =    2.36835458863D+00
    2525. 

  2525. <a name="l02461"></a>02461     xtab(42) =    2.65197243543D+00
    2526. 

  2526. <a name="l02462"></a>02462     xtab(43) =    2.93735082300D+00
    2527. 

  2527. <a name="l02463"></a>02463     xtab(44) =    3.22473129199D+00
    2528. 

  2528. <a name="l02464"></a>02464     xtab(45) =    3.51437593574D+00
    2529. 

  2529. <a name="l02465"></a>02465     xtab(46) =    3.80657151395D+00
    2530. 

  2530. <a name="l02466"></a>02466     xtab(47) =    4.10163447457D+00
    2531. 

  2531. <a name="l02467"></a>02467     xtab(48) =    4.39991716823D+00
    2532. 

  2532. <a name="l02468"></a>02468     xtab(49) =    4.70181564741D+00
    2533. 

  2533. <a name="l02469"></a>02469     xtab(50) =    5.00777960220D+00
    2534. 

  2534. <a name="l02470"></a>02470     xtab(51) =    5.31832522463D+00
    2535. 

  2535. <a name="l02471"></a>02471     xtab(52) =    5.63405216435D+00
    2536. 

  2536. <a name="l02472"></a>02472     xtab(53) =    5.95566632680D+00
    2537. 

  2537. <a name="l02473"></a>02473     xtab(54) =    6.28401122877D+00
    2538. 

  2538. <a name="l02474"></a>02474     xtab(55) =    6.62011226264D+00
    2539. 

  2539. <a name="l02475"></a>02475     xtab(56) =    6.96524112055D+00
    2540. 

  2540. <a name="l02476"></a>02476     xtab(57) =    7.32101303278D+00
    2541. 

  2541. <a name="l02477"></a>02477     xtab(58) =    7.68954016404D+00
    2542. 

  2542. <a name="l02478"></a>02478     xtab(59) =    8.07368728501D+00
    2543. 

  2543. <a name="l02479"></a>02479     xtab(60) =    8.47752908338D+00
    2544. 

  2544. <a name="l02480"></a>02480     xtab(61) =    8.90724909996D+00
    2545. 

  2545. <a name="l02481"></a>02481     xtab(62) =    9.37315954965D+00
    2546. 

  2546. <a name="l02482"></a>02482     xtab(63) =    9.89528758683D+00
    2547. 

  2547. <a name="l02483"></a>02483     xtab(64) =    10.5261231680D+00
    2548. 

  2548. <a name="l02484"></a>02484 
    2549. 

  2549. <a name="l02485"></a>02485     weight( 1) =   0.553570653584D-48
    2550. 

  2550. <a name="l02486"></a>02486     weight( 2) =   0.167974799010D-42
    2551. 

  2551. <a name="l02487"></a>02487     weight( 3) =   0.342113801099D-38
    2552. 

  2552. <a name="l02488"></a>02488     weight( 4) =   0.155739062462D-34
    2553. 

  2553. <a name="l02489"></a>02489     weight( 5) =   0.254966089910D-31
    2554. 

  2554. <a name="l02490"></a>02490     weight( 6) =   0.192910359546D-28
    2555. 

  2555. <a name="l02491"></a>02491     weight( 7) =   0.786179778889D-26
    2556. 

  2556. <a name="l02492"></a>02492     weight( 8) =   0.191170688329D-23
    2557. 

  2557. <a name="l02493"></a>02493     weight( 9) =   0.298286278427D-21
    2558. 

  2558. <a name="l02494"></a>02494     weight(10) =   0.315225456649D-19
    2559. 

  2559. <a name="l02495"></a>02495     weight(11) =   0.235188471067D-17
    2560. 

  2560. <a name="l02496"></a>02496     weight(12) =   0.128009339117D-15
    2561. 

  2561. <a name="l02497"></a>02497     weight(13) =   0.521862372645D-14
    2562. 

  2562. <a name="l02498"></a>02498     weight(14) =   0.162834073070D-12
    2563. 

  2563. <a name="l02499"></a>02499     weight(15) =   0.395917776693D-11
    2564. 

  2564. <a name="l02500"></a>02500     weight(16) =   0.761521725012D-10
    2565. 

  2565. <a name="l02501"></a>02501     weight(17) =   0.117361674232D-08
    2566. 

  2566. <a name="l02502"></a>02502     weight(18) =   0.146512531647D-07
    2567. 

  2567. <a name="l02503"></a>02503     weight(19) =   0.149553293672D-06
    2568. 

  2568. <a name="l02504"></a>02504     weight(20) =   0.125834025103D-05
    2569. 

  2569. <a name="l02505"></a>02505     weight(21) =   0.878849923082D-05
    2570. 

  2570. <a name="l02506"></a>02506     weight(22) =   0.512592913577D-04
    2571. 

  2571. <a name="l02507"></a>02507     weight(23) =   0.250983698512D-03
    2572. 

  2572. <a name="l02508"></a>02508     weight(24) =   0.103632909950D-02
    2573. 

  2573. <a name="l02509"></a>02509     weight(25) =   0.362258697852D-02
    2574. 

  2574. <a name="l02510"></a>02510     weight(26) =   0.107560405098D-01
    2575. 

  2575. <a name="l02511"></a>02511     weight(27) =   0.272031289536D-01
    2576. 

  2576. <a name="l02512"></a>02512     weight(28) =   0.587399819634D-01
    2577. 

  2577. <a name="l02513"></a>02513     weight(29) =   0.108498349306D+00
    2578. 

  2578. <a name="l02514"></a>02514     weight(30) =   0.171685842349D+00
    2579. 

  2579. <a name="l02515"></a>02515     weight(31) =   0.232994786062D+00
    2580. 

  2580. <a name="l02516"></a>02516     weight(32) =   0.271377424940D+00
    2581. 

  2581. <a name="l02517"></a>02517     weight(33) =   0.271377424940D+00
    2582. 

  2582. <a name="l02518"></a>02518     weight(34) =   0.232994786062D+00
    2583. 

  2583. <a name="l02519"></a>02519     weight(35) =   0.171685842349D+00
    2584. 

  2584. <a name="l02520"></a>02520     weight(36) =   0.108498349306D+00
    2585. 

  2585. <a name="l02521"></a>02521     weight(37) =   0.587399819634D-01
    2586. 

  2586. <a name="l02522"></a>02522     weight(38) =   0.272031289536D-01
    2587. 

  2587. <a name="l02523"></a>02523     weight(39) =   0.107560405098D-01
    2588. 

  2588. <a name="l02524"></a>02524     weight(40) =   0.362258697852D-02
    2589. 

  2589. <a name="l02525"></a>02525     weight(41) =   0.103632909950D-02
    2590. 

  2590. <a name="l02526"></a>02526     weight(42) =   0.250983698512D-03
    2591. 

  2591. <a name="l02527"></a>02527     weight(43) =   0.512592913577D-04
    2592. 

  2592. <a name="l02528"></a>02528     weight(44) =   0.878849923082D-05
    2593. 

  2593. <a name="l02529"></a>02529     weight(45) =   0.125834025103D-05
    2594. 

  2594. <a name="l02530"></a>02530     weight(46) =   0.149553293672D-06
    2595. 

  2595. <a name="l02531"></a>02531     weight(47) =   0.146512531647D-07
    2596. 

  2596. <a name="l02532"></a>02532     weight(48) =   0.117361674232D-08
    2597. 

  2597. <a name="l02533"></a>02533     weight(49) =   0.761521725012D-10
    2598. 

  2598. <a name="l02534"></a>02534     weight(50) =   0.395917776693D-11
    2599. 

  2599. <a name="l02535"></a>02535     weight(51) =   0.162834073070D-12
    2600. 

  2600. <a name="l02536"></a>02536     weight(52) =   0.521862372645D-14
    2601. 

  2601. <a name="l02537"></a>02537     weight(53) =   0.128009339117D-15
    2602. 

  2602. <a name="l02538"></a>02538     weight(54) =   0.235188471067D-17
    2603. 

  2603. <a name="l02539"></a>02539     weight(55) =   0.315225456649D-19
    2604. 

  2604. <a name="l02540"></a>02540     weight(56) =   0.298286278427D-21
    2605. 

  2605. <a name="l02541"></a>02541     weight(57) =   0.191170688329D-23
    2606. 

  2606. <a name="l02542"></a>02542     weight(58) =   0.786179778889D-26
    2607. 

  2607. <a name="l02543"></a>02543     weight(59) =   0.192910359546D-28
    2608. 

  2608. <a name="l02544"></a>02544     weight(60) =   0.254966089910D-31
    2609. 

  2609. <a name="l02545"></a>02545     weight(61) =   0.155739062462D-34
    2610. 

  2610. <a name="l02546"></a>02546     weight(62) =   0.342113801099D-38
    2611. 

  2611. <a name="l02547"></a>02547     weight(63) =   0.167974799010D-42
    2612. 

  2612. <a name="l02548"></a>02548     weight(64) =   0.553570653584D-48
    2613. 

  2613. <a name="l02549"></a>02549 
    2614. 

  2614. <a name="l02550"></a>02550   <span class="keyword">else</span>
    2615. 

  2615. <a name="l02551"></a>02551 
    2616. 

  2616. <a name="l02552"></a>02552     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    2617. 

  2617. <a name="l02553"></a>02553     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;HERMITE_SET - Fatal error!&#39;</span>
    2618. 

  2618. <a name="l02554"></a>02554     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    2619. 

  2619. <a name="l02555"></a>02555     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 1 to 20,&#39;</span>
    2620. 

  2620. <a name="l02556"></a>02556     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  30, 32, 40, 50, 60 and 64.&#39;</span>
    2621. 

  2621. <a name="l02557"></a>02557     stop
    2622. 

  2622. <a name="l02558"></a>02558 
    2623. 

  2623. <a name="l02559"></a>02559   <span class="keyword">end if</span>
    2624. 

  2624. <a name="l02560"></a>02560 
    2625. 

  2625. <a name="l02561"></a>02561   return
    2626. 

  2626. <a name="l02562"></a>02562 <span class="keyword">end</span>
    2627. 

  2627. <a name="l02563"></a><a class="code" href="quadrule_8f90.html#a85d3b6982259e08e48b68f923ebaf48a">02563</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a85d3b6982259e08e48b68f923ebaf48a">jacobi_com</a> ( norder, xtab, weight, alpha, beta )
    2628. 

  2628. <a name="l02564"></a>02564 <span class="comment">!</span>
    2629. 

  2629. <a name="l02565"></a>02565 <span class="comment">!*******************************************************************************</span>
    2630. 

  2630. <a name="l02566"></a>02566 <span class="comment">!</span>
    2631. 

  2631. <a name="l02567"></a>02567 <span class="comment">!! JACOBI_COM computes the abscissa and weights for Gauss-Jacobi quadrature.</span>
    2632. 

  2632. <a name="l02568"></a>02568 <span class="comment">!</span>
    2633. 

  2633. <a name="l02569"></a>02569 <span class="comment">!</span>
    2634. 

  2634. <a name="l02570"></a>02570 <span class="comment">!  Integration interval:</span>
    2635. 

  2635. <a name="l02571"></a>02571 <span class="comment">!</span>
    2636. 

  2636. <a name="l02572"></a>02572 <span class="comment">!    [ -1, 1 ]</span>
    2637. 

  2637. <a name="l02573"></a>02573 <span class="comment">!</span>
    2638. 

  2638. <a name="l02574"></a>02574 <span class="comment">!  Weight function:</span>
    2639. 

  2639. <a name="l02575"></a>02575 <span class="comment">!</span>
    2640. 

  2640. <a name="l02576"></a>02576 <span class="comment">!    1.0D+00</span>
    2641. 

  2641. <a name="l02577"></a>02577 <span class="comment">!</span>
    2642. 

  2642. <a name="l02578"></a>02578 <span class="comment">!  Integral to approximate:</span>
    2643. 

  2643. <a name="l02579"></a>02579 <span class="comment">!</span>
    2644. 

  2644. <a name="l02580"></a>02580 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) (1+X)**ALPHA * (1-X)**BETA * F(X) dX</span>
    2645. 

  2645. <a name="l02581"></a>02581 <span class="comment">!</span>
    2646. 

  2646. <a name="l02582"></a>02582 <span class="comment">!  Approximate integral:</span>
    2647. 

  2647. <a name="l02583"></a>02583 <span class="comment">!</span>
    2648. 

  2648. <a name="l02584"></a>02584 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    2649. 

  2649. <a name="l02585"></a>02585 <span class="comment">!</span>
    2650. 

  2650. <a name="l02586"></a>02586 <span class="comment">!  Reference:</span>
    2651. 

  2651. <a name="l02587"></a>02587 <span class="comment">!</span>
    2652. 

  2652. <a name="l02588"></a>02588 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    2653. 

  2653. <a name="l02589"></a>02589 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    2654. 

  2654. <a name="l02590"></a>02590 <span class="comment">!    Prentice Hall, 1966.</span>
    2655. 

  2655. <a name="l02591"></a>02591 <span class="comment">!</span>
    2656. 

  2656. <a name="l02592"></a>02592 <span class="comment">!  Modified:</span>
    2657. 

  2657. <a name="l02593"></a>02593 <span class="comment">!</span>
    2658. 

  2658. <a name="l02594"></a>02594 <span class="comment">!    09 September 2000</span>
    2659. 

  2659. <a name="l02595"></a>02595 <span class="comment">!</span>
    2660. 

  2660. <a name="l02596"></a>02596 <span class="comment">!  Parameters:</span>
    2661. 

  2661. <a name="l02597"></a>02597 <span class="comment">!</span>
    2662. 

  2662. <a name="l02598"></a>02598 <span class="comment">!    Input, integer NORDER, the order of the quadrature rule to be computed.</span>
    2663. 

  2663. <a name="l02599"></a>02599 <span class="comment">!</span>
    2664. 

  2664. <a name="l02600"></a>02600 <span class="comment">!    Output, double precision XTAB(NORDER), the Gauss-Jacobi abscissas.</span>
    2665. 

  2665. <a name="l02601"></a>02601 <span class="comment">!</span>
    2666. 

  2666. <a name="l02602"></a>02602 <span class="comment">!    Output, double precision WEIGHT(NORDER), the Gauss-Jacobi weights.</span>
    2667. 

  2667. <a name="l02603"></a>02603 <span class="comment">!</span>
    2668. 

  2668. <a name="l02604"></a>02604 <span class="comment">!    Input, double precision ALPHA, BETA, the exponents of (1+X) and</span>
    2669. 

  2669. <a name="l02605"></a>02605 <span class="comment">!    (1-X) in the quadrature rule.  For simple Gauss-Legendre quadrature,</span>
    2670. 

  2670. <a name="l02606"></a>02606 <span class="comment">!    set ALPHA = BETA = 0.0.</span>
    2671. 

  2671. <a name="l02607"></a>02607 <span class="comment">!</span>
    2672. 

  2672. <a name="l02608"></a>02608   <span class="keyword">implicit none</span>
    2673. 

  2673. <a name="l02609"></a>02609 <span class="comment">!</span>
    2674. 

  2674. <a name="l02610"></a>02610   <span class="keywordtype">integer</span> norder
    2675. 

  2675. <a name="l02611"></a>02611 <span class="comment">!</span>
    2676. 

  2676. <a name="l02612"></a>02612   <span class="keywordtype">double precision</span> alpha
    2677. 

  2677. <a name="l02613"></a>02613   <span class="keywordtype">double precision</span> an
    2678. 

  2678. <a name="l02614"></a>02614   <span class="keywordtype">double precision</span> b(norder)
    2679. 

  2679. <a name="l02615"></a>02615   <span class="keywordtype">double precision</span> beta
    2680. 

  2680. <a name="l02616"></a>02616   <span class="keywordtype">double precision</span> bn
    2681. 

  2681. <a name="l02617"></a>02617   <span class="keywordtype">double precision</span> c(norder)
    2682. 

  2682. <a name="l02618"></a>02618   <span class="keywordtype">double precision</span> cc
    2683. 

  2683. <a name="l02619"></a>02619   <span class="keywordtype">double precision</span> delta
    2684. 

  2684. <a name="l02620"></a>02620   <span class="keywordtype">double precision</span> dp2
    2685. 

  2685. <a name="l02621"></a>02621   <span class="keywordtype">double precision</span> log_gamma
    2686. 

  2686. <a name="l02622"></a>02622   <span class="keywordtype">integer</span> i
    2687. 

  2687. <a name="l02623"></a>02623   <span class="keywordtype">double precision</span> p1
    2688. 

  2688. <a name="l02624"></a>02624   <span class="keywordtype">double precision</span> r1
    2689. 

  2689. <a name="l02625"></a>02625   <span class="keywordtype">double precision</span> r2
    2690. 

  2690. <a name="l02626"></a>02626   <span class="keywordtype">double precision</span> r3
    2691. 

  2691. <a name="l02627"></a>02627   <span class="keywordtype">double precision</span> temp
    2692. 

  2692. <a name="l02628"></a>02628   <span class="keywordtype">double precision</span> weight(norder)
    2693. 

  2693. <a name="l02629"></a>02629   <span class="keywordtype">double precision</span> x
    2694. 

  2694. <a name="l02630"></a>02630   <span class="keywordtype">double precision</span> xtab(norder)
    2695. 

  2695. <a name="l02631"></a>02631 <span class="comment">!</span>
    2696. 

  2696. <a name="l02632"></a>02632 <span class="comment">!  Set the recursion coefficients.</span>
    2697. 

  2697. <a name="l02633"></a>02633 <span class="comment">!</span>
    2698. 

  2698. <a name="l02634"></a>02634   <span class="keyword">do</span> i = 1, norder
    2699. 

  2699. <a name="l02635"></a>02635 
    2700. 

  2700. <a name="l02636"></a>02636     <span class="keyword">if</span> ( alpha + beta == 0.0D+00 .or. beta - alpha == 0.0D+00) <span class="keyword">then</span>
    2701. 

  2701. <a name="l02637"></a>02637 
    2702. 

  2702. <a name="l02638"></a>02638       b(i) = 0.0D+00
    2703. 

  2703. <a name="l02639"></a>02639 
    2704. 

  2704. <a name="l02640"></a>02640     <span class="keyword">else</span>
    2705. 

  2705. <a name="l02641"></a>02641 
    2706. 

  2706. <a name="l02642"></a>02642       b(i) = ( alpha + beta ) * ( beta - alpha ) / &amp;
    2707. 

  2707. <a name="l02643"></a>02643             ( ( alpha + beta + dble ( 2 * i ) ) &amp;
    2708. 

  2708. <a name="l02644"></a>02644             * ( alpha + beta + dble ( 2 * i - 2 ) ) )
    2709. 

  2709. <a name="l02645"></a>02645 
    2710. 

  2710. <a name="l02646"></a>02646     <span class="keyword">end if</span>
    2711. 

  2711. <a name="l02647"></a>02647 
    2712. 

  2712. <a name="l02648"></a>02648     <span class="keyword">if</span> ( i == 1 ) <span class="keyword">then</span>
    2713. 

  2713. <a name="l02649"></a>02649 
    2714. 

  2714. <a name="l02650"></a>02650       c(i) = 0.0D+00
    2715. 

  2715. <a name="l02651"></a>02651 
    2716. 

  2716. <a name="l02652"></a>02652     <span class="keyword">else</span>
    2717. 

  2717. <a name="l02653"></a>02653 
    2718. 

  2718. <a name="l02654"></a>02654       c(i) = 4.0D+00 * dble ( i - 1 ) * ( alpha + dble ( i - 1 ) ) &amp;
    2719. 

  2719. <a name="l02655"></a>02655             * ( beta + dble ( i - 1 ) ) &amp;
    2720. 

  2720. <a name="l02656"></a>02656             * ( alpha + beta + dble ( i - 1 ) ) / &amp;
    2721. 

  2721. <a name="l02657"></a>02657             ( ( alpha + beta + dble ( 2 * i - 1 ) ) &amp;
    2722. 

  2722. <a name="l02658"></a>02658             * ( alpha + beta + dble ( 2 * i - 2 ) )**2 &amp;
    2723. 

  2723. <a name="l02659"></a>02659             * ( alpha + beta + dble ( 2 * i - 3 ) ) )
    2724. 

  2724. <a name="l02660"></a>02660 
    2725. 

  2725. <a name="l02661"></a>02661     <span class="keyword">end if</span>
    2726. 

  2726. <a name="l02662"></a>02662 
    2727. 

  2727. <a name="l02663"></a>02663   <span class="keyword">end do</span>
    2728. 

  2728. <a name="l02664"></a>02664 
    2729. 

  2729. <a name="l02665"></a>02665   delta = exp ( log_gamma ( alpha + 1.0D+00 ) + log_gamma ( beta + 1.0D+00) &amp;
    2730. 

  2730. <a name="l02666"></a>02666     + log_gamma ( alpha + beta + 2.0D+00 ) )
    2731. 

  2731. <a name="l02667"></a>02667 
    2732. 

  2732. <a name="l02668"></a>02668   cc = delta * 2.0D+00**( alpha + beta + 1.0D+00 ) * product ( c(2:norder) )
    2733. 

  2733. <a name="l02669"></a>02669 
    2734. 

  2734. <a name="l02670"></a>02670   <span class="keyword">do</span> i = 1, norder
    2735. 

  2735. <a name="l02671"></a>02671 
    2736. 

  2736. <a name="l02672"></a>02672     <span class="keyword">if</span> ( i == 1 ) <span class="keyword">then</span>
    2737. 

  2737. <a name="l02673"></a>02673 
    2738. 

  2738. <a name="l02674"></a>02674       an = alpha / dble ( norder )
    2739. 

  2739. <a name="l02675"></a>02675       bn = beta / dble ( norder )
    2740. 

  2740. <a name="l02676"></a>02676 
    2741. 

  2741. <a name="l02677"></a>02677       r1 = ( 1.0D+00 + alpha ) * ( 2.78D+00 / ( 4.0D+00+ dble ( norder**2 ) ) &amp;
    2742. 

  2742. <a name="l02678"></a>02678         + 0.768D+00 * an / dble ( norder ) )
    2743. 

  2743. <a name="l02679"></a>02679 
    2744. 

  2744. <a name="l02680"></a>02680       r2 = 1.0D+00 + 1.48D+00 * an + 0.96D+00 * bn &amp;
    2745. 

  2745. <a name="l02681"></a>02681         + 0.452D+00 * an**2 + 0.83D+00 * an * bn
    2746. 

  2746. <a name="l02682"></a>02682 
    2747. 

  2747. <a name="l02683"></a>02683       x = ( r2 - r1 ) / r2
    2748. 

  2748. <a name="l02684"></a>02684 
    2749. 

  2749. <a name="l02685"></a>02685     <span class="keyword">else</span> <span class="keyword">if</span> ( i == 2 ) <span class="keyword">then</span>
    2750. 

  2750. <a name="l02686"></a>02686 
    2751. 

  2751. <a name="l02687"></a>02687       r1 = ( 4.1D+00 + alpha ) / &amp;
    2752. 

  2752. <a name="l02688"></a>02688         ( ( 1.0D+00 + alpha ) * ( 1.0D+00 + 0.156D+00 * alpha ) )
    2753. 

  2753. <a name="l02689"></a>02689 
    2754. 

  2754. <a name="l02690"></a>02690       r2 = 1.0D+00 + 0.06D+00 * ( dble ( norder ) - 8.0D+00 ) * &amp;
    2755. 

  2755. <a name="l02691"></a>02691         ( 1.0D+00 + 0.12D+00 * alpha ) / dble ( norder )
    2756. 

  2756. <a name="l02692"></a>02692 
    2757. 

  2757. <a name="l02693"></a>02693       r3 = 1.0D+00 + 0.012D+00 * beta * &amp;
    2758. 

  2758. <a name="l02694"></a>02694         ( 1.0D+00 + 0.25D+00 * abs ( alpha ) ) / dble ( norder )
    2759. 

  2759. <a name="l02695"></a>02695 
    2760. 

  2760. <a name="l02696"></a>02696       x = x - r1 * r2 * r3 * ( 1.0D+00 - x )
    2761. 

  2761. <a name="l02697"></a>02697 
    2762. 

  2762. <a name="l02698"></a>02698     <span class="keyword">else</span> <span class="keyword">if</span> ( i == 3 ) <span class="keyword">then</span>
    2763. 

  2763. <a name="l02699"></a>02699 
    2764. 

  2764. <a name="l02700"></a>02700       r1 = ( 1.67D+00 + 0.28D+00 * alpha ) / ( 1.0D+00 + 0.37D+00 * alpha )
    2765. 

  2765. <a name="l02701"></a>02701 
    2766. 

  2766. <a name="l02702"></a>02702       r2 = 1.0D+00 + 0.22D+00 * ( dble ( norder ) - 8.0D+00 ) / dble ( norder )
    2767. 

  2767. <a name="l02703"></a>02703 
    2768. 

  2768. <a name="l02704"></a>02704       r3 = 1.0D+00 + 8.0D+00 * beta / &amp;
    2769. 

  2769. <a name="l02705"></a>02705         ( ( 6.28D+00 + beta ) * dble ( norder**2 ) )
    2770. 

  2770. <a name="l02706"></a>02706 
    2771. 

  2771. <a name="l02707"></a>02707       x = x - r1 * r2 * r3 * ( xtab(1) - x )
    2772. 

  2772. <a name="l02708"></a>02708 
    2773. 

  2773. <a name="l02709"></a>02709     <span class="keyword">else</span> <span class="keyword">if</span> ( i &lt; norder - 1 ) <span class="keyword">then</span>
    2774. 

  2774. <a name="l02710"></a>02710 
    2775. 

  2775. <a name="l02711"></a>02711       x = 3.0D+00 * xtab(i-1) - 3.0D+00 * xtab(i-2) + xtab(i-3)
    2776. 

  2776. <a name="l02712"></a>02712 
    2777. 

  2777. <a name="l02713"></a>02713     <span class="keyword">else</span> <span class="keyword">if</span> ( i == norder - 1 ) <span class="keyword">then</span>
    2778. 

  2778. <a name="l02714"></a>02714 
    2779. 

  2779. <a name="l02715"></a>02715       r1 = ( 1.0D+00 + 0.235D+00 * beta ) / ( 0.766D+00 + 0.119D+00 * beta )
    2780. 

  2780. <a name="l02716"></a>02716 
    2781. 

  2781. <a name="l02717"></a>02717       r2 = 1.0D+00 / ( 1.0D+00 + 0.639D+00 * ( dble ( norder ) - 4.0D+00 ) &amp;
    2782. 

  2782. <a name="l02718"></a>02718         / ( 1.0D+00 + 0.71D+00 * ( dble ( norder ) - 4.0D+00 ) ) )
    2783. 

  2783. <a name="l02719"></a>02719 
    2784. 

  2784. <a name="l02720"></a>02720       r3 = 1.0D+00 / ( 1.0D+00 + 20.0D+00 * alpha / ( ( 7.5D+00 + alpha ) * &amp;
    2785. 

  2785. <a name="l02721"></a>02721         dble ( norder**2 ) ) )
    2786. 

  2786. <a name="l02722"></a>02722 
    2787. 

  2787. <a name="l02723"></a>02723       x = x + r1 * r2 * r3 * ( x - xtab(i-2) )
    2788. 

  2788. <a name="l02724"></a>02724 
    2789. 

  2789. <a name="l02725"></a>02725     <span class="keyword">else</span> <span class="keyword">if</span> ( i == norder ) <span class="keyword">then</span>
    2790. 

  2790. <a name="l02726"></a>02726 
    2791. 

  2791. <a name="l02727"></a>02727       r1 = ( 1.0D+00 + 0.37D+00 * beta ) / ( 1.67D+00 + 0.28D+00 * beta )
    2792. 

  2792. <a name="l02728"></a>02728 
    2793. 

  2793. <a name="l02729"></a>02729       r2 = 1.0D+00 / &amp;
    2794. 

  2794. <a name="l02730"></a>02730         ( 1.0D+00 + 0.22D+00 * ( dble ( norder ) - 8.0D+00 ) / dble ( norder ) )
    2795. 

  2795. <a name="l02731"></a>02731 
    2796. 

  2796. <a name="l02732"></a>02732       r3 = 1.0D+00 / ( 1.0D+00 + 8.0D+00 * alpha / &amp;
    2797. 

  2797. <a name="l02733"></a>02733         ( ( 6.28D+00 + alpha ) * dble ( norder**2 ) ) )
    2798. 

  2798. <a name="l02734"></a>02734 
    2799. 

  2799. <a name="l02735"></a>02735       x = x + r1 * r2 * r3 * ( x - xtab(i-2) )
    2800. 

  2800. <a name="l02736"></a>02736 
    2801. 

  2801. <a name="l02737"></a>02737     <span class="keyword">end if</span>
    2802. 

  2802. <a name="l02738"></a>02738 
    2803. 

  2803. <a name="l02739"></a>02739     call <a class="code" href="quadrule_8f90.html#a37ab0713ac179df20db1cbade4750d7c">jacobi_root </a>( x, norder, alpha, beta, dp2, p1, b, c )
    2804. 

  2804. <a name="l02740"></a>02740 
    2805. 

  2805. <a name="l02741"></a>02741     xtab(i) = x
    2806. 

  2806. <a name="l02742"></a>02742     weight(i) = cc / ( dp2 * p1 )
    2807. 

  2807. <a name="l02743"></a>02743 
    2808. 

  2808. <a name="l02744"></a>02744   <span class="keyword">end do</span>
    2809. 

  2809. <a name="l02745"></a>02745 <span class="comment">!</span>
    2810. 

  2810. <a name="l02746"></a>02746 <span class="comment">!  Reverse the order of the XTAB values.</span>
    2811. 

  2811. <a name="l02747"></a>02747 <span class="comment">!</span>
    2812. 

  2812. <a name="l02748"></a>02748   call <a class="code" href="quadrule_8f90.html#a7841cf442902dd98d08b6a4d89a9a7bf">dvec_reverse </a>( norder, xtab )
    2813. 

  2813. <a name="l02749"></a>02749 
    2814. 

  2814. <a name="l02750"></a>02750   return
    2815. 

  2815. <a name="l02751"></a>02751 <span class="keyword">end</span>
    2816. 

  2816. <a name="l02752"></a><a class="code" href="quadrule_8f90.html#a23d5d91dbc68f334297c326bf251545b">02752</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a23d5d91dbc68f334297c326bf251545b">jacobi_recur</a> ( p2, dp2, p1, x, norder, alpha, beta, b, c )
    2817. 

  2817. <a name="l02753"></a>02753 <span class="comment">!</span>
    2818. 

  2818. <a name="l02754"></a>02754 <span class="comment">!*******************************************************************************</span>
    2819. 

  2819. <a name="l02755"></a>02755 <span class="comment">!</span>
    2820. 

  2820. <a name="l02756"></a>02756 <span class="comment">!! JACOBI_RECUR finds the value and derivative of a Jacobi polynomial.</span>
    2821. 

  2821. <a name="l02757"></a>02757 <span class="comment">!</span>
    2822. 

  2822. <a name="l02758"></a>02758 <span class="comment">!</span>
    2823. 

  2823. <a name="l02759"></a>02759 <span class="comment">!  Reference:</span>
    2824. 

  2824. <a name="l02760"></a>02760 <span class="comment">!</span>
    2825. 

  2825. <a name="l02761"></a>02761 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    2826. 

  2826. <a name="l02762"></a>02762 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    2827. 

  2827. <a name="l02763"></a>02763 <span class="comment">!    Prentice Hall, 1966.</span>
    2828. 

  2828. <a name="l02764"></a>02764 <span class="comment">!</span>
    2829. 

  2829. <a name="l02765"></a>02765 <span class="comment">!  Modified:</span>
    2830. 

  2830. <a name="l02766"></a>02766 <span class="comment">!</span>
    2831. 

  2831. <a name="l02767"></a>02767 <span class="comment">!    19 September 1998</span>
    2832. 

  2832. <a name="l02768"></a>02768 <span class="comment">!</span>
    2833. 

  2833. <a name="l02769"></a>02769 <span class="comment">!  Parameters:</span>
    2834. 

  2834. <a name="l02770"></a>02770 <span class="comment">!</span>
    2835. 

  2835. <a name="l02771"></a>02771 <span class="comment">!    Output, double precision P2, the value of J(NORDER)(X).</span>
    2836. 

  2836. <a name="l02772"></a>02772 <span class="comment">!</span>
    2837. 

  2837. <a name="l02773"></a>02773 <span class="comment">!    Output, double precision DP2, the value of J&#39;(NORDER)(X).</span>
    2838. 

  2838. <a name="l02774"></a>02774 <span class="comment">!</span>
    2839. 

  2839. <a name="l02775"></a>02775 <span class="comment">!    Output, double precision P1, the value of J(NORDER-1)(X).</span>
    2840. 

  2840. <a name="l02776"></a>02776 <span class="comment">!</span>
    2841. 

  2841. <a name="l02777"></a>02777 <span class="comment">!    Input, double precision X, the point at which polynomials are evaluated.</span>
    2842. 

  2842. <a name="l02778"></a>02778 <span class="comment">!</span>
    2843. 

  2843. <a name="l02779"></a>02779 <span class="comment">!    Input, integer NORDER, the order of the polynomial to be computed.</span>
    2844. 

  2844. <a name="l02780"></a>02780 <span class="comment">!</span>
    2845. 

  2845. <a name="l02781"></a>02781 <span class="comment">!    Input, double precision ALPHA, BETA, the exponents of (1+X) and</span>
    2846. 

  2846. <a name="l02782"></a>02782 <span class="comment">!    (1-X) in the quadrature rule.</span>
    2847. 

  2847. <a name="l02783"></a>02783 <span class="comment">!</span>
    2848. 

  2848. <a name="l02784"></a>02784 <span class="comment">!    Input, double precision B(NORDER), C(NORDER), the recursion</span>
    2849. 

  2849. <a name="l02785"></a>02785 <span class="comment">!    coefficients.</span>
    2850. 

  2850. <a name="l02786"></a>02786 <span class="comment">!</span>
    2851. 

  2851. <a name="l02787"></a>02787   <span class="keyword">implicit none</span>
    2852. 

  2852. <a name="l02788"></a>02788 <span class="comment">!</span>
    2853. 

  2853. <a name="l02789"></a>02789   <span class="keywordtype">integer</span> norder
    2854. 

  2854. <a name="l02790"></a>02790 <span class="comment">!</span>
    2855. 

  2855. <a name="l02791"></a>02791   <span class="keywordtype">double precision</span> alpha
    2856. 

  2856. <a name="l02792"></a>02792   <span class="keywordtype">double precision</span> b(norder)
    2857. 

  2857. <a name="l02793"></a>02793   <span class="keywordtype">double precision</span> beta
    2858. 

  2858. <a name="l02794"></a>02794   <span class="keywordtype">double precision</span> c(norder)
    2859. 

  2859. <a name="l02795"></a>02795   <span class="keywordtype">double precision</span> dp0
    2860. 

  2860. <a name="l02796"></a>02796   <span class="keywordtype">double precision</span> dp1
    2861. 

  2861. <a name="l02797"></a>02797   <span class="keywordtype">double precision</span> dp2
    2862. 

  2862. <a name="l02798"></a>02798   <span class="keywordtype">integer</span> i
    2863. 

  2863. <a name="l02799"></a>02799   <span class="keywordtype">double precision</span> p0
    2864. 

  2864. <a name="l02800"></a>02800   <span class="keywordtype">double precision</span> p1
    2865. 

  2865. <a name="l02801"></a>02801   <span class="keywordtype">double precision</span> p2
    2866. 

  2866. <a name="l02802"></a>02802   <span class="keywordtype">double precision</span> x
    2867. 

  2867. <a name="l02803"></a>02803 <span class="comment">!</span>
    2868. 

  2868. <a name="l02804"></a>02804   p1 = 1.0D+00
    2869. 

  2869. <a name="l02805"></a>02805   dp1 = 0.0D+00
    2870. 

  2870. <a name="l02806"></a>02806 
    2871. 

  2871. <a name="l02807"></a>02807   p2 = x + ( alpha - beta ) / ( alpha + beta + 2.0D+00 )
    2872. 

  2872. <a name="l02808"></a>02808   dp2 = 1.0D+00
    2873. 

  2873. <a name="l02809"></a>02809 
    2874. 

  2874. <a name="l02810"></a>02810   <span class="keyword">do</span> i = 2, norder
    2875. 

  2875. <a name="l02811"></a>02811 
    2876. 

  2876. <a name="l02812"></a>02812     p0 = p1
    2877. 

  2877. <a name="l02813"></a>02813     dp0 = dp1
    2878. 

  2878. <a name="l02814"></a>02814 
    2879. 

  2879. <a name="l02815"></a>02815     p1 = p2
    2880. 

  2880. <a name="l02816"></a>02816     dp1 = dp2
    2881. 

  2881. <a name="l02817"></a>02817 
    2882. 

  2882. <a name="l02818"></a>02818     p2 = ( x - b(i) ) * p1 - c(i) * p0
    2883. 

  2883. <a name="l02819"></a>02819     dp2 = ( x - b(i) ) * dp1 + p1 - c(i) * dp0
    2884. 

  2884. <a name="l02820"></a>02820 
    2885. 

  2885. <a name="l02821"></a>02821   <span class="keyword">end do</span>
    2886. 

  2886. <a name="l02822"></a>02822 
    2887. 

  2887. <a name="l02823"></a>02823   return
    2888. 

  2888. <a name="l02824"></a>02824 <span class="keyword">end</span>
    2889. 

  2889. <a name="l02825"></a><a class="code" href="quadrule_8f90.html#a37ab0713ac179df20db1cbade4750d7c">02825</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a37ab0713ac179df20db1cbade4750d7c">jacobi_root</a> ( x, norder, alpha, beta, dp2, p1, b, c )
    2890. 

  2890. <a name="l02826"></a>02826 <span class="comment">!</span>
    2891. 

  2891. <a name="l02827"></a>02827 <span class="comment">!*******************************************************************************</span>
    2892. 

  2892. <a name="l02828"></a>02828 <span class="comment">!</span>
    2893. 

  2893. <a name="l02829"></a>02829 <span class="comment">!! JACOBI_ROOT improves an approximate root of a Jacobi polynomial.</span>
    2894. 

  2894. <a name="l02830"></a>02830 <span class="comment">!</span>
    2895. 

  2895. <a name="l02831"></a>02831 <span class="comment">!</span>
    2896. 

  2896. <a name="l02832"></a>02832 <span class="comment">!  Reference:</span>
    2897. 

  2897. <a name="l02833"></a>02833 <span class="comment">!</span>
    2898. 

  2898. <a name="l02834"></a>02834 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    2899. 

  2899. <a name="l02835"></a>02835 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    2900. 

  2900. <a name="l02836"></a>02836 <span class="comment">!    Prentice Hall, 1966.</span>
    2901. 

  2901. <a name="l02837"></a>02837 <span class="comment">!</span>
    2902. 

  2902. <a name="l02838"></a>02838 <span class="comment">!  Modified:</span>
    2903. 

  2903. <a name="l02839"></a>02839 <span class="comment">!</span>
    2904. 

  2904. <a name="l02840"></a>02840 <span class="comment">!    09 December 2000</span>
    2905. 

  2905. <a name="l02841"></a>02841 <span class="comment">!</span>
    2906. 

  2906. <a name="l02842"></a>02842 <span class="comment">!  Parameters:</span>
    2907. 

  2907. <a name="l02843"></a>02843 <span class="comment">!</span>
    2908. 

  2908. <a name="l02844"></a>02844 <span class="comment">!    Input/output, double precision X, the approximate root, which</span>
    2909. 

  2909. <a name="l02845"></a>02845 <span class="comment">!    should be improved on output.</span>
    2910. 

  2910. <a name="l02846"></a>02846 <span class="comment">!</span>
    2911. 

  2911. <a name="l02847"></a>02847 <span class="comment">!    Input, integer NORDER, the order of the polynomial to be computed.</span>
    2912. 

  2912. <a name="l02848"></a>02848 <span class="comment">!</span>
    2913. 

  2913. <a name="l02849"></a>02849 <span class="comment">!    Input, double precision ALPHA, BETA, the exponents of (1+X) and</span>
    2914. 

  2914. <a name="l02850"></a>02850 <span class="comment">!    (1-X) in the quadrature rule.</span>
    2915. 

  2915. <a name="l02851"></a>02851 <span class="comment">!</span>
    2916. 

  2916. <a name="l02852"></a>02852 <span class="comment">!    Output, double precision DP2, the value of J&#39;(NORDER)(X).</span>
    2917. 

  2917. <a name="l02853"></a>02853 <span class="comment">!</span>
    2918. 

  2918. <a name="l02854"></a>02854 <span class="comment">!    Output, double precision P1, the value of J(NORDER-1)(X).</span>
    2919. 

  2919. <a name="l02855"></a>02855 <span class="comment">!</span>
    2920. 

  2920. <a name="l02856"></a>02856 <span class="comment">!    Input, double precision B(NORDER), C(NORDER), the recursion coefficients.</span>
    2921. 

  2921. <a name="l02857"></a>02857 <span class="comment">!</span>
    2922. 

  2922. <a name="l02858"></a>02858   <span class="keyword">implicit none</span>
    2923. 

  2923. <a name="l02859"></a>02859 <span class="comment">!</span>
    2924. 

  2924. <a name="l02860"></a>02860   <span class="keywordtype">integer</span> norder
    2925. 

  2925. <a name="l02861"></a>02861 <span class="comment">!</span>
    2926. 

  2926. <a name="l02862"></a>02862   <span class="keywordtype">double precision</span> alpha
    2927. 

  2927. <a name="l02863"></a>02863   <span class="keywordtype">double precision</span> b(norder)
    2928. 

  2928. <a name="l02864"></a>02864   <span class="keywordtype">double precision</span> beta
    2929. 

  2929. <a name="l02865"></a>02865   <span class="keywordtype">double precision</span> c(norder)
    2930. 

  2930. <a name="l02866"></a>02866   <span class="keywordtype">double precision</span> d
    2931. 

  2931. <a name="l02867"></a>02867   <span class="keywordtype">double precision</span> dp2
    2932. 

  2932. <a name="l02868"></a>02868   <span class="keywordtype">double precision</span> eps
    2933. 

  2933. <a name="l02869"></a>02869   <span class="keywordtype">integer</span> i
    2934. 

  2934. <a name="l02870"></a>02870   <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxstep = 10
    2935. 

  2935. <a name="l02871"></a>02871   <span class="keywordtype">double precision</span> p1
    2936. 

  2936. <a name="l02872"></a>02872   <span class="keywordtype">double precision</span> p2
    2937. 

  2937. <a name="l02873"></a>02873   <span class="keywordtype">double precision</span> x
    2938. 

  2938. <a name="l02874"></a>02874 <span class="comment">!</span>
    2939. 

  2939. <a name="l02875"></a>02875   eps = epsilon ( x )
    2940. 

  2940. <a name="l02876"></a>02876 
    2941. 

  2941. <a name="l02877"></a>02877   <span class="keyword">do</span> i = 1, maxstep
    2942. 

  2942. <a name="l02878"></a>02878 
    2943. 

  2943. <a name="l02879"></a>02879     call <a class="code" href="quadrule_8f90.html#a23d5d91dbc68f334297c326bf251545b">jacobi_recur </a>( p2, dp2, p1, x, norder, alpha, beta, b, c )
    2944. 

  2944. <a name="l02880"></a>02880 
    2945. 

  2945. <a name="l02881"></a>02881     d = p2 / dp2
    2946. 

  2946. <a name="l02882"></a>02882     x = x - d
    2947. 

  2947. <a name="l02883"></a>02883 
    2948. 

  2948. <a name="l02884"></a>02884     <span class="keyword">if</span> ( abs ( d ) &lt;= eps * ( abs ( x ) + 1.0D+00 ) ) <span class="keyword">then</span>
    2949. 

  2949. <a name="l02885"></a>02885       return
    2950. 

  2950. <a name="l02886"></a>02886     <span class="keyword">end if</span>
    2951. 

  2951. <a name="l02887"></a>02887 
    2952. 

  2952. <a name="l02888"></a>02888   <span class="keyword">end do</span>
    2953. 

  2953. <a name="l02889"></a>02889 
    2954. 

  2954. <a name="l02890"></a>02890   return
    2955. 

  2955. <a name="l02891"></a>02891 <span class="keyword">end</span>
    2956. 

  2956. <a name="l02892"></a><a class="code" href="quadrule_8f90.html#a0fea29cd1cc25389b93d13d5680c4cc1">02892</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a0fea29cd1cc25389b93d13d5680c4cc1">kronrod_set</a> ( norder, xtab, weight )
    2957. 

  2957. <a name="l02893"></a>02893 <span class="comment">!</span>
    2958. 

  2958. <a name="l02894"></a>02894 <span class="comment">!*******************************************************************************</span>
    2959. 

  2959. <a name="l02895"></a>02895 <span class="comment">!</span>
    2960. 

  2960. <a name="l02896"></a>02896 <span class="comment">!! KRONROD_SET sets abscissas and weights for Gauss-Kronrod quadrature.</span>
    2961. 

  2961. <a name="l02897"></a>02897 <span class="comment">!</span>
    2962. 

  2962. <a name="l02898"></a>02898 <span class="comment">!</span>
    2963. 

  2963. <a name="l02899"></a>02899 <span class="comment">!  Integration interval:</span>
    2964. 

  2964. <a name="l02900"></a>02900 <span class="comment">!</span>
    2965. 

  2965. <a name="l02901"></a>02901 <span class="comment">!    [ -1, 1 ]</span>
    2966. 

  2966. <a name="l02902"></a>02902 <span class="comment">!</span>
    2967. 

  2967. <a name="l02903"></a>02903 <span class="comment">!  Weight function:</span>
    2968. 

  2968. <a name="l02904"></a>02904 <span class="comment">!</span>
    2969. 

  2969. <a name="l02905"></a>02905 <span class="comment">!    1.0D+00</span>
    2970. 

  2970. <a name="l02906"></a>02906 <span class="comment">!</span>
    2971. 

  2971. <a name="l02907"></a>02907 <span class="comment">!  Integral to approximate:</span>
    2972. 

  2972. <a name="l02908"></a>02908 <span class="comment">!</span>
    2973. 

  2973. <a name="l02909"></a>02909 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    2974. 

  2974. <a name="l02910"></a>02910 <span class="comment">!</span>
    2975. 

  2975. <a name="l02911"></a>02911 <span class="comment">!  Approximate integral:</span>
    2976. 

  2976. <a name="l02912"></a>02912 <span class="comment">!</span>
    2977. 

  2977. <a name="l02913"></a>02913 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    2978. 

  2978. <a name="l02914"></a>02914 <span class="comment">!</span>
    2979. 

  2979. <a name="l02915"></a>02915 <span class="comment">!  Note:</span>
    2980. 

  2980. <a name="l02916"></a>02916 <span class="comment">!</span>
    2981. 

  2981. <a name="l02917"></a>02917 <span class="comment">!    A Kronrod rule is used in conjunction with a lower order</span>
    2982. 

  2982. <a name="l02918"></a>02918 <span class="comment">!    Gauss rule, and provides an efficient error estimation.</span>
    2983. 

  2983. <a name="l02919"></a>02919 <span class="comment">!</span>
    2984. 

  2984. <a name="l02920"></a>02920 <span class="comment">!    The error may be estimated as the difference in the two integral</span>
    2985. 

  2985. <a name="l02921"></a>02921 <span class="comment">!    approximations.</span>
    2986. 

  2986. <a name="l02922"></a>02922 <span class="comment">!</span>
    2987. 

  2987. <a name="l02923"></a>02923 <span class="comment">!    The efficiency comes about because the Kronrod uses the abscissas</span>
    2988. 

  2988. <a name="l02924"></a>02924 <span class="comment">!    of the Gauss rule, thus saving on the number of function evaluations</span>
    2989. 

  2989. <a name="l02925"></a>02925 <span class="comment">!    necessary.  If the Kronrod rule were replaced by a Gauss rule of</span>
    2990. 

  2990. <a name="l02926"></a>02926 <span class="comment">!    the same order, a higher precision integral estimate would be</span>
    2991. 

  2991. <a name="l02927"></a>02927 <span class="comment">!    made, but the function would have to be evaluated at many more</span>
    2992. 

  2992. <a name="l02928"></a>02928 <span class="comment">!    points.</span>
    2993. 

  2993. <a name="l02929"></a>02929 <span class="comment">!</span>
    2994. 

  2994. <a name="l02930"></a>02930 <span class="comment">!    The Gauss Kronrod pair of rules involves an ( NORDER + 1 ) / 2</span>
    2995. 

  2995. <a name="l02931"></a>02931 <span class="comment">!    point Gauss-Legendre rule and an NORDER point Kronrod rule.</span>
    2996. 

  2996. <a name="l02932"></a>02932 <span class="comment">!    Thus, the 15 point Kronrod rule should be paired with the</span>
    2997. 

  2997. <a name="l02933"></a>02933 <span class="comment">!    Gauss-Legendre 7 point rule.</span>
    2998. 

  2998. <a name="l02934"></a>02934 <span class="comment">!</span>
    2999. 

  2999. <a name="l02935"></a>02935 <span class="comment">!  Reference:</span>
    3000. 

  3000. <a name="l02936"></a>02936 <span class="comment">!</span>
    3001. 

  3001. <a name="l02937"></a>02937 <span class="comment">!    R Piessens, E de Doncker-Kapenger, C Ueberhuber, D Kahaner,</span>
    3002. 

  3002. <a name="l02938"></a>02938 <span class="comment">!    QUADPACK, A Subroutine Package for Automatic Integration,</span>
    3003. 

  3003. <a name="l02939"></a>02939 <span class="comment">!    Springer Verlag, 1983.</span>
    3004. 

  3004. <a name="l02940"></a>02940 <span class="comment">!</span>
    3005. 

  3005. <a name="l02941"></a>02941 <span class="comment">!  Modified:</span>
    3006. 

  3006. <a name="l02942"></a>02942 <span class="comment">!</span>
    3007. 

  3007. <a name="l02943"></a>02943 <span class="comment">!    16 September 1998</span>
    3008. 

  3008. <a name="l02944"></a>02944 <span class="comment">!</span>
    3009. 

  3009. <a name="l02945"></a>02945 <span class="comment">!  Author:</span>
    3010. 

  3010. <a name="l02946"></a>02946 <span class="comment">!</span>
    3011. 

  3011. <a name="l02947"></a>02947 <span class="comment">!    John Burkardt</span>
    3012. 

  3012. <a name="l02948"></a>02948 <span class="comment">!</span>
    3013. 

  3013. <a name="l02949"></a>02949 <span class="comment">!  Parameters:</span>
    3014. 

  3014. <a name="l02950"></a>02950 <span class="comment">!</span>
    3015. 

  3015. <a name="l02951"></a>02951 <span class="comment">!    Input, integer NORDER, the order of the rule, which may be</span>
    3016. 

  3016. <a name="l02952"></a>02952 <span class="comment">!    15, 21, 31 or 41, corresponding to Gauss-Legendre rules of</span>
    3017. 

  3017. <a name="l02953"></a>02953 <span class="comment">!    order 7, 10, 15 or 20.</span>
    3018. 

  3018. <a name="l02954"></a>02954 <span class="comment">!</span>
    3019. 

  3019. <a name="l02955"></a>02955 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule, which</span>
    3020. 

  3020. <a name="l02956"></a>02956 <span class="comment">!    are symmetrically places in [-1,1].</span>
    3021. 

  3021. <a name="l02957"></a>02957 <span class="comment">!</span>
    3022. 

  3022. <a name="l02958"></a>02958 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    3023. 

  3023. <a name="l02959"></a>02959 <span class="comment">!    The weights are positive, symmetric, and should sum to 2.</span>
    3024. 

  3024. <a name="l02960"></a>02960 <span class="comment">!</span>
    3025. 

  3025. <a name="l02961"></a>02961   <span class="keyword">implicit none</span>
    3026. 

  3026. <a name="l02962"></a>02962 <span class="comment">!</span>
    3027. 

  3027. <a name="l02963"></a>02963   <span class="keywordtype">integer</span> norder
    3028. 

  3028. <a name="l02964"></a>02964 <span class="comment">!</span>
    3029. 

  3029. <a name="l02965"></a>02965   <span class="keywordtype">double precision</span> weight(norder)
    3030. 

  3030. <a name="l02966"></a>02966   <span class="keywordtype">double precision</span> xtab(norder)
    3031. 

  3031. <a name="l02967"></a>02967 <span class="comment">!</span>
    3032. 

  3032. <a name="l02968"></a>02968   <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
    3033. 

  3033. <a name="l02969"></a>02969 
    3034. 

  3034. <a name="l02970"></a>02970     xtab(1) =  - 0.9914553711208126D+00
    3035. 

  3035. <a name="l02971"></a>02971     xtab(2) =  - 0.9491079123427585D+00
    3036. 

  3036. <a name="l02972"></a>02972     xtab(3) =  - 0.8648644233597691D+00
    3037. 

  3037. <a name="l02973"></a>02973     xtab(4) =  - 0.7415311855993944D+00
    3038. 

  3038. <a name="l02974"></a>02974     xtab(5) =  - 0.5860872354676911D+00
    3039. 

  3039. <a name="l02975"></a>02975     xtab(6) =  - 0.4058451513773972D+00
    3040. 

  3040. <a name="l02976"></a>02976     xtab(7) =  - 0.2077849550789850D+00
    3041. 

  3041. <a name="l02977"></a>02977     xtab(8) =    0.0D+00
    3042. 

  3042. <a name="l02978"></a>02978     xtab(9) =    0.2077849550789850D+00
    3043. 

  3043. <a name="l02979"></a>02979     xtab(10) =   0.4058451513773972D+00
    3044. 

  3044. <a name="l02980"></a>02980     xtab(11) =   0.5860872354676911D+00
    3045. 

  3045. <a name="l02981"></a>02981     xtab(12) =   0.7415311855993944D+00
    3046. 

  3046. <a name="l02982"></a>02982     xtab(13) =   0.8648644233597691D+00
    3047. 

  3047. <a name="l02983"></a>02983     xtab(14) =   0.9491079123427585D+00
    3048. 

  3048. <a name="l02984"></a>02984     xtab(15) =   0.9914553711208126D+00
    3049. 

  3049. <a name="l02985"></a>02985 
    3050. 

  3050. <a name="l02986"></a>02986     weight(1) =  0.2293532201052922D-01
    3051. 

  3051. <a name="l02987"></a>02987     weight(2) =  0.6309209262997855D-01
    3052. 

  3052. <a name="l02988"></a>02988     weight(3) =  0.1047900103222502D+00
    3053. 

  3053. <a name="l02989"></a>02989     weight(4) =  0.1406532597155259D+00
    3054. 

  3054. <a name="l02990"></a>02990     weight(5) =  0.1690047266392679D+00
    3055. 

  3055. <a name="l02991"></a>02991     weight(6) =  0.1903505780647854D+00
    3056. 

  3056. <a name="l02992"></a>02992     weight(7) =  0.2044329400752989D+00
    3057. 

  3057. <a name="l02993"></a>02993     weight(8) =  0.2094821410847278D+00
    3058. 

  3058. <a name="l02994"></a>02994     weight(9) =  0.2044329400752989D+00
    3059. 

  3059. <a name="l02995"></a>02995     weight(10) = 0.1903505780647854D+00
    3060. 

  3060. <a name="l02996"></a>02996     weight(11) = 0.1690047266392679D+00
    3061. 

  3061. <a name="l02997"></a>02997     weight(12) = 0.1406532597155259D+00
    3062. 

  3062. <a name="l02998"></a>02998     weight(13) = 0.1047900103222502D+00
    3063. 

  3063. <a name="l02999"></a>02999     weight(14) = 0.6309209262997855D-01
    3064. 

  3064. <a name="l03000"></a>03000     weight(15) = 0.2293532201052922D-01
    3065. 

  3065. <a name="l03001"></a>03001 
    3066. 

  3066. <a name="l03002"></a>03002   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 21 ) <span class="keyword">then</span>
    3067. 

  3067. <a name="l03003"></a>03003 
    3068. 

  3068. <a name="l03004"></a>03004     xtab(1) =  - 0.9956571630258081D+00
    3069. 

  3069. <a name="l03005"></a>03005     xtab(2) =  - 0.9739065285171717D+00
    3070. 

  3070. <a name="l03006"></a>03006     xtab(3) =  - 0.9301574913557082D+00
    3071. 

  3071. <a name="l03007"></a>03007     xtab(4) =  - 0.8650633666889845D+00
    3072. 

  3072. <a name="l03008"></a>03008     xtab(5) =  - 0.7808177265864169D+00
    3073. 

  3073. <a name="l03009"></a>03009     xtab(6) =  - 0.6794095682990244D+00
    3074. 

  3074. <a name="l03010"></a>03010     xtab(7) =  - 0.5627571346686047D+00
    3075. 

  3075. <a name="l03011"></a>03011     xtab(8) =  - 0.4333953941292472D+00
    3076. 

  3076. <a name="l03012"></a>03012     xtab(9) =  - 0.2943928627014602D+00
    3077. 

  3077. <a name="l03013"></a>03013     xtab(10) = - 0.1488743389816312D+00
    3078. 

  3078. <a name="l03014"></a>03014     xtab(11) =   0.0D+00
    3079. 

  3079. <a name="l03015"></a>03015     xtab(12) =   0.1488743389816312D+00
    3080. 

  3080. <a name="l03016"></a>03016     xtab(13) =   0.2943928627014602D+00
    3081. 

  3081. <a name="l03017"></a>03017     xtab(14) =   0.4333953941292472D+00
    3082. 

  3082. <a name="l03018"></a>03018     xtab(15) =   0.5627571346686047D+00
    3083. 

  3083. <a name="l03019"></a>03019     xtab(16) =   0.6794095682990244D+00
    3084. 

  3084. <a name="l03020"></a>03020     xtab(17) =   0.7808177265864169D+00
    3085. 

  3085. <a name="l03021"></a>03021     xtab(18) =   0.8650633666889845D+00
    3086. 

  3086. <a name="l03022"></a>03022     xtab(19) =   0.9301574913557082D+00
    3087. 

  3087. <a name="l03023"></a>03023     xtab(20) =   0.9739065285171717D+00
    3088. 

  3088. <a name="l03024"></a>03024     xtab(21) =   0.9956571630258081D+00
    3089. 

  3089. <a name="l03025"></a>03025 
    3090. 

  3090. <a name="l03026"></a>03026     weight(1) =  0.1169463886737187D-01
    3091. 

  3091. <a name="l03027"></a>03027     weight(2) =  0.3255816230796473D-01
    3092. 

  3092. <a name="l03028"></a>03028     weight(3) =  0.5475589657435200D-01
    3093. 

  3093. <a name="l03029"></a>03029     weight(4) =  0.7503967481091995D-01
    3094. 

  3094. <a name="l03030"></a>03030     weight(5) =  0.9312545458369761D-01
    3095. 

  3095. <a name="l03031"></a>03031     weight(6) =  0.1093871588022976D+00
    3096. 

  3096. <a name="l03032"></a>03032     weight(7) =  0.1234919762620659D+00
    3097. 

  3097. <a name="l03033"></a>03033     weight(8) =  0.1347092173114733D+00
    3098. 

  3098. <a name="l03034"></a>03034     weight(9) =  0.1427759385770601D+00
    3099. 

  3099. <a name="l03035"></a>03035     weight(10) = 0.1477391049013385D+00
    3100. 

  3100. <a name="l03036"></a>03036     weight(11) = 0.1494455540029169D+00
    3101. 

  3101. <a name="l03037"></a>03037     weight(12) = 0.1477391049013385D+00
    3102. 

  3102. <a name="l03038"></a>03038     weight(13) = 0.1427759385770601D+00
    3103. 

  3103. <a name="l03039"></a>03039     weight(14) = 0.1347092173114733D+00
    3104. 

  3104. <a name="l03040"></a>03040     weight(15) = 0.1234919762620659D+00
    3105. 

  3105. <a name="l03041"></a>03041     weight(16) = 0.1093871588022976D+00
    3106. 

  3106. <a name="l03042"></a>03042     weight(17) = 0.9312545458369761D-01
    3107. 

  3107. <a name="l03043"></a>03043     weight(18) = 0.7503967481091995D-01
    3108. 

  3108. <a name="l03044"></a>03044     weight(19) = 0.5475589657435200D-01
    3109. 

  3109. <a name="l03045"></a>03045     weight(20) = 0.3255816230796473D-01
    3110. 

  3110. <a name="l03046"></a>03046     weight(21) = 0.1169463886737187D-01
    3111. 

  3111. <a name="l03047"></a>03047 
    3112. 

  3112. <a name="l03048"></a>03048   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 31 ) <span class="keyword">then</span>
    3113. 

  3113. <a name="l03049"></a>03049 
    3114. 

  3114. <a name="l03050"></a>03050     xtab(1) =  - 0.9980022986933971D+00
    3115. 

  3115. <a name="l03051"></a>03051     xtab(2) =  - 0.9879925180204854D+00
    3116. 

  3116. <a name="l03052"></a>03052     xtab(3) =  - 0.9677390756791391D+00
    3117. 

  3117. <a name="l03053"></a>03053     xtab(4) =  - 0.9372733924007059D+00
    3118. 

  3118. <a name="l03054"></a>03054     xtab(5) =  - 0.8972645323440819D+00
    3119. 

  3119. <a name="l03055"></a>03055     xtab(6) =  - 0.8482065834104272D+00
    3120. 

  3120. <a name="l03056"></a>03056     xtab(7) =  - 0.7904185014424659D+00
    3121. 

  3121. <a name="l03057"></a>03057     xtab(8) =  - 0.7244177313601700D+00
    3122. 

  3122. <a name="l03058"></a>03058     xtab(9) =  - 0.6509967412974170D+00
    3123. 

  3123. <a name="l03059"></a>03059     xtab(10) = - 0.5709721726085388D+00
    3124. 

  3124. <a name="l03060"></a>03060     xtab(11) = - 0.4850818636402397D+00
    3125. 

  3125. <a name="l03061"></a>03061     xtab(12) = - 0.3941513470775634D+00
    3126. 

  3126. <a name="l03062"></a>03062     xtab(13) = - 0.2991800071531688D+00
    3127. 

  3127. <a name="l03063"></a>03063     xtab(14) = - 0.2011940939974345D+00
    3128. 

  3128. <a name="l03064"></a>03064     xtab(15) = - 0.1011420669187175D+00
    3129. 

  3129. <a name="l03065"></a>03065     xtab(16) =   0.0D+00
    3130. 

  3130. <a name="l03066"></a>03066     xtab(17) =   0.1011420669187175D+00
    3131. 

  3131. <a name="l03067"></a>03067     xtab(18) =   0.2011940939974345D+00
    3132. 

  3132. <a name="l03068"></a>03068     xtab(19) =   0.2991800071531688D+00
    3133. 

  3133. <a name="l03069"></a>03069     xtab(20) =   0.3941513470775634D+00
    3134. 

  3134. <a name="l03070"></a>03070     xtab(21) =   0.4850818636402397D+00
    3135. 

  3135. <a name="l03071"></a>03071     xtab(22) =   0.5709721726085388D+00
    3136. 

  3136. <a name="l03072"></a>03072     xtab(23) =   0.6509967412974170D+00
    3137. 

  3137. <a name="l03073"></a>03073     xtab(24) =   0.7244177313601700D+00
    3138. 

  3138. <a name="l03074"></a>03074     xtab(25) =   0.7904185014424659D+00
    3139. 

  3139. <a name="l03075"></a>03075     xtab(26) =   0.8482065834104272D+00
    3140. 

  3140. <a name="l03076"></a>03076     xtab(27) =   0.8972645323440819D+00
    3141. 

  3141. <a name="l03077"></a>03077     xtab(28) =   0.9372733924007059D+00
    3142. 

  3142. <a name="l03078"></a>03078     xtab(29) =   0.9677390756791391D+00
    3143. 

  3143. <a name="l03079"></a>03079     xtab(30) =   0.9879925180204854D+00
    3144. 

  3144. <a name="l03080"></a>03080     xtab(31) =   0.9980022986933971D+00
    3145. 

  3145. <a name="l03081"></a>03081 
    3146. 

  3146. <a name="l03082"></a>03082     weight(1) =  0.5377479872923349D-02
    3147. 

  3147. <a name="l03083"></a>03083     weight(2) =  0.1500794732931612D-01
    3148. 

  3148. <a name="l03084"></a>03084     weight(3) =  0.2546084732671532D-01
    3149. 

  3149. <a name="l03085"></a>03085     weight(4) =  0.3534636079137585D-01
    3150. 

  3150. <a name="l03086"></a>03086     weight(5) =  0.4458975132476488D-01
    3151. 

  3151. <a name="l03087"></a>03087     weight(6) =  0.5348152469092809D-01
    3152. 

  3152. <a name="l03088"></a>03088     weight(7) =  0.6200956780067064D-01
    3153. 

  3153. <a name="l03089"></a>03089     weight(8) =  0.6985412131872826D-01
    3154. 

  3154. <a name="l03090"></a>03090     weight(9) =  0.7684968075772038D-01
    3155. 

  3155. <a name="l03091"></a>03091     weight(10) = 0.8308050282313302D-01
    3156. 

  3156. <a name="l03092"></a>03092     weight(11) = 0.8856444305621177D-01
    3157. 

  3157. <a name="l03093"></a>03093     weight(12) = 0.9312659817082532D-01
    3158. 

  3158. <a name="l03094"></a>03094     weight(13) = 0.9664272698362368D-01
    3159. 

  3159. <a name="l03095"></a>03095     weight(14) = 0.9917359872179196D-01
    3160. 

  3160. <a name="l03096"></a>03096     weight(15) = 0.1007698455238756D+00
    3161. 

  3161. <a name="l03097"></a>03097     weight(16) = 0.1013300070147915D+00
    3162. 

  3162. <a name="l03098"></a>03098     weight(17) = 0.1007698455238756D+00
    3163. 

  3163. <a name="l03099"></a>03099     weight(18) = 0.9917359872179196D-01
    3164. 

  3164. <a name="l03100"></a>03100     weight(19) = 0.9664272698362368D-01
    3165. 

  3165. <a name="l03101"></a>03101     weight(20) = 0.9312659817082532D-01
    3166. 

  3166. <a name="l03102"></a>03102     weight(21) = 0.8856444305621177D-01
    3167. 

  3167. <a name="l03103"></a>03103     weight(22) = 0.8308050282313302D-01
    3168. 

  3168. <a name="l03104"></a>03104     weight(23) = 0.7684968075772038D-01
    3169. 

  3169. <a name="l03105"></a>03105     weight(24) = 0.6985412131872826D-01
    3170. 

  3170. <a name="l03106"></a>03106     weight(25) = 0.6200956780067064D-01
    3171. 

  3171. <a name="l03107"></a>03107     weight(26) = 0.5348152469092809D-01
    3172. 

  3172. <a name="l03108"></a>03108     weight(27) = 0.4458975132476488D-01
    3173. 

  3173. <a name="l03109"></a>03109     weight(28) = 0.3534636079137585D-01
    3174. 

  3174. <a name="l03110"></a>03110     weight(29) = 0.2546084732671532D-01
    3175. 

  3175. <a name="l03111"></a>03111     weight(30) = 0.1500794732931612D-01
    3176. 

  3176. <a name="l03112"></a>03112     weight(31) = 0.5377479872923349D-02
    3177. 

  3177. <a name="l03113"></a>03113 
    3178. 

  3178. <a name="l03114"></a>03114   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 41 ) <span class="keyword">then</span>
    3179. 

  3179. <a name="l03115"></a>03115 
    3180. 

  3180. <a name="l03116"></a>03116     xtab(1) =  - 0.9988590315882777D+00
    3181. 

  3181. <a name="l03117"></a>03117     xtab(2) =  - 0.9931285991850949D+00
    3182. 

  3182. <a name="l03118"></a>03118     xtab(3) =  - 0.9815078774502503D+00
    3183. 

  3183. <a name="l03119"></a>03119     xtab(4) =  - 0.9639719272779138D+00
    3184. 

  3184. <a name="l03120"></a>03120     xtab(5) =  - 0.9408226338317548D+00
    3185. 

  3185. <a name="l03121"></a>03121     xtab(6) =  - 0.9122344282513259D+00
    3186. 

  3186. <a name="l03122"></a>03122     xtab(7) =  - 0.8782768112522820D+00
    3187. 

  3187. <a name="l03123"></a>03123     xtab(8) =  - 0.8391169718222188D+00
    3188. 

  3188. <a name="l03124"></a>03124     xtab(9) =  - 0.7950414288375512D+00
    3189. 

  3189. <a name="l03125"></a>03125     xtab(10) = - 0.7463319064601508D+00
    3190. 

  3190. <a name="l03126"></a>03126     xtab(11) = - 0.6932376563347514D+00
    3191. 

  3191. <a name="l03127"></a>03127     xtab(12) = - 0.6360536807265150D+00
    3192. 

  3192. <a name="l03128"></a>03128     xtab(13) = - 0.5751404468197103D+00
    3193. 

  3193. <a name="l03129"></a>03129     xtab(14) = - 0.5108670019508271D+00
    3194. 

  3194. <a name="l03130"></a>03130     xtab(15) = - 0.4435931752387251D+00
    3195. 

  3195. <a name="l03131"></a>03131     xtab(16) = - 0.3737060887154196D+00
    3196. 

  3196. <a name="l03132"></a>03132     xtab(17) = - 0.3016278681149130D+00
    3197. 

  3197. <a name="l03133"></a>03133     xtab(18) = - 0.2277858511416451D+00
    3198. 

  3198. <a name="l03134"></a>03134     xtab(19) = - 0.1526054652409227D+00
    3199. 

  3199. <a name="l03135"></a>03135     xtab(20) = - 0.7652652113349733D-01
    3200. 

  3200. <a name="l03136"></a>03136     xtab(21) =   0.0D+00
    3201. 

  3201. <a name="l03137"></a>03137     xtab(22) =   0.7652652113349733D-01
    3202. 

  3202. <a name="l03138"></a>03138     xtab(23) =   0.1526054652409227D+00
    3203. 

  3203. <a name="l03139"></a>03139     xtab(24) =   0.2277858511416451D+00
    3204. 

  3204. <a name="l03140"></a>03140     xtab(25) =   0.3016278681149130D+00
    3205. 

  3205. <a name="l03141"></a>03141     xtab(26) =   0.3737060887154196D+00
    3206. 

  3206. <a name="l03142"></a>03142     xtab(27) =   0.4435931752387251D+00
    3207. 

  3207. <a name="l03143"></a>03143     xtab(28) =   0.5108670019508271D+00
    3208. 

  3208. <a name="l03144"></a>03144     xtab(29) =   0.5751404468197103D+00
    3209. 

  3209. <a name="l03145"></a>03145     xtab(30) =   0.6360536807265150D+00
    3210. 

  3210. <a name="l03146"></a>03146     xtab(31) =   0.6932376563347514D+00
    3211. 

  3211. <a name="l03147"></a>03147     xtab(32) =   0.7463319064601508D+00
    3212. 

  3212. <a name="l03148"></a>03148     xtab(33) =   0.7950414288375512D+00
    3213. 

  3213. <a name="l03149"></a>03149     xtab(34) =   0.8391169718222188D+00
    3214. 

  3214. <a name="l03150"></a>03150     xtab(35) =   0.8782768112522820D+00
    3215. 

  3215. <a name="l03151"></a>03151     xtab(36) =   0.9122344282513259D+00
    3216. 

  3216. <a name="l03152"></a>03152     xtab(37) =   0.9408226338317548D+00
    3217. 

  3217. <a name="l03153"></a>03153     xtab(38) =   0.9639719272779138D+00
    3218. 

  3218. <a name="l03154"></a>03154     xtab(39) =   0.9815078774502503D+00
    3219. 

  3219. <a name="l03155"></a>03155     xtab(40) =   0.9931285991850949D+00
    3220. 

  3220. <a name="l03156"></a>03156     xtab(41) =   0.9988590315882777D+00
    3221. 

  3221. <a name="l03157"></a>03157 
    3222. 

  3222. <a name="l03158"></a>03158     weight(1) =  0.3073583718520532D-02
    3223. 

  3223. <a name="l03159"></a>03159     weight(2) =  0.8600269855642942D-02
    3224. 

  3224. <a name="l03160"></a>03160     weight(3) =  0.1462616925697125D-01
    3225. 

  3225. <a name="l03161"></a>03161     weight(4) =  0.2038837346126652D-01
    3226. 

  3226. <a name="l03162"></a>03162     weight(5) =  0.2588213360495116D-01
    3227. 

  3227. <a name="l03163"></a>03163     weight(6) =  0.3128730677703280D-01
    3228. 

  3228. <a name="l03164"></a>03164     weight(7) =  0.3660016975820080D-01
    3229. 

  3229. <a name="l03165"></a>03165     weight(8) =  0.4166887332797369D-01
    3230. 

  3230. <a name="l03166"></a>03166     weight(9) =  0.4643482186749767D-01
    3231. 

  3231. <a name="l03167"></a>03167     weight(10) = 0.5094457392372869D-01
    3232. 

  3232. <a name="l03168"></a>03168     weight(11) = 0.5519510534828599D-01
    3233. 

  3233. <a name="l03169"></a>03169     weight(12) = 0.5911140088063957D-01
    3234. 

  3234. <a name="l03170"></a>03170     weight(13) = 0.6265323755478117D-01
    3235. 

  3235. <a name="l03171"></a>03171     weight(14) = 0.6583459713361842D-01
    3236. 

  3236. <a name="l03172"></a>03172     weight(15) = 0.6864867292852162D-01
    3237. 

  3237. <a name="l03173"></a>03173     weight(16) = 0.7105442355344407D-01
    3238. 

  3238. <a name="l03174"></a>03174     weight(17) = 0.7303069033278667D-01
    3239. 

  3239. <a name="l03175"></a>03175     weight(18) = 0.7458287540049919D-01
    3240. 

  3240. <a name="l03176"></a>03176     weight(19) = 0.7570449768455667D-01
    3241. 

  3241. <a name="l03177"></a>03177     weight(20) = 0.7637786767208074D-01
    3242. 

  3242. <a name="l03178"></a>03178     weight(21) = 0.7660071191799966D-01
    3243. 

  3243. <a name="l03179"></a>03179     weight(22) = 0.7637786767208074D-01
    3244. 

  3244. <a name="l03180"></a>03180     weight(23) = 0.7570449768455667D-01
    3245. 

  3245. <a name="l03181"></a>03181     weight(24) = 0.7458287540049919D-01
    3246. 

  3246. <a name="l03182"></a>03182     weight(25) = 0.7303069033278667D-01
    3247. 

  3247. <a name="l03183"></a>03183     weight(26) = 0.7105442355344407D-01
    3248. 

  3248. <a name="l03184"></a>03184     weight(27) = 0.6864867292852162D-01
    3249. 

  3249. <a name="l03185"></a>03185     weight(28) = 0.6583459713361842D-01
    3250. 

  3250. <a name="l03186"></a>03186     weight(29) = 0.6265323755478117D-01
    3251. 

  3251. <a name="l03187"></a>03187     weight(30) = 0.5911140088063957D-01
    3252. 

  3252. <a name="l03188"></a>03188     weight(31) = 0.5519510534828599D-01
    3253. 

  3253. <a name="l03189"></a>03189     weight(32) = 0.5094457392372869D-01
    3254. 

  3254. <a name="l03190"></a>03190     weight(33) = 0.4643482186749767D-01
    3255. 

  3255. <a name="l03191"></a>03191     weight(34) = 0.4166887332797369D-01
    3256. 

  3256. <a name="l03192"></a>03192     weight(35) = 0.3660016975820080D-01
    3257. 

  3257. <a name="l03193"></a>03193     weight(36) = 0.3128730677703280D-01
    3258. 

  3258. <a name="l03194"></a>03194     weight(37) = 0.2588213360495116D-01
    3259. 

  3259. <a name="l03195"></a>03195     weight(38) = 0.2038837346126652D-01
    3260. 

  3260. <a name="l03196"></a>03196     weight(39) = 0.1462616925697125D-01
    3261. 

  3261. <a name="l03197"></a>03197     weight(40) = 0.8600269855642942D-02
    3262. 

  3262. <a name="l03198"></a>03198     weight(41) = 0.3073583718520532D-02
    3263. 

  3263. <a name="l03199"></a>03199 
    3264. 

  3264. <a name="l03200"></a>03200   <span class="keyword">else</span>
    3265. 

  3265. <a name="l03201"></a>03201 
    3266. 

  3266. <a name="l03202"></a>03202     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    3267. 

  3267. <a name="l03203"></a>03203     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;KRONROD_SET - Fatal error!&#39;</span>
    3268. 

  3268. <a name="l03204"></a>03204     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    3269. 

  3269. <a name="l03205"></a>03205     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 15, 21, 31 or 41.&#39;</span>
    3270. 

  3270. <a name="l03206"></a>03206     stop
    3271. 

  3271. <a name="l03207"></a>03207 
    3272. 

  3272. <a name="l03208"></a>03208   <span class="keyword">end if</span>
    3273. 

  3273. <a name="l03209"></a>03209 
    3274. 

  3274. <a name="l03210"></a>03210   return
    3275. 

  3275. <a name="l03211"></a>03211 <span class="keyword">end</span>
    3276. 

  3276. <a name="l03212"></a><a class="code" href="quadrule_8f90.html#a5e526b2dfca36cb4303a7ac532cc7e55">03212</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a5e526b2dfca36cb4303a7ac532cc7e55">laguerre_com</a> ( norder, xtab, weight, alpha )
    3277. 

  3277. <a name="l03213"></a>03213 <span class="comment">!</span>
    3278. 

  3278. <a name="l03214"></a>03214 <span class="comment">!*******************************************************************************</span>
    3279. 

  3279. <a name="l03215"></a>03215 <span class="comment">!</span>
    3280. 

  3280. <a name="l03216"></a>03216 <span class="comment">!! LAGUERRE_COM computes the abscissa and weights for Gauss-Laguerre quadrature.</span>
    3281. 

  3281. <a name="l03217"></a>03217 <span class="comment">!</span>
    3282. 

  3282. <a name="l03218"></a>03218 <span class="comment">!</span>
    3283. 

  3283. <a name="l03219"></a>03219 <span class="comment">!  Discussion:</span>
    3284. 

  3284. <a name="l03220"></a>03220 <span class="comment">!</span>
    3285. 

  3285. <a name="l03221"></a>03221 <span class="comment">!    In the simplest case, ALPHA is 0, and we are approximating the</span>
    3286. 

  3286. <a name="l03222"></a>03222 <span class="comment">!    integral from 0 to INFINITY of EXP(-X) * F(X).  When this is so,</span>
    3287. 

  3287. <a name="l03223"></a>03223 <span class="comment">!    it is easy to modify the rule to approximate the integral from</span>
    3288. 

  3288. <a name="l03224"></a>03224 <span class="comment">!    A to INFINITY as well.</span>
    3289. 

  3289. <a name="l03225"></a>03225 <span class="comment">!</span>
    3290. 

  3290. <a name="l03226"></a>03226 <span class="comment">!    If ALPHA is nonzero, then there is no simple way to extend the</span>
    3291. 

  3291. <a name="l03227"></a>03227 <span class="comment">!    rule to approximate the integral from A to INFINITY.  The simplest</span>
    3292. 

  3292. <a name="l03228"></a>03228 <span class="comment">!    procedures would be to approximate the integral from 0 to A.</span>
    3293. 

  3293. <a name="l03229"></a>03229 <span class="comment">!</span>
    3294. 

  3294. <a name="l03230"></a>03230 <span class="comment">!  Integration interval:</span>
    3295. 

  3295. <a name="l03231"></a>03231 <span class="comment">!</span>
    3296. 

  3296. <a name="l03232"></a>03232 <span class="comment">!      [ A, +Infinity ) or [ 0, +Infinity )</span>
    3297. 

  3297. <a name="l03233"></a>03233 <span class="comment">!</span>
    3298. 

  3298. <a name="l03234"></a>03234 <span class="comment">!  Weight function:</span>
    3299. 

  3299. <a name="l03235"></a>03235 <span class="comment">!</span>
    3300. 

  3300. <a name="l03236"></a>03236 <span class="comment">!      EXP ( - X ) or EXP ( - X ) * X**ALPHA</span>
    3301. 

  3301. <a name="l03237"></a>03237 <span class="comment">!</span>
    3302. 

  3302. <a name="l03238"></a>03238 <span class="comment">!  Integral to approximate:</span>
    3303. 

  3303. <a name="l03239"></a>03239 <span class="comment">!</span>
    3304. 

  3304. <a name="l03240"></a>03240 <span class="comment">!      Integral ( A &lt;= X &lt; +INFINITY ) EXP ( - X ) * F(X) dX</span>
    3305. 

  3305. <a name="l03241"></a>03241 <span class="comment">!    or</span>
    3306. 

  3306. <a name="l03242"></a>03242 <span class="comment">!      Integral ( 0 &lt;= X &lt; +INFINITY ) EXP ( - X ) * X**ALPHA * F(X) dX</span>
    3307. 

  3307. <a name="l03243"></a>03243 <span class="comment">!</span>
    3308. 

  3308. <a name="l03244"></a>03244 <span class="comment">!  Approximate integral:</span>
    3309. 

  3309. <a name="l03245"></a>03245 <span class="comment">!</span>
    3310. 

  3310. <a name="l03246"></a>03246 <span class="comment">!      EXP ( - A ) * Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( A+XTAB(I) )</span>
    3311. 

  3311. <a name="l03247"></a>03247 <span class="comment">!    or</span>
    3312. 

  3312. <a name="l03248"></a>03248 <span class="comment">!      Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    3313. 

  3313. <a name="l03249"></a>03249 <span class="comment">!</span>
    3314. 

  3314. <a name="l03250"></a>03250 <span class="comment">!  Reference:</span>
    3315. 

  3315. <a name="l03251"></a>03251 <span class="comment">!</span>
    3316. 

  3316. <a name="l03252"></a>03252 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    3317. 

  3317. <a name="l03253"></a>03253 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    3318. 

  3318. <a name="l03254"></a>03254 <span class="comment">!    Prentice Hall, 1966.</span>
    3319. 

  3319. <a name="l03255"></a>03255 <span class="comment">!</span>
    3320. 

  3320. <a name="l03256"></a>03256 <span class="comment">!  Modified:</span>
    3321. 

  3321. <a name="l03257"></a>03257 <span class="comment">!</span>
    3322. 

  3322. <a name="l03258"></a>03258 <span class="comment">!    15 March 2000</span>
    3323. 

  3323. <a name="l03259"></a>03259 <span class="comment">!</span>
    3324. 

  3324. <a name="l03260"></a>03260 <span class="comment">!  Parameters:</span>
    3325. 

  3325. <a name="l03261"></a>03261 <span class="comment">!</span>
    3326. 

  3326. <a name="l03262"></a>03262 <span class="comment">!    Input, integer NORDER, the order of the quadrature rule to be computed.</span>
    3327. 

  3327. <a name="l03263"></a>03263 <span class="comment">!    NORDER must be at least 1.</span>
    3328. 

  3328. <a name="l03264"></a>03264 <span class="comment">!</span>
    3329. 

  3329. <a name="l03265"></a>03265 <span class="comment">!    Output, double precision XTAB(NORDER), the Gauss-Laguerre abscissas.</span>
    3330. 

  3330. <a name="l03266"></a>03266 <span class="comment">!</span>
    3331. 

  3331. <a name="l03267"></a>03267 <span class="comment">!    Output, double precision WEIGHT(NORDER), the Gauss-Laguerre weights.</span>
    3332. 

  3332. <a name="l03268"></a>03268 <span class="comment">!</span>
    3333. 

  3333. <a name="l03269"></a>03269 <span class="comment">!    Input, double precision ALPHA, the exponent of the X factor.</span>
    3334. 

  3334. <a name="l03270"></a>03270 <span class="comment">!    Set ALPHA = 0.0D+00 for the simplest rule.</span>
    3335. 

  3335. <a name="l03271"></a>03271 <span class="comment">!    ALPHA must be nonnegative.</span>
    3336. 

  3336. <a name="l03272"></a>03272 <span class="comment">!</span>
    3337. 

  3337. <a name="l03273"></a>03273   <span class="keyword">implicit none</span>
    3338. 

  3338. <a name="l03274"></a>03274 <span class="comment">!</span>
    3339. 

  3339. <a name="l03275"></a>03275   <span class="keywordtype">integer</span> norder
    3340. 

  3340. <a name="l03276"></a>03276 <span class="comment">!</span>
    3341. 

  3341. <a name="l03277"></a>03277   <span class="keywordtype">double precision</span> alpha
    3342. 

  3342. <a name="l03278"></a>03278   <span class="keywordtype">double precision</span> b(norder)
    3343. 

  3343. <a name="l03279"></a>03279   <span class="keywordtype">double precision</span> c(norder)
    3344. 

  3344. <a name="l03280"></a>03280   <span class="keywordtype">double precision</span> cc
    3345. 

  3345. <a name="l03281"></a>03281   <span class="keywordtype">double precision</span> dp2
    3346. 

  3346. <a name="l03282"></a>03282   <span class="keywordtype">double precision</span> gamma
    3347. 

  3347. <a name="l03283"></a>03283   <span class="keywordtype">integer</span> i
    3348. 

  3348. <a name="l03284"></a>03284   <span class="keywordtype">double precision</span> p1
    3349. 

  3349. <a name="l03285"></a>03285   <span class="keywordtype">double precision</span> r1
    3350. 

  3350. <a name="l03286"></a>03286   <span class="keywordtype">double precision</span> r2
    3351. 

  3351. <a name="l03287"></a>03287   <span class="keywordtype">double precision</span> ratio
    3352. 

  3352. <a name="l03288"></a>03288   <span class="keywordtype">double precision</span> weight(norder)
    3353. 

  3353. <a name="l03289"></a>03289   <span class="keywordtype">double precision</span> x
    3354. 

  3354. <a name="l03290"></a>03290   <span class="keywordtype">double precision</span> xtab(norder)
    3355. 

  3355. <a name="l03291"></a>03291 <span class="comment">!</span>
    3356. 

  3356. <a name="l03292"></a>03292 <span class="comment">!  Set the recursion coefficients.</span>
    3357. 

  3357. <a name="l03293"></a>03293 <span class="comment">!</span>
    3358. 

  3358. <a name="l03294"></a>03294   <span class="keyword">do</span> i = 1, norder
    3359. 

  3359. <a name="l03295"></a>03295     b(i) = ( alpha + dble ( 2 * i - 1 ) )
    3360. 

  3360. <a name="l03296"></a>03296   <span class="keyword">end do</span>
    3361. 

  3361. <a name="l03297"></a>03297 
    3362. 

  3362. <a name="l03298"></a>03298   <span class="keyword">do</span> i = 1, norder
    3363. 

  3363. <a name="l03299"></a>03299     c(i) = dble ( i - 1 ) * ( alpha + dble ( i - 1 ) )
    3364. 

  3364. <a name="l03300"></a>03300   <span class="keyword">end do</span>
    3365. 

  3365. <a name="l03301"></a>03301 
    3366. 

  3366. <a name="l03302"></a>03302   cc = gamma ( alpha + 1.0D+00 ) * product ( c(2:norder) )
    3367. 

  3367. <a name="l03303"></a>03303 
    3368. 

  3368. <a name="l03304"></a>03304   <span class="keyword">do</span> i = 1, norder
    3369. 

  3369. <a name="l03305"></a>03305 <span class="comment">!</span>
    3370. 

  3370. <a name="l03306"></a>03306 <span class="comment">!  Compute an estimate for the root.</span>
    3371. 

  3371. <a name="l03307"></a>03307 <span class="comment">!</span>
    3372. 

  3372. <a name="l03308"></a>03308     <span class="keyword">if</span> ( i == 1 ) <span class="keyword">then</span>
    3373. 

  3373. <a name="l03309"></a>03309 
    3374. 

  3374. <a name="l03310"></a>03310       x = ( 1.0D+00 + alpha ) * ( 3.0D+00+ 0.92 * alpha ) / &amp;
    3375. 

  3375. <a name="l03311"></a>03311         ( 1.0D+00 + 2.4D+00 * dble ( norder ) + 1.8D+00 * alpha )
    3376. 

  3376. <a name="l03312"></a>03312 
    3377. 

  3377. <a name="l03313"></a>03313     <span class="keyword">else</span> <span class="keyword">if</span> ( i == 2 ) <span class="keyword">then</span>
    3378. 

  3378. <a name="l03314"></a>03314 
    3379. 

  3379. <a name="l03315"></a>03315       x = x + ( 15.0D+00 + 6.25D+00 * alpha ) / &amp;
    3380. 

  3380. <a name="l03316"></a>03316         ( 1.0D+00 + 0.9D+00 * alpha + 2.5D+00 * dble ( norder ) )
    3381. 

  3381. <a name="l03317"></a>03317 
    3382. 

  3382. <a name="l03318"></a>03318     <span class="keyword">else</span>
    3383. 

  3383. <a name="l03319"></a>03319 
    3384. 

  3384. <a name="l03320"></a>03320       r1 = ( 1.0D+00 + 2.55D+00 * dble ( i - 2 ) ) / ( 1.9D+00 * dble ( i - 2 ) )
    3385. 

  3385. <a name="l03321"></a>03321 
    3386. 

  3386. <a name="l03322"></a>03322       r2 = 1.26D+00 * dble ( i - 2 ) * alpha / &amp;
    3387. 

  3387. <a name="l03323"></a>03323         ( 1.0D+00 + 3.5D+00 * dble ( i - 2 ) )
    3388. 

  3388. <a name="l03324"></a>03324 
    3389. 

  3389. <a name="l03325"></a>03325       ratio = ( r1 + r2 ) / ( 1.0D+00 + 0.3D+00 * alpha )
    3390. 

  3390. <a name="l03326"></a>03326 
    3391. 

  3391. <a name="l03327"></a>03327       x = x + ratio * ( x - xtab(i-2) )
    3392. 

  3392. <a name="l03328"></a>03328 
    3393. 

  3393. <a name="l03329"></a>03329     <span class="keyword">end if</span>
    3394. 

  3394. <a name="l03330"></a>03330 <span class="comment">!</span>
    3395. 

  3395. <a name="l03331"></a>03331 <span class="comment">!  Use iteration to find the root.</span>
    3396. 

  3396. <a name="l03332"></a>03332 <span class="comment">!</span>
    3397. 

  3397. <a name="l03333"></a>03333     call <a class="code" href="quadrule_8f90.html#a50878552a6862bdc03e4e7d904d7b154">laguerre_root </a>( x, norder, alpha, dp2, p1, b, c )
    3398. 

  3398. <a name="l03334"></a>03334 <span class="comment">!</span>
    3399. 

  3399. <a name="l03335"></a>03335 <span class="comment">!  Set the abscissa and weight.</span>
    3400. 

  3400. <a name="l03336"></a>03336 <span class="comment">!</span>
    3401. 

  3401. <a name="l03337"></a>03337     xtab(i) = x
    3402. 

  3402. <a name="l03338"></a>03338     weight(i) = ( cc / dp2 ) / p1
    3403. 

  3403. <a name="l03339"></a>03339 
    3404. 

  3404. <a name="l03340"></a>03340   <span class="keyword">end do</span>
    3405. 

  3405. <a name="l03341"></a>03341 
    3406. 

  3406. <a name="l03342"></a>03342   return
    3407. 

  3407. <a name="l03343"></a>03343 <span class="keyword">end</span>
    3408. 

  3408. <a name="l03344"></a><a class="code" href="quadrule_8f90.html#a37a4edc203821495156eaa63b1c4d7fa">03344</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a37a4edc203821495156eaa63b1c4d7fa">laguerre_recur</a> ( p2, dp2, p1, x, norder, alpha, b, c )
    3409. 

  3409. <a name="l03345"></a>03345 <span class="comment">!</span>
    3410. 

  3410. <a name="l03346"></a>03346 <span class="comment">!*******************************************************************************</span>
    3411. 

  3411. <a name="l03347"></a>03347 <span class="comment">!</span>
    3412. 

  3412. <a name="l03348"></a>03348 <span class="comment">!! LAGUERRE_RECUR finds the value and derivative of a Laguerre polynomial.</span>
    3413. 

  3413. <a name="l03349"></a>03349 <span class="comment">!</span>
    3414. 

  3414. <a name="l03350"></a>03350 <span class="comment">!</span>
    3415. 

  3415. <a name="l03351"></a>03351 <span class="comment">!  Reference:</span>
    3416. 

  3416. <a name="l03352"></a>03352 <span class="comment">!</span>
    3417. 

  3417. <a name="l03353"></a>03353 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    3418. 

  3418. <a name="l03354"></a>03354 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    3419. 

  3419. <a name="l03355"></a>03355 <span class="comment">!    Prentice Hall, 1966.</span>
    3420. 

  3420. <a name="l03356"></a>03356 <span class="comment">!</span>
    3421. 

  3421. <a name="l03357"></a>03357 <span class="comment">!  Modified:</span>
    3422. 

  3422. <a name="l03358"></a>03358 <span class="comment">!</span>
    3423. 

  3423. <a name="l03359"></a>03359 <span class="comment">!    19 September 1998</span>
    3424. 

  3424. <a name="l03360"></a>03360 <span class="comment">!</span>
    3425. 

  3425. <a name="l03361"></a>03361 <span class="comment">!  Parameters:</span>
    3426. 

  3426. <a name="l03362"></a>03362 <span class="comment">!</span>
    3427. 

  3427. <a name="l03363"></a>03363 <span class="comment">!    Output, double precision P2, the value of L(NORDER)(X).</span>
    3428. 

  3428. <a name="l03364"></a>03364 <span class="comment">!</span>
    3429. 

  3429. <a name="l03365"></a>03365 <span class="comment">!    Output, double precision DP2, the value of L&#39;(NORDER)(X).</span>
    3430. 

  3430. <a name="l03366"></a>03366 <span class="comment">!</span>
    3431. 

  3431. <a name="l03367"></a>03367 <span class="comment">!    Output, double precision P1, the value of L(NORDER-1)(X).</span>
    3432. 

  3432. <a name="l03368"></a>03368 <span class="comment">!</span>
    3433. 

  3433. <a name="l03369"></a>03369 <span class="comment">!    Input, double precision X, the point at which polynomials are evaluated.</span>
    3434. 

  3434. <a name="l03370"></a>03370 <span class="comment">!</span>
    3435. 

  3435. <a name="l03371"></a>03371 <span class="comment">!    Input, integer NORDER, the order of the polynomial to be computed.</span>
    3436. 

  3436. <a name="l03372"></a>03372 <span class="comment">!</span>
    3437. 

  3437. <a name="l03373"></a>03373 <span class="comment">!    Input, double precision ALPHA, the exponent of the X factor in the</span>
    3438. 

  3438. <a name="l03374"></a>03374 <span class="comment">!    integrand.</span>
    3439. 

  3439. <a name="l03375"></a>03375 <span class="comment">!</span>
    3440. 

  3440. <a name="l03376"></a>03376 <span class="comment">!    Input, double precision B(NORDER), C(NORDER), the recursion</span>
    3441. 

  3441. <a name="l03377"></a>03377 <span class="comment">!    coefficients.</span>
    3442. 

  3442. <a name="l03378"></a>03378 <span class="comment">!</span>
    3443. 

  3443. <a name="l03379"></a>03379   <span class="keyword">implicit none</span>
    3444. 

  3444. <a name="l03380"></a>03380 <span class="comment">!</span>
    3445. 

  3445. <a name="l03381"></a>03381   <span class="keywordtype">integer</span> norder
    3446. 

  3446. <a name="l03382"></a>03382 <span class="comment">!</span>
    3447. 

  3447. <a name="l03383"></a>03383   <span class="keywordtype">double precision</span> alpha
    3448. 

  3448. <a name="l03384"></a>03384   <span class="keywordtype">double precision</span> b(norder)
    3449. 

  3449. <a name="l03385"></a>03385   <span class="keywordtype">double precision</span> c(norder)
    3450. 

  3450. <a name="l03386"></a>03386   <span class="keywordtype">double precision</span> dp0
    3451. 

  3451. <a name="l03387"></a>03387   <span class="keywordtype">double precision</span> dp1
    3452. 

  3452. <a name="l03388"></a>03388   <span class="keywordtype">double precision</span> dp2
    3453. 

  3453. <a name="l03389"></a>03389   <span class="keywordtype">integer</span> i
    3454. 

  3454. <a name="l03390"></a>03390   <span class="keywordtype">double precision</span> p0
    3455. 

  3455. <a name="l03391"></a>03391   <span class="keywordtype">double precision</span> p1
    3456. 

  3456. <a name="l03392"></a>03392   <span class="keywordtype">double precision</span> p2
    3457. 

  3457. <a name="l03393"></a>03393   <span class="keywordtype">double precision</span> x
    3458. 

  3458. <a name="l03394"></a>03394 <span class="comment">!</span>
    3459. 

  3459. <a name="l03395"></a>03395   p1 = 1.0D+00
    3460. 

  3460. <a name="l03396"></a>03396   dp1 = 0.0D+00
    3461. 

  3461. <a name="l03397"></a>03397 
    3462. 

  3462. <a name="l03398"></a>03398   p2 = x - alpha - 1.0D+00
    3463. 

  3463. <a name="l03399"></a>03399   dp2 = 1.0D+00
    3464. 

  3464. <a name="l03400"></a>03400 
    3465. 

  3465. <a name="l03401"></a>03401   <span class="keyword">do</span> i = 2, norder
    3466. 

  3466. <a name="l03402"></a>03402 
    3467. 

  3467. <a name="l03403"></a>03403     p0 = p1
    3468. 

  3468. <a name="l03404"></a>03404     dp0 = dp1
    3469. 

  3469. <a name="l03405"></a>03405 
    3470. 

  3470. <a name="l03406"></a>03406     p1 = p2
    3471. 

  3471. <a name="l03407"></a>03407     dp1 = dp2
    3472. 

  3472. <a name="l03408"></a>03408 
    3473. 

  3473. <a name="l03409"></a>03409     p2 = ( x - b(i) ) * p1 - c(i) * p0
    3474. 

  3474. <a name="l03410"></a>03410     dp2 = ( x - b(i) ) * dp1 + p1 - c(i) * dp0
    3475. 

  3475. <a name="l03411"></a>03411 
    3476. 

  3476. <a name="l03412"></a>03412   <span class="keyword">end do</span>
    3477. 

  3477. <a name="l03413"></a>03413 
    3478. 

  3478. <a name="l03414"></a>03414   return
    3479. 

  3479. <a name="l03415"></a>03415 <span class="keyword">end</span>
    3480. 

  3480. <a name="l03416"></a><a class="code" href="quadrule_8f90.html#a50878552a6862bdc03e4e7d904d7b154">03416</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a50878552a6862bdc03e4e7d904d7b154">laguerre_root</a> ( x, norder, alpha, dp2, p1, b, c )
    3481. 

  3481. <a name="l03417"></a>03417 <span class="comment">!</span>
    3482. 

  3482. <a name="l03418"></a>03418 <span class="comment">!*******************************************************************************</span>
    3483. 

  3483. <a name="l03419"></a>03419 <span class="comment">!</span>
    3484. 

  3484. <a name="l03420"></a>03420 <span class="comment">!! LAGUERRE_ROOT improves an approximate root of a Laguerre polynomial.</span>
    3485. 

  3485. <a name="l03421"></a>03421 <span class="comment">!</span>
    3486. 

  3486. <a name="l03422"></a>03422 <span class="comment">!</span>
    3487. 

  3487. <a name="l03423"></a>03423 <span class="comment">!  Reference:</span>
    3488. 

  3488. <a name="l03424"></a>03424 <span class="comment">!</span>
    3489. 

  3489. <a name="l03425"></a>03425 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    3490. 

  3490. <a name="l03426"></a>03426 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    3491. 

  3491. <a name="l03427"></a>03427 <span class="comment">!    Prentice Hall, 1966.</span>
    3492. 

  3492. <a name="l03428"></a>03428 <span class="comment">!</span>
    3493. 

  3493. <a name="l03429"></a>03429 <span class="comment">!  Modified:</span>
    3494. 

  3494. <a name="l03430"></a>03430 <span class="comment">!</span>
    3495. 

  3495. <a name="l03431"></a>03431 <span class="comment">!    09 December 2000</span>
    3496. 

  3496. <a name="l03432"></a>03432 <span class="comment">!</span>
    3497. 

  3497. <a name="l03433"></a>03433 <span class="comment">!  Parameters:</span>
    3498. 

  3498. <a name="l03434"></a>03434 <span class="comment">!</span>
    3499. 

  3499. <a name="l03435"></a>03435 <span class="comment">!    Input/output, double precision X, the approximate root, which</span>
    3500. 

  3500. <a name="l03436"></a>03436 <span class="comment">!    should be improved on output.</span>
    3501. 

  3501. <a name="l03437"></a>03437 <span class="comment">!</span>
    3502. 

  3502. <a name="l03438"></a>03438 <span class="comment">!    Input, integer NORDER, the order of the polynomial to be computed.</span>
    3503. 

  3503. <a name="l03439"></a>03439 <span class="comment">!</span>
    3504. 

  3504. <a name="l03440"></a>03440 <span class="comment">!    Input, double precision ALPHA, the exponent of the X factor.</span>
    3505. 

  3505. <a name="l03441"></a>03441 <span class="comment">!</span>
    3506. 

  3506. <a name="l03442"></a>03442 <span class="comment">!    Output, double precision DP2, the value of L&#39;(NORDER)(X).</span>
    3507. 

  3507. <a name="l03443"></a>03443 <span class="comment">!</span>
    3508. 

  3508. <a name="l03444"></a>03444 <span class="comment">!    Output, double precision P1, the value of L(NORDER-1)(X).</span>
    3509. 

  3509. <a name="l03445"></a>03445 <span class="comment">!</span>
    3510. 

  3510. <a name="l03446"></a>03446 <span class="comment">!    Input, double precision B(NORDER), C(NORDER), the recursion coefficients.</span>
    3511. 

  3511. <a name="l03447"></a>03447 <span class="comment">!</span>
    3512. 

  3512. <a name="l03448"></a>03448   <span class="keyword">implicit none</span>
    3513. 

  3513. <a name="l03449"></a>03449 <span class="comment">!</span>
    3514. 

  3514. <a name="l03450"></a>03450   <span class="keywordtype">integer</span> norder
    3515. 

  3515. <a name="l03451"></a>03451 <span class="comment">!</span>
    3516. 

  3516. <a name="l03452"></a>03452   <span class="keywordtype">double precision</span> alpha
    3517. 

  3517. <a name="l03453"></a>03453   <span class="keywordtype">double precision</span> b(norder)
    3518. 

  3518. <a name="l03454"></a>03454   <span class="keywordtype">double precision</span> c(norder)
    3519. 

  3519. <a name="l03455"></a>03455   <span class="keywordtype">double precision</span> d
    3520. 

  3520. <a name="l03456"></a>03456   <span class="keywordtype">double precision</span> dp2
    3521. 

  3521. <a name="l03457"></a>03457   <span class="keywordtype">double precision</span> eps
    3522. 

  3522. <a name="l03458"></a>03458   <span class="keywordtype">integer</span> i
    3523. 

  3523. <a name="l03459"></a>03459   <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxstep = 10
    3524. 

  3524. <a name="l03460"></a>03460   <span class="keywordtype">double precision</span> p1
    3525. 

  3525. <a name="l03461"></a>03461   <span class="keywordtype">double precision</span> p2
    3526. 

  3526. <a name="l03462"></a>03462   <span class="keywordtype">double precision</span> x
    3527. 

  3527. <a name="l03463"></a>03463 <span class="comment">!</span>
    3528. 

  3528. <a name="l03464"></a>03464   eps = epsilon ( x )
    3529. 

  3529. <a name="l03465"></a>03465 
    3530. 

  3530. <a name="l03466"></a>03466   <span class="keyword">do</span> i = 1, maxstep
    3531. 

  3531. <a name="l03467"></a>03467 
    3532. 

  3532. <a name="l03468"></a>03468     call <a class="code" href="quadrule_8f90.html#a37a4edc203821495156eaa63b1c4d7fa">laguerre_recur </a>( p2, dp2, p1, x, norder, alpha, b, c )
    3533. 

  3533. <a name="l03469"></a>03469 
    3534. 

  3534. <a name="l03470"></a>03470     d = p2 / dp2
    3535. 

  3535. <a name="l03471"></a>03471     x = x - d
    3536. 

  3536. <a name="l03472"></a>03472 
    3537. 

  3537. <a name="l03473"></a>03473     <span class="keyword">if</span> ( abs ( d ) &lt;= eps * ( abs ( x ) + 1.0D+00 ) ) <span class="keyword">then</span>
    3538. 

  3538. <a name="l03474"></a>03474       return
    3539. 

  3539. <a name="l03475"></a>03475     <span class="keyword">end if</span>
    3540. 

  3540. <a name="l03476"></a>03476 
    3541. 

  3541. <a name="l03477"></a>03477   <span class="keyword">end do</span>
    3542. 

  3542. <a name="l03478"></a>03478 
    3543. 

  3543. <a name="l03479"></a>03479   return
    3544. 

  3544. <a name="l03480"></a>03480 <span class="keyword">end</span>
    3545. 

  3545. <a name="l03481"></a><a class="code" href="quadrule_8f90.html#a35fe6a5ac275303facfa7b695addee7f">03481</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a35fe6a5ac275303facfa7b695addee7f">laguerre_set</a> ( norder, xtab, weight )
    3546. 

  3546. <a name="l03482"></a>03482 <span class="comment">!</span>
    3547. 

  3547. <a name="l03483"></a>03483 <span class="comment">!*******************************************************************************</span>
    3548. 

  3548. <a name="l03484"></a>03484 <span class="comment">!</span>
    3549. 

  3549. <a name="l03485"></a>03485 <span class="comment">!! LAGUERRE_SET sets abscissas and weights for Laguerre quadrature.</span>
    3550. 

  3550. <a name="l03486"></a>03486 <span class="comment">!</span>
    3551. 

  3551. <a name="l03487"></a>03487 <span class="comment">!</span>
    3552. 

  3552. <a name="l03488"></a>03488 <span class="comment">!  Integration interval:</span>
    3553. 

  3553. <a name="l03489"></a>03489 <span class="comment">!</span>
    3554. 

  3554. <a name="l03490"></a>03490 <span class="comment">!    [ 0, +Infinity )</span>
    3555. 

  3555. <a name="l03491"></a>03491 <span class="comment">!</span>
    3556. 

  3556. <a name="l03492"></a>03492 <span class="comment">!  Weight function:</span>
    3557. 

  3557. <a name="l03493"></a>03493 <span class="comment">!</span>
    3558. 

  3558. <a name="l03494"></a>03494 <span class="comment">!    EXP ( - X )</span>
    3559. 

  3559. <a name="l03495"></a>03495 <span class="comment">!</span>
    3560. 

  3560. <a name="l03496"></a>03496 <span class="comment">!  Integral to approximate:</span>
    3561. 

  3561. <a name="l03497"></a>03497 <span class="comment">!</span>
    3562. 

  3562. <a name="l03498"></a>03498 <span class="comment">!    Integral ( 0 &lt;= X &lt; +INFINITY ) EXP ( - X ) * F(X) dX</span>
    3563. 

  3563. <a name="l03499"></a>03499 <span class="comment">!</span>
    3564. 

  3564. <a name="l03500"></a>03500 <span class="comment">!  Approximate integral:</span>
    3565. 

  3565. <a name="l03501"></a>03501 <span class="comment">!</span>
    3566. 

  3566. <a name="l03502"></a>03502 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    3567. 

  3567. <a name="l03503"></a>03503 <span class="comment">!</span>
    3568. 

  3568. <a name="l03504"></a>03504 <span class="comment">!  Note:</span>
    3569. 

  3569. <a name="l03505"></a>03505 <span class="comment">!</span>
    3570. 

  3570. <a name="l03506"></a>03506 <span class="comment">!    The abscissas are the zeroes of the Laguerre polynomial L(NORDER)(X).</span>
    3571. 

  3571. <a name="l03507"></a>03507 <span class="comment">!</span>
    3572. 

  3572. <a name="l03508"></a>03508 <span class="comment">!  Reference:</span>
    3573. 

  3573. <a name="l03509"></a>03509 <span class="comment">!</span>
    3574. 

  3574. <a name="l03510"></a>03510 <span class="comment">!    Abramowitz and Stegun,</span>
    3575. 

  3575. <a name="l03511"></a>03511 <span class="comment">!    Handbook of Mathematical Functions,</span>
    3576. 

  3576. <a name="l03512"></a>03512 <span class="comment">!    National Bureau of Standards, 1964.</span>
    3577. 

  3577. <a name="l03513"></a>03513 <span class="comment">!</span>
    3578. 

  3578. <a name="l03514"></a>03514 <span class="comment">!    Vladimir Krylov,</span>
    3579. 

  3579. <a name="l03515"></a>03515 <span class="comment">!    Approximate Calculation of Integrals,</span>
    3580. 

  3580. <a name="l03516"></a>03516 <span class="comment">!    MacMillan, 1962.</span>
    3581. 

  3581. <a name="l03517"></a>03517 <span class="comment">!</span>
    3582. 

  3582. <a name="l03518"></a>03518 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    3583. 

  3583. <a name="l03519"></a>03519 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    3584. 

  3584. <a name="l03520"></a>03520 <span class="comment">!    Prentice Hall, 1966.</span>
    3585. 

  3585. <a name="l03521"></a>03521 <span class="comment">!</span>
    3586. 

  3586. <a name="l03522"></a>03522 <span class="comment">!    Daniel Zwillinger, editor,</span>
    3587. 

  3587. <a name="l03523"></a>03523 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    3588. 

  3588. <a name="l03524"></a>03524 <span class="comment">!    30th Edition,</span>
    3589. 

  3589. <a name="l03525"></a>03525 <span class="comment">!    CRC Press, 1996.</span>
    3590. 

  3590. <a name="l03526"></a>03526 <span class="comment">!</span>
    3591. 

  3591. <a name="l03527"></a>03527 <span class="comment">!  Modified:</span>
    3592. 

  3592. <a name="l03528"></a>03528 <span class="comment">!</span>
    3593. 

  3593. <a name="l03529"></a>03529 <span class="comment">!    17 September 1998</span>
    3594. 

  3594. <a name="l03530"></a>03530 <span class="comment">!</span>
    3595. 

  3595. <a name="l03531"></a>03531 <span class="comment">!  Author:</span>
    3596. 

  3596. <a name="l03532"></a>03532 <span class="comment">!</span>
    3597. 

  3597. <a name="l03533"></a>03533 <span class="comment">!    John Burkardt</span>
    3598. 

  3598. <a name="l03534"></a>03534 <span class="comment">!</span>
    3599. 

  3599. <a name="l03535"></a>03535 <span class="comment">!  Parameters:</span>
    3600. 

  3600. <a name="l03536"></a>03536 <span class="comment">!</span>
    3601. 

  3601. <a name="l03537"></a>03537 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    3602. 

  3602. <a name="l03538"></a>03538 <span class="comment">!    NORDER must be between 1 and 20.</span>
    3603. 

  3603. <a name="l03539"></a>03539 <span class="comment">!</span>
    3604. 

  3604. <a name="l03540"></a>03540 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    3605. 

  3605. <a name="l03541"></a>03541 <span class="comment">!</span>
    3606. 

  3606. <a name="l03542"></a>03542 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    3607. 

  3607. <a name="l03543"></a>03543 <span class="comment">!    The weights are positive, and should add to 1.</span>
    3608. 

  3608. <a name="l03544"></a>03544 <span class="comment">!</span>
    3609. 

  3609. <a name="l03545"></a>03545   <span class="keyword">implicit none</span>
    3610. 

  3610. <a name="l03546"></a>03546 <span class="comment">!</span>
    3611. 

  3611. <a name="l03547"></a>03547   <span class="keywordtype">integer</span> norder
    3612. 

  3612. <a name="l03548"></a>03548 <span class="comment">!</span>
    3613. 

  3613. <a name="l03549"></a>03549   <span class="keywordtype">double precision</span> weight(norder)
    3614. 

  3614. <a name="l03550"></a>03550   <span class="keywordtype">double precision</span> xtab(norder)
    3615. 

  3615. <a name="l03551"></a>03551 <span class="comment">!</span>
    3616. 

  3616. <a name="l03552"></a>03552   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    3617. 

  3617. <a name="l03553"></a>03553 
    3618. 

  3618. <a name="l03554"></a>03554     xtab(1) =    1.0D+00
    3619. 

  3619. <a name="l03555"></a>03555     weight(1) =  1.0D+00
    3620. 

  3620. <a name="l03556"></a>03556 
    3621. 

  3621. <a name="l03557"></a>03557   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    3622. 

  3622. <a name="l03558"></a>03558 
    3623. 

  3623. <a name="l03559"></a>03559     xtab(1) =    0.585786437626904951198311275790D+00
    3624. 

  3624. <a name="l03560"></a>03560     xtab(2) =    0.341421356237309504880168872421D+01
    3625. 

  3625. <a name="l03561"></a>03561 
    3626. 

  3626. <a name="l03562"></a>03562     weight(1) =  0.853553390593273762200422181052D+00
    3627. 

  3627. <a name="l03563"></a>03563     weight(2) =  0.146446609406726237799577818948D+00
    3628. 

  3628. <a name="l03564"></a>03564 
    3629. 

  3629. <a name="l03565"></a>03565   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    3630. 

  3630. <a name="l03566"></a>03566 
    3631. 

  3631. <a name="l03567"></a>03567     xtab(1) =    0.415774556783479083311533873128D+00
    3632. 

  3632. <a name="l03568"></a>03568     xtab(2) =    0.229428036027904171982205036136D+01
    3633. 

  3633. <a name="l03569"></a>03569     xtab(3) =    0.628994508293747919686641576551D+01
    3634. 

  3634. <a name="l03570"></a>03570 
    3635. 

  3635. <a name="l03571"></a>03571     weight(1) =  0.711093009929173015449590191143D+00
    3636. 

  3636. <a name="l03572"></a>03572     weight(2) =  0.278517733569240848801444888457D+00
    3637. 

  3637. <a name="l03573"></a>03573     weight(3) =  0.103892565015861357489649204007D-01
    3638. 

  3638. <a name="l03574"></a>03574 
    3639. 

  3639. <a name="l03575"></a>03575   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    3640. 

  3640. <a name="l03576"></a>03576 
    3641. 

  3641. <a name="l03577"></a>03577     xtab(1) =    0.322547689619392311800361943361D+00
    3642. 

  3642. <a name="l03578"></a>03578     xtab(2) =    0.174576110115834657568681671252D+01
    3643. 

  3643. <a name="l03579"></a>03579     xtab(3) =    0.453662029692112798327928538496D+01
    3644. 

  3644. <a name="l03580"></a>03580     xtab(4) =    0.939507091230113312923353644342D+01
    3645. 

  3645. <a name="l03581"></a>03581 
    3646. 

  3646. <a name="l03582"></a>03582     weight(1) =  0.603154104341633601635966023818D+00
    3647. 

  3647. <a name="l03583"></a>03583     weight(2) =  0.357418692437799686641492017458D+00
    3648. 

  3648. <a name="l03584"></a>03584     weight(3) =  0.388879085150053842724381681562D-01
    3649. 

  3649. <a name="l03585"></a>03585     weight(4) =  0.539294705561327450103790567621D-03
    3650. 

  3650. <a name="l03586"></a>03586 
    3651. 

  3651. <a name="l03587"></a>03587   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    3652. 

  3652. <a name="l03588"></a>03588 
    3653. 

  3653. <a name="l03589"></a>03589     xtab(1) =    0.263560319718140910203061943361D+00
    3654. 

  3654. <a name="l03590"></a>03590     xtab(2) =    0.141340305910651679221840798019D+01
    3655. 

  3655. <a name="l03591"></a>03591     xtab(3) =    0.359642577104072208122318658878D+01
    3656. 

  3656. <a name="l03592"></a>03592     xtab(4) =    0.708581000585883755692212418111D+01
    3657. 

  3657. <a name="l03593"></a>03593     xtab(5) =    0.126408008442757826594332193066D+02
    3658. 

  3658. <a name="l03594"></a>03594 
    3659. 

  3659. <a name="l03595"></a>03595     weight(1) =  0.521755610582808652475860928792D+00
    3660. 

  3660. <a name="l03596"></a>03596     weight(2) =  0.398666811083175927454133348144D+00
    3661. 

  3661. <a name="l03597"></a>03597     weight(3) =  0.759424496817075953876533114055D-01
    3662. 

  3662. <a name="l03598"></a>03598     weight(4) =  0.361175867992204845446126257304D-02
    3663. 

  3663. <a name="l03599"></a>03599     weight(5) =  0.233699723857762278911490845516D-04
    3664. 

  3664. <a name="l03600"></a>03600 
    3665. 

  3665. <a name="l03601"></a>03601   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    3666. 

  3666. <a name="l03602"></a>03602 
    3667. 

  3667. <a name="l03603"></a>03603     xtab(1) =    0.222846604179260689464354826787D+00
    3668. 

  3668. <a name="l03604"></a>03604     xtab(2) =    0.118893210167262303074315092194D+01
    3669. 

  3669. <a name="l03605"></a>03605     xtab(3) =    0.299273632605931407769132528451D+01
    3670. 

  3670. <a name="l03606"></a>03606     xtab(4) =    0.577514356910451050183983036943D+01
    3671. 

  3671. <a name="l03607"></a>03607     xtab(5) =    0.983746741838258991771554702994D+01
    3672. 

  3672. <a name="l03608"></a>03608     xtab(6) =    0.159828739806017017825457915674D+02
    3673. 

  3673. <a name="l03609"></a>03609 
    3674. 

  3674. <a name="l03610"></a>03610     weight(1) =  0.458964673949963593568284877709D+00
    3675. 

  3675. <a name="l03611"></a>03611     weight(2) =  0.417000830772120994113377566193D+00
    3676. 

  3676. <a name="l03612"></a>03612     weight(3) =  0.113373382074044975738706185098D+00
    3677. 

  3677. <a name="l03613"></a>03613     weight(4) =  0.103991974531490748989133028469D-01
    3678. 

  3678. <a name="l03614"></a>03614     weight(5) =  0.261017202814932059479242860001D-03
    3679. 

  3679. <a name="l03615"></a>03615     weight(6) =  0.898547906429621238825292052825D-06
    3680. 

  3680. <a name="l03616"></a>03616 
    3681. 

  3681. <a name="l03617"></a>03617   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    3682. 

  3682. <a name="l03618"></a>03618 
    3683. 

  3683. <a name="l03619"></a>03619     xtab(1) =    0.193043676560362413838247885004D+00
    3684. 

  3684. <a name="l03620"></a>03620     xtab(2) =    0.102666489533919195034519944317D+01
    3685. 

  3685. <a name="l03621"></a>03621     xtab(3) =    0.256787674495074620690778622666D+01
    3686. 

  3686. <a name="l03622"></a>03622     xtab(4) =    0.490035308452648456810171437810D+01
    3687. 

  3687. <a name="l03623"></a>03623     xtab(5) =    0.818215344456286079108182755123D+01
    3688. 

  3688. <a name="l03624"></a>03624     xtab(6) =    0.127341802917978137580126424582D+02
    3689. 

  3689. <a name="l03625"></a>03625     xtab(7) =    0.193957278622625403117125820576D+02
    3690. 

  3690. <a name="l03626"></a>03626 
    3691. 

  3691. <a name="l03627"></a>03627     weight(1) =  0.409318951701273902130432880018D+00
    3692. 

  3692. <a name="l03628"></a>03628     weight(2) =  0.421831277861719779929281005417D+00
    3693. 

  3693. <a name="l03629"></a>03629     weight(3) =  0.147126348657505278395374184637D+00
    3694. 

  3694. <a name="l03630"></a>03630     weight(4) =  0.206335144687169398657056149642D-01
    3695. 

  3695. <a name="l03631"></a>03631     weight(5) =  0.107401014328074552213195962843D-02
    3696. 

  3696. <a name="l03632"></a>03632     weight(6) =  0.158654643485642012687326223234D-04
    3697. 

  3697. <a name="l03633"></a>03633     weight(7) =  0.317031547899558056227132215385D-07
    3698. 

  3698. <a name="l03634"></a>03634 
    3699. 

  3699. <a name="l03635"></a>03635   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    3700. 

  3700. <a name="l03636"></a>03636 
    3701. 

  3701. <a name="l03637"></a>03637     xtab(1) =    0.170279632305100999788861856608D+00
    3702. 

  3702. <a name="l03638"></a>03638     xtab(2) =    0.903701776799379912186020223555D+00
    3703. 

  3703. <a name="l03639"></a>03639     xtab(3) =    0.225108662986613068930711836697D+01
    3704. 

  3704. <a name="l03640"></a>03640     xtab(4) =    0.426670017028765879364942182690D+01
    3705. 

  3705. <a name="l03641"></a>03641     xtab(5) =    0.704590540239346569727932548212D+01
    3706. 

  3706. <a name="l03642"></a>03642     xtab(6) =    0.107585160101809952240599567880D+02
    3707. 

  3707. <a name="l03643"></a>03643     xtab(7) =    0.157406786412780045780287611584D+02
    3708. 

  3708. <a name="l03644"></a>03644     xtab(8) =    0.228631317368892641057005342974D+02
    3709. 

  3709. <a name="l03645"></a>03645 
    3710. 

  3710. <a name="l03646"></a>03646     weight(1) =  0.369188589341637529920582839376D+00
    3711. 

  3711. <a name="l03647"></a>03647     weight(2) =  0.418786780814342956076978581333D+00
    3712. 

  3712. <a name="l03648"></a>03648     weight(3) =  0.175794986637171805699659866777D+00
    3713. 

  3713. <a name="l03649"></a>03649     weight(4) =  0.333434922612156515221325349344D-01
    3714. 

  3714. <a name="l03650"></a>03650     weight(5) =  0.279453623522567252493892414793D-02
    3715. 

  3715. <a name="l03651"></a>03651     weight(6) =  0.907650877335821310423850149336D-04
    3716. 

  3716. <a name="l03652"></a>03652     weight(7) =  0.848574671627253154486801830893D-06
    3717. 

  3717. <a name="l03653"></a>03653     weight(8) =  0.104800117487151038161508853552D-08
    3718. 

  3718. <a name="l03654"></a>03654 
    3719. 

  3719. <a name="l03655"></a>03655   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    3720. 

  3720. <a name="l03656"></a>03656 
    3721. 

  3721. <a name="l03657"></a>03657     xtab(1) =    0.152322227731808247428107073127D+00
    3722. 

  3722. <a name="l03658"></a>03658     xtab(2) =    0.807220022742255847741419210952D+00
    3723. 

  3723. <a name="l03659"></a>03659     xtab(3) =    0.200513515561934712298303324701D+01
    3724. 

  3724. <a name="l03660"></a>03660     xtab(4) =    0.378347397333123299167540609364D+01
    3725. 

  3725. <a name="l03661"></a>03661     xtab(5) =    0.620495677787661260697353521006D+01
    3726. 

  3726. <a name="l03662"></a>03662     xtab(6) =    0.937298525168757620180971073215D+01
    3727. 

  3727. <a name="l03663"></a>03663     xtab(7) =    0.134662369110920935710978818397D+02
    3728. 

  3728. <a name="l03664"></a>03664     xtab(8) =    0.188335977889916966141498992996D+02
    3729. 

  3729. <a name="l03665"></a>03665     xtab(9) =    0.263740718909273767961410072937D+02
    3730. 

  3730. <a name="l03666"></a>03666 
    3731. 

  3731. <a name="l03667"></a>03667     weight(1) =  0.336126421797962519673467717606D+00
    3732. 

  3732. <a name="l03668"></a>03668     weight(2) =  0.411213980423984387309146942793D+00
    3733. 

  3733. <a name="l03669"></a>03669     weight(3) =  0.199287525370885580860575607212D+00
    3734. 

  3734. <a name="l03670"></a>03670     weight(4) =  0.474605627656515992621163600479D-01
    3735. 

  3735. <a name="l03671"></a>03671     weight(5) =  0.559962661079458317700419900556D-02
    3736. 

  3736. <a name="l03672"></a>03672     weight(6) =  0.305249767093210566305412824291D-03
    3737. 

  3737. <a name="l03673"></a>03673     weight(7) =  0.659212302607535239225572284875D-05
    3738. 

  3738. <a name="l03674"></a>03674     weight(8) =  0.411076933034954844290241040330D-07
    3739. 

  3739. <a name="l03675"></a>03675     weight(9) =  0.329087403035070757646681380323D-10
    3740. 

  3740. <a name="l03676"></a>03676 
    3741. 

  3741. <a name="l03677"></a>03677   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
    3742. 

  3742. <a name="l03678"></a>03678 
    3743. 

  3743. <a name="l03679"></a>03679     xtab(1) =    0.137793470540492430830772505653D+00
    3744. 

  3744. <a name="l03680"></a>03680     xtab(2) =    0.729454549503170498160373121676D+00
    3745. 

  3745. <a name="l03681"></a>03681     xtab(3) =    0.180834290174031604823292007575D+01
    3746. 

  3746. <a name="l03682"></a>03682     xtab(4) =    0.340143369785489951448253222141D+01
    3747. 

  3747. <a name="l03683"></a>03683     xtab(5) =    0.555249614006380363241755848687D+01
    3748. 

  3748. <a name="l03684"></a>03684     xtab(6) =    0.833015274676449670023876719727D+01
    3749. 

  3749. <a name="l03685"></a>03685     xtab(7) =    0.118437858379000655649185389191D+02
    3750. 

  3750. <a name="l03686"></a>03686     xtab(8) =    0.162792578313781020995326539358D+02
    3751. 

  3751. <a name="l03687"></a>03687     xtab(9) =    0.219965858119807619512770901956D+02
    3752. 

  3752. <a name="l03688"></a>03688     xtab(10) =   0.299206970122738915599087933408D+02
    3753. 

  3753. <a name="l03689"></a>03689 
    3754. 

  3754. <a name="l03690"></a>03690     weight(1) =  0.308441115765020141547470834678D+00
    3755. 

  3755. <a name="l03691"></a>03691     weight(2) =  0.401119929155273551515780309913D+00
    3756. 

  3756. <a name="l03692"></a>03692     weight(3) =  0.218068287611809421588648523475D+00
    3757. 

  3757. <a name="l03693"></a>03693     weight(4) =  0.620874560986777473929021293135D-01
    3758. 

  3758. <a name="l03694"></a>03694     weight(5) =  0.950151697518110055383907219417D-02
    3759. 

  3759. <a name="l03695"></a>03695     weight(6) =  0.753008388587538775455964353676D-03
    3760. 

  3760. <a name="l03696"></a>03696     weight(7) =  0.282592334959956556742256382685D-04
    3761. 

  3761. <a name="l03697"></a>03697     weight(8) =  0.424931398496268637258657665975D-06
    3762. 

  3762. <a name="l03698"></a>03698     weight(9) =  0.183956482397963078092153522436D-08
    3763. 

  3763. <a name="l03699"></a>03699     weight(10) = 0.991182721960900855837754728324D-12
    3764. 

  3764. <a name="l03700"></a>03700 
    3765. 

  3765. <a name="l03701"></a>03701   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 11 ) <span class="keyword">then</span>
    3766. 

  3766. <a name="l03702"></a>03702 
    3767. 

  3767. <a name="l03703"></a>03703     xtab(1) =    0.125796442187967522675794577516D+00
    3768. 

  3768. <a name="l03704"></a>03704     xtab(2) =    0.665418255839227841678127839420D+00
    3769. 

  3769. <a name="l03705"></a>03705     xtab(3) =    0.164715054587216930958700321365D+01
    3770. 

  3770. <a name="l03706"></a>03706     xtab(4) =    0.309113814303525495330195934259D+01
    3771. 

  3771. <a name="l03707"></a>03707     xtab(5) =    0.502928440157983321236999508366D+01
    3772. 

  3772. <a name="l03708"></a>03708     xtab(6) =    0.750988786380661681941099714450D+01
    3773. 

  3773. <a name="l03709"></a>03709     xtab(7) =    0.106059509995469677805559216457D+02
    3774. 

  3774. <a name="l03710"></a>03710     xtab(8) =    0.144316137580641855353200450349D+02
    3775. 

  3775. <a name="l03711"></a>03711     xtab(9) =    0.191788574032146786478174853989D+02
    3776. 

  3776. <a name="l03712"></a>03712     xtab(10) =   0.252177093396775611040909447797D+02
    3777. 

  3777. <a name="l03713"></a>03713     xtab(11) =   0.334971928471755372731917259395D+02
    3778. 

  3778. <a name="l03714"></a>03714 
    3779. 

  3779. <a name="l03715"></a>03715     weight(1) =  0.284933212894200605056051024724D+00
    3780. 

  3780. <a name="l03716"></a>03716     weight(2) =  0.389720889527849377937553508048D+00
    3781. 

  3781. <a name="l03717"></a>03717     weight(3) =  0.232781831848991333940223795543D+00
    3782. 

  3782. <a name="l03718"></a>03718     weight(4) =  0.765644535461966864008541790132D-01
    3783. 

  3783. <a name="l03719"></a>03719     weight(5) =  0.143932827673506950918639187409D-01
    3784. 

  3784. <a name="l03720"></a>03720     weight(6) =  0.151888084648487306984777640042D-02
    3785. 

  3785. <a name="l03721"></a>03721     weight(7) =  0.851312243547192259720424170600D-04
    3786. 

  3786. <a name="l03722"></a>03722     weight(8) =  0.229240387957450407857683270709D-05
    3787. 

  3787. <a name="l03723"></a>03723     weight(9) =  0.248635370276779587373391491114D-07
    3788. 

  3788. <a name="l03724"></a>03724     weight(10) = 0.771262693369132047028152590222D-10
    3789. 

  3789. <a name="l03725"></a>03725     weight(11) = 0.288377586832362386159777761217D-13
    3790. 

  3790. <a name="l03726"></a>03726 
    3791. 

  3791. <a name="l03727"></a>03727   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 12 ) <span class="keyword">then</span>
    3792. 

  3792. <a name="l03728"></a>03728 
    3793. 

  3793. <a name="l03729"></a>03729     xtab(1) =    0.115722117358020675267196428240D+00
    3794. 

  3794. <a name="l03730"></a>03730     xtab(2) =    0.611757484515130665391630053042D+00
    3795. 

  3795. <a name="l03731"></a>03731     xtab(3) =    0.151261026977641878678173792687D+01
    3796. 

  3796. <a name="l03732"></a>03732     xtab(4) =    0.283375133774350722862747177657D+01
    3797. 

  3797. <a name="l03733"></a>03733     xtab(5) =    0.459922763941834848460572922485D+01
    3798. 

  3798. <a name="l03734"></a>03734     xtab(6) =    0.684452545311517734775433041849D+01
    3799. 

  3799. <a name="l03735"></a>03735     xtab(7) =    0.962131684245686704391238234923D+01
    3800. 

  3800. <a name="l03736"></a>03736     xtab(8) =    0.130060549933063477203460524294D+02
    3801. 

  3801. <a name="l03737"></a>03737     xtab(9) =    0.171168551874622557281840528008D+02
    3802. 

  3802. <a name="l03738"></a>03738     xtab(10) =   0.221510903793970056699218950837D+02
    3803. 

  3803. <a name="l03739"></a>03739     xtab(11) =   0.284879672509840003125686072325D+02
    3804. 

  3804. <a name="l03740"></a>03740     xtab(12) =   0.370991210444669203366389142764D+02
    3805. 

  3805. <a name="l03741"></a>03741 
    3806. 

  3806. <a name="l03742"></a>03742     weight(1) =  0.264731371055443190349738892056D+00
    3807. 

  3807. <a name="l03743"></a>03743     weight(2) =  0.377759275873137982024490556707D+00
    3808. 

  3808. <a name="l03744"></a>03744     weight(3) =  0.244082011319877564254870818274D+00
    3809. 

  3809. <a name="l03745"></a>03745     weight(4) =  0.904492222116809307275054934667D-01
    3810. 

  3810. <a name="l03746"></a>03746     weight(5) =  0.201023811546340965226612867827D-01
    3811. 

  3811. <a name="l03747"></a>03747     weight(6) =  0.266397354186531588105415760678D-02
    3812. 

  3812. <a name="l03748"></a>03748     weight(7) =  0.203231592662999392121432860438D-03
    3813. 

  3813. <a name="l03749"></a>03749     weight(8) =  0.836505585681979874533632766396D-05
    3814. 

  3814. <a name="l03750"></a>03750     weight(9) =  0.166849387654091026116989532619D-06
    3815. 

  3815. <a name="l03751"></a>03751     weight(10) = 0.134239103051500414552392025055D-08
    3816. 

  3816. <a name="l03752"></a>03752     weight(11) = 0.306160163503502078142407718971D-11
    3817. 

  3817. <a name="l03753"></a>03753     weight(12) = 0.814807746742624168247311868103D-15
    3818. 

  3818. <a name="l03754"></a>03754 
    3819. 

  3819. <a name="l03755"></a>03755   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 13 ) <span class="keyword">then</span>
    3820. 

  3820. <a name="l03756"></a>03756 
    3821. 

  3821. <a name="l03757"></a>03757     xtab(1) =    0.107142388472252310648493376977D+00
    3822. 

  3822. <a name="l03758"></a>03758     xtab(2) =    0.566131899040401853406036347177D+00
    3823. 

  3823. <a name="l03759"></a>03759     xtab(3) =    0.139856433645101971792750259921D+01
    3824. 

  3824. <a name="l03760"></a>03760     xtab(4) =    0.261659710840641129808364008472D+01
    3825. 

  3825. <a name="l03761"></a>03761     xtab(5) =    0.423884592901703327937303389926D+01
    3826. 

  3826. <a name="l03762"></a>03762     xtab(6) =    0.629225627114007378039376523025D+01
    3827. 

  3827. <a name="l03763"></a>03763     xtab(7) =    0.881500194118697804733348868036D+01
    3828. 

  3828. <a name="l03764"></a>03764     xtab(8) =    0.118614035888112425762212021880D+02
    3829. 

  3829. <a name="l03765"></a>03765     xtab(9) =    0.155107620377037527818478532958D+02
    3830. 

  3830. <a name="l03766"></a>03766     xtab(10) =   0.198846356638802283332036594634D+02
    3831. 

  3831. <a name="l03767"></a>03767     xtab(11) =   0.251852638646777580842970297823D+02
    3832. 

  3832. <a name="l03768"></a>03768     xtab(12) =   0.318003863019472683713663283526D+02
    3833. 

  3833. <a name="l03769"></a>03769     xtab(13) =   0.407230086692655795658979667001D+02
    3834. 

  3834. <a name="l03770"></a>03770 
    3835. 

  3835. <a name="l03771"></a>03771     weight(1) =  0.247188708429962621346249185964D+00
    3836. 

  3836. <a name="l03772"></a>03772     weight(2) =  0.365688822900521945306717530893D+00
    3837. 

  3837. <a name="l03773"></a>03773     weight(3) =  0.252562420057658502356824288815D+00
    3838. 

  3838. <a name="l03774"></a>03774     weight(4) =  0.103470758024183705114218631672D+00
    3839. 

  3839. <a name="l03775"></a>03775     weight(5) =  0.264327544155616157781587735702D-01
    3840. 

  3840. <a name="l03776"></a>03776     weight(6) =  0.422039604025475276555209292644D-02
    3841. 

  3841. <a name="l03777"></a>03777     weight(7) =  0.411881770472734774892472527082D-03
    3842. 

  3842. <a name="l03778"></a>03778     weight(8) =  0.235154739815532386882897300772D-04
    3843. 

  3843. <a name="l03779"></a>03779     weight(9) =  0.731731162024909910401047197761D-06
    3844. 

  3844. <a name="l03780"></a>03780     weight(10) = 0.110884162570398067979150974759D-07
    3845. 

  3845. <a name="l03781"></a>03781     weight(11) = 0.677082669220589884064621459082D-10
    3846. 

  3846. <a name="l03782"></a>03782     weight(12) = 0.115997995990507606094507145382D-12
    3847. 

  3847. <a name="l03783"></a>03783     weight(13) = 0.224509320389275841599187226865D-16
    3848. 

  3848. <a name="l03784"></a>03784 
    3849. 

  3849. <a name="l03785"></a>03785   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 14 ) <span class="keyword">then</span>
    3850. 

  3850. <a name="l03786"></a>03786 
    3851. 

  3851. <a name="l03787"></a>03787     xtab(1) =    0.997475070325975745736829452514D-01
    3852. 

  3852. <a name="l03788"></a>03788     xtab(2) =    0.526857648851902896404583451502D+00
    3853. 

  3853. <a name="l03789"></a>03789     xtab(3) =    0.130062912125149648170842022116D+01
    3854. 

  3854. <a name="l03790"></a>03790     xtab(4) =    0.243080107873084463616999751038D+01
    3855. 

  3855. <a name="l03791"></a>03791     xtab(5) =    0.393210282229321888213134366778D+01
    3856. 

  3856. <a name="l03792"></a>03792     xtab(6) =    0.582553621830170841933899983898D+01
    3857. 

  3857. <a name="l03793"></a>03793     xtab(7) =    0.814024014156514503005978046052D+01
    3858. 

  3858. <a name="l03794"></a>03794     xtab(8) =    0.109164995073660188408130510904D+02
    3859. 

  3859. <a name="l03795"></a>03795     xtab(9) =    0.142108050111612886831059780825D+02
    3860. 

  3860. <a name="l03796"></a>03796     xtab(10) =   0.181048922202180984125546272083D+02
    3861. 

  3861. <a name="l03797"></a>03797     xtab(11) =   0.227233816282696248232280886985D+02
    3862. 

  3862. <a name="l03798"></a>03798     xtab(12) =   0.282729817232482056954158923218D+02
    3863. 

  3863. <a name="l03799"></a>03799     xtab(13) =   0.351494436605924265828643121364D+02
    3864. 

  3864. <a name="l03800"></a>03800     xtab(14) =   0.443660817111174230416312423666D+02
    3865. 

  3865. <a name="l03801"></a>03801 
    3866. 

  3866. <a name="l03802"></a>03802     weight(1) =  0.231815577144864977840774861104D+00
    3867. 

  3867. <a name="l03803"></a>03803     weight(2) =  0.353784691597543151802331301273D+00
    3868. 

  3868. <a name="l03804"></a>03804     weight(3) =  0.258734610245428085987320561144D+00
    3869. 

  3869. <a name="l03805"></a>03805     weight(4) =  0.115482893556923210087304988673D+00
    3870. 

  3870. <a name="l03806"></a>03806     weight(5) =  0.331920921593373600387499587137D-01
    3871. 

  3871. <a name="l03807"></a>03807     weight(6) =  0.619286943700661021678785967675D-02
    3872. 

  3872. <a name="l03808"></a>03808     weight(7) =  0.739890377867385942425890907080D-03
    3873. 

  3873. <a name="l03809"></a>03809     weight(8) =  0.549071946684169837857331777667D-04
    3874. 

  3874. <a name="l03810"></a>03810     weight(9) =  0.240958576408537749675775256553D-05
    3875. 

  3875. <a name="l03811"></a>03811     weight(10) = 0.580154398167649518088619303904D-07
    3876. 

  3876. <a name="l03812"></a>03812     weight(11) = 0.681931469248497411961562387084D-09
    3877. 

  3877. <a name="l03813"></a>03813     weight(12) = 0.322120775189484793980885399656D-11
    3878. 

  3878. <a name="l03814"></a>03814     weight(13) = 0.422135244051658735159797335643D-14
    3879. 

  3879. <a name="l03815"></a>03815     weight(14) = 0.605237502228918880839870806281D-18
    3880. 

  3880. <a name="l03816"></a>03816 
    3881. 

  3881. <a name="l03817"></a>03817   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
    3882. 

  3882. <a name="l03818"></a>03818 
    3883. 

  3883. <a name="l03819"></a>03819     xtab(1) =    0.933078120172818047629030383672D-01
    3884. 

  3884. <a name="l03820"></a>03820     xtab(2) =    0.492691740301883908960101791412D+00
    3885. 

  3885. <a name="l03821"></a>03821     xtab(3) =    0.121559541207094946372992716488D+01
    3886. 

  3886. <a name="l03822"></a>03822     xtab(4) =    0.226994952620374320247421741375D+01
    3887. 

  3887. <a name="l03823"></a>03823     xtab(5) =    0.366762272175143727724905959436D+01
    3888. 

  3888. <a name="l03824"></a>03824     xtab(6) =    0.542533662741355316534358132596D+01
    3889. 

  3889. <a name="l03825"></a>03825     xtab(7) =    0.756591622661306786049739555812D+01
    3890. 

  3890. <a name="l03826"></a>03826     xtab(8) =    0.101202285680191127347927394568D+02
    3891. 

  3891. <a name="l03827"></a>03827     xtab(9) =    0.131302824821757235640991204176D+02
    3892. 

  3892. <a name="l03828"></a>03828     xtab(10) =   0.166544077083299578225202408430D+02
    3893. 

  3893. <a name="l03829"></a>03829     xtab(11) =   0.207764788994487667729157175676D+02
    3894. 

  3894. <a name="l03830"></a>03830     xtab(12) =   0.256238942267287801445868285977D+02
    3895. 

  3895. <a name="l03831"></a>03831     xtab(13) =   0.314075191697539385152432196202D+02
    3896. 

  3896. <a name="l03832"></a>03832     xtab(14) =   0.385306833064860094162515167595D+02
    3897. 

  3897. <a name="l03833"></a>03833     xtab(15) =   0.480260855726857943465734308508D+02
    3898. 

  3898. <a name="l03834"></a>03834 
    3899. 

  3899. <a name="l03835"></a>03835     weight(1) =  0.218234885940086889856413236448D+00
    3900. 

  3900. <a name="l03836"></a>03836     weight(2) =  0.342210177922883329638948956807D+00
    3901. 

  3901. <a name="l03837"></a>03837     weight(3) =  0.263027577941680097414812275022D+00
    3902. 

  3902. <a name="l03838"></a>03838     weight(4) =  0.126425818105930535843030549378D+00
    3903. 

  3903. <a name="l03839"></a>03839     weight(5) =  0.402068649210009148415854789871D-01
    3904. 

  3904. <a name="l03840"></a>03840     weight(6) =  0.856387780361183836391575987649D-02
    3905. 

  3905. <a name="l03841"></a>03841     weight(7) =  0.121243614721425207621920522467D-02
    3906. 

  3906. <a name="l03842"></a>03842     weight(8) =  0.111674392344251941992578595518D-03
    3907. 

  3907. <a name="l03843"></a>03843     weight(9) =  0.645992676202290092465319025312D-05
    3908. 

  3908. <a name="l03844"></a>03844     weight(10) = 0.222631690709627263033182809179D-06
    3909. 

  3909. <a name="l03845"></a>03845     weight(11) = 0.422743038497936500735127949331D-08
    3910. 

  3910. <a name="l03846"></a>03846     weight(12) = 0.392189726704108929038460981949D-10
    3911. 

  3911. <a name="l03847"></a>03847     weight(13) = 0.145651526407312640633273963455D-12
    3912. 

  3912. <a name="l03848"></a>03848     weight(14) = 0.148302705111330133546164737187D-15
    3913. 

  3913. <a name="l03849"></a>03849     weight(15) = 0.160059490621113323104997812370D-19
    3914. 

  3914. <a name="l03850"></a>03850 
    3915. 

  3915. <a name="l03851"></a>03851   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
    3916. 

  3916. <a name="l03852"></a>03852 
    3917. 

  3917. <a name="l03853"></a>03853     xtab(1) =    0.876494104789278403601980973401D-01
    3918. 

  3918. <a name="l03854"></a>03854     xtab(2) =    0.462696328915080831880838260664D+00
    3919. 

  3919. <a name="l03855"></a>03855     xtab(3) =    0.114105777483122685687794501811D+01
    3920. 

  3920. <a name="l03856"></a>03856     xtab(4) =    0.212928364509838061632615907066D+01
    3921. 

  3921. <a name="l03857"></a>03857     xtab(5) =    0.343708663389320664523510701675D+01
    3922. 

  3922. <a name="l03858"></a>03858     xtab(6) =    0.507801861454976791292305830814D+01
    3923. 

  3923. <a name="l03859"></a>03859     xtab(7) =    0.707033853504823413039598947080D+01
    3924. 

  3924. <a name="l03860"></a>03860     xtab(8) =    0.943831433639193878394724672911D+01
    3925. 

  3925. <a name="l03861"></a>03861     xtab(9) =    0.122142233688661587369391246088D+02
    3926. 

  3926. <a name="l03862"></a>03862     xtab(10) =   0.154415273687816170767647741622D+02
    3927. 

  3927. <a name="l03863"></a>03863     xtab(11) =   0.191801568567531348546631409497D+02
    3928. 

  3928. <a name="l03864"></a>03864     xtab(12) =   0.235159056939919085318231872752D+02
    3929. 

  3929. <a name="l03865"></a>03865     xtab(13) =   0.285787297428821403675206137099D+02
    3930. 

  3930. <a name="l03866"></a>03866     xtab(14) =   0.345833987022866258145276871778D+02
    3931. 

  3931. <a name="l03867"></a>03867     xtab(15) =   0.419404526476883326354722330252D+02
    3932. 

  3932. <a name="l03868"></a>03868     xtab(16) =   0.517011603395433183643426971197D+02
    3933. 

  3933. <a name="l03869"></a>03869 
    3934. 

  3934. <a name="l03870"></a>03870     weight(1) =  0.206151714957800994334273636741D+00
    3935. 

  3935. <a name="l03871"></a>03871     weight(2) =  0.331057854950884165992983098710D+00
    3936. 

  3936. <a name="l03872"></a>03872     weight(3) =  0.265795777644214152599502020650D+00
    3937. 

  3937. <a name="l03873"></a>03873     weight(4) =  0.136296934296377539975547513526D+00
    3938. 

  3938. <a name="l03874"></a>03874     weight(5) =  0.473289286941252189780623392781D-01
    3939. 

  3939. <a name="l03875"></a>03875     weight(6) =  0.112999000803394532312490459701D-01
    3940. 

  3940. <a name="l03876"></a>03876     weight(7) =  0.184907094352631086429176783252D-02
    3941. 

  3941. <a name="l03877"></a>03877     weight(8) =  0.204271915308278460126018338421D-03
    3942. 

  3942. <a name="l03878"></a>03878     weight(9) =  0.148445868739812987713515067551D-04
    3943. 

  3943. <a name="l03879"></a>03879     weight(10) = 0.682831933087119956439559590327D-06
    3944. 

  3944. <a name="l03880"></a>03880     weight(11) = 0.188102484107967321388159920418D-07
    3945. 

  3945. <a name="l03881"></a>03881     weight(12) = 0.286235024297388161963062629156D-09
    3946. 

  3946. <a name="l03882"></a>03882     weight(13) = 0.212707903322410296739033610978D-11
    3947. 

  3947. <a name="l03883"></a>03883     weight(14) = 0.629796700251786778717446214552D-14
    3948. 

  3948. <a name="l03884"></a>03884     weight(15) = 0.505047370003551282040213233303D-17
    3949. 

  3949. <a name="l03885"></a>03885     weight(16) = 0.416146237037285519042648356116D-21
    3950. 

  3950. <a name="l03886"></a>03886 
    3951. 

  3951. <a name="l03887"></a>03887   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 17 ) <span class="keyword">then</span>
    3952. 

  3952. <a name="l03888"></a>03888 
    3953. 

  3953. <a name="l03889"></a>03889     xtab(1) =    0.826382147089476690543986151980D-01
    3954. 

  3954. <a name="l03890"></a>03890     xtab(2) =    0.436150323558710436375959029847D+00
    3955. 

  3955. <a name="l03891"></a>03891     xtab(3) =    0.107517657751142857732980316755D+01
    3956. 

  3956. <a name="l03892"></a>03892     xtab(4) =    0.200519353164923224070293371933D+01
    3957. 

  3957. <a name="l03893"></a>03893     xtab(5) =    0.323425612404744376157380120696D+01
    3958. 

  3958. <a name="l03894"></a>03894     xtab(6) =    0.477351351370019726480932076262D+01
    3959. 

  3959. <a name="l03895"></a>03895     xtab(7) =    0.663782920536495266541643929703D+01
    3960. 

  3960. <a name="l03896"></a>03896     xtab(8) =    0.884668551116980005369470571184D+01
    3961. 

  3961. <a name="l03897"></a>03897     xtab(9) =    0.114255293193733525869726151469D+02
    3962. 

  3962. <a name="l03898"></a>03898     xtab(10) =   0.144078230374813180021982874959D+02
    3963. 

  3963. <a name="l03899"></a>03899     xtab(11) =   0.178382847307011409290658752412D+02
    3964. 

  3964. <a name="l03900"></a>03900     xtab(12) =   0.217782682577222653261749080522D+02
    3965. 

  3965. <a name="l03901"></a>03901     xtab(13) =   0.263153178112487997766149598369D+02
    3966. 

  3966. <a name="l03902"></a>03902     xtab(14) =   0.315817716804567331343908517497D+02
    3967. 

  3967. <a name="l03903"></a>03903     xtab(15) =   0.377960938374771007286092846663D+02
    3968. 

  3968. <a name="l03904"></a>03904     xtab(16) =   0.453757165339889661829258363215D+02
    3969. 

  3969. <a name="l03905"></a>03905     xtab(17) =   0.553897517898396106640900199790D+02
    3970. 

  3970. <a name="l03906"></a>03906 
    3971. 

  3971. <a name="l03907"></a>03907     weight(1) =  0.195332205251770832145927297697D+00
    3972. 

  3972. <a name="l03908"></a>03908     weight(2) =  0.320375357274540281336625631970D+00
    3973. 

  3973. <a name="l03909"></a>03909     weight(3) =  0.267329726357171097238809604160D+00
    3974. 

  3974. <a name="l03910"></a>03910     weight(4) =  0.145129854358758625407426447473D+00
    3975. 

  3975. <a name="l03911"></a>03911     weight(5) =  0.544369432453384577793805803066D-01
    3976. 

  3976. <a name="l03912"></a>03912     weight(6) =  0.143572977660618672917767247431D-01
    3977. 

  3977. <a name="l03913"></a>03913     weight(7) =  0.266282473557277256843236250006D-02
    3978. 

  3978. <a name="l03914"></a>03914     weight(8) =  0.343679727156299920611775097985D-03
    3979. 

  3979. <a name="l03915"></a>03915     weight(9) =  0.302755178378287010943703641131D-04
    3980. 

  3980. <a name="l03916"></a>03916     weight(10) = 0.176851505323167689538081156159D-05
    3981. 

  3981. <a name="l03917"></a>03917     weight(11) = 0.657627288681043332199222748162D-07
    3982. 

  3982. <a name="l03918"></a>03918     weight(12) = 0.146973093215954679034375821888D-08
    3983. 

  3983. <a name="l03919"></a>03919     weight(13) = 0.181691036255544979555476861323D-10
    3984. 

  3984. <a name="l03920"></a>03920     weight(14) = 0.109540138892868740297645078918D-12
    3985. 

  3985. <a name="l03921"></a>03921     weight(15) = 0.261737388222337042155132062413D-15
    3986. 

  3986. <a name="l03922"></a>03922     weight(16) = 0.167293569314615469085022374652D-18
    3987. 

  3987. <a name="l03923"></a>03923     weight(17) = 0.106562631627404278815253271162D-22
    3988. 

  3988. <a name="l03924"></a>03924 
    3989. 

  3989. <a name="l03925"></a>03925   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 18 ) <span class="keyword">then</span>
    3990. 

  3990. <a name="l03926"></a>03926 
    3991. 

  3991. <a name="l03927"></a>03927     xtab(1) =    0.781691666697054712986747615334D-01
    3992. 

  3992. <a name="l03928"></a>03928     xtab(2) =    0.412490085259129291039101536536D+00
    3993. 

  3993. <a name="l03929"></a>03929     xtab(3) =    0.101652017962353968919093686187D+01
    3994. 

  3994. <a name="l03930"></a>03930     xtab(4) =    0.189488850996976091426727831954D+01
    3995. 

  3995. <a name="l03931"></a>03931     xtab(5) =    0.305435311320265975115241130719D+01
    3996. 

  3996. <a name="l03932"></a>03932     xtab(6) =    0.450420553888989282633795571455D+01
    3997. 

  3997. <a name="l03933"></a>03933     xtab(7) =    0.625672507394911145274209116326D+01
    3998. 

  3998. <a name="l03934"></a>03934     xtab(8) =    0.832782515660563002170470261564D+01
    3999. 

  3999. <a name="l03935"></a>03935     xtab(9) =    0.107379900477576093352179033397D+02
    4000. 

  4000. <a name="l03936"></a>03936     xtab(10) =   0.135136562075550898190863812108D+02
    4001. 

  4001. <a name="l03937"></a>03937     xtab(11) =   0.166893062819301059378183984163D+02
    4002. 

  4002. <a name="l03938"></a>03938     xtab(12) =   0.203107676262677428561313764553D+02
    4003. 

  4003. <a name="l03939"></a>03939     xtab(13) =   0.244406813592837027656442257980D+02
    4004. 

  4004. <a name="l03940"></a>03940     xtab(14) =   0.291682086625796161312980677805D+02
    4005. 

  4005. <a name="l03941"></a>03941     xtab(15) =   0.346279270656601721454012429438D+02
    4006. 

  4006. <a name="l03942"></a>03942     xtab(16) =   0.410418167728087581392948614284D+02
    4007. 

  4007. <a name="l03943"></a>03943     xtab(17) =   0.488339227160865227486586093290D+02
    4008. 

  4008. <a name="l03944"></a>03944     xtab(18) =   0.590905464359012507037157810181D+02
    4009. 

  4009. <a name="l03945"></a>03945 
    4010. 

  4010. <a name="l03946"></a>03946     weight(1) =  0.185588603146918805623337752284D+00
    4011. 

  4011. <a name="l03947"></a>03947     weight(2) =  0.310181766370225293649597595713D+00
    4012. 

  4012. <a name="l03948"></a>03948     weight(3) =  0.267866567148536354820854394783D+00
    4013. 

  4013. <a name="l03949"></a>03949     weight(4) =  0.152979747468074906553843082053D+00
    4014. 

  4014. <a name="l03950"></a>03950     weight(5) =  0.614349178609616527076780103487D-01
    4015. 

  4015. <a name="l03951"></a>03951     weight(6) =  0.176872130807729312772600233761D-01
    4016. 

  4016. <a name="l03952"></a>03952     weight(7) =  0.366017976775991779802657207890D-02
    4017. 

  4017. <a name="l03953"></a>03953     weight(8) =  0.540622787007735323128416319257D-03
    4018. 

  4018. <a name="l03954"></a>03954     weight(9) =  0.561696505121423113817929049294D-04
    4019. 

  4019. <a name="l03955"></a>03955     weight(10) = 0.401530788370115755858883625279D-05
    4020. 

  4020. <a name="l03956"></a>03956     weight(11) = 0.191466985667567497969210011321D-06
    4021. 

  4021. <a name="l03957"></a>03957     weight(12) = 0.583609526863159412918086289717D-08
    4022. 

  4022. <a name="l03958"></a>03958     weight(13) = 0.107171126695539012772851317562D-09
    4023. 

  4023. <a name="l03959"></a>03959     weight(14) = 0.108909871388883385562011298291D-11
    4024. 

  4024. <a name="l03960"></a>03960     weight(15) = 0.538666474837830887608094323164D-14
    4025. 

  4025. <a name="l03961"></a>03961     weight(16) = 0.104986597803570340877859934846D-16
    4026. 

  4026. <a name="l03962"></a>03962     weight(17) = 0.540539845163105364356554467358D-20
    4027. 

  4027. <a name="l03963"></a>03963     weight(18) = 0.269165326920102862708377715980D-24
    4028. 

  4028. <a name="l03964"></a>03964 
    4029. 

  4029. <a name="l03965"></a>03965   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 19 ) <span class="keyword">then</span>
    4030. 

  4030. <a name="l03966"></a>03966 
    4031. 

  4031. <a name="l03967"></a>03967     xtab(1) =    0.741587837572050877131369916024D-01
    4032. 

  4032. <a name="l03968"></a>03968     xtab(2) =    0.391268613319994607337648350299D+00
    4033. 

  4033. <a name="l03969"></a>03969     xtab(3) =    0.963957343997958058624879377130D+00
    4034. 

  4034. <a name="l03970"></a>03970     xtab(4) =    0.179617558206832812557725825252D+01
    4035. 

  4035. <a name="l03971"></a>03971     xtab(5) =    0.289365138187378399116494713237D+01
    4036. 

  4036. <a name="l03972"></a>03972     xtab(6) =    0.426421553962776647436040018167D+01
    4037. 

  4037. <a name="l03973"></a>03973     xtab(7) =    0.591814156164404855815360191408D+01
    4038. 

  4038. <a name="l03974"></a>03974     xtab(8) =    0.786861891533473373105668358176D+01
    4039. 

  4039. <a name="l03975"></a>03975     xtab(9) =    0.101324237168152659251627415800D+02
    4040. 

  4040. <a name="l03976"></a>03976     xtab(10) =   0.127308814638423980045092979656D+02
    4041. 

  4041. <a name="l03977"></a>03977     xtab(11) =   0.156912783398358885454136069861D+02
    4042. 

  4042. <a name="l03978"></a>03978     xtab(12) =   0.190489932098235501532136429732D+02
    4043. 

  4043. <a name="l03979"></a>03979     xtab(13) =   0.228508497608294829323930586693D+02
    4044. 

  4044. <a name="l03980"></a>03980     xtab(14) =   0.271606693274114488789963947149D+02
    4045. 

  4045. <a name="l03981"></a>03981     xtab(15) =   0.320691222518622423224362865906D+02
    4046. 

  4046. <a name="l03982"></a>03982     xtab(16) =   0.377129058012196494770647508283D+02
    4047. 

  4047. <a name="l03983"></a>03983     xtab(17) =   0.443173627958314961196067736013D+02
    4048. 

  4048. <a name="l03984"></a>03984     xtab(18) =   0.523129024574043831658644222420D+02
    4049. 

  4049. <a name="l03985"></a>03985     xtab(19) =   0.628024231535003758413504690673D+02
    4050. 

  4050. <a name="l03986"></a>03986 
    4051. 

  4051. <a name="l03987"></a>03987     weight(1) =  0.176768474915912502251035479815D+00
    4052. 

  4052. <a name="l03988"></a>03988     weight(2) =  0.300478143607254379482156807712D+00
    4053. 

  4053. <a name="l03989"></a>03989     weight(3) =  0.267599547038175030772695440648D+00
    4054. 

  4054. <a name="l03990"></a>03990     weight(4) =  0.159913372135580216785512147895D+00
    4055. 

  4055. <a name="l03991"></a>03991     weight(5) =  0.682493799761491134552355368344D-01
    4056. 

  4056. <a name="l03992"></a>03992     weight(6) =  0.212393076065443249244062193091D-01
    4057. 

  4057. <a name="l03993"></a>03993     weight(7) =  0.484162735114839596725013121019D-02
    4058. 

  4058. <a name="l03994"></a>03994     weight(8) =  0.804912747381366766594647138204D-03
    4059. 

  4059. <a name="l03995"></a>03995     weight(9) =  0.965247209315350170843161738801D-04
    4060. 

  4060. <a name="l03996"></a>03996     weight(10) = 0.820730525805103054408982992869D-05
    4061. 

  4061. <a name="l03997"></a>03997     weight(11) = 0.483056672473077253944806671560D-06
    4062. 

  4062. <a name="l03998"></a>03998     weight(12) = 0.190499136112328569993615674552D-07
    4063. 

  4063. <a name="l03999"></a>03999     weight(13) = 0.481668463092806155766936380273D-09
    4064. 

  4064. <a name="l04000"></a>04000     weight(14) = 0.734825883955114437684376840171D-11
    4065. 

  4065. <a name="l04001"></a>04001     weight(15) = 0.620227538757261639893719012423D-13
    4066. 

  4066. <a name="l04002"></a>04002     weight(16) = 0.254143084301542272371866857954D-15
    4067. 

  4067. <a name="l04003"></a>04003     weight(17) = 0.407886129682571235007187465134D-18
    4068. 

  4068. <a name="l04004"></a>04004     weight(18) = 0.170775018759383706100412325084D-21
    4069. 

  4069. <a name="l04005"></a>04005     weight(19) = 0.671506464990818995998969111749D-26
    4070. 

  4070. <a name="l04006"></a>04006 
    4071. 

  4071. <a name="l04007"></a>04007   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 20 ) <span class="keyword">then</span>
    4072. 

  4072. <a name="l04008"></a>04008 
    4073. 

  4073. <a name="l04009"></a>04009     xtab(1) =    0.705398896919887533666890045842D-01
    4074. 

  4074. <a name="l04010"></a>04010     xtab(2) =    0.372126818001611443794241388761D+00
    4075. 

  4075. <a name="l04011"></a>04011     xtab(3) =    0.916582102483273564667716277074D+00
    4076. 

  4076. <a name="l04012"></a>04012     xtab(4) =    0.170730653102834388068768966741D+01
    4077. 

  4077. <a name="l04013"></a>04013     xtab(5) =    0.274919925530943212964503046049D+01
    4078. 

  4078. <a name="l04014"></a>04014     xtab(6) =    0.404892531385088692237495336913D+01
    4079. 

  4079. <a name="l04015"></a>04015     xtab(7) =    0.561517497086161651410453988565D+01
    4080. 

  4080. <a name="l04016"></a>04016     xtab(8) =    0.745901745367106330976886021837D+01
    4081. 

  4081. <a name="l04017"></a>04017     xtab(9) =    0.959439286958109677247367273428D+01
    4082. 

  4082. <a name="l04018"></a>04018     xtab(10) =   0.120388025469643163096234092989D+02
    4083. 

  4083. <a name="l04019"></a>04019     xtab(11) =   0.148142934426307399785126797100D+02
    4084. 

  4084. <a name="l04020"></a>04020     xtab(12) =   0.179488955205193760173657909926D+02
    4085. 

  4085. <a name="l04021"></a>04021     xtab(13) =   0.214787882402850109757351703696D+02
    4086. 

  4086. <a name="l04022"></a>04022     xtab(14) =   0.254517027931869055035186774846D+02
    4087. 

  4087. <a name="l04023"></a>04023     xtab(15) =   0.299325546317006120067136561352D+02
    4088. 

  4088. <a name="l04024"></a>04024     xtab(16) =   0.350134342404790000062849359067D+02
    4089. 

  4089. <a name="l04025"></a>04025     xtab(17) =   0.408330570567285710620295677078D+02
    4090. 

  4090. <a name="l04026"></a>04026     xtab(18) =   0.476199940473465021399416271529D+02
    4091. 

  4091. <a name="l04027"></a>04027     xtab(19) =   0.558107957500638988907507734445D+02
    4092. 

  4092. <a name="l04028"></a>04028     xtab(20) =   0.665244165256157538186403187915D+02
    4093. 

  4093. <a name="l04029"></a>04029 
    4094. 

  4094. <a name="l04030"></a>04030     weight(1) =  0.168746801851113862149223899689D+00
    4095. 

  4095. <a name="l04031"></a>04031     weight(2) =  0.291254362006068281716795323812D+00
    4096. 

  4096. <a name="l04032"></a>04032     weight(3) =  0.266686102867001288549520868998D+00
    4097. 

  4097. <a name="l04033"></a>04033     weight(4) =  0.166002453269506840031469127816D+00
    4098. 

  4098. <a name="l04034"></a>04034     weight(5) =  0.748260646687923705400624639615D-01
    4099. 

  4099. <a name="l04035"></a>04035     weight(6) =  0.249644173092832210728227383234D-01
    4100. 

  4100. <a name="l04036"></a>04036     weight(7) =  0.620255084457223684744754785395D-02
    4101. 

  4101. <a name="l04037"></a>04037     weight(8) =  0.114496238647690824203955356969D-02
    4102. 

  4102. <a name="l04038"></a>04038     weight(9) =  0.155741773027811974779809513214D-03
    4103. 

  4103. <a name="l04039"></a>04039     weight(10) = 0.154014408652249156893806714048D-04
    4104. 

  4104. <a name="l04040"></a>04040     weight(11) = 0.108648636651798235147970004439D-05
    4105. 

  4105. <a name="l04041"></a>04041     weight(12) = 0.533012090955671475092780244305D-07
    4106. 

  4106. <a name="l04042"></a>04042     weight(13) = 0.175798117905058200357787637840D-08
    4107. 

  4107. <a name="l04043"></a>04043     weight(14) = 0.372550240251232087262924585338D-10
    4108. 

  4108. <a name="l04044"></a>04044     weight(15) = 0.476752925157819052449488071613D-12
    4109. 

  4109. <a name="l04045"></a>04045     weight(16) = 0.337284424336243841236506064991D-14
    4110. 

  4110. <a name="l04046"></a>04046     weight(17) = 0.115501433950039883096396247181D-16
    4111. 

  4111. <a name="l04047"></a>04047     weight(18) = 0.153952214058234355346383319667D-19
    4112. 

  4112. <a name="l04048"></a>04048     weight(19) = 0.528644272556915782880273587683D-23
    4113. 

  4113. <a name="l04049"></a>04049     weight(20) = 0.165645661249902329590781908529D-27
    4114. 

  4114. <a name="l04050"></a>04050 
    4115. 

  4115. <a name="l04051"></a>04051   <span class="keyword">else</span>
    4116. 

  4116. <a name="l04052"></a>04052 
    4117. 

  4117. <a name="l04053"></a>04053     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    4118. 

  4118. <a name="l04054"></a>04054     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LAGUERRE_SET - Fatal error!&#39;</span>
    4119. 

  4119. <a name="l04055"></a>04055     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    4120. 

  4120. <a name="l04056"></a>04056     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 1 to 20.&#39;</span>
    4121. 

  4121. <a name="l04057"></a>04057     stop
    4122. 

  4122. <a name="l04058"></a>04058 
    4123. 

  4123. <a name="l04059"></a>04059   <span class="keyword">end if</span>
    4124. 

  4124. <a name="l04060"></a>04060 
    4125. 

  4125. <a name="l04061"></a>04061   return
    4126. 

  4126. <a name="l04062"></a>04062 <span class="keyword">end</span>
    4127. 

  4127. <a name="l04063"></a><a class="code" href="quadrule_8f90.html#a5b2ffde45facf187cd2716ab11d0dbef">04063</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a5b2ffde45facf187cd2716ab11d0dbef">laguerre_sum</a> ( func, a, norder, xtab, weight, result )
    4128. 

  4128. <a name="l04064"></a>04064 <span class="comment">!</span>
    4129. 

  4129. <a name="l04065"></a>04065 <span class="comment">!*******************************************************************************</span>
    4130. 

  4130. <a name="l04066"></a>04066 <span class="comment">!</span>
    4131. 

  4131. <a name="l04067"></a>04067 <span class="comment">!! LAGUERRE_SUM carries out Laguerre quadrature over [ A, +Infinity ).</span>
    4132. 

  4132. <a name="l04068"></a>04068 <span class="comment">!</span>
    4133. 

  4133. <a name="l04069"></a>04069 <span class="comment">!</span>
    4134. 

  4134. <a name="l04070"></a>04070 <span class="comment">!  Discussion:</span>
    4135. 

  4135. <a name="l04071"></a>04071 <span class="comment">!</span>
    4136. 

  4136. <a name="l04072"></a>04072 <span class="comment">!    The simplest Laguerre integral to approximate is the</span>
    4137. 

  4137. <a name="l04073"></a>04073 <span class="comment">!    integral from 0 to INFINITY of EXP(-X) * F(X).  When this is so,</span>
    4138. 

  4138. <a name="l04074"></a>04074 <span class="comment">!    it is easy to modify the rule to approximate the integral from</span>
    4139. 

  4139. <a name="l04075"></a>04075 <span class="comment">!    A to INFINITY as well.</span>
    4140. 

  4140. <a name="l04076"></a>04076 <span class="comment">!</span>
    4141. 

  4141. <a name="l04077"></a>04077 <span class="comment">!    Another common Laguerre integral to approximate is the</span>
    4142. 

  4142. <a name="l04078"></a>04078 <span class="comment">!    integral from 0 to Infinity of EXP(-X) * X**ALPHA * F(X).</span>
    4143. 

  4143. <a name="l04079"></a>04079 <span class="comment">!    This routine may be used to sum up the terms of the Laguerre</span>
    4144. 

  4144. <a name="l04080"></a>04080 <span class="comment">!    rule for such an integral as well.  However, if ALPHA is nonzero,</span>
    4145. 

  4145. <a name="l04081"></a>04081 <span class="comment">!    then there is no simple way to extend the rule to approximate the</span>
    4146. 

  4146. <a name="l04082"></a>04082 <span class="comment">!    integral from A to INFINITY.  The simplest procedures would be</span>
    4147. 

  4147. <a name="l04083"></a>04083 <span class="comment">!    to approximate the integral from 0 to A.</span>
    4148. 

  4148. <a name="l04084"></a>04084 <span class="comment">!</span>
    4149. 

  4149. <a name="l04085"></a>04085 <span class="comment">!  Integration interval:</span>
    4150. 

  4150. <a name="l04086"></a>04086 <span class="comment">!</span>
    4151. 

  4151. <a name="l04087"></a>04087 <span class="comment">!    [ A, +Infinity ) or [ 0, +Infinity )</span>
    4152. 

  4152. <a name="l04088"></a>04088 <span class="comment">!</span>
    4153. 

  4153. <a name="l04089"></a>04089 <span class="comment">!  Weight function:</span>
    4154. 

  4154. <a name="l04090"></a>04090 <span class="comment">!</span>
    4155. 

  4155. <a name="l04091"></a>04091 <span class="comment">!    EXP ( - X ) or EXP ( - X ) * X**ALPHA</span>
    4156. 

  4156. <a name="l04092"></a>04092 <span class="comment">!</span>
    4157. 

  4157. <a name="l04093"></a>04093 <span class="comment">!  Integral to approximate:</span>
    4158. 

  4158. <a name="l04094"></a>04094 <span class="comment">!</span>
    4159. 

  4159. <a name="l04095"></a>04095 <span class="comment">!    Integral ( A &lt;= X &lt;= +Infinity ) EXP ( -X ) * F(X) dX or</span>
    4160. 

  4160. <a name="l04096"></a>04096 <span class="comment">!    Integral ( 0 &lt;= X &lt;= +Infinity ) EXP ( -X ) * X**ALPHA * F(X) dX</span>
    4161. 

  4161. <a name="l04097"></a>04097 <span class="comment">!</span>
    4162. 

  4162. <a name="l04098"></a>04098 <span class="comment">!  Approximate integral:</span>
    4163. 

  4163. <a name="l04099"></a>04099 <span class="comment">!</span>
    4164. 

  4164. <a name="l04100"></a>04100 <span class="comment">!    EXP ( - A ) * Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) + A ) </span>
    4165. 

  4165. <a name="l04101"></a>04101 <span class="comment">!</span>
    4166. 

  4166. <a name="l04102"></a>04102 <span class="comment">!    or</span>
    4167. 

  4167. <a name="l04103"></a>04103 <span class="comment">!</span>
    4168. 

  4168. <a name="l04104"></a>04104 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    4169. 

  4169. <a name="l04105"></a>04105 <span class="comment">!</span>
    4170. 

  4170. <a name="l04106"></a>04106 <span class="comment">!  Reference:</span>
    4171. 

  4171. <a name="l04107"></a>04107 <span class="comment">!</span>
    4172. 

  4172. <a name="l04108"></a>04108 <span class="comment">!    Abramowitz and Stegun,</span>
    4173. 

  4173. <a name="l04109"></a>04109 <span class="comment">!    Handbook of Mathematical Functions,</span>
    4174. 

  4174. <a name="l04110"></a>04110 <span class="comment">!    National Bureau of Standards, 1964.</span>
    4175. 

  4175. <a name="l04111"></a>04111 <span class="comment">!</span>
    4176. 

  4176. <a name="l04112"></a>04112 <span class="comment">!    Daniel Zwillinger, editor,</span>
    4177. 

  4177. <a name="l04113"></a>04113 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    4178. 

  4178. <a name="l04114"></a>04114 <span class="comment">!    30th Edition,</span>
    4179. 

  4179. <a name="l04115"></a>04115 <span class="comment">!    CRC Press, 1996.</span>
    4180. 

  4180. <a name="l04116"></a>04116 <span class="comment">!</span>
    4181. 

  4181. <a name="l04117"></a>04117 <span class="comment">!  Modified:</span>
    4182. 

  4182. <a name="l04118"></a>04118 <span class="comment">!</span>
    4183. 

  4183. <a name="l04119"></a>04119 <span class="comment">!    15 March 2000</span>
    4184. 

  4184. <a name="l04120"></a>04120 <span class="comment">!</span>
    4185. 

  4185. <a name="l04121"></a>04121 <span class="comment">!  Author:</span>
    4186. 

  4186. <a name="l04122"></a>04122 <span class="comment">!</span>
    4187. 

  4187. <a name="l04123"></a>04123 <span class="comment">!    John Burkardt</span>
    4188. 

  4188. <a name="l04124"></a>04124 <span class="comment">!</span>
    4189. 

  4189. <a name="l04125"></a>04125 <span class="comment">!  Parameters:</span>
    4190. 

  4190. <a name="l04126"></a>04126 <span class="comment">!</span>
    4191. 

  4191. <a name="l04127"></a>04127 <span class="comment">!    Input, external FUNC, the name of the FORTRAN function which</span>
    4192. 

  4192. <a name="l04128"></a>04128 <span class="comment">!    evaluates the integrand.  The function must have the form</span>
    4193. 

  4193. <a name="l04129"></a>04129 <span class="comment">!      double precision func ( x ).</span>
    4194. 

  4194. <a name="l04130"></a>04130 <span class="comment">!</span>
    4195. 

  4195. <a name="l04131"></a>04131 <span class="comment">!    Input, double precision A, the beginning of the integration interval.</span>
    4196. 

  4196. <a name="l04132"></a>04132 <span class="comment">!</span>
    4197. 

  4197. <a name="l04133"></a>04133 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    4198. 

  4198. <a name="l04134"></a>04134 <span class="comment">!</span>
    4199. 

  4199. <a name="l04135"></a>04135 <span class="comment">!    Input, double precision XTAB(NORDER), the abscissas of the rule.</span>
    4200. 

  4200. <a name="l04136"></a>04136 <span class="comment">!</span>
    4201. 

  4201. <a name="l04137"></a>04137 <span class="comment">!    Input, double precision WEIGHT(NORDER), the weights of the rule.</span>
    4202. 

  4202. <a name="l04138"></a>04138 <span class="comment">!</span>
    4203. 

  4203. <a name="l04139"></a>04139 <span class="comment">!    Output, double precision RESULT, the approximate value of the integral.</span>
    4204. 

  4204. <a name="l04140"></a>04140 <span class="comment">!</span>
    4205. 

  4205. <a name="l04141"></a>04141   <span class="keyword">implicit none</span>
    4206. 

  4206. <a name="l04142"></a>04142 <span class="comment">!</span>
    4207. 

  4207. <a name="l04143"></a>04143   <span class="keywordtype">integer</span> norder
    4208. 

  4208. <a name="l04144"></a>04144 <span class="comment">!</span>
    4209. 

  4209. <a name="l04145"></a>04145   <span class="keywordtype">double precision</span> a
    4210. 

  4210. <a name="l04146"></a>04146   <span class="keywordtype">double precision</span>, <span class="keywordtype">external</span> :: func
    4211. 

  4211. <a name="l04147"></a>04147   <span class="keywordtype">integer</span> i
    4212. 

  4212. <a name="l04148"></a>04148   <span class="keywordtype">double precision</span> result
    4213. 

  4213. <a name="l04149"></a>04149   <span class="keywordtype">double precision</span> xtab(norder)
    4214. 

  4214. <a name="l04150"></a>04150   <span class="keywordtype">double precision</span> weight(norder)
    4215. 

  4215. <a name="l04151"></a>04151 <span class="comment">!</span>
    4216. 

  4216. <a name="l04152"></a>04152   <span class="keyword">if</span> ( norder &lt; 1 ) <span class="keyword">then</span>
    4217. 

  4217. <a name="l04153"></a>04153     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    4218. 

  4218. <a name="l04154"></a>04154     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LAGUERRE_SUM - Fatal error!&#39;</span>
    4219. 

  4219. <a name="l04155"></a>04155     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Nonpositive NORDER = &#39;</span>, norder
    4220. 

  4220. <a name="l04156"></a>04156     stop
    4221. 

  4221. <a name="l04157"></a>04157   <span class="keyword">end if</span>
    4222. 

  4222. <a name="l04158"></a>04158 
    4223. 

  4223. <a name="l04159"></a>04159   result = 0.0D+00
    4224. 

  4224. <a name="l04160"></a>04160   <span class="keyword">do</span> i = 1, norder
    4225. 

  4225. <a name="l04161"></a>04161     result = result + weight(i) * func ( xtab(i) + a )
    4226. 

  4226. <a name="l04162"></a>04162   <span class="keyword">end do</span>
    4227. 

  4227. <a name="l04163"></a>04163   result = exp ( - a ) * result
    4228. 

  4228. <a name="l04164"></a>04164 
    4229. 

  4229. <a name="l04165"></a>04165   return
    4230. 

  4230. <a name="l04166"></a>04166 <span class="keyword">end</span>
    4231. 

  4231. <a name="l04167"></a><a class="code" href="quadrule_8f90.html#a0a7d1ce74b60aacdf3cab1fe515cb484">04167</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a0a7d1ce74b60aacdf3cab1fe515cb484">legendre_com</a> ( norder, xtab, weight )
    4232. 

  4232. <a name="l04168"></a>04168 <span class="comment">!</span>
    4233. 

  4233. <a name="l04169"></a>04169 <span class="comment">!*******************************************************************************</span>
    4234. 

  4234. <a name="l04170"></a>04170 <span class="comment">!</span>
    4235. 

  4235. <a name="l04171"></a>04171 <span class="comment">!! LEGENDRE_COM computes abscissas and weights for Gauss-Legendre quadrature.</span>
    4236. 

  4236. <a name="l04172"></a>04172 <span class="comment">!</span>
    4237. 

  4237. <a name="l04173"></a>04173 <span class="comment">!</span>
    4238. 

  4238. <a name="l04174"></a>04174 <span class="comment">!  Integration interval:</span>
    4239. 

  4239. <a name="l04175"></a>04175 <span class="comment">!</span>
    4240. 

  4240. <a name="l04176"></a>04176 <span class="comment">!    [ -1, 1 ]</span>
    4241. 

  4241. <a name="l04177"></a>04177 <span class="comment">!</span>
    4242. 

  4242. <a name="l04178"></a>04178 <span class="comment">!  Weight function:</span>
    4243. 

  4243. <a name="l04179"></a>04179 <span class="comment">!</span>
    4244. 

  4244. <a name="l04180"></a>04180 <span class="comment">!    1.0D+00</span>
    4245. 

  4245. <a name="l04181"></a>04181 <span class="comment">!</span>
    4246. 

  4246. <a name="l04182"></a>04182 <span class="comment">!  Integral to approximate:</span>
    4247. 

  4247. <a name="l04183"></a>04183 <span class="comment">!</span>
    4248. 

  4248. <a name="l04184"></a>04184 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    4249. 

  4249. <a name="l04185"></a>04185 <span class="comment">!</span>
    4250. 

  4250. <a name="l04186"></a>04186 <span class="comment">!  Approximate integral:</span>
    4251. 

  4251. <a name="l04187"></a>04187 <span class="comment">!</span>
    4252. 

  4252. <a name="l04188"></a>04188 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    4253. 

  4253. <a name="l04189"></a>04189 <span class="comment">!</span>
    4254. 

  4254. <a name="l04190"></a>04190 <span class="comment">!  Modified:</span>
    4255. 

  4255. <a name="l04191"></a>04191 <span class="comment">!</span>
    4256. 

  4256. <a name="l04192"></a>04192 <span class="comment">!    16 September 1998</span>
    4257. 

  4257. <a name="l04193"></a>04193 <span class="comment">!</span>
    4258. 

  4258. <a name="l04194"></a>04194 <span class="comment">!  Parameters:</span>
    4259. 

  4259. <a name="l04195"></a>04195 <span class="comment">!</span>
    4260. 

  4260. <a name="l04196"></a>04196 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    4261. 

  4261. <a name="l04197"></a>04197 <span class="comment">!    NORDER must be greater than 0.</span>
    4262. 

  4262. <a name="l04198"></a>04198 <span class="comment">!</span>
    4263. 

  4263. <a name="l04199"></a>04199 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    4264. 

  4264. <a name="l04200"></a>04200 <span class="comment">!</span>
    4265. 

  4265. <a name="l04201"></a>04201 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    4266. 

  4266. <a name="l04202"></a>04202 <span class="comment">!    The weights are positive, symmetric, and should sum to 2.</span>
    4267. 

  4267. <a name="l04203"></a>04203 <span class="comment">!</span>
    4268. 

  4268. <a name="l04204"></a>04204   <span class="keyword">implicit none</span>
    4269. 

  4269. <a name="l04205"></a>04205 <span class="comment">!</span>
    4270. 

  4270. <a name="l04206"></a>04206   <span class="keywordtype">integer</span> norder
    4271. 

  4271. <a name="l04207"></a>04207 <span class="comment">!</span>
    4272. 

  4272. <a name="l04208"></a>04208   <span class="keywordtype">double precision</span> d1
    4273. 

  4273. <a name="l04209"></a>04209   <span class="keywordtype">double precision</span> d2pn
    4274. 

  4274. <a name="l04210"></a>04210   <span class="keywordtype">double precision</span> d3pn
    4275. 

  4275. <a name="l04211"></a>04211   <span class="keywordtype">double precision</span> d4pn
    4276. 

  4276. <a name="l04212"></a>04212   <span class="keywordtype">double precision</span> dp
    4277. 

  4277. <a name="l04213"></a>04213   <span class="keywordtype">double precision</span> d_pi
    4278. 

  4278. <a name="l04214"></a>04214   <span class="keywordtype">double precision</span> dpn
    4279. 

  4279. <a name="l04215"></a>04215   <span class="keywordtype">double precision</span> e1
    4280. 

  4280. <a name="l04216"></a>04216   <span class="keywordtype">double precision</span> fx
    4281. 

  4281. <a name="l04217"></a>04217   <span class="keywordtype">double precision</span> h
    4282. 

  4282. <a name="l04218"></a>04218   <span class="keywordtype">integer</span> i
    4283. 

  4283. <a name="l04219"></a>04219   <span class="keywordtype">integer</span> iback
    4284. 

  4284. <a name="l04220"></a>04220   <span class="keywordtype">integer</span> k
    4285. 

  4285. <a name="l04221"></a>04221   <span class="keywordtype">integer</span> m
    4286. 

  4286. <a name="l04222"></a>04222   <span class="keywordtype">integer</span> mp1mi
    4287. 

  4287. <a name="l04223"></a>04223   <span class="keywordtype">integer</span> ncopy
    4288. 

  4288. <a name="l04224"></a>04224   <span class="keywordtype">integer</span> nmove
    4289. 

  4289. <a name="l04225"></a>04225   <span class="keywordtype">double precision</span> p
    4290. 

  4290. <a name="l04226"></a>04226   <span class="keywordtype">double precision</span> pk
    4291. 

  4291. <a name="l04227"></a>04227   <span class="keywordtype">double precision</span> pkm1
    4292. 

  4292. <a name="l04228"></a>04228   <span class="keywordtype">double precision</span> pkp1
    4293. 

  4293. <a name="l04229"></a>04229   <span class="keywordtype">double precision</span> t
    4294. 

  4294. <a name="l04230"></a>04230   <span class="keywordtype">double precision</span> u
    4295. 

  4295. <a name="l04231"></a>04231   <span class="keywordtype">double precision</span> v
    4296. 

  4296. <a name="l04232"></a>04232   <span class="keywordtype">double precision</span> x0
    4297. 

  4297. <a name="l04233"></a>04233   <span class="keywordtype">double precision</span> xtab(norder)
    4298. 

  4298. <a name="l04234"></a>04234   <span class="keywordtype">double precision</span> xtemp
    4299. 

  4299. <a name="l04235"></a>04235   <span class="keywordtype">double precision</span> weight(norder)
    4300. 

  4300. <a name="l04236"></a>04236 <span class="comment">!</span>
    4301. 

  4301. <a name="l04237"></a>04237   <span class="keyword">if</span> ( norder &lt; 1 ) <span class="keyword">then</span>
    4302. 

  4302. <a name="l04238"></a>04238     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    4303. 

  4303. <a name="l04239"></a>04239     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_COM - Fatal error!&#39;</span>
    4304. 

  4304. <a name="l04240"></a>04240     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    4305. 

  4305. <a name="l04241"></a>04241     stop
    4306. 

  4306. <a name="l04242"></a>04242   <span class="keyword">end if</span>
    4307. 

  4307. <a name="l04243"></a>04243 
    4308. 

  4308. <a name="l04244"></a>04244   e1 = dble ( norder * ( norder + 1 ) )
    4309. 

  4309. <a name="l04245"></a>04245 
    4310. 

  4310. <a name="l04246"></a>04246   m = ( norder + 1 ) / 2
    4311. 

  4311. <a name="l04247"></a>04247 
    4312. 

  4312. <a name="l04248"></a>04248   <span class="keyword">do</span> i = 1, ( norder + 1 ) / 2
    4313. 

  4313. <a name="l04249"></a>04249 
    4314. 

  4314. <a name="l04250"></a>04250     mp1mi = m + 1 - i
    4315. 

  4315. <a name="l04251"></a>04251     t = dble ( 4 * i - 1 ) * d_pi ( ) / dble ( 4 * norder + 2 )
    4316. 

  4316. <a name="l04252"></a>04252     x0 = cos(t) * ( 1.0D+00 - ( 1.0D+00 - 1.0D+00 / dble ( norder ) ) &amp;
    4317. 

  4317. <a name="l04253"></a>04253       / dble ( 8 * norder**2 ) )
    4318. 

  4318. <a name="l04254"></a>04254 
    4319. 

  4319. <a name="l04255"></a>04255     pkm1 = 1.0D+00
    4320. 

  4320. <a name="l04256"></a>04256     pk = x0
    4321. 

  4321. <a name="l04257"></a>04257 
    4322. 

  4322. <a name="l04258"></a>04258     <span class="keyword">do</span> k = 2, norder
    4323. 

  4323. <a name="l04259"></a>04259       pkp1 = 2.0D+00 * x0 * pk - pkm1 - ( x0 * pk - pkm1 ) / dble ( k )
    4324. 

  4324. <a name="l04260"></a>04260       pkm1 = pk
    4325. 

  4325. <a name="l04261"></a>04261       pk = pkp1
    4326. 

  4326. <a name="l04262"></a>04262     <span class="keyword">end do</span>
    4327. 

  4327. <a name="l04263"></a>04263 
    4328. 

  4328. <a name="l04264"></a>04264     d1 = dble ( norder ) * ( pkm1 - x0 * pk )
    4329. 

  4329. <a name="l04265"></a>04265 
    4330. 

  4330. <a name="l04266"></a>04266     dpn = d1 / ( 1.0D+00 - x0**2 )
    4331. 

  4331. <a name="l04267"></a>04267 
    4332. 

  4332. <a name="l04268"></a>04268     d2pn = ( 2.0D+00 * x0 * dpn - e1 * pk ) / ( 1.0D+00 - x0**2 )
    4333. 

  4333. <a name="l04269"></a>04269 
    4334. 

  4334. <a name="l04270"></a>04270     d3pn = ( 4.0D+00 * x0 * d2pn + ( 2.0D+00 - e1 ) * dpn ) &amp;
    4335. 

  4335. <a name="l04271"></a>04271       / ( 1.0D+00 - x0**2 )
    4336. 

  4336. <a name="l04272"></a>04272 
    4337. 

  4337. <a name="l04273"></a>04273     d4pn = ( 6.0D+00 * x0 * d3pn + ( 6.0D+00 - e1 ) * d2pn ) / &amp;
    4338. 

  4338. <a name="l04274"></a>04274       ( 1.0D+00 - x0**2 )
    4339. 

  4339. <a name="l04275"></a>04275 
    4340. 

  4340. <a name="l04276"></a>04276     u = pk / dpn
    4341. 

  4341. <a name="l04277"></a>04277     v = d2pn / dpn
    4342. 

  4342. <a name="l04278"></a>04278 <span class="comment">!</span>
    4343. 

  4343. <a name="l04279"></a>04279 <span class="comment">!  Initial approximation H:</span>
    4344. 

  4344. <a name="l04280"></a>04280 <span class="comment">!</span>
    4345. 

  4345. <a name="l04281"></a>04281     h = - u * ( 1.0D+00 + 0.5D+00 * u * ( v + u * ( v**2 - d3pn / &amp;
    4346. 

  4346. <a name="l04282"></a>04282       ( 3.0D+00 * dpn ) ) ) )
    4347. 

  4347. <a name="l04283"></a>04283 <span class="comment">!</span>
    4348. 

  4348. <a name="l04284"></a>04284 <span class="comment">!  Refine H using one step of Newton&#39;s method:</span>
    4349. 

  4349. <a name="l04285"></a>04285 <span class="comment">!</span>
    4350. 

  4350. <a name="l04286"></a>04286     p = pk + h * ( dpn + 0.5D+00 * h * ( d2pn + h / 3.0D+00 &amp;
    4351. 

  4351. <a name="l04287"></a>04287       * ( d3pn + 0.25D+00 * h * d4pn ) ) )
    4352. 

  4352. <a name="l04288"></a>04288 
    4353. 

  4353. <a name="l04289"></a>04289     dp = dpn + h * ( d2pn + 0.5D+00 * h * ( d3pn + h * d4pn / 3.0D+00 ) )
    4354. 

  4354. <a name="l04290"></a>04290 
    4355. 

  4355. <a name="l04291"></a>04291     h = h - p / dp
    4356. 

  4356. <a name="l04292"></a>04292 
    4357. 

  4357. <a name="l04293"></a>04293     xtemp = x0 + h
    4358. 

  4358. <a name="l04294"></a>04294 
    4359. 

  4359. <a name="l04295"></a>04295     xtab(mp1mi) = xtemp
    4360. 

  4360. <a name="l04296"></a>04296 
    4361. 

  4361. <a name="l04297"></a>04297     fx = d1 - h * e1 * ( pk + 0.5D+00 * h * ( dpn + h / 3.0D+00 &amp;
    4362. 

  4362. <a name="l04298"></a>04298       * ( d2pn + 0.25D+00 * h * ( d3pn + 0.2D+00 * h * d4pn ) ) ) )
    4363. 

  4363. <a name="l04299"></a>04299 
    4364. 

  4364. <a name="l04300"></a>04300     weight(mp1mi) = 2.0D+00 * ( 1.0D+00 - xtemp**2 ) / fx**2
    4365. 

  4365. <a name="l04301"></a>04301 
    4366. 

  4366. <a name="l04302"></a>04302   <span class="keyword">end do</span>
    4367. 

  4367. <a name="l04303"></a>04303 
    4368. 

  4368. <a name="l04304"></a>04304   <span class="keyword">if</span> ( mod ( norder, 2 ) == 1 ) <span class="keyword">then</span>
    4369. 

  4369. <a name="l04305"></a>04305     xtab(1) = 0.0D+00
    4370. 

  4370. <a name="l04306"></a>04306   <span class="keyword">end if</span>
    4371. 

  4371. <a name="l04307"></a>04307 <span class="comment">!</span>
    4372. 

  4372. <a name="l04308"></a>04308 <span class="comment">!  Shift the data up.</span>
    4373. 

  4373. <a name="l04309"></a>04309 <span class="comment">!</span>
    4374. 

  4374. <a name="l04310"></a>04310   nmove = ( norder + 1 ) / 2
    4375. 

  4375. <a name="l04311"></a>04311   ncopy = norder - nmove
    4376. 

  4376. <a name="l04312"></a>04312 
    4377. 

  4377. <a name="l04313"></a>04313   <span class="keyword">do</span> i = 1, nmove
    4378. 

  4378. <a name="l04314"></a>04314     iback = norder + 1 - i
    4379. 

  4379. <a name="l04315"></a>04315     xtab(iback) = xtab(iback-ncopy)
    4380. 

  4380. <a name="l04316"></a>04316     weight(iback) = weight(iback-ncopy)
    4381. 

  4381. <a name="l04317"></a>04317   <span class="keyword">end do</span>
    4382. 

  4382. <a name="l04318"></a>04318 <span class="comment">!</span>
    4383. 

  4383. <a name="l04319"></a>04319 <span class="comment">!  Reflect values for the negative abscissas.</span>
    4384. 

  4384. <a name="l04320"></a>04320 <span class="comment">!</span>
    4385. 

  4385. <a name="l04321"></a>04321   <span class="keyword">do</span> i = 1, norder - nmove
    4386. 

  4386. <a name="l04322"></a>04322     xtab(i) = - xtab(norder+1-i)
    4387. 

  4387. <a name="l04323"></a>04323     weight(i) = weight(norder+1-i)
    4388. 

  4388. <a name="l04324"></a>04324   <span class="keyword">end do</span>
    4389. 

  4389. <a name="l04325"></a>04325 
    4390. 

  4390. <a name="l04326"></a>04326   return
    4391. 

  4391. <a name="l04327"></a>04327 <span class="keyword">end</span>
    4392. 

  4392. <a name="l04328"></a><a class="code" href="quadrule_8f90.html#a0204938f840315c0ede180bd7ddf3d7a">04328</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a0204938f840315c0ede180bd7ddf3d7a">legendre_recur</a> ( p2, dp2, p1, x, norder )
    4393. 

  4393. <a name="l04329"></a>04329 <span class="comment">!</span>
    4394. 

  4394. <a name="l04330"></a>04330 <span class="comment">!*******************************************************************************</span>
    4395. 

  4395. <a name="l04331"></a>04331 <span class="comment">!</span>
    4396. 

  4396. <a name="l04332"></a>04332 <span class="comment">!! LEGENDRE_RECUR finds the value and derivative of a Legendre polynomial.</span>
    4397. 

  4397. <a name="l04333"></a>04333 <span class="comment">!</span>
    4398. 

  4398. <a name="l04334"></a>04334 <span class="comment">!</span>
    4399. 

  4399. <a name="l04335"></a>04335 <span class="comment">!  Reference:</span>
    4400. 

  4400. <a name="l04336"></a>04336 <span class="comment">!</span>
    4401. 

  4401. <a name="l04337"></a>04337 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    4402. 

  4402. <a name="l04338"></a>04338 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    4403. 

  4403. <a name="l04339"></a>04339 <span class="comment">!    Prentice Hall, 1966.</span>
    4404. 

  4404. <a name="l04340"></a>04340 <span class="comment">!</span>
    4405. 

  4405. <a name="l04341"></a>04341 <span class="comment">!  Modified:</span>
    4406. 

  4406. <a name="l04342"></a>04342 <span class="comment">!</span>
    4407. 

  4407. <a name="l04343"></a>04343 <span class="comment">!    19 September 1998</span>
    4408. 

  4408. <a name="l04344"></a>04344 <span class="comment">!</span>
    4409. 

  4409. <a name="l04345"></a>04345 <span class="comment">!  Parameters:</span>
    4410. 

  4410. <a name="l04346"></a>04346 <span class="comment">!</span>
    4411. 

  4411. <a name="l04347"></a>04347 <span class="comment">!    Output, double precision P2, the value of P(NORDER)(X).</span>
    4412. 

  4412. <a name="l04348"></a>04348 <span class="comment">!</span>
    4413. 

  4413. <a name="l04349"></a>04349 <span class="comment">!    Output, double precision DP2, the value of P&#39;(NORDER)(X).</span>
    4414. 

  4414. <a name="l04350"></a>04350 <span class="comment">!</span>
    4415. 

  4415. <a name="l04351"></a>04351 <span class="comment">!    Output, double precision P1, the value of P(NORDER-1)(X).</span>
    4416. 

  4416. <a name="l04352"></a>04352 <span class="comment">!</span>
    4417. 

  4417. <a name="l04353"></a>04353 <span class="comment">!    Input, double precision X, the point at which polynomials are evaluated.</span>
    4418. 

  4418. <a name="l04354"></a>04354 <span class="comment">!</span>
    4419. 

  4419. <a name="l04355"></a>04355 <span class="comment">!    Input, integer NORDER, the order of the polynomial to be computed.</span>
    4420. 

  4420. <a name="l04356"></a>04356 <span class="comment">!</span>
    4421. 

  4421. <a name="l04357"></a>04357   <span class="keyword">implicit none</span>
    4422. 

  4422. <a name="l04358"></a>04358 <span class="comment">!</span>
    4423. 

  4423. <a name="l04359"></a>04359   <span class="keywordtype">integer</span> norder
    4424. 

  4424. <a name="l04360"></a>04360 <span class="comment">!</span>
    4425. 

  4425. <a name="l04361"></a>04361   <span class="keywordtype">double precision</span> dp0
    4426. 

  4426. <a name="l04362"></a>04362   <span class="keywordtype">double precision</span> dp1
    4427. 

  4427. <a name="l04363"></a>04363   <span class="keywordtype">double precision</span> dp2
    4428. 

  4428. <a name="l04364"></a>04364   <span class="keywordtype">integer</span> i
    4429. 

  4429. <a name="l04365"></a>04365   <span class="keywordtype">double precision</span> p0
    4430. 

  4430. <a name="l04366"></a>04366   <span class="keywordtype">double precision</span> p1
    4431. 

  4431. <a name="l04367"></a>04367   <span class="keywordtype">double precision</span> p2
    4432. 

  4432. <a name="l04368"></a>04368   <span class="keywordtype">double precision</span> x
    4433. 

  4433. <a name="l04369"></a>04369 <span class="comment">!</span>
    4434. 

  4434. <a name="l04370"></a>04370   p1 = 1.0D+00
    4435. 

  4435. <a name="l04371"></a>04371   dp1 = 0.0D+00
    4436. 

  4436. <a name="l04372"></a>04372 
    4437. 

  4437. <a name="l04373"></a>04373   p2 = x
    4438. 

  4438. <a name="l04374"></a>04374   dp2 = 1.0D+00
    4439. 

  4439. <a name="l04375"></a>04375 
    4440. 

  4440. <a name="l04376"></a>04376   <span class="keyword">do</span> i = 2, norder
    4441. 

  4441. <a name="l04377"></a>04377 
    4442. 

  4442. <a name="l04378"></a>04378     p0 = p1
    4443. 

  4443. <a name="l04379"></a>04379     dp0 = dp1
    4444. 

  4444. <a name="l04380"></a>04380 
    4445. 

  4445. <a name="l04381"></a>04381     p1 = p2
    4446. 

  4446. <a name="l04382"></a>04382     dp1 = dp2
    4447. 

  4447. <a name="l04383"></a>04383 
    4448. 

  4448. <a name="l04384"></a>04384     p2 = ( dble ( 2 * i - 1 ) * x * p1 - dble ( i - 1 ) * p0 ) / dble ( i )
    4449. 

  4449. <a name="l04385"></a>04385 
    4450. 

  4450. <a name="l04386"></a>04386     dp2 = ( dble ( 2 * i - 1 ) * ( p1 + x * dp1 ) - dble ( i - 1 ) * dp0 ) &amp;
    4451. 

  4451. <a name="l04387"></a>04387       / dble ( i )
    4452. 

  4452. <a name="l04388"></a>04388 
    4453. 

  4453. <a name="l04389"></a>04389   <span class="keyword">end do</span>
    4454. 

  4454. <a name="l04390"></a>04390 
    4455. 

  4455. <a name="l04391"></a>04391   return
    4456. 

  4456. <a name="l04392"></a>04392 <span class="keyword">end</span>
    4457. 

  4457. <a name="l04393"></a><a class="code" href="quadrule_8f90.html#a68e328951e712e3b7e2bc9f6dcf8fc6a">04393</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a68e328951e712e3b7e2bc9f6dcf8fc6a">legendre_set</a> ( norder, xtab, weight )
    4458. 

  4458. <a name="l04394"></a>04394 <span class="comment">!</span>
    4459. 

  4459. <a name="l04395"></a>04395 <span class="comment">!*******************************************************************************</span>
    4460. 

  4460. <a name="l04396"></a>04396 <span class="comment">!</span>
    4461. 

  4461. <a name="l04397"></a>04397 <span class="comment">!! LEGENDRE_SET sets abscissas and weights for Gauss-Legendre quadrature.</span>
    4462. 

  4462. <a name="l04398"></a>04398 <span class="comment">!</span>
    4463. 

  4463. <a name="l04399"></a>04399 <span class="comment">!</span>
    4464. 

  4464. <a name="l04400"></a>04400 <span class="comment">!  Integration interval:</span>
    4465. 

  4465. <a name="l04401"></a>04401 <span class="comment">!</span>
    4466. 

  4466. <a name="l04402"></a>04402 <span class="comment">!    [ -1, 1 ]</span>
    4467. 

  4467. <a name="l04403"></a>04403 <span class="comment">!</span>
    4468. 

  4468. <a name="l04404"></a>04404 <span class="comment">!  Weight function:</span>
    4469. 

  4469. <a name="l04405"></a>04405 <span class="comment">!</span>
    4470. 

  4470. <a name="l04406"></a>04406 <span class="comment">!    1.0D+00</span>
    4471. 

  4471. <a name="l04407"></a>04407 <span class="comment">!</span>
    4472. 

  4472. <a name="l04408"></a>04408 <span class="comment">!  Integral to approximate:</span>
    4473. 

  4473. <a name="l04409"></a>04409 <span class="comment">!</span>
    4474. 

  4474. <a name="l04410"></a>04410 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    4475. 

  4475. <a name="l04411"></a>04411 <span class="comment">!</span>
    4476. 

  4476. <a name="l04412"></a>04412 <span class="comment">!  Approximate integral:</span>
    4477. 

  4477. <a name="l04413"></a>04413 <span class="comment">!</span>
    4478. 

  4478. <a name="l04414"></a>04414 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    4479. 

  4479. <a name="l04415"></a>04415 <span class="comment">!</span>
    4480. 

  4480. <a name="l04416"></a>04416 <span class="comment">!  Precision:</span>
    4481. 

  4481. <a name="l04417"></a>04417 <span class="comment">!</span>
    4482. 

  4482. <a name="l04418"></a>04418 <span class="comment">!    The quadrature rule will integrate exactly all polynomials up to</span>
    4483. 

  4483. <a name="l04419"></a>04419 <span class="comment">!    X**(2*NORDER-1).</span>
    4484. 

  4484. <a name="l04420"></a>04420 <span class="comment">!</span>
    4485. 

  4485. <a name="l04421"></a>04421 <span class="comment">!  Note:</span>
    4486. 

  4486. <a name="l04422"></a>04422 <span class="comment">!</span>
    4487. 

  4487. <a name="l04423"></a>04423 <span class="comment">!    The abscissas of the rule are the zeroes of the Legendre polynomial</span>
    4488. 

  4488. <a name="l04424"></a>04424 <span class="comment">!    P(NORDER)(X).</span>
    4489. 

  4489. <a name="l04425"></a>04425 <span class="comment">!</span>
    4490. 

  4490. <a name="l04426"></a>04426 <span class="comment">!    The integral produced by a Gauss-Legendre rule is equal to the</span>
    4491. 

  4491. <a name="l04427"></a>04427 <span class="comment">!    integral of the unique polynomial of degree NORDER-1 which</span>
    4492. 

  4492. <a name="l04428"></a>04428 <span class="comment">!    agrees with the function at the NORDER abscissas of the rule.</span>
    4493. 

  4493. <a name="l04429"></a>04429 <span class="comment">!</span>
    4494. 

  4494. <a name="l04430"></a>04430 <span class="comment">!  Reference:</span>
    4495. 

  4495. <a name="l04431"></a>04431 <span class="comment">!</span>
    4496. 

  4496. <a name="l04432"></a>04432 <span class="comment">!    Abramowitz and Stegun,</span>
    4497. 

  4497. <a name="l04433"></a>04433 <span class="comment">!    Handbook of Mathematical Functions,</span>
    4498. 

  4498. <a name="l04434"></a>04434 <span class="comment">!    National Bureau of Standards, 1964.</span>
    4499. 

  4499. <a name="l04435"></a>04435 <span class="comment">!</span>
    4500. 

  4500. <a name="l04436"></a>04436 <span class="comment">!    Vladimir Krylov,</span>
    4501. 

  4501. <a name="l04437"></a>04437 <span class="comment">!    Approximate Calculation of Integrals,</span>
    4502. 

  4502. <a name="l04438"></a>04438 <span class="comment">!    MacMillan, 1962.</span>
    4503. 

  4503. <a name="l04439"></a>04439 <span class="comment">!</span>
    4504. 

  4504. <a name="l04440"></a>04440 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    4505. 

  4505. <a name="l04441"></a>04441 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    4506. 

  4506. <a name="l04442"></a>04442 <span class="comment">!    Prentice Hall, 1966.</span>
    4507. 

  4507. <a name="l04443"></a>04443 <span class="comment">!</span>
    4508. 

  4508. <a name="l04444"></a>04444 <span class="comment">!    Daniel Zwillinger, editor,</span>
    4509. 

  4509. <a name="l04445"></a>04445 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    4510. 

  4510. <a name="l04446"></a>04446 <span class="comment">!    30th Edition,</span>
    4511. 

  4511. <a name="l04447"></a>04447 <span class="comment">!    CRC Press, 1996.</span>
    4512. 

  4512. <a name="l04448"></a>04448 <span class="comment">!</span>
    4513. 

  4513. <a name="l04449"></a>04449 <span class="comment">!  Modified:</span>
    4514. 

  4514. <a name="l04450"></a>04450 <span class="comment">!</span>
    4515. 

  4515. <a name="l04451"></a>04451 <span class="comment">!    18 December 2000</span>
    4516. 

  4516. <a name="l04452"></a>04452 <span class="comment">!</span>
    4517. 

  4517. <a name="l04453"></a>04453 <span class="comment">!  Author:</span>
    4518. 

  4518. <a name="l04454"></a>04454 <span class="comment">!</span>
    4519. 

  4519. <a name="l04455"></a>04455 <span class="comment">!    John Burkardt</span>
    4520. 

  4520. <a name="l04456"></a>04456 <span class="comment">!</span>
    4521. 

  4521. <a name="l04457"></a>04457 <span class="comment">!  Parameters:</span>
    4522. 

  4522. <a name="l04458"></a>04458 <span class="comment">!</span>
    4523. 

  4523. <a name="l04459"></a>04459 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    4524. 

  4524. <a name="l04460"></a>04460 <span class="comment">!    NORDER must be between 1 and 20, 32 or 64.</span>
    4525. 

  4525. <a name="l04461"></a>04461 <span class="comment">!</span>
    4526. 

  4526. <a name="l04462"></a>04462 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    4527. 

  4527. <a name="l04463"></a>04463 <span class="comment">!</span>
    4528. 

  4528. <a name="l04464"></a>04464 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    4529. 

  4529. <a name="l04465"></a>04465 <span class="comment">!    The weights are positive, symmetric and should sum to 2.</span>
    4530. 

  4530. <a name="l04466"></a>04466 <span class="comment">!</span>
    4531. 

  4531. <a name="l04467"></a>04467   <span class="keyword">implicit none</span>
    4532. 

  4532. <a name="l04468"></a>04468 <span class="comment">!</span>
    4533. 

  4533. <a name="l04469"></a>04469   <span class="keywordtype">integer</span> norder
    4534. 

  4534. <a name="l04470"></a>04470 <span class="comment">!</span>
    4535. 

  4535. <a name="l04471"></a>04471   <span class="keywordtype">double precision</span> xtab(norder)
    4536. 

  4536. <a name="l04472"></a>04472   <span class="keywordtype">double precision</span> weight(norder)
    4537. 

  4537. <a name="l04473"></a>04473 <span class="comment">!</span>
    4538. 

  4538. <a name="l04474"></a>04474   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    4539. 

  4539. <a name="l04475"></a>04475 
    4540. 

  4540. <a name="l04476"></a>04476     xtab(1) =   0.0D+00
    4541. 

  4541. <a name="l04477"></a>04477 
    4542. 

  4542. <a name="l04478"></a>04478     weight(1) = 2.0D+00
    4543. 

  4543. <a name="l04479"></a>04479 
    4544. 

  4544. <a name="l04480"></a>04480   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    4545. 

  4545. <a name="l04481"></a>04481 
    4546. 

  4546. <a name="l04482"></a>04482     xtab(1) = - 0.577350269189625764509148780502D+00
    4547. 

  4547. <a name="l04483"></a>04483     xtab(2) =   0.577350269189625764509148780502D+00
    4548. 

  4548. <a name="l04484"></a>04484 
    4549. 

  4549. <a name="l04485"></a>04485     weight(1) = 1.0D+00
    4550. 

  4550. <a name="l04486"></a>04486     weight(2) = 1.0D+00
    4551. 

  4551. <a name="l04487"></a>04487 
    4552. 

  4552. <a name="l04488"></a>04488   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    4553. 

  4553. <a name="l04489"></a>04489 
    4554. 

  4554. <a name="l04490"></a>04490     xtab(1) = - 0.774596669241483377035853079956D+00
    4555. 

  4555. <a name="l04491"></a>04491     xtab(2) =   0.0D+00
    4556. 

  4556. <a name="l04492"></a>04492     xtab(3) =   0.774596669241483377035853079956D+00
    4557. 

  4557. <a name="l04493"></a>04493 
    4558. 

  4558. <a name="l04494"></a>04494     weight(1) = 5.0D+00 / 9.0D+00
    4559. 

  4559. <a name="l04495"></a>04495     weight(2) = 8.0D+00 / 9.0D+00
    4560. 

  4560. <a name="l04496"></a>04496     weight(3) = 5.0D+00 / 9.0D+00
    4561. 

  4561. <a name="l04497"></a>04497 
    4562. 

  4562. <a name="l04498"></a>04498   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    4563. 

  4563. <a name="l04499"></a>04499 
    4564. 

  4564. <a name="l04500"></a>04500     xtab(1) = - 0.861136311594052575223946488893D+00
    4565. 

  4565. <a name="l04501"></a>04501     xtab(2) = - 0.339981043584856264802665759103D+00
    4566. 

  4566. <a name="l04502"></a>04502     xtab(3) =   0.339981043584856264802665759103D+00
    4567. 

  4567. <a name="l04503"></a>04503     xtab(4) =   0.861136311594052575223946488893D+00
    4568. 

  4568. <a name="l04504"></a>04504 
    4569. 

  4569. <a name="l04505"></a>04505     weight(1) = 0.347854845137453857373063949222D+00
    4570. 

  4570. <a name="l04506"></a>04506     weight(2) = 0.652145154862546142626936050778D+00
    4571. 

  4571. <a name="l04507"></a>04507     weight(3) = 0.652145154862546142626936050778D+00
    4572. 

  4572. <a name="l04508"></a>04508     weight(4) = 0.347854845137453857373063949222D+00
    4573. 

  4573. <a name="l04509"></a>04509 
    4574. 

  4574. <a name="l04510"></a>04510   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    4575. 

  4575. <a name="l04511"></a>04511 
    4576. 

  4576. <a name="l04512"></a>04512     xtab(1) = - 0.906179845938663992797626878299D+00
    4577. 

  4577. <a name="l04513"></a>04513     xtab(2) = - 0.538469310105683091036314420700D+00
    4578. 

  4578. <a name="l04514"></a>04514     xtab(3) =   0.0D+00
    4579. 

  4579. <a name="l04515"></a>04515     xtab(4) =   0.538469310105683091036314420700D+00
    4580. 

  4580. <a name="l04516"></a>04516     xtab(5) =   0.906179845938663992797626878299D+00
    4581. 

  4581. <a name="l04517"></a>04517 
    4582. 

  4582. <a name="l04518"></a>04518     weight(1) = 0.236926885056189087514264040720D+00
    4583. 

  4583. <a name="l04519"></a>04519     weight(2) = 0.478628670499366468041291514836D+00
    4584. 

  4584. <a name="l04520"></a>04520     weight(3) = 0.568888888888888888888888888889D+00
    4585. 

  4585. <a name="l04521"></a>04521     weight(4) = 0.478628670499366468041291514836D+00
    4586. 

  4586. <a name="l04522"></a>04522     weight(5) = 0.236926885056189087514264040720D+00
    4587. 

  4587. <a name="l04523"></a>04523 
    4588. 

  4588. <a name="l04524"></a>04524   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    4589. 

  4589. <a name="l04525"></a>04525 
    4590. 

  4590. <a name="l04526"></a>04526     xtab(1) = - 0.932469514203152027812301554494D+00
    4591. 

  4591. <a name="l04527"></a>04527     xtab(2) = - 0.661209386466264513661399595020D+00
    4592. 

  4592. <a name="l04528"></a>04528     xtab(3) = - 0.238619186083196908630501721681D+00
    4593. 

  4593. <a name="l04529"></a>04529     xtab(4) =   0.238619186083196908630501721681D+00
    4594. 

  4594. <a name="l04530"></a>04530     xtab(5) =   0.661209386466264513661399595020D+00
    4595. 

  4595. <a name="l04531"></a>04531     xtab(6) =   0.932469514203152027812301554494D+00
    4596. 

  4596. <a name="l04532"></a>04532 
    4597. 

  4597. <a name="l04533"></a>04533     weight(1) = 0.171324492379170345040296142173D+00
    4598. 

  4598. <a name="l04534"></a>04534     weight(2) = 0.360761573048138607569833513838D+00
    4599. 

  4599. <a name="l04535"></a>04535     weight(3) = 0.467913934572691047389870343990D+00
    4600. 

  4600. <a name="l04536"></a>04536     weight(4) = 0.467913934572691047389870343990D+00
    4601. 

  4601. <a name="l04537"></a>04537     weight(5) = 0.360761573048138607569833513838D+00
    4602. 

  4602. <a name="l04538"></a>04538     weight(6) = 0.171324492379170345040296142173D+00
    4603. 

  4603. <a name="l04539"></a>04539 
    4604. 

  4604. <a name="l04540"></a>04540   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    4605. 

  4605. <a name="l04541"></a>04541 
    4606. 

  4606. <a name="l04542"></a>04542     xtab(1) = - 0.949107912342758524526189684048D+00
    4607. 

  4607. <a name="l04543"></a>04543     xtab(2) = - 0.741531185599394439863864773281D+00
    4608. 

  4608. <a name="l04544"></a>04544     xtab(3) = - 0.405845151377397166906606412077D+00
    4609. 

  4609. <a name="l04545"></a>04545     xtab(4) =   0.0D+00
    4610. 

  4610. <a name="l04546"></a>04546     xtab(5) =   0.405845151377397166906606412077D+00
    4611. 

  4611. <a name="l04547"></a>04547     xtab(6) =   0.741531185599394439863864773281D+00
    4612. 

  4612. <a name="l04548"></a>04548     xtab(7) =   0.949107912342758524526189684048D+00
    4613. 

  4613. <a name="l04549"></a>04549 
    4614. 

  4614. <a name="l04550"></a>04550     weight(1) = 0.129484966168869693270611432679D+00
    4615. 

  4615. <a name="l04551"></a>04551     weight(2) = 0.279705391489276667901467771424D+00
    4616. 

  4616. <a name="l04552"></a>04552     weight(3) = 0.381830050505118944950369775489D+00
    4617. 

  4617. <a name="l04553"></a>04553     weight(4) = 0.417959183673469387755102040816D+00
    4618. 

  4618. <a name="l04554"></a>04554     weight(5) = 0.381830050505118944950369775489D+00
    4619. 

  4619. <a name="l04555"></a>04555     weight(6) = 0.279705391489276667901467771424D+00
    4620. 

  4620. <a name="l04556"></a>04556     weight(7) = 0.129484966168869693270611432679D+00
    4621. 

  4621. <a name="l04557"></a>04557 
    4622. 

  4622. <a name="l04558"></a>04558   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    4623. 

  4623. <a name="l04559"></a>04559 
    4624. 

  4624. <a name="l04560"></a>04560     xtab(1) = - 0.960289856497536231683560868569D+00
    4625. 

  4625. <a name="l04561"></a>04561     xtab(2) = - 0.796666477413626739591553936476D+00
    4626. 

  4626. <a name="l04562"></a>04562     xtab(3) = - 0.525532409916328985817739049189D+00
    4627. 

  4627. <a name="l04563"></a>04563     xtab(4) = - 0.183434642495649804939476142360D+00
    4628. 

  4628. <a name="l04564"></a>04564     xtab(5) =   0.183434642495649804939476142360D+00
    4629. 

  4629. <a name="l04565"></a>04565     xtab(6) =   0.525532409916328985817739049189D+00
    4630. 

  4630. <a name="l04566"></a>04566     xtab(7) =   0.796666477413626739591553936476D+00
    4631. 

  4631. <a name="l04567"></a>04567     xtab(8) =   0.960289856497536231683560868569D+00
    4632. 

  4632. <a name="l04568"></a>04568 
    4633. 

  4633. <a name="l04569"></a>04569     weight(1) = 0.101228536290376259152531354310D+00
    4634. 

  4634. <a name="l04570"></a>04570     weight(2) = 0.222381034453374470544355994426D+00
    4635. 

  4635. <a name="l04571"></a>04571     weight(3) = 0.313706645877887287337962201987D+00
    4636. 

  4636. <a name="l04572"></a>04572     weight(4) = 0.362683783378361982965150449277D+00
    4637. 

  4637. <a name="l04573"></a>04573     weight(5) = 0.362683783378361982965150449277D+00
    4638. 

  4638. <a name="l04574"></a>04574     weight(6) = 0.313706645877887287337962201987D+00
    4639. 

  4639. <a name="l04575"></a>04575     weight(7) = 0.222381034453374470544355994426D+00
    4640. 

  4640. <a name="l04576"></a>04576     weight(8) = 0.101228536290376259152531354310D+00
    4641. 

  4641. <a name="l04577"></a>04577 
    4642. 

  4642. <a name="l04578"></a>04578   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    4643. 

  4643. <a name="l04579"></a>04579 
    4644. 

  4644. <a name="l04580"></a>04580     xtab(1) = - 0.968160239507626089835576202904D+00
    4645. 

  4645. <a name="l04581"></a>04581     xtab(2) = - 0.836031107326635794299429788070D+00
    4646. 

  4646. <a name="l04582"></a>04582     xtab(3) = - 0.613371432700590397308702039341D+00
    4647. 

  4647. <a name="l04583"></a>04583     xtab(4) = - 0.324253423403808929038538014643D+00
    4648. 

  4648. <a name="l04584"></a>04584     xtab(5) =   0.0D+00
    4649. 

  4649. <a name="l04585"></a>04585     xtab(6) =   0.324253423403808929038538014643D+00
    4650. 

  4650. <a name="l04586"></a>04586     xtab(7) =   0.613371432700590397308702039341D+00
    4651. 

  4651. <a name="l04587"></a>04587     xtab(8) =   0.836031107326635794299429788070D+00
    4652. 

  4652. <a name="l04588"></a>04588     xtab(9) =   0.968160239507626089835576202904D+00
    4653. 

  4653. <a name="l04589"></a>04589 
    4654. 

  4654. <a name="l04590"></a>04590     weight(1) = 0.812743883615744119718921581105D-01
    4655. 

  4655. <a name="l04591"></a>04591     weight(2) = 0.180648160694857404058472031243D+00
    4656. 

  4656. <a name="l04592"></a>04592     weight(3) = 0.260610696402935462318742869419D+00
    4657. 

  4657. <a name="l04593"></a>04593     weight(4) = 0.312347077040002840068630406584D+00
    4658. 

  4658. <a name="l04594"></a>04594     weight(5) = 0.330239355001259763164525069287D+00
    4659. 

  4659. <a name="l04595"></a>04595     weight(6) = 0.312347077040002840068630406584D+00
    4660. 

  4660. <a name="l04596"></a>04596     weight(7) = 0.260610696402935462318742869419D+00
    4661. 

  4661. <a name="l04597"></a>04597     weight(8) = 0.180648160694857404058472031243D+00
    4662. 

  4662. <a name="l04598"></a>04598     weight(9) = 0.812743883615744119718921581105D-01
    4663. 

  4663. <a name="l04599"></a>04599 
    4664. 

  4664. <a name="l04600"></a>04600   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
    4665. 

  4665. <a name="l04601"></a>04601 
    4666. 

  4666. <a name="l04602"></a>04602     xtab(1) =  - 0.973906528517171720077964012084D+00
    4667. 

  4667. <a name="l04603"></a>04603     xtab(2) =  - 0.865063366688984510732096688423D+00
    4668. 

  4668. <a name="l04604"></a>04604     xtab(3) =  - 0.679409568299024406234327365115D+00
    4669. 

  4669. <a name="l04605"></a>04605     xtab(4) =  - 0.433395394129247190799265943166D+00
    4670. 

  4670. <a name="l04606"></a>04606     xtab(5) =  - 0.148874338981631210884826001130D+00
    4671. 

  4671. <a name="l04607"></a>04607     xtab(6) =    0.148874338981631210884826001130D+00
    4672. 

  4672. <a name="l04608"></a>04608     xtab(7) =    0.433395394129247190799265943166D+00
    4673. 

  4673. <a name="l04609"></a>04609     xtab(8) =    0.679409568299024406234327365115D+00
    4674. 

  4674. <a name="l04610"></a>04610     xtab(9) =    0.865063366688984510732096688423D+00
    4675. 

  4675. <a name="l04611"></a>04611     xtab(10) =   0.973906528517171720077964012084D+00
    4676. 

  4676. <a name="l04612"></a>04612 
    4677. 

  4677. <a name="l04613"></a>04613     weight(1) =  0.666713443086881375935688098933D-01
    4678. 

  4678. <a name="l04614"></a>04614     weight(2) =  0.149451349150580593145776339658D+00
    4679. 

  4679. <a name="l04615"></a>04615     weight(3) =  0.219086362515982043995534934228D+00
    4680. 

  4680. <a name="l04616"></a>04616     weight(4) =  0.269266719309996355091226921569D+00
    4681. 

  4681. <a name="l04617"></a>04617     weight(5) =  0.295524224714752870173892994651D+00
    4682. 

  4682. <a name="l04618"></a>04618     weight(6) =  0.295524224714752870173892994651D+00
    4683. 

  4683. <a name="l04619"></a>04619     weight(7) =  0.269266719309996355091226921569D+00
    4684. 

  4684. <a name="l04620"></a>04620     weight(8) =  0.219086362515982043995534934228D+00
    4685. 

  4685. <a name="l04621"></a>04621     weight(9) =  0.149451349150580593145776339658D+00
    4686. 

  4686. <a name="l04622"></a>04622     weight(10) = 0.666713443086881375935688098933D-01
    4687. 

  4687. <a name="l04623"></a>04623 
    4688. 

  4688. <a name="l04624"></a>04624   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 11 ) <span class="keyword">then</span>
    4689. 

  4689. <a name="l04625"></a>04625 
    4690. 

  4690. <a name="l04626"></a>04626     xtab(1) =  - 0.978228658146056992803938001123D+00
    4691. 

  4691. <a name="l04627"></a>04627     xtab(2) =  - 0.887062599768095299075157769304D+00
    4692. 

  4692. <a name="l04628"></a>04628     xtab(3) =  - 0.730152005574049324093416252031D+00
    4693. 

  4693. <a name="l04629"></a>04629     xtab(4) =  - 0.519096129206811815925725669459D+00
    4694. 

  4694. <a name="l04630"></a>04630     xtab(5) =  - 0.269543155952344972331531985401D+00
    4695. 

  4695. <a name="l04631"></a>04631     xtab(6) =    0.0D+00
    4696. 

  4696. <a name="l04632"></a>04632     xtab(7) =    0.269543155952344972331531985401D+00
    4697. 

  4697. <a name="l04633"></a>04633     xtab(8) =    0.519096129206811815925725669459D+00
    4698. 

  4698. <a name="l04634"></a>04634     xtab(9) =    0.730152005574049324093416252031D+00
    4699. 

  4699. <a name="l04635"></a>04635     xtab(10) =   0.887062599768095299075157769304D+00
    4700. 

  4700. <a name="l04636"></a>04636     xtab(11) =   0.978228658146056992803938001123D+00
    4701. 

  4701. <a name="l04637"></a>04637 
    4702. 

  4702. <a name="l04638"></a>04638     weight(1) =  0.556685671161736664827537204425D-01
    4703. 

  4703. <a name="l04639"></a>04639     weight(2) =  0.125580369464904624634694299224D+00
    4704. 

  4704. <a name="l04640"></a>04640     weight(3) =  0.186290210927734251426097641432D+00
    4705. 

  4705. <a name="l04641"></a>04641     weight(4) =  0.233193764591990479918523704843D+00
    4706. 

  4706. <a name="l04642"></a>04642     weight(5) =  0.262804544510246662180688869891D+00
    4707. 

  4707. <a name="l04643"></a>04643     weight(6) =  0.272925086777900630714483528336D+00
    4708. 

  4708. <a name="l04644"></a>04644     weight(7) =  0.262804544510246662180688869891D+00
    4709. 

  4709. <a name="l04645"></a>04645     weight(8) =  0.233193764591990479918523704843D+00
    4710. 

  4710. <a name="l04646"></a>04646     weight(9) =  0.186290210927734251426097641432D+00
    4711. 

  4711. <a name="l04647"></a>04647     weight(10) = 0.125580369464904624634694299224D+00
    4712. 

  4712. <a name="l04648"></a>04648     weight(11) = 0.556685671161736664827537204425D-01
    4713. 

  4713. <a name="l04649"></a>04649 
    4714. 

  4714. <a name="l04650"></a>04650   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 12 ) <span class="keyword">then</span>
    4715. 

  4715. <a name="l04651"></a>04651 
    4716. 

  4716. <a name="l04652"></a>04652     xtab(1) =  - 0.981560634246719250690549090149D+00
    4717. 

  4717. <a name="l04653"></a>04653     xtab(2) =  - 0.904117256370474856678465866119D+00
    4718. 

  4718. <a name="l04654"></a>04654     xtab(3) =  - 0.769902674194304687036893833213D+00
    4719. 

  4719. <a name="l04655"></a>04655     xtab(4) =  - 0.587317954286617447296702418941D+00
    4720. 

  4720. <a name="l04656"></a>04656     xtab(5) =  - 0.367831498998180193752691536644D+00
    4721. 

  4721. <a name="l04657"></a>04657     xtab(6) =  - 0.125233408511468915472441369464D+00
    4722. 

  4722. <a name="l04658"></a>04658     xtab(7) =    0.125233408511468915472441369464D+00
    4723. 

  4723. <a name="l04659"></a>04659     xtab(8) =    0.367831498998180193752691536644D+00
    4724. 

  4724. <a name="l04660"></a>04660     xtab(9) =    0.587317954286617447296702418941D+00
    4725. 

  4725. <a name="l04661"></a>04661     xtab(10) =   0.769902674194304687036893833213D+00
    4726. 

  4726. <a name="l04662"></a>04662     xtab(11) =   0.904117256370474856678465866119D+00
    4727. 

  4727. <a name="l04663"></a>04663     xtab(12) =   0.981560634246719250690549090149D+00
    4728. 

  4728. <a name="l04664"></a>04664 
    4729. 

  4729. <a name="l04665"></a>04665     weight(1) =  0.471753363865118271946159614850D-01
    4730. 

  4730. <a name="l04666"></a>04666     weight(2) =  0.106939325995318430960254718194D+00
    4731. 

  4731. <a name="l04667"></a>04667     weight(3) =  0.160078328543346226334652529543D+00
    4732. 

  4732. <a name="l04668"></a>04668     weight(4) =  0.203167426723065921749064455810D+00
    4733. 

  4733. <a name="l04669"></a>04669     weight(5) =  0.233492536538354808760849898925D+00
    4734. 

  4734. <a name="l04670"></a>04670     weight(6) =  0.249147045813402785000562436043D+00
    4735. 

  4735. <a name="l04671"></a>04671     weight(7) =  0.249147045813402785000562436043D+00
    4736. 

  4736. <a name="l04672"></a>04672     weight(8) =  0.233492536538354808760849898925D+00
    4737. 

  4737. <a name="l04673"></a>04673     weight(9) =  0.203167426723065921749064455810D+00
    4738. 

  4738. <a name="l04674"></a>04674     weight(10) = 0.160078328543346226334652529543D+00
    4739. 

  4739. <a name="l04675"></a>04675     weight(11) = 0.106939325995318430960254718194D+00
    4740. 

  4740. <a name="l04676"></a>04676     weight(12) = 0.471753363865118271946159614850D-01
    4741. 

  4741. <a name="l04677"></a>04677 
    4742. 

  4742. <a name="l04678"></a>04678   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 13 ) <span class="keyword">then</span>
    4743. 

  4743. <a name="l04679"></a>04679 
    4744. 

  4744. <a name="l04680"></a>04680     xtab(1) =  - 0.984183054718588149472829448807D+00
    4745. 

  4745. <a name="l04681"></a>04681     xtab(2) =  - 0.917598399222977965206547836501D+00
    4746. 

  4746. <a name="l04682"></a>04682     xtab(3) =  - 0.801578090733309912794206489583D+00
    4747. 

  4747. <a name="l04683"></a>04683     xtab(4) =  - 0.642349339440340220643984606996D+00
    4748. 

  4748. <a name="l04684"></a>04684     xtab(5) =  - 0.448492751036446852877912852128D+00
    4749. 

  4749. <a name="l04685"></a>04685     xtab(6) =  - 0.230458315955134794065528121098D+00
    4750. 

  4750. <a name="l04686"></a>04686     xtab(7) =    0.0D+00
    4751. 

  4751. <a name="l04687"></a>04687     xtab(8) =    0.230458315955134794065528121098D+00
    4752. 

  4752. <a name="l04688"></a>04688     xtab(9) =    0.448492751036446852877912852128D+00
    4753. 

  4753. <a name="l04689"></a>04689     xtab(10) =   0.642349339440340220643984606996D+00
    4754. 

  4754. <a name="l04690"></a>04690     xtab(11) =   0.801578090733309912794206489583D+00
    4755. 

  4755. <a name="l04691"></a>04691     xtab(12) =   0.917598399222977965206547836501D+00
    4756. 

  4756. <a name="l04692"></a>04692     xtab(13) =   0.984183054718588149472829448807D+00
    4757. 

  4757. <a name="l04693"></a>04693 
    4758. 

  4758. <a name="l04694"></a>04694     weight(1) =  0.404840047653158795200215922010D-01
    4759. 

  4759. <a name="l04695"></a>04695     weight(2) =  0.921214998377284479144217759538D-01
    4760. 

  4760. <a name="l04696"></a>04696     weight(3) =  0.138873510219787238463601776869D+00
    4761. 

  4761. <a name="l04697"></a>04697     weight(4) =  0.178145980761945738280046691996D+00
    4762. 

  4762. <a name="l04698"></a>04698     weight(5) =  0.207816047536888502312523219306D+00
    4763. 

  4763. <a name="l04699"></a>04699     weight(6) =  0.226283180262897238412090186040D+00
    4764. 

  4764. <a name="l04700"></a>04700     weight(7) =  0.232551553230873910194589515269D+00
    4765. 

  4765. <a name="l04701"></a>04701     weight(8) =  0.226283180262897238412090186040D+00
    4766. 

  4766. <a name="l04702"></a>04702     weight(9) =  0.207816047536888502312523219306D+00
    4767. 

  4767. <a name="l04703"></a>04703     weight(10) = 0.178145980761945738280046691996D+00
    4768. 

  4768. <a name="l04704"></a>04704     weight(11) = 0.138873510219787238463601776869D+00
    4769. 

  4769. <a name="l04705"></a>04705     weight(12) = 0.921214998377284479144217759538D-01
    4770. 

  4770. <a name="l04706"></a>04706     weight(13) = 0.404840047653158795200215922010D-01
    4771. 

  4771. <a name="l04707"></a>04707 
    4772. 

  4772. <a name="l04708"></a>04708   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 14 ) <span class="keyword">then</span>
    4773. 

  4773. <a name="l04709"></a>04709 
    4774. 

  4774. <a name="l04710"></a>04710     xtab(1) =  - 0.986283808696812338841597266704D+00
    4775. 

  4775. <a name="l04711"></a>04711     xtab(2) =  - 0.928434883663573517336391139378D+00
    4776. 

  4776. <a name="l04712"></a>04712     xtab(3) =  - 0.827201315069764993189794742650D+00
    4777. 

  4777. <a name="l04713"></a>04713     xtab(4) =  - 0.687292904811685470148019803019D+00
    4778. 

  4778. <a name="l04714"></a>04714     xtab(5) =  - 0.515248636358154091965290718551D+00
    4779. 

  4779. <a name="l04715"></a>04715     xtab(6) =  - 0.319112368927889760435671824168D+00
    4780. 

  4780. <a name="l04716"></a>04716     xtab(7) =  - 0.108054948707343662066244650220D+00
    4781. 

  4781. <a name="l04717"></a>04717     xtab(8) =    0.108054948707343662066244650220D+00
    4782. 

  4782. <a name="l04718"></a>04718     xtab(9) =    0.319112368927889760435671824168D+00
    4783. 

  4783. <a name="l04719"></a>04719     xtab(10) =   0.515248636358154091965290718551D+00
    4784. 

  4784. <a name="l04720"></a>04720     xtab(11) =   0.687292904811685470148019803019D+00
    4785. 

  4785. <a name="l04721"></a>04721     xtab(12) =   0.827201315069764993189794742650D+00
    4786. 

  4786. <a name="l04722"></a>04722     xtab(13) =   0.928434883663573517336391139378D+00
    4787. 

  4787. <a name="l04723"></a>04723     xtab(14) =   0.986283808696812338841597266704D+00
    4788. 

  4788. <a name="l04724"></a>04724 
    4789. 

  4789. <a name="l04725"></a>04725     weight(1) =  0.351194603317518630318328761382D-01
    4790. 

  4790. <a name="l04726"></a>04726     weight(2) =  0.801580871597602098056332770629D-01
    4791. 

  4791. <a name="l04727"></a>04727     weight(3) =  0.121518570687903184689414809072D+00
    4792. 

  4792. <a name="l04728"></a>04728     weight(4) =  0.157203167158193534569601938624D+00
    4793. 

  4793. <a name="l04729"></a>04729     weight(5) =  0.185538397477937813741716590125D+00
    4794. 

  4794. <a name="l04730"></a>04730     weight(6) =  0.205198463721295603965924065661D+00
    4795. 

  4795. <a name="l04731"></a>04731     weight(7) =  0.215263853463157790195876443316D+00
    4796. 

  4796. <a name="l04732"></a>04732     weight(8) =  0.215263853463157790195876443316D+00
    4797. 

  4797. <a name="l04733"></a>04733     weight(9) =  0.205198463721295603965924065661D+00
    4798. 

  4798. <a name="l04734"></a>04734     weight(10) = 0.185538397477937813741716590125D+00
    4799. 

  4799. <a name="l04735"></a>04735     weight(11) = 0.157203167158193534569601938624D+00
    4800. 

  4800. <a name="l04736"></a>04736     weight(12) = 0.121518570687903184689414809072D+00
    4801. 

  4801. <a name="l04737"></a>04737     weight(13) = 0.801580871597602098056332770629D-01
    4802. 

  4802. <a name="l04738"></a>04738     weight(14) = 0.351194603317518630318328761382D-01
    4803. 

  4803. <a name="l04739"></a>04739 
    4804. 

  4804. <a name="l04740"></a>04740   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
    4805. 

  4805. <a name="l04741"></a>04741 
    4806. 

  4806. <a name="l04742"></a>04742     xtab(1) =  - 0.987992518020485428489565718587D+00
    4807. 

  4807. <a name="l04743"></a>04743     xtab(2) =  - 0.937273392400705904307758947710D+00
    4808. 

  4808. <a name="l04744"></a>04744     xtab(3) =  - 0.848206583410427216200648320774D+00
    4809. 

  4809. <a name="l04745"></a>04745     xtab(4) =  - 0.724417731360170047416186054614D+00
    4810. 

  4810. <a name="l04746"></a>04746     xtab(5) =  - 0.570972172608538847537226737254D+00
    4811. 

  4811. <a name="l04747"></a>04747     xtab(6) =  - 0.394151347077563369897207370981D+00
    4812. 

  4812. <a name="l04748"></a>04748     xtab(7) =  - 0.201194093997434522300628303395D+00
    4813. 

  4813. <a name="l04749"></a>04749     xtab(8) =    0.0D+00
    4814. 

  4814. <a name="l04750"></a>04750     xtab(9) =    0.201194093997434522300628303395D+00
    4815. 

  4815. <a name="l04751"></a>04751     xtab(10) =   0.394151347077563369897207370981D+00
    4816. 

  4816. <a name="l04752"></a>04752     xtab(11) =   0.570972172608538847537226737254D+00
    4817. 

  4817. <a name="l04753"></a>04753     xtab(12) =   0.724417731360170047416186054614D+00
    4818. 

  4818. <a name="l04754"></a>04754     xtab(13) =   0.848206583410427216200648320774D+00
    4819. 

  4819. <a name="l04755"></a>04755     xtab(14) =   0.937273392400705904307758947710D+00
    4820. 

  4820. <a name="l04756"></a>04756     xtab(15) =   0.987992518020485428489565718587D+00
    4821. 

  4821. <a name="l04757"></a>04757 
    4822. 

  4822. <a name="l04758"></a>04758     weight(1) =  0.307532419961172683546283935772D-01
    4823. 

  4823. <a name="l04759"></a>04759     weight(2) =  0.703660474881081247092674164507D-01
    4824. 

  4824. <a name="l04760"></a>04760     weight(3) =  0.107159220467171935011869546686D+00
    4825. 

  4825. <a name="l04761"></a>04761     weight(4) =  0.139570677926154314447804794511D+00
    4826. 

  4826. <a name="l04762"></a>04762     weight(5) =  0.166269205816993933553200860481D+00
    4827. 

  4827. <a name="l04763"></a>04763     weight(6) =  0.186161000015562211026800561866D+00
    4828. 

  4828. <a name="l04764"></a>04764     weight(7) =  0.198431485327111576456118326444D+00
    4829. 

  4829. <a name="l04765"></a>04765     weight(8) =  0.202578241925561272880620199968D+00
    4830. 

  4830. <a name="l04766"></a>04766     weight(9) =  0.198431485327111576456118326444D+00
    4831. 

  4831. <a name="l04767"></a>04767     weight(10) = 0.186161000015562211026800561866D+00
    4832. 

  4832. <a name="l04768"></a>04768     weight(11) = 0.166269205816993933553200860481D+00
    4833. 

  4833. <a name="l04769"></a>04769     weight(12) = 0.139570677926154314447804794511D+00
    4834. 

  4834. <a name="l04770"></a>04770     weight(13) = 0.107159220467171935011869546686D+00
    4835. 

  4835. <a name="l04771"></a>04771     weight(14) = 0.703660474881081247092674164507D-01
    4836. 

  4836. <a name="l04772"></a>04772     weight(15) = 0.307532419961172683546283935772D-01
    4837. 

  4837. <a name="l04773"></a>04773 
    4838. 

  4838. <a name="l04774"></a>04774   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
    4839. 

  4839. <a name="l04775"></a>04775 
    4840. 

  4840. <a name="l04776"></a>04776     xtab(1) =  - 0.989400934991649932596154173450D+00
    4841. 

  4841. <a name="l04777"></a>04777     xtab(2) =  - 0.944575023073232576077988415535D+00
    4842. 

  4842. <a name="l04778"></a>04778     xtab(3) =  - 0.865631202387831743880467897712D+00
    4843. 

  4843. <a name="l04779"></a>04779     xtab(4) =  - 0.755404408355003033895101194847D+00
    4844. 

  4844. <a name="l04780"></a>04780     xtab(5) =  - 0.617876244402643748446671764049D+00
    4845. 

  4845. <a name="l04781"></a>04781     xtab(6) =  - 0.458016777657227386342419442984D+00
    4846. 

  4846. <a name="l04782"></a>04782     xtab(7) =  - 0.281603550779258913230460501460D+00
    4847. 

  4847. <a name="l04783"></a>04783     xtab(8) =  - 0.950125098376374401853193354250D-01
    4848. 

  4848. <a name="l04784"></a>04784     xtab(9) =    0.950125098376374401853193354250D-01
    4849. 

  4849. <a name="l04785"></a>04785     xtab(10) =   0.281603550779258913230460501460D+00
    4850. 

  4850. <a name="l04786"></a>04786     xtab(11) =   0.458016777657227386342419442984D+00
    4851. 

  4851. <a name="l04787"></a>04787     xtab(12) =   0.617876244402643748446671764049D+00
    4852. 

  4852. <a name="l04788"></a>04788     xtab(13) =   0.755404408355003033895101194847D+00
    4853. 

  4853. <a name="l04789"></a>04789     xtab(14) =   0.865631202387831743880467897712D+00
    4854. 

  4854. <a name="l04790"></a>04790     xtab(15) =   0.944575023073232576077988415535D+00
    4855. 

  4855. <a name="l04791"></a>04791     xtab(16) =   0.989400934991649932596154173450D+00
    4856. 

  4856. <a name="l04792"></a>04792 
    4857. 

  4857. <a name="l04793"></a>04793     weight(1) =  0.271524594117540948517805724560D-01
    4858. 

  4858. <a name="l04794"></a>04794     weight(2) =  0.622535239386478928628438369944D-01
    4859. 

  4859. <a name="l04795"></a>04795     weight(3) =  0.951585116824927848099251076022D-01
    4860. 

  4860. <a name="l04796"></a>04796     weight(4) =  0.124628971255533872052476282192D+00
    4861. 

  4861. <a name="l04797"></a>04797     weight(5) =  0.149595988816576732081501730547D+00
    4862. 

  4862. <a name="l04798"></a>04798     weight(6) =  0.169156519395002538189312079030D+00
    4863. 

  4863. <a name="l04799"></a>04799     weight(7) =  0.182603415044923588866763667969D+00
    4864. 

  4864. <a name="l04800"></a>04800     weight(8) =  0.189450610455068496285396723208D+00
    4865. 

  4865. <a name="l04801"></a>04801     weight(9) =  0.189450610455068496285396723208D+00
    4866. 

  4866. <a name="l04802"></a>04802     weight(10) = 0.182603415044923588866763667969D+00
    4867. 

  4867. <a name="l04803"></a>04803     weight(11) = 0.169156519395002538189312079030D+00
    4868. 

  4868. <a name="l04804"></a>04804     weight(12) = 0.149595988816576732081501730547D+00
    4869. 

  4869. <a name="l04805"></a>04805     weight(13) = 0.124628971255533872052476282192D+00
    4870. 

  4870. <a name="l04806"></a>04806     weight(14) = 0.951585116824927848099251076022D-01
    4871. 

  4871. <a name="l04807"></a>04807     weight(15) = 0.622535239386478928628438369944D-01
    4872. 

  4872. <a name="l04808"></a>04808     weight(16) = 0.271524594117540948517805724560D-01
    4873. 

  4873. <a name="l04809"></a>04809 
    4874. 

  4874. <a name="l04810"></a>04810   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 17 ) <span class="keyword">then</span>
    4875. 

  4875. <a name="l04811"></a>04811 
    4876. 

  4876. <a name="l04812"></a>04812     xtab(1) =  - 0.990575475314417335675434019941D+00
    4877. 

  4877. <a name="l04813"></a>04813     xtab(2) =  - 0.950675521768767761222716957896D+00
    4878. 

  4878. <a name="l04814"></a>04814     xtab(3) =  - 0.880239153726985902122955694488D+00
    4879. 

  4879. <a name="l04815"></a>04815     xtab(4) =  - 0.781514003896801406925230055520D+00
    4880. 

  4880. <a name="l04816"></a>04816     xtab(5) =  - 0.657671159216690765850302216643D+00
    4881. 

  4881. <a name="l04817"></a>04817     xtab(6) =  - 0.512690537086476967886246568630D+00
    4882. 

  4882. <a name="l04818"></a>04818     xtab(7) =  - 0.351231763453876315297185517095D+00
    4883. 

  4883. <a name="l04819"></a>04819     xtab(8) =  - 0.178484181495847855850677493654D+00
    4884. 

  4884. <a name="l04820"></a>04820     xtab(9) =    0.0D+00
    4885. 

  4885. <a name="l04821"></a>04821     xtab(10) =   0.178484181495847855850677493654D+00
    4886. 

  4886. <a name="l04822"></a>04822     xtab(11) =   0.351231763453876315297185517095D+00
    4887. 

  4887. <a name="l04823"></a>04823     xtab(12) =   0.512690537086476967886246568630D+00
    4888. 

  4888. <a name="l04824"></a>04824     xtab(13) =   0.657671159216690765850302216643D+00
    4889. 

  4889. <a name="l04825"></a>04825     xtab(14) =   0.781514003896801406925230055520D+00
    4890. 

  4890. <a name="l04826"></a>04826     xtab(15) =   0.880239153726985902122955694488D+00
    4891. 

  4891. <a name="l04827"></a>04827     xtab(16) =   0.950675521768767761222716957896D+00
    4892. 

  4892. <a name="l04828"></a>04828     xtab(17) =   0.990575475314417335675434019941D+00
    4893. 

  4893. <a name="l04829"></a>04829 
    4894. 

  4894. <a name="l04830"></a>04830     weight(1) =  0.241483028685479319601100262876D-01
    4895. 

  4895. <a name="l04831"></a>04831     weight(2) =  0.554595293739872011294401653582D-01
    4896. 

  4896. <a name="l04832"></a>04832     weight(3) =  0.850361483171791808835353701911D-01
    4897. 

  4897. <a name="l04833"></a>04833     weight(4) =  0.111883847193403971094788385626D+00
    4898. 

  4898. <a name="l04834"></a>04834     weight(5) =  0.135136368468525473286319981702D+00
    4899. 

  4899. <a name="l04835"></a>04835     weight(6) =  0.154045761076810288081431594802D+00
    4900. 

  4900. <a name="l04836"></a>04836     weight(7) =  0.168004102156450044509970663788D+00
    4901. 

  4901. <a name="l04837"></a>04837     weight(8) =  0.176562705366992646325270990113D+00
    4902. 

  4902. <a name="l04838"></a>04838     weight(9) =  0.179446470356206525458265644262D+00
    4903. 

  4903. <a name="l04839"></a>04839     weight(10) = 0.176562705366992646325270990113D+00
    4904. 

  4904. <a name="l04840"></a>04840     weight(11) = 0.168004102156450044509970663788D+00
    4905. 

  4905. <a name="l04841"></a>04841     weight(12) = 0.154045761076810288081431594802D+00
    4906. 

  4906. <a name="l04842"></a>04842     weight(13) = 0.135136368468525473286319981702D+00
    4907. 

  4907. <a name="l04843"></a>04843     weight(14) = 0.111883847193403971094788385626D+00
    4908. 

  4908. <a name="l04844"></a>04844     weight(15) = 0.850361483171791808835353701911D-01
    4909. 

  4909. <a name="l04845"></a>04845     weight(16) = 0.554595293739872011294401653582D-01
    4910. 

  4910. <a name="l04846"></a>04846     weight(17) = 0.241483028685479319601100262876D-01
    4911. 

  4911. <a name="l04847"></a>04847 
    4912. 

  4912. <a name="l04848"></a>04848   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 18 ) <span class="keyword">then</span>
    4913. 

  4913. <a name="l04849"></a>04849 
    4914. 

  4914. <a name="l04850"></a>04850     xtab(1) =  - 0.991565168420930946730016004706D+00
    4915. 

  4915. <a name="l04851"></a>04851     xtab(2) =  - 0.955823949571397755181195892930D+00
    4916. 

  4916. <a name="l04852"></a>04852     xtab(3) =  - 0.892602466497555739206060591127D+00
    4917. 

  4917. <a name="l04853"></a>04853     xtab(4) =  - 0.803704958972523115682417455015D+00
    4918. 

  4918. <a name="l04854"></a>04854     xtab(5) =  - 0.691687043060353207874891081289D+00
    4919. 

  4919. <a name="l04855"></a>04855     xtab(6) =  - 0.559770831073947534607871548525D+00
    4920. 

  4920. <a name="l04856"></a>04856     xtab(7) =  - 0.411751161462842646035931793833D+00
    4921. 

  4921. <a name="l04857"></a>04857     xtab(8) =  - 0.251886225691505509588972854878D+00
    4922. 

  4922. <a name="l04858"></a>04858     xtab(9) =  - 0.847750130417353012422618529358D-01
    4923. 

  4923. <a name="l04859"></a>04859     xtab(10) =   0.847750130417353012422618529358D-01
    4924. 

  4924. <a name="l04860"></a>04860     xtab(11) =   0.251886225691505509588972854878D+00
    4925. 

  4925. <a name="l04861"></a>04861     xtab(12) =   0.411751161462842646035931793833D+00
    4926. 

  4926. <a name="l04862"></a>04862     xtab(13) =   0.559770831073947534607871548525D+00
    4927. 

  4927. <a name="l04863"></a>04863     xtab(14) =   0.691687043060353207874891081289D+00
    4928. 

  4928. <a name="l04864"></a>04864     xtab(15) =   0.803704958972523115682417455015D+00
    4929. 

  4929. <a name="l04865"></a>04865     xtab(16) =   0.892602466497555739206060591127D+00
    4930. 

  4930. <a name="l04866"></a>04866     xtab(17) =   0.955823949571397755181195892930D+00
    4931. 

  4931. <a name="l04867"></a>04867     xtab(18) =   0.991565168420930946730016004706D+00
    4932. 

  4932. <a name="l04868"></a>04868 
    4933. 

  4933. <a name="l04869"></a>04869     weight(1) =  0.216160135264833103133427102665D-01
    4934. 

  4934. <a name="l04870"></a>04870     weight(2) =  0.497145488949697964533349462026D-01
    4935. 

  4935. <a name="l04871"></a>04871     weight(3) =  0.764257302548890565291296776166D-01
    4936. 

  4936. <a name="l04872"></a>04872     weight(4) =  0.100942044106287165562813984925D+00
    4937. 

  4937. <a name="l04873"></a>04873     weight(5) =  0.122555206711478460184519126800D+00
    4938. 

  4938. <a name="l04874"></a>04874     weight(6) =  0.140642914670650651204731303752D+00
    4939. 

  4939. <a name="l04875"></a>04875     weight(7) =  0.154684675126265244925418003836D+00
    4940. 

  4940. <a name="l04876"></a>04876     weight(8) =  0.164276483745832722986053776466D+00
    4941. 

  4941. <a name="l04877"></a>04877     weight(9) =  0.169142382963143591840656470135D+00
    4942. 

  4942. <a name="l04878"></a>04878     weight(10) = 0.169142382963143591840656470135D+00
    4943. 

  4943. <a name="l04879"></a>04879     weight(11) = 0.164276483745832722986053776466D+00
    4944. 

  4944. <a name="l04880"></a>04880     weight(12) = 0.154684675126265244925418003836D+00
    4945. 

  4945. <a name="l04881"></a>04881     weight(13) = 0.140642914670650651204731303752D+00
    4946. 

  4946. <a name="l04882"></a>04882     weight(14) = 0.122555206711478460184519126800D+00
    4947. 

  4947. <a name="l04883"></a>04883     weight(15) = 0.100942044106287165562813984925D+00
    4948. 

  4948. <a name="l04884"></a>04884     weight(16) = 0.764257302548890565291296776166D-01
    4949. 

  4949. <a name="l04885"></a>04885     weight(17) = 0.497145488949697964533349462026D-01
    4950. 

  4950. <a name="l04886"></a>04886     weight(18) = 0.216160135264833103133427102665D-01
    4951. 

  4951. <a name="l04887"></a>04887 
    4952. 

  4952. <a name="l04888"></a>04888   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 19 ) <span class="keyword">then</span>
    4953. 

  4953. <a name="l04889"></a>04889 
    4954. 

  4954. <a name="l04890"></a>04890     xtab(1) =  - 0.992406843843584403189017670253D+00
    4955. 

  4955. <a name="l04891"></a>04891     xtab(2) =  - 0.960208152134830030852778840688D+00
    4956. 

  4956. <a name="l04892"></a>04892     xtab(3) =  - 0.903155903614817901642660928532D+00
    4957. 

  4957. <a name="l04893"></a>04893     xtab(4) =  - 0.822714656537142824978922486713D+00
    4958. 

  4958. <a name="l04894"></a>04894     xtab(5) =  - 0.720966177335229378617095860824D+00
    4959. 

  4959. <a name="l04895"></a>04895     xtab(6) =  - 0.600545304661681023469638164946D+00
    4960. 

  4960. <a name="l04896"></a>04896     xtab(7) =  - 0.464570741375960945717267148104D+00
    4961. 

  4961. <a name="l04897"></a>04897     xtab(8) =  - 0.316564099963629831990117328850D+00
    4962. 

  4962. <a name="l04898"></a>04898     xtab(9) =  - 0.160358645640225375868096115741D+00
    4963. 

  4963. <a name="l04899"></a>04899     xtab(10) =   0.0D+00
    4964. 

  4964. <a name="l04900"></a>04900     xtab(11) =   0.160358645640225375868096115741D+00
    4965. 

  4965. <a name="l04901"></a>04901     xtab(12) =   0.316564099963629831990117328850D+00
    4966. 

  4966. <a name="l04902"></a>04902     xtab(13) =   0.464570741375960945717267148104D+00
    4967. 

  4967. <a name="l04903"></a>04903     xtab(14) =   0.600545304661681023469638164946D+00
    4968. 

  4968. <a name="l04904"></a>04904     xtab(15) =   0.720966177335229378617095860824D+00
    4969. 

  4969. <a name="l04905"></a>04905     xtab(16) =   0.822714656537142824978922486713D+00
    4970. 

  4970. <a name="l04906"></a>04906     xtab(17) =   0.903155903614817901642660928532D+00
    4971. 

  4971. <a name="l04907"></a>04907     xtab(18) =   0.960208152134830030852778840688D+00
    4972. 

  4972. <a name="l04908"></a>04908     xtab(19) =   0.992406843843584403189017670253D+00
    4973. 

  4973. <a name="l04909"></a>04909 
    4974. 

  4974. <a name="l04910"></a>04910     weight(1) =  0.194617882297264770363120414644D-01
    4975. 

  4975. <a name="l04911"></a>04911     weight(2) =  0.448142267656996003328381574020D-01
    4976. 

  4976. <a name="l04912"></a>04912     weight(3) =  0.690445427376412265807082580060D-01
    4977. 

  4977. <a name="l04913"></a>04913     weight(4) =  0.914900216224499994644620941238D-01
    4978. 

  4978. <a name="l04914"></a>04914     weight(5) =  0.111566645547333994716023901682D+00
    4979. 

  4979. <a name="l04915"></a>04915     weight(6) =  0.128753962539336227675515784857D+00
    4980. 

  4980. <a name="l04916"></a>04916     weight(7) =  0.142606702173606611775746109442D+00
    4981. 

  4981. <a name="l04917"></a>04917     weight(8) =  0.152766042065859666778855400898D+00
    4982. 

  4982. <a name="l04918"></a>04918     weight(9) =  0.158968843393954347649956439465D+00
    4983. 

  4983. <a name="l04919"></a>04919     weight(10) = 0.161054449848783695979163625321D+00
    4984. 

  4984. <a name="l04920"></a>04920     weight(11) = 0.158968843393954347649956439465D+00
    4985. 

  4985. <a name="l04921"></a>04921     weight(12) = 0.152766042065859666778855400898D+00
    4986. 

  4986. <a name="l04922"></a>04922     weight(13) = 0.142606702173606611775746109442D+00
    4987. 

  4987. <a name="l04923"></a>04923     weight(14) = 0.128753962539336227675515784857D+00
    4988. 

  4988. <a name="l04924"></a>04924     weight(15) = 0.111566645547333994716023901682D+00
    4989. 

  4989. <a name="l04925"></a>04925     weight(16) = 0.914900216224499994644620941238D-01
    4990. 

  4990. <a name="l04926"></a>04926     weight(17) = 0.690445427376412265807082580060D-01
    4991. 

  4991. <a name="l04927"></a>04927     weight(18) = 0.448142267656996003328381574020D-01
    4992. 

  4992. <a name="l04928"></a>04928     weight(19) = 0.194617882297264770363120414644D-01
    4993. 

  4993. <a name="l04929"></a>04929 
    4994. 

  4994. <a name="l04930"></a>04930   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 20 ) <span class="keyword">then</span>
    4995. 

  4995. <a name="l04931"></a>04931 
    4996. 

  4996. <a name="l04932"></a>04932     xtab(1) =  - 0.993128599185094924786122388471D+00
    4997. 

  4997. <a name="l04933"></a>04933     xtab(2) =  - 0.963971927277913791267666131197D+00
    4998. 

  4998. <a name="l04934"></a>04934     xtab(3) =  - 0.912234428251325905867752441203D+00
    4999. 

  4999. <a name="l04935"></a>04935     xtab(4) =  - 0.839116971822218823394529061702D+00
    5000. 

  5000. <a name="l04936"></a>04936     xtab(5) =  - 0.746331906460150792614305070356D+00
    5001. 

  5001. <a name="l04937"></a>04937     xtab(6) =  - 0.636053680726515025452836696226D+00
    5002. 

  5002. <a name="l04938"></a>04938     xtab(7) =  - 0.510867001950827098004364050955D+00
    5003. 

  5003. <a name="l04939"></a>04939     xtab(8) =  - 0.373706088715419560672548177025D+00
    5004. 

  5004. <a name="l04940"></a>04940     xtab(9) =  - 0.227785851141645078080496195369D+00
    5005. 

  5005. <a name="l04941"></a>04941     xtab(10) = - 0.765265211334973337546404093988D-01
    5006. 

  5006. <a name="l04942"></a>04942     xtab(11) =   0.765265211334973337546404093988D-01
    5007. 

  5007. <a name="l04943"></a>04943     xtab(12) =   0.227785851141645078080496195369D+00
    5008. 

  5008. <a name="l04944"></a>04944     xtab(13) =   0.373706088715419560672548177025D+00
    5009. 

  5009. <a name="l04945"></a>04945     xtab(14) =   0.510867001950827098004364050955D+00
    5010. 

  5010. <a name="l04946"></a>04946     xtab(15) =   0.636053680726515025452836696226D+00
    5011. 

  5011. <a name="l04947"></a>04947     xtab(16) =   0.746331906460150792614305070356D+00
    5012. 

  5012. <a name="l04948"></a>04948     xtab(17) =   0.839116971822218823394529061702D+00
    5013. 

  5013. <a name="l04949"></a>04949     xtab(18) =   0.912234428251325905867752441203D+00
    5014. 

  5014. <a name="l04950"></a>04950     xtab(19) =   0.963971927277913791267666131197D+00
    5015. 

  5015. <a name="l04951"></a>04951     xtab(20) =   0.993128599185094924786122388471D+00
    5016. 

  5016. <a name="l04952"></a>04952 
    5017. 

  5017. <a name="l04953"></a>04953     weight(1) =  0.176140071391521183118619623519D-01
    5018. 

  5018. <a name="l04954"></a>04954     weight(2) =  0.406014298003869413310399522749D-01
    5019. 

  5019. <a name="l04955"></a>04955     weight(3) =  0.626720483341090635695065351870D-01
    5020. 

  5020. <a name="l04956"></a>04956     weight(4) =  0.832767415767047487247581432220D-01
    5021. 

  5021. <a name="l04957"></a>04957     weight(5) =  0.101930119817240435036750135480D+00
    5022. 

  5022. <a name="l04958"></a>04958     weight(6) =  0.118194531961518417312377377711D+00
    5023. 

  5023. <a name="l04959"></a>04959     weight(7) =  0.131688638449176626898494499748D+00
    5024. 

  5024. <a name="l04960"></a>04960     weight(8) =  0.142096109318382051329298325067D+00
    5025. 

  5025. <a name="l04961"></a>04961     weight(9) =  0.149172986472603746787828737002D+00
    5026. 

  5026. <a name="l04962"></a>04962     weight(10) = 0.152753387130725850698084331955D+00
    5027. 

  5027. <a name="l04963"></a>04963     weight(11) = 0.152753387130725850698084331955D+00
    5028. 

  5028. <a name="l04964"></a>04964     weight(12) = 0.149172986472603746787828737002D+00
    5029. 

  5029. <a name="l04965"></a>04965     weight(13) = 0.142096109318382051329298325067D+00
    5030. 

  5030. <a name="l04966"></a>04966     weight(14) = 0.131688638449176626898494499748D+00
    5031. 

  5031. <a name="l04967"></a>04967     weight(15) = 0.118194531961518417312377377711D+00
    5032. 

  5032. <a name="l04968"></a>04968     weight(16) = 0.101930119817240435036750135480D+00
    5033. 

  5033. <a name="l04969"></a>04969     weight(17) = 0.832767415767047487247581432220D-01
    5034. 

  5034. <a name="l04970"></a>04970     weight(18) = 0.626720483341090635695065351870D-01
    5035. 

  5035. <a name="l04971"></a>04971     weight(19) = 0.406014298003869413310399522749D-01
    5036. 

  5036. <a name="l04972"></a>04972     weight(20) = 0.176140071391521183118619623519D-01
    5037. 

  5037. <a name="l04973"></a>04973 
    5038. 

  5038. <a name="l04974"></a>04974   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 32 ) <span class="keyword">then</span>
    5039. 

  5039. <a name="l04975"></a>04975 
    5040. 

  5040. <a name="l04976"></a>04976     xtab(1) =  - 0.997263861849481563544981128665D+00
    5041. 

  5041. <a name="l04977"></a>04977     xtab(2) =  - 0.985611511545268335400175044631D+00
    5042. 

  5042. <a name="l04978"></a>04978     xtab(3) =  - 0.964762255587506430773811928118D+00
    5043. 

  5043. <a name="l04979"></a>04979     xtab(4) =  - 0.934906075937739689170919134835D+00
    5044. 

  5044. <a name="l04980"></a>04980     xtab(5) =  - 0.896321155766052123965307243719D+00
    5045. 

  5045. <a name="l04981"></a>04981     xtab(6) =  - 0.849367613732569970133693004968D+00
    5046. 

  5046. <a name="l04982"></a>04982     xtab(7) =  - 0.794483795967942406963097298970D+00
    5047. 

  5047. <a name="l04983"></a>04983     xtab(8) =  - 0.732182118740289680387426665091D+00
    5048. 

  5048. <a name="l04984"></a>04984     xtab(9) =  - 0.663044266930215200975115168663D+00
    5049. 

  5049. <a name="l04985"></a>04985     xtab(10) = - 0.587715757240762329040745476402D+00
    5050. 

  5050. <a name="l04986"></a>04986     xtab(11) = - 0.506899908932229390023747474378D+00
    5051. 

  5051. <a name="l04987"></a>04987     xtab(12) = - 0.421351276130635345364119436172D+00
    5052. 

  5052. <a name="l04988"></a>04988     xtab(13) = - 0.331868602282127649779916805730D+00
    5053. 

  5053. <a name="l04989"></a>04989     xtab(14) = - 0.239287362252137074544603209166D+00
    5054. 

  5054. <a name="l04990"></a>04990     xtab(15) = - 0.144471961582796493485186373599D+00
    5055. 

  5055. <a name="l04991"></a>04991     xtab(16) = - 0.483076656877383162348125704405D-01
    5056. 

  5056. <a name="l04992"></a>04992     xtab(17) =   0.483076656877383162348125704405D-01
    5057. 

  5057. <a name="l04993"></a>04993     xtab(18) =   0.144471961582796493485186373599D+00
    5058. 

  5058. <a name="l04994"></a>04994     xtab(19) =   0.239287362252137074544603209166D+00
    5059. 

  5059. <a name="l04995"></a>04995     xtab(20) =   0.331868602282127649779916805730D+00
    5060. 

  5060. <a name="l04996"></a>04996     xtab(21) =   0.421351276130635345364119436172D+00
    5061. 

  5061. <a name="l04997"></a>04997     xtab(22) =   0.506899908932229390023747474378D+00
    5062. 

  5062. <a name="l04998"></a>04998     xtab(23) =   0.587715757240762329040745476402D+00
    5063. 

  5063. <a name="l04999"></a>04999     xtab(24) =   0.663044266930215200975115168663D+00
    5064. 

  5064. <a name="l05000"></a>05000     xtab(25) =   0.732182118740289680387426665091D+00
    5065. 

  5065. <a name="l05001"></a>05001     xtab(26) =   0.794483795967942406963097298970D+00
    5066. 

  5066. <a name="l05002"></a>05002     xtab(27) =   0.849367613732569970133693004968D+00
    5067. 

  5067. <a name="l05003"></a>05003     xtab(28) =   0.896321155766052123965307243719D+00
    5068. 

  5068. <a name="l05004"></a>05004     xtab(29) =   0.934906075937739689170919134835D+00
    5069. 

  5069. <a name="l05005"></a>05005     xtab(30) =   0.964762255587506430773811928118D+00
    5070. 

  5070. <a name="l05006"></a>05006     xtab(31) =   0.985611511545268335400175044631D+00
    5071. 

  5071. <a name="l05007"></a>05007     xtab(32) =   0.997263861849481563544981128665D+00
    5072. 

  5072. <a name="l05008"></a>05008 
    5073. 

  5073. <a name="l05009"></a>05009     weight(1) =  0.701861000947009660040706373885D-02
    5074. 

  5074. <a name="l05010"></a>05010     weight(2) =  0.162743947309056706051705622064D-01
    5075. 

  5075. <a name="l05011"></a>05011     weight(3) =  0.253920653092620594557525897892D-01
    5076. 

  5076. <a name="l05012"></a>05012     weight(4) =  0.342738629130214331026877322524D-01
    5077. 

  5077. <a name="l05013"></a>05013     weight(5) =  0.428358980222266806568786466061D-01
    5078. 

  5078. <a name="l05014"></a>05014     weight(6) =  0.509980592623761761961632446895D-01
    5079. 

  5079. <a name="l05015"></a>05015     weight(7) =  0.586840934785355471452836373002D-01
    5080. 

  5080. <a name="l05016"></a>05016     weight(8) =  0.658222227763618468376500637069D-01
    5081. 

  5081. <a name="l05017"></a>05017     weight(9) =  0.723457941088485062253993564785D-01
    5082. 

  5082. <a name="l05018"></a>05018     weight(10) = 0.781938957870703064717409188283D-01
    5083. 

  5083. <a name="l05019"></a>05019     weight(11) = 0.833119242269467552221990746043D-01
    5084. 

  5084. <a name="l05020"></a>05020     weight(12) = 0.876520930044038111427714627518D-01
    5085. 

  5085. <a name="l05021"></a>05021     weight(13) = 0.911738786957638847128685771116D-01
    5086. 

  5086. <a name="l05022"></a>05022     weight(14) = 0.938443990808045656391802376681D-01
    5087. 

  5087. <a name="l05023"></a>05023     weight(15) = 0.956387200792748594190820022041D-01
    5088. 

  5088. <a name="l05024"></a>05024     weight(16) = 0.965400885147278005667648300636D-01
    5089. 

  5089. <a name="l05025"></a>05025     weight(17) = 0.965400885147278005667648300636D-01
    5090. 

  5090. <a name="l05026"></a>05026     weight(18) = 0.956387200792748594190820022041D-01
    5091. 

  5091. <a name="l05027"></a>05027     weight(19) = 0.938443990808045656391802376681D-01
    5092. 

  5092. <a name="l05028"></a>05028     weight(20) = 0.911738786957638847128685771116D-01
    5093. 

  5093. <a name="l05029"></a>05029     weight(21) = 0.876520930044038111427714627518D-01
    5094. 

  5094. <a name="l05030"></a>05030     weight(22) = 0.833119242269467552221990746043D-01
    5095. 

  5095. <a name="l05031"></a>05031     weight(23) = 0.781938957870703064717409188283D-01
    5096. 

  5096. <a name="l05032"></a>05032     weight(24) = 0.723457941088485062253993564785D-01
    5097. 

  5097. <a name="l05033"></a>05033     weight(25) = 0.658222227763618468376500637069D-01
    5098. 

  5098. <a name="l05034"></a>05034     weight(26) = 0.586840934785355471452836373002D-01
    5099. 

  5099. <a name="l05035"></a>05035     weight(27) = 0.509980592623761761961632446895D-01
    5100. 

  5100. <a name="l05036"></a>05036     weight(28) = 0.428358980222266806568786466061D-01
    5101. 

  5101. <a name="l05037"></a>05037     weight(29) = 0.342738629130214331026877322524D-01
    5102. 

  5102. <a name="l05038"></a>05038     weight(30) = 0.253920653092620594557525897892D-01
    5103. 

  5103. <a name="l05039"></a>05039     weight(31) = 0.162743947309056706051705622064D-01
    5104. 

  5104. <a name="l05040"></a>05040     weight(32) = 0.701861000947009660040706373885D-02
    5105. 

  5105. <a name="l05041"></a>05041 
    5106. 

  5106. <a name="l05042"></a>05042   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 64 ) <span class="keyword">then</span>
    5107. 

  5107. <a name="l05043"></a>05043 
    5108. 

  5108. <a name="l05044"></a>05044     xtab(1) =  - 0.999305041735772139456905624346D+00
    5109. 

  5109. <a name="l05045"></a>05045     xtab(2) =  - 0.996340116771955279346924500676D+00
    5110. 

  5110. <a name="l05046"></a>05046     xtab(3) =  - 0.991013371476744320739382383443D+00
    5111. 

  5111. <a name="l05047"></a>05047     xtab(4) =  - 0.983336253884625956931299302157D+00
    5112. 

  5112. <a name="l05048"></a>05048     xtab(5) =  - 0.973326827789910963741853507352D+00
    5113. 

  5113. <a name="l05049"></a>05049     xtab(6) =  - 0.961008799652053718918614121897D+00
    5114. 

  5114. <a name="l05050"></a>05050     xtab(7) =  - 0.946411374858402816062481491347D+00
    5115. 

  5115. <a name="l05051"></a>05051     xtab(8) =  - 0.929569172131939575821490154559D+00
    5116. 

  5116. <a name="l05052"></a>05052     xtab(9) =  - 0.910522137078502805756380668008D+00
    5117. 

  5117. <a name="l05053"></a>05053     xtab(10) = - 0.889315445995114105853404038273D+00
    5118. 

  5118. <a name="l05054"></a>05054     xtab(11) = - 0.865999398154092819760783385070D+00
    5119. 

  5119. <a name="l05055"></a>05055     xtab(12) = - 0.840629296252580362751691544696D+00
    5120. 

  5120. <a name="l05056"></a>05056     xtab(13) = - 0.813265315122797559741923338086D+00
    5121. 

  5121. <a name="l05057"></a>05057     xtab(14) = - 0.783972358943341407610220525214D+00
    5122. 

  5122. <a name="l05058"></a>05058     xtab(15) = - 0.752819907260531896611863774886D+00
    5123. 

  5123. <a name="l05059"></a>05059     xtab(16) = - 0.719881850171610826848940217832D+00
    5124. 

  5124. <a name="l05060"></a>05060     xtab(17) = - 0.685236313054233242563558371031D+00
    5125. 

  5125. <a name="l05061"></a>05061     xtab(18) = - 0.648965471254657339857761231993D+00
    5126. 

  5126. <a name="l05062"></a>05062     xtab(19) = - 0.611155355172393250248852971019D+00
    5127. 

  5127. <a name="l05063"></a>05063     xtab(20) = - 0.571895646202634034283878116659D+00
    5128. 

  5128. <a name="l05064"></a>05064     xtab(21) = - 0.531279464019894545658013903544D+00
    5129. 

  5129. <a name="l05065"></a>05065     xtab(22) = - 0.489403145707052957478526307022D+00
    5130. 

  5130. <a name="l05066"></a>05066     xtab(23) = - 0.446366017253464087984947714759D+00
    5131. 

  5131. <a name="l05067"></a>05067     xtab(24) = - 0.402270157963991603695766771260D+00
    5132. 

  5132. <a name="l05068"></a>05068     xtab(25) = - 0.357220158337668115950442615046D+00
    5133. 

  5133. <a name="l05069"></a>05069     xtab(26) = - 0.311322871990210956157512698560D+00
    5134. 

  5134. <a name="l05070"></a>05070     xtab(27) = - 0.264687162208767416373964172510D+00
    5135. 

  5135. <a name="l05071"></a>05071     xtab(28) = - 0.217423643740007084149648748989D+00
    5136. 

  5136. <a name="l05072"></a>05072     xtab(29) = - 0.169644420423992818037313629748D+00
    5137. 

  5137. <a name="l05073"></a>05073     xtab(30) = - 0.121462819296120554470376463492D+00
    5138. 

  5138. <a name="l05074"></a>05074     xtab(31) = - 0.729931217877990394495429419403D-01
    5139. 

  5139. <a name="l05075"></a>05075     xtab(32) = - 0.243502926634244325089558428537D-01
    5140. 

  5140. <a name="l05076"></a>05076     xtab(33) =   0.243502926634244325089558428537D-01
    5141. 

  5141. <a name="l05077"></a>05077     xtab(34) =   0.729931217877990394495429419403D-01
    5142. 

  5142. <a name="l05078"></a>05078     xtab(35) =   0.121462819296120554470376463492D+00
    5143. 

  5143. <a name="l05079"></a>05079     xtab(36) =   0.169644420423992818037313629748D+00
    5144. 

  5144. <a name="l05080"></a>05080     xtab(37) =   0.217423643740007084149648748989D+00
    5145. 

  5145. <a name="l05081"></a>05081     xtab(38) =   0.264687162208767416373964172510D+00
    5146. 

  5146. <a name="l05082"></a>05082     xtab(39) =   0.311322871990210956157512698560D+00
    5147. 

  5147. <a name="l05083"></a>05083     xtab(40) =   0.357220158337668115950442615046D+00
    5148. 

  5148. <a name="l05084"></a>05084     xtab(41) =   0.402270157963991603695766771260D+00
    5149. 

  5149. <a name="l05085"></a>05085     xtab(42) =   0.446366017253464087984947714759D+00
    5150. 

  5150. <a name="l05086"></a>05086     xtab(43) =   0.489403145707052957478526307022D+00
    5151. 

  5151. <a name="l05087"></a>05087     xtab(44) =   0.531279464019894545658013903544D+00
    5152. 

  5152. <a name="l05088"></a>05088     xtab(45) =   0.571895646202634034283878116659D+00
    5153. 

  5153. <a name="l05089"></a>05089     xtab(46) =   0.611155355172393250248852971019D+00
    5154. 

  5154. <a name="l05090"></a>05090     xtab(47) =   0.648965471254657339857761231993D+00
    5155. 

  5155. <a name="l05091"></a>05091     xtab(48) =   0.685236313054233242563558371031D+00
    5156. 

  5156. <a name="l05092"></a>05092     xtab(49) =   0.719881850171610826848940217832D+00
    5157. 

  5157. <a name="l05093"></a>05093     xtab(50) =   0.752819907260531896611863774886D+00
    5158. 

  5158. <a name="l05094"></a>05094     xtab(51) =   0.783972358943341407610220525214D+00
    5159. 

  5159. <a name="l05095"></a>05095     xtab(52) =   0.813265315122797559741923338086D+00
    5160. 

  5160. <a name="l05096"></a>05096     xtab(53) =   0.840629296252580362751691544696D+00
    5161. 

  5161. <a name="l05097"></a>05097     xtab(54) =   0.865999398154092819760783385070D+00
    5162. 

  5162. <a name="l05098"></a>05098     xtab(55) =   0.889315445995114105853404038273D+00
    5163. 

  5163. <a name="l05099"></a>05099     xtab(56) =   0.910522137078502805756380668008D+00
    5164. 

  5164. <a name="l05100"></a>05100     xtab(57) =   0.929569172131939575821490154559D+00
    5165. 

  5165. <a name="l05101"></a>05101     xtab(58) =   0.946411374858402816062481491347D+00
    5166. 

  5166. <a name="l05102"></a>05102     xtab(59) =   0.961008799652053718918614121897D+00
    5167. 

  5167. <a name="l05103"></a>05103     xtab(60) =   0.973326827789910963741853507352D+00
    5168. 

  5168. <a name="l05104"></a>05104     xtab(61) =   0.983336253884625956931299302157D+00
    5169. 

  5169. <a name="l05105"></a>05105     xtab(62) =   0.991013371476744320739382383443D+00
    5170. 

  5170. <a name="l05106"></a>05106     xtab(63) =   0.996340116771955279346924500676D+00
    5171. 

  5171. <a name="l05107"></a>05107     xtab(64) =   0.999305041735772139456905624346D+00
    5172. 

  5172. <a name="l05108"></a>05108 
    5173. 

  5173. <a name="l05109"></a>05109     weight(1) =  0.178328072169643294729607914497D-02
    5174. 

  5174. <a name="l05110"></a>05110     weight(2) =  0.414703326056246763528753572855D-02
    5175. 

  5175. <a name="l05111"></a>05111     weight(3) =  0.650445796897836285611736039998D-02
    5176. 

  5176. <a name="l05112"></a>05112     weight(4) =  0.884675982636394772303091465973D-02
    5177. 

  5177. <a name="l05113"></a>05113     weight(5) =  0.111681394601311288185904930192D-01
    5178. 

  5178. <a name="l05114"></a>05114     weight(6) =  0.134630478967186425980607666860D-01
    5179. 

  5179. <a name="l05115"></a>05115     weight(7) =  0.157260304760247193219659952975D-01
    5180. 

  5180. <a name="l05116"></a>05116     weight(8) =  0.179517157756973430850453020011D-01
    5181. 

  5181. <a name="l05117"></a>05117     weight(9) =  0.201348231535302093723403167285D-01
    5182. 

  5182. <a name="l05118"></a>05118     weight(10) = 0.222701738083832541592983303842D-01
    5183. 

  5183. <a name="l05119"></a>05119     weight(11) = 0.243527025687108733381775504091D-01
    5184. 

  5184. <a name="l05120"></a>05120     weight(12) = 0.263774697150546586716917926252D-01
    5185. 

  5185. <a name="l05121"></a>05121     weight(13) = 0.283396726142594832275113052002D-01
    5186. 

  5186. <a name="l05122"></a>05122     weight(14) = 0.302346570724024788679740598195D-01
    5187. 

  5187. <a name="l05123"></a>05123     weight(15) = 0.320579283548515535854675043479D-01
    5188. 

  5188. <a name="l05124"></a>05124     weight(16) = 0.338051618371416093915654821107D-01
    5189. 

  5189. <a name="l05125"></a>05125     weight(17) = 0.354722132568823838106931467152D-01
    5190. 

  5190. <a name="l05126"></a>05126     weight(18) = 0.370551285402400460404151018096D-01
    5191. 

  5191. <a name="l05127"></a>05127     weight(19) = 0.385501531786156291289624969468D-01
    5192. 

  5192. <a name="l05128"></a>05128     weight(20) = 0.399537411327203413866569261283D-01
    5193. 

  5193. <a name="l05129"></a>05129     weight(21) = 0.412625632426235286101562974736D-01
    5194. 

  5194. <a name="l05130"></a>05130     weight(22) = 0.424735151236535890073397679088D-01
    5195. 

  5195. <a name="l05131"></a>05131     weight(23) = 0.435837245293234533768278609737D-01
    5196. 

  5196. <a name="l05132"></a>05132     weight(24) = 0.445905581637565630601347100309D-01
    5197. 

  5197. <a name="l05133"></a>05133     weight(25) = 0.454916279274181444797709969713D-01
    5198. 

  5198. <a name="l05134"></a>05134     weight(26) = 0.462847965813144172959532492323D-01
    5199. 

  5199. <a name="l05135"></a>05135     weight(27) = 0.469681828162100173253262857546D-01
    5200. 

  5200. <a name="l05136"></a>05136     weight(28) = 0.475401657148303086622822069442D-01
    5201. 

  5201. <a name="l05137"></a>05137     weight(29) = 0.479993885964583077281261798713D-01
    5202. 

  5202. <a name="l05138"></a>05138     weight(30) = 0.483447622348029571697695271580D-01
    5203. 

  5203. <a name="l05139"></a>05139     weight(31) = 0.485754674415034269347990667840D-01
    5204. 

  5204. <a name="l05140"></a>05140     weight(32) = 0.486909570091397203833653907347D-01
    5205. 

  5205. <a name="l05141"></a>05141     weight(33) = 0.486909570091397203833653907347D-01
    5206. 

  5206. <a name="l05142"></a>05142     weight(34) = 0.485754674415034269347990667840D-01
    5207. 

  5207. <a name="l05143"></a>05143     weight(35) = 0.483447622348029571697695271580D-01
    5208. 

  5208. <a name="l05144"></a>05144     weight(36) = 0.479993885964583077281261798713D-01
    5209. 

  5209. <a name="l05145"></a>05145     weight(37) = 0.475401657148303086622822069442D-01
    5210. 

  5210. <a name="l05146"></a>05146     weight(38) = 0.469681828162100173253262857546D-01
    5211. 

  5211. <a name="l05147"></a>05147     weight(39) = 0.462847965813144172959532492323D-01
    5212. 

  5212. <a name="l05148"></a>05148     weight(40) = 0.454916279274181444797709969713D-01
    5213. 

  5213. <a name="l05149"></a>05149     weight(41) = 0.445905581637565630601347100309D-01
    5214. 

  5214. <a name="l05150"></a>05150     weight(42) = 0.435837245293234533768278609737D-01
    5215. 

  5215. <a name="l05151"></a>05151     weight(43) = 0.424735151236535890073397679088D-01
    5216. 

  5216. <a name="l05152"></a>05152     weight(44) = 0.412625632426235286101562974736D-01
    5217. 

  5217. <a name="l05153"></a>05153     weight(45) = 0.399537411327203413866569261283D-01
    5218. 

  5218. <a name="l05154"></a>05154     weight(46) = 0.385501531786156291289624969468D-01
    5219. 

  5219. <a name="l05155"></a>05155     weight(47) = 0.370551285402400460404151018096D-01
    5220. 

  5220. <a name="l05156"></a>05156     weight(48) = 0.354722132568823838106931467152D-01
    5221. 

  5221. <a name="l05157"></a>05157     weight(49) = 0.338051618371416093915654821107D-01
    5222. 

  5222. <a name="l05158"></a>05158     weight(50) = 0.320579283548515535854675043479D-01
    5223. 

  5223. <a name="l05159"></a>05159     weight(51) = 0.302346570724024788679740598195D-01
    5224. 

  5224. <a name="l05160"></a>05160     weight(52) = 0.283396726142594832275113052002D-01
    5225. 

  5225. <a name="l05161"></a>05161     weight(53) = 0.263774697150546586716917926252D-01
    5226. 

  5226. <a name="l05162"></a>05162     weight(54) = 0.243527025687108733381775504091D-01
    5227. 

  5227. <a name="l05163"></a>05163     weight(55) = 0.222701738083832541592983303842D-01
    5228. 

  5228. <a name="l05164"></a>05164     weight(56) = 0.201348231535302093723403167285D-01
    5229. 

  5229. <a name="l05165"></a>05165     weight(57) = 0.179517157756973430850453020011D-01
    5230. 

  5230. <a name="l05166"></a>05166     weight(58) = 0.157260304760247193219659952975D-01
    5231. 

  5231. <a name="l05167"></a>05167     weight(59) = 0.134630478967186425980607666860D-01
    5232. 

  5232. <a name="l05168"></a>05168     weight(60) = 0.111681394601311288185904930192D-01
    5233. 

  5233. <a name="l05169"></a>05169     weight(61) = 0.884675982636394772303091465973D-02
    5234. 

  5234. <a name="l05170"></a>05170     weight(62) = 0.650445796897836285611736039998D-02
    5235. 

  5235. <a name="l05171"></a>05171     weight(63) = 0.414703326056246763528753572855D-02
    5236. 

  5236. <a name="l05172"></a>05172     weight(64) = 0.178328072169643294729607914497D-02
    5237. 

  5237. <a name="l05173"></a>05173 
    5238. 

  5238. <a name="l05174"></a>05174   <span class="keyword">else</span>
    5239. 

  5239. <a name="l05175"></a>05175 
    5240. 

  5240. <a name="l05176"></a>05176     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    5241. 

  5241. <a name="l05177"></a>05177     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_SET - Fatal error!&#39;</span>
    5242. 

  5242. <a name="l05178"></a>05178     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    5243. 

  5243. <a name="l05179"></a>05179     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 1 to 20, 32 or 64.&#39;</span>
    5244. 

  5244. <a name="l05180"></a>05180     stop
    5245. 

  5245. <a name="l05181"></a>05181 
    5246. 

  5246. <a name="l05182"></a>05182   <span class="keyword">end if</span>
    5247. 

  5247. <a name="l05183"></a>05183 
    5248. 

  5248. <a name="l05184"></a>05184   return
    5249. 

  5249. <a name="l05185"></a>05185 <span class="keyword">end</span>
    5250. 

  5250. <a name="l05186"></a><a class="code" href="quadrule_8f90.html#a5bc99575d37146760cfa51cfccd5b400">05186</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a5bc99575d37146760cfa51cfccd5b400">legendre_set_cos</a> ( norder, xtab, weight )
    5251. 

  5251. <a name="l05187"></a>05187 <span class="comment">!</span>
    5252. 

  5252. <a name="l05188"></a>05188 <span class="comment">!*******************************************************************************</span>
    5253. 

  5253. <a name="l05189"></a>05189 <span class="comment">!</span>
    5254. 

  5254. <a name="l05190"></a>05190 <span class="comment">!! LEGENDRE_SET_COS sets a Gauss-Legendre rule for COS(X) * F(X) on [-PI/2,PI/2].</span>
    5255. 

  5255. <a name="l05191"></a>05191 <span class="comment">!</span>
    5256. 

  5256. <a name="l05192"></a>05192 <span class="comment">!</span>
    5257. 

  5257. <a name="l05193"></a>05193 <span class="comment">!  Integration interval:</span>
    5258. 

  5258. <a name="l05194"></a>05194 <span class="comment">!</span>
    5259. 

  5259. <a name="l05195"></a>05195 <span class="comment">!    [ -PI/2, PI/2 ]</span>
    5260. 

  5260. <a name="l05196"></a>05196 <span class="comment">!</span>
    5261. 

  5261. <a name="l05197"></a>05197 <span class="comment">!  Weight function:</span>
    5262. 

  5262. <a name="l05198"></a>05198 <span class="comment">!</span>
    5263. 

  5263. <a name="l05199"></a>05199 <span class="comment">!    COS(X) * F(X)</span>
    5264. 

  5264. <a name="l05200"></a>05200 <span class="comment">!</span>
    5265. 

  5265. <a name="l05201"></a>05201 <span class="comment">!  Integral to approximate:</span>
    5266. 

  5266. <a name="l05202"></a>05202 <span class="comment">!</span>
    5267. 

  5267. <a name="l05203"></a>05203 <span class="comment">!    Integral ( -PI/2 &lt;= X &lt;= PI/2 ) COS(X) * F(X) dX</span>
    5268. 

  5268. <a name="l05204"></a>05204 <span class="comment">!</span>
    5269. 

  5269. <a name="l05205"></a>05205 <span class="comment">!  Approximate integral:</span>
    5270. 

  5270. <a name="l05206"></a>05206 <span class="comment">!</span>
    5271. 

  5271. <a name="l05207"></a>05207 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    5272. 

  5272. <a name="l05208"></a>05208 <span class="comment">!</span>
    5273. 

  5273. <a name="l05209"></a>05209 <span class="comment">!  Discussion:</span>
    5274. 

  5274. <a name="l05210"></a>05210 <span class="comment">!</span>
    5275. 

  5275. <a name="l05211"></a>05211 <span class="comment">!    The same rule can be used to approximate</span>
    5276. 

  5276. <a name="l05212"></a>05212 <span class="comment">!</span>
    5277. 

  5277. <a name="l05213"></a>05213 <span class="comment">!      Integral ( 0 &lt;= X &lt;= PI ) SIN(X) * F(X) dX</span>
    5278. 

  5278. <a name="l05214"></a>05214 <span class="comment">!</span>
    5279. 

  5279. <a name="l05215"></a>05215 <span class="comment">!    as</span>
    5280. 

  5280. <a name="l05216"></a>05216 <span class="comment">!</span>
    5281. 

  5281. <a name="l05217"></a>05217 <span class="comment">!      Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) + PI/2 )</span>
    5282. 

  5282. <a name="l05218"></a>05218 <span class="comment">!</span>
    5283. 

  5283. <a name="l05219"></a>05219 <span class="comment">!  Reference:</span>
    5284. 

  5284. <a name="l05220"></a>05220 <span class="comment">!</span>
    5285. 

  5285. <a name="l05221"></a>05221 <span class="comment">!    Gwynne Evans,</span>
    5286. 

  5286. <a name="l05222"></a>05222 <span class="comment">!    Practical Numerical Integration,</span>
    5287. 

  5287. <a name="l05223"></a>05223 <span class="comment">!    Wiley, 1993, QA299.3E93, page 310.</span>
    5288. 

  5288. <a name="l05224"></a>05224 <span class="comment">!</span>
    5289. 

  5289. <a name="l05225"></a>05225 <span class="comment">!  Modified:</span>
    5290. 

  5290. <a name="l05226"></a>05226 <span class="comment">!</span>
    5291. 

  5291. <a name="l05227"></a>05227 <span class="comment">!    23 November 2000</span>
    5292. 

  5292. <a name="l05228"></a>05228 <span class="comment">!</span>
    5293. 

  5293. <a name="l05229"></a>05229 <span class="comment">!  Author:</span>
    5294. 

  5294. <a name="l05230"></a>05230 <span class="comment">!</span>
    5295. 

  5295. <a name="l05231"></a>05231 <span class="comment">!    John Burkardt</span>
    5296. 

  5296. <a name="l05232"></a>05232 <span class="comment">!</span>
    5297. 

  5297. <a name="l05233"></a>05233 <span class="comment">!  Parameters:</span>
    5298. 

  5298. <a name="l05234"></a>05234 <span class="comment">!</span>
    5299. 

  5299. <a name="l05235"></a>05235 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    5300. 

  5300. <a name="l05236"></a>05236 <span class="comment">!    NORDER must be between 1, 2, 4, 8 or 16.</span>
    5301. 

  5301. <a name="l05237"></a>05237 <span class="comment">!</span>
    5302. 

  5302. <a name="l05238"></a>05238 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    5303. 

  5303. <a name="l05239"></a>05239 <span class="comment">!</span>
    5304. 

  5304. <a name="l05240"></a>05240 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    5305. 

  5305. <a name="l05241"></a>05241 <span class="comment">!</span>
    5306. 

  5306. <a name="l05242"></a>05242   <span class="keyword">implicit none</span>
    5307. 

  5307. <a name="l05243"></a>05243 <span class="comment">!</span>
    5308. 

  5308. <a name="l05244"></a>05244   <span class="keywordtype">integer</span> norder
    5309. 

  5309. <a name="l05245"></a>05245 <span class="comment">!</span>
    5310. 

  5310. <a name="l05246"></a>05246   <span class="keywordtype">double precision</span> xtab(norder)
    5311. 

  5311. <a name="l05247"></a>05247   <span class="keywordtype">double precision</span> weight(norder)
    5312. 

  5312. <a name="l05248"></a>05248 <span class="comment">!</span>
    5313. 

  5313. <a name="l05249"></a>05249   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    5314. 

  5314. <a name="l05250"></a>05250 
    5315. 

  5315. <a name="l05251"></a>05251     xtab(1) = 0.0D+00
    5316. 

  5316. <a name="l05252"></a>05252 
    5317. 

  5317. <a name="l05253"></a>05253     weight(1) = 2.0D+00
    5318. 

  5318. <a name="l05254"></a>05254 
    5319. 

  5319. <a name="l05255"></a>05255   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    5320. 

  5320. <a name="l05256"></a>05256 
    5321. 

  5321. <a name="l05257"></a>05257     xtab(1) = - 0.68366739008990304094D+00
    5322. 

  5322. <a name="l05258"></a>05258     xtab(2) =   0.68366739008990304094D+00
    5323. 

  5323. <a name="l05259"></a>05259 
    5324. 

  5324. <a name="l05260"></a>05260     weight(1) = 1.0D+00
    5325. 

  5325. <a name="l05261"></a>05261     weight(2) = 1.0D+00
    5326. 

  5326. <a name="l05262"></a>05262 
    5327. 

  5327. <a name="l05263"></a>05263   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    5328. 

  5328. <a name="l05264"></a>05264 
    5329. 

  5329. <a name="l05265"></a>05265     xtab(1) = - 1.1906765638948557415D+00
    5330. 

  5330. <a name="l05266"></a>05266     xtab(2) = - 0.43928746686001514756D+00
    5331. 

  5331. <a name="l05267"></a>05267     xtab(3) =   0.43928746686001514756D+00
    5332. 

  5332. <a name="l05268"></a>05268     xtab(4) =   1.1906765638948557415D+00
    5333. 

  5333. <a name="l05269"></a>05269 
    5334. 

  5334. <a name="l05270"></a>05270     weight(1) = 0.22407061812762016065D+00
    5335. 

  5335. <a name="l05271"></a>05271     weight(2) = 0.77592938187237983935D+00
    5336. 

  5336. <a name="l05272"></a>05272     weight(3) = 0.77592938187237983935D+00
    5337. 

  5337. <a name="l05273"></a>05273     weight(4) = 0.22407061812762016065D+00
    5338. 

  5338. <a name="l05274"></a>05274 
    5339. 

  5339. <a name="l05275"></a>05275   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    5340. 

  5340. <a name="l05276"></a>05276 
    5341. 

  5341. <a name="l05277"></a>05277     xtab(1) = - 1.4414905401823575701D+00
    5342. 

  5342. <a name="l05278"></a>05278     xtab(2) = - 1.1537256454567275850D+00
    5343. 

  5343. <a name="l05279"></a>05279     xtab(3) = - 0.74346864787549244989D+00
    5344. 

  5344. <a name="l05280"></a>05280     xtab(4) = - 0.25649650741623123020D+00
    5345. 

  5345. <a name="l05281"></a>05281     xtab(5) =   0.25649650741623123020D+00
    5346. 

  5346. <a name="l05282"></a>05282     xtab(6) =   0.74346864787549244989D+00
    5347. 

  5347. <a name="l05283"></a>05283     xtab(7) =   1.1537256454567275850D+00
    5348. 

  5348. <a name="l05284"></a>05284     xtab(8) =   1.4414905401823575701D+00
    5349. 

  5349. <a name="l05285"></a>05285 
    5350. 

  5350. <a name="l05286"></a>05286     weight(1) = 0.027535633513767011149D+00
    5351. 

  5351. <a name="l05287"></a>05287     weight(2) = 0.14420409203022750950D+00
    5352. 

  5352. <a name="l05288"></a>05288     weight(3) = 0.33626447785280459621D+00
    5353. 

  5353. <a name="l05289"></a>05289     weight(4) = 0.49199579660320088314D+00
    5354. 

  5354. <a name="l05290"></a>05290     weight(5) = 0.49199579660320088314D+00
    5355. 

  5355. <a name="l05291"></a>05291     weight(6) = 0.33626447785280459621D+00
    5356. 

  5356. <a name="l05292"></a>05292     weight(7) = 0.14420409203022750950D+00
    5357. 

  5357. <a name="l05293"></a>05293     weight(8) = 0.027535633513767011149D+00
    5358. 

  5358. <a name="l05294"></a>05294 
    5359. 

  5359. <a name="l05295"></a>05295   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
    5360. 

  5360. <a name="l05296"></a>05296 
    5361. 

  5361. <a name="l05297"></a>05297     xtab( 1) = - 1.5327507132362304779D+00
    5362. 

  5362. <a name="l05298"></a>05298     xtab( 2) = - 1.4446014873666514608D+00
    5363. 

  5363. <a name="l05299"></a>05299     xtab( 3) = - 1.3097818904452936698D+00
    5364. 

  5364. <a name="l05300"></a>05300     xtab( 4) = - 1.1330068786005003695D+00
    5365. 

  5365. <a name="l05301"></a>05301     xtab( 5) = - 0.92027786206637096497D+00
    5366. 

  5366. <a name="l05302"></a>05302     xtab( 6) = - 0.67861108097560545347D+00
    5367. 

  5367. <a name="l05303"></a>05303     xtab( 7) = - 0.41577197673418943962D+00
    5368. 

  5368. <a name="l05304"></a>05304     xtab( 8) = - 0.14003444424696773778D+00
    5369. 

  5369. <a name="l05305"></a>05305     xtab( 9) =   0.14003444424696773778D+00
    5370. 

  5370. <a name="l05306"></a>05306     xtab(10) =   0.41577197673418943962D+00
    5371. 

  5371. <a name="l05307"></a>05307     xtab(11) =   0.67861108097560545347D+00
    5372. 

  5372. <a name="l05308"></a>05308     xtab(12) =   0.92027786206637096497D+00
    5373. 

  5373. <a name="l05309"></a>05309     xtab(13) =   1.1330068786005003695D+00
    5374. 

  5374. <a name="l05310"></a>05310     xtab(14) =   1.3097818904452936698D+00
    5375. 

  5375. <a name="l05311"></a>05311     xtab(15) =   1.4446014873666514608D+00
    5376. 

  5376. <a name="l05312"></a>05312     xtab(16) =   1.5327507132362304779D+00
    5377. 

  5377. <a name="l05313"></a>05313 
    5378. 

  5378. <a name="l05314"></a>05314     weight( 1) = 0.0024194677567615628193D+00
    5379. 

  5379. <a name="l05315"></a>05315     weight( 2) = 0.014115268156854008264D+00
    5380. 

  5380. <a name="l05316"></a>05316     weight( 3) = 0.040437893946503669410D+00
    5381. 

  5381. <a name="l05317"></a>05317     weight( 4) = 0.083026647573217742131D+00
    5382. 

  5382. <a name="l05318"></a>05318     weight( 5) = 0.13834195526951273359D+00
    5383. 

  5383. <a name="l05319"></a>05319     weight( 6) = 0.19741148870253455567D+00
    5384. 

  5384. <a name="l05320"></a>05320     weight( 7) = 0.24763632094635522403D+00
    5385. 

  5385. <a name="l05321"></a>05321     weight( 8) = 0.27661095764826050408D+00
    5386. 

  5386. <a name="l05322"></a>05322     weight( 9) = 0.27661095764826050408D+00
    5387. 

  5387. <a name="l05323"></a>05323     weight(10) = 0.24763632094635522403D+00
    5388. 

  5388. <a name="l05324"></a>05324     weight(11) = 0.19741148870253455567D+00
    5389. 

  5389. <a name="l05325"></a>05325     weight(12) = 0.13834195526951273359D+00
    5390. 

  5390. <a name="l05326"></a>05326     weight(13) = 0.083026647573217742131D+00
    5391. 

  5391. <a name="l05327"></a>05327     weight(14) = 0.040437893946503669410D+00
    5392. 

  5392. <a name="l05328"></a>05328     weight(15) = 0.014115268156854008264D+00
    5393. 

  5393. <a name="l05329"></a>05329     weight(16) = 0.0024194677567615628193D+00
    5394. 

  5394. <a name="l05330"></a>05330 
    5395. 

  5395. <a name="l05331"></a>05331   <span class="keyword">else</span>
    5396. 

  5396. <a name="l05332"></a>05332 
    5397. 

  5397. <a name="l05333"></a>05333     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    5398. 

  5398. <a name="l05334"></a>05334     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_SET_COS - Fatal error!&#39;</span>
    5399. 

  5399. <a name="l05335"></a>05335     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    5400. 

  5400. <a name="l05336"></a>05336     stop
    5401. 

  5401. <a name="l05337"></a>05337 
    5402. 

  5402. <a name="l05338"></a>05338   <span class="keyword">end if</span>
    5403. 

  5403. <a name="l05339"></a>05339 
    5404. 

  5404. <a name="l05340"></a>05340   return
    5405. 

  5405. <a name="l05341"></a>05341 <span class="keyword">end</span>
    5406. 

  5406. <a name="l05342"></a><a class="code" href="quadrule_8f90.html#acc5a8a6f431a042e02f59fbc20041ae0">05342</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#acc5a8a6f431a042e02f59fbc20041ae0">legendre_set_cos2</a> ( norder, xtab, weight )
    5407. 

  5407. <a name="l05343"></a>05343 <span class="comment">!</span>
    5408. 

  5408. <a name="l05344"></a>05344 <span class="comment">!*******************************************************************************</span>
    5409. 

  5409. <a name="l05345"></a>05345 <span class="comment">!</span>
    5410. 

  5410. <a name="l05346"></a>05346 <span class="comment">!! LEGENDRE_SET_COS2 sets a Gauss-Legendre rule for COS(X) * F(X) on [0,PI/2].</span>
    5411. 

  5411. <a name="l05347"></a>05347 <span class="comment">!</span>
    5412. 

  5412. <a name="l05348"></a>05348 <span class="comment">!</span>
    5413. 

  5413. <a name="l05349"></a>05349 <span class="comment">!  Integration interval:</span>
    5414. 

  5414. <a name="l05350"></a>05350 <span class="comment">!</span>
    5415. 

  5415. <a name="l05351"></a>05351 <span class="comment">!    [ 0, PI/2 ]</span>
    5416. 

  5416. <a name="l05352"></a>05352 <span class="comment">!</span>
    5417. 

  5417. <a name="l05353"></a>05353 <span class="comment">!  Weight function:</span>
    5418. 

  5418. <a name="l05354"></a>05354 <span class="comment">!</span>
    5419. 

  5419. <a name="l05355"></a>05355 <span class="comment">!    COS(X) * F(X)</span>
    5420. 

  5420. <a name="l05356"></a>05356 <span class="comment">!</span>
    5421. 

  5421. <a name="l05357"></a>05357 <span class="comment">!  Integral to approximate:</span>
    5422. 

  5422. <a name="l05358"></a>05358 <span class="comment">!</span>
    5423. 

  5423. <a name="l05359"></a>05359 <span class="comment">!    Integral ( 0 &lt;= X &lt;= PI/2 ) COS(X) * F(X) dX</span>
    5424. 

  5424. <a name="l05360"></a>05360 <span class="comment">!</span>
    5425. 

  5425. <a name="l05361"></a>05361 <span class="comment">!  Approximate integral:</span>
    5426. 

  5426. <a name="l05362"></a>05362 <span class="comment">!</span>
    5427. 

  5427. <a name="l05363"></a>05363 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    5428. 

  5428. <a name="l05364"></a>05364 <span class="comment">!</span>
    5429. 

  5429. <a name="l05365"></a>05365 <span class="comment">!  Discussion:</span>
    5430. 

  5430. <a name="l05366"></a>05366 <span class="comment">!</span>
    5431. 

  5431. <a name="l05367"></a>05367 <span class="comment">!    The same rule can be used to approximate</span>
    5432. 

  5432. <a name="l05368"></a>05368 <span class="comment">!</span>
    5433. 

  5433. <a name="l05369"></a>05369 <span class="comment">!      Integral ( 0 &lt;= X &lt;= PI/2 ) SIN(X) * F(X) dX</span>
    5434. 

  5434. <a name="l05370"></a>05370 <span class="comment">!</span>
    5435. 

  5435. <a name="l05371"></a>05371 <span class="comment">!    as</span>
    5436. 

  5436. <a name="l05372"></a>05372 <span class="comment">!</span>
    5437. 

  5437. <a name="l05373"></a>05373 <span class="comment">!      Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( PI/2 - XTAB(I) )</span>
    5438. 

  5438. <a name="l05374"></a>05374 <span class="comment">!</span>
    5439. 

  5439. <a name="l05375"></a>05375 <span class="comment">!  Reference:</span>
    5440. 

  5440. <a name="l05376"></a>05376 <span class="comment">!</span>
    5441. 

  5441. <a name="l05377"></a>05377 <span class="comment">!    Gwynne Evans,</span>
    5442. 

  5442. <a name="l05378"></a>05378 <span class="comment">!    Practical Numerical Integration,</span>
    5443. 

  5443. <a name="l05379"></a>05379 <span class="comment">!    Wiley, 1993, QA299.3E93, page 311.</span>
    5444. 

  5444. <a name="l05380"></a>05380 <span class="comment">!</span>
    5445. 

  5445. <a name="l05381"></a>05381 <span class="comment">!  Modified:</span>
    5446. 

  5446. <a name="l05382"></a>05382 <span class="comment">!</span>
    5447. 

  5447. <a name="l05383"></a>05383 <span class="comment">!    24 November 2000</span>
    5448. 

  5448. <a name="l05384"></a>05384 <span class="comment">!</span>
    5449. 

  5449. <a name="l05385"></a>05385 <span class="comment">!  Author:</span>
    5450. 

  5450. <a name="l05386"></a>05386 <span class="comment">!</span>
    5451. 

  5451. <a name="l05387"></a>05387 <span class="comment">!    John Burkardt</span>
    5452. 

  5452. <a name="l05388"></a>05388 <span class="comment">!</span>
    5453. 

  5453. <a name="l05389"></a>05389 <span class="comment">!  Parameters:</span>
    5454. 

  5454. <a name="l05390"></a>05390 <span class="comment">!</span>
    5455. 

  5455. <a name="l05391"></a>05391 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    5456. 

  5456. <a name="l05392"></a>05392 <span class="comment">!    NORDER must be between 2, 4, 8 or 16.</span>
    5457. 

  5457. <a name="l05393"></a>05393 <span class="comment">!</span>
    5458. 

  5458. <a name="l05394"></a>05394 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    5459. 

  5459. <a name="l05395"></a>05395 <span class="comment">!</span>
    5460. 

  5460. <a name="l05396"></a>05396 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    5461. 

  5461. <a name="l05397"></a>05397 <span class="comment">!</span>
    5462. 

  5462. <a name="l05398"></a>05398   <span class="keyword">implicit none</span>
    5463. 

  5463. <a name="l05399"></a>05399 <span class="comment">!</span>
    5464. 

  5464. <a name="l05400"></a>05400   <span class="keywordtype">integer</span> norder
    5465. 

  5465. <a name="l05401"></a>05401 <span class="comment">!</span>
    5466. 

  5466. <a name="l05402"></a>05402   <span class="keywordtype">double precision</span> xtab(norder)
    5467. 

  5467. <a name="l05403"></a>05403   <span class="keywordtype">double precision</span> weight(norder)
    5468. 

  5468. <a name="l05404"></a>05404 <span class="comment">!</span>
    5469. 

  5469. <a name="l05405"></a>05405   <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    5470. 

  5470. <a name="l05406"></a>05406 
    5471. 

  5471. <a name="l05407"></a>05407     xtab(1) = 0.26587388056307823382D+00
    5472. 

  5472. <a name="l05408"></a>05408     xtab(2) = 1.0351526093171315182D+00
    5473. 

  5473. <a name="l05409"></a>05409 
    5474. 

  5474. <a name="l05410"></a>05410     weight(1) = 0.60362553280827113087D+00
    5475. 

  5475. <a name="l05411"></a>05411     weight(2) = 0.39637446719172886913D+00
    5476. 

  5476. <a name="l05412"></a>05412 
    5477. 

  5477. <a name="l05413"></a>05413   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    5478. 

  5478. <a name="l05414"></a>05414 
    5479. 

  5479. <a name="l05415"></a>05415     xtab(1) = 0.095669389196858636773D+00
    5480. 

  5480. <a name="l05416"></a>05416     xtab(2) = 0.45240902327067096554D+00
    5481. 

  5481. <a name="l05417"></a>05417     xtab(3) = 0.93185057672024082424D+00
    5482. 

  5482. <a name="l05418"></a>05418     xtab(4) = 1.3564439599666466230D+00
    5483. 

  5483. <a name="l05419"></a>05419 
    5484. 

  5484. <a name="l05420"></a>05420     weight( 1) = 0.23783071419515504517D+00
    5485. 

  5485. <a name="l05421"></a>05421     weight( 2) = 0.40265695523581253512D+00
    5486. 

  5486. <a name="l05422"></a>05422     weight( 3) = 0.28681737948564715225D+00
    5487. 

  5487. <a name="l05423"></a>05423     weight( 4) = 0.072694951083385267446D+00
    5488. 

  5488. <a name="l05424"></a>05424 
    5489. 

  5489. <a name="l05425"></a>05425   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    5490. 

  5490. <a name="l05426"></a>05426 
    5491. 

  5491. <a name="l05427"></a>05427     xtab(1) = 0.029023729768913933432D+00
    5492. 

  5492. <a name="l05428"></a>05428     xtab(2) = 0.14828524404581819442D+00
    5493. 

  5493. <a name="l05429"></a>05429     xtab(3) = 0.34531111151664787488D+00
    5494. 

  5494. <a name="l05430"></a>05430     xtab(4) = 0.59447696797658360178D+00
    5495. 

  5495. <a name="l05431"></a>05431     xtab(5) = 0.86538380686123504827D+00
    5496. 

  5496. <a name="l05432"></a>05432     xtab(6) = 1.1263076093187456632D+00
    5497. 

  5497. <a name="l05433"></a>05433     xtab(7) = 1.3470150460281258016D+00
    5498. 

  5498. <a name="l05434"></a>05434     xtab(8) = 1.5015603622059195568D+00
    5499. 

  5499. <a name="l05435"></a>05435 
    5500. 

  5500. <a name="l05436"></a>05436     weight( 1) = 0.073908998095117384985D+00
    5501. 

  5501. <a name="l05437"></a>05437     weight( 2) = 0.16002993702338006099D+00
    5502. 

  5502. <a name="l05438"></a>05438     weight( 3) = 0.21444434341803549108D+00
    5503. 

  5503. <a name="l05439"></a>05439     weight( 4) = 0.21979581268851903339D+00
    5504. 

  5504. <a name="l05440"></a>05440     weight( 5) = 0.17581164478209568886D+00
    5505. 

  5505. <a name="l05441"></a>05441     weight( 6) = 0.10560448025308322171D+00
    5506. 

  5506. <a name="l05442"></a>05442     weight( 7) = 0.042485497299217201089D+00
    5507. 

  5507. <a name="l05443"></a>05443     weight( 8) = 0.0079192864405519178899D+00
    5508. 

  5508. <a name="l05444"></a>05444 
    5509. 

  5509. <a name="l05445"></a>05445   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
    5510. 

  5510. <a name="l05446"></a>05446 
    5511. 

  5511. <a name="l05447"></a>05447     xtab( 1) = 0.0080145034906295973494D+00
    5512. 

  5512. <a name="l05448"></a>05448     xtab( 2) = 0.041893031354246254797D+00
    5513. 

  5513. <a name="l05449"></a>05449     xtab( 3) = 0.10149954486757579459D+00
    5514. 

  5514. <a name="l05450"></a>05450     xtab( 4) = 0.18463185923836617507D+00
    5515. 

  5515. <a name="l05451"></a>05451     xtab( 5) = 0.28826388487760574589D+00
    5516. 

  5516. <a name="l05452"></a>05452     xtab( 6) = 0.40870579076464794191D+00
    5517. 

  5517. <a name="l05453"></a>05453     xtab( 7) = 0.54176054986913847463D+00
    5518. 

  5518. <a name="l05454"></a>05454     xtab( 8) = 0.68287636658719416893D+00
    5519. 

  5519. <a name="l05455"></a>05455     xtab( 9) = 0.82729287620416833520D+00
    5520. 

  5520. <a name="l05456"></a>05456     xtab(10) = 0.97018212594829367065D+00
    5521. 

  5521. <a name="l05457"></a>05457     xtab(11) = 1.1067865150286247873D+00
    5522. 

  5522. <a name="l05458"></a>05458     xtab(12) = 1.2325555697227748824D+00
    5523. 

  5523. <a name="l05459"></a>05459     xtab(13) = 1.3432821921580721861D+00
    5524. 

  5524. <a name="l05460"></a>05460     xtab(14) = 1.4352370549295032923D+00
    5525. 

  5525. <a name="l05461"></a>05461     xtab(15) = 1.5052970876794669248D+00
    5526. 

  5526. <a name="l05462"></a>05462     xtab(16) = 1.5510586944086135769D+00
    5527. 

  5527. <a name="l05463"></a>05463 
    5528. 

  5528. <a name="l05464"></a>05464     weight( 1) = 0.020528714977215248902D+00
    5529. 

  5529. <a name="l05465"></a>05465     weight( 2) = 0.046990919853597958123D+00
    5530. 

  5530. <a name="l05466"></a>05466     weight( 3) = 0.071441021312218541698D+00
    5531. 

  5531. <a name="l05467"></a>05467     weight( 4) = 0.092350338329243052271D+00
    5532. 

  5532. <a name="l05468"></a>05468     weight( 5) = 0.10804928026816236935D+00
    5533. 

  5533. <a name="l05469"></a>05469     weight( 6) = 0.11698241243306261791D+00
    5534. 

  5534. <a name="l05470"></a>05470     weight( 7) = 0.11812395361762037649D+00
    5535. 

  5535. <a name="l05471"></a>05471     weight( 8) = 0.11137584940420091049D+00
    5536. 

  5536. <a name="l05472"></a>05472     weight( 9) = 0.097778236145946543110D+00
    5537. 

  5537. <a name="l05473"></a>05473     weight(10) = 0.079418758985944482077D+00
    5538. 

  5538. <a name="l05474"></a>05474     weight(11) = 0.059039620053768691402D+00
    5539. 

  5539. <a name="l05475"></a>05475     weight(12) = 0.039458876783728165671D+00
    5540. 

  5540. <a name="l05476"></a>05476     weight(13) = 0.022987785677206847531D+00
    5541. 

  5541. <a name="l05477"></a>05477     weight(14) = 0.011010405600421536861D+00
    5542. 

  5542. <a name="l05478"></a>05478     weight(15) = 0.0038123928030499915653D+00
    5543. 

  5543. <a name="l05479"></a>05479     weight(16) = 0.00065143375461266656171D+00
    5544. 

  5544. <a name="l05480"></a>05480 
    5545. 

  5545. <a name="l05481"></a>05481   <span class="keyword">else</span>
    5546. 

  5546. <a name="l05482"></a>05482 
    5547. 

  5547. <a name="l05483"></a>05483     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    5548. 

  5548. <a name="l05484"></a>05484     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_SET_COS2 - Fatal error!&#39;</span>
    5549. 

  5549. <a name="l05485"></a>05485     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    5550. 

  5550. <a name="l05486"></a>05486     stop
    5551. 

  5551. <a name="l05487"></a>05487 
    5552. 

  5552. <a name="l05488"></a>05488   <span class="keyword">end if</span>
    5553. 

  5553. <a name="l05489"></a>05489 
    5554. 

  5554. <a name="l05490"></a>05490   return
    5555. 

  5555. <a name="l05491"></a>05491 <span class="keyword">end</span>
    5556. 

  5556. <a name="l05492"></a><a class="code" href="quadrule_8f90.html#aa56be14b0d5564b164cc213f31c0d137">05492</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#aa56be14b0d5564b164cc213f31c0d137">legendre_set_log</a> ( norder, xtab, weight )
    5557. 

  5557. <a name="l05493"></a>05493 <span class="comment">!</span>
    5558. 

  5558. <a name="l05494"></a>05494 <span class="comment">!*******************************************************************************</span>
    5559. 

  5559. <a name="l05495"></a>05495 <span class="comment">!</span>
    5560. 

  5560. <a name="l05496"></a>05496 <span class="comment">!! LEGENDRE_SET_LOG sets a Gauss-Legendre rule for - LOG(X) * F(X) on [0,1].</span>
    5561. 

  5561. <a name="l05497"></a>05497 <span class="comment">!</span>
    5562. 

  5562. <a name="l05498"></a>05498 <span class="comment">!</span>
    5563. 

  5563. <a name="l05499"></a>05499 <span class="comment">!  Integration interval:</span>
    5564. 

  5564. <a name="l05500"></a>05500 <span class="comment">!</span>
    5565. 

  5565. <a name="l05501"></a>05501 <span class="comment">!    [ 0, 1 ]</span>
    5566. 

  5566. <a name="l05502"></a>05502 <span class="comment">!</span>
    5567. 

  5567. <a name="l05503"></a>05503 <span class="comment">!  Weight function:</span>
    5568. 

  5568. <a name="l05504"></a>05504 <span class="comment">!</span>
    5569. 

  5569. <a name="l05505"></a>05505 <span class="comment">!    - LOG(X) * F(X)</span>
    5570. 

  5570. <a name="l05506"></a>05506 <span class="comment">!</span>
    5571. 

  5571. <a name="l05507"></a>05507 <span class="comment">!  Integral to approximate:</span>
    5572. 

  5572. <a name="l05508"></a>05508 <span class="comment">!</span>
    5573. 

  5573. <a name="l05509"></a>05509 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) - LOG(X) * F(X) dX</span>
    5574. 

  5574. <a name="l05510"></a>05510 <span class="comment">!</span>
    5575. 

  5575. <a name="l05511"></a>05511 <span class="comment">!  Approximate integral:</span>
    5576. 

  5576. <a name="l05512"></a>05512 <span class="comment">!</span>
    5577. 

  5577. <a name="l05513"></a>05513 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    5578. 

  5578. <a name="l05514"></a>05514 <span class="comment">!</span>
    5579. 

  5579. <a name="l05515"></a>05515 <span class="comment">!  Reference:</span>
    5580. 

  5580. <a name="l05516"></a>05516 <span class="comment">!</span>
    5581. 

  5581. <a name="l05517"></a>05517 <span class="comment">!    Abramowitz and Stegun,</span>
    5582. 

  5582. <a name="l05518"></a>05518 <span class="comment">!    Handbook of Mathematical Functions,</span>
    5583. 

  5583. <a name="l05519"></a>05519 <span class="comment">!    National Bureau of Standards, 1964, page 920.</span>
    5584. 

  5584. <a name="l05520"></a>05520 <span class="comment">!</span>
    5585. 

  5585. <a name="l05521"></a>05521 <span class="comment">!    Gwynne Evans,</span>
    5586. 

  5586. <a name="l05522"></a>05522 <span class="comment">!    Practical Numerical Integration,</span>
    5587. 

  5587. <a name="l05523"></a>05523 <span class="comment">!    Wiley, 1993, QA299.3E93, page 309.</span>
    5588. 

  5588. <a name="l05524"></a>05524 <span class="comment">!</span>
    5589. 

  5589. <a name="l05525"></a>05525 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    5590. 

  5590. <a name="l05526"></a>05526 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    5591. 

  5591. <a name="l05527"></a>05527 <span class="comment">!    Prentice Hall, 1966.</span>
    5592. 

  5592. <a name="l05528"></a>05528 <span class="comment">!</span>
    5593. 

  5593. <a name="l05529"></a>05529 <span class="comment">!  Modified:</span>
    5594. 

  5594. <a name="l05530"></a>05530 <span class="comment">!</span>
    5595. 

  5595. <a name="l05531"></a>05531 <span class="comment">!    05 December 2000</span>
    5596. 

  5596. <a name="l05532"></a>05532 <span class="comment">!</span>
    5597. 

  5597. <a name="l05533"></a>05533 <span class="comment">!  Author:</span>
    5598. 

  5598. <a name="l05534"></a>05534 <span class="comment">!</span>
    5599. 

  5599. <a name="l05535"></a>05535 <span class="comment">!    John Burkardt</span>
    5600. 

  5600. <a name="l05536"></a>05536 <span class="comment">!</span>
    5601. 

  5601. <a name="l05537"></a>05537 <span class="comment">!  Parameters:</span>
    5602. 

  5602. <a name="l05538"></a>05538 <span class="comment">!</span>
    5603. 

  5603. <a name="l05539"></a>05539 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    5604. 

  5604. <a name="l05540"></a>05540 <span class="comment">!    NORDER must be between 1 through 8, or 16.</span>
    5605. 

  5605. <a name="l05541"></a>05541 <span class="comment">!</span>
    5606. 

  5606. <a name="l05542"></a>05542 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    5607. 

  5607. <a name="l05543"></a>05543 <span class="comment">!</span>
    5608. 

  5608. <a name="l05544"></a>05544 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    5609. 

  5609. <a name="l05545"></a>05545 <span class="comment">!</span>
    5610. 

  5610. <a name="l05546"></a>05546   <span class="keyword">implicit none</span>
    5611. 

  5611. <a name="l05547"></a>05547 <span class="comment">!</span>
    5612. 

  5612. <a name="l05548"></a>05548   <span class="keywordtype">integer</span> norder
    5613. 

  5613. <a name="l05549"></a>05549 <span class="comment">!</span>
    5614. 

  5614. <a name="l05550"></a>05550   <span class="keywordtype">double precision</span> xtab(norder)
    5615. 

  5615. <a name="l05551"></a>05551   <span class="keywordtype">double precision</span> weight(norder)
    5616. 

  5616. <a name="l05552"></a>05552 <span class="comment">!</span>
    5617. 

  5617. <a name="l05553"></a>05553   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    5618. 

  5618. <a name="l05554"></a>05554 
    5619. 

  5619. <a name="l05555"></a>05555     xtab(1) = 0.25D+00
    5620. 

  5620. <a name="l05556"></a>05556 
    5621. 

  5621. <a name="l05557"></a>05557     weight(1) = 1.0D+00
    5622. 

  5622. <a name="l05558"></a>05558 
    5623. 

  5623. <a name="l05559"></a>05559   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    5624. 

  5624. <a name="l05560"></a>05560 
    5625. 

  5625. <a name="l05561"></a>05561     xtab(1) = 0.112008806166976182957205488948D+00
    5626. 

  5626. <a name="l05562"></a>05562     xtab(2) = 0.602276908118738102757080225338D+00
    5627. 

  5627. <a name="l05563"></a>05563 
    5628. 

  5628. <a name="l05564"></a>05564     weight(1) = 0.718539319030384440665510200891D+00
    5629. 

  5629. <a name="l05565"></a>05565     weight(2) = 0.281460680969615559334489799109D+00
    5630. 

  5630. <a name="l05566"></a>05566 
    5631. 

  5631. <a name="l05567"></a>05567   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    5632. 

  5632. <a name="l05568"></a>05568 
    5633. 

  5633. <a name="l05569"></a>05569     xtab(1) = 0.0638907930873254049961166031363D+00
    5634. 

  5634. <a name="l05570"></a>05570     xtab(2) = 0.368997063715618765546197645857D+00
    5635. 

  5635. <a name="l05571"></a>05571     xtab(3) = 0.766880303938941455423682659817D+00
    5636. 

  5636. <a name="l05572"></a>05572 
    5637. 

  5637. <a name="l05573"></a>05573     weight(1) = 0.513404552232363325129300497567D+00
    5638. 

  5638. <a name="l05574"></a>05574     weight(2) = 0.391980041201487554806287180966D+00
    5639. 

  5639. <a name="l05575"></a>05575     weight(3) = 0.0946154065661491200644123214672D+00
    5640. 

  5640. <a name="l05576"></a>05576 
    5641. 

  5641. <a name="l05577"></a>05577   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    5642. 

  5642. <a name="l05578"></a>05578 
    5643. 

  5643. <a name="l05579"></a>05579     xtab(1) = 0.0414484801993832208033213101564D+00
    5644. 

  5644. <a name="l05580"></a>05580     xtab(2) = 0.245274914320602251939675759523D+00
    5645. 

  5645. <a name="l05581"></a>05581     xtab(3) = 0.556165453560275837180184354376D+00
    5646. 

  5646. <a name="l05582"></a>05582     xtab(4) = 0.848982394532985174647849188085D+00
    5647. 

  5647. <a name="l05583"></a>05583 
    5648. 

  5648. <a name="l05584"></a>05584     weight(1) = 0.383464068145135124850046522343D+00
    5649. 

  5649. <a name="l05585"></a>05585     weight(2) = 0.386875317774762627336008234554D+00
    5650. 

  5650. <a name="l05586"></a>05586     weight(3) = 0.190435126950142415361360014547D+00
    5651. 

  5651. <a name="l05587"></a>05587     weight(4) = 0.0392254871299598324525852285552D+00
    5652. 

  5652. <a name="l05588"></a>05588 
    5653. 

  5653. <a name="l05589"></a>05589   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    5654. 

  5654. <a name="l05590"></a>05590 
    5655. 

  5655. <a name="l05591"></a>05591     xtab(1) = 0.0291344721519720533037267621154D+00
    5656. 

  5656. <a name="l05592"></a>05592     xtab(2) = 0.173977213320897628701139710829D+00
    5657. 

  5657. <a name="l05593"></a>05593     xtab(3) = 0.411702520284902043174931924646D+00
    5658. 

  5658. <a name="l05594"></a>05594     xtab(4) = 0.677314174582820380701802667998D+00
    5659. 

  5659. <a name="l05595"></a>05595     xtab(5) = 0.894771361031008283638886204455D+00
    5660. 

  5660. <a name="l05596"></a>05596 
    5661. 

  5661. <a name="l05597"></a>05597     weight(1) = 0.297893471782894457272257877888D+00
    5662. 

  5662. <a name="l05598"></a>05598     weight(2) = 0.349776226513224180375071870307D+00
    5663. 

  5663. <a name="l05599"></a>05599     weight(3) = 0.234488290044052418886906857943D+00
    5664. 

  5664. <a name="l05600"></a>05600     weight(4) = 0.0989304595166331469761807114404D+00
    5665. 

  5665. <a name="l05601"></a>05601     weight(5) = 0.0189115521431957964895826824218D+00
    5666. 

  5666. <a name="l05602"></a>05602 
    5667. 

  5667. <a name="l05603"></a>05603   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    5668. 

  5668. <a name="l05604"></a>05604 
    5669. 

  5669. <a name="l05605"></a>05605     xtab(1) = 0.0216340058441169489956958558537D+00
    5670. 

  5670. <a name="l05606"></a>05606     xtab(2) = 0.129583391154950796131158505009D+00
    5671. 

  5671. <a name="l05607"></a>05607     xtab(3) = 0.314020449914765508798248188420D+00
    5672. 

  5672. <a name="l05608"></a>05608     xtab(4) = 0.538657217351802144548941893993D+00
    5673. 

  5673. <a name="l05609"></a>05609     xtab(5) = 0.756915337377402852164544156139D+00
    5674. 

  5674. <a name="l05610"></a>05610     xtab(6) = 0.922668851372120237333873231507D+00
    5675. 

  5675. <a name="l05611"></a>05611 
    5676. 

  5676. <a name="l05612"></a>05612     weight(1) = 0.238763662578547569722268303330D+00
    5677. 

  5677. <a name="l05613"></a>05613     weight(2) = 0.308286573273946792969383109211D+00
    5678. 

  5678. <a name="l05614"></a>05614     weight(3) = 0.245317426563210385984932540188D+00
    5679. 

  5679. <a name="l05615"></a>05615     weight(4) = 0.142008756566476685421345576030D+00
    5680. 

  5680. <a name="l05616"></a>05616     weight(5) = 0.0554546223248862900151353549662D+00
    5681. 

  5681. <a name="l05617"></a>05617     weight(6) = 0.0101689586929322758869351162755D+00
    5682. 

  5682. <a name="l05618"></a>05618 
    5683. 

  5683. <a name="l05619"></a>05619   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    5684. 

  5684. <a name="l05620"></a>05620 
    5685. 

  5685. <a name="l05621"></a>05621     xtab(1) = 0.0167193554082585159416673609320D+00
    5686. 

  5686. <a name="l05622"></a>05622     xtab(2) = 0.100185677915675121586885031757D+00
    5687. 

  5687. <a name="l05623"></a>05623     xtab(3) = 0.246294246207930599046668547239D+00
    5688. 

  5688. <a name="l05624"></a>05624     xtab(4) = 0.433463493257033105832882482601D+00
    5689. 

  5689. <a name="l05625"></a>05625     xtab(5) = 0.632350988047766088461805812245D+00
    5690. 

  5690. <a name="l05626"></a>05626     xtab(6) = 0.811118626740105576526226796782D+00
    5691. 

  5691. <a name="l05627"></a>05627     xtab(7) = 0.940848166743347721760134113379D+00
    5692. 

  5692. <a name="l05628"></a>05628 
    5693. 

  5693. <a name="l05629"></a>05629     weight(1) = 0.196169389425248207525427377585D+00
    5694. 

  5694. <a name="l05630"></a>05630     weight(2) = 0.270302644247272982145271719533D+00
    5695. 

  5695. <a name="l05631"></a>05631     weight(3) = 0.239681873007690948308072785252D+00
    5696. 

  5696. <a name="l05632"></a>05632     weight(4) = 0.165775774810432906560869687736D+00
    5697. 

  5697. <a name="l05633"></a>05633     weight(5) = 0.0889432271376579644357238403458D+00
    5698. 

  5698. <a name="l05634"></a>05634     weight(6) = 0.0331943043565710670254494111034D+00
    5699. 

  5699. <a name="l05635"></a>05635     weight(7) = 0.00593278701512592399918517844468D+00
    5700. 

  5700. <a name="l05636"></a>05636 
    5701. 

  5701. <a name="l05637"></a>05637   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    5702. 

  5702. <a name="l05638"></a>05638 
    5703. 

  5703. <a name="l05639"></a>05639     xtab(1) = 0.0133202441608924650122526725243D+00
    5704. 

  5704. <a name="l05640"></a>05640     xtab(2) = 0.0797504290138949384098277291424D+00
    5705. 

  5705. <a name="l05641"></a>05641     xtab(3) = 0.197871029326188053794476159516D+00
    5706. 

  5706. <a name="l05642"></a>05642     xtab(4) = 0.354153994351909419671463603538D+00
    5707. 

  5707. <a name="l05643"></a>05643     xtab(5) = 0.529458575234917277706149699996D+00
    5708. 

  5708. <a name="l05644"></a>05644     xtab(6) = 0.701814529939099963837152670310D+00
    5709. 

  5709. <a name="l05645"></a>05645     xtab(7) = 0.849379320441106676048309202301D+00
    5710. 

  5710. <a name="l05646"></a>05646     xtab(8) = 0.953326450056359788767379678514D+00
    5711. 

  5711. <a name="l05647"></a>05647 
    5712. 

  5712. <a name="l05648"></a>05648     weight(1) = 0.164416604728002886831472568326D+00
    5713. 

  5713. <a name="l05649"></a>05649     weight(2) = 0.237525610023306020501348561960D+00
    5714. 

  5714. <a name="l05650"></a>05650     weight(3) = 0.226841984431919126368780402936D+00
    5715. 

  5715. <a name="l05651"></a>05651     weight(4) = 0.175754079006070244988056212006D+00
    5716. 

  5716. <a name="l05652"></a>05652     weight(5) = 0.112924030246759051855000442086D+00
    5717. 

  5717. <a name="l05653"></a>05653     weight(6) = 0.0578722107177820723985279672940D+00
    5718. 

  5718. <a name="l05654"></a>05654     weight(7) = 0.0209790737421329780434615241150D+00
    5719. 

  5719. <a name="l05655"></a>05655     weight(8) = 0.00368640710402761901335232127647D+00
    5720. 

  5720. <a name="l05656"></a>05656 
    5721. 

  5721. <a name="l05657"></a>05657   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
    5722. 

  5722. <a name="l05658"></a>05658 
    5723. 

  5723. <a name="l05659"></a>05659     xtab( 1) = 0.00389783448711591592405360527037D+00
    5724. 

  5724. <a name="l05660"></a>05660     xtab( 2) = 0.0230289456168732398203176309848D+00
    5725. 

  5725. <a name="l05661"></a>05661     xtab( 3) = 0.0582803983062404123483532298394D+00
    5726. 

  5726. <a name="l05662"></a>05662     xtab( 4) = 0.108678365091054036487713613051D+00
    5727. 

  5727. <a name="l05663"></a>05663     xtab( 5) = 0.172609454909843937760843776232D+00
    5728. 

  5728. <a name="l05664"></a>05664     xtab( 6) = 0.247937054470578495147671753047D+00
    5729. 

  5729. <a name="l05665"></a>05665     xtab( 7) = 0.332094549129917155984755859320D+00
    5730. 

  5730. <a name="l05666"></a>05666     xtab( 8) = 0.422183910581948600115088366745D+00
    5731. 

  5731. <a name="l05667"></a>05667     xtab( 9) = 0.515082473381462603476277704052D+00
    5732. 

  5732. <a name="l05668"></a>05668     xtab(10) = 0.607556120447728724086384921709D+00
    5733. 

  5733. <a name="l05669"></a>05669     xtab(11) = 0.696375653228214061156318166581D+00
    5734. 

  5734. <a name="l05670"></a>05670     xtab(12) = 0.778432565873265405203868167732D+00
    5735. 

  5735. <a name="l05671"></a>05671     xtab(13) = 0.850850269715391083233822761319D+00
    5736. 

  5736. <a name="l05672"></a>05672     xtab(14) = 0.911086857222271905418818994060D+00
    5737. 

  5737. <a name="l05673"></a>05673     xtab(15) = 0.957025571703542157591520509383D+00
    5738. 

  5738. <a name="l05674"></a>05674     xtab(16) = 0.987047800247984476758697436516D+00
    5739. 

  5739. <a name="l05675"></a>05675 
    5740. 

  5740. <a name="l05676"></a>05676     weight( 1) = 0.0607917100435912328511733871235D+00
    5741. 

  5741. <a name="l05677"></a>05677     weight( 2) = 0.102915677517582144387691736210D+00
    5742. 

  5742. <a name="l05678"></a>05678     weight( 3) = 0.122355662046009193557547513197D+00
    5743. 

  5743. <a name="l05679"></a>05679     weight( 4) = 0.127569246937015988717042209239D+00
    5744. 

  5744. <a name="l05680"></a>05680     weight( 5) = 0.123013574600070915423123365137D+00
    5745. 

  5745. <a name="l05681"></a>05681     weight( 6) = 0.111847244855485722621848903429D+00
    5746. 

  5746. <a name="l05682"></a>05682     weight( 7) = 0.0965963851521243412529681650802D+00
    5747. 

  5747. <a name="l05683"></a>05683     weight( 8) = 0.0793566643514731387824416770520D+00
    5748. 

  5748. <a name="l05684"></a>05684     weight( 9) = 0.0618504945819652070951360853113D+00
    5749. 

  5749. <a name="l05685"></a>05685     weight(10) = 0.0454352465077266686288299526509D+00
    5750. 

  5750. <a name="l05686"></a>05686     weight(11) = 0.0310989747515818064092528627927D+00
    5751. 

  5751. <a name="l05687"></a>05687     weight(12) = 0.0194597659273608420780860268669D+00
    5752. 

  5752. <a name="l05688"></a>05688     weight(13) = 0.0107762549632055256455393162159D+00
    5753. 

  5753. <a name="l05689"></a>05689     weight(14) = 0.00497254289008764171250524951646D+00
    5754. 

  5754. <a name="l05690"></a>05690     weight(15) = 0.00167820111005119451503546419059D+00
    5755. 

  5755. <a name="l05691"></a>05691     weight(16) = 0.000282353764668436321778085987413D+00
    5756. 

  5756. <a name="l05692"></a>05692 
    5757. 

  5757. <a name="l05693"></a>05693   <span class="keyword">else</span>
    5758. 

  5758. <a name="l05694"></a>05694 
    5759. 

  5759. <a name="l05695"></a>05695     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    5760. 

  5760. <a name="l05696"></a>05696     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_SET_LOG - Fatal error!&#39;</span>
    5761. 

  5761. <a name="l05697"></a>05697     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    5762. 

  5762. <a name="l05698"></a>05698     stop
    5763. 

  5763. <a name="l05699"></a>05699 
    5764. 

  5764. <a name="l05700"></a>05700   <span class="keyword">end if</span>
    5765. 

  5765. <a name="l05701"></a>05701 
    5766. 

  5766. <a name="l05702"></a>05702   return
    5767. 

  5767. <a name="l05703"></a>05703 <span class="keyword">end</span>
    5768. 

  5768. <a name="l05704"></a><a class="code" href="quadrule_8f90.html#a86c4a711a482034df5404bc3c78e55fd">05704</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a86c4a711a482034df5404bc3c78e55fd">legendre_set_sqrtx_01</a> ( norder, xtab, weight )
    5769. 

  5769. <a name="l05705"></a>05705 <span class="comment">!</span>
    5770. 

  5770. <a name="l05706"></a>05706 <span class="comment">!*******************************************************************************</span>
    5771. 

  5771. <a name="l05707"></a>05707 <span class="comment">!</span>
    5772. 

  5772. <a name="l05708"></a>05708 <span class="comment">!! LEGENDRE_SET_SQRTX_01 sets a Gauss-Legendre rule for SQRT(X) * F(X) on [0,1].</span>
    5773. 

  5773. <a name="l05709"></a>05709 <span class="comment">!</span>
    5774. 

  5774. <a name="l05710"></a>05710 <span class="comment">!</span>
    5775. 

  5775. <a name="l05711"></a>05711 <span class="comment">!  Integration interval:</span>
    5776. 

  5776. <a name="l05712"></a>05712 <span class="comment">!</span>
    5777. 

  5777. <a name="l05713"></a>05713 <span class="comment">!    [ 0, 1 ]</span>
    5778. 

  5778. <a name="l05714"></a>05714 <span class="comment">!</span>
    5779. 

  5779. <a name="l05715"></a>05715 <span class="comment">!  Weight function:</span>
    5780. 

  5780. <a name="l05716"></a>05716 <span class="comment">!</span>
    5781. 

  5781. <a name="l05717"></a>05717 <span class="comment">!    SQRT ( X )</span>
    5782. 

  5782. <a name="l05718"></a>05718 <span class="comment">!</span>
    5783. 

  5783. <a name="l05719"></a>05719 <span class="comment">!  Integral to approximate:</span>
    5784. 

  5784. <a name="l05720"></a>05720 <span class="comment">!</span>
    5785. 

  5785. <a name="l05721"></a>05721 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) SQRT ( X ) * F(X) dX =</span>
    5786. 

  5786. <a name="l05722"></a>05722 <span class="comment">!    Integral ( 0 &lt;= Y &lt;= 1 ) 2 * Y**2 * F(Y**2) dY.</span>
    5787. 

  5787. <a name="l05723"></a>05723 <span class="comment">!    (using Y = SQRT(X) )</span>
    5788. 

  5788. <a name="l05724"></a>05724 <span class="comment">!</span>
    5789. 

  5789. <a name="l05725"></a>05725 <span class="comment">!  Approximate integral:</span>
    5790. 

  5790. <a name="l05726"></a>05726 <span class="comment">!</span>
    5791. 

  5791. <a name="l05727"></a>05727 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    5792. 

  5792. <a name="l05728"></a>05728 <span class="comment">!</span>
    5793. 

  5793. <a name="l05729"></a>05729 <span class="comment">!  Reference:</span>
    5794. 

  5794. <a name="l05730"></a>05730 <span class="comment">!</span>
    5795. 

  5795. <a name="l05731"></a>05731 <span class="comment">!    Daniel Zwillinger, editor,</span>
    5796. 

  5796. <a name="l05732"></a>05732 <span class="comment">!    CRC Standard Mathematical Tables and Formulae,</span>
    5797. 

  5797. <a name="l05733"></a>05733 <span class="comment">!    CRC Press, 30th Edition, 2000, page 696.</span>
    5798. 

  5798. <a name="l05734"></a>05734 <span class="comment">!</span>
    5799. 

  5799. <a name="l05735"></a>05735 <span class="comment">!  Modified:</span>
    5800. 

  5800. <a name="l05736"></a>05736 <span class="comment">!</span>
    5801. 

  5801. <a name="l05737"></a>05737 <span class="comment">!    23 January 2001</span>
    5802. 

  5802. <a name="l05738"></a>05738 <span class="comment">!</span>
    5803. 

  5803. <a name="l05739"></a>05739 <span class="comment">!  Author:</span>
    5804. 

  5804. <a name="l05740"></a>05740 <span class="comment">!</span>
    5805. 

  5805. <a name="l05741"></a>05741 <span class="comment">!    John Burkardt</span>
    5806. 

  5806. <a name="l05742"></a>05742 <span class="comment">!</span>
    5807. 

  5807. <a name="l05743"></a>05743 <span class="comment">!  Parameters:</span>
    5808. 

  5808. <a name="l05744"></a>05744 <span class="comment">!</span>
    5809. 

  5809. <a name="l05745"></a>05745 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    5810. 

  5810. <a name="l05746"></a>05746 <span class="comment">!</span>
    5811. 

  5811. <a name="l05747"></a>05747 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    5812. 

  5812. <a name="l05748"></a>05748 <span class="comment">!</span>
    5813. 

  5813. <a name="l05749"></a>05749 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    5814. 

  5814. <a name="l05750"></a>05750 <span class="comment">!</span>
    5815. 

  5815. <a name="l05751"></a>05751   <span class="keyword">implicit none</span>
    5816. 

  5816. <a name="l05752"></a>05752 <span class="comment">!</span>
    5817. 

  5817. <a name="l05753"></a>05753   <span class="keywordtype">integer</span> norder
    5818. 

  5818. <a name="l05754"></a>05754 <span class="comment">!</span>
    5819. 

  5819. <a name="l05755"></a>05755   <span class="keywordtype">integer</span> norder2
    5820. 

  5820. <a name="l05756"></a>05756   <span class="keywordtype">double precision</span> xtab(norder)
    5821. 

  5821. <a name="l05757"></a>05757   <span class="keywordtype">double precision</span> xtab2(2*norder+1)
    5822. 

  5822. <a name="l05758"></a>05758   <span class="keywordtype">double precision</span> weight(norder)
    5823. 

  5823. <a name="l05759"></a>05759   <span class="keywordtype">double precision</span> weight2(2*norder+1)
    5824. 

  5824. <a name="l05760"></a>05760 <span class="comment">!</span>
    5825. 

  5825. <a name="l05761"></a>05761   norder2 = 2 * norder + 1
    5826. 

  5826. <a name="l05762"></a>05762 
    5827. 

  5827. <a name="l05763"></a>05763   call <a class="code" href="quadrule_8f90.html#a68e328951e712e3b7e2bc9f6dcf8fc6a">legendre_set </a>( norder2, xtab2, weight2 )
    5828. 

  5828. <a name="l05764"></a>05764 
    5829. 

  5829. <a name="l05765"></a>05765   xtab(1:norder) = xtab2(norder+2:2*norder+1)**2
    5830. 

  5830. <a name="l05766"></a>05766   weight(1:norder) = 2.0D+00 * weight2(norder+2:2*norder+1) * xtab(1:norder)
    5831. 

  5831. <a name="l05767"></a>05767 
    5832. 

  5832. <a name="l05768"></a>05768   return
    5833. 

  5833. <a name="l05769"></a>05769 <span class="keyword">end</span>
    5834. 

  5834. <a name="l05770"></a><a class="code" href="quadrule_8f90.html#a66bcf2a4c79e18ca6f0bcd21e9a665ad">05770</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a66bcf2a4c79e18ca6f0bcd21e9a665ad">legendre_set_sqrtx2_01</a> ( norder, xtab, weight )
    5835. 

  5835. <a name="l05771"></a>05771 <span class="comment">!</span>
    5836. 

  5836. <a name="l05772"></a>05772 <span class="comment">!*******************************************************************************</span>
    5837. 

  5837. <a name="l05773"></a>05773 <span class="comment">!</span>
    5838. 

  5838. <a name="l05774"></a>05774 <span class="comment">!! LEGENDRE_SET_SQRTX2_01 sets a Gauss-Legendre rule for F(X) / SQRT(X) on [0,1].</span>
    5839. 

  5839. <a name="l05775"></a>05775 <span class="comment">!</span>
    5840. 

  5840. <a name="l05776"></a>05776 <span class="comment">!</span>
    5841. 

  5841. <a name="l05777"></a>05777 <span class="comment">!  Integration interval:</span>
    5842. 

  5842. <a name="l05778"></a>05778 <span class="comment">!</span>
    5843. 

  5843. <a name="l05779"></a>05779 <span class="comment">!    [ 0, 1 ]</span>
    5844. 

  5844. <a name="l05780"></a>05780 <span class="comment">!</span>
    5845. 

  5845. <a name="l05781"></a>05781 <span class="comment">!  Weight function:</span>
    5846. 

  5846. <a name="l05782"></a>05782 <span class="comment">!</span>
    5847. 

  5847. <a name="l05783"></a>05783 <span class="comment">!    1 / SQRT ( X )</span>
    5848. 

  5848. <a name="l05784"></a>05784 <span class="comment">!</span>
    5849. 

  5849. <a name="l05785"></a>05785 <span class="comment">!  Integral to approximate:</span>
    5850. 

  5850. <a name="l05786"></a>05786 <span class="comment">!</span>
    5851. 

  5851. <a name="l05787"></a>05787 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) F(X) / SQRT ( X ) dX</span>
    5852. 

  5852. <a name="l05788"></a>05788 <span class="comment">!</span>
    5853. 

  5853. <a name="l05789"></a>05789 <span class="comment">!  Approximate integral:</span>
    5854. 

  5854. <a name="l05790"></a>05790 <span class="comment">!</span>
    5855. 

  5855. <a name="l05791"></a>05791 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    5856. 

  5856. <a name="l05792"></a>05792 <span class="comment">!</span>
    5857. 

  5857. <a name="l05793"></a>05793 <span class="comment">!  Reference:</span>
    5858. 

  5858. <a name="l05794"></a>05794 <span class="comment">!</span>
    5859. 

  5859. <a name="l05795"></a>05795 <span class="comment">!    Daniel Zwillinger, editor,</span>
    5860. 

  5860. <a name="l05796"></a>05796 <span class="comment">!    CRC Standard Mathematical Tables and Formulae,</span>
    5861. 

  5861. <a name="l05797"></a>05797 <span class="comment">!    CRC Press, 30th Edition, 2000, page 696.</span>
    5862. 

  5862. <a name="l05798"></a>05798 <span class="comment">!</span>
    5863. 

  5863. <a name="l05799"></a>05799 <span class="comment">!  Modified:</span>
    5864. 

  5864. <a name="l05800"></a>05800 <span class="comment">!</span>
    5865. 

  5865. <a name="l05801"></a>05801 <span class="comment">!    21 January 2001</span>
    5866. 

  5866. <a name="l05802"></a>05802 <span class="comment">!</span>
    5867. 

  5867. <a name="l05803"></a>05803 <span class="comment">!  Author:</span>
    5868. 

  5868. <a name="l05804"></a>05804 <span class="comment">!</span>
    5869. 

  5869. <a name="l05805"></a>05805 <span class="comment">!    John Burkardt</span>
    5870. 

  5870. <a name="l05806"></a>05806 <span class="comment">!</span>
    5871. 

  5871. <a name="l05807"></a>05807 <span class="comment">!  Parameters:</span>
    5872. 

  5872. <a name="l05808"></a>05808 <span class="comment">!</span>
    5873. 

  5873. <a name="l05809"></a>05809 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    5874. 

  5874. <a name="l05810"></a>05810 <span class="comment">!</span>
    5875. 

  5875. <a name="l05811"></a>05811 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    5876. 

  5876. <a name="l05812"></a>05812 <span class="comment">!</span>
    5877. 

  5877. <a name="l05813"></a>05813 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    5878. 

  5878. <a name="l05814"></a>05814 <span class="comment">!</span>
    5879. 

  5879. <a name="l05815"></a>05815   <span class="keyword">implicit none</span>
    5880. 

  5880. <a name="l05816"></a>05816 <span class="comment">!</span>
    5881. 

  5881. <a name="l05817"></a>05817   <span class="keywordtype">integer</span> norder
    5882. 

  5882. <a name="l05818"></a>05818 <span class="comment">!</span>
    5883. 

  5883. <a name="l05819"></a>05819   <span class="keywordtype">integer</span> norder2
    5884. 

  5884. <a name="l05820"></a>05820   <span class="keywordtype">double precision</span> xtab(norder)
    5885. 

  5885. <a name="l05821"></a>05821   <span class="keywordtype">double precision</span> xtab2(2*norder+1)
    5886. 

  5886. <a name="l05822"></a>05822   <span class="keywordtype">double precision</span> weight(norder)
    5887. 

  5887. <a name="l05823"></a>05823   <span class="keywordtype">double precision</span> weight2(2*norder+1)
    5888. 

  5888. <a name="l05824"></a>05824 <span class="comment">!</span>
    5889. 

  5889. <a name="l05825"></a>05825   norder2 = 2 * norder + 1
    5890. 

  5890. <a name="l05826"></a>05826 
    5891. 

  5891. <a name="l05827"></a>05827   call <a class="code" href="quadrule_8f90.html#a68e328951e712e3b7e2bc9f6dcf8fc6a">legendre_set </a>( norder2, xtab2, weight2 )
    5892. 

  5892. <a name="l05828"></a>05828 
    5893. 

  5893. <a name="l05829"></a>05829   xtab(1:norder) = xtab2(norder+2:2*norder+1)**2
    5894. 

  5894. <a name="l05830"></a>05830   weight(1:norder) = 2.0D+00 * weight2(norder+2:2*norder+1)
    5895. 

  5895. <a name="l05831"></a>05831 
    5896. 

  5896. <a name="l05832"></a>05832   return
    5897. 

  5897. <a name="l05833"></a>05833 <span class="keyword">end</span>
    5898. 

  5898. <a name="l05834"></a><a class="code" href="quadrule_8f90.html#a1c24bdbb65fec4d3f0f0d2f066002c62">05834</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a1c24bdbb65fec4d3f0f0d2f066002c62">legendre_set_x0_01</a> ( norder, xtab, weight )
    5899. 

  5899. <a name="l05835"></a>05835 <span class="comment">!</span>
    5900. 

  5900. <a name="l05836"></a>05836 <span class="comment">!*******************************************************************************</span>
    5901. 

  5901. <a name="l05837"></a>05837 <span class="comment">!</span>
    5902. 

  5902. <a name="l05838"></a>05838 <span class="comment">!! LEGENDRE_SET_X0_01 sets a Gauss-Legendre rule for F(X) on [0,1].</span>
    5903. 

  5903. <a name="l05839"></a>05839 <span class="comment">!</span>
    5904. 

  5904. <a name="l05840"></a>05840 <span class="comment">!</span>
    5905. 

  5905. <a name="l05841"></a>05841 <span class="comment">!  Integration interval:</span>
    5906. 

  5906. <a name="l05842"></a>05842 <span class="comment">!</span>
    5907. 

  5907. <a name="l05843"></a>05843 <span class="comment">!    [ 0, 1 ]</span>
    5908. 

  5908. <a name="l05844"></a>05844 <span class="comment">!</span>
    5909. 

  5909. <a name="l05845"></a>05845 <span class="comment">!  Weight function:</span>
    5910. 

  5910. <a name="l05846"></a>05846 <span class="comment">!</span>
    5911. 

  5911. <a name="l05847"></a>05847 <span class="comment">!    1.0D+00</span>
    5912. 

  5912. <a name="l05848"></a>05848 <span class="comment">!</span>
    5913. 

  5913. <a name="l05849"></a>05849 <span class="comment">!  Integral to approximate:</span>
    5914. 

  5914. <a name="l05850"></a>05850 <span class="comment">!</span>
    5915. 

  5915. <a name="l05851"></a>05851 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) F(X) dX</span>
    5916. 

  5916. <a name="l05852"></a>05852 <span class="comment">!</span>
    5917. 

  5917. <a name="l05853"></a>05853 <span class="comment">!  Approximate integral:</span>
    5918. 

  5918. <a name="l05854"></a>05854 <span class="comment">!</span>
    5919. 

  5919. <a name="l05855"></a>05855 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    5920. 

  5920. <a name="l05856"></a>05856 <span class="comment">!</span>
    5921. 

  5921. <a name="l05857"></a>05857 <span class="comment">!  Reference:</span>
    5922. 

  5922. <a name="l05858"></a>05858 <span class="comment">!</span>
    5923. 

  5923. <a name="l05859"></a>05859 <span class="comment">!    Abramowitz and Stegun,</span>
    5924. 

  5924. <a name="l05860"></a>05860 <span class="comment">!    Handbook of Mathematical Functions,</span>
    5925. 

  5925. <a name="l05861"></a>05861 <span class="comment">!    National Bureau of Standards, 1964, page 921.</span>
    5926. 

  5926. <a name="l05862"></a>05862 <span class="comment">!</span>
    5927. 

  5927. <a name="l05863"></a>05863 <span class="comment">!  Modified:</span>
    5928. 

  5928. <a name="l05864"></a>05864 <span class="comment">!</span>
    5929. 

  5929. <a name="l05865"></a>05865 <span class="comment">!    18 November 2000</span>
    5930. 

  5930. <a name="l05866"></a>05866 <span class="comment">!</span>
    5931. 

  5931. <a name="l05867"></a>05867 <span class="comment">!  Author:</span>
    5932. 

  5932. <a name="l05868"></a>05868 <span class="comment">!</span>
    5933. 

  5933. <a name="l05869"></a>05869 <span class="comment">!    John Burkardt</span>
    5934. 

  5934. <a name="l05870"></a>05870 <span class="comment">!</span>
    5935. 

  5935. <a name="l05871"></a>05871 <span class="comment">!  Parameters:</span>
    5936. 

  5936. <a name="l05872"></a>05872 <span class="comment">!</span>
    5937. 

  5937. <a name="l05873"></a>05873 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    5938. 

  5938. <a name="l05874"></a>05874 <span class="comment">!    NORDER must be between 1 and 8.</span>
    5939. 

  5939. <a name="l05875"></a>05875 <span class="comment">!</span>
    5940. 

  5940. <a name="l05876"></a>05876 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    5941. 

  5941. <a name="l05877"></a>05877 <span class="comment">!</span>
    5942. 

  5942. <a name="l05878"></a>05878 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    5943. 

  5943. <a name="l05879"></a>05879 <span class="comment">!</span>
    5944. 

  5944. <a name="l05880"></a>05880   <span class="keyword">implicit none</span>
    5945. 

  5945. <a name="l05881"></a>05881 <span class="comment">!</span>
    5946. 

  5946. <a name="l05882"></a>05882   <span class="keywordtype">integer</span> norder
    5947. 

  5947. <a name="l05883"></a>05883 <span class="comment">!</span>
    5948. 

  5948. <a name="l05884"></a>05884   <span class="keywordtype">double precision</span> xtab(norder)
    5949. 

  5949. <a name="l05885"></a>05885   <span class="keywordtype">double precision</span> weight(norder)
    5950. 

  5950. <a name="l05886"></a>05886 <span class="comment">!</span>
    5951. 

  5951. <a name="l05887"></a>05887   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    5952. 

  5952. <a name="l05888"></a>05888 
    5953. 

  5953. <a name="l05889"></a>05889     xtab(1) =   0.5D+00
    5954. 

  5954. <a name="l05890"></a>05890 
    5955. 

  5955. <a name="l05891"></a>05891     weight(1) = 1.0D+00
    5956. 

  5956. <a name="l05892"></a>05892 
    5957. 

  5957. <a name="l05893"></a>05893   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    5958. 

  5958. <a name="l05894"></a>05894 
    5959. 

  5959. <a name="l05895"></a>05895     xtab(1) = 0.2113248654D+00
    5960. 

  5960. <a name="l05896"></a>05896     xtab(2) = 0.7886751346D+00
    5961. 

  5961. <a name="l05897"></a>05897 
    5962. 

  5962. <a name="l05898"></a>05898     weight(1) = 0.5D+00
    5963. 

  5963. <a name="l05899"></a>05899     weight(2) = 0.5D+00
    5964. 

  5964. <a name="l05900"></a>05900 
    5965. 

  5965. <a name="l05901"></a>05901   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    5966. 

  5966. <a name="l05902"></a>05902 
    5967. 

  5967. <a name="l05903"></a>05903     xtab(1) = 0.1127016654D+00
    5968. 

  5968. <a name="l05904"></a>05904     xtab(2) = 0.5000000000D+00
    5969. 

  5969. <a name="l05905"></a>05905     xtab(3) = 0.8872983346D+00
    5970. 

  5970. <a name="l05906"></a>05906 
    5971. 

  5971. <a name="l05907"></a>05907     weight(1) = 5.0D+00 / 18.0D+00
    5972. 

  5972. <a name="l05908"></a>05908     weight(2) = 8.0D+00 / 18.0D+00
    5973. 

  5973. <a name="l05909"></a>05909     weight(3) = 5.0D+00 / 18.0D+00
    5974. 

  5974. <a name="l05910"></a>05910 
    5975. 

  5975. <a name="l05911"></a>05911   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    5976. 

  5976. <a name="l05912"></a>05912 
    5977. 

  5977. <a name="l05913"></a>05913     xtab(1) = 0.0694318442D+00
    5978. 

  5978. <a name="l05914"></a>05914     xtab(2) = 0.3300094782D+00
    5979. 

  5979. <a name="l05915"></a>05915     xtab(3) = 0.6699905218D+00
    5980. 

  5980. <a name="l05916"></a>05916     xtab(4) = 0.9305681558D+00
    5981. 

  5981. <a name="l05917"></a>05917 
    5982. 

  5982. <a name="l05918"></a>05918     weight(1) = 0.1739274226D+00
    5983. 

  5983. <a name="l05919"></a>05919     weight(2) = 0.3260725774D+00
    5984. 

  5984. <a name="l05920"></a>05920     weight(3) = 0.3260725774D+00
    5985. 

  5985. <a name="l05921"></a>05921     weight(4) = 0.1739274226D+00
    5986. 

  5986. <a name="l05922"></a>05922 
    5987. 

  5987. <a name="l05923"></a>05923   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    5988. 

  5988. <a name="l05924"></a>05924 
    5989. 

  5989. <a name="l05925"></a>05925     xtab(1) = 0.0469100770D+00
    5990. 

  5990. <a name="l05926"></a>05926     xtab(2) = 0.2307653449D+00
    5991. 

  5991. <a name="l05927"></a>05927     xtab(3) = 0.5000000000D+00
    5992. 

  5992. <a name="l05928"></a>05928     xtab(4) = 0.7692346551D+00
    5993. 

  5993. <a name="l05929"></a>05929     xtab(5) = 0.9530899230D+00
    5994. 

  5994. <a name="l05930"></a>05930 
    5995. 

  5995. <a name="l05931"></a>05931     weight(1) = 0.1184634425D+00
    5996. 

  5996. <a name="l05932"></a>05932     weight(2) = 0.2393143352D+00
    5997. 

  5997. <a name="l05933"></a>05933     weight(3) = 0.2844444444D+00
    5998. 

  5998. <a name="l05934"></a>05934     weight(4) = 0.2393143352D+00
    5999. 

  5999. <a name="l05935"></a>05935     weight(5) = 0.1184634425D+00
    6000. 

  6000. <a name="l05936"></a>05936 
    6001. 

  6001. <a name="l05937"></a>05937   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    6002. 

  6002. <a name="l05938"></a>05938 
    6003. 

  6003. <a name="l05939"></a>05939     xtab(1) = 0.0337652429D+00
    6004. 

  6004. <a name="l05940"></a>05940     xtab(2) = 0.1693953068D+00
    6005. 

  6005. <a name="l05941"></a>05941     xtab(3) = 0.3806904070D+00
    6006. 

  6006. <a name="l05942"></a>05942     xtab(4) = 0.6193095930D+00
    6007. 

  6007. <a name="l05943"></a>05943     xtab(5) = 0.8306046932D+00
    6008. 

  6008. <a name="l05944"></a>05944     xtab(6) = 0.9662347571D+00
    6009. 

  6009. <a name="l05945"></a>05945 
    6010. 

  6010. <a name="l05946"></a>05946     weight(1) = 0.0856622462D+00
    6011. 

  6011. <a name="l05947"></a>05947     weight(2) = 0.1803807865D+00
    6012. 

  6012. <a name="l05948"></a>05948     weight(3) = 0.2339569673D+00
    6013. 

  6013. <a name="l05949"></a>05949     weight(4) = 0.2339569673D+00
    6014. 

  6014. <a name="l05950"></a>05950     weight(5) = 0.1803807865D+00
    6015. 

  6015. <a name="l05951"></a>05951     weight(6) = 0.0856622462D+00
    6016. 

  6016. <a name="l05952"></a>05952 
    6017. 

  6017. <a name="l05953"></a>05953   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    6018. 

  6018. <a name="l05954"></a>05954 
    6019. 

  6019. <a name="l05955"></a>05955     xtab(1) = 0.0254460438D+00
    6020. 

  6020. <a name="l05956"></a>05956     xtab(2) = 0.1292344072D+00
    6021. 

  6021. <a name="l05957"></a>05957     xtab(3) = 0.2970774243D+00
    6022. 

  6022. <a name="l05958"></a>05958     xtab(4) = 0.5000000000D+00
    6023. 

  6023. <a name="l05959"></a>05959     xtab(5) = 0.7029225757D+00
    6024. 

  6024. <a name="l05960"></a>05960     xtab(6) = 0.8707655928D+00
    6025. 

  6025. <a name="l05961"></a>05961     xtab(7) = 0.9745539562D+00
    6026. 

  6026. <a name="l05962"></a>05962 
    6027. 

  6027. <a name="l05963"></a>05963     weight(1) = 0.0647424831D+00
    6028. 

  6028. <a name="l05964"></a>05964     weight(2) = 0.1398526957D+00
    6029. 

  6029. <a name="l05965"></a>05965     weight(3) = 0.1909150253D+00
    6030. 

  6030. <a name="l05966"></a>05966     weight(4) = 0.2089795918D+00
    6031. 

  6031. <a name="l05967"></a>05967     weight(5) = 0.1909150253D+00
    6032. 

  6032. <a name="l05968"></a>05968     weight(6) = 0.1398526957D+00
    6033. 

  6033. <a name="l05969"></a>05969     weight(7) = 0.0647424831D+00
    6034. 

  6034. <a name="l05970"></a>05970 
    6035. 

  6035. <a name="l05971"></a>05971   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    6036. 

  6036. <a name="l05972"></a>05972 
    6037. 

  6037. <a name="l05973"></a>05973     xtab(1) = 0.0198550718D+00
    6038. 

  6038. <a name="l05974"></a>05974     xtab(2) = 0.1016667613D+00
    6039. 

  6039. <a name="l05975"></a>05975     xtab(3) = 0.2372337950D+00
    6040. 

  6040. <a name="l05976"></a>05976     xtab(4) = 0.4082826788D+00
    6041. 

  6041. <a name="l05977"></a>05977     xtab(5) = 0.5917173212D+00
    6042. 

  6042. <a name="l05978"></a>05978     xtab(6) = 0.7627662050D+00
    6043. 

  6043. <a name="l05979"></a>05979     xtab(7) = 0.8983332387D+00
    6044. 

  6044. <a name="l05980"></a>05980     xtab(8) = 0.9801449282D+00
    6045. 

  6045. <a name="l05981"></a>05981 
    6046. 

  6046. <a name="l05982"></a>05982     weight(1) = 0.0506142681D+00
    6047. 

  6047. <a name="l05983"></a>05983     weight(2) = 0.1111905172D+00
    6048. 

  6048. <a name="l05984"></a>05984     weight(3) = 0.1568533229D+00
    6049. 

  6049. <a name="l05985"></a>05985     weight(4) = 0.1813418917D+00
    6050. 

  6050. <a name="l05986"></a>05986     weight(5) = 0.1813418917D+00
    6051. 

  6051. <a name="l05987"></a>05987     weight(6) = 0.1568533229D+00
    6052. 

  6052. <a name="l05988"></a>05988     weight(7) = 0.1111905172D+00
    6053. 

  6053. <a name="l05989"></a>05989     weight(8) = 0.0506142681D+00
    6054. 

  6054. <a name="l05990"></a>05990 
    6055. 

  6055. <a name="l05991"></a>05991   <span class="keyword">else</span>
    6056. 

  6056. <a name="l05992"></a>05992 
    6057. 

  6057. <a name="l05993"></a>05993     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    6058. 

  6058. <a name="l05994"></a>05994     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_SET_X0_01 - Fatal error!&#39;</span>
    6059. 

  6059. <a name="l05995"></a>05995     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    6060. 

  6060. <a name="l05996"></a>05996     stop
    6061. 

  6061. <a name="l05997"></a>05997 
    6062. 

  6062. <a name="l05998"></a>05998   <span class="keyword">end if</span>
    6063. 

  6063. <a name="l05999"></a>05999 
    6064. 

  6064. <a name="l06000"></a>06000   return
    6065. 

  6065. <a name="l06001"></a>06001 <span class="keyword">end</span>
    6066. 

  6066. <a name="l06002"></a><a class="code" href="quadrule_8f90.html#a18d682e70c431b86cae6a7d62b8148fa">06002</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a18d682e70c431b86cae6a7d62b8148fa">legendre_set_x1</a> ( norder, xtab, weight )
    6067. 

  6067. <a name="l06003"></a>06003 <span class="comment">!</span>
    6068. 

  6068. <a name="l06004"></a>06004 <span class="comment">!*******************************************************************************</span>
    6069. 

  6069. <a name="l06005"></a>06005 <span class="comment">!</span>
    6070. 

  6070. <a name="l06006"></a>06006 <span class="comment">!! LEGENDRE_SET_X1 sets a Gauss-Legendre rule for ( 1 + X ) * F(X) on [-1,1].</span>
    6071. 

  6071. <a name="l06007"></a>06007 <span class="comment">!</span>
    6072. 

  6072. <a name="l06008"></a>06008 <span class="comment">!</span>
    6073. 

  6073. <a name="l06009"></a>06009 <span class="comment">!  Integration interval:</span>
    6074. 

  6074. <a name="l06010"></a>06010 <span class="comment">!</span>
    6075. 

  6075. <a name="l06011"></a>06011 <span class="comment">!    [ -1, 1 ]</span>
    6076. 

  6076. <a name="l06012"></a>06012 <span class="comment">!</span>
    6077. 

  6077. <a name="l06013"></a>06013 <span class="comment">!  Weight function:</span>
    6078. 

  6078. <a name="l06014"></a>06014 <span class="comment">!</span>
    6079. 

  6079. <a name="l06015"></a>06015 <span class="comment">!    1 + X</span>
    6080. 

  6080. <a name="l06016"></a>06016 <span class="comment">!</span>
    6081. 

  6081. <a name="l06017"></a>06017 <span class="comment">!  Integral to approximate:</span>
    6082. 

  6082. <a name="l06018"></a>06018 <span class="comment">!</span>
    6083. 

  6083. <a name="l06019"></a>06019 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) ( 1 + X ) * F(X) dX</span>
    6084. 

  6084. <a name="l06020"></a>06020 <span class="comment">!</span>
    6085. 

  6085. <a name="l06021"></a>06021 <span class="comment">!  Approximate integral:</span>
    6086. 

  6086. <a name="l06022"></a>06022 <span class="comment">!</span>
    6087. 

  6087. <a name="l06023"></a>06023 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    6088. 

  6088. <a name="l06024"></a>06024 <span class="comment">!</span>
    6089. 

  6089. <a name="l06025"></a>06025 <span class="comment">!  Reference:</span>
    6090. 

  6090. <a name="l06026"></a>06026 <span class="comment">!</span>
    6091. 

  6091. <a name="l06027"></a>06027 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    6092. 

  6092. <a name="l06028"></a>06028 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    6093. 

  6093. <a name="l06029"></a>06029 <span class="comment">!    Prentice Hall, 1966, Table #3.</span>
    6094. 

  6094. <a name="l06030"></a>06030 <span class="comment">!</span>
    6095. 

  6095. <a name="l06031"></a>06031 <span class="comment">!  Modified:</span>
    6096. 

  6096. <a name="l06032"></a>06032 <span class="comment">!</span>
    6097. 

  6097. <a name="l06033"></a>06033 <span class="comment">!    18 December 2000</span>
    6098. 

  6098. <a name="l06034"></a>06034 <span class="comment">!</span>
    6099. 

  6099. <a name="l06035"></a>06035 <span class="comment">!  Author:</span>
    6100. 

  6100. <a name="l06036"></a>06036 <span class="comment">!</span>
    6101. 

  6101. <a name="l06037"></a>06037 <span class="comment">!    John Burkardt</span>
    6102. 

  6102. <a name="l06038"></a>06038 <span class="comment">!</span>
    6103. 

  6103. <a name="l06039"></a>06039 <span class="comment">!  Parameters:</span>
    6104. 

  6104. <a name="l06040"></a>06040 <span class="comment">!</span>
    6105. 

  6105. <a name="l06041"></a>06041 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    6106. 

  6106. <a name="l06042"></a>06042 <span class="comment">!    NORDER must be between 1 and 9.</span>
    6107. 

  6107. <a name="l06043"></a>06043 <span class="comment">!</span>
    6108. 

  6108. <a name="l06044"></a>06044 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    6109. 

  6109. <a name="l06045"></a>06045 <span class="comment">!</span>
    6110. 

  6110. <a name="l06046"></a>06046 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    6111. 

  6111. <a name="l06047"></a>06047 <span class="comment">!</span>
    6112. 

  6112. <a name="l06048"></a>06048   <span class="keyword">implicit none</span>
    6113. 

  6113. <a name="l06049"></a>06049 <span class="comment">!</span>
    6114. 

  6114. <a name="l06050"></a>06050   <span class="keywordtype">integer</span> norder
    6115. 

  6115. <a name="l06051"></a>06051 <span class="comment">!</span>
    6116. 

  6116. <a name="l06052"></a>06052   <span class="keywordtype">double precision</span> xtab(norder)
    6117. 

  6117. <a name="l06053"></a>06053   <span class="keywordtype">double precision</span> weight(norder)
    6118. 

  6118. <a name="l06054"></a>06054 <span class="comment">!</span>
    6119. 

  6119. <a name="l06055"></a>06055   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    6120. 

  6120. <a name="l06056"></a>06056 
    6121. 

  6121. <a name="l06057"></a>06057     xtab(1) =  0.333333333333333333333333333333D+00
    6122. 

  6122. <a name="l06058"></a>06058 
    6123. 

  6123. <a name="l06059"></a>06059     weight(1) = 2.0D+00
    6124. 

  6124. <a name="l06060"></a>06060 
    6125. 

  6125. <a name="l06061"></a>06061   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    6126. 

  6126. <a name="l06062"></a>06062 
    6127. 

  6127. <a name="l06063"></a>06063     xtab(1) = -0.289897948556635619639456814941D+00
    6128. 

  6128. <a name="l06064"></a>06064     xtab(2) =  0.689897948556635619639456814941D+00
    6129. 

  6129. <a name="l06065"></a>06065 
    6130. 

  6130. <a name="l06066"></a>06066     weight(1) =  0.727834473024091322422523991699D+00
    6131. 

  6131. <a name="l06067"></a>06067     weight(2) =  1.27216552697590867757747600830D+00
    6132. 

  6132. <a name="l06068"></a>06068 
    6133. 

  6133. <a name="l06069"></a>06069   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    6134. 

  6134. <a name="l06070"></a>06070 
    6135. 

  6135. <a name="l06071"></a>06071     xtab(1) = -0.575318923521694112050483779752D+00
    6136. 

  6136. <a name="l06072"></a>06072     xtab(2) =  0.181066271118530578270147495862D+00
    6137. 

  6137. <a name="l06073"></a>06073     xtab(3) =  0.822824080974592105208907712461D+00
    6138. 

  6138. <a name="l06074"></a>06074 
    6139. 

  6139. <a name="l06075"></a>06075     weight(1) =  0.279307919605816490135525088716D+00
    6140. 

  6140. <a name="l06076"></a>06076     weight(2) =  0.916964425438344986775682378225D+00
    6141. 

  6141. <a name="l06077"></a>06077     weight(3) =  0.803727654955838523088792533058D+00
    6142. 

  6142. <a name="l06078"></a>06078 
    6143. 

  6143. <a name="l06079"></a>06079   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    6144. 

  6144. <a name="l06080"></a>06080 
    6145. 

  6145. <a name="l06081"></a>06081     xtab(1) = -0.720480271312438895695825837750D+00
    6146. 

  6146. <a name="l06082"></a>06082     xtab(2) = -0.167180864737833640113395337326D+00
    6147. 

  6147. <a name="l06083"></a>06083     xtab(3) =  0.446313972723752344639908004629D+00
    6148. 

  6148. <a name="l06084"></a>06084     xtab(4) =  0.885791607770964635613757614892D+00
    6149. 

  6149. <a name="l06085"></a>06085 
    6150. 

  6150. <a name="l06086"></a>06086     weight(1) =  0.124723883800032328695500588386D+00
    6151. 

  6151. <a name="l06087"></a>06087     weight(2) =  0.519390190432929763305824811559D+00
    6152. 

  6152. <a name="l06088"></a>06088     weight(3) =  0.813858272041085443165617903743D+00
    6153. 

  6153. <a name="l06089"></a>06089     weight(4) =  0.542027653725952464833056696312D+00
    6154. 

  6154. <a name="l06090"></a>06090 
    6155. 

  6155. <a name="l06091"></a>06091   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    6156. 

  6156. <a name="l06092"></a>06092 
    6157. 

  6157. <a name="l06093"></a>06093     xtab(1) = -0.802929828402347147753002204224D+00
    6158. 

  6158. <a name="l06094"></a>06094     xtab(2) = -0.390928546707272189029229647442D+00
    6159. 

  6159. <a name="l06095"></a>06095     xtab(3) =  0.124050379505227711989974959990D+00
    6160. 

  6160. <a name="l06096"></a>06096     xtab(4) =  0.603973164252783654928415726409D+00
    6161. 

  6161. <a name="l06097"></a>06097     xtab(5) =  0.920380285897062515318386619813D+00
    6162. 

  6162. <a name="l06098"></a>06098 
    6163. 

  6163. <a name="l06099"></a>06099     weight(1) =  0.0629916580867691047411692662740D+00
    6164. 

  6164. <a name="l06100"></a>06100     weight(2) =  0.295635480290466681402532877367D+00
    6165. 

  6165. <a name="l06101"></a>06101     weight(3) =  0.585547948338679234792151477424D+00
    6166. 

  6166. <a name="l06102"></a>06102     weight(4) =  0.668698552377478261966702492391D+00
    6167. 

  6167. <a name="l06103"></a>06103     weight(5) =  0.387126360906606717097443886545D+00
    6168. 

  6168. <a name="l06104"></a>06104 
    6169. 

  6169. <a name="l06105"></a>06105   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    6170. 

  6170. <a name="l06106"></a>06106 
    6171. 

  6171. <a name="l06107"></a>06107     xtab(1) = -0.853891342639482229703747931639D+00
    6172. 

  6172. <a name="l06108"></a>06108     xtab(2) = -0.538467724060109001833766720231D+00
    6173. 

  6173. <a name="l06109"></a>06109     xtab(3) = -0.117343037543100264162786683611D+00
    6174. 

  6174. <a name="l06110"></a>06110     xtab(4) =  0.326030619437691401805894055838D+00
    6175. 

  6175. <a name="l06111"></a>06111     xtab(5) =  0.703842800663031416300046295008D+00
    6176. 

  6176. <a name="l06112"></a>06112     xtab(6) =  0.941367145680430216055899446174D+00
    6177. 

  6177. <a name="l06113"></a>06113 
    6178. 

  6178. <a name="l06114"></a>06114     weight(1) =  0.0349532072544381270240692132496D+00
    6179. 

  6179. <a name="l06115"></a>06115     weight(2) =  0.175820662202035902032706497222D+00
    6180. 

  6180. <a name="l06116"></a>06116     weight(3) =  0.394644603562621056482338042193D+00
    6181. 

  6181. <a name="l06117"></a>06117     weight(4) =  0.563170215152795712476307356284D+00
    6182. 

  6182. <a name="l06118"></a>06118     weight(5) =  0.542169988926074467362761586552D+00
    6183. 

  6183. <a name="l06119"></a>06119     weight(6) =  0.289241322902034734621817304499D+00
    6184. 

  6184. <a name="l06120"></a>06120 
    6185. 

  6185. <a name="l06121"></a>06121   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    6186. 

  6186. <a name="l06122"></a>06122 
    6187. 

  6187. <a name="l06123"></a>06123     xtab(1) = -0.887474878926155707068695617935D+00
    6188. 

  6188. <a name="l06124"></a>06124     xtab(2) = -0.639518616526215270024840114382D+00
    6189. 

  6189. <a name="l06125"></a>06125     xtab(3) = -0.294750565773660725252184459658D+00
    6190. 

  6190. <a name="l06126"></a>06126     xtab(4) =  0.0943072526611107660028971153047D+00
    6191. 

  6191. <a name="l06127"></a>06127     xtab(5) =  0.468420354430821063046421216613D+00
    6192. 

  6192. <a name="l06128"></a>06128     xtab(6) =  0.770641893678191536180719525865D+00
    6193. 

  6193. <a name="l06129"></a>06129     xtab(7) =  0.955041227122575003782349000858D+00
    6194. 

  6194. <a name="l06130"></a>06130 
    6195. 

  6195. <a name="l06131"></a>06131     weight(1) =  0.0208574488112296163587654972151D+00
    6196. 

  6196. <a name="l06132"></a>06132     weight(2) =  0.109633426887493901777324193433D+00
    6197. 

  6197. <a name="l06133"></a>06133     weight(3) =  0.265538785861965879934591955055D+00
    6198. 

  6198. <a name="l06134"></a>06134     weight(4) =  0.428500262783494679963649011999D+00
    6199. 

  6199. <a name="l06135"></a>06135     weight(5) =  0.509563589198353307674937943100D+00
    6200. 

  6200. <a name="l06136"></a>06136     weight(6) =  0.442037032763498409684482945478D+00
    6201. 

  6201. <a name="l06137"></a>06137     weight(7) =  0.223869453693964204606248453720D+00
    6202. 

  6202. <a name="l06138"></a>06138 
    6203. 

  6203. <a name="l06139"></a>06139   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    6204. 

  6204. <a name="l06140"></a>06140 
    6205. 

  6205. <a name="l06141"></a>06141     xtab(1) = -0.910732089420060298533757956283D+00
    6206. 

  6206. <a name="l06142"></a>06142     xtab(2) = -0.711267485915708857029562959544D+00
    6207. 

  6207. <a name="l06143"></a>06143     xtab(3) = -0.426350485711138962102627520502D+00
    6208. 

  6208. <a name="l06144"></a>06144     xtab(4) = -0.0903733696068532980645444599064D+00
    6209. 

  6209. <a name="l06145"></a>06145     xtab(5) =  0.256135670833455395138292079035D+00
    6210. 

  6210. <a name="l06146"></a>06146     xtab(6) =  0.571383041208738483284917464837D+00
    6211. 

  6211. <a name="l06147"></a>06147     xtab(7) =  0.817352784200412087992517083851D+00
    6212. 

  6212. <a name="l06148"></a>06148     xtab(8) =  0.964440169705273096373589797925D+00
    6213. 

  6213. <a name="l06149"></a>06149 
    6214. 

  6214. <a name="l06150"></a>06150     weight(1) =  0.0131807657689951954189692640444D+00
    6215. 

  6215. <a name="l06151"></a>06151     weight(2) =  0.0713716106239448335742111888042D+00
    6216. 

  6216. <a name="l06152"></a>06152     weight(3) =  0.181757278018795592332221684383D+00
    6217. 

  6217. <a name="l06153"></a>06153     weight(4) =  0.316798397969276640481632757440D+00
    6218. 

  6218. <a name="l06154"></a>06154     weight(5) =  0.424189437743720042818124385645D+00
    6219. 

  6219. <a name="l06155"></a>06155     weight(6) =  0.450023197883549464687088394417D+00
    6220. 

  6220. <a name="l06156"></a>06156     weight(7) =  0.364476094545494505382889847132D+00
    6221. 

  6221. <a name="l06157"></a>06157     weight(8) =  0.178203217446223725304862478136D+00
    6222. 

  6222. <a name="l06158"></a>06158 
    6223. 

  6223. <a name="l06159"></a>06159   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    6224. 

  6224. <a name="l06160"></a>06160 
    6225. 

  6225. <a name="l06161"></a>06161     xtab(1) = -0.927484374233581078117671398464D+00
    6226. 

  6226. <a name="l06162"></a>06162     xtab(2) = -0.763842042420002599615429776011D+00
    6227. 

  6227. <a name="l06163"></a>06163     xtab(3) = -0.525646030370079229365386614293D+00
    6228. 

  6228. <a name="l06164"></a>06164     xtab(4) = -0.236234469390588049278459503207D+00
    6229. 

  6229. <a name="l06165"></a>06165     xtab(5) =  0.0760591978379781302337137826389D+00
    6230. 

  6230. <a name="l06166"></a>06166     xtab(6) =  0.380664840144724365880759065541D+00
    6231. 

  6231. <a name="l06167"></a>06167     xtab(7) =  0.647766687674009436273648507855D+00
    6232. 

  6232. <a name="l06168"></a>06168     xtab(8) =  0.851225220581607910728163628088D+00
    6233. 

  6233. <a name="l06169"></a>06169     xtab(9) =  0.971175180702246902734346518378D+00
    6234. 

  6234. <a name="l06170"></a>06170 
    6235. 

  6235. <a name="l06171"></a>06171     weight(1) =  0.00872338834309252349019620448007D+00
    6236. 

  6236. <a name="l06172"></a>06172     weight(2) =  0.0482400171391415162069086091476D+00
    6237. 

  6237. <a name="l06173"></a>06173     weight(3) =  0.127219285964216005046760427743D+00
    6238. 

  6238. <a name="l06174"></a>06174     weight(4) =  0.233604781180660442262926091607D+00
    6239. 

  6239. <a name="l06175"></a>06175     weight(5) =  0.337433287379681397577000079834D+00
    6240. 

  6240. <a name="l06176"></a>06176     weight(6) =  0.401235236773473158616600898930D+00
    6241. 

  6241. <a name="l06177"></a>06177     weight(7) =  0.394134968689382820640692081477D+00
    6242. 

  6242. <a name="l06178"></a>06178     weight(8) =  0.304297020437232650320317215016D+00
    6243. 

  6243. <a name="l06179"></a>06179     weight(9) =  0.145112014093119485838598391765D+00
    6244. 

  6244. <a name="l06180"></a>06180 
    6245. 

  6245. <a name="l06181"></a>06181   <span class="keyword">else</span>
    6246. 

  6246. <a name="l06182"></a>06182 
    6247. 

  6247. <a name="l06183"></a>06183     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    6248. 

  6248. <a name="l06184"></a>06184     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_SET_X1 - Fatal error!&#39;</span>
    6249. 

  6249. <a name="l06185"></a>06185     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal input value of NORDER = &#39;</span>, norder
    6250. 

  6250. <a name="l06186"></a>06186     stop
    6251. 

  6251. <a name="l06187"></a>06187 
    6252. 

  6252. <a name="l06188"></a>06188   <span class="keyword">end if</span>
    6253. 

  6253. <a name="l06189"></a>06189 
    6254. 

  6254. <a name="l06190"></a>06190   return
    6255. 

  6255. <a name="l06191"></a>06191 <span class="keyword">end</span>
    6256. 

  6256. <a name="l06192"></a><a class="code" href="quadrule_8f90.html#a05a8f595777fdbdfaa618868856a48a5">06192</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a05a8f595777fdbdfaa618868856a48a5">legendre_set_x1_01</a> ( norder, xtab, weight )
    6257. 

  6257. <a name="l06193"></a>06193 <span class="comment">!</span>
    6258. 

  6258. <a name="l06194"></a>06194 <span class="comment">!*******************************************************************************</span>
    6259. 

  6259. <a name="l06195"></a>06195 <span class="comment">!</span>
    6260. 

  6260. <a name="l06196"></a>06196 <span class="comment">!! LEGENDRE_SET_X1_01 sets a Gauss-Legendre rule for X * F(X) on [0,1].</span>
    6261. 

  6261. <a name="l06197"></a>06197 <span class="comment">!</span>
    6262. 

  6262. <a name="l06198"></a>06198 <span class="comment">!</span>
    6263. 

  6263. <a name="l06199"></a>06199 <span class="comment">!  Integration interval:</span>
    6264. 

  6264. <a name="l06200"></a>06200 <span class="comment">!</span>
    6265. 

  6265. <a name="l06201"></a>06201 <span class="comment">!    [ 0, 1 ]</span>
    6266. 

  6266. <a name="l06202"></a>06202 <span class="comment">!</span>
    6267. 

  6267. <a name="l06203"></a>06203 <span class="comment">!  Weight function:</span>
    6268. 

  6268. <a name="l06204"></a>06204 <span class="comment">!</span>
    6269. 

  6269. <a name="l06205"></a>06205 <span class="comment">!    X</span>
    6270. 

  6270. <a name="l06206"></a>06206 <span class="comment">!</span>
    6271. 

  6271. <a name="l06207"></a>06207 <span class="comment">!  Integral to approximate:</span>
    6272. 

  6272. <a name="l06208"></a>06208 <span class="comment">!</span>
    6273. 

  6273. <a name="l06209"></a>06209 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) X * F(X) dX</span>
    6274. 

  6274. <a name="l06210"></a>06210 <span class="comment">!</span>
    6275. 

  6275. <a name="l06211"></a>06211 <span class="comment">!  Approximate integral:</span>
    6276. 

  6276. <a name="l06212"></a>06212 <span class="comment">!</span>
    6277. 

  6277. <a name="l06213"></a>06213 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    6278. 

  6278. <a name="l06214"></a>06214 <span class="comment">!</span>
    6279. 

  6279. <a name="l06215"></a>06215 <span class="comment">!  Reference:</span>
    6280. 

  6280. <a name="l06216"></a>06216 <span class="comment">!</span>
    6281. 

  6281. <a name="l06217"></a>06217 <span class="comment">!    Abramowitz and Stegun,</span>
    6282. 

  6282. <a name="l06218"></a>06218 <span class="comment">!    Handbook of Mathematical Functions,</span>
    6283. 

  6283. <a name="l06219"></a>06219 <span class="comment">!    National Bureau of Standards, 1964, page 921.</span>
    6284. 

  6284. <a name="l06220"></a>06220 <span class="comment">!</span>
    6285. 

  6285. <a name="l06221"></a>06221 <span class="comment">!  Modified:</span>
    6286. 

  6286. <a name="l06222"></a>06222 <span class="comment">!</span>
    6287. 

  6287. <a name="l06223"></a>06223 <span class="comment">!    18 November 2000</span>
    6288. 

  6288. <a name="l06224"></a>06224 <span class="comment">!</span>
    6289. 

  6289. <a name="l06225"></a>06225 <span class="comment">!  Author:</span>
    6290. 

  6290. <a name="l06226"></a>06226 <span class="comment">!</span>
    6291. 

  6291. <a name="l06227"></a>06227 <span class="comment">!    John Burkardt</span>
    6292. 

  6292. <a name="l06228"></a>06228 <span class="comment">!</span>
    6293. 

  6293. <a name="l06229"></a>06229 <span class="comment">!  Parameters:</span>
    6294. 

  6294. <a name="l06230"></a>06230 <span class="comment">!</span>
    6295. 

  6295. <a name="l06231"></a>06231 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    6296. 

  6296. <a name="l06232"></a>06232 <span class="comment">!    NORDER must be between 1 and 8.</span>
    6297. 

  6297. <a name="l06233"></a>06233 <span class="comment">!</span>
    6298. 

  6298. <a name="l06234"></a>06234 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    6299. 

  6299. <a name="l06235"></a>06235 <span class="comment">!</span>
    6300. 

  6300. <a name="l06236"></a>06236 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    6301. 

  6301. <a name="l06237"></a>06237 <span class="comment">!</span>
    6302. 

  6302. <a name="l06238"></a>06238   <span class="keyword">implicit none</span>
    6303. 

  6303. <a name="l06239"></a>06239 <span class="comment">!</span>
    6304. 

  6304. <a name="l06240"></a>06240   <span class="keywordtype">integer</span> norder
    6305. 

  6305. <a name="l06241"></a>06241 <span class="comment">!</span>
    6306. 

  6306. <a name="l06242"></a>06242   <span class="keywordtype">double precision</span> xtab(norder)
    6307. 

  6307. <a name="l06243"></a>06243   <span class="keywordtype">double precision</span> weight(norder)
    6308. 

  6308. <a name="l06244"></a>06244 <span class="comment">!</span>
    6309. 

  6309. <a name="l06245"></a>06245   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    6310. 

  6310. <a name="l06246"></a>06246 
    6311. 

  6311. <a name="l06247"></a>06247     xtab(1) =   0.6666666667D+00
    6312. 

  6312. <a name="l06248"></a>06248 
    6313. 

  6313. <a name="l06249"></a>06249     weight(1) = 0.5000000000D+00
    6314. 

  6314. <a name="l06250"></a>06250 
    6315. 

  6315. <a name="l06251"></a>06251   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    6316. 

  6316. <a name="l06252"></a>06252 
    6317. 

  6317. <a name="l06253"></a>06253     xtab(1) = 0.3550510257D+00
    6318. 

  6318. <a name="l06254"></a>06254     xtab(2) = 0.8449489743D+00
    6319. 

  6319. <a name="l06255"></a>06255 
    6320. 

  6320. <a name="l06256"></a>06256     weight(1) = 0.1819586183D+00
    6321. 

  6321. <a name="l06257"></a>06257     weight(2) = 0.3180413817D+00
    6322. 

  6322. <a name="l06258"></a>06258 
    6323. 

  6323. <a name="l06259"></a>06259   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    6324. 

  6324. <a name="l06260"></a>06260 
    6325. 

  6325. <a name="l06261"></a>06261     xtab(1) = 0.2123405382D+00
    6326. 

  6326. <a name="l06262"></a>06262     xtab(2) = 0.5905331356D+00
    6327. 

  6327. <a name="l06263"></a>06263     xtab(3) = 0.9114120405D+00
    6328. 

  6328. <a name="l06264"></a>06264 
    6329. 

  6329. <a name="l06265"></a>06265     weight(1) = 0.0698269799D+00
    6330. 

  6330. <a name="l06266"></a>06266     weight(2) = 0.2292411064D+00
    6331. 

  6331. <a name="l06267"></a>06267     weight(3) = 0.2009319137D+00
    6332. 

  6332. <a name="l06268"></a>06268 
    6333. 

  6333. <a name="l06269"></a>06269   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    6334. 

  6334. <a name="l06270"></a>06270 
    6335. 

  6335. <a name="l06271"></a>06271     xtab(1) = 0.1397598643D+00
    6336. 

  6336. <a name="l06272"></a>06272     xtab(2) = 0.4164095676D+00
    6337. 

  6337. <a name="l06273"></a>06273     xtab(3) = 0.7231569864D+00
    6338. 

  6338. <a name="l06274"></a>06274     xtab(4) = 0.9428958039D+00
    6339. 

  6339. <a name="l06275"></a>06275 
    6340. 

  6340. <a name="l06276"></a>06276     weight(1) = 0.0311809710D+00
    6341. 

  6341. <a name="l06277"></a>06277     weight(2) = 0.1298475476D+00
    6342. 

  6342. <a name="l06278"></a>06278     weight(3) = 0.2034645680D+00
    6343. 

  6343. <a name="l06279"></a>06279     weight(4) = 0.1355069134D+00
    6344. 

  6344. <a name="l06280"></a>06280 
    6345. 

  6345. <a name="l06281"></a>06281   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    6346. 

  6346. <a name="l06282"></a>06282 
    6347. 

  6347. <a name="l06283"></a>06283     xtab(1) = 0.0985350858D+00
    6348. 

  6348. <a name="l06284"></a>06284     xtab(2) = 0.3045357266D+00
    6349. 

  6349. <a name="l06285"></a>06285     xtab(3) = 0.5620251898D+00
    6350. 

  6350. <a name="l06286"></a>06286     xtab(4) = 0.8019865821D+00
    6351. 

  6351. <a name="l06287"></a>06287     xtab(5) = 0.9601901429D+00
    6352. 

  6352. <a name="l06288"></a>06288 
    6353. 

  6353. <a name="l06289"></a>06289     weight(1) = 0.0157479145D+00
    6354. 

  6354. <a name="l06290"></a>06290     weight(2) = 0.0739088701D+00
    6355. 

  6355. <a name="l06291"></a>06291     weight(3) = 0.1463888701D+00
    6356. 

  6356. <a name="l06292"></a>06292     weight(4) = 0.1671746381D+00
    6357. 

  6357. <a name="l06293"></a>06293     weight(5) = 0.0967815902D+00
    6358. 

  6358. <a name="l06294"></a>06294 
    6359. 

  6359. <a name="l06295"></a>06295   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    6360. 

  6360. <a name="l06296"></a>06296 
    6361. 

  6361. <a name="l06297"></a>06297     xtab(1) = 0.0730543287D+00
    6362. 

  6362. <a name="l06298"></a>06298     xtab(2) = 0.2307661380D+00
    6363. 

  6363. <a name="l06299"></a>06299     xtab(3) = 0.4413284812D+00
    6364. 

  6364. <a name="l06300"></a>06300     xtab(4) = 0.6630153097D+00
    6365. 

  6365. <a name="l06301"></a>06301     xtab(5) = 0.8519214003D+00
    6366. 

  6366. <a name="l06302"></a>06302     xtab(6) = 0.9706835728D+00
    6367. 

  6367. <a name="l06303"></a>06303 
    6368. 

  6368. <a name="l06304"></a>06304     weight(1) = 0.0087383108D+00
    6369. 

  6369. <a name="l06305"></a>06305     weight(2) = 0.0439551656D+00
    6370. 

  6370. <a name="l06306"></a>06306     weight(3) = 0.0986611509D+00
    6371. 

  6371. <a name="l06307"></a>06307     weight(4) = 0.1407925538D+00
    6372. 

  6372. <a name="l06308"></a>06308     weight(5) = 0.1355424972D+00
    6373. 

  6373. <a name="l06309"></a>06309     weight(6) = 0.0723103307D+00
    6374. 

  6374. <a name="l06310"></a>06310 
    6375. 

  6375. <a name="l06311"></a>06311   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    6376. 

  6376. <a name="l06312"></a>06312 
    6377. 

  6377. <a name="l06313"></a>06313     xtab(1) = 0.0562625605D+00
    6378. 

  6378. <a name="l06314"></a>06314     xtab(2) = 0.1802406917D+00
    6379. 

  6379. <a name="l06315"></a>06315     xtab(3) = 0.3526247171D+00
    6380. 

  6380. <a name="l06316"></a>06316     xtab(4) = 0.5471536263D+00
    6381. 

  6381. <a name="l06317"></a>06317     xtab(5) = 0.7342101772D+00
    6382. 

  6382. <a name="l06318"></a>06318     xtab(6) = 0.8853209468D+00
    6383. 

  6383. <a name="l06319"></a>06319     xtab(7) = 0.9775206136D+00
    6384. 

  6384. <a name="l06320"></a>06320 
    6385. 

  6385. <a name="l06321"></a>06321     weight(1) = 0.0052143622D+00
    6386. 

  6386. <a name="l06322"></a>06322     weight(2) = 0.0274083567D+00
    6387. 

  6387. <a name="l06323"></a>06323     weight(3) = 0.0663846965D+00
    6388. 

  6388. <a name="l06324"></a>06324     weight(4) = 0.1071250657D+00
    6389. 

  6389. <a name="l06325"></a>06325     weight(5) = 0.1273908973D+00
    6390. 

  6390. <a name="l06326"></a>06326     weight(6) = 0.1105092582D+00
    6391. 

  6391. <a name="l06327"></a>06327     weight(7) = 0.0559673634D+00
    6392. 

  6392. <a name="l06328"></a>06328 
    6393. 

  6393. <a name="l06329"></a>06329   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    6394. 

  6394. <a name="l06330"></a>06330 
    6395. 

  6395. <a name="l06331"></a>06331     xtab(1) = 0.0446339553D+00
    6396. 

  6396. <a name="l06332"></a>06332     xtab(2) = 0.1443662570D+00
    6397. 

  6397. <a name="l06333"></a>06333     xtab(3) = 0.2868247571D+00
    6398. 

  6398. <a name="l06334"></a>06334     xtab(4) = 0.4548133152D+00
    6399. 

  6399. <a name="l06335"></a>06335     xtab(5) = 0.6280678354D+00
    6400. 

  6400. <a name="l06336"></a>06336     xtab(6) = 0.7856915206D+00
    6401. 

  6401. <a name="l06337"></a>06337     xtab(7) = 0.9086763921D+00
    6402. 

  6402. <a name="l06338"></a>06338     xtab(8) = 0.9822200849D+00
    6403. 

  6403. <a name="l06339"></a>06339 
    6404. 

  6404. <a name="l06340"></a>06340     weight(1) = 0.0032951914D+00
    6405. 

  6405. <a name="l06341"></a>06341     weight(2) = 0.0178429027D+00
    6406. 

  6406. <a name="l06342"></a>06342     weight(3) = 0.0454393195D+00
    6407. 

  6407. <a name="l06343"></a>06343     weight(4) = 0.0791995995D+00
    6408. 

  6408. <a name="l06344"></a>06344     weight(5) = 0.1060473594D+00
    6409. 

  6409. <a name="l06345"></a>06345     weight(6) = 0.1125057995D+00
    6410. 

  6410. <a name="l06346"></a>06346     weight(7) = 0.0911190236D+00
    6411. 

  6411. <a name="l06347"></a>06347     weight(8) = 0.0445508044D+00
    6412. 

  6412. <a name="l06348"></a>06348 
    6413. 

  6413. <a name="l06349"></a>06349   <span class="keyword">else</span>
    6414. 

  6414. <a name="l06350"></a>06350 
    6415. 

  6415. <a name="l06351"></a>06351     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    6416. 

  6416. <a name="l06352"></a>06352     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_SET_X1_01 - Fatal error!&#39;</span>
    6417. 

  6417. <a name="l06353"></a>06353     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    6418. 

  6418. <a name="l06354"></a>06354     stop
    6419. 

  6419. <a name="l06355"></a>06355 
    6420. 

  6420. <a name="l06356"></a>06356   <span class="keyword">end if</span>
    6421. 

  6421. <a name="l06357"></a>06357 
    6422. 

  6422. <a name="l06358"></a>06358   return
    6423. 

  6423. <a name="l06359"></a>06359 <span class="keyword">end</span>
    6424. 

  6424. <a name="l06360"></a><a class="code" href="quadrule_8f90.html#a8323fd380b28f282745e9b88ab0f5a74">06360</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a8323fd380b28f282745e9b88ab0f5a74">legendre_set_x2</a> ( norder, xtab, weight )
    6425. 

  6425. <a name="l06361"></a>06361 <span class="comment">!</span>
    6426. 

  6426. <a name="l06362"></a>06362 <span class="comment">!*******************************************************************************</span>
    6427. 

  6427. <a name="l06363"></a>06363 <span class="comment">!</span>
    6428. 

  6428. <a name="l06364"></a>06364 <span class="comment">!! LEGENDRE_SET_X2 sets a Gauss-Legendre rule for ( 1 + X )**2 * F(X) on [-1,1].</span>
    6429. 

  6429. <a name="l06365"></a>06365 <span class="comment">!</span>
    6430. 

  6430. <a name="l06366"></a>06366 <span class="comment">!</span>
    6431. 

  6431. <a name="l06367"></a>06367 <span class="comment">!  Integration interval:</span>
    6432. 

  6432. <a name="l06368"></a>06368 <span class="comment">!</span>
    6433. 

  6433. <a name="l06369"></a>06369 <span class="comment">!    [ -1, 1 ]</span>
    6434. 

  6434. <a name="l06370"></a>06370 <span class="comment">!</span>
    6435. 

  6435. <a name="l06371"></a>06371 <span class="comment">!  Weight function:</span>
    6436. 

  6436. <a name="l06372"></a>06372 <span class="comment">!</span>
    6437. 

  6437. <a name="l06373"></a>06373 <span class="comment">!    ( 1 + X )**2</span>
    6438. 

  6438. <a name="l06374"></a>06374 <span class="comment">!</span>
    6439. 

  6439. <a name="l06375"></a>06375 <span class="comment">!  Integral to approximate:</span>
    6440. 

  6440. <a name="l06376"></a>06376 <span class="comment">!</span>
    6441. 

  6441. <a name="l06377"></a>06377 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) ( 1 + X )**2 * F(X) dX</span>
    6442. 

  6442. <a name="l06378"></a>06378 <span class="comment">!</span>
    6443. 

  6443. <a name="l06379"></a>06379 <span class="comment">!  Approximate integral:</span>
    6444. 

  6444. <a name="l06380"></a>06380 <span class="comment">!</span>
    6445. 

  6445. <a name="l06381"></a>06381 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    6446. 

  6446. <a name="l06382"></a>06382 <span class="comment">!</span>
    6447. 

  6447. <a name="l06383"></a>06383 <span class="comment">!  Reference:</span>
    6448. 

  6448. <a name="l06384"></a>06384 <span class="comment">!</span>
    6449. 

  6449. <a name="l06385"></a>06385 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    6450. 

  6450. <a name="l06386"></a>06386 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    6451. 

  6451. <a name="l06387"></a>06387 <span class="comment">!    Prentice Hall, 1966, Table #3.</span>
    6452. 

  6452. <a name="l06388"></a>06388 <span class="comment">!</span>
    6453. 

  6453. <a name="l06389"></a>06389 <span class="comment">!  Modified:</span>
    6454. 

  6454. <a name="l06390"></a>06390 <span class="comment">!</span>
    6455. 

  6455. <a name="l06391"></a>06391 <span class="comment">!    18 December 2000</span>
    6456. 

  6456. <a name="l06392"></a>06392 <span class="comment">!</span>
    6457. 

  6457. <a name="l06393"></a>06393 <span class="comment">!  Author:</span>
    6458. 

  6458. <a name="l06394"></a>06394 <span class="comment">!</span>
    6459. 

  6459. <a name="l06395"></a>06395 <span class="comment">!    John Burkardt</span>
    6460. 

  6460. <a name="l06396"></a>06396 <span class="comment">!</span>
    6461. 

  6461. <a name="l06397"></a>06397 <span class="comment">!  Parameters:</span>
    6462. 

  6462. <a name="l06398"></a>06398 <span class="comment">!</span>
    6463. 

  6463. <a name="l06399"></a>06399 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    6464. 

  6464. <a name="l06400"></a>06400 <span class="comment">!    NORDER must be between 1 and 9.</span>
    6465. 

  6465. <a name="l06401"></a>06401 <span class="comment">!</span>
    6466. 

  6466. <a name="l06402"></a>06402 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    6467. 

  6467. <a name="l06403"></a>06403 <span class="comment">!</span>
    6468. 

  6468. <a name="l06404"></a>06404 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    6469. 

  6469. <a name="l06405"></a>06405 <span class="comment">!</span>
    6470. 

  6470. <a name="l06406"></a>06406   <span class="keyword">implicit none</span>
    6471. 

  6471. <a name="l06407"></a>06407 <span class="comment">!</span>
    6472. 

  6472. <a name="l06408"></a>06408   <span class="keywordtype">integer</span> norder
    6473. 

  6473. <a name="l06409"></a>06409 <span class="comment">!</span>
    6474. 

  6474. <a name="l06410"></a>06410   <span class="keywordtype">double precision</span> xtab(norder)
    6475. 

  6475. <a name="l06411"></a>06411   <span class="keywordtype">double precision</span> weight(norder)
    6476. 

  6476. <a name="l06412"></a>06412 <span class="comment">!</span>
    6477. 

  6477. <a name="l06413"></a>06413   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    6478. 

  6478. <a name="l06414"></a>06414 
    6479. 

  6479. <a name="l06415"></a>06415     xtab(1) =  0.5D+00
    6480. 

  6480. <a name="l06416"></a>06416 
    6481. 

  6481. <a name="l06417"></a>06417     weight(1) =  2.66666666666666666666666666666D+00
    6482. 

  6482. <a name="l06418"></a>06418 
    6483. 

  6483. <a name="l06419"></a>06419   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    6484. 

  6484. <a name="l06420"></a>06420 
    6485. 

  6485. <a name="l06421"></a>06421     xtab(1) = -0.0883036880224505775998524725910D+00
    6486. 

  6486. <a name="l06422"></a>06422     xtab(2) =  0.754970354689117244266519139258D+00
    6487. 

  6487. <a name="l06423"></a>06423 
    6488. 

  6488. <a name="l06424"></a>06424     weight(1) =  0.806287056638603444666851075928D+00
    6489. 

  6489. <a name="l06425"></a>06425     weight(2) =  1.86037961002806322199981559074D+00
    6490. 

  6490. <a name="l06426"></a>06426 
    6491. 

  6491. <a name="l06427"></a>06427   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    6492. 

  6492. <a name="l06428"></a>06428 
    6493. 

  6493. <a name="l06429"></a>06429     xtab(1) = -0.410004419776996766244796955168D+00
    6494. 

  6494. <a name="l06430"></a>06430     xtab(2) =  0.305992467923296230556472913192D+00
    6495. 

  6495. <a name="l06431"></a>06431     xtab(3) =  0.854011951853700535688324041976D+00
    6496. 

  6496. <a name="l06432"></a>06432 
    6497. 

  6497. <a name="l06433"></a>06433     weight(1) =  0.239605624068645584091811926047D+00
    6498. 

  6498. <a name="l06434"></a>06434     weight(2) =  1.16997015407892817602809616291D+00
    6499. 

  6499. <a name="l06435"></a>06435     weight(3) =  1.25709088851909290654675857771D+00
    6500. 

  6500. <a name="l06436"></a>06436 
    6501. 

  6501. <a name="l06437"></a>06437   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    6502. 

  6502. <a name="l06438"></a>06438 
    6503. 

  6503. <a name="l06439"></a>06439     xtab(1) = -0.591702835793545726606755921586D+00
    6504. 

  6504. <a name="l06440"></a>06440     xtab(2) = -0.0340945902087350046811467387661D+00
    6505. 

  6505. <a name="l06441"></a>06441     xtab(3) =  0.522798524896275389882037174551D+00
    6506. 

  6506. <a name="l06442"></a>06442     xtab(4) =  0.902998901106005341405865485802D+00
    6507. 

  6507. <a name="l06443"></a>06443 
    6508. 

  6508. <a name="l06444"></a>06444     weight(1) =  0.0828179259993445222751812523731D+00
    6509. 

  6509. <a name="l06445"></a>06445     weight(2) =  0.549071097383384602539010760334D+00
    6510. 

  6510. <a name="l06446"></a>06446     weight(3) =  1.14767031839371367238662411421D+00
    6511. 

  6511. <a name="l06447"></a>06447     weight(4) =  0.887107324890223869465850539752D+00
    6512. 

  6512. <a name="l06448"></a>06448 
    6513. 

  6513. <a name="l06449"></a>06449   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    6514. 

  6514. <a name="l06450"></a>06450 
    6515. 

  6515. <a name="l06451"></a>06451     xtab(1) = -0.702108425894032836232448374820D+00
    6516. 

  6516. <a name="l06452"></a>06452     xtab(2) = -0.268666945261773544694327777841D+00
    6517. 

  6517. <a name="l06453"></a>06453     xtab(3) =  0.220227225868961343518209179230D+00
    6518. 

  6518. <a name="l06454"></a>06454     xtab(4) =  0.653039358456608553790815164028D+00
    6519. 

  6519. <a name="l06455"></a>06455     xtab(5) =  0.930842120163569816951085142737D+00
    6520. 

  6520. <a name="l06456"></a>06456 
    6521. 

  6521. <a name="l06457"></a>06457     weight(1) =  0.0329106016247920636689299329544D+00
    6522. 

  6522. <a name="l06458"></a>06458     weight(2) =  0.256444805783695354037991444453D+00
    6523. 

  6523. <a name="l06459"></a>06459     weight(3) =  0.713601289772720001490035944563D+00
    6524. 

  6524. <a name="l06460"></a>06460     weight(4) =  1.00959169519929190423066348132D+00
    6525. 

  6525. <a name="l06461"></a>06461     weight(5) =  0.654118274286167343239045863379D+00
    6526. 

  6526. <a name="l06462"></a>06462 
    6527. 

  6527. <a name="l06463"></a>06463   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    6528. 

  6528. <a name="l06464"></a>06464 
    6529. 

  6529. <a name="l06465"></a>06465     xtab(1) = -0.773611232355123732602532012021D+00
    6530. 

  6530. <a name="l06466"></a>06466     xtab(2) = -0.431362254623427837535325249187D+00
    6531. 

  6531. <a name="l06467"></a>06467     xtab(3) = -0.0180728263295041680220798103354D+00
    6532. 

  6532. <a name="l06468"></a>06468     xtab(4) =  0.395126163954217534500188844163D+00
    6533. 

  6533. <a name="l06469"></a>06469     xtab(5) =  0.736872116684029732026178298518D+00
    6534. 

  6534. <a name="l06470"></a>06470     xtab(6) =  0.948190889812665614490712786006D+00
    6535. 

  6535. <a name="l06471"></a>06471 
    6536. 

  6536. <a name="l06472"></a>06472     weight(1) =  0.0146486064549543818622276447204D+00
    6537. 

  6537. <a name="l06473"></a>06473     weight(2) =  0.125762377479560410622810097040D+00
    6538. 

  6538. <a name="l06474"></a>06474     weight(3) =  0.410316569036929681761034600615D+00
    6539. 

  6539. <a name="l06475"></a>06475     weight(4) =  0.756617493988329628546336413760D+00
    6540. 

  6540. <a name="l06476"></a>06476     weight(5) =  0.859011997894245060846045458784D+00
    6541. 

  6541. <a name="l06477"></a>06477     weight(6) =  0.500309621812647503028212451747D+00
    6542. 

  6542. <a name="l06478"></a>06478 
    6543. 

  6543. <a name="l06479"></a>06479   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    6544. 

  6544. <a name="l06480"></a>06480 
    6545. 

  6545. <a name="l06481"></a>06481     xtab(1) = -0.822366333126005527278634734418D+00
    6546. 

  6546. <a name="l06482"></a>06482     xtab(2) = -0.547034493182875002223997992852D+00
    6547. 

  6547. <a name="l06483"></a>06483     xtab(3) = -0.200043026557985860387937545780D+00
    6548. 

  6548. <a name="l06484"></a>06484     xtab(4) =  0.171995710805880507163425502299D+00
    6549. 

  6549. <a name="l06485"></a>06485     xtab(5) =  0.518891747903884926692601716998D+00
    6550. 

  6550. <a name="l06486"></a>06486     xtab(6) =  0.793821941703901970495546427988D+00
    6551. 

  6551. <a name="l06487"></a>06487     xtab(7) =  0.959734452453198985538996625765D+00
    6552. 

  6552. <a name="l06488"></a>06488 
    6553. 

  6553. <a name="l06489"></a>06489     weight(1) =  0.00714150426951365443207221475404D+00
    6554. 

  6554. <a name="l06490"></a>06490     weight(2) =  0.0653034050584375560578544725498D+00
    6555. 

  6555. <a name="l06491"></a>06491     weight(3) =  0.235377690316228918725962815880D+00
    6556. 

  6556. <a name="l06492"></a>06492     weight(4) =  0.505171029671130381676271523850D+00
    6557. 

  6557. <a name="l06493"></a>06493     weight(5) =  0.733870426238362032891332767175D+00
    6558. 

  6558. <a name="l06494"></a>06494     weight(6) =  0.725590596901489156295739839779D+00
    6559. 

  6559. <a name="l06495"></a>06495     weight(7) =  0.394212014211504966587433032679D+00
    6560. 

  6560. <a name="l06496"></a>06496 
    6561. 

  6561. <a name="l06497"></a>06497   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    6562. 

  6562. <a name="l06498"></a>06498 
    6563. 

  6563. <a name="l06499"></a>06499     xtab(1) = -0.857017929919813794402037235698D+00
    6564. 

  6564. <a name="l06500"></a>06500     xtab(2) = -0.631543407166567521509503573952D+00
    6565. 

  6565. <a name="l06501"></a>06501     xtab(3) = -0.339104543648722903660229021109D+00
    6566. 

  6566. <a name="l06502"></a>06502     xtab(4) = -0.0111941563689783438801237300122D+00
    6567. 

  6567. <a name="l06503"></a>06503     xtab(5) =  0.316696017045595559454075475675D+00
    6568. 

  6568. <a name="l06504"></a>06504     xtab(6) =  0.609049663022520165351466780939D+00
    6569. 

  6569. <a name="l06505"></a>06505     xtab(7) =  0.834198765028697794599267293239D+00
    6570. 

  6570. <a name="l06506"></a>06506     xtab(8) =  0.967804480896157932935972899807D+00
    6571. 

  6571. <a name="l06507"></a>06507 
    6572. 

  6572. <a name="l06508"></a>06508     weight(1) =  0.00374814227227757804631954025851D+00
    6573. 

  6573. <a name="l06509"></a>06509     weight(2) =  0.0357961737041152639660521680263D+00
    6574. 

  6574. <a name="l06510"></a>06510     weight(3) =  0.137974910241879862433949246199D+00
    6575. 

  6575. <a name="l06511"></a>06511     weight(4) =  0.326515411108352185491692769217D+00
    6576. 

  6576. <a name="l06512"></a>06512     weight(5) =  0.547577467373226177976217604887D+00
    6577. 

  6577. <a name="l06513"></a>06513     weight(6) =  0.682278153375510121675529810121D+00
    6578. 

  6578. <a name="l06514"></a>06514     weight(7) =  0.614544746137780998436053880546D+00
    6579. 

  6579. <a name="l06515"></a>06515     weight(8) =  0.318231662453524478640851647411D+00
    6580. 

  6580. <a name="l06516"></a>06516 
    6581. 

  6581. <a name="l06517"></a>06517   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    6582. 

  6582. <a name="l06518"></a>06518 
    6583. 

  6583. <a name="l06519"></a>06519     xtab(1) = -0.882491728426548422828684254270D+00
    6584. 

  6584. <a name="l06520"></a>06520     xtab(2) = -0.694873684026474640346360850039D+00
    6585. 

  6585. <a name="l06521"></a>06521     xtab(3) = -0.446537143480670863635920316400D+00
    6586. 

  6586. <a name="l06522"></a>06522     xtab(4) = -0.159388112702326252531544826624D+00
    6587. 

  6587. <a name="l06523"></a>06523     xtab(5) =  0.141092709224374414981503995427D+00
    6588. 

  6588. <a name="l06524"></a>06524     xtab(6) =  0.428217823321559204544020866175D+00
    6589. 

  6589. <a name="l06525"></a>06525     xtab(7) =  0.676480966471850715860378175342D+00
    6590. 

  6590. <a name="l06526"></a>06526     xtab(8) =  0.863830940812464825046988286026D+00
    6591. 

  6591. <a name="l06527"></a>06527     xtab(9) =  0.973668228805771018909618924364D+00
    6592. 

  6592. <a name="l06528"></a>06528 
    6593. 

  6593. <a name="l06529"></a>06529     weight(1) =  0.00209009877215570354392734918986D+00
    6594. 

  6594. <a name="l06530"></a>06530     weight(2) =  0.0205951891648697848186537272448D+00
    6595. 

  6595. <a name="l06531"></a>06531     weight(3) =  0.0832489326348178964194106978875D+00
    6596. 

  6596. <a name="l06532"></a>06532     weight(4) =  0.210746247220398685903797568021D+00
    6597. 

  6597. <a name="l06533"></a>06533     weight(5) =  0.388325022916052063676224499399D+00
    6598. 

  6598. <a name="l06534"></a>06534     weight(6) =  0.554275165518437673725822282791D+00
    6599. 

  6599. <a name="l06535"></a>06535     weight(7) =  0.621388553284444032628761363828D+00
    6600. 

  6600. <a name="l06536"></a>06536     weight(8) =  0.523916296267173054255512857631D+00
    6601. 

  6601. <a name="l06537"></a>06537     weight(9) =  0.262081160888317771694556320674D+00
    6602. 

  6602. <a name="l06538"></a>06538 
    6603. 

  6603. <a name="l06539"></a>06539   <span class="keyword">else</span>
    6604. 

  6604. <a name="l06540"></a>06540 
    6605. 

  6605. <a name="l06541"></a>06541     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    6606. 

  6606. <a name="l06542"></a>06542     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_SET_X2 - Fatal error!&#39;</span>
    6607. 

  6607. <a name="l06543"></a>06543     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal input value of NORDER = &#39;</span>, norder
    6608. 

  6608. <a name="l06544"></a>06544     stop
    6609. 

  6609. <a name="l06545"></a>06545 
    6610. 

  6610. <a name="l06546"></a>06546   <span class="keyword">end if</span>
    6611. 

  6611. <a name="l06547"></a>06547 
    6612. 

  6612. <a name="l06548"></a>06548   return
    6613. 

  6613. <a name="l06549"></a>06549 <span class="keyword">end</span>
    6614. 

  6614. <a name="l06550"></a><a class="code" href="quadrule_8f90.html#a82fb68c4ded02b55802a7f1768f66d76">06550</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a82fb68c4ded02b55802a7f1768f66d76">legendre_set_x2_01</a> ( norder, xtab, weight )
    6615. 

  6615. <a name="l06551"></a>06551 <span class="comment">!</span>
    6616. 

  6616. <a name="l06552"></a>06552 <span class="comment">!*******************************************************************************</span>
    6617. 

  6617. <a name="l06553"></a>06553 <span class="comment">!</span>
    6618. 

  6618. <a name="l06554"></a>06554 <span class="comment">!! LEGENDRE_SET_X2_01 sets a Gauss-Legendre rule for X**2 * F(X) on [0,1].</span>
    6619. 

  6619. <a name="l06555"></a>06555 <span class="comment">!</span>
    6620. 

  6620. <a name="l06556"></a>06556 <span class="comment">!</span>
    6621. 

  6621. <a name="l06557"></a>06557 <span class="comment">!  Integration interval:</span>
    6622. 

  6622. <a name="l06558"></a>06558 <span class="comment">!</span>
    6623. 

  6623. <a name="l06559"></a>06559 <span class="comment">!    [ 0, 1 ]</span>
    6624. 

  6624. <a name="l06560"></a>06560 <span class="comment">!</span>
    6625. 

  6625. <a name="l06561"></a>06561 <span class="comment">!  Weight function:</span>
    6626. 

  6626. <a name="l06562"></a>06562 <span class="comment">!</span>
    6627. 

  6627. <a name="l06563"></a>06563 <span class="comment">!    X**2</span>
    6628. 

  6628. <a name="l06564"></a>06564 <span class="comment">!</span>
    6629. 

  6629. <a name="l06565"></a>06565 <span class="comment">!  Integral to approximate:</span>
    6630. 

  6630. <a name="l06566"></a>06566 <span class="comment">!</span>
    6631. 

  6631. <a name="l06567"></a>06567 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) X*X * F(X) dX</span>
    6632. 

  6632. <a name="l06568"></a>06568 <span class="comment">!</span>
    6633. 

  6633. <a name="l06569"></a>06569 <span class="comment">!  Approximate integral:</span>
    6634. 

  6634. <a name="l06570"></a>06570 <span class="comment">!</span>
    6635. 

  6635. <a name="l06571"></a>06571 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    6636. 

  6636. <a name="l06572"></a>06572 <span class="comment">!</span>
    6637. 

  6637. <a name="l06573"></a>06573 <span class="comment">!  Reference:</span>
    6638. 

  6638. <a name="l06574"></a>06574 <span class="comment">!</span>
    6639. 

  6639. <a name="l06575"></a>06575 <span class="comment">!    Abramowitz and Stegun,</span>
    6640. 

  6640. <a name="l06576"></a>06576 <span class="comment">!    Handbook of Mathematical Functions,</span>
    6641. 

  6641. <a name="l06577"></a>06577 <span class="comment">!    National Bureau of Standards, 1964, page 921.</span>
    6642. 

  6642. <a name="l06578"></a>06578 <span class="comment">!</span>
    6643. 

  6643. <a name="l06579"></a>06579 <span class="comment">!  Modified:</span>
    6644. 

  6644. <a name="l06580"></a>06580 <span class="comment">!</span>
    6645. 

  6645. <a name="l06581"></a>06581 <span class="comment">!    18 November 2000</span>
    6646. 

  6646. <a name="l06582"></a>06582 <span class="comment">!</span>
    6647. 

  6647. <a name="l06583"></a>06583 <span class="comment">!  Author:</span>
    6648. 

  6648. <a name="l06584"></a>06584 <span class="comment">!</span>
    6649. 

  6649. <a name="l06585"></a>06585 <span class="comment">!    John Burkardt</span>
    6650. 

  6650. <a name="l06586"></a>06586 <span class="comment">!</span>
    6651. 

  6651. <a name="l06587"></a>06587 <span class="comment">!  Parameters:</span>
    6652. 

  6652. <a name="l06588"></a>06588 <span class="comment">!</span>
    6653. 

  6653. <a name="l06589"></a>06589 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    6654. 

  6654. <a name="l06590"></a>06590 <span class="comment">!    NORDER must be between 1 and 8.</span>
    6655. 

  6655. <a name="l06591"></a>06591 <span class="comment">!</span>
    6656. 

  6656. <a name="l06592"></a>06592 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    6657. 

  6657. <a name="l06593"></a>06593 <span class="comment">!</span>
    6658. 

  6658. <a name="l06594"></a>06594 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    6659. 

  6659. <a name="l06595"></a>06595 <span class="comment">!</span>
    6660. 

  6660. <a name="l06596"></a>06596   <span class="keyword">implicit none</span>
    6661. 

  6661. <a name="l06597"></a>06597 <span class="comment">!</span>
    6662. 

  6662. <a name="l06598"></a>06598   <span class="keywordtype">integer</span> norder
    6663. 

  6663. <a name="l06599"></a>06599 <span class="comment">!</span>
    6664. 

  6664. <a name="l06600"></a>06600   <span class="keywordtype">double precision</span> xtab(norder)
    6665. 

  6665. <a name="l06601"></a>06601   <span class="keywordtype">double precision</span> weight(norder)
    6666. 

  6666. <a name="l06602"></a>06602 <span class="comment">!</span>
    6667. 

  6667. <a name="l06603"></a>06603   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    6668. 

  6668. <a name="l06604"></a>06604 
    6669. 

  6669. <a name="l06605"></a>06605     xtab(1) =   0.75D+00
    6670. 

  6670. <a name="l06606"></a>06606 
    6671. 

  6671. <a name="l06607"></a>06607     weight(1) = 1.0D+00 / 3.0D+00
    6672. 

  6672. <a name="l06608"></a>06608 
    6673. 

  6673. <a name="l06609"></a>06609   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    6674. 

  6674. <a name="l06610"></a>06610 
    6675. 

  6675. <a name="l06611"></a>06611     xtab(1) = 0.4558481560D+00
    6676. 

  6676. <a name="l06612"></a>06612     xtab(2) = 0.8774851773D+00
    6677. 

  6677. <a name="l06613"></a>06613 
    6678. 

  6678. <a name="l06614"></a>06614     weight(1) = 0.1007858821D+00
    6679. 

  6679. <a name="l06615"></a>06615     weight(2) = 0.2325474513D+00
    6680. 

  6680. <a name="l06616"></a>06616 
    6681. 

  6681. <a name="l06617"></a>06617   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    6682. 

  6682. <a name="l06618"></a>06618 
    6683. 

  6683. <a name="l06619"></a>06619     xtab(1) = 0.2949977901D+00
    6684. 

  6684. <a name="l06620"></a>06620     xtab(2) = 0.6529962340D+00
    6685. 

  6685. <a name="l06621"></a>06621     xtab(3) = 0.9270059759D+00
    6686. 

  6686. <a name="l06622"></a>06622 
    6687. 

  6687. <a name="l06623"></a>06623     weight(1) = 0.0299507030D+00
    6688. 

  6688. <a name="l06624"></a>06624     weight(2) = 0.1462462693D+00
    6689. 

  6689. <a name="l06625"></a>06625     weight(3) = 0.1571363611D+00
    6690. 

  6690. <a name="l06626"></a>06626 
    6691. 

  6691. <a name="l06627"></a>06627   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    6692. 

  6692. <a name="l06628"></a>06628 
    6693. 

  6693. <a name="l06629"></a>06629     xtab(1) = 0.2041485821D+00
    6694. 

  6694. <a name="l06630"></a>06630     xtab(2) = 0.4829527049D+00
    6695. 

  6695. <a name="l06631"></a>06631     xtab(3) = 0.7613992624D+00
    6696. 

  6696. <a name="l06632"></a>06632     xtab(4) = 0.9514994506D+00
    6697. 

  6697. <a name="l06633"></a>06633 
    6698. 

  6698. <a name="l06634"></a>06634     weight(1) = 0.0103522408D+00
    6699. 

  6699. <a name="l06635"></a>06635     weight(2) = 0.0686338872D+00
    6700. 

  6700. <a name="l06636"></a>06636     weight(3) = 0.1434587898D+00
    6701. 

  6701. <a name="l06637"></a>06637     weight(4) = 0.1108884156D+00
    6702. 

  6702. <a name="l06638"></a>06638 
    6703. 

  6703. <a name="l06639"></a>06639   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    6704. 

  6704. <a name="l06640"></a>06640 
    6705. 

  6705. <a name="l06641"></a>06641     xtab(1) = 0.1489457871D+00
    6706. 

  6706. <a name="l06642"></a>06642     xtab(2) = 0.3656665274D+00
    6707. 

  6707. <a name="l06643"></a>06643     xtab(3) = 0.6101136129D+00
    6708. 

  6708. <a name="l06644"></a>06644     xtab(4) = 0.8265196792D+00
    6709. 

  6709. <a name="l06645"></a>06645     xtab(5) = 0.9654210601D+00
    6710. 

  6710. <a name="l06646"></a>06646 
    6711. 

  6711. <a name="l06647"></a>06647     weight(1) = 0.0041138252D+00
    6712. 

  6712. <a name="l06648"></a>06648     weight(2) = 0.0320556007D+00
    6713. 

  6713. <a name="l06649"></a>06649     weight(3) = 0.0892001612D+00
    6714. 

  6714. <a name="l06650"></a>06650     weight(4) = 0.1261989619D+00
    6715. 

  6715. <a name="l06651"></a>06651     weight(5) = 0.0817647843D+00
    6716. 

  6716. <a name="l06652"></a>06652 
    6717. 

  6717. <a name="l06653"></a>06653   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    6718. 

  6718. <a name="l06654"></a>06654 
    6719. 

  6719. <a name="l06655"></a>06655     xtab(1) = 0.1131943838D+00
    6720. 

  6720. <a name="l06656"></a>06656     xtab(2) = 0.2843188727D+00
    6721. 

  6721. <a name="l06657"></a>06657     xtab(3) = 0.4909635868D+00
    6722. 

  6722. <a name="l06658"></a>06658     xtab(4) = 0.6975630820D+00
    6723. 

  6723. <a name="l06659"></a>06659     xtab(5) = 0.8684360583D+00
    6724. 

  6724. <a name="l06660"></a>06660     xtab(6) = 0.9740954449D+00
    6725. 

  6725. <a name="l06661"></a>06661 
    6726. 

  6726. <a name="l06662"></a>06662     weight(1) = 0.0018310758D+00
    6727. 

  6727. <a name="l06663"></a>06663     weight(2) = 0.0157202972D+00
    6728. 

  6728. <a name="l06664"></a>06664     weight(3) = 0.0512895711D+00
    6729. 

  6729. <a name="l06665"></a>06665     weight(4) = 0.0945771867D+00
    6730. 

  6730. <a name="l06666"></a>06666     weight(5) = 0.1073764997D+00
    6731. 

  6731. <a name="l06667"></a>06667     weight(6) = 0.0625387027D+00
    6732. 

  6732. <a name="l06668"></a>06668 
    6733. 

  6733. <a name="l06669"></a>06669   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    6734. 

  6734. <a name="l06670"></a>06670 
    6735. 

  6735. <a name="l06671"></a>06671     xtab(1) = 0.0888168334D+00
    6736. 

  6736. <a name="l06672"></a>06672     xtab(2) = 0.2264827534D+00
    6737. 

  6737. <a name="l06673"></a>06673     xtab(3) = 0.3999784867D+00
    6738. 

  6738. <a name="l06674"></a>06674     xtab(4) = 0.5859978554D+00
    6739. 

  6739. <a name="l06675"></a>06675     xtab(5) = 0.7594458740D+00
    6740. 

  6740. <a name="l06676"></a>06676     xtab(6) = 0.8969109709D+00
    6741. 

  6741. <a name="l06677"></a>06677     xtab(7) = 0.9798672262D+00
    6742. 

  6742. <a name="l06678"></a>06678 
    6743. 

  6743. <a name="l06679"></a>06679     weight(1) = 0.0008926880D+00
    6744. 

  6744. <a name="l06680"></a>06680     weight(2) = 0.0081629256D+00
    6745. 

  6745. <a name="l06681"></a>06681     weight(3) = 0.0294222113D+00
    6746. 

  6746. <a name="l06682"></a>06682     weight(4) = 0.0631463787D+00
    6747. 

  6747. <a name="l06683"></a>06683     weight(5) = 0.0917338033D+00
    6748. 

  6748. <a name="l06684"></a>06684     weight(6) = 0.0906988246D+00
    6749. 

  6749. <a name="l06685"></a>06685     weight(7) = 0.0492765018D+00
    6750. 

  6750. <a name="l06686"></a>06686 
    6751. 

  6751. <a name="l06687"></a>06687   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    6752. 

  6752. <a name="l06688"></a>06688 
    6753. 

  6753. <a name="l06689"></a>06689     xtab(1) = 0.0714910350D+00
    6754. 

  6754. <a name="l06690"></a>06690     xtab(2) = 0.1842282964D+00
    6755. 

  6755. <a name="l06691"></a>06691     xtab(3) = 0.3304477282D+00
    6756. 

  6756. <a name="l06692"></a>06692     xtab(4) = 0.4944029218D+00
    6757. 

  6757. <a name="l06693"></a>06693     xtab(5) = 0.6583480085D+00
    6758. 

  6758. <a name="l06694"></a>06694     xtab(6) = 0.8045248315D+00
    6759. 

  6759. <a name="l06695"></a>06695     xtab(7) = 0.9170993825D+00
    6760. 

  6760. <a name="l06696"></a>06696     xtab(8) = 0.9839022404D+00
    6761. 

  6761. <a name="l06697"></a>06697 
    6762. 

  6762. <a name="l06698"></a>06698     weight(1) = 0.0004685178D+00
    6763. 

  6763. <a name="l06699"></a>06699     weight(2) = 0.0044745217D+00
    6764. 

  6764. <a name="l06700"></a>06700     weight(3) = 0.0172468638D+00
    6765. 

  6765. <a name="l06701"></a>06701     weight(4) = 0.0408144264D+00
    6766. 

  6766. <a name="l06702"></a>06702     weight(5) = 0.0684471834D+00
    6767. 

  6767. <a name="l06703"></a>06703     weight(6) = 0.0852847692D+00
    6768. 

  6768. <a name="l06704"></a>06704     weight(7) = 0.0768180933D+00
    6769. 

  6769. <a name="l06705"></a>06705     weight(8) = 0.0397789578D+00
    6770. 

  6770. <a name="l06706"></a>06706 
    6771. 

  6771. <a name="l06707"></a>06707   <span class="keyword">else</span>
    6772. 

  6772. <a name="l06708"></a>06708 
    6773. 

  6773. <a name="l06709"></a>06709     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    6774. 

  6774. <a name="l06710"></a>06710     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LEGENDRE_SET_X2_01 - Fatal error!&#39;</span>
    6775. 

  6775. <a name="l06711"></a>06711     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    6776. 

  6776. <a name="l06712"></a>06712     stop
    6777. 

  6777. <a name="l06713"></a>06713 
    6778. 

  6778. <a name="l06714"></a>06714   <span class="keyword">end if</span>
    6779. 

  6779. <a name="l06715"></a>06715 
    6780. 

  6780. <a name="l06716"></a>06716   return
    6781. 

  6781. <a name="l06717"></a>06717 <span class="keyword">end</span>
    6782. 

  6782. <a name="l06718"></a><a class="code" href="quadrule_8f90.html#a78a0044231676591f20f6a799a9177cd">06718</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a78a0044231676591f20f6a799a9177cd">lobatto_set</a> ( norder, xtab, weight )
    6783. 

  6783. <a name="l06719"></a>06719 <span class="comment">!</span>
    6784. 

  6784. <a name="l06720"></a>06720 <span class="comment">!*******************************************************************************</span>
    6785. 

  6785. <a name="l06721"></a>06721 <span class="comment">!</span>
    6786. 

  6786. <a name="l06722"></a>06722 <span class="comment">!! LOBATTO_SET sets abscissas and weights for Lobatto quadrature.</span>
    6787. 

  6787. <a name="l06723"></a>06723 <span class="comment">!</span>
    6788. 

  6788. <a name="l06724"></a>06724 <span class="comment">!</span>
    6789. 

  6789. <a name="l06725"></a>06725 <span class="comment">!  Integration interval:</span>
    6790. 

  6790. <a name="l06726"></a>06726 <span class="comment">!</span>
    6791. 

  6791. <a name="l06727"></a>06727 <span class="comment">!    [ -1, 1 ].</span>
    6792. 

  6792. <a name="l06728"></a>06728 <span class="comment">!</span>
    6793. 

  6793. <a name="l06729"></a>06729 <span class="comment">!  Weight function:</span>
    6794. 

  6794. <a name="l06730"></a>06730 <span class="comment">!</span>
    6795. 

  6795. <a name="l06731"></a>06731 <span class="comment">!    1.0D+00</span>
    6796. 

  6796. <a name="l06732"></a>06732 <span class="comment">!</span>
    6797. 

  6797. <a name="l06733"></a>06733 <span class="comment">!  Integral to approximate:</span>
    6798. 

  6798. <a name="l06734"></a>06734 <span class="comment">!</span>
    6799. 

  6799. <a name="l06735"></a>06735 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    6800. 

  6800. <a name="l06736"></a>06736 <span class="comment">!</span>
    6801. 

  6801. <a name="l06737"></a>06737 <span class="comment">!  Approximate integral:</span>
    6802. 

  6802. <a name="l06738"></a>06738 <span class="comment">!</span>
    6803. 

  6803. <a name="l06739"></a>06739 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    6804. 

  6804. <a name="l06740"></a>06740 <span class="comment">!</span>
    6805. 

  6805. <a name="l06741"></a>06741 <span class="comment">!  Precision:</span>
    6806. 

  6806. <a name="l06742"></a>06742 <span class="comment">!</span>
    6807. 

  6807. <a name="l06743"></a>06743 <span class="comment">!    The quadrature rule will integrate exactly all polynomials up to</span>
    6808. 

  6808. <a name="l06744"></a>06744 <span class="comment">!    X**(2*NORDER-3).</span>
    6809. 

  6809. <a name="l06745"></a>06745 <span class="comment">!</span>
    6810. 

  6810. <a name="l06746"></a>06746 <span class="comment">!  Note:</span>
    6811. 

  6811. <a name="l06747"></a>06747 <span class="comment">!</span>
    6812. 

  6812. <a name="l06748"></a>06748 <span class="comment">!    The Lobatto rule is distinguished by the fact that both endpoints</span>
    6813. 

  6813. <a name="l06749"></a>06749 <span class="comment">!    (-1 and 1) are always abscissas of the rule.</span>
    6814. 

  6814. <a name="l06750"></a>06750 <span class="comment">!</span>
    6815. 

  6815. <a name="l06751"></a>06751 <span class="comment">!  Reference:</span>
    6816. 

  6816. <a name="l06752"></a>06752 <span class="comment">!</span>
    6817. 

  6817. <a name="l06753"></a>06753 <span class="comment">!    Abramowitz and Stegun,</span>
    6818. 

  6818. <a name="l06754"></a>06754 <span class="comment">!    Handbook of Mathematical Functions,</span>
    6819. 

  6819. <a name="l06755"></a>06755 <span class="comment">!    National Bureau of Standards, 1964.</span>
    6820. 

  6820. <a name="l06756"></a>06756 <span class="comment">!</span>
    6821. 

  6821. <a name="l06757"></a>06757 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    6822. 

  6822. <a name="l06758"></a>06758 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    6823. 

  6823. <a name="l06759"></a>06759 <span class="comment">!    Prentice Hall, 1966.</span>
    6824. 

  6824. <a name="l06760"></a>06760 <span class="comment">!</span>
    6825. 

  6825. <a name="l06761"></a>06761 <span class="comment">!    Daniel Zwillinger, editor,</span>
    6826. 

  6826. <a name="l06762"></a>06762 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    6827. 

  6827. <a name="l06763"></a>06763 <span class="comment">!    30th Edition,</span>
    6828. 

  6828. <a name="l06764"></a>06764 <span class="comment">!    CRC Press, 1996.</span>
    6829. 

  6829. <a name="l06765"></a>06765 <span class="comment">!</span>
    6830. 

  6830. <a name="l06766"></a>06766 <span class="comment">!  Modified:</span>
    6831. 

  6831. <a name="l06767"></a>06767 <span class="comment">!</span>
    6832. 

  6832. <a name="l06768"></a>06768 <span class="comment">!    20 September 1998</span>
    6833. 

  6833. <a name="l06769"></a>06769 <span class="comment">!</span>
    6834. 

  6834. <a name="l06770"></a>06770 <span class="comment">!  Author:</span>
    6835. 

  6835. <a name="l06771"></a>06771 <span class="comment">!</span>
    6836. 

  6836. <a name="l06772"></a>06772 <span class="comment">!    John Burkardt</span>
    6837. 

  6837. <a name="l06773"></a>06773 <span class="comment">!</span>
    6838. 

  6838. <a name="l06774"></a>06774 <span class="comment">!  Parameters:</span>
    6839. 

  6839. <a name="l06775"></a>06775 <span class="comment">!</span>
    6840. 

  6840. <a name="l06776"></a>06776 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    6841. 

  6841. <a name="l06777"></a>06777 <span class="comment">!    NORDER must be between 2 and 20.</span>
    6842. 

  6842. <a name="l06778"></a>06778 <span class="comment">!</span>
    6843. 

  6843. <a name="l06779"></a>06779 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas for the rule.</span>
    6844. 

  6844. <a name="l06780"></a>06780 <span class="comment">!</span>
    6845. 

  6845. <a name="l06781"></a>06781 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    6846. 

  6846. <a name="l06782"></a>06782 <span class="comment">!    The weights are positive, symmetric and should sum to 2.</span>
    6847. 

  6847. <a name="l06783"></a>06783 <span class="comment">!</span>
    6848. 

  6848. <a name="l06784"></a>06784   <span class="keyword">implicit none</span>
    6849. 

  6849. <a name="l06785"></a>06785 <span class="comment">!</span>
    6850. 

  6850. <a name="l06786"></a>06786   <span class="keywordtype">integer</span> norder
    6851. 

  6851. <a name="l06787"></a>06787 <span class="comment">!</span>
    6852. 

  6852. <a name="l06788"></a>06788   <span class="keywordtype">double precision</span> xtab(norder)
    6853. 

  6853. <a name="l06789"></a>06789   <span class="keywordtype">double precision</span> weight(norder)
    6854. 

  6854. <a name="l06790"></a>06790 <span class="comment">!</span>
    6855. 

  6855. <a name="l06791"></a>06791   <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    6856. 

  6856. <a name="l06792"></a>06792 
    6857. 

  6857. <a name="l06793"></a>06793     xtab(1) =  - 1.0D+00
    6858. 

  6858. <a name="l06794"></a>06794     xtab(2) =    1.0D+00
    6859. 

  6859. <a name="l06795"></a>06795 
    6860. 

  6860. <a name="l06796"></a>06796     weight(1) =  1.0D+00
    6861. 

  6861. <a name="l06797"></a>06797     weight(2) =  1.0D+00
    6862. 

  6862. <a name="l06798"></a>06798 
    6863. 

  6863. <a name="l06799"></a>06799   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    6864. 

  6864. <a name="l06800"></a>06800 
    6865. 

  6865. <a name="l06801"></a>06801     xtab(1) =  - 1.0D+00
    6866. 

  6866. <a name="l06802"></a>06802     xtab(2) =    0.0D+00
    6867. 

  6867. <a name="l06803"></a>06803     xtab(3) =    1.0D+00
    6868. 

  6868. <a name="l06804"></a>06804 
    6869. 

  6869. <a name="l06805"></a>06805     weight(1) =  1.0D+00 / 3.0D+00
    6870. 

  6870. <a name="l06806"></a>06806     weight(2) =  4.0D+00 / 3.0D+00
    6871. 

  6871. <a name="l06807"></a>06807     weight(3) =  1.0D+00 / 3.0D+00
    6872. 

  6872. <a name="l06808"></a>06808 
    6873. 

  6873. <a name="l06809"></a>06809   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    6874. 

  6874. <a name="l06810"></a>06810 
    6875. 

  6875. <a name="l06811"></a>06811     xtab(1) =  - 1.0D+00
    6876. 

  6876. <a name="l06812"></a>06812     xtab(2) =  - 0.447213595499957939281834733746D+00
    6877. 

  6877. <a name="l06813"></a>06813     xtab(3) =    0.447213595499957939281834733746D+00
    6878. 

  6878. <a name="l06814"></a>06814     xtab(4) =    1.0D+00
    6879. 

  6879. <a name="l06815"></a>06815 
    6880. 

  6880. <a name="l06816"></a>06816     weight(1) =  1.0D+00 / 6.0D+00
    6881. 

  6881. <a name="l06817"></a>06817     weight(2) =  5.0D+00 / 6.0D+00
    6882. 

  6882. <a name="l06818"></a>06818     weight(3) =  5.0D+00 / 6.0D+00
    6883. 

  6883. <a name="l06819"></a>06819     weight(4) =  1.0D+00 / 6.0D+00
    6884. 

  6884. <a name="l06820"></a>06820 
    6885. 

  6885. <a name="l06821"></a>06821   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    6886. 

  6886. <a name="l06822"></a>06822 
    6887. 

  6887. <a name="l06823"></a>06823     xtab(1) =  - 1.0D+00
    6888. 

  6888. <a name="l06824"></a>06824     xtab(2) =  - 0.654653670707977143798292456247D+00
    6889. 

  6889. <a name="l06825"></a>06825     xtab(3) =    0.0D+00
    6890. 

  6890. <a name="l06826"></a>06826     xtab(4) =    0.654653670707977143798292456247D+00
    6891. 

  6891. <a name="l06827"></a>06827     xtab(5) =    1.0D+00
    6892. 

  6892. <a name="l06828"></a>06828 
    6893. 

  6893. <a name="l06829"></a>06829     weight(1) =  9.0D+00 / 90.0D+00
    6894. 

  6894. <a name="l06830"></a>06830     weight(2) = 49.0D+00 / 90.0D+00
    6895. 

  6895. <a name="l06831"></a>06831     weight(3) = 64.0D+00 / 90.0D+00
    6896. 

  6896. <a name="l06832"></a>06832     weight(4) = 49.0D+00 / 90.0D+00
    6897. 

  6897. <a name="l06833"></a>06833     weight(5) =  9.0D+00 / 90.0D+00
    6898. 

  6898. <a name="l06834"></a>06834 
    6899. 

  6899. <a name="l06835"></a>06835   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    6900. 

  6900. <a name="l06836"></a>06836 
    6901. 

  6901. <a name="l06837"></a>06837     xtab(1) =  - 1.0D+00
    6902. 

  6902. <a name="l06838"></a>06838     xtab(2) =  - 0.765055323929464692851002973959D+00
    6903. 

  6903. <a name="l06839"></a>06839     xtab(3) =  - 0.285231516480645096314150994041D+00
    6904. 

  6904. <a name="l06840"></a>06840     xtab(4) =    0.285231516480645096314150994041D+00
    6905. 

  6905. <a name="l06841"></a>06841     xtab(5) =    0.765055323929464692851002973959D+00
    6906. 

  6906. <a name="l06842"></a>06842     xtab(6) =    1.0D+00
    6907. 

  6907. <a name="l06843"></a>06843 
    6908. 

  6908. <a name="l06844"></a>06844     weight(1) =  0.066666666666666666666666666667D+00
    6909. 

  6909. <a name="l06845"></a>06845     weight(2) =  0.378474956297846980316612808212D+00
    6910. 

  6910. <a name="l06846"></a>06846     weight(3) =  0.554858377035486353016720525121D+00
    6911. 

  6911. <a name="l06847"></a>06847     weight(4) =  0.554858377035486353016720525121D+00
    6912. 

  6912. <a name="l06848"></a>06848     weight(5) =  0.378474956297846980316612808212D+00
    6913. 

  6913. <a name="l06849"></a>06849     weight(6) =  0.066666666666666666666666666667D+00
    6914. 

  6914. <a name="l06850"></a>06850 
    6915. 

  6915. <a name="l06851"></a>06851   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    6916. 

  6916. <a name="l06852"></a>06852 
    6917. 

  6917. <a name="l06853"></a>06853     xtab(1) =  - 1.0D+00
    6918. 

  6918. <a name="l06854"></a>06854     xtab(2) =  - 0.830223896278566929872032213967D+00
    6919. 

  6919. <a name="l06855"></a>06855     xtab(3) =  - 0.468848793470714213803771881909D+00
    6920. 

  6920. <a name="l06856"></a>06856     xtab(4) =    0.0D+00
    6921. 

  6921. <a name="l06857"></a>06857     xtab(5) =    0.468848793470714213803771881909D+00
    6922. 

  6922. <a name="l06858"></a>06858     xtab(6) =    0.830223896278566929872032213967D+00
    6923. 

  6923. <a name="l06859"></a>06859     xtab(7) =    1.0D+00
    6924. 

  6924. <a name="l06860"></a>06860 
    6925. 

  6925. <a name="l06861"></a>06861     weight(1) =  0.476190476190476190476190476190D-01
    6926. 

  6926. <a name="l06862"></a>06862     weight(2) =  0.276826047361565948010700406290D+00
    6927. 

  6927. <a name="l06863"></a>06863     weight(3) =  0.431745381209862623417871022281D+00
    6928. 

  6928. <a name="l06864"></a>06864     weight(4) =  0.487619047619047619047619047619D+00
    6929. 

  6929. <a name="l06865"></a>06865     weight(5) =  0.431745381209862623417871022281D+00
    6930. 

  6930. <a name="l06866"></a>06866     weight(6) =  0.276826047361565948010700406290D+00
    6931. 

  6931. <a name="l06867"></a>06867     weight(7) =  0.476190476190476190476190476190D-01
    6932. 

  6932. <a name="l06868"></a>06868 
    6933. 

  6933. <a name="l06869"></a>06869   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    6934. 

  6934. <a name="l06870"></a>06870 
    6935. 

  6935. <a name="l06871"></a>06871     xtab(1) =  - 1.0D+00
    6936. 

  6936. <a name="l06872"></a>06872     xtab(2) =  - 0.871740148509606615337445761221D+00
    6937. 

  6937. <a name="l06873"></a>06873     xtab(3) =  - 0.591700181433142302144510731398D+00
    6938. 

  6938. <a name="l06874"></a>06874     xtab(4) =  - 0.209299217902478868768657260345D+00
    6939. 

  6939. <a name="l06875"></a>06875     xtab(5) =    0.209299217902478868768657260345D+00
    6940. 

  6940. <a name="l06876"></a>06876     xtab(6) =    0.591700181433142302144510731398D+00
    6941. 

  6941. <a name="l06877"></a>06877     xtab(7) =    0.871740148509606615337445761221D+00
    6942. 

  6942. <a name="l06878"></a>06878     xtab(8) =    1.0D+00
    6943. 

  6943. <a name="l06879"></a>06879 
    6944. 

  6944. <a name="l06880"></a>06880     weight(1) =  0.357142857142857142857142857143D-01
    6945. 

  6945. <a name="l06881"></a>06881     weight(2) =  0.210704227143506039382991065776D+00
    6946. 

  6946. <a name="l06882"></a>06882     weight(3) =  0.341122692483504364764240677108D+00
    6947. 

  6947. <a name="l06883"></a>06883     weight(4) =  0.412458794658703881567052971402D+00
    6948. 

  6948. <a name="l06884"></a>06884     weight(5) =  0.412458794658703881567052971402D+00
    6949. 

  6949. <a name="l06885"></a>06885     weight(6) =  0.341122692483504364764240677108D+00
    6950. 

  6950. <a name="l06886"></a>06886     weight(7) =  0.210704227143506039382991065776D+00
    6951. 

  6951. <a name="l06887"></a>06887     weight(8) =  0.357142857142857142857142857143D-01
    6952. 

  6952. <a name="l06888"></a>06888 
    6953. 

  6953. <a name="l06889"></a>06889   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    6954. 

  6954. <a name="l06890"></a>06890 
    6955. 

  6955. <a name="l06891"></a>06891     xtab(1) =  - 1.0D+00
    6956. 

  6956. <a name="l06892"></a>06892     xtab(2) =  - 0.899757995411460157312345244418D+00
    6957. 

  6957. <a name="l06893"></a>06893     xtab(3) =  - 0.677186279510737753445885427091D+00
    6958. 

  6958. <a name="l06894"></a>06894     xtab(4) =  - 0.363117463826178158710752068709D+00
    6959. 

  6959. <a name="l06895"></a>06895     xtab(5) =    0.0D+00
    6960. 

  6960. <a name="l06896"></a>06896     xtab(6) =    0.363117463826178158710752068709D+00
    6961. 

  6961. <a name="l06897"></a>06897     xtab(7) =    0.677186279510737753445885427091D+00
    6962. 

  6962. <a name="l06898"></a>06898     xtab(8) =    0.899757995411460157312345244418D+00
    6963. 

  6963. <a name="l06899"></a>06899     xtab(9) =    1.0D+00
    6964. 

  6964. <a name="l06900"></a>06900 
    6965. 

  6965. <a name="l06901"></a>06901     weight(1) =  0.277777777777777777777777777778D-01
    6966. 

  6966. <a name="l06902"></a>06902     weight(2) =  0.165495361560805525046339720029D+00
    6967. 

  6967. <a name="l06903"></a>06903     weight(3) =  0.274538712500161735280705618579D+00
    6968. 

  6968. <a name="l06904"></a>06904     weight(4) =  0.346428510973046345115131532140D+00
    6969. 

  6969. <a name="l06905"></a>06905     weight(5) =  0.371519274376417233560090702948D+00
    6970. 

  6970. <a name="l06906"></a>06906     weight(6) =  0.346428510973046345115131532140D+00
    6971. 

  6971. <a name="l06907"></a>06907     weight(7) =  0.274538712500161735280705618579D+00
    6972. 

  6972. <a name="l06908"></a>06908     weight(8) =  0.165495361560805525046339720029D+00
    6973. 

  6973. <a name="l06909"></a>06909     weight(9) =  0.277777777777777777777777777778D-01
    6974. 

  6974. <a name="l06910"></a>06910 
    6975. 

  6975. <a name="l06911"></a>06911   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
    6976. 

  6976. <a name="l06912"></a>06912 
    6977. 

  6977. <a name="l06913"></a>06913     xtab(1) =  - 1.0D+00
    6978. 

  6978. <a name="l06914"></a>06914     xtab(2) =  - 0.919533908166458813828932660822D+00
    6979. 

  6979. <a name="l06915"></a>06915     xtab(3) =  - 0.738773865105505075003106174860D+00
    6980. 

  6980. <a name="l06916"></a>06916     xtab(4) =  - 0.477924949810444495661175092731D+00
    6981. 

  6981. <a name="l06917"></a>06917     xtab(5) =  - 0.165278957666387024626219765958D+00
    6982. 

  6982. <a name="l06918"></a>06918     xtab(6) =    0.165278957666387024626219765958D+00
    6983. 

  6983. <a name="l06919"></a>06919     xtab(7) =    0.477924949810444495661175092731D+00
    6984. 

  6984. <a name="l06920"></a>06920     xtab(8) =    0.738773865105505075003106174860D+00
    6985. 

  6985. <a name="l06921"></a>06921     xtab(9) =    0.919533908166458813828932660822D+00
    6986. 

  6986. <a name="l06922"></a>06922     xtab(10) =   1.0D+00
    6987. 

  6987. <a name="l06923"></a>06923 
    6988. 

  6988. <a name="l06924"></a>06924     weight(1) =  0.222222222222222222222222222222D-01
    6989. 

  6989. <a name="l06925"></a>06925     weight(2) =  0.133305990851070111126227170755D+00
    6990. 

  6990. <a name="l06926"></a>06926     weight(3) =  0.224889342063126452119457821731D+00
    6991. 

  6991. <a name="l06927"></a>06927     weight(4) =  0.292042683679683757875582257374D+00
    6992. 

  6992. <a name="l06928"></a>06928     weight(5) =  0.327539761183897456656510527917D+00
    6993. 

  6993. <a name="l06929"></a>06929     weight(6) =  0.327539761183897456656510527917D+00
    6994. 

  6994. <a name="l06930"></a>06930     weight(7) =  0.292042683679683757875582257374D+00
    6995. 

  6995. <a name="l06931"></a>06931     weight(8) =  0.224889342063126452119457821731D+00
    6996. 

  6996. <a name="l06932"></a>06932     weight(9) =  0.133305990851070111126227170755D+00
    6997. 

  6997. <a name="l06933"></a>06933     weight(10) = 0.222222222222222222222222222222D-01
    6998. 

  6998. <a name="l06934"></a>06934 
    6999. 

  6999. <a name="l06935"></a>06935   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 11 ) <span class="keyword">then</span>
    7000. 

  7000. <a name="l06936"></a>06936 
    7001. 

  7001. <a name="l06937"></a>06937     xtab(1) =  - 1.0D+00
    7002. 

  7002. <a name="l06938"></a>06938     xtab(2) =  - 0.934001430408059134332274136099D+00
    7003. 

  7003. <a name="l06939"></a>06939     xtab(3) =  - 0.784483473663144418622417816108D+00
    7004. 

  7004. <a name="l06940"></a>06940     xtab(4) =  - 0.565235326996205006470963969478D+00
    7005. 

  7005. <a name="l06941"></a>06941     xtab(5) =  - 0.295758135586939391431911515559D+00
    7006. 

  7006. <a name="l06942"></a>06942     xtab(6) =    0.0D+00
    7007. 

  7007. <a name="l06943"></a>06943     xtab(7) =    0.295758135586939391431911515559D+00
    7008. 

  7008. <a name="l06944"></a>06944     xtab(8) =    0.565235326996205006470963969478D+00
    7009. 

  7009. <a name="l06945"></a>06945     xtab(9) =    0.784483473663144418622417816108D+00
    7010. 

  7010. <a name="l06946"></a>06946     xtab(10) =   0.934001430408059134332274136099D+00
    7011. 

  7011. <a name="l06947"></a>06947     xtab(11) =   1.0D+00
    7012. 

  7012. <a name="l06948"></a>06948 
    7013. 

  7013. <a name="l06949"></a>06949     weight(1) =  0.181818181818181818181818181818D-01
    7014. 

  7014. <a name="l06950"></a>06950     weight(2) =  0.109612273266994864461403449580D+00
    7015. 

  7015. <a name="l06951"></a>06951     weight(3) =  0.187169881780305204108141521899D+00
    7016. 

  7016. <a name="l06952"></a>06952     weight(4) =  0.248048104264028314040084866422D+00
    7017. 

  7017. <a name="l06953"></a>06953     weight(5) =  0.286879124779008088679222403332D+00
    7018. 

  7018. <a name="l06954"></a>06954     weight(6) =  0.300217595455690693785931881170D+00
    7019. 

  7019. <a name="l06955"></a>06955     weight(7) =  0.286879124779008088679222403332D+00
    7020. 

  7020. <a name="l06956"></a>06956     weight(8) =  0.248048104264028314040084866422D+00
    7021. 

  7021. <a name="l06957"></a>06957     weight(9) =  0.187169881780305204108141521899D+00
    7022. 

  7022. <a name="l06958"></a>06958     weight(10) = 0.109612273266994864461403449580D+00
    7023. 

  7023. <a name="l06959"></a>06959     weight(11) = 0.181818181818181818181818181818D-01
    7024. 

  7024. <a name="l06960"></a>06960 
    7025. 

  7025. <a name="l06961"></a>06961   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 12 ) <span class="keyword">then</span>
    7026. 

  7026. <a name="l06962"></a>06962 
    7027. 

  7027. <a name="l06963"></a>06963     xtab(1) =  - 1.0D+00
    7028. 

  7028. <a name="l06964"></a>06964     xtab(2) =  - 0.944899272222882223407580138303D+00
    7029. 

  7029. <a name="l06965"></a>06965     xtab(3) =  - 0.819279321644006678348641581717D+00
    7030. 

  7030. <a name="l06966"></a>06966     xtab(4) =  - 0.632876153031869677662404854444D+00
    7031. 

  7031. <a name="l06967"></a>06967     xtab(5) =  - 0.399530940965348932264349791567D+00
    7032. 

  7032. <a name="l06968"></a>06968     xtab(6) =  - 0.136552932854927554864061855740D+00
    7033. 

  7033. <a name="l06969"></a>06969     xtab(7) =    0.136552932854927554864061855740D+00
    7034. 

  7034. <a name="l06970"></a>06970     xtab(8) =    0.399530940965348932264349791567D+00
    7035. 

  7035. <a name="l06971"></a>06971     xtab(9) =    0.632876153031869677662404854444D+00
    7036. 

  7036. <a name="l06972"></a>06972     xtab(10) =   0.819279321644006678348641581717D+00
    7037. 

  7037. <a name="l06973"></a>06973     xtab(11) =   0.944899272222882223407580138303D+00
    7038. 

  7038. <a name="l06974"></a>06974     xtab(12) =   1.0D+00
    7039. 

  7039. <a name="l06975"></a>06975 
    7040. 

  7040. <a name="l06976"></a>06976     weight(1) =  0.151515151515151515151515151515D-01
    7041. 

  7041. <a name="l06977"></a>06977     weight(2) =  0.916845174131961306683425941341D-01
    7042. 

  7042. <a name="l06978"></a>06978     weight(3) =  0.157974705564370115164671062700D+00
    7043. 

  7043. <a name="l06979"></a>06979     weight(4) =  0.212508417761021145358302077367D+00
    7044. 

  7044. <a name="l06980"></a>06980     weight(5) =  0.251275603199201280293244412148D+00
    7045. 

  7045. <a name="l06981"></a>06981     weight(6) =  0.271405240910696177000288338500D+00
    7046. 

  7046. <a name="l06982"></a>06982     weight(7) =  0.271405240910696177000288338500D+00
    7047. 

  7047. <a name="l06983"></a>06983     weight(8) =  0.251275603199201280293244412148D+00
    7048. 

  7048. <a name="l06984"></a>06984     weight(9) =  0.212508417761021145358302077367D+00
    7049. 

  7049. <a name="l06985"></a>06985     weight(10) = 0.157974705564370115164671062700D+00
    7050. 

  7050. <a name="l06986"></a>06986     weight(11) = 0.916845174131961306683425941341D-01
    7051. 

  7051. <a name="l06987"></a>06987     weight(12) = 0.151515151515151515151515151515D-01
    7052. 

  7052. <a name="l06988"></a>06988 
    7053. 

  7053. <a name="l06989"></a>06989   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 13 ) <span class="keyword">then</span>
    7054. 

  7054. <a name="l06990"></a>06990 
    7055. 

  7055. <a name="l06991"></a>06991     xtab(1) =  - 1.0D+00
    7056. 

  7056. <a name="l06992"></a>06992     xtab(2) =  - 0.953309846642163911896905464755D+00
    7057. 

  7057. <a name="l06993"></a>06993     xtab(3) =  - 0.846347564651872316865925607099D+00
    7058. 

  7058. <a name="l06994"></a>06994     xtab(4) =  - 0.686188469081757426072759039566D+00
    7059. 

  7059. <a name="l06995"></a>06995     xtab(5) =  - 0.482909821091336201746937233637D+00
    7060. 

  7060. <a name="l06996"></a>06996     xtab(6) =  - 0.249286930106239992568673700374D+00
    7061. 

  7061. <a name="l06997"></a>06997     xtab(7) =    0.0D+00
    7062. 

  7062. <a name="l06998"></a>06998     xtab(8) =    0.249286930106239992568673700374D+00
    7063. 

  7063. <a name="l06999"></a>06999     xtab(9) =    0.482909821091336201746937233637D+00
    7064. 

  7064. <a name="l07000"></a>07000     xtab(10) =   0.686188469081757426072759039566D+00
    7065. 

  7065. <a name="l07001"></a>07001     xtab(11) =   0.846347564651872316865925607099D+00
    7066. 

  7066. <a name="l07002"></a>07002     xtab(12) =   0.953309846642163911896905464755D+00
    7067. 

  7067. <a name="l07003"></a>07003     xtab(13) =   1.0D+00
    7068. 

  7068. <a name="l07004"></a>07004 
    7069. 

  7069. <a name="l07005"></a>07005     weight(1) =  0.128205128205128205128205128205D-01
    7070. 

  7070. <a name="l07006"></a>07006     weight(2) =  0.778016867468189277935889883331D-01
    7071. 

  7071. <a name="l07007"></a>07007     weight(3) =  0.134981926689608349119914762589D+00
    7072. 

  7072. <a name="l07008"></a>07008     weight(4) =  0.183646865203550092007494258747D+00
    7073. 

  7073. <a name="l07009"></a>07009     weight(5) =  0.220767793566110086085534008379D+00
    7074. 

  7074. <a name="l07010"></a>07010     weight(6) =  0.244015790306676356458578148360D+00
    7075. 

  7075. <a name="l07011"></a>07011     weight(7) =  0.251930849333446736044138641541D+00
    7076. 

  7076. <a name="l07012"></a>07012     weight(8) =  0.244015790306676356458578148360D+00
    7077. 

  7077. <a name="l07013"></a>07013     weight(9) =  0.220767793566110086085534008379D+00
    7078. 

  7078. <a name="l07014"></a>07014     weight(10) = 0.183646865203550092007494258747D+00
    7079. 

  7079. <a name="l07015"></a>07015     weight(11) = 0.134981926689608349119914762589D+00
    7080. 

  7080. <a name="l07016"></a>07016     weight(12) = 0.778016867468189277935889883331D-01
    7081. 

  7081. <a name="l07017"></a>07017     weight(13) = 0.128205128205128205128205128205D-01
    7082. 

  7082. <a name="l07018"></a>07018 
    7083. 

  7083. <a name="l07019"></a>07019   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 14 ) <span class="keyword">then</span>
    7084. 

  7084. <a name="l07020"></a>07020 
    7085. 

  7085. <a name="l07021"></a>07021     xtab(1) =  - 1.0D+00
    7086. 

  7086. <a name="l07022"></a>07022     xtab(2) =  - 0.959935045267260901355100162015D+00
    7087. 

  7087. <a name="l07023"></a>07023     xtab(3) =  - 0.867801053830347251000220202908D+00
    7088. 

  7088. <a name="l07024"></a>07024     xtab(4) =  - 0.728868599091326140584672400521D+00
    7089. 

  7089. <a name="l07025"></a>07025     xtab(5) =  - 0.550639402928647055316622705859D+00
    7090. 

  7090. <a name="l07026"></a>07026     xtab(6) =  - 0.342724013342712845043903403642D+00
    7091. 

  7091. <a name="l07027"></a>07027     xtab(7) =  - 0.116331868883703867658776709736D+00
    7092. 

  7092. <a name="l07028"></a>07028     xtab(8) =    0.116331868883703867658776709736D+00
    7093. 

  7093. <a name="l07029"></a>07029     xtab(9) =    0.342724013342712845043903403642D+00
    7094. 

  7094. <a name="l07030"></a>07030     xtab(10) =   0.550639402928647055316622705859D+00
    7095. 

  7095. <a name="l07031"></a>07031     xtab(11) =   0.728868599091326140584672400521D+00
    7096. 

  7096. <a name="l07032"></a>07032     xtab(12) =   0.867801053830347251000220202908D+00
    7097. 

  7097. <a name="l07033"></a>07033     xtab(13) =   0.959935045267260901355100162015D+00
    7098. 

  7098. <a name="l07034"></a>07034     xtab(14) =   1.0D+00
    7099. 

  7099. <a name="l07035"></a>07035 
    7100. 

  7100. <a name="l07036"></a>07036     weight(1) =  0.109890109890109890109890109890D-01
    7101. 

  7101. <a name="l07037"></a>07037     weight(2) =  0.668372844976812846340706607461D-01
    7102. 

  7102. <a name="l07038"></a>07038     weight(3) =  0.116586655898711651540996670655D+00
    7103. 

  7103. <a name="l07039"></a>07039     weight(4) =  0.160021851762952142412820997988D+00
    7104. 

  7104. <a name="l07040"></a>07040     weight(5) =  0.194826149373416118640331778376D+00
    7105. 

  7105. <a name="l07041"></a>07041     weight(6) =  0.219126253009770754871162523954D+00
    7106. 

  7106. <a name="l07042"></a>07042     weight(7) =  0.231612794468457058889628357293D+00
    7107. 

  7107. <a name="l07043"></a>07043     weight(8) =  0.231612794468457058889628357293D+00
    7108. 

  7108. <a name="l07044"></a>07044     weight(9) =  0.219126253009770754871162523954D+00
    7109. 

  7109. <a name="l07045"></a>07045     weight(10) = 0.194826149373416118640331778376D+00
    7110. 

  7110. <a name="l07046"></a>07046     weight(11) = 0.160021851762952142412820997988D+00
    7111. 

  7111. <a name="l07047"></a>07047     weight(12) = 0.116586655898711651540996670655D+00
    7112. 

  7112. <a name="l07048"></a>07048     weight(13) = 0.668372844976812846340706607461D-01
    7113. 

  7113. <a name="l07049"></a>07049     weight(14) = 0.109890109890109890109890109890D-01
    7114. 

  7114. <a name="l07050"></a>07050 
    7115. 

  7115. <a name="l07051"></a>07051   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
    7116. 

  7116. <a name="l07052"></a>07052 
    7117. 

  7117. <a name="l07053"></a>07053     xtab(1) =  - 1.0D+00
    7118. 

  7118. <a name="l07054"></a>07054     xtab(2) =  - 0.965245926503838572795851392070D+00
    7119. 

  7119. <a name="l07055"></a>07055     xtab(3) =  - 0.885082044222976298825401631482D+00
    7120. 

  7120. <a name="l07056"></a>07056     xtab(4) =  - 0.763519689951815200704118475976D+00
    7121. 

  7121. <a name="l07057"></a>07057     xtab(5) =  - 0.606253205469845711123529938637D+00
    7122. 

  7122. <a name="l07058"></a>07058     xtab(6) =  - 0.420638054713672480921896938739D+00
    7123. 

  7123. <a name="l07059"></a>07059     xtab(7) =  - 0.215353955363794238225679446273D+00
    7124. 

  7124. <a name="l07060"></a>07060     xtab(8) =    0.0D+00
    7125. 

  7125. <a name="l07061"></a>07061     xtab(9) =    0.215353955363794238225679446273D+00
    7126. 

  7126. <a name="l07062"></a>07062     xtab(10) =   0.420638054713672480921896938739D+00
    7127. 

  7127. <a name="l07063"></a>07063     xtab(11) =   0.606253205469845711123529938637D+00
    7128. 

  7128. <a name="l07064"></a>07064     xtab(12) =   0.763519689951815200704118475976D+00
    7129. 

  7129. <a name="l07065"></a>07065     xtab(13) =   0.885082044222976298825401631482D+00
    7130. 

  7130. <a name="l07066"></a>07066     xtab(14) =   0.965245926503838572795851392070D+00
    7131. 

  7131. <a name="l07067"></a>07067     xtab(15) =   1.0D+00
    7132. 

  7132. <a name="l07068"></a>07068 
    7133. 

  7133. <a name="l07069"></a>07069     weight(1) =  0.952380952380952380952380952381D-02
    7134. 

  7134. <a name="l07070"></a>07070     weight(2) =  0.580298930286012490968805840253D-01
    7135. 

  7135. <a name="l07071"></a>07071     weight(3) =  0.101660070325718067603666170789D+00
    7136. 

  7136. <a name="l07072"></a>07072     weight(4) =  0.140511699802428109460446805644D+00
    7137. 

  7137. <a name="l07073"></a>07073     weight(5) =  0.172789647253600949052077099408D+00
    7138. 

  7138. <a name="l07074"></a>07074     weight(6) =  0.196987235964613356092500346507D+00
    7139. 

  7139. <a name="l07075"></a>07075     weight(7) =  0.211973585926820920127430076977D+00
    7140. 

  7140. <a name="l07076"></a>07076     weight(8) =  0.217048116348815649514950214251D+00
    7141. 

  7141. <a name="l07077"></a>07077     weight(9) =  0.211973585926820920127430076977D+00
    7142. 

  7142. <a name="l07078"></a>07078     weight(10) = 0.196987235964613356092500346507D+00
    7143. 

  7143. <a name="l07079"></a>07079     weight(11) = 0.172789647253600949052077099408D+00
    7144. 

  7144. <a name="l07080"></a>07080     weight(12) = 0.140511699802428109460446805644D+00
    7145. 

  7145. <a name="l07081"></a>07081     weight(13) = 0.101660070325718067603666170789D+00
    7146. 

  7146. <a name="l07082"></a>07082     weight(14) = 0.580298930286012490968805840253D-01
    7147. 

  7147. <a name="l07083"></a>07083     weight(15) = 0.952380952380952380952380952381D-02
    7148. 

  7148. <a name="l07084"></a>07084 
    7149. 

  7149. <a name="l07085"></a>07085   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
    7150. 

  7150. <a name="l07086"></a>07086 
    7151. 

  7151. <a name="l07087"></a>07087     xtab(1) =  - 1.0D+00
    7152. 

  7152. <a name="l07088"></a>07088     xtab(2) =  - 0.969568046270217932952242738367D+00
    7153. 

  7153. <a name="l07089"></a>07089     xtab(3) =  - 0.899200533093472092994628261520D+00
    7154. 

  7154. <a name="l07090"></a>07090     xtab(4) =  - 0.792008291861815063931088270963D+00
    7155. 

  7155. <a name="l07091"></a>07091     xtab(5) =  - 0.652388702882493089467883219641D+00
    7156. 

  7156. <a name="l07092"></a>07092     xtab(6) =  - 0.486059421887137611781890785847D+00
    7157. 

  7157. <a name="l07093"></a>07093     xtab(7) =  - 0.299830468900763208098353454722D+00
    7158. 

  7158. <a name="l07094"></a>07094     xtab(8) =  - 0.101326273521949447843033005046D+00
    7159. 

  7159. <a name="l07095"></a>07095     xtab(9) =    0.101326273521949447843033005046D+00
    7160. 

  7160. <a name="l07096"></a>07096     xtab(10) =   0.299830468900763208098353454722D+00
    7161. 

  7161. <a name="l07097"></a>07097     xtab(11) =   0.486059421887137611781890785847D+00
    7162. 

  7162. <a name="l07098"></a>07098     xtab(12) =   0.652388702882493089467883219641D+00
    7163. 

  7163. <a name="l07099"></a>07099     xtab(13) =   0.792008291861815063931088270963D+00
    7164. 

  7164. <a name="l07100"></a>07100     xtab(14) =   0.899200533093472092994628261520D+00
    7165. 

  7165. <a name="l07101"></a>07101     xtab(15) =   0.969568046270217932952242738367D+00
    7166. 

  7166. <a name="l07102"></a>07102     xtab(16) =   1.0D+00
    7167. 

  7167. <a name="l07103"></a>07103 
    7168. 

  7168. <a name="l07104"></a>07104     weight(1) =  0.833333333333333333333333333333D-02
    7169. 

  7169. <a name="l07105"></a>07105     weight(2) =  0.508503610059199054032449195655D-01
    7170. 

  7170. <a name="l07106"></a>07106     weight(3) =  0.893936973259308009910520801661D-01
    7171. 

  7171. <a name="l07107"></a>07107     weight(4) =  0.124255382132514098349536332657D+00
    7172. 

  7172. <a name="l07108"></a>07108     weight(5) =  0.154026980807164280815644940485D+00
    7173. 

  7173. <a name="l07109"></a>07109     weight(6) =  0.177491913391704125301075669528D+00
    7174. 

  7174. <a name="l07110"></a>07110     weight(7) =  0.193690023825203584316913598854D+00
    7175. 

  7175. <a name="l07111"></a>07111     weight(8) =  0.201958308178229871489199125411D+00
    7176. 

  7176. <a name="l07112"></a>07112     weight(9) =  0.201958308178229871489199125411D+00
    7177. 

  7177. <a name="l07113"></a>07113     weight(10) = 0.193690023825203584316913598854D+00
    7178. 

  7178. <a name="l07114"></a>07114     weight(11) = 0.177491913391704125301075669528D+00
    7179. 

  7179. <a name="l07115"></a>07115     weight(12) = 0.154026980807164280815644940485D+00
    7180. 

  7180. <a name="l07116"></a>07116     weight(13) = 0.124255382132514098349536332657D+00
    7181. 

  7181. <a name="l07117"></a>07117     weight(14) = 0.893936973259308009910520801661D-01
    7182. 

  7182. <a name="l07118"></a>07118     weight(15) = 0.508503610059199054032449195655D-01
    7183. 

  7183. <a name="l07119"></a>07119     weight(16) = 0.833333333333333333333333333333D-02
    7184. 

  7184. <a name="l07120"></a>07120 
    7185. 

  7185. <a name="l07121"></a>07121   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 17 ) <span class="keyword">then</span>
    7186. 

  7186. <a name="l07122"></a>07122 
    7187. 

  7187. <a name="l07123"></a>07123     xtab(1) =  - 1.0D+00
    7188. 

  7188. <a name="l07124"></a>07124     xtab(2) =  - 0.973132176631418314156979501874D+00
    7189. 

  7189. <a name="l07125"></a>07125     xtab(3) =  - 0.910879995915573595623802506398D+00
    7190. 

  7190. <a name="l07126"></a>07126     xtab(4) =  - 0.815696251221770307106750553238D+00
    7191. 

  7191. <a name="l07127"></a>07127     xtab(5) =  - 0.691028980627684705394919357372D+00
    7192. 

  7192. <a name="l07128"></a>07128     xtab(6) =  - 0.541385399330101539123733407504D+00
    7193. 

  7193. <a name="l07129"></a>07129     xtab(7) =  - 0.372174433565477041907234680735D+00
    7194. 

  7194. <a name="l07130"></a>07130     xtab(8) =  - 0.189511973518317388304263014753D+00
    7195. 

  7195. <a name="l07131"></a>07131     xtab(9) =    0.0D+00
    7196. 

  7196. <a name="l07132"></a>07132     xtab(10) =   0.189511973518317388304263014753D+00
    7197. 

  7197. <a name="l07133"></a>07133     xtab(11) =   0.372174433565477041907234680735D+00
    7198. 

  7198. <a name="l07134"></a>07134     xtab(12) =   0.541385399330101539123733407504D+00
    7199. 

  7199. <a name="l07135"></a>07135     xtab(13) =   0.691028980627684705394919357372D+00
    7200. 

  7200. <a name="l07136"></a>07136     xtab(14) =   0.815696251221770307106750553238D+00
    7201. 

  7201. <a name="l07137"></a>07137     xtab(15) =   0.910879995915573595623802506398D+00
    7202. 

  7202. <a name="l07138"></a>07138     xtab(16) =   0.973132176631418314156979501874D+00
    7203. 

  7203. <a name="l07139"></a>07139     xtab(17) =   1.0D+00
    7204. 

  7204. <a name="l07140"></a>07140 
    7205. 

  7205. <a name="l07141"></a>07141     weight(1) =  0.735294117647058823529411764706D-02
    7206. 

  7206. <a name="l07142"></a>07142     weight(2) =  0.449219405432542096474009546232D-01
    7207. 

  7207. <a name="l07143"></a>07143     weight(3) =  0.791982705036871191902644299528D-01
    7208. 

  7208. <a name="l07144"></a>07144     weight(4) =  0.110592909007028161375772705220D+00
    7209. 

  7209. <a name="l07145"></a>07145     weight(5) =  0.137987746201926559056201574954D+00
    7210. 

  7210. <a name="l07146"></a>07146     weight(6) =  0.160394661997621539516328365865D+00
    7211. 

  7211. <a name="l07147"></a>07147     weight(7) =  0.177004253515657870436945745363D+00
    7212. 

  7212. <a name="l07148"></a>07148     weight(8) =  0.187216339677619235892088482861D+00
    7213. 

  7213. <a name="l07149"></a>07149     weight(9) =  0.190661874753469433299407247028D+00
    7214. 

  7214. <a name="l07150"></a>07150     weight(10) = 0.187216339677619235892088482861D+00
    7215. 

  7215. <a name="l07151"></a>07151     weight(11) = 0.177004253515657870436945745363D+00
    7216. 

  7216. <a name="l07152"></a>07152     weight(12) = 0.160394661997621539516328365865D+00
    7217. 

  7217. <a name="l07153"></a>07153     weight(13) = 0.137987746201926559056201574954D+00
    7218. 

  7218. <a name="l07154"></a>07154     weight(14) = 0.110592909007028161375772705220D+00
    7219. 

  7219. <a name="l07155"></a>07155     weight(15) = 0.791982705036871191902644299528D-01
    7220. 

  7220. <a name="l07156"></a>07156     weight(16) = 0.449219405432542096474009546232D-01
    7221. 

  7221. <a name="l07157"></a>07157     weight(17) = 0.735294117647058823529411764706D-02
    7222. 

  7222. <a name="l07158"></a>07158 
    7223. 

  7223. <a name="l07159"></a>07159   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 18 ) <span class="keyword">then</span>
    7224. 

  7224. <a name="l07160"></a>07160 
    7225. 

  7225. <a name="l07161"></a>07161     xtab(1) =  - 1.0D+00
    7226. 

  7226. <a name="l07162"></a>07162     xtab(2) =  - 0.976105557412198542864518924342D+00
    7227. 

  7227. <a name="l07163"></a>07163     xtab(3) =  - 0.920649185347533873837854625431D+00
    7228. 

  7228. <a name="l07164"></a>07164     xtab(4) =  - 0.835593535218090213713646362328D+00
    7229. 

  7229. <a name="l07165"></a>07165     xtab(5) =  - 0.723679329283242681306210365302D+00
    7230. 

  7230. <a name="l07166"></a>07166     xtab(6) =  - 0.588504834318661761173535893194D+00
    7231. 

  7231. <a name="l07167"></a>07167     xtab(7) =  - 0.434415036912123975342287136741D+00
    7232. 

  7232. <a name="l07168"></a>07168     xtab(8) =  - 0.266362652878280984167665332026D+00
    7233. 

  7233. <a name="l07169"></a>07169     xtab(9) =  - 0.897490934846521110226450100886D-01
    7234. 

  7234. <a name="l07170"></a>07170     xtab(10) =   0.897490934846521110226450100886D-01
    7235. 

  7235. <a name="l07171"></a>07171     xtab(11) =   0.266362652878280984167665332026D+00
    7236. 

  7236. <a name="l07172"></a>07172     xtab(12) =   0.434415036912123975342287136741D+00
    7237. 

  7237. <a name="l07173"></a>07173     xtab(13) =   0.588504834318661761173535893194D+00
    7238. 

  7238. <a name="l07174"></a>07174     xtab(14) =   0.723679329283242681306210365302D+00
    7239. 

  7239. <a name="l07175"></a>07175     xtab(15) =   0.835593535218090213713646362328D+00
    7240. 

  7240. <a name="l07176"></a>07176     xtab(16) =   0.920649185347533873837854625431D+00
    7241. 

  7241. <a name="l07177"></a>07177     xtab(17) =   0.976105557412198542864518924342D+00
    7242. 

  7242. <a name="l07178"></a>07178     xtab(18) =   1.0D+00
    7243. 

  7243. <a name="l07179"></a>07179 
    7244. 

  7244. <a name="l07180"></a>07180     weight(1) =  0.653594771241830065359477124183D-02
    7245. 

  7245. <a name="l07181"></a>07181     weight(2) =  0.399706288109140661375991764101D-01
    7246. 

  7246. <a name="l07182"></a>07182     weight(3) =  0.706371668856336649992229601678D-01
    7247. 

  7247. <a name="l07183"></a>07183     weight(4) =  0.990162717175028023944236053187D-01
    7248. 

  7248. <a name="l07184"></a>07184     weight(5) =  0.124210533132967100263396358897D+00
    7249. 

  7249. <a name="l07185"></a>07185     weight(6) =  0.145411961573802267983003210494D+00
    7250. 

  7250. <a name="l07186"></a>07186     weight(7) =  0.161939517237602489264326706700D+00
    7251. 

  7251. <a name="l07187"></a>07187     weight(8) =  0.173262109489456226010614403827D+00
    7252. 

  7252. <a name="l07188"></a>07188     weight(9) =  0.179015863439703082293818806944D+00
    7253. 

  7253. <a name="l07189"></a>07189     weight(10) = 0.179015863439703082293818806944D+00
    7254. 

  7254. <a name="l07190"></a>07190     weight(11) = 0.173262109489456226010614403827D+00
    7255. 

  7255. <a name="l07191"></a>07191     weight(12) = 0.161939517237602489264326706700D+00
    7256. 

  7256. <a name="l07192"></a>07192     weight(13) = 0.145411961573802267983003210494D+00
    7257. 

  7257. <a name="l07193"></a>07193     weight(14) = 0.124210533132967100263396358897D+00
    7258. 

  7258. <a name="l07194"></a>07194     weight(15) = 0.990162717175028023944236053187D-01
    7259. 

  7259. <a name="l07195"></a>07195     weight(16) = 0.706371668856336649992229601678D-01
    7260. 

  7260. <a name="l07196"></a>07196     weight(17) = 0.399706288109140661375991764101D-01
    7261. 

  7261. <a name="l07197"></a>07197     weight(18) = 0.653594771241830065359477124183D-02
    7262. 

  7262. <a name="l07198"></a>07198 
    7263. 

  7263. <a name="l07199"></a>07199   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 19 ) <span class="keyword">then</span>
    7264. 

  7264. <a name="l07200"></a>07200 
    7265. 

  7265. <a name="l07201"></a>07201     xtab(1) =  - 1.0D+00
    7266. 

  7266. <a name="l07202"></a>07202     xtab(2) =  - 0.978611766222080095152634063110D+00
    7267. 

  7267. <a name="l07203"></a>07203     xtab(3) =  - 0.928901528152586243717940258797D+00
    7268. 

  7268. <a name="l07204"></a>07204     xtab(4) =  - 0.852460577796646093085955970041D+00
    7269. 

  7269. <a name="l07205"></a>07205     xtab(5) =  - 0.751494202552613014163637489634D+00
    7270. 

  7270. <a name="l07206"></a>07206     xtab(6) =  - 0.628908137265220497766832306229D+00
    7271. 

  7271. <a name="l07207"></a>07207     xtab(7) =  - 0.488229285680713502777909637625D+00
    7272. 

  7272. <a name="l07208"></a>07208     xtab(8) =  - 0.333504847824498610298500103845D+00
    7273. 

  7273. <a name="l07209"></a>07209     xtab(9) =  - 0.169186023409281571375154153445D+00
    7274. 

  7274. <a name="l07210"></a>07210     xtab(10) =   0.0D+00
    7275. 

  7275. <a name="l07211"></a>07211     xtab(11) =   0.169186023409281571375154153445D+00
    7276. 

  7276. <a name="l07212"></a>07212     xtab(12) =   0.333504847824498610298500103845D+00
    7277. 

  7277. <a name="l07213"></a>07213     xtab(13) =   0.488229285680713502777909637625D+00
    7278. 

  7278. <a name="l07214"></a>07214     xtab(14) =   0.628908137265220497766832306229D+00
    7279. 

  7279. <a name="l07215"></a>07215     xtab(15) =   0.751494202552613014163637489634D+00
    7280. 

  7280. <a name="l07216"></a>07216     xtab(16) =   0.852460577796646093085955970041D+00
    7281. 

  7281. <a name="l07217"></a>07217     xtab(17) =   0.928901528152586243717940258797D+00
    7282. 

  7282. <a name="l07218"></a>07218     xtab(18) =   0.978611766222080095152634063110D+00
    7283. 

  7283. <a name="l07219"></a>07219     xtab(19) =   1.0D+00
    7284. 

  7284. <a name="l07220"></a>07220 
    7285. 

  7285. <a name="l07221"></a>07221     weight(1) =  0.584795321637426900584795321637D-02
    7286. 

  7286. <a name="l07222"></a>07222     weight(2) =  0.357933651861764771154255690351D-01
    7287. 

  7287. <a name="l07223"></a>07223     weight(3) =  0.633818917626297368516956904183D-01
    7288. 

  7288. <a name="l07224"></a>07224     weight(4) =  0.891317570992070844480087905562D-01
    7289. 

  7289. <a name="l07225"></a>07225     weight(5) =  0.112315341477305044070910015464D+00
    7290. 

  7290. <a name="l07226"></a>07226     weight(6) =  0.132267280448750776926046733910D+00
    7291. 

  7291. <a name="l07227"></a>07227     weight(7) =  0.148413942595938885009680643668D+00
    7292. 

  7292. <a name="l07228"></a>07228     weight(8) =  0.160290924044061241979910968184D+00
    7293. 

  7293. <a name="l07229"></a>07229     weight(9) =  0.167556584527142867270137277740D+00
    7294. 

  7294. <a name="l07230"></a>07230     weight(10) = 0.170001919284827234644672715617D+00
    7295. 

  7295. <a name="l07231"></a>07231     weight(11) = 0.167556584527142867270137277740D+00
    7296. 

  7296. <a name="l07232"></a>07232     weight(12) = 0.160290924044061241979910968184D+00
    7297. 

  7297. <a name="l07233"></a>07233     weight(13) = 0.148413942595938885009680643668D+00
    7298. 

  7298. <a name="l07234"></a>07234     weight(14) = 0.132267280448750776926046733910D+00
    7299. 

  7299. <a name="l07235"></a>07235     weight(15) = 0.112315341477305044070910015464D+00
    7300. 

  7300. <a name="l07236"></a>07236     weight(16) = 0.891317570992070844480087905562D-01
    7301. 

  7301. <a name="l07237"></a>07237     weight(17) = 0.633818917626297368516956904183D-01
    7302. 

  7302. <a name="l07238"></a>07238     weight(18) = 0.357933651861764771154255690351D-01
    7303. 

  7303. <a name="l07239"></a>07239     weight(19) = 0.584795321637426900584795321637D-02
    7304. 

  7304. <a name="l07240"></a>07240 
    7305. 

  7305. <a name="l07241"></a>07241   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 20 ) <span class="keyword">then</span>
    7306. 

  7306. <a name="l07242"></a>07242 
    7307. 

  7307. <a name="l07243"></a>07243     xtab(1) =  - 1.0D+00
    7308. 

  7308. <a name="l07244"></a>07244     xtab(2) =  - 0.980743704893914171925446438584D+00
    7309. 

  7309. <a name="l07245"></a>07245     xtab(3) =  - 0.935934498812665435716181584931D+00
    7310. 

  7310. <a name="l07246"></a>07246     xtab(4) =  - 0.866877978089950141309847214616D+00
    7311. 

  7311. <a name="l07247"></a>07247     xtab(5) =  - 0.775368260952055870414317527595D+00
    7312. 

  7312. <a name="l07248"></a>07248     xtab(6) =  - 0.663776402290311289846403322971D+00
    7313. 

  7313. <a name="l07249"></a>07249     xtab(7) =  - 0.534992864031886261648135961829D+00
    7314. 

  7314. <a name="l07250"></a>07250     xtab(8) =  - 0.392353183713909299386474703816D+00
    7315. 

  7315. <a name="l07251"></a>07251     xtab(9) =  - 0.239551705922986495182401356927D+00
    7316. 

  7316. <a name="l07252"></a>07252     xtab(10) = - 0.805459372388218379759445181596D-01
    7317. 

  7317. <a name="l07253"></a>07253     xtab(11) =   0.805459372388218379759445181596D-01
    7318. 

  7318. <a name="l07254"></a>07254     xtab(12) =   0.239551705922986495182401356927D+00
    7319. 

  7319. <a name="l07255"></a>07255     xtab(13) =   0.392353183713909299386474703816D+00
    7320. 

  7320. <a name="l07256"></a>07256     xtab(14) =   0.534992864031886261648135961829D+00
    7321. 

  7321. <a name="l07257"></a>07257     xtab(15) =   0.663776402290311289846403322971D+00
    7322. 

  7322. <a name="l07258"></a>07258     xtab(16) =   0.775368260952055870414317527595D+00
    7323. 

  7323. <a name="l07259"></a>07259     xtab(17) =   0.866877978089950141309847214616D+00
    7324. 

  7324. <a name="l07260"></a>07260     xtab(18) =   0.935934498812665435716181584931D+00
    7325. 

  7325. <a name="l07261"></a>07261     xtab(19) =   0.980743704893914171925446438584D+00
    7326. 

  7326. <a name="l07262"></a>07262     xtab(20) =   1.0D+00
    7327. 

  7327. <a name="l07263"></a>07263 
    7328. 

  7328. <a name="l07264"></a>07264     weight(1) =  0.526315789473684210526315789474D-02
    7329. 

  7329. <a name="l07265"></a>07265     weight(2) =  0.322371231884889414916050281173D-01
    7330. 

  7330. <a name="l07266"></a>07266     weight(3) =  0.571818021275668260047536271732D-01
    7331. 

  7331. <a name="l07267"></a>07267     weight(4) =  0.806317639961196031447768461137D-01
    7332. 

  7332. <a name="l07268"></a>07268     weight(5) =  0.101991499699450815683781205733D+00
    7333. 

  7333. <a name="l07269"></a>07269     weight(6) =  0.120709227628674725099429705002D+00
    7334. 

  7334. <a name="l07270"></a>07270     weight(7) =  0.136300482358724184489780792989D+00
    7335. 

  7335. <a name="l07271"></a>07271     weight(8) =  0.148361554070916825814713013734D+00
    7336. 

  7336. <a name="l07272"></a>07272     weight(9) =  0.156580102647475487158169896794D+00
    7337. 

  7337. <a name="l07273"></a>07273     weight(10) = 0.160743286387845749007726726449D+00
    7338. 

  7338. <a name="l07274"></a>07274     weight(11) = 0.160743286387845749007726726449D+00
    7339. 

  7339. <a name="l07275"></a>07275     weight(12) = 0.156580102647475487158169896794D+00
    7340. 

  7340. <a name="l07276"></a>07276     weight(13) = 0.148361554070916825814713013734D+00
    7341. 

  7341. <a name="l07277"></a>07277     weight(14) = 0.136300482358724184489780792989D+00
    7342. 

  7342. <a name="l07278"></a>07278     weight(15) = 0.120709227628674725099429705002D+00
    7343. 

  7343. <a name="l07279"></a>07279     weight(16) = 0.101991499699450815683781205733D+00
    7344. 

  7344. <a name="l07280"></a>07280     weight(17) = 0.806317639961196031447768461137D-01
    7345. 

  7345. <a name="l07281"></a>07281     weight(18) = 0.571818021275668260047536271732D-01
    7346. 

  7346. <a name="l07282"></a>07282     weight(19) = 0.322371231884889414916050281173D-01
    7347. 

  7347. <a name="l07283"></a>07283     weight(20) = 0.526315789473684210526315789474D-02
    7348. 

  7348. <a name="l07284"></a>07284 
    7349. 

  7349. <a name="l07285"></a>07285   <span class="keyword">else</span>
    7350. 

  7350. <a name="l07286"></a>07286 
    7351. 

  7351. <a name="l07287"></a>07287     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    7352. 

  7352. <a name="l07288"></a>07288     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LOBATTO_SET - Fatal error!&#39;</span>
    7353. 

  7353. <a name="l07289"></a>07289     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    7354. 

  7354. <a name="l07290"></a>07290     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are between 2 and 20.&#39;</span>
    7355. 

  7355. <a name="l07291"></a>07291     stop
    7356. 

  7356. <a name="l07292"></a>07292 
    7357. 

  7357. <a name="l07293"></a>07293   <span class="keyword">end if</span>
    7358. 

  7358. <a name="l07294"></a>07294 
    7359. 

  7359. <a name="l07295"></a>07295   return
    7360. 

  7360. <a name="l07296"></a>07296 <span class="keyword">end</span>
    7361. 

  7361. <a name="l07297"></a><a class="code" href="quadrule_8f90.html#a6bd375a88b7077d216c6532d98f9425c">07297</a> <span class="keyword">function </span>log_gamma ( x )
    7362. 

  7362. <a name="l07298"></a>07298 <span class="comment">!</span>
    7363. 

  7363. <a name="l07299"></a>07299 <span class="comment">!*******************************************************************************</span>
    7364. 

  7364. <a name="l07300"></a>07300 <span class="comment">!</span>
    7365. 

  7365. <a name="l07301"></a>07301 <span class="comment">!! LOG_GAMMA calculates the natural logarithm of GAMMA(X).</span>
    7366. 

  7366. <a name="l07302"></a>07302 <span class="comment">!</span>
    7367. 

  7367. <a name="l07303"></a>07303 <span class="comment">!</span>
    7368. 

  7368. <a name="l07304"></a>07304 <span class="comment">!  Discussion:</span>
    7369. 

  7369. <a name="l07305"></a>07305 <span class="comment">!</span>
    7370. 

  7370. <a name="l07306"></a>07306 <span class="comment">!    The method uses Stirling&#39;s approximation, and is accurate to about</span>
    7371. 

  7371. <a name="l07307"></a>07307 <span class="comment">!    12 decimal places.</span>
    7372. 

  7372. <a name="l07308"></a>07308 <span class="comment">!</span>
    7373. 

  7373. <a name="l07309"></a>07309 <span class="comment">!  Reference:</span>
    7374. 

  7374. <a name="l07310"></a>07310 <span class="comment">!</span>
    7375. 

  7375. <a name="l07311"></a>07311 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    7376. 

  7376. <a name="l07312"></a>07312 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    7377. 

  7377. <a name="l07313"></a>07313 <span class="comment">!    Prentice Hall, 1966.</span>
    7378. 

  7378. <a name="l07314"></a>07314 <span class="comment">!</span>
    7379. 

  7379. <a name="l07315"></a>07315 <span class="comment">!  Modified:</span>
    7380. 

  7380. <a name="l07316"></a>07316 <span class="comment">!</span>
    7381. 

  7381. <a name="l07317"></a>07317 <span class="comment">!    19 September 1998</span>
    7382. 

  7382. <a name="l07318"></a>07318 <span class="comment">!</span>
    7383. 

  7383. <a name="l07319"></a>07319 <span class="comment">!  Parameters:</span>
    7384. 

  7384. <a name="l07320"></a>07320 <span class="comment">!</span>
    7385. 

  7385. <a name="l07321"></a>07321 <span class="comment">!    Input, double precision X, the evaluation point.  The routine</span>
    7386. 

  7386. <a name="l07322"></a>07322 <span class="comment">!    will fail if GAMMA(X) is not positive.  X should be greater than 0.</span>
    7387. 

  7387. <a name="l07323"></a>07323 <span class="comment">!</span>
    7388. 

  7388. <a name="l07324"></a>07324 <span class="comment">!    Output, double precision LOG_GAMMA, the natural logarithm of the</span>
    7389. 

  7389. <a name="l07325"></a>07325 <span class="comment">!    gamma function of X.</span>
    7390. 

  7390. <a name="l07326"></a>07326 <span class="comment">!</span>
    7391. 

  7391. <a name="l07327"></a>07327   <span class="keyword">implicit none</span>
    7392. 

  7392. <a name="l07328"></a>07328 <span class="comment">!</span>
    7393. 

  7393. <a name="l07329"></a>07329   <span class="keywordtype">double precision</span> d_pi
    7394. 

  7394. <a name="l07330"></a>07330   <span class="keywordtype">integer</span> i
    7395. 

  7395. <a name="l07331"></a>07331   <span class="keywordtype">integer</span> k
    7396. 

  7396. <a name="l07332"></a>07332   <span class="keywordtype">double precision</span> log_gamma
    7397. 

  7397. <a name="l07333"></a>07333   <span class="keywordtype">integer</span> m
    7398. 

  7398. <a name="l07334"></a>07334   <span class="keywordtype">double precision</span> p
    7399. 

  7399. <a name="l07335"></a>07335   <span class="keywordtype">double precision</span> x
    7400. 

  7400. <a name="l07336"></a>07336   <span class="keywordtype">double precision</span> x2
    7401. 

  7401. <a name="l07337"></a>07337   <span class="keywordtype">double precision</span> y
    7402. 

  7402. <a name="l07338"></a>07338   <span class="keywordtype">double precision</span> z
    7403. 

  7403. <a name="l07339"></a>07339 <span class="comment">!</span>
    7404. 

  7404. <a name="l07340"></a>07340   <span class="keyword">if</span> ( x &lt; 0.5 ) <span class="keyword">then</span>
    7405. 

  7405. <a name="l07341"></a>07341 
    7406. 

  7406. <a name="l07342"></a>07342     m = 1
    7407. 

  7407. <a name="l07343"></a>07343     x2 = 1.0D+00 - x
    7408. 

  7408. <a name="l07344"></a>07344 
    7409. 

  7409. <a name="l07345"></a>07345   <span class="keyword">else</span>
    7410. 

  7410. <a name="l07346"></a>07346 
    7411. 

  7411. <a name="l07347"></a>07347     m = 0
    7412. 

  7412. <a name="l07348"></a>07348     x2 = x
    7413. 

  7413. <a name="l07349"></a>07349 
    7414. 

  7414. <a name="l07350"></a>07350   <span class="keyword">end if</span>
    7415. 

  7415. <a name="l07351"></a>07351 
    7416. 

  7416. <a name="l07352"></a>07352   k = - 1
    7417. 

  7417. <a name="l07353"></a>07353 
    7418. 

  7418. <a name="l07354"></a>07354   <span class="keyword">do</span>
    7419. 

  7419. <a name="l07355"></a>07355 
    7420. 

  7420. <a name="l07356"></a>07356     k = k + 1
    7421. 

  7421. <a name="l07357"></a>07357 
    7422. 

  7422. <a name="l07358"></a>07358     <span class="keyword">if</span> ( x2 + dble ( k ) &gt; 6.0D+00 ) <span class="keyword">then</span>
    7423. 

  7423. <a name="l07359"></a>07359       exit
    7424. 

  7424. <a name="l07360"></a>07360     <span class="keyword">end if</span>
    7425. 

  7425. <a name="l07361"></a>07361 
    7426. 

  7426. <a name="l07362"></a>07362   <span class="keyword">end do</span>
    7427. 

  7427. <a name="l07363"></a>07363 
    7428. 

  7428. <a name="l07364"></a>07364   z = x2 + dble ( k )
    7429. 

  7429. <a name="l07365"></a>07365 
    7430. 

  7430. <a name="l07366"></a>07366   y = ( z - 0.5 ) * log ( z ) - z + 0.9189385332047D+00 + &amp;
    7431. 

  7431. <a name="l07367"></a>07367        ( ( ( ( ( &amp;
    7432. 

  7432. <a name="l07368"></a>07368        - 4146.0D+00 / z**2 &amp;
    7433. 

  7433. <a name="l07369"></a>07369        + 1820.0D+00 ) / z**2 &amp;
    7434. 

  7434. <a name="l07370"></a>07370        - 1287.0D+00 ) / z**2 &amp;
    7435. 

  7435. <a name="l07371"></a>07371        + 1716.0D+00 ) / z**2 &amp;
    7436. 

  7436. <a name="l07372"></a>07372        - 6006.0D+00 ) / z**2 &amp;
    7437. 

  7437. <a name="l07373"></a>07373        + 180180.0D+00 ) / z / 2162160.0D+00
    7438. 

  7438. <a name="l07374"></a>07374 
    7439. 

  7439. <a name="l07375"></a>07375   <span class="keyword">if</span> ( k &gt; 0 ) <span class="keyword">then</span>
    7440. 

  7440. <a name="l07376"></a>07376 
    7441. 

  7441. <a name="l07377"></a>07377     <span class="keyword">do</span> i = 1, k
    7442. 

  7442. <a name="l07378"></a>07378       y = y - log ( x2 + dble ( k - i ) )
    7443. 

  7443. <a name="l07379"></a>07379     <span class="keyword">end do</span>
    7444. 

  7444. <a name="l07380"></a>07380 
    7445. 

  7445. <a name="l07381"></a>07381   <span class="keyword">end if</span>
    7446. 

  7446. <a name="l07382"></a>07382 
    7447. 

  7447. <a name="l07383"></a>07383   <span class="keyword">if</span> ( m /= 0 ) <span class="keyword">then</span>
    7448. 

  7448. <a name="l07384"></a>07384 
    7449. 

  7449. <a name="l07385"></a>07385     p = d_pi ( ) / sin ( d_pi ( ) * ( 1.0D+00 - x2 ) )
    7450. 

  7450. <a name="l07386"></a>07386 
    7451. 

  7451. <a name="l07387"></a>07387     <span class="keyword">if</span> ( p &lt;= 0.0D+00 ) <span class="keyword">then</span>
    7452. 

  7452. <a name="l07388"></a>07388 
    7453. 

  7453. <a name="l07389"></a>07389       <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    7454. 

  7454. <a name="l07390"></a>07390       <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;LOG_GAMMA - fatal error!&#39;</span>
    7455. 

  7455. <a name="l07391"></a>07391       stop
    7456. 

  7456. <a name="l07392"></a>07392 
    7457. 

  7457. <a name="l07393"></a>07393     <span class="keyword">else</span>
    7458. 

  7458. <a name="l07394"></a>07394 
    7459. 

  7459. <a name="l07395"></a>07395       y = log ( p ) - y
    7460. 

  7460. <a name="l07396"></a>07396 
    7461. 

  7461. <a name="l07397"></a>07397     <span class="keyword">end if</span>
    7462. 

  7462. <a name="l07398"></a>07398 
    7463. 

  7463. <a name="l07399"></a>07399   <span class="keyword">end if</span>
    7464. 

  7464. <a name="l07400"></a>07400 
    7465. 

  7465. <a name="l07401"></a>07401   log_gamma = y
    7466. 

  7466. <a name="l07402"></a>07402 
    7467. 

  7467. <a name="l07403"></a>07403   return
    7468. 

  7468. <a name="l07404"></a>07404 <span class="keyword">end</span>
    7469. 

  7469. <a name="l07405"></a><a class="code" href="quadrule_8f90.html#a7b182dbe7e6b57c218f9a6d3f89b5130">07405</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a7b182dbe7e6b57c218f9a6d3f89b5130">moulton_set</a> ( norder, xtab, weight )
    7470. 

  7470. <a name="l07406"></a>07406 <span class="comment">!</span>
    7471. 

  7471. <a name="l07407"></a>07407 <span class="comment">!*******************************************************************************</span>
    7472. 

  7472. <a name="l07408"></a>07408 <span class="comment">!</span>
    7473. 

  7473. <a name="l07409"></a>07409 <span class="comment">!! MOULTON_SET sets weights for Adams-Moulton quadrature.</span>
    7474. 

  7474. <a name="l07410"></a>07410 <span class="comment">!</span>
    7475. 

  7475. <a name="l07411"></a>07411 <span class="comment">!</span>
    7476. 

  7476. <a name="l07412"></a>07412 <span class="comment">!  Definition:</span>
    7477. 

  7477. <a name="l07413"></a>07413 <span class="comment">!</span>
    7478. 

  7478. <a name="l07414"></a>07414 <span class="comment">!    Adams-Moulton quadrature formulas are normally used in solving</span>
    7479. 

  7479. <a name="l07415"></a>07415 <span class="comment">!    ordinary differential equations, and are not suitable for general</span>
    7480. 

  7480. <a name="l07416"></a>07416 <span class="comment">!    quadrature computations.  However, an Adams-Moulton formula is</span>
    7481. 

  7481. <a name="l07417"></a>07417 <span class="comment">!    equivalent to approximating the integral of F(Y(X)) between X(M)</span>
    7482. 

  7482. <a name="l07418"></a>07418 <span class="comment">!    and X(M+1), using an implicit formula that relies on known values</span>
    7483. 

  7483. <a name="l07419"></a>07419 <span class="comment">!    of F(Y(X)) at X(M-N+1) through X(M), plus the unknown value at X(M+1).</span>
    7484. 

  7484. <a name="l07420"></a>07420 <span class="comment">!</span>
    7485. 

  7485. <a name="l07421"></a>07421 <span class="comment">!    Suppose the unknown function is denoted by Y(X), with derivative F(Y(X)),</span>
    7486. 

  7486. <a name="l07422"></a>07422 <span class="comment">!    and that approximate values of the function are known at a series of</span>
    7487. 

  7487. <a name="l07423"></a>07423 <span class="comment">!    X values, which we write as X(1), X(2), ..., X(M).  We write the value</span>
    7488. 

  7488. <a name="l07424"></a>07424 <span class="comment">!    Y(X(1)) as Y(1) and so on.</span>
    7489. 

  7489. <a name="l07425"></a>07425 <span class="comment">!</span>
    7490. 

  7490. <a name="l07426"></a>07426 <span class="comment">!    Then the solution of the ODE Y&#39; = F(X,Y) at the next point X(M+1) is</span>
    7491. 

  7491. <a name="l07427"></a>07427 <span class="comment">!    computed by:</span>
    7492. 

  7492. <a name="l07428"></a>07428 <span class="comment">!</span>
    7493. 

  7493. <a name="l07429"></a>07429 <span class="comment">!      Y(M+1) = Y(M) + Integral ( X(M) &lt; X &lt; X(M+1) ) F(Y(X)) dX</span>
    7494. 

  7494. <a name="l07430"></a>07430 <span class="comment">!             = Y(M) + H * Sum ( I = 1 to N ) W(I) * F(Y(M+2-I)) approximately.</span>
    7495. 

  7495. <a name="l07431"></a>07431 <span class="comment">!</span>
    7496. 

  7496. <a name="l07432"></a>07432 <span class="comment">!    Note that this formula is implicit, since the unknown value Y(M+1)</span>
    7497. 

  7497. <a name="l07433"></a>07433 <span class="comment">!    appears on the right hand side.  Hence, in ODE applications, this</span>
    7498. 

  7498. <a name="l07434"></a>07434 <span class="comment">!    equation must be solved via a nonlinear equation solver.  For</span>
    7499. 

  7499. <a name="l07435"></a>07435 <span class="comment">!    quadrature problems, where the function to be integrated is known</span>
    7500. 

  7500. <a name="l07436"></a>07436 <span class="comment">!    beforehand, this is not a problem, and the calculation is explicit.</span>
    7501. 

  7501. <a name="l07437"></a>07437 <span class="comment">!</span>
    7502. 

  7502. <a name="l07438"></a>07438 <span class="comment">!    In the documentation that follows, we replace F(Y(X)) by F(X).</span>
    7503. 

  7503. <a name="l07439"></a>07439 <span class="comment">!</span>
    7504. 

  7504. <a name="l07440"></a>07440 <span class="comment">!  Integration interval:</span>
    7505. 

  7505. <a name="l07441"></a>07441 <span class="comment">!</span>
    7506. 

  7506. <a name="l07442"></a>07442 <span class="comment">!    [ 0, 1 ]</span>
    7507. 

  7507. <a name="l07443"></a>07443 <span class="comment">!</span>
    7508. 

  7508. <a name="l07444"></a>07444 <span class="comment">!  Weight function:</span>
    7509. 

  7509. <a name="l07445"></a>07445 <span class="comment">!</span>
    7510. 

  7510. <a name="l07446"></a>07446 <span class="comment">!    1.0D+00</span>
    7511. 

  7511. <a name="l07447"></a>07447 <span class="comment">!</span>
    7512. 

  7512. <a name="l07448"></a>07448 <span class="comment">!  Integral to approximate:</span>
    7513. 

  7513. <a name="l07449"></a>07449 <span class="comment">!</span>
    7514. 

  7514. <a name="l07450"></a>07450 <span class="comment">!    Integral ( 0 &lt;= X &lt;= 1 ) F(X) dX</span>
    7515. 

  7515. <a name="l07451"></a>07451 <span class="comment">!</span>
    7516. 

  7516. <a name="l07452"></a>07452 <span class="comment">!  Approximate integral:</span>
    7517. 

  7517. <a name="l07453"></a>07453 <span class="comment">!</span>
    7518. 

  7518. <a name="l07454"></a>07454 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( 2 - I )</span>
    7519. 

  7519. <a name="l07455"></a>07455 <span class="comment">!</span>
    7520. 

  7520. <a name="l07456"></a>07456 <span class="comment">!  Note:</span>
    7521. 

  7521. <a name="l07457"></a>07457 <span class="comment">!</span>
    7522. 

  7522. <a name="l07458"></a>07458 <span class="comment">!    The Adams-Moulton formulas require equally spaced data.</span>
    7523. 

  7523. <a name="l07459"></a>07459 <span class="comment">!</span>
    7524. 

  7524. <a name="l07460"></a>07460 <span class="comment">!    Here is how the formula is applied in the case with non-unit spacing:</span>
    7525. 

  7525. <a name="l07461"></a>07461 <span class="comment">!</span>
    7526. 

  7526. <a name="l07462"></a>07462 <span class="comment">!      Integral ( A &lt;= X &lt;= A+H ) F(X) dX =</span>
    7527. 

  7527. <a name="l07463"></a>07463 <span class="comment">!      H * Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( A - (I-2)*H ), approximately.</span>
    7528. 

  7528. <a name="l07464"></a>07464 <span class="comment">!</span>
    7529. 

  7529. <a name="l07465"></a>07465 <span class="comment">!  Reference:</span>
    7530. 

  7530. <a name="l07466"></a>07466 <span class="comment">!</span>
    7531. 

  7531. <a name="l07467"></a>07467 <span class="comment">!    Abramowitz and Stegun,</span>
    7532. 

  7532. <a name="l07468"></a>07468 <span class="comment">!    Handbook of Mathematical Functions,</span>
    7533. 

  7533. <a name="l07469"></a>07469 <span class="comment">!    National Bureau of Standards, 1964,</span>
    7534. 

  7534. <a name="l07470"></a>07470 <span class="comment">!    page 915 (&quot;Lagrangian Integration Coefficients&quot;).</span>
    7535. 

  7535. <a name="l07471"></a>07471 <span class="comment">!</span>
    7536. 

  7536. <a name="l07472"></a>07472 <span class="comment">!    Jean Lapidus and John Seinfeld,</span>
    7537. 

  7537. <a name="l07473"></a>07473 <span class="comment">!    Numerical Solution of Ordinary Differential Equations,</span>
    7538. 

  7538. <a name="l07474"></a>07474 <span class="comment">!    Academic Press, 1971.</span>
    7539. 

  7539. <a name="l07475"></a>07475 <span class="comment">!</span>
    7540. 

  7540. <a name="l07476"></a>07476 <span class="comment">!    Daniel Zwillinger, editor,</span>
    7541. 

  7541. <a name="l07477"></a>07477 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    7542. 

  7542. <a name="l07478"></a>07478 <span class="comment">!    30th Edition,</span>
    7543. 

  7543. <a name="l07479"></a>07479 <span class="comment">!    CRC Press, 1996.</span>
    7544. 

  7544. <a name="l07480"></a>07480 <span class="comment">!</span>
    7545. 

  7545. <a name="l07481"></a>07481 <span class="comment">!  Modified:</span>
    7546. 

  7546. <a name="l07482"></a>07482 <span class="comment">!</span>
    7547. 

  7547. <a name="l07483"></a>07483 <span class="comment">!    16 September 1998</span>
    7548. 

  7548. <a name="l07484"></a>07484 <span class="comment">!</span>
    7549. 

  7549. <a name="l07485"></a>07485 <span class="comment">!  Author:</span>
    7550. 

  7550. <a name="l07486"></a>07486 <span class="comment">!</span>
    7551. 

  7551. <a name="l07487"></a>07487 <span class="comment">!    John Burkardt</span>
    7552. 

  7552. <a name="l07488"></a>07488 <span class="comment">!</span>
    7553. 

  7553. <a name="l07489"></a>07489 <span class="comment">!  Parameters:</span>
    7554. 

  7554. <a name="l07490"></a>07490 <span class="comment">!</span>
    7555. 

  7555. <a name="l07491"></a>07491 <span class="comment">!    Input, integer NORDER, the order of the rule.  NORDER must be</span>
    7556. 

  7556. <a name="l07492"></a>07492 <span class="comment">!    between 1 and 10.</span>
    7557. 

  7557. <a name="l07493"></a>07493 <span class="comment">!</span>
    7558. 

  7558. <a name="l07494"></a>07494 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    7559. 

  7559. <a name="l07495"></a>07495 <span class="comment">!</span>
    7560. 

  7560. <a name="l07496"></a>07496 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    7561. 

  7561. <a name="l07497"></a>07497 <span class="comment">!    WEIGHT(1) is the weight at X = 1, WEIGHT(2) the weight at X = 0, and so on.</span>
    7562. 

  7562. <a name="l07498"></a>07498 <span class="comment">!    The weights are rational.  The weights are not symmetric, and</span>
    7563. 

  7563. <a name="l07499"></a>07499 <span class="comment">!    some weights may be negative.  They should sum to 1.</span>
    7564. 

  7564. <a name="l07500"></a>07500 <span class="comment">!</span>
    7565. 

  7565. <a name="l07501"></a>07501   <span class="keyword">implicit none</span>
    7566. 

  7566. <a name="l07502"></a>07502 <span class="comment">!</span>
    7567. 

  7567. <a name="l07503"></a>07503   <span class="keywordtype">integer</span> norder
    7568. 

  7568. <a name="l07504"></a>07504 <span class="comment">!</span>
    7569. 

  7569. <a name="l07505"></a>07505   <span class="keywordtype">double precision</span> d
    7570. 

  7570. <a name="l07506"></a>07506   <span class="keywordtype">integer</span> i
    7571. 

  7571. <a name="l07507"></a>07507   <span class="keywordtype">double precision</span> weight(norder)
    7572. 

  7572. <a name="l07508"></a>07508   <span class="keywordtype">double precision</span> xtab(norder)
    7573. 

  7573. <a name="l07509"></a>07509 <span class="comment">!</span>
    7574. 

  7574. <a name="l07510"></a>07510   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    7575. 

  7575. <a name="l07511"></a>07511 
    7576. 

  7576. <a name="l07512"></a>07512     weight(1) =  1.0D+00
    7577. 

  7577. <a name="l07513"></a>07513 
    7578. 

  7578. <a name="l07514"></a>07514   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    7579. 

  7579. <a name="l07515"></a>07515 
    7580. 

  7580. <a name="l07516"></a>07516     d = 2.0D+00
    7581. 

  7581. <a name="l07517"></a>07517 
    7582. 

  7582. <a name="l07518"></a>07518     weight(1) =  1.0D+00 / d
    7583. 

  7583. <a name="l07519"></a>07519     weight(2) =  1.0D+00 / d
    7584. 

  7584. <a name="l07520"></a>07520 
    7585. 

  7585. <a name="l07521"></a>07521   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    7586. 

  7586. <a name="l07522"></a>07522 
    7587. 

  7587. <a name="l07523"></a>07523     d = 12.0D+00
    7588. 

  7588. <a name="l07524"></a>07524 
    7589. 

  7589. <a name="l07525"></a>07525     weight(1) =    5.0D+00 / d
    7590. 

  7590. <a name="l07526"></a>07526     weight(2) =    8.0D+00 / d
    7591. 

  7591. <a name="l07527"></a>07527     weight(3) =  - 1.0D+00 / d
    7592. 

  7592. <a name="l07528"></a>07528 
    7593. 

  7593. <a name="l07529"></a>07529   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    7594. 

  7594. <a name="l07530"></a>07530 
    7595. 

  7595. <a name="l07531"></a>07531     d = 24.0D+00
    7596. 

  7596. <a name="l07532"></a>07532 
    7597. 

  7597. <a name="l07533"></a>07533     weight(1) =    9.0D+00 / d
    7598. 

  7598. <a name="l07534"></a>07534     weight(2) =   19.0D+00 / d
    7599. 

  7599. <a name="l07535"></a>07535     weight(3) =  - 5.0D+00 / d
    7600. 

  7600. <a name="l07536"></a>07536     weight(4) =    1.0D+00 / d
    7601. 

  7601. <a name="l07537"></a>07537 
    7602. 

  7602. <a name="l07538"></a>07538   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    7603. 

  7603. <a name="l07539"></a>07539 
    7604. 

  7604. <a name="l07540"></a>07540     d = 720.0D+00
    7605. 

  7605. <a name="l07541"></a>07541 
    7606. 

  7606. <a name="l07542"></a>07542     weight(1) =    251.0D+00 / d
    7607. 

  7607. <a name="l07543"></a>07543     weight(2) =    646.0D+00 / d
    7608. 

  7608. <a name="l07544"></a>07544     weight(3) =  - 264.0D+00 / d
    7609. 

  7609. <a name="l07545"></a>07545     weight(4) =    106.0D+00 / d
    7610. 

  7610. <a name="l07546"></a>07546     weight(5) =   - 19.0D+00 / d
    7611. 

  7611. <a name="l07547"></a>07547 
    7612. 

  7612. <a name="l07548"></a>07548   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    7613. 

  7613. <a name="l07549"></a>07549 
    7614. 

  7614. <a name="l07550"></a>07550     d = 1440.0D+00
    7615. 

  7615. <a name="l07551"></a>07551 
    7616. 

  7616. <a name="l07552"></a>07552     weight(1) =    475.0D+00 / d
    7617. 

  7617. <a name="l07553"></a>07553     weight(2) =   1427.0D+00 / d
    7618. 

  7618. <a name="l07554"></a>07554     weight(3) =  - 798.0D+00 / d
    7619. 

  7619. <a name="l07555"></a>07555     weight(4) =    482.0D+00 / d
    7620. 

  7620. <a name="l07556"></a>07556     weight(5) =  - 173.0D+00 / d
    7621. 

  7621. <a name="l07557"></a>07557     weight(6) =     27.0D+00 / d
    7622. 

  7622. <a name="l07558"></a>07558 
    7623. 

  7623. <a name="l07559"></a>07559   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    7624. 

  7624. <a name="l07560"></a>07560 
    7625. 

  7625. <a name="l07561"></a>07561     d = 60480.0D+00
    7626. 

  7626. <a name="l07562"></a>07562 
    7627. 

  7627. <a name="l07563"></a>07563     weight(1) =    19087.0D+00 / d
    7628. 

  7628. <a name="l07564"></a>07564     weight(2) =    65112.0D+00 / d
    7629. 

  7629. <a name="l07565"></a>07565     weight(3) =  - 46461.0D+00 / d
    7630. 

  7630. <a name="l07566"></a>07566     weight(4) =    37504.0D+00 / d
    7631. 

  7631. <a name="l07567"></a>07567     weight(5) =  - 20211.0D+00 / d
    7632. 

  7632. <a name="l07568"></a>07568     weight(6) =     6312.0D+00 / d
    7633. 

  7633. <a name="l07569"></a>07569     weight(7) =    - 863.0D+00 / d
    7634. 

  7634. <a name="l07570"></a>07570 
    7635. 

  7635. <a name="l07571"></a>07571   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    7636. 

  7636. <a name="l07572"></a>07572 
    7637. 

  7637. <a name="l07573"></a>07573     d = 120960.0D+00
    7638. 

  7638. <a name="l07574"></a>07574 
    7639. 

  7639. <a name="l07575"></a>07575     weight(1) =    36799.0D+00 / d
    7640. 

  7640. <a name="l07576"></a>07576     weight(2) =   139849.0D+00 / d
    7641. 

  7641. <a name="l07577"></a>07577     weight(3) = - 121797.0D+00 / d
    7642. 

  7642. <a name="l07578"></a>07578     weight(4) =   123133.0D+00 / d
    7643. 

  7643. <a name="l07579"></a>07579     weight(5) =  - 88547.0D+00 / d
    7644. 

  7644. <a name="l07580"></a>07580     weight(6) =    41499.0D+00 / d
    7645. 

  7645. <a name="l07581"></a>07581     weight(7) =  - 11351.0D+00 / d
    7646. 

  7646. <a name="l07582"></a>07582     weight(8) =     1375.0D+00 / d
    7647. 

  7647. <a name="l07583"></a>07583 
    7648. 

  7648. <a name="l07584"></a>07584   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    7649. 

  7649. <a name="l07585"></a>07585 
    7650. 

  7650. <a name="l07586"></a>07586     d = 3628800.0D+00
    7651. 

  7651. <a name="l07587"></a>07587 
    7652. 

  7652. <a name="l07588"></a>07588     weight(1) =   1070017.0D+00 / d
    7653. 

  7653. <a name="l07589"></a>07589     weight(2) =   4467094.0D+00 / d
    7654. 

  7654. <a name="l07590"></a>07590     weight(3) = - 4604594.0D+00 / d
    7655. 

  7655. <a name="l07591"></a>07591     weight(4) =   5595358.0D+00 / d
    7656. 

  7656. <a name="l07592"></a>07592     weight(5) = - 5033120.0D+00 / d
    7657. 

  7657. <a name="l07593"></a>07593     weight(6) =   3146338.0D+00 / d
    7658. 

  7658. <a name="l07594"></a>07594     weight(7) = - 1291214.0D+00 / d
    7659. 

  7659. <a name="l07595"></a>07595     weight(8) =    312874.0D+00 / d
    7660. 

  7660. <a name="l07596"></a>07596     weight(9) =   - 33953.0D+00 / d
    7661. 

  7661. <a name="l07597"></a>07597 
    7662. 

  7662. <a name="l07598"></a>07598   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
    7663. 

  7663. <a name="l07599"></a>07599 
    7664. 

  7664. <a name="l07600"></a>07600     d = 7257600.0D+00
    7665. 

  7665. <a name="l07601"></a>07601 
    7666. 

  7666. <a name="l07602"></a>07602     weight(1) =    2082753.0D+00 / d
    7667. 

  7667. <a name="l07603"></a>07603     weight(2) =    9449717.0D+00 / d
    7668. 

  7668. <a name="l07604"></a>07604     weight(3) = - 11271304.0D+00 / d
    7669. 

  7669. <a name="l07605"></a>07605     weight(4) =   16002320.0D+00 / d
    7670. 

  7670. <a name="l07606"></a>07606     weight(5) = - 17283646.0D+00 / d
    7671. 

  7671. <a name="l07607"></a>07607     weight(6) =   13510082.0D+00 / d
    7672. 

  7672. <a name="l07608"></a>07608     weight(7) =  - 7394032.0D+00 / d
    7673. 

  7673. <a name="l07609"></a>07609     weight(8) =    2687864.0D+00 / d
    7674. 

  7674. <a name="l07610"></a>07610     weight(9) =   - 583435.0D+00 / d
    7675. 

  7675. <a name="l07611"></a>07611     weight(10) =     57281.0D+00 / d
    7676. 

  7676. <a name="l07612"></a>07612 
    7677. 

  7677. <a name="l07613"></a>07613   <span class="keyword">else</span>
    7678. 

  7678. <a name="l07614"></a>07614 
    7679. 

  7679. <a name="l07615"></a>07615     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    7680. 

  7680. <a name="l07616"></a>07616     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;MOULTON_SET - Fatal error!&#39;</span>
    7681. 

  7681. <a name="l07617"></a>07617     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    7682. 

  7682. <a name="l07618"></a>07618     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 1 through 10.&#39;</span>
    7683. 

  7683. <a name="l07619"></a>07619     stop
    7684. 

  7684. <a name="l07620"></a>07620 
    7685. 

  7685. <a name="l07621"></a>07621   <span class="keyword">end if</span>
    7686. 

  7686. <a name="l07622"></a>07622 
    7687. 

  7687. <a name="l07623"></a>07623   <span class="keyword">do</span> i = 1, norder
    7688. 

  7688. <a name="l07624"></a>07624     xtab(i) = dble ( 2 - i )
    7689. 

  7689. <a name="l07625"></a>07625   <span class="keyword">end do</span>
    7690. 

  7690. <a name="l07626"></a>07626 
    7691. 

  7691. <a name="l07627"></a>07627   return
    7692. 

  7692. <a name="l07628"></a>07628 <span class="keyword">end</span>
    7693. 

  7693. <a name="l07629"></a><a class="code" href="quadrule_8f90.html#a661d42ddf0d8116d8f9353e456918ca0">07629</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a661d42ddf0d8116d8f9353e456918ca0">ncc_com</a> ( norder, xtab, weight )
    7694. 

  7694. <a name="l07630"></a>07630 <span class="comment">!</span>
    7695. 

  7695. <a name="l07631"></a>07631 <span class="comment">!*******************************************************************************</span>
    7696. 

  7696. <a name="l07632"></a>07632 <span class="comment">!</span>
    7697. 

  7697. <a name="l07633"></a>07633 <span class="comment">!! NCC_COM computes the coefficients of a Newton-Cotes closed quadrature rule.</span>
    7698. 

  7698. <a name="l07634"></a>07634 <span class="comment">!</span>
    7699. 

  7699. <a name="l07635"></a>07635 <span class="comment">!</span>
    7700. 

  7700. <a name="l07636"></a>07636 <span class="comment">!  Definition:</span>
    7701. 

  7701. <a name="l07637"></a>07637 <span class="comment">!</span>
    7702. 

  7702. <a name="l07638"></a>07638 <span class="comment">!    For the interval [-1,1], the Newton-Cotes open quadrature rule</span>
    7703. 

  7703. <a name="l07639"></a>07639 <span class="comment">!    estimates</span>
    7704. 

  7704. <a name="l07640"></a>07640 <span class="comment">!</span>
    7705. 

  7705. <a name="l07641"></a>07641 <span class="comment">!      Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    7706. 

  7706. <a name="l07642"></a>07642 <span class="comment">!</span>
    7707. 

  7707. <a name="l07643"></a>07643 <span class="comment">!    using NORDER equally spaced abscissas XTAB(I) and a weight vector</span>
    7708. 

  7708. <a name="l07644"></a>07644 <span class="comment">!    WEIGHT(I):</span>
    7709. 

  7709. <a name="l07645"></a>07645 <span class="comment">!</span>
    7710. 

  7710. <a name="l07646"></a>07646 <span class="comment">!      Sum ( I = 1 to N ) WEIGHT(I) * F ( XTAB(I) ).</span>
    7711. 

  7711. <a name="l07647"></a>07647 <span class="comment">!</span>
    7712. 

  7712. <a name="l07648"></a>07648 <span class="comment">!    For the CLOSED rule, the abscissas include A and B.</span>
    7713. 

  7713. <a name="l07649"></a>07649 <span class="comment">!</span>
    7714. 

  7714. <a name="l07650"></a>07650 <span class="comment">!  Modified:</span>
    7715. 

  7715. <a name="l07651"></a>07651 <span class="comment">!</span>
    7716. 

  7716. <a name="l07652"></a>07652 <span class="comment">!    25 September 1998</span>
    7717. 

  7717. <a name="l07653"></a>07653 <span class="comment">!</span>
    7718. 

  7718. <a name="l07654"></a>07654 <span class="comment">!  Author:</span>
    7719. 

  7719. <a name="l07655"></a>07655 <span class="comment">!</span>
    7720. 

  7720. <a name="l07656"></a>07656 <span class="comment">!    John Burkardt</span>
    7721. 

  7721. <a name="l07657"></a>07657 <span class="comment">!</span>
    7722. 

  7722. <a name="l07658"></a>07658 <span class="comment">!  Parameters:</span>
    7723. 

  7723. <a name="l07659"></a>07659 <span class="comment">!</span>
    7724. 

  7724. <a name="l07660"></a>07660 <span class="comment">!    Input, integer NORDER, the order of the rule, which should be</span>
    7725. 

  7725. <a name="l07661"></a>07661 <span class="comment">!    at least 2.</span>
    7726. 

  7726. <a name="l07662"></a>07662 <span class="comment">!</span>
    7727. 

  7727. <a name="l07663"></a>07663 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    7728. 

  7728. <a name="l07664"></a>07664 <span class="comment">!</span>
    7729. 

  7729. <a name="l07665"></a>07665 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    7730. 

  7730. <a name="l07666"></a>07666 <span class="comment">!</span>
    7731. 

  7731. <a name="l07667"></a>07667   <span class="keyword">implicit none</span>
    7732. 

  7732. <a name="l07668"></a>07668 <span class="comment">!</span>
    7733. 

  7733. <a name="l07669"></a>07669   <span class="keywordtype">integer</span> norder
    7734. 

  7734. <a name="l07670"></a>07670 <span class="comment">!</span>
    7735. 

  7735. <a name="l07671"></a>07671   <span class="keywordtype">double precision</span> a
    7736. 

  7736. <a name="l07672"></a>07672   <span class="keywordtype">double precision</span> b
    7737. 

  7737. <a name="l07673"></a>07673   <span class="keywordtype">integer</span> i
    7738. 

  7738. <a name="l07674"></a>07674   <span class="keywordtype">double precision</span> weight(norder)
    7739. 

  7739. <a name="l07675"></a>07675   <span class="keywordtype">double precision</span> xtab(norder)
    7740. 

  7740. <a name="l07676"></a>07676 <span class="comment">!</span>
    7741. 

  7741. <a name="l07677"></a>07677 <span class="comment">!  Compute a closed quadrature rule.</span>
    7742. 

  7742. <a name="l07678"></a>07678 <span class="comment">!</span>
    7743. 

  7743. <a name="l07679"></a>07679   a = -1.0D+00
    7744. 

  7744. <a name="l07680"></a>07680   b =  1.0D+00
    7745. 

  7745. <a name="l07681"></a>07681 
    7746. 

  7746. <a name="l07682"></a>07682   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    7747. 

  7747. <a name="l07683"></a>07683 
    7748. 

  7748. <a name="l07684"></a>07684     xtab(1) = 0.0D+00
    7749. 

  7749. <a name="l07685"></a>07685     weight(1) = 2.0D+00
    7750. 

  7750. <a name="l07686"></a>07686     return
    7751. 

  7751. <a name="l07687"></a>07687 
    7752. 

  7752. <a name="l07688"></a>07688   <span class="keyword">else</span>
    7753. 

  7753. <a name="l07689"></a>07689 
    7754. 

  7754. <a name="l07690"></a>07690     <span class="keyword">do</span> i = 1, norder
    7755. 

  7755. <a name="l07691"></a>07691       xtab(i) = ( dble ( norder - i ) * a + dble ( i - 1 ) * b ) / &amp;
    7756. 

  7756. <a name="l07692"></a>07692         dble ( norder - 1 )
    7757. 

  7757. <a name="l07693"></a>07693     <span class="keyword">end do</span>
    7758. 

  7758. <a name="l07694"></a>07694 
    7759. 

  7759. <a name="l07695"></a>07695   <span class="keyword">end if</span>
    7760. 

  7760. <a name="l07696"></a>07696 
    7761. 

  7761. <a name="l07697"></a>07697   call <a class="code" href="quadrule_8f90.html#a0b336aacd3856d5d5e724522dd3e6e8a">nc_com </a>( norder, a, b, xtab, weight )
    7762. 

  7762. <a name="l07698"></a>07698 
    7763. 

  7763. <a name="l07699"></a>07699   return
    7764. 

  7764. <a name="l07700"></a>07700 <span class="keyword">end</span>
    7765. 

  7765. <a name="l07701"></a><a class="code" href="quadrule_8f90.html#a0b336aacd3856d5d5e724522dd3e6e8a">07701</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a0b336aacd3856d5d5e724522dd3e6e8a">nc_com</a> ( norder, a, b, xtab, weight )
    7766. 

  7766. <a name="l07702"></a>07702 <span class="comment">!</span>
    7767. 

  7767. <a name="l07703"></a>07703 <span class="comment">!*******************************************************************************</span>
    7768. 

  7768. <a name="l07704"></a>07704 <span class="comment">!</span>
    7769. 

  7769. <a name="l07705"></a>07705 <span class="comment">!! NC_COM computes the coefficients of a Newton-Cotes quadrature rule.</span>
    7770. 

  7770. <a name="l07706"></a>07706 <span class="comment">!</span>
    7771. 

  7771. <a name="l07707"></a>07707 <span class="comment">!</span>
    7772. 

  7772. <a name="l07708"></a>07708 <span class="comment">!  Definition:</span>
    7773. 

  7773. <a name="l07709"></a>07709 <span class="comment">!</span>
    7774. 

  7774. <a name="l07710"></a>07710 <span class="comment">!    For the interval [A,B], the Newton-Cotes quadrature rule estimates</span>
    7775. 

  7775. <a name="l07711"></a>07711 <span class="comment">!</span>
    7776. 

  7776. <a name="l07712"></a>07712 <span class="comment">!      Integral ( A &lt;= X &lt;= B ) F(X) dX</span>
    7777. 

  7777. <a name="l07713"></a>07713 <span class="comment">!</span>
    7778. 

  7778. <a name="l07714"></a>07714 <span class="comment">!    using NORDER equally spaced abscissas XTAB(I) and a weight vector</span>
    7779. 

  7779. <a name="l07715"></a>07715 <span class="comment">!    WEIGHT(I):</span>
    7780. 

  7780. <a name="l07716"></a>07716 <span class="comment">!</span>
    7781. 

  7781. <a name="l07717"></a>07717 <span class="comment">!      Sum ( I = 1 to N ) WEIGHT(I) * F ( XTAB(I) ).</span>
    7782. 

  7782. <a name="l07718"></a>07718 <span class="comment">!</span>
    7783. 

  7783. <a name="l07719"></a>07719 <span class="comment">!    For the CLOSED rule, the abscissas include the points A and B.</span>
    7784. 

  7784. <a name="l07720"></a>07720 <span class="comment">!    For the OPEN rule, the abscissas do not include A and B.</span>
    7785. 

  7785. <a name="l07721"></a>07721 <span class="comment">!</span>
    7786. 

  7786. <a name="l07722"></a>07722 <span class="comment">!  Modified:</span>
    7787. 

  7787. <a name="l07723"></a>07723 <span class="comment">!</span>
    7788. 

  7788. <a name="l07724"></a>07724 <span class="comment">!    25 September 1998</span>
    7789. 

  7789. <a name="l07725"></a>07725 <span class="comment">!</span>
    7790. 

  7790. <a name="l07726"></a>07726 <span class="comment">!  Author:</span>
    7791. 

  7791. <a name="l07727"></a>07727 <span class="comment">!</span>
    7792. 

  7792. <a name="l07728"></a>07728 <span class="comment">!    John Burkardt</span>
    7793. 

  7793. <a name="l07729"></a>07729 <span class="comment">!</span>
    7794. 

  7794. <a name="l07730"></a>07730 <span class="comment">!  Parameters:</span>
    7795. 

  7795. <a name="l07731"></a>07731 <span class="comment">!</span>
    7796. 

  7796. <a name="l07732"></a>07732 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    7797. 

  7797. <a name="l07733"></a>07733 <span class="comment">!</span>
    7798. 

  7798. <a name="l07734"></a>07734 <span class="comment">!    Input, double precision A, B, the left and right endpoints of the interval</span>
    7799. 

  7799. <a name="l07735"></a>07735 <span class="comment">!    over which the quadrature rule is to be applied.</span>
    7800. 

  7800. <a name="l07736"></a>07736 <span class="comment">!</span>
    7801. 

  7801. <a name="l07737"></a>07737 <span class="comment">!    Input, double precision XTAB(NORDER), the abscissas of the rule.</span>
    7802. 

  7802. <a name="l07738"></a>07738 <span class="comment">!</span>
    7803. 

  7803. <a name="l07739"></a>07739 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    7804. 

  7804. <a name="l07740"></a>07740 <span class="comment">!</span>
    7805. 

  7805. <a name="l07741"></a>07741   <span class="keyword">implicit none</span>
    7806. 

  7806. <a name="l07742"></a>07742 <span class="comment">!</span>
    7807. 

  7807. <a name="l07743"></a>07743   <span class="keywordtype">integer</span> norder
    7808. 

  7808. <a name="l07744"></a>07744 <span class="comment">!</span>
    7809. 

  7809. <a name="l07745"></a>07745   <span class="keywordtype">double precision</span> a
    7810. 

  7810. <a name="l07746"></a>07746   <span class="keywordtype">double precision</span> b
    7811. 

  7811. <a name="l07747"></a>07747   <span class="keywordtype">double precision</span> diftab(norder)
    7812. 

  7812. <a name="l07748"></a>07748   <span class="keywordtype">integer</span> i
    7813. 

  7813. <a name="l07749"></a>07749   <span class="keywordtype">integer</span> j
    7814. 

  7814. <a name="l07750"></a>07750   <span class="keywordtype">integer</span> k
    7815. 

  7815. <a name="l07751"></a>07751   <span class="keywordtype">double precision</span> weight(norder)
    7816. 

  7816. <a name="l07752"></a>07752   <span class="keywordtype">double precision</span> xtab(norder)
    7817. 

  7817. <a name="l07753"></a>07753   <span class="keywordtype">double precision</span> yvala
    7818. 

  7818. <a name="l07754"></a>07754   <span class="keywordtype">double precision</span> yvalb
    7819. 

  7819. <a name="l07755"></a>07755 <span class="comment">!</span>
    7820. 

  7820. <a name="l07756"></a>07756   <span class="keyword">do</span> i = 1, norder
    7821. 

  7821. <a name="l07757"></a>07757 <span class="comment">!</span>
    7822. 

  7822. <a name="l07758"></a>07758 <span class="comment">!  Compute the Lagrange basis polynomial which is 1 at XTAB(I),</span>
    7823. 

  7823. <a name="l07759"></a>07759 <span class="comment">!  and zero at the other nodes.</span>
    7824. 

  7824. <a name="l07760"></a>07760 <span class="comment">!</span>
    7825. 

  7825. <a name="l07761"></a>07761     diftab(1:norder) = 0.0D+00
    7826. 

  7826. <a name="l07762"></a>07762     diftab(i) = 1.0D+00
    7827. 

  7827. <a name="l07763"></a>07763 
    7828. 

  7828. <a name="l07764"></a>07764     <span class="keyword">do</span> j = 2, norder
    7829. 

  7829. <a name="l07765"></a>07765       <span class="keyword">do</span> k = j, norder
    7830. 

  7830. <a name="l07766"></a>07766         diftab(norder+j-k) = ( diftab(norder+j-k-1) - diftab(norder+j-k) ) &amp;
    7831. 

  7831. <a name="l07767"></a>07767           / ( xtab(norder+1-k) - xtab(norder+j-k) )
    7832. 

  7832. <a name="l07768"></a>07768       <span class="keyword">end do</span>
    7833. 

  7833. <a name="l07769"></a>07769     <span class="keyword">end do</span>
    7834. 

  7834. <a name="l07770"></a>07770 
    7835. 

  7835. <a name="l07771"></a>07771     <span class="keyword">do</span> j = 1, norder-1
    7836. 

  7836. <a name="l07772"></a>07772       <span class="keyword">do</span> k = 1, norder-j
    7837. 

  7837. <a name="l07773"></a>07773         diftab(norder-k) = diftab(norder-k) - xtab(norder-k-j+1) * &amp;
    7838. 

  7838. <a name="l07774"></a>07774           diftab(norder-k+1)
    7839. 

  7839. <a name="l07775"></a>07775       <span class="keyword">end do</span>
    7840. 

  7840. <a name="l07776"></a>07776     <span class="keyword">end do</span>
    7841. 

  7841. <a name="l07777"></a>07777 <span class="comment">!</span>
    7842. 

  7842. <a name="l07778"></a>07778 <span class="comment">!  Evaluate the antiderivative of the polynomial at the left and</span>
    7843. 

  7843. <a name="l07779"></a>07779 <span class="comment">!  right endpoints.</span>
    7844. 

  7844. <a name="l07780"></a>07780 <span class="comment">!</span>
    7845. 

  7845. <a name="l07781"></a>07781     yvala = diftab(norder) / dble ( norder )
    7846. 

  7846. <a name="l07782"></a>07782     <span class="keyword">do</span> j = norder-1, 1, -1
    7847. 

  7847. <a name="l07783"></a>07783       yvala = yvala * a + diftab(j) / dble ( j )
    7848. 

  7848. <a name="l07784"></a>07784     <span class="keyword">end do</span>
    7849. 

  7849. <a name="l07785"></a>07785     yvala = yvala * a
    7850. 

  7850. <a name="l07786"></a>07786 
    7851. 

  7851. <a name="l07787"></a>07787     yvalb = diftab(norder) / dble ( norder )
    7852. 

  7852. <a name="l07788"></a>07788     <span class="keyword">do</span> j = norder-1, 1, -1
    7853. 

  7853. <a name="l07789"></a>07789       yvalb = yvalb * b + diftab(j) / dble ( j )
    7854. 

  7854. <a name="l07790"></a>07790     <span class="keyword">end do</span>
    7855. 

  7855. <a name="l07791"></a>07791     yvalb = yvalb * b
    7856. 

  7856. <a name="l07792"></a>07792 
    7857. 

  7857. <a name="l07793"></a>07793     weight(i) = yvalb - yvala
    7858. 

  7858. <a name="l07794"></a>07794 
    7859. 

  7859. <a name="l07795"></a>07795   <span class="keyword">end do</span>
    7860. 

  7860. <a name="l07796"></a>07796 
    7861. 

  7861. <a name="l07797"></a>07797   return
    7862. 

  7862. <a name="l07798"></a>07798 <span class="keyword">end</span>
    7863. 

  7863. <a name="l07799"></a><a class="code" href="quadrule_8f90.html#a45c034914a08b905c6dbe38d8ef5c5d9">07799</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a45c034914a08b905c6dbe38d8ef5c5d9">ncc_set</a> ( norder, xtab, weight )
    7864. 

  7864. <a name="l07800"></a>07800 <span class="comment">!</span>
    7865. 

  7865. <a name="l07801"></a>07801 <span class="comment">!*******************************************************************************</span>
    7866. 

  7866. <a name="l07802"></a>07802 <span class="comment">!</span>
    7867. 

  7867. <a name="l07803"></a>07803 <span class="comment">!! NCC_SET sets abscissas and weights for closed Newton-Cotes quadrature.</span>
    7868. 

  7868. <a name="l07804"></a>07804 <span class="comment">!</span>
    7869. 

  7869. <a name="l07805"></a>07805 <span class="comment">!</span>
    7870. 

  7870. <a name="l07806"></a>07806 <span class="comment">!  Integration interval:</span>
    7871. 

  7871. <a name="l07807"></a>07807 <span class="comment">!</span>
    7872. 

  7872. <a name="l07808"></a>07808 <span class="comment">!    [ -1, 1 ]</span>
    7873. 

  7873. <a name="l07809"></a>07809 <span class="comment">!</span>
    7874. 

  7874. <a name="l07810"></a>07810 <span class="comment">!  Weight function:</span>
    7875. 

  7875. <a name="l07811"></a>07811 <span class="comment">!</span>
    7876. 

  7876. <a name="l07812"></a>07812 <span class="comment">!    1.0D+00</span>
    7877. 

  7877. <a name="l07813"></a>07813 <span class="comment">!</span>
    7878. 

  7878. <a name="l07814"></a>07814 <span class="comment">!  Integral to approximate:</span>
    7879. 

  7879. <a name="l07815"></a>07815 <span class="comment">!</span>
    7880. 

  7880. <a name="l07816"></a>07816 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    7881. 

  7881. <a name="l07817"></a>07817 <span class="comment">!</span>
    7882. 

  7882. <a name="l07818"></a>07818 <span class="comment">!  Approximate integral:</span>
    7883. 

  7883. <a name="l07819"></a>07819 <span class="comment">!</span>
    7884. 

  7884. <a name="l07820"></a>07820 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    7885. 

  7885. <a name="l07821"></a>07821 <span class="comment">!</span>
    7886. 

  7886. <a name="l07822"></a>07822 <span class="comment">!  Note:</span>
    7887. 

  7887. <a name="l07823"></a>07823 <span class="comment">!</span>
    7888. 

  7888. <a name="l07824"></a>07824 <span class="comment">!    The closed Newton-Cotes rules use equally spaced abscissas, and</span>
    7889. 

  7889. <a name="l07825"></a>07825 <span class="comment">!    hence may be used with tabulated function data.</span>
    7890. 

  7890. <a name="l07826"></a>07826 <span class="comment">!</span>
    7891. 

  7891. <a name="l07827"></a>07827 <span class="comment">!    The rules are called &quot;closed&quot; because they include the endpoints.</span>
    7892. 

  7892. <a name="l07828"></a>07828 <span class="comment">!</span>
    7893. 

  7893. <a name="l07829"></a>07829 <span class="comment">!    The higher order rules involve negative weights.  These can produce</span>
    7894. 

  7894. <a name="l07830"></a>07830 <span class="comment">!    loss of accuracy due to the subtraction of large, nearly equal quantities.</span>
    7895. 

  7895. <a name="l07831"></a>07831 <span class="comment">!</span>
    7896. 

  7896. <a name="l07832"></a>07832 <span class="comment">!    NORDER = 2 is the trapezoidal rule.</span>
    7897. 

  7897. <a name="l07833"></a>07833 <span class="comment">!    NORDER = 3 is Simpson&#39;s rule.</span>
    7898. 

  7898. <a name="l07834"></a>07834 <span class="comment">!    NORDER = 4 is Simpson&#39;s 3/8 rule.</span>
    7899. 

  7899. <a name="l07835"></a>07835 <span class="comment">!    NORDER = 5 is Bode&#39;s rule.</span>
    7900. 

  7900. <a name="l07836"></a>07836 <span class="comment">!</span>
    7901. 

  7901. <a name="l07837"></a>07837 <span class="comment">!    The Kopal reference for NORDER = 12 lists</span>
    7902. 

  7902. <a name="l07838"></a>07838 <span class="comment">!      WEIGHT(6) = 15494566.0D+00 / 43545600.0D+00</span>
    7903. 

  7903. <a name="l07839"></a>07839 <span class="comment">!    but this results in a set of coeffients that don&#39;t add up to 2.</span>
    7904. 

  7904. <a name="l07840"></a>07840 <span class="comment">!    The correct value is</span>
    7905. 

  7905. <a name="l07841"></a>07841 <span class="comment">!      WEIGHT(6) = 15493566.0D+00 / 43545600.0.</span>
    7906. 

  7906. <a name="l07842"></a>07842 <span class="comment">!</span>
    7907. 

  7907. <a name="l07843"></a>07843 <span class="comment">!  Reference:</span>
    7908. 

  7908. <a name="l07844"></a>07844 <span class="comment">!</span>
    7909. 

  7909. <a name="l07845"></a>07845 <span class="comment">!    Abramowitz and Stegun,</span>
    7910. 

  7910. <a name="l07846"></a>07846 <span class="comment">!    Handbook of Mathematical Functions,</span>
    7911. 

  7911. <a name="l07847"></a>07847 <span class="comment">!    National Bureau of Standards, 1964.</span>
    7912. 

  7912. <a name="l07848"></a>07848 <span class="comment">!</span>
    7913. 

  7913. <a name="l07849"></a>07849 <span class="comment">!    Johnson,</span>
    7914. 

  7914. <a name="l07850"></a>07850 <span class="comment">!    Quarterly Journal of Mathematics,</span>
    7915. 

  7915. <a name="l07851"></a>07851 <span class="comment">!    Volume 46, Number 52, 1915.</span>
    7916. 

  7916. <a name="l07852"></a>07852 <span class="comment">!</span>
    7917. 

  7917. <a name="l07853"></a>07853 <span class="comment">!    Zdenek Kopal,</span>
    7918. 

  7918. <a name="l07854"></a>07854 <span class="comment">!    Numerical Analysis,</span>
    7919. 

  7919. <a name="l07855"></a>07855 <span class="comment">!    John Wiley, 1955.</span>
    7920. 

  7920. <a name="l07856"></a>07856 <span class="comment">!</span>
    7921. 

  7921. <a name="l07857"></a>07857 <span class="comment">!    Daniel Zwillinger, editor,</span>
    7922. 

  7922. <a name="l07858"></a>07858 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    7923. 

  7923. <a name="l07859"></a>07859 <span class="comment">!    30th Edition,</span>
    7924. 

  7924. <a name="l07860"></a>07860 <span class="comment">!    CRC Press, 1996.</span>
    7925. 

  7925. <a name="l07861"></a>07861 <span class="comment">!</span>
    7926. 

  7926. <a name="l07862"></a>07862 <span class="comment">!  Modified:</span>
    7927. 

  7927. <a name="l07863"></a>07863 <span class="comment">!</span>
    7928. 

  7928. <a name="l07864"></a>07864 <span class="comment">!    16 September 1998</span>
    7929. 

  7929. <a name="l07865"></a>07865 <span class="comment">!</span>
    7930. 

  7930. <a name="l07866"></a>07866 <span class="comment">!  Author:</span>
    7931. 

  7931. <a name="l07867"></a>07867 <span class="comment">!</span>
    7932. 

  7932. <a name="l07868"></a>07868 <span class="comment">!    John Burkardt</span>
    7933. 

  7933. <a name="l07869"></a>07869 <span class="comment">!</span>
    7934. 

  7934. <a name="l07870"></a>07870 <span class="comment">!  Parameters:</span>
    7935. 

  7935. <a name="l07871"></a>07871 <span class="comment">!</span>
    7936. 

  7936. <a name="l07872"></a>07872 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    7937. 

  7937. <a name="l07873"></a>07873 <span class="comment">!    NORDER must be between 2 and 20.</span>
    7938. 

  7938. <a name="l07874"></a>07874 <span class="comment">!</span>
    7939. 

  7939. <a name="l07875"></a>07875 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    7940. 

  7940. <a name="l07876"></a>07876 <span class="comment">!    The abscissas are uniformly spaced in the interval, and include</span>
    7941. 

  7941. <a name="l07877"></a>07877 <span class="comment">!    -1 and 1.</span>
    7942. 

  7942. <a name="l07878"></a>07878 <span class="comment">!</span>
    7943. 

  7943. <a name="l07879"></a>07879 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    7944. 

  7944. <a name="l07880"></a>07880 <span class="comment">!    The weights are symmetric, rational, and should sum to 2.0.</span>
    7945. 

  7945. <a name="l07881"></a>07881 <span class="comment">!    Some weights may be negative.</span>
    7946. 

  7946. <a name="l07882"></a>07882 <span class="comment">!</span>
    7947. 

  7947. <a name="l07883"></a>07883   <span class="keyword">implicit none</span>
    7948. 

  7948. <a name="l07884"></a>07884 <span class="comment">!</span>
    7949. 

  7949. <a name="l07885"></a>07885   <span class="keywordtype">integer</span> norder
    7950. 

  7950. <a name="l07886"></a>07886 <span class="comment">!</span>
    7951. 

  7951. <a name="l07887"></a>07887   <span class="keywordtype">double precision</span> d
    7952. 

  7952. <a name="l07888"></a>07888   <span class="keywordtype">integer</span> i
    7953. 

  7953. <a name="l07889"></a>07889   <span class="keywordtype">double precision</span> weight(norder)
    7954. 

  7954. <a name="l07890"></a>07890   <span class="keywordtype">double precision</span> xtab(norder)
    7955. 

  7955. <a name="l07891"></a>07891 <span class="comment">!</span>
    7956. 

  7956. <a name="l07892"></a>07892   <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    7957. 

  7957. <a name="l07893"></a>07893 
    7958. 

  7958. <a name="l07894"></a>07894     weight(1) = 1.0D+00
    7959. 

  7959. <a name="l07895"></a>07895     weight(2) = 1.0D+00
    7960. 

  7960. <a name="l07896"></a>07896 
    7961. 

  7961. <a name="l07897"></a>07897   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    7962. 

  7962. <a name="l07898"></a>07898 
    7963. 

  7963. <a name="l07899"></a>07899     d = 3.0D+00
    7964. 

  7964. <a name="l07900"></a>07900 
    7965. 

  7965. <a name="l07901"></a>07901     weight(1) = 1.0D+00 / d
    7966. 

  7966. <a name="l07902"></a>07902     weight(2) = 4.0D+00 / d
    7967. 

  7967. <a name="l07903"></a>07903     weight(3) = 1.0D+00 / d
    7968. 

  7968. <a name="l07904"></a>07904 
    7969. 

  7969. <a name="l07905"></a>07905   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    7970. 

  7970. <a name="l07906"></a>07906 
    7971. 

  7971. <a name="l07907"></a>07907     d = 4.0D+00
    7972. 

  7972. <a name="l07908"></a>07908 
    7973. 

  7973. <a name="l07909"></a>07909     weight(1) = 1.0D+00 / d
    7974. 

  7974. <a name="l07910"></a>07910     weight(2) = 3.0D+00 / d
    7975. 

  7975. <a name="l07911"></a>07911     weight(3) = 3.0D+00 / d
    7976. 

  7976. <a name="l07912"></a>07912     weight(4) = 1.0D+00 / d
    7977. 

  7977. <a name="l07913"></a>07913 
    7978. 

  7978. <a name="l07914"></a>07914   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    7979. 

  7979. <a name="l07915"></a>07915 
    7980. 

  7980. <a name="l07916"></a>07916     d = 45.0D+00
    7981. 

  7981. <a name="l07917"></a>07917 
    7982. 

  7982. <a name="l07918"></a>07918     weight(1) =  7.0D+00 / d
    7983. 

  7983. <a name="l07919"></a>07919     weight(2) = 32.0D+00 / d
    7984. 

  7984. <a name="l07920"></a>07920     weight(3) = 12.0D+00 / d
    7985. 

  7985. <a name="l07921"></a>07921     weight(4) = 32.0D+00 / d
    7986. 

  7986. <a name="l07922"></a>07922     weight(5) =  7.0D+00 / d
    7987. 

  7987. <a name="l07923"></a>07923 
    7988. 

  7988. <a name="l07924"></a>07924   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    7989. 

  7989. <a name="l07925"></a>07925 
    7990. 

  7990. <a name="l07926"></a>07926     d = 144.0D+00
    7991. 

  7991. <a name="l07927"></a>07927 
    7992. 

  7992. <a name="l07928"></a>07928     weight(1) = 19.0D+00 / d
    7993. 

  7993. <a name="l07929"></a>07929     weight(2) = 75.0D+00 / d
    7994. 

  7994. <a name="l07930"></a>07930     weight(3) = 50.0D+00 / d
    7995. 

  7995. <a name="l07931"></a>07931     weight(4) = 50.0D+00 / d
    7996. 

  7996. <a name="l07932"></a>07932     weight(5) = 75.0D+00 / d
    7997. 

  7997. <a name="l07933"></a>07933     weight(6) = 19.0D+00 / d
    7998. 

  7998. <a name="l07934"></a>07934 
    7999. 

  7999. <a name="l07935"></a>07935   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    8000. 

  8000. <a name="l07936"></a>07936 
    8001. 

  8001. <a name="l07937"></a>07937     d = 420.0D+00
    8002. 

  8002. <a name="l07938"></a>07938 
    8003. 

  8003. <a name="l07939"></a>07939     weight(1) =  41.0D+00 / d
    8004. 

  8004. <a name="l07940"></a>07940     weight(2) = 216.0D+00 / d
    8005. 

  8005. <a name="l07941"></a>07941     weight(3) =  27.0D+00 / d
    8006. 

  8006. <a name="l07942"></a>07942     weight(4) = 272.0D+00 / d
    8007. 

  8007. <a name="l07943"></a>07943     weight(5) =  27.0D+00 / d
    8008. 

  8008. <a name="l07944"></a>07944     weight(6) = 216.0D+00 / d
    8009. 

  8009. <a name="l07945"></a>07945     weight(7) =  41.0D+00 / d
    8010. 

  8010. <a name="l07946"></a>07946 
    8011. 

  8011. <a name="l07947"></a>07947   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    8012. 

  8012. <a name="l07948"></a>07948 
    8013. 

  8013. <a name="l07949"></a>07949     d = 8640.0D+00
    8014. 

  8014. <a name="l07950"></a>07950 
    8015. 

  8015. <a name="l07951"></a>07951     weight(1) =  751.0D+00 / d
    8016. 

  8016. <a name="l07952"></a>07952     weight(2) = 3577.0D+00 / d
    8017. 

  8017. <a name="l07953"></a>07953     weight(3) = 1323.0D+00 / d
    8018. 

  8018. <a name="l07954"></a>07954     weight(4) = 2989.0D+00 / d
    8019. 

  8019. <a name="l07955"></a>07955     weight(5) = 2989.0D+00 / d
    8020. 

  8020. <a name="l07956"></a>07956     weight(6) = 1323.0D+00 / d
    8021. 

  8021. <a name="l07957"></a>07957     weight(7) = 3577.0D+00 / d
    8022. 

  8022. <a name="l07958"></a>07958     weight(8) =  751.0D+00 / d
    8023. 

  8023. <a name="l07959"></a>07959 
    8024. 

  8024. <a name="l07960"></a>07960   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    8025. 

  8025. <a name="l07961"></a>07961 
    8026. 

  8026. <a name="l07962"></a>07962     d = 14175.0D+00
    8027. 

  8027. <a name="l07963"></a>07963 
    8028. 

  8028. <a name="l07964"></a>07964     weight(1) =    989.0D+00 / d
    8029. 

  8029. <a name="l07965"></a>07965     weight(2) =   5888.0D+00 / d
    8030. 

  8030. <a name="l07966"></a>07966     weight(3) =  - 928.0D+00 / d
    8031. 

  8031. <a name="l07967"></a>07967     weight(4) =  10496.0D+00 / d
    8032. 

  8032. <a name="l07968"></a>07968     weight(5) = - 4540.0D+00 / d
    8033. 

  8033. <a name="l07969"></a>07969     weight(6) =  10496.0D+00 / d
    8034. 

  8034. <a name="l07970"></a>07970     weight(7) =  - 928.0D+00 / d
    8035. 

  8035. <a name="l07971"></a>07971     weight(8) =   5888.0D+00 / d
    8036. 

  8036. <a name="l07972"></a>07972     weight(9) =    989.0D+00 / d
    8037. 

  8037. <a name="l07973"></a>07973 
    8038. 

  8038. <a name="l07974"></a>07974   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
    8039. 

  8039. <a name="l07975"></a>07975 
    8040. 

  8040. <a name="l07976"></a>07976     d = 44800.0D+00
    8041. 

  8041. <a name="l07977"></a>07977 
    8042. 

  8042. <a name="l07978"></a>07978     weight(1) =   2857.0D+00 / d
    8043. 

  8043. <a name="l07979"></a>07979     weight(2) =  15741.0D+00 / d
    8044. 

  8044. <a name="l07980"></a>07980     weight(3) =   1080.0D+00 / d
    8045. 

  8045. <a name="l07981"></a>07981     weight(4) =  19344.0D+00 / d
    8046. 

  8046. <a name="l07982"></a>07982     weight(5) =   5778.0D+00 / d
    8047. 

  8047. <a name="l07983"></a>07983     weight(6) =   5778.0D+00 / d
    8048. 

  8048. <a name="l07984"></a>07984     weight(7) =  19344.0D+00 / d
    8049. 

  8049. <a name="l07985"></a>07985     weight(8) =   1080.0D+00 / d
    8050. 

  8050. <a name="l07986"></a>07986     weight(9) =  15741.0D+00 / d
    8051. 

  8051. <a name="l07987"></a>07987     weight(10) =  2857.0D+00 / d
    8052. 

  8052. <a name="l07988"></a>07988 
    8053. 

  8053. <a name="l07989"></a>07989   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 11 ) <span class="keyword">then</span>
    8054. 

  8054. <a name="l07990"></a>07990 
    8055. 

  8055. <a name="l07991"></a>07991     d = 299376.0D+00
    8056. 

  8056. <a name="l07992"></a>07992 
    8057. 

  8057. <a name="l07993"></a>07993     weight(1) =     16067.0D+00 / d
    8058. 

  8058. <a name="l07994"></a>07994     weight(2) =    106300.0D+00 / d
    8059. 

  8059. <a name="l07995"></a>07995     weight(3) =   - 48525.0D+00 / d
    8060. 

  8060. <a name="l07996"></a>07996     weight(4) =    272400.0D+00 / d
    8061. 

  8061. <a name="l07997"></a>07997     weight(5) =  - 260550.0D+00 / d
    8062. 

  8062. <a name="l07998"></a>07998     weight(6) =    427368.0D+00 / d
    8063. 

  8063. <a name="l07999"></a>07999     weight(7) =  - 260550.0D+00 / d
    8064. 

  8064. <a name="l08000"></a>08000     weight(8) =    272400.0D+00 / d
    8065. 

  8065. <a name="l08001"></a>08001     weight(9) =   - 48525.0D+00 / d
    8066. 

  8066. <a name="l08002"></a>08002     weight(10) =   106300.0D+00 / d
    8067. 

  8067. <a name="l08003"></a>08003     weight(11) =    16067.0D+00 / d
    8068. 

  8068. <a name="l08004"></a>08004 
    8069. 

  8069. <a name="l08005"></a>08005   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 12 ) <span class="keyword">then</span>
    8070. 

  8070. <a name="l08006"></a>08006 
    8071. 

  8071. <a name="l08007"></a>08007     d = 43545600.0D+00
    8072. 

  8072. <a name="l08008"></a>08008 
    8073. 

  8073. <a name="l08009"></a>08009     weight(1) =     2171465.0D+00 / d
    8074. 

  8074. <a name="l08010"></a>08010     weight(2) =    13486539.0D+00 / d
    8075. 

  8075. <a name="l08011"></a>08011     weight(3) =   - 3237113.0D+00 / d
    8076. 

  8076. <a name="l08012"></a>08012     weight(4) =    25226685.0D+00 / d
    8077. 

  8077. <a name="l08013"></a>08013     weight(5) =   - 9595542.0D+00 / d
    8078. 

  8078. <a name="l08014"></a>08014     weight(6) =    15493566.0D+00 / d
    8079. 

  8079. <a name="l08015"></a>08015     weight(7) =    15493566.0D+00 / d
    8080. 

  8080. <a name="l08016"></a>08016     weight(8) =   - 9595542.0D+00 / d
    8081. 

  8081. <a name="l08017"></a>08017     weight(9) =    25226685.0D+00 / d
    8082. 

  8082. <a name="l08018"></a>08018     weight(10) =  - 3237113.0D+00 / d
    8083. 

  8083. <a name="l08019"></a>08019     weight(11) =   13486539.0D+00 / d
    8084. 

  8084. <a name="l08020"></a>08020     weight(12) =    2171465.0D+00 / d
    8085. 

  8085. <a name="l08021"></a>08021 
    8086. 

  8086. <a name="l08022"></a>08022   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 13 ) <span class="keyword">then</span>
    8087. 

  8087. <a name="l08023"></a>08023 
    8088. 

  8088. <a name="l08024"></a>08024     d = 31531500.0D+00
    8089. 

  8089. <a name="l08025"></a>08025 
    8090. 

  8090. <a name="l08026"></a>08026     weight(1) =      1364651.0D+00 / d
    8091. 

  8091. <a name="l08027"></a>08027     weight(2) =      9903168.0D+00 / d
    8092. 

  8092. <a name="l08028"></a>08028     weight(3) =    - 7587864.0D+00 / d
    8093. 

  8093. <a name="l08029"></a>08029     weight(4) =     35725120.0D+00 / d
    8094. 

  8094. <a name="l08030"></a>08030     weight(5) =   - 51491295.0D+00 / d
    8095. 

  8095. <a name="l08031"></a>08031     weight(6) =     87516288.0D+00 / d
    8096. 

  8096. <a name="l08032"></a>08032     weight(7) =   - 87797136.0D+00 / d
    8097. 

  8097. <a name="l08033"></a>08033     weight(8) =     87516288.0D+00 / d
    8098. 

  8098. <a name="l08034"></a>08034     weight(9) =   - 51491295.0D+00 / d
    8099. 

  8099. <a name="l08035"></a>08035     weight(10) =    35725120.0D+00 / d
    8100. 

  8100. <a name="l08036"></a>08036     weight(11) =   - 7587864.0D+00 / d
    8101. 

  8101. <a name="l08037"></a>08037     weight(12) =     9903168.0D+00 / d
    8102. 

  8102. <a name="l08038"></a>08038     weight(13) =     1364651.0D+00 / d
    8103. 

  8103. <a name="l08039"></a>08039 
    8104. 

  8104. <a name="l08040"></a>08040   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 14 ) <span class="keyword">then</span>
    8105. 

  8105. <a name="l08041"></a>08041 
    8106. 

  8106. <a name="l08042"></a>08042     d = 150885504000.0D+00
    8107. 

  8107. <a name="l08043"></a>08043 
    8108. 

  8108. <a name="l08044"></a>08044     weight(1) =      6137698213.0D+00 / d
    8109. 

  8109. <a name="l08045"></a>08045     weight(2) =     42194238652.0D+00 / d
    8110. 

  8110. <a name="l08046"></a>08046     weight(3) =   - 23361540993.0D+00 / d
    8111. 

  8111. <a name="l08047"></a>08047     weight(4) =    116778274403.0D+00 / d
    8112. 

  8112. <a name="l08048"></a>08048     weight(5) =  - 113219777650.0D+00 / d
    8113. 

  8113. <a name="l08049"></a>08049     weight(6) =    154424590209.0D+00 / d
    8114. 

  8114. <a name="l08050"></a>08050     weight(7) =   - 32067978834.0D+00 / d
    8115. 

  8115. <a name="l08051"></a>08051     weight(8) =   - 32067978834.0D+00 / d
    8116. 

  8116. <a name="l08052"></a>08052     weight(9) =    154424590209.0D+00 / d
    8117. 

  8117. <a name="l08053"></a>08053     weight(10) = - 113219777650.0D+00 / d
    8118. 

  8118. <a name="l08054"></a>08054     weight(11) =   116778274403.0D+00 / d
    8119. 

  8119. <a name="l08055"></a>08055     weight(12) =  - 23361540993.0D+00 / d
    8120. 

  8120. <a name="l08056"></a>08056     weight(13) =    42194238652.0D+00 / d
    8121. 

  8121. <a name="l08057"></a>08057     weight(14) =     6137698213.0D+00 / d
    8122. 

  8122. <a name="l08058"></a>08058 
    8123. 

  8123. <a name="l08059"></a>08059   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
    8124. 

  8124. <a name="l08060"></a>08060 
    8125. 

  8125. <a name="l08061"></a>08061     d = 2501928000.0D+00
    8126. 

  8126. <a name="l08062"></a>08062 
    8127. 

  8127. <a name="l08063"></a>08063     weight(1) =       90241897.0D+00 / d
    8128. 

  8128. <a name="l08064"></a>08064     weight(2) =      710986864.0D+00 / d
    8129. 

  8129. <a name="l08065"></a>08065     weight(3) =    - 770720657.0D+00 / d
    8130. 

  8130. <a name="l08066"></a>08066     weight(4) =     3501442784.0D+00 / d
    8131. 

  8131. <a name="l08067"></a>08067     weight(5) =   - 6625093363.0D+00 / d
    8132. 

  8132. <a name="l08068"></a>08068     weight(6) =    12630121616.0D+00 / d
    8133. 

  8133. <a name="l08069"></a>08069     weight(7) =  - 16802270373.0D+00 / d
    8134. 

  8134. <a name="l08070"></a>08070     weight(8) =    19534438464.0D+00 / d
    8135. 

  8135. <a name="l08071"></a>08071     weight(9) =  - 16802270373.0D+00 / d
    8136. 

  8136. <a name="l08072"></a>08072     weight(10) =   12630121616.0D+00 / d
    8137. 

  8137. <a name="l08073"></a>08073     weight(11) =  - 6625093363.0D+00 / d
    8138. 

  8138. <a name="l08074"></a>08074     weight(12) =    3501442784.0D+00 / d
    8139. 

  8139. <a name="l08075"></a>08075     weight(13) =   - 770720657.0D+00 / d
    8140. 

  8140. <a name="l08076"></a>08076     weight(14) =     710986864.0D+00 / d
    8141. 

  8141. <a name="l08077"></a>08077     weight(15) =      90241897.0D+00 / d
    8142. 

  8142. <a name="l08078"></a>08078 
    8143. 

  8143. <a name="l08079"></a>08079   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
    8144. 

  8144. <a name="l08080"></a>08080 
    8145. 

  8145. <a name="l08081"></a>08081     d = 3099672576.0D+00
    8146. 

  8146. <a name="l08082"></a>08082 
    8147. 

  8147. <a name="l08083"></a>08083     weight(1) =     105930069.0D+00 / d
    8148. 

  8148. <a name="l08084"></a>08084     weight(2) =     796661595.0D+00 / d
    8149. 

  8149. <a name="l08085"></a>08085     weight(3) =   - 698808195.0D+00 / d
    8150. 

  8150. <a name="l08086"></a>08086     weight(4) =    3143332755.0D+00 / d
    8151. 

  8151. <a name="l08087"></a>08087     weight(5) =  - 4688522055.0D+00 / d
    8152. 

  8152. <a name="l08088"></a>08088     weight(6) =    7385654007.0D+00 / d
    8153. 

  8153. <a name="l08089"></a>08089     weight(7) =  - 6000998415.0D+00 / d
    8154. 

  8154. <a name="l08090"></a>08090     weight(8) =    3056422815.0D+00 / d
    8155. 

  8155. <a name="l08091"></a>08091     weight(9) =    3056422815.0D+00 / d
    8156. 

  8156. <a name="l08092"></a>08092     weight(10) = - 6000998415.0D+00 / d
    8157. 

  8157. <a name="l08093"></a>08093     weight(11) =   7385654007.0D+00 / d
    8158. 

  8158. <a name="l08094"></a>08094     weight(12) = - 4688522055.0D+00 / d
    8159. 

  8159. <a name="l08095"></a>08095     weight(13) =   3143332755.0D+00 / d
    8160. 

  8160. <a name="l08096"></a>08096     weight(14) =  - 698808195.0D+00 / d
    8161. 

  8161. <a name="l08097"></a>08097     weight(15) =    796661595.0D+00 / d
    8162. 

  8162. <a name="l08098"></a>08098     weight(16) =    105930069.0D+00 / d
    8163. 

  8163. <a name="l08099"></a>08099 
    8164. 

  8164. <a name="l08100"></a>08100   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 17 ) <span class="keyword">then</span>
    8165. 

  8165. <a name="l08101"></a>08101 
    8166. 

  8166. <a name="l08102"></a>08102     d = 488462349375.0D+00
    8167. 

  8167. <a name="l08103"></a>08103 
    8168. 

  8168. <a name="l08104"></a>08104     weight(1) =       15043611773.0D+00 / d
    8169. 

  8169. <a name="l08105"></a>08105     weight(2) =      127626606592.0D+00 / d
    8170. 

  8170. <a name="l08106"></a>08106     weight(3) =    - 179731134720.0D+00 / d
    8171. 

  8171. <a name="l08107"></a>08107     weight(4) =      832211855360.0D+00 / d
    8172. 

  8172. <a name="l08108"></a>08108     weight(5) =   - 1929498607520.0D+00 / d
    8173. 

  8173. <a name="l08109"></a>08109     weight(6) =     4177588893696.0D+00 / d
    8174. 

  8174. <a name="l08110"></a>08110     weight(7) =   - 6806534407936.0D+00 / d
    8175. 

  8175. <a name="l08111"></a>08111     weight(8) =     9368875018240.0D+00 / d
    8176. 

  8176. <a name="l08112"></a>08112     weight(9) =  - 10234238972220.0D+00 / d
    8177. 

  8177. <a name="l08113"></a>08113     weight(10) =    9368875018240.0D+00 / d
    8178. 

  8178. <a name="l08114"></a>08114     weight(11) =  - 6806534407936.0D+00 / d
    8179. 

  8179. <a name="l08115"></a>08115     weight(12) =    4177588893696.0D+00 / d
    8180. 

  8180. <a name="l08116"></a>08116     weight(13) =  - 1929498607520.0D+00 / d
    8181. 

  8181. <a name="l08117"></a>08117     weight(14) =     832211855360.0D+00 / d
    8182. 

  8182. <a name="l08118"></a>08118     weight(15) =   - 179731134720.0D+00 / d
    8183. 

  8183. <a name="l08119"></a>08119     weight(16) =     127626606592.0D+00 / d
    8184. 

  8184. <a name="l08120"></a>08120     weight(17) =      15043611773.0D+00 / d
    8185. 

  8185. <a name="l08121"></a>08121 
    8186. 

  8186. <a name="l08122"></a>08122   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 18 ) <span class="keyword">then</span>
    8187. 

  8187. <a name="l08123"></a>08123 
    8188. 

  8188. <a name="l08124"></a>08124     d = 1883051089920000.0D+00
    8189. 

  8189. <a name="l08125"></a>08125 
    8190. 

  8190. <a name="l08126"></a>08126     weight(1) =       55294720874657.0D+00 / d
    8191. 

  8191. <a name="l08127"></a>08127     weight(2) =      450185515446285.0D+00 / d
    8192. 

  8192. <a name="l08128"></a>08128     weight(3) =    - 542023437008852.0D+00 / d
    8193. 

  8193. <a name="l08129"></a>08129     weight(4) =     2428636525764260.0D+00 / d
    8194. 

  8194. <a name="l08130"></a>08130     weight(5) =   - 4768916800123440.0D+00 / d
    8195. 

  8195. <a name="l08131"></a>08131     weight(6) =     8855416648684984.0D+00 / d
    8196. 

  8196. <a name="l08132"></a>08132     weight(7) =  - 10905371859796660.0D+00 / d
    8197. 

  8197. <a name="l08133"></a>08133     weight(8) =    10069615750132836.0D+00 / d
    8198. 

  8198. <a name="l08134"></a>08134     weight(9) =   - 3759785974054070.0D+00 / d
    8199. 

  8199. <a name="l08135"></a>08135     weight(10) =  - 3759785974054070.0D+00 / d
    8200. 

  8200. <a name="l08136"></a>08136     weight(11) =   10069615750132836.0D+00 / d
    8201. 

  8201. <a name="l08137"></a>08137     weight(12) = - 10905371859796660.0D+00 / d
    8202. 

  8202. <a name="l08138"></a>08138     weight(13) =    8855416648684984.0D+00 / d
    8203. 

  8203. <a name="l08139"></a>08139     weight(14) =  - 4768916800123440.0D+00 / d
    8204. 

  8204. <a name="l08140"></a>08140     weight(15) =    2428636525764260.0D+00 / d
    8205. 

  8205. <a name="l08141"></a>08141     weight(16) =   - 542023437008852.0D+00 / d
    8206. 

  8206. <a name="l08142"></a>08142     weight(17) =     450185515446285.0D+00 / d
    8207. 

  8207. <a name="l08143"></a>08143     weight(18) =      55294720874657.0D+00 / d
    8208. 

  8208. <a name="l08144"></a>08144 
    8209. 

  8209. <a name="l08145"></a>08145   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 19 ) <span class="keyword">then</span>
    8210. 

  8210. <a name="l08146"></a>08146 
    8211. 

  8211. <a name="l08147"></a>08147     d = 7604556960000.0D+00
    8212. 

  8212. <a name="l08148"></a>08148 
    8213. 

  8213. <a name="l08149"></a>08149     weight(1) =       203732352169.0D+00 / d
    8214. 

  8214. <a name="l08150"></a>08150     weight(2) =      1848730221900.0D+00 / d
    8215. 

  8215. <a name="l08151"></a>08151     weight(3) =    - 3212744374395.0D+00 / d
    8216. 

  8216. <a name="l08152"></a>08152     weight(4) =     15529830312096.0D+00 / d
    8217. 

  8217. <a name="l08153"></a>08153     weight(5) =   - 42368630685840.0D+00 / d
    8218. 

  8218. <a name="l08154"></a>08154     weight(6) =    103680563465808.0D+00 / d
    8219. 

  8219. <a name="l08155"></a>08155     weight(7) =  - 198648429867720.0D+00 / d
    8220. 

  8220. <a name="l08156"></a>08156     weight(8) =    319035784479840.0D+00 / d
    8221. 

  8221. <a name="l08157"></a>08157     weight(9) =  - 419127951114198.0D+00 / d
    8222. 

  8222. <a name="l08158"></a>08158     weight(10) =   461327344340680.0D+00 / d
    8223. 

  8223. <a name="l08159"></a>08159     weight(11) = - 419127951114198.0D+00 / d
    8224. 

  8224. <a name="l08160"></a>08160     weight(12) =   319035784479840.0D+00 / d
    8225. 

  8225. <a name="l08161"></a>08161     weight(13) = - 198648429867720.0D+00 / d
    8226. 

  8226. <a name="l08162"></a>08162     weight(14) =   103680563465808.0D+00 / d
    8227. 

  8227. <a name="l08163"></a>08163     weight(15) =  - 42368630685840.0D+00 / d
    8228. 

  8228. <a name="l08164"></a>08164     weight(16) =    15529830312096.0D+00 / d
    8229. 

  8229. <a name="l08165"></a>08165     weight(17) =   - 3212744374395.0D+00 / d
    8230. 

  8230. <a name="l08166"></a>08166     weight(18) =     1848730221900.0D+00 / d
    8231. 

  8231. <a name="l08167"></a>08167     weight(19) =      203732352169.0D+00 / d
    8232. 

  8232. <a name="l08168"></a>08168 
    8233. 

  8233. <a name="l08169"></a>08169   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 20 ) <span class="keyword">then</span>
    8234. 

  8234. <a name="l08170"></a>08170 
    8235. 

  8235. <a name="l08171"></a>08171     d = 2688996956405760000.0D+00
    8236. 

  8236. <a name="l08172"></a>08172 
    8237. 

  8237. <a name="l08173"></a>08173     weight(1) =       69028763155644023.0D+00 / d
    8238. 

  8238. <a name="l08174"></a>08174     weight(2) =      603652082270808125.0D+00 / d
    8239. 

  8239. <a name="l08175"></a>08175     weight(3) =    - 926840515700222955.0D+00 / d
    8240. 

  8240. <a name="l08176"></a>08176     weight(4) =     4301581538450500095.0D+00 / d
    8241. 

  8241. <a name="l08177"></a>08177     weight(5) =  - 10343692234243192788.0D+00 / d
    8242. 

  8242. <a name="l08178"></a>08178     weight(6) =    22336420328479961316.0D+00 / d
    8243. 

  8243. <a name="l08179"></a>08179     weight(7) =  - 35331888421114781580.0D+00 / d
    8244. 

  8244. <a name="l08180"></a>08180     weight(8) =    43920768370565135580.0D+00 / d
    8245. 

  8245. <a name="l08181"></a>08181     weight(9) =  - 37088370261379851390.0D+00 / d
    8246. 

  8246. <a name="l08182"></a>08182     weight(10) =   15148337305921759574.0D+00 / d
    8247. 

  8247. <a name="l08183"></a>08183     weight(11) =   15148337305921759574.0D+00 / d
    8248. 

  8248. <a name="l08184"></a>08184     weight(12) = - 37088370261379851390.0D+00 / d
    8249. 

  8249. <a name="l08185"></a>08185     weight(13) =   43920768370565135580.0D+00 / d
    8250. 

  8250. <a name="l08186"></a>08186     weight(14) = - 35331888421114781580.0D+00 / d
    8251. 

  8251. <a name="l08187"></a>08187     weight(15) =   22336420328479961316.0D+00 / d
    8252. 

  8252. <a name="l08188"></a>08188     weight(16) = - 10343692234243192788.0D+00 / d
    8253. 

  8253. <a name="l08189"></a>08189     weight(17) =    4301581538450500095.0D+00 / d
    8254. 

  8254. <a name="l08190"></a>08190     weight(18) =   - 926840515700222955.0D+00 / d
    8255. 

  8255. <a name="l08191"></a>08191     weight(19) =     603652082270808125.0D+00 / d
    8256. 

  8256. <a name="l08192"></a>08192     weight(20) =      69028763155644023.0D+00 / d
    8257. 

  8257. <a name="l08193"></a>08193 
    8258. 

  8258. <a name="l08194"></a>08194   <span class="keyword">else</span>
    8259. 

  8259. <a name="l08195"></a>08195 
    8260. 

  8260. <a name="l08196"></a>08196     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    8261. 

  8261. <a name="l08197"></a>08197     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;NCC_SET - Fatal error!&#39;</span>
    8262. 

  8262. <a name="l08198"></a>08198     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    8263. 

  8263. <a name="l08199"></a>08199     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 2 through 20.&#39;</span>
    8264. 

  8264. <a name="l08200"></a>08200     stop
    8265. 

  8265. <a name="l08201"></a>08201 
    8266. 

  8266. <a name="l08202"></a>08202   <span class="keyword">end if</span>
    8267. 

  8267. <a name="l08203"></a>08203 <span class="comment">!</span>
    8268. 

  8268. <a name="l08204"></a>08204 <span class="comment">!  The abscissas are uniformly spaced.</span>
    8269. 

  8269. <a name="l08205"></a>08205 <span class="comment">!</span>
    8270. 

  8270. <a name="l08206"></a>08206   <span class="keyword">do</span> i = 1, norder
    8271. 

  8271. <a name="l08207"></a>08207     xtab(i) = dble ( 2 * i - 1 - norder ) / dble ( norder - 1 )
    8272. 

  8272. <a name="l08208"></a>08208   <span class="keyword">end do</span>
    8273. 

  8273. <a name="l08209"></a>08209 
    8274. 

  8274. <a name="l08210"></a>08210   return
    8275. 

  8275. <a name="l08211"></a>08211 <span class="keyword">end</span>
    8276. 

  8276. <a name="l08212"></a><a class="code" href="quadrule_8f90.html#a2ab54bf6aad3867d7b66db6bc056b420">08212</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a2ab54bf6aad3867d7b66db6bc056b420">nco_com</a> ( norder, xtab, weight )
    8277. 

  8277. <a name="l08213"></a>08213 <span class="comment">!</span>
    8278. 

  8278. <a name="l08214"></a>08214 <span class="comment">!*******************************************************************************</span>
    8279. 

  8279. <a name="l08215"></a>08215 <span class="comment">!</span>
    8280. 

  8280. <a name="l08216"></a>08216 <span class="comment">!! NCO_COM computes the coefficients of a Newton-Cotes open quadrature rule.</span>
    8281. 

  8281. <a name="l08217"></a>08217 <span class="comment">!</span>
    8282. 

  8282. <a name="l08218"></a>08218 <span class="comment">!</span>
    8283. 

  8283. <a name="l08219"></a>08219 <span class="comment">!  Definition:</span>
    8284. 

  8284. <a name="l08220"></a>08220 <span class="comment">!</span>
    8285. 

  8285. <a name="l08221"></a>08221 <span class="comment">!    For the interval [-1,1], the Newton-Cotes open quadrature rule</span>
    8286. 

  8286. <a name="l08222"></a>08222 <span class="comment">!    estimates</span>
    8287. 

  8287. <a name="l08223"></a>08223 <span class="comment">!</span>
    8288. 

  8288. <a name="l08224"></a>08224 <span class="comment">!      Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    8289. 

  8289. <a name="l08225"></a>08225 <span class="comment">!</span>
    8290. 

  8290. <a name="l08226"></a>08226 <span class="comment">!    using NORDER equally spaced abscissas XTAB(I) and a weight vector</span>
    8291. 

  8291. <a name="l08227"></a>08227 <span class="comment">!    WEIGHT(I):</span>
    8292. 

  8292. <a name="l08228"></a>08228 <span class="comment">!</span>
    8293. 

  8293. <a name="l08229"></a>08229 <span class="comment">!      Sum ( I = 1 to N ) WEIGHT(I) * F ( XTAB(I) ).</span>
    8294. 

  8294. <a name="l08230"></a>08230 <span class="comment">!</span>
    8295. 

  8295. <a name="l08231"></a>08231 <span class="comment">!    For the OPEN rule, the abscissas do not include A and B.</span>
    8296. 

  8296. <a name="l08232"></a>08232 <span class="comment">!</span>
    8297. 

  8297. <a name="l08233"></a>08233 <span class="comment">!  Modified:</span>
    8298. 

  8298. <a name="l08234"></a>08234 <span class="comment">!</span>
    8299. 

  8299. <a name="l08235"></a>08235 <span class="comment">!    25 September 1998</span>
    8300. 

  8300. <a name="l08236"></a>08236 <span class="comment">!</span>
    8301. 

  8301. <a name="l08237"></a>08237 <span class="comment">!  Author:</span>
    8302. 

  8302. <a name="l08238"></a>08238 <span class="comment">!</span>
    8303. 

  8303. <a name="l08239"></a>08239 <span class="comment">!    John Burkardt</span>
    8304. 

  8304. <a name="l08240"></a>08240 <span class="comment">!</span>
    8305. 

  8305. <a name="l08241"></a>08241 <span class="comment">!  Parameters:</span>
    8306. 

  8306. <a name="l08242"></a>08242 <span class="comment">!</span>
    8307. 

  8307. <a name="l08243"></a>08243 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    8308. 

  8308. <a name="l08244"></a>08244 <span class="comment">!</span>
    8309. 

  8309. <a name="l08245"></a>08245 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    8310. 

  8310. <a name="l08246"></a>08246 <span class="comment">!</span>
    8311. 

  8311. <a name="l08247"></a>08247 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the  rule.</span>
    8312. 

  8312. <a name="l08248"></a>08248 <span class="comment">!</span>
    8313. 

  8313. <a name="l08249"></a>08249   <span class="keyword">implicit none</span>
    8314. 

  8314. <a name="l08250"></a>08250 <span class="comment">!</span>
    8315. 

  8315. <a name="l08251"></a>08251   <span class="keywordtype">integer</span> norder
    8316. 

  8316. <a name="l08252"></a>08252 <span class="comment">!</span>
    8317. 

  8317. <a name="l08253"></a>08253   <span class="keywordtype">double precision</span> a
    8318. 

  8318. <a name="l08254"></a>08254   <span class="keywordtype">double precision</span> b
    8319. 

  8319. <a name="l08255"></a>08255   <span class="keywordtype">integer</span> i
    8320. 

  8320. <a name="l08256"></a>08256   <span class="keywordtype">double precision</span> weight(norder)
    8321. 

  8321. <a name="l08257"></a>08257   <span class="keywordtype">double precision</span> xtab(norder)
    8322. 

  8322. <a name="l08258"></a>08258 <span class="comment">!</span>
    8323. 

  8323. <a name="l08259"></a>08259   a = -1.0D+00
    8324. 

  8324. <a name="l08260"></a>08260   b =  1.0D+00
    8325. 

  8325. <a name="l08261"></a>08261 
    8326. 

  8326. <a name="l08262"></a>08262   <span class="keyword">do</span> i = 1, norder
    8327. 

  8327. <a name="l08263"></a>08263     xtab(i) = ( dble ( norder + 1 - i ) * a + dble ( i ) * b ) &amp;
    8328. 

  8328. <a name="l08264"></a>08264       / dble ( norder + 1 )
    8329. 

  8329. <a name="l08265"></a>08265   <span class="keyword">end do</span>
    8330. 

  8330. <a name="l08266"></a>08266 
    8331. 

  8331. <a name="l08267"></a>08267   call <a class="code" href="quadrule_8f90.html#a0b336aacd3856d5d5e724522dd3e6e8a">nc_com </a>( norder, a, b, xtab, weight )
    8332. 

  8332. <a name="l08268"></a>08268 
    8333. 

  8333. <a name="l08269"></a>08269   return
    8334. 

  8334. <a name="l08270"></a>08270 <span class="keyword">end</span>
    8335. 

  8335. <a name="l08271"></a><a class="code" href="quadrule_8f90.html#a27acf87e9cb1d5f166f347d6e2650710">08271</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a27acf87e9cb1d5f166f347d6e2650710">nco_set</a> ( norder, xtab, weight )
    8336. 

  8336. <a name="l08272"></a>08272 <span class="comment">!</span>
    8337. 

  8337. <a name="l08273"></a>08273 <span class="comment">!*******************************************************************************</span>
    8338. 

  8338. <a name="l08274"></a>08274 <span class="comment">!</span>
    8339. 

  8339. <a name="l08275"></a>08275 <span class="comment">!! NCO_SET sets abscissas and weights for open Newton-Cotes quadrature.</span>
    8340. 

  8340. <a name="l08276"></a>08276 <span class="comment">!</span>
    8341. 

  8341. <a name="l08277"></a>08277 <span class="comment">!</span>
    8342. 

  8342. <a name="l08278"></a>08278 <span class="comment">!  Integration interval:</span>
    8343. 

  8343. <a name="l08279"></a>08279 <span class="comment">!</span>
    8344. 

  8344. <a name="l08280"></a>08280 <span class="comment">!    [ -1, 1 ]</span>
    8345. 

  8345. <a name="l08281"></a>08281 <span class="comment">!</span>
    8346. 

  8346. <a name="l08282"></a>08282 <span class="comment">!  Weight function:</span>
    8347. 

  8347. <a name="l08283"></a>08283 <span class="comment">!</span>
    8348. 

  8348. <a name="l08284"></a>08284 <span class="comment">!    1.0D+00</span>
    8349. 

  8349. <a name="l08285"></a>08285 <span class="comment">!</span>
    8350. 

  8350. <a name="l08286"></a>08286 <span class="comment">!  Integral to approximate:</span>
    8351. 

  8351. <a name="l08287"></a>08287 <span class="comment">!</span>
    8352. 

  8352. <a name="l08288"></a>08288 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    8353. 

  8353. <a name="l08289"></a>08289 <span class="comment">!</span>
    8354. 

  8354. <a name="l08290"></a>08290 <span class="comment">!  Approximate integral:</span>
    8355. 

  8355. <a name="l08291"></a>08291 <span class="comment">!</span>
    8356. 

  8356. <a name="l08292"></a>08292 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    8357. 

  8357. <a name="l08293"></a>08293 <span class="comment">!</span>
    8358. 

  8358. <a name="l08294"></a>08294 <span class="comment">!  Note:</span>
    8359. 

  8359. <a name="l08295"></a>08295 <span class="comment">!</span>
    8360. 

  8360. <a name="l08296"></a>08296 <span class="comment">!    The open Newton-Cotes rules use equally spaced abscissas, and</span>
    8361. 

  8361. <a name="l08297"></a>08297 <span class="comment">!    hence may be used with equally spaced data.</span>
    8362. 

  8362. <a name="l08298"></a>08298 <span class="comment">!</span>
    8363. 

  8363. <a name="l08299"></a>08299 <span class="comment">!    The rules are called &quot;open&quot; because they do not include the interval</span>
    8364. 

  8364. <a name="l08300"></a>08300 <span class="comment">!    endpoints.</span>
    8365. 

  8365. <a name="l08301"></a>08301 <span class="comment">!</span>
    8366. 

  8366. <a name="l08302"></a>08302 <span class="comment">!    Most of the rules involve negative weights.  These can produce loss</span>
    8367. 

  8367. <a name="l08303"></a>08303 <span class="comment">!    of accuracy due to the subtraction of large, nearly equal quantities.</span>
    8368. 

  8368. <a name="l08304"></a>08304 <span class="comment">!</span>
    8369. 

  8369. <a name="l08305"></a>08305 <span class="comment">!  Reference:</span>
    8370. 

  8370. <a name="l08306"></a>08306 <span class="comment">!</span>
    8371. 

  8371. <a name="l08307"></a>08307 <span class="comment">!    Abramowitz and Stegun,</span>
    8372. 

  8372. <a name="l08308"></a>08308 <span class="comment">!    Handbook of Mathematical Functions,</span>
    8373. 

  8373. <a name="l08309"></a>08309 <span class="comment">!    National Bureau of Standards, 1964.</span>
    8374. 

  8374. <a name="l08310"></a>08310 <span class="comment">!</span>
    8375. 

  8375. <a name="l08311"></a>08311 <span class="comment">!    Daniel Zwillinger, editor,</span>
    8376. 

  8376. <a name="l08312"></a>08312 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    8377. 

  8377. <a name="l08313"></a>08313 <span class="comment">!    30th Edition,</span>
    8378. 

  8378. <a name="l08314"></a>08314 <span class="comment">!    CRC Press, 1996.</span>
    8379. 

  8379. <a name="l08315"></a>08315 <span class="comment">!</span>
    8380. 

  8380. <a name="l08316"></a>08316 <span class="comment">!  Modified:</span>
    8381. 

  8381. <a name="l08317"></a>08317 <span class="comment">!</span>
    8382. 

  8382. <a name="l08318"></a>08318 <span class="comment">!    15 September 1998</span>
    8383. 

  8383. <a name="l08319"></a>08319 <span class="comment">!</span>
    8384. 

  8384. <a name="l08320"></a>08320 <span class="comment">!  Author:</span>
    8385. 

  8385. <a name="l08321"></a>08321 <span class="comment">!</span>
    8386. 

  8386. <a name="l08322"></a>08322 <span class="comment">!    John Burkardt</span>
    8387. 

  8387. <a name="l08323"></a>08323 <span class="comment">!</span>
    8388. 

  8388. <a name="l08324"></a>08324 <span class="comment">!  Parameters:</span>
    8389. 

  8389. <a name="l08325"></a>08325 <span class="comment">!</span>
    8390. 

  8390. <a name="l08326"></a>08326 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    8391. 

  8391. <a name="l08327"></a>08327 <span class="comment">!    NORDER must be between 1 and 7, and 9.</span>
    8392. 

  8392. <a name="l08328"></a>08328 <span class="comment">!</span>
    8393. 

  8393. <a name="l08329"></a>08329 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    8394. 

  8394. <a name="l08330"></a>08330 <span class="comment">!</span>
    8395. 

  8395. <a name="l08331"></a>08331 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    8396. 

  8396. <a name="l08332"></a>08332 <span class="comment">!    The weights are rational, symmetric, and should sum to 2.</span>
    8397. 

  8397. <a name="l08333"></a>08333 <span class="comment">!    Some weights may be negative.</span>
    8398. 

  8398. <a name="l08334"></a>08334 <span class="comment">!</span>
    8399. 

  8399. <a name="l08335"></a>08335   <span class="keyword">implicit none</span>
    8400. 

  8400. <a name="l08336"></a>08336 <span class="comment">!</span>
    8401. 

  8401. <a name="l08337"></a>08337   <span class="keywordtype">integer</span> norder
    8402. 

  8402. <a name="l08338"></a>08338 <span class="comment">!</span>
    8403. 

  8403. <a name="l08339"></a>08339   <span class="keywordtype">double precision</span> d
    8404. 

  8404. <a name="l08340"></a>08340   <span class="keywordtype">integer</span> i
    8405. 

  8405. <a name="l08341"></a>08341   <span class="keywordtype">double precision</span> weight(norder)
    8406. 

  8406. <a name="l08342"></a>08342   <span class="keywordtype">double precision</span> xtab(norder)
    8407. 

  8407. <a name="l08343"></a>08343 <span class="comment">!</span>
    8408. 

  8408. <a name="l08344"></a>08344   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    8409. 

  8409. <a name="l08345"></a>08345 
    8410. 

  8410. <a name="l08346"></a>08346     weight(1) = 2.0D+00
    8411. 

  8411. <a name="l08347"></a>08347 
    8412. 

  8412. <a name="l08348"></a>08348   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    8413. 

  8413. <a name="l08349"></a>08349 
    8414. 

  8414. <a name="l08350"></a>08350     weight(1) = 1.0D+00
    8415. 

  8415. <a name="l08351"></a>08351     weight(2) = 1.0D+00
    8416. 

  8416. <a name="l08352"></a>08352 
    8417. 

  8417. <a name="l08353"></a>08353   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    8418. 

  8418. <a name="l08354"></a>08354 
    8419. 

  8419. <a name="l08355"></a>08355     d = 3.0D+00
    8420. 

  8420. <a name="l08356"></a>08356 
    8421. 

  8421. <a name="l08357"></a>08357     weight(1) =   4.0D+00 / d
    8422. 

  8422. <a name="l08358"></a>08358     weight(2) = - 2.0D+00 / d
    8423. 

  8423. <a name="l08359"></a>08359     weight(3) =   4.0D+00 / d
    8424. 

  8424. <a name="l08360"></a>08360 
    8425. 

  8425. <a name="l08361"></a>08361   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    8426. 

  8426. <a name="l08362"></a>08362 
    8427. 

  8427. <a name="l08363"></a>08363     d = 12.0D+00
    8428. 

  8428. <a name="l08364"></a>08364 
    8429. 

  8429. <a name="l08365"></a>08365     weight(1) = 11.0D+00 / d
    8430. 

  8430. <a name="l08366"></a>08366     weight(2) =  1.0D+00 / d
    8431. 

  8431. <a name="l08367"></a>08367     weight(3) =  1.0D+00 / d
    8432. 

  8432. <a name="l08368"></a>08368     weight(4) = 11.0D+00 / d
    8433. 

  8433. <a name="l08369"></a>08369 
    8434. 

  8434. <a name="l08370"></a>08370   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    8435. 

  8435. <a name="l08371"></a>08371 
    8436. 

  8436. <a name="l08372"></a>08372     d = 10.0D+00
    8437. 

  8437. <a name="l08373"></a>08373 
    8438. 

  8438. <a name="l08374"></a>08374     weight(1) =   11.0D+00 / d
    8439. 

  8439. <a name="l08375"></a>08375     weight(2) = - 14.0D+00 / d
    8440. 

  8440. <a name="l08376"></a>08376     weight(3) =   26.0D+00 / d
    8441. 

  8441. <a name="l08377"></a>08377     weight(4) = - 14.0D+00 / d
    8442. 

  8442. <a name="l08378"></a>08378     weight(5) =   11.0D+00 / d
    8443. 

  8443. <a name="l08379"></a>08379 
    8444. 

  8444. <a name="l08380"></a>08380   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    8445. 

  8445. <a name="l08381"></a>08381 
    8446. 

  8446. <a name="l08382"></a>08382     d = 1440.0D+00
    8447. 

  8447. <a name="l08383"></a>08383 
    8448. 

  8448. <a name="l08384"></a>08384     weight(1) =  1222.0D+00 / d
    8449. 

  8449. <a name="l08385"></a>08385     weight(2) = - 906.0D+00 / d
    8450. 

  8450. <a name="l08386"></a>08386     weight(3) =  1124.0D+00 / d
    8451. 

  8451. <a name="l08387"></a>08387     weight(4) =  1124.0D+00 / d
    8452. 

  8452. <a name="l08388"></a>08388     weight(5) = - 906.0D+00 / d
    8453. 

  8453. <a name="l08389"></a>08389     weight(6) =  1222.0D+00 / d
    8454. 

  8454. <a name="l08390"></a>08390 
    8455. 

  8455. <a name="l08391"></a>08391   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    8456. 

  8456. <a name="l08392"></a>08392 
    8457. 

  8457. <a name="l08393"></a>08393     d = 945.0D+00
    8458. 

  8458. <a name="l08394"></a>08394 
    8459. 

  8459. <a name="l08395"></a>08395     weight(1) =    920.0D+00 / d
    8460. 

  8460. <a name="l08396"></a>08396     weight(2) = - 1908.0D+00 / d
    8461. 

  8461. <a name="l08397"></a>08397     weight(3) =   4392.0D+00 / d
    8462. 

  8462. <a name="l08398"></a>08398     weight(4) = - 4918.0D+00 / d
    8463. 

  8463. <a name="l08399"></a>08399     weight(5) =   4392.0D+00 / d
    8464. 

  8464. <a name="l08400"></a>08400     weight(6) = - 1908.0D+00 / d
    8465. 

  8465. <a name="l08401"></a>08401     weight(7) =    920.0D+00 / d
    8466. 

  8466. <a name="l08402"></a>08402 
    8467. 

  8467. <a name="l08403"></a>08403   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    8468. 

  8468. <a name="l08404"></a>08404 
    8469. 

  8469. <a name="l08405"></a>08405     d = 4536.0D+00
    8470. 

  8470. <a name="l08406"></a>08406 
    8471. 

  8471. <a name="l08407"></a>08407     weight(1) =    4045.0D+00 / d
    8472. 

  8472. <a name="l08408"></a>08408     weight(2) = - 11690.0D+00 / d
    8473. 

  8473. <a name="l08409"></a>08409     weight(3) =   33340.0D+00 / d
    8474. 

  8474. <a name="l08410"></a>08410     weight(4) = - 55070.0D+00 / d
    8475. 

  8475. <a name="l08411"></a>08411     weight(5) =   67822.0D+00 / d
    8476. 

  8476. <a name="l08412"></a>08412     weight(6) = - 55070.0D+00 / d
    8477. 

  8477. <a name="l08413"></a>08413     weight(7) =   33340.0D+00 / d
    8478. 

  8478. <a name="l08414"></a>08414     weight(8) = - 11690.0D+00 / d
    8479. 

  8479. <a name="l08415"></a>08415     weight(9) =    4045.0D+00 / d
    8480. 

  8480. <a name="l08416"></a>08416 
    8481. 

  8481. <a name="l08417"></a>08417   <span class="keyword">else</span>
    8482. 

  8482. <a name="l08418"></a>08418 
    8483. 

  8483. <a name="l08419"></a>08419     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    8484. 

  8484. <a name="l08420"></a>08420     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;NCO_SET - Fatal error!&#39;</span>
    8485. 

  8485. <a name="l08421"></a>08421     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    8486. 

  8486. <a name="l08422"></a>08422     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 1 to 7, and 9.&#39;</span>
    8487. 

  8487. <a name="l08423"></a>08423     stop
    8488. 

  8488. <a name="l08424"></a>08424 
    8489. 

  8489. <a name="l08425"></a>08425   <span class="keyword">end if</span>
    8490. 

  8490. <a name="l08426"></a>08426 <span class="comment">!</span>
    8491. 

  8491. <a name="l08427"></a>08427 <span class="comment">!  Set the abscissas.</span>
    8492. 

  8492. <a name="l08428"></a>08428 <span class="comment">!</span>
    8493. 

  8493. <a name="l08429"></a>08429   <span class="keyword">do</span> i = 1, norder
    8494. 

  8494. <a name="l08430"></a>08430     xtab(i) = dble ( 2 * i - norder - 1 ) / dble ( norder + 1 )
    8495. 

  8495. <a name="l08431"></a>08431   <span class="keyword">end do</span>
    8496. 

  8496. <a name="l08432"></a>08432 
    8497. 

  8497. <a name="l08433"></a>08433   return
    8498. 

  8498. <a name="l08434"></a>08434 <span class="keyword">end</span>
    8499. 

  8499. <a name="l08435"></a><a class="code" href="quadrule_8f90.html#a0e44da10711c05b4fb80b5add1efa261">08435</a> <span class="keyword">function </span><a class="code" href="quadrule_8f90.html#a0e44da10711c05b4fb80b5add1efa261">r_pi</a> ( )
    8500. 

  8500. <a name="l08436"></a>08436 <span class="comment">!</span>
    8501. 

  8501. <a name="l08437"></a>08437 <span class="comment">!*******************************************************************************</span>
    8502. 

  8502. <a name="l08438"></a>08438 <span class="comment">!</span>
    8503. 

  8503. <a name="l08439"></a>08439 <span class="comment">!! R_PI returns the value of pi as a real quantity.</span>
    8504. 

  8504. <a name="l08440"></a>08440 <span class="comment">!</span>
    8505. 

  8505. <a name="l08441"></a>08441 <span class="comment">!</span>
    8506. 

  8506. <a name="l08442"></a>08442 <span class="comment">!  Modified:</span>
    8507. 

  8507. <a name="l08443"></a>08443 <span class="comment">!</span>
    8508. 

  8508. <a name="l08444"></a>08444 <span class="comment">!    28 April 2000</span>
    8509. 

  8509. <a name="l08445"></a>08445 <span class="comment">!</span>
    8510. 

  8510. <a name="l08446"></a>08446 <span class="comment">!  Author:</span>
    8511. 

  8511. <a name="l08447"></a>08447 <span class="comment">!</span>
    8512. 

  8512. <a name="l08448"></a>08448 <span class="comment">!    John Burkardt</span>
    8513. 

  8513. <a name="l08449"></a>08449 <span class="comment">!</span>
    8514. 

  8514. <a name="l08450"></a>08450 <span class="comment">!  Parameters:</span>
    8515. 

  8515. <a name="l08451"></a>08451 <span class="comment">!</span>
    8516. 

  8516. <a name="l08452"></a>08452 <span class="comment">!    Output, real PI, the value of pi.</span>
    8517. 

  8517. <a name="l08453"></a>08453 <span class="comment">!</span>
    8518. 

  8518. <a name="l08454"></a>08454   <span class="keyword">implicit none</span>
    8519. 

  8519. <a name="l08455"></a>08455 <span class="comment">!</span>
    8520. 

  8520. <a name="l08456"></a>08456   <span class="keywordtype">real</span> r_pi
    8521. 

  8521. <a name="l08457"></a>08457 <span class="comment">!</span>
    8522. 

  8522. <a name="l08458"></a>08458   r_pi = 3.14159265358979323846264338327950288419716939937510E+00
    8523. 

  8523. <a name="l08459"></a>08459 
    8524. 

  8524. <a name="l08460"></a>08460   return
    8525. 

  8525. <a name="l08461"></a>08461 <span class="keyword">end</span>
    8526. 

  8526. <a name="l08462"></a><a class="code" href="quadrule_8f90.html#a707a104aaec64bd98bd8996e11171677">08462</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a707a104aaec64bd98bd8996e11171677">radau_set</a> ( norder, xtab, weight )
    8527. 

  8527. <a name="l08463"></a>08463 <span class="comment">!</span>
    8528. 

  8528. <a name="l08464"></a>08464 <span class="comment">!*******************************************************************************</span>
    8529. 

  8529. <a name="l08465"></a>08465 <span class="comment">!</span>
    8530. 

  8530. <a name="l08466"></a>08466 <span class="comment">!! RADAU_SET sets abscissas and weights for Radau quadrature.</span>
    8531. 

  8531. <a name="l08467"></a>08467 <span class="comment">!</span>
    8532. 

  8532. <a name="l08468"></a>08468 <span class="comment">!</span>
    8533. 

  8533. <a name="l08469"></a>08469 <span class="comment">!  Integration interval:</span>
    8534. 

  8534. <a name="l08470"></a>08470 <span class="comment">!</span>
    8535. 

  8535. <a name="l08471"></a>08471 <span class="comment">!    [ -1, 1 ]</span>
    8536. 

  8536. <a name="l08472"></a>08472 <span class="comment">!</span>
    8537. 

  8537. <a name="l08473"></a>08473 <span class="comment">!  Weight function:</span>
    8538. 

  8538. <a name="l08474"></a>08474 <span class="comment">!</span>
    8539. 

  8539. <a name="l08475"></a>08475 <span class="comment">!    1.0D+00</span>
    8540. 

  8540. <a name="l08476"></a>08476 <span class="comment">!</span>
    8541. 

  8541. <a name="l08477"></a>08477 <span class="comment">!  Integral to approximate:</span>
    8542. 

  8542. <a name="l08478"></a>08478 <span class="comment">!</span>
    8543. 

  8543. <a name="l08479"></a>08479 <span class="comment">!    Integral ( -1 &lt;= X &lt;= 1 ) F(X) dX</span>
    8544. 

  8544. <a name="l08480"></a>08480 <span class="comment">!</span>
    8545. 

  8545. <a name="l08481"></a>08481 <span class="comment">!  Approximate integral:</span>
    8546. 

  8546. <a name="l08482"></a>08482 <span class="comment">!</span>
    8547. 

  8547. <a name="l08483"></a>08483 <span class="comment">!    Sum ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
    8548. 

  8548. <a name="l08484"></a>08484 <span class="comment">!</span>
    8549. 

  8549. <a name="l08485"></a>08485 <span class="comment">!  Precision:</span>
    8550. 

  8550. <a name="l08486"></a>08486 <span class="comment">!</span>
    8551. 

  8551. <a name="l08487"></a>08487 <span class="comment">!    The quadrature rule will integrate exactly all polynomials up to</span>
    8552. 

  8552. <a name="l08488"></a>08488 <span class="comment">!    X**(2*NORDER-2).</span>
    8553. 

  8553. <a name="l08489"></a>08489 <span class="comment">!</span>
    8554. 

  8554. <a name="l08490"></a>08490 <span class="comment">!  Note:</span>
    8555. 

  8555. <a name="l08491"></a>08491 <span class="comment">!</span>
    8556. 

  8556. <a name="l08492"></a>08492 <span class="comment">!    The Radau rule is distinguished by the fact that the left endpoint</span>
    8557. 

  8557. <a name="l08493"></a>08493 <span class="comment">!    (-1) is always an abscissa.</span>
    8558. 

  8558. <a name="l08494"></a>08494 <span class="comment">!</span>
    8559. 

  8559. <a name="l08495"></a>08495 <span class="comment">!  Reference:</span>
    8560. 

  8560. <a name="l08496"></a>08496 <span class="comment">!</span>
    8561. 

  8561. <a name="l08497"></a>08497 <span class="comment">!    Abramowitz and Stegun,</span>
    8562. 

  8562. <a name="l08498"></a>08498 <span class="comment">!    Handbook of Mathematical Functions,</span>
    8563. 

  8563. <a name="l08499"></a>08499 <span class="comment">!    National Bureau of Standards, 1964.</span>
    8564. 

  8564. <a name="l08500"></a>08500 <span class="comment">!</span>
    8565. 

  8565. <a name="l08501"></a>08501 <span class="comment">!    Arthur Stroud and Don Secrest,</span>
    8566. 

  8566. <a name="l08502"></a>08502 <span class="comment">!    Gaussian Quadrature Formulas,</span>
    8567. 

  8567. <a name="l08503"></a>08503 <span class="comment">!    Prentice Hall, 1966.</span>
    8568. 

  8568. <a name="l08504"></a>08504 <span class="comment">!</span>
    8569. 

  8569. <a name="l08505"></a>08505 <span class="comment">!    Daniel Zwillinger, editor,</span>
    8570. 

  8570. <a name="l08506"></a>08506 <span class="comment">!    Standard Mathematical Tables and Formulae,</span>
    8571. 

  8571. <a name="l08507"></a>08507 <span class="comment">!    30th Edition,</span>
    8572. 

  8572. <a name="l08508"></a>08508 <span class="comment">!    CRC Press, 1996.</span>
    8573. 

  8573. <a name="l08509"></a>08509 <span class="comment">!</span>
    8574. 

  8574. <a name="l08510"></a>08510 <span class="comment">!  Modified:</span>
    8575. 

  8575. <a name="l08511"></a>08511 <span class="comment">!</span>
    8576. 

  8576. <a name="l08512"></a>08512 <span class="comment">!    16 September 1998</span>
    8577. 

  8577. <a name="l08513"></a>08513 <span class="comment">!</span>
    8578. 

  8578. <a name="l08514"></a>08514 <span class="comment">!  Author:</span>
    8579. 

  8579. <a name="l08515"></a>08515 <span class="comment">!</span>
    8580. 

  8580. <a name="l08516"></a>08516 <span class="comment">!    John Burkardt</span>
    8581. 

  8581. <a name="l08517"></a>08517 <span class="comment">!</span>
    8582. 

  8582. <a name="l08518"></a>08518 <span class="comment">!  Parameters:</span>
    8583. 

  8583. <a name="l08519"></a>08519 <span class="comment">!</span>
    8584. 

  8584. <a name="l08520"></a>08520 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    8585. 

  8585. <a name="l08521"></a>08521 <span class="comment">!    NORDER must be between 1 and 15.</span>
    8586. 

  8586. <a name="l08522"></a>08522 <span class="comment">!</span>
    8587. 

  8587. <a name="l08523"></a>08523 <span class="comment">!    Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
    8588. 

  8588. <a name="l08524"></a>08524 <span class="comment">!</span>
    8589. 

  8589. <a name="l08525"></a>08525 <span class="comment">!    Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
    8590. 

  8590. <a name="l08526"></a>08526 <span class="comment">!    The weights are positive.  The weights are not symmetric.</span>
    8591. 

  8591. <a name="l08527"></a>08527 <span class="comment">!    The weights should sum to 2.  WEIGHT(1) should equal 2 / NORDER**2.</span>
    8592. 

  8592. <a name="l08528"></a>08528 <span class="comment">!</span>
    8593. 

  8593. <a name="l08529"></a>08529   <span class="keyword">implicit none</span>
    8594. 

  8594. <a name="l08530"></a>08530 <span class="comment">!</span>
    8595. 

  8595. <a name="l08531"></a>08531   <span class="keywordtype">integer</span> norder
    8596. 

  8596. <a name="l08532"></a>08532 <span class="comment">!</span>
    8597. 

  8597. <a name="l08533"></a>08533   <span class="keywordtype">double precision</span> xtab(norder)
    8598. 

  8598. <a name="l08534"></a>08534   <span class="keywordtype">double precision</span> weight(norder)
    8599. 

  8599. <a name="l08535"></a>08535 <span class="comment">!</span>
    8600. 

  8600. <a name="l08536"></a>08536   <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
    8601. 

  8601. <a name="l08537"></a>08537 
    8602. 

  8602. <a name="l08538"></a>08538     xtab(1) =   - 1.0D+00
    8603. 

  8603. <a name="l08539"></a>08539     weight(1) =   2.0D+00
    8604. 

  8604. <a name="l08540"></a>08540 
    8605. 

  8605. <a name="l08541"></a>08541   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
    8606. 

  8606. <a name="l08542"></a>08542 
    8607. 

  8607. <a name="l08543"></a>08543     xtab(1) =  - 1.0D+00
    8608. 

  8608. <a name="l08544"></a>08544     xtab(2) =    1.0D+00 / 3.0D+00
    8609. 

  8609. <a name="l08545"></a>08545 
    8610. 

  8610. <a name="l08546"></a>08546     weight(1) =  0.5D+00
    8611. 

  8611. <a name="l08547"></a>08547     weight(2) =  1.5D+00
    8612. 

  8612. <a name="l08548"></a>08548 
    8613. 

  8613. <a name="l08549"></a>08549   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
    8614. 

  8614. <a name="l08550"></a>08550 
    8615. 

  8615. <a name="l08551"></a>08551     xtab(1) =   - 1.0D+00
    8616. 

  8616. <a name="l08552"></a>08552     xtab(2) =   - 0.289897948556635619639456814941D+00
    8617. 

  8617. <a name="l08553"></a>08553     xtab(3) =     0.689897948556635619639456814941D+00
    8618. 

  8618. <a name="l08554"></a>08554 
    8619. 

  8619. <a name="l08555"></a>08555     weight(1) =  0.222222222222222222222222222222D+00
    8620. 

  8620. <a name="l08556"></a>08556     weight(2) =  0.102497165237684322767762689304D+01
    8621. 

  8621. <a name="l08557"></a>08557     weight(3) =  0.752806125400934550100150884739D+00
    8622. 

  8622. <a name="l08558"></a>08558 
    8623. 

  8623. <a name="l08559"></a>08559   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
    8624. 

  8624. <a name="l08560"></a>08560 
    8625. 

  8625. <a name="l08561"></a>08561     xtab(1) =  - 1.0D+00
    8626. 

  8626. <a name="l08562"></a>08562     xtab(2) =  - 0.575318923521694112050483779752D+00
    8627. 

  8627. <a name="l08563"></a>08563     xtab(3) =    0.181066271118530578270147495862D+00
    8628. 

  8628. <a name="l08564"></a>08564     xtab(4) =    0.822824080974592105208907712461D+00
    8629. 

  8629. <a name="l08565"></a>08565 
    8630. 

  8630. <a name="l08566"></a>08566     weight(1) =  0.125D+00
    8631. 

  8631. <a name="l08567"></a>08567     weight(2) =  0.657688639960119487888578442146D+00
    8632. 

  8632. <a name="l08568"></a>08568     weight(3) =  0.776386937686343761560464613780D+00
    8633. 

  8633. <a name="l08569"></a>08569     weight(4) =  0.440924422353536750550956944074D+00
    8634. 

  8634. <a name="l08570"></a>08570 
    8635. 

  8635. <a name="l08571"></a>08571   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
    8636. 

  8636. <a name="l08572"></a>08572 
    8637. 

  8637. <a name="l08573"></a>08573     xtab(1) =  - 1.0D+00
    8638. 

  8638. <a name="l08574"></a>08574     xtab(2) =  - 0.720480271312438895695825837750D+00
    8639. 

  8639. <a name="l08575"></a>08575     xtab(3) =  - 0.167180864737833640113395337326D+00
    8640. 

  8640. <a name="l08576"></a>08576     xtab(4) =    0.446313972723752344639908004629D+00
    8641. 

  8641. <a name="l08577"></a>08577     xtab(5) =    0.885791607770964635613757614892D+00
    8642. 

  8642. <a name="l08578"></a>08578 
    8643. 

  8643. <a name="l08579"></a>08579     weight(1) =  0.08D+00
    8644. 

  8644. <a name="l08580"></a>08580     weight(2) =  0.446207802167141488805120436457D+00
    8645. 

  8645. <a name="l08581"></a>08581     weight(3) =  0.623653045951482508163709823153D+00
    8646. 

  8646. <a name="l08582"></a>08582     weight(4) =  0.562712030298924120384345300681D+00
    8647. 

  8647. <a name="l08583"></a>08583     weight(5) =  0.287427121582451882646824439708D+00
    8648. 

  8648. <a name="l08584"></a>08584 
    8649. 

  8649. <a name="l08585"></a>08585   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
    8650. 

  8650. <a name="l08586"></a>08586 
    8651. 

  8651. <a name="l08587"></a>08587     xtab(1) =  - 1.0D+00
    8652. 

  8652. <a name="l08588"></a>08588     xtab(2) =  - 0.802929828402347147753002204224D+00
    8653. 

  8653. <a name="l08589"></a>08589     xtab(3) =  - 0.390928546707272189029229647442D+00
    8654. 

  8654. <a name="l08590"></a>08590     xtab(4) =    0.124050379505227711989974959990D+00
    8655. 

  8655. <a name="l08591"></a>08591     xtab(5) =    0.603973164252783654928415726409D+00
    8656. 

  8656. <a name="l08592"></a>08592     xtab(6) =    0.920380285897062515318386619813D+00
    8657. 

  8657. <a name="l08593"></a>08593 
    8658. 

  8658. <a name="l08594"></a>08594     weight(1) =  0.555555555555555555555555555556D-01
    8659. 

  8659. <a name="l08595"></a>08595     weight(2) =  0.319640753220510966545779983796D+00
    8660. 

  8660. <a name="l08596"></a>08596     weight(3) =  0.485387188468969916159827915587D+00
    8661. 

  8661. <a name="l08597"></a>08597     weight(4) =  0.520926783189574982570229406570D+00
    8662. 

  8662. <a name="l08598"></a>08598     weight(5) =  0.416901334311907738959406382743D+00
    8663. 

  8663. <a name="l08599"></a>08599     weight(6) =  0.201588385253480840209200755749D+00
    8664. 

  8664. <a name="l08600"></a>08600 
    8665. 

  8665. <a name="l08601"></a>08601   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
    8666. 

  8666. <a name="l08602"></a>08602 
    8667. 

  8667. <a name="l08603"></a>08603     xtab(1) =  - 1.0D+00
    8668. 

  8668. <a name="l08604"></a>08604     xtab(2) =  - 0.853891342639482229703747931639D+00
    8669. 

  8669. <a name="l08605"></a>08605     xtab(3) =  - 0.538467724060109001833766720231D+00
    8670. 

  8670. <a name="l08606"></a>08606     xtab(4) =  - 0.117343037543100264162786683611D+00
    8671. 

  8671. <a name="l08607"></a>08607     xtab(5) =    0.326030619437691401805894055838D+00
    8672. 

  8672. <a name="l08608"></a>08608     xtab(6) =    0.703842800663031416300046295008D+00
    8673. 

  8673. <a name="l08609"></a>08609     xtab(7) =    0.941367145680430216055899446174D+00
    8674. 

  8674. <a name="l08610"></a>08610 
    8675. 

  8675. <a name="l08611"></a>08611     weight(1) =  0.408163265306122448979591836735D-01
    8676. 

  8676. <a name="l08612"></a>08612     weight(2) =  0.239227489225312405787077480770D+00
    8677. 

  8677. <a name="l08613"></a>08613     weight(3) =  0.380949873644231153805938347876D+00
    8678. 

  8678. <a name="l08614"></a>08614     weight(4) =  0.447109829014566469499348953642D+00
    8679. 

  8679. <a name="l08615"></a>08615     weight(5) =  0.424703779005955608398308039150D+00
    8680. 

  8680. <a name="l08616"></a>08616     weight(6) =  0.318204231467301481744870434470D+00
    8681. 

  8681. <a name="l08617"></a>08617     weight(7) =  0.148988471112020635866497560418D+00
    8682. 

  8682. <a name="l08618"></a>08618 
    8683. 

  8683. <a name="l08619"></a>08619   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
    8684. 

  8684. <a name="l08620"></a>08620 
    8685. 

  8685. <a name="l08621"></a>08621     xtab(1) =  - 1.0D+00
    8686. 

  8686. <a name="l08622"></a>08622     xtab(2) =  - 0.887474878926155707068695617935D+00
    8687. 

  8687. <a name="l08623"></a>08623     xtab(3) =  - 0.639518616526215270024840114382D+00
    8688. 

  8688. <a name="l08624"></a>08624     xtab(4) =  - 0.294750565773660725252184459658D+00
    8689. 

  8689. <a name="l08625"></a>08625     xtab(5) =    0.943072526611107660028971153047D-01
    8690. 

  8690. <a name="l08626"></a>08626     xtab(6) =    0.468420354430821063046421216613D+00
    8691. 

  8691. <a name="l08627"></a>08627     xtab(7) =    0.770641893678191536180719525865D+00
    8692. 

  8692. <a name="l08628"></a>08628     xtab(8) =    0.955041227122575003782349000858D+00
    8693. 

  8693. <a name="l08629"></a>08629 
    8694. 

  8694. <a name="l08630"></a>08630     weight(1) =  0.03125D+00
    8695. 

  8695. <a name="l08631"></a>08631     weight(2) =  0.185358154802979278540728972699D+00
    8696. 

  8696. <a name="l08632"></a>08632     weight(3) =  0.304130620646785128975743291400D+00
    8697. 

  8697. <a name="l08633"></a>08633     weight(4) =  0.376517545389118556572129261442D+00
    8698. 

  8698. <a name="l08634"></a>08634     weight(5) =  0.391572167452493593082499534004D+00
    8699. 

  8699. <a name="l08635"></a>08635     weight(6) =  0.347014795634501280228675918422D+00
    8700. 

  8700. <a name="l08636"></a>08636     weight(7) =  0.249647901329864963257869293513D+00
    8701. 

  8701. <a name="l08637"></a>08637     weight(8) =  0.114508814744257199342353728520D+00
    8702. 

  8702. <a name="l08638"></a>08638 
    8703. 

  8703. <a name="l08639"></a>08639   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
    8704. 

  8704. <a name="l08640"></a>08640 
    8705. 

  8705. <a name="l08641"></a>08641     xtab(1) =  - 1.0D+00
    8706. 

  8706. <a name="l08642"></a>08642     xtab(2) =  - 0.910732089420060298533757956283D+00
    8707. 

  8707. <a name="l08643"></a>08643     xtab(3) =  - 0.711267485915708857029562959544D+00
    8708. 

  8708. <a name="l08644"></a>08644     xtab(4) =  - 0.426350485711138962102627520502D+00
    8709. 

  8709. <a name="l08645"></a>08645     xtab(5) =  - 0.903733696068532980645444599064D-01
    8710. 

  8710. <a name="l08646"></a>08646     xtab(6) =    0.256135670833455395138292079035D+00
    8711. 

  8711. <a name="l08647"></a>08647     xtab(7) =    0.571383041208738483284917464837D+00
    8712. 

  8712. <a name="l08648"></a>08648     xtab(8) =    0.817352784200412087992517083851D+00
    8713. 

  8713. <a name="l08649"></a>08649     xtab(9) =    0.964440169705273096373589797925D+00
    8714. 

  8714. <a name="l08650"></a>08650 
    8715. 

  8715. <a name="l08651"></a>08651     weight(1) =  0.246913580246913580246913580247D-01
    8716. 

  8716. <a name="l08652"></a>08652     weight(2) =  0.147654019046315385819588499802D+00
    8717. 

  8717. <a name="l08653"></a>08653     weight(3) =  0.247189378204593052361239794969D+00
    8718. 

  8718. <a name="l08654"></a>08654     weight(4) =  0.316843775670437978338000849642D+00
    8719. 

  8719. <a name="l08655"></a>08655     weight(5) =  0.348273002772966594071991031186D+00
    8720. 

  8720. <a name="l08656"></a>08656     weight(6) =  0.337693966975929585803724239792D+00
    8721. 

  8721. <a name="l08657"></a>08657     weight(7) =  0.286386696357231171146705637752D+00
    8722. 

  8722. <a name="l08658"></a>08658     weight(8) =  0.200553298024551957421165090417D+00
    8723. 

  8723. <a name="l08659"></a>08659     weight(9) =  0.907145049232829170128934984159D-01
    8724. 

  8724. <a name="l08660"></a>08660 
    8725. 

  8725. <a name="l08661"></a>08661   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
    8726. 

  8726. <a name="l08662"></a>08662 
    8727. 

  8727. <a name="l08663"></a>08663     xtab(1) =  - 1.0D+00
    8728. 

  8728. <a name="l08664"></a>08664     xtab(2) =  - 0.927484374233581078117671398464D+00
    8729. 

  8729. <a name="l08665"></a>08665     xtab(3) =  - 0.763842042420002599615429776011D+00
    8730. 

  8730. <a name="l08666"></a>08666     xtab(4) =  - 0.525646030370079229365386614293D+00
    8731. 

  8731. <a name="l08667"></a>08667     xtab(5) =  - 0.236234469390588049278459503207D+00
    8732. 

  8732. <a name="l08668"></a>08668     xtab(6) =    0.760591978379781302337137826389D-01
    8733. 

  8733. <a name="l08669"></a>08669     xtab(7) =    0.380664840144724365880759065541D+00
    8734. 

  8734. <a name="l08670"></a>08670     xtab(8) =    0.647766687674009436273648507855D+00
    8735. 

  8735. <a name="l08671"></a>08671     xtab(9) =    0.851225220581607910728163628088D+00
    8736. 

  8736. <a name="l08672"></a>08672     xtab(10) =   0.971175180702246902734346518378D+00
    8737. 

  8737. <a name="l08673"></a>08673 
    8738. 

  8738. <a name="l08674"></a>08674     weight(1) =  0.02D+00
    8739. 

  8739. <a name="l08675"></a>08675     weight(2) =  0.120296670557481631517310522702D+00
    8740. 

  8740. <a name="l08676"></a>08676     weight(3) =  0.204270131879000675555788672223D+00
    8741. 

  8741. <a name="l08677"></a>08677     weight(4) =  0.268194837841178696058554475262D+00
    8742. 

  8742. <a name="l08678"></a>08678     weight(5) =  0.305859287724422621016275475401D+00
    8743. 

  8743. <a name="l08679"></a>08679     weight(6) =  0.313582457226938376695902847302D+00
    8744. 

  8744. <a name="l08680"></a>08680     weight(7) =  0.290610164832918311146863077963D+00
    8745. 

  8745. <a name="l08681"></a>08681     weight(8) =  0.239193431714379713376571966160D+00
    8746. 

  8746. <a name="l08682"></a>08682     weight(9) =  0.164376012736921475701681668908D+00
    8747. 

  8747. <a name="l08683"></a>08683     weight(10) = 0.736170054867584989310512940790D-01
    8748. 

  8748. <a name="l08684"></a>08684 
    8749. 

  8749. <a name="l08685"></a>08685   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 11 ) <span class="keyword">then</span>
    8750. 

  8750. <a name="l08686"></a>08686 
    8751. 

  8751. <a name="l08687"></a>08687     xtab(1) =  - 1.0D+00
    8752. 

  8752. <a name="l08688"></a>08688     xtab(2) =  - 0.939941935677027005913871284731D+00
    8753. 

  8753. <a name="l08689"></a>08689     xtab(3) =  - 0.803421975580293540697597956820D+00
    8754. 

  8754. <a name="l08690"></a>08690     xtab(4) =  - 0.601957842073797690275892603234D+00
    8755. 

  8755. <a name="l08691"></a>08691     xtab(5) =  - 0.351888923353330214714301017870D+00
    8756. 

  8756. <a name="l08692"></a>08692     xtab(6) =  - 0.734775314313212657461903554238D-01
    8757. 

  8757. <a name="l08693"></a>08693     xtab(7) =    0.210720306228426314076095789845D+00
    8758. 

  8758. <a name="l08694"></a>08694     xtab(8) =    0.477680647983087519467896683890D+00
    8759. 

  8759. <a name="l08695"></a>08695     xtab(9) =    0.705777100713859519144801128840D+00
    8760. 

  8760. <a name="l08696"></a>08696     xtab(10) =   0.876535856245703748954741265611D+00
    8761. 

  8761. <a name="l08697"></a>08697     xtab(11) =   0.976164773135168806180508826082D+00
    8762. 

  8762. <a name="l08698"></a>08698 
    8763. 

  8763. <a name="l08699"></a>08699     weight(1) =  0.165289256198347107438016528926D-01
    8764. 

  8764. <a name="l08700"></a>08700     weight(2) =  0.998460819079680638957534695802D-01
    8765. 

  8765. <a name="l08701"></a>08701     weight(3) =  0.171317619206659836486712649042D+00
    8766. 

  8766. <a name="l08702"></a>08702     weight(4) =  0.228866123848976624401683231126D+00
    8767. 

  8767. <a name="l08703"></a>08703     weight(5) =  0.267867086189684177806638163355D+00
    8768. 

  8768. <a name="l08704"></a>08704     weight(6) =  0.285165563941007337460004408915D+00
    8769. 

  8769. <a name="l08705"></a>08705     weight(7) =  0.279361333103383045188962195720D+00
    8770. 

  8770. <a name="l08706"></a>08706     weight(8) =  0.250925377697128394649140267633D+00
    8771. 

  8771. <a name="l08707"></a>08707     weight(9) =  0.202163108540024418349931754266D+00
    8772. 

  8772. <a name="l08708"></a>08708     weight(10) = 0.137033682133202256310153880580D+00
    8773. 

  8773. <a name="l08709"></a>08709     weight(11) = 0.609250978121311347072183268883D-01
    8774. 

  8774. <a name="l08710"></a>08710 
    8775. 

  8775. <a name="l08711"></a>08711   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 12 ) <span class="keyword">then</span>
    8776. 

  8776. <a name="l08712"></a>08712 
    8777. 

  8777. <a name="l08713"></a>08713     xtab(1) =  - 1.0D+00
    8778. 

  8778. <a name="l08714"></a>08714     xtab(2) =  - 0.949452759204959300493337627077D+00
    8779. 

  8779. <a name="l08715"></a>08715     xtab(3) =  - 0.833916773105189706586269254036D+00
    8780. 

  8780. <a name="l08716"></a>08716     xtab(4) =  - 0.661649799245637148061133087811D+00
    8781. 

  8781. <a name="l08717"></a>08717     xtab(5) =  - 0.444406569781935851126642615609D+00
    8782. 

  8782. <a name="l08718"></a>08718     xtab(6) =  - 0.196994559534278366455441427346D+00
    8783. 

  8783. <a name="l08719"></a>08719     xtab(7) =    0.637247738208319158337792384845D-01
    8784. 

  8784. <a name="l08720"></a>08720     xtab(8) =    0.319983684170669623532789532206D+00
    8785. 

  8785. <a name="l08721"></a>08721     xtab(9) =    0.554318785912324288984337093085D+00
    8786. 

  8786. <a name="l08722"></a>08722     xtab(10) =   0.750761549711113852529400825472D+00
    8787. 

  8787. <a name="l08723"></a>08723     xtab(11) =   0.895929097745638894832914608454D+00
    8788. 

  8788. <a name="l08724"></a>08724     xtab(12) =   0.979963439076639188313950540264D+00
    8789. 

  8789. <a name="l08725"></a>08725 
    8790. 

  8790. <a name="l08726"></a>08726     weight(1) =  0.138888888888888888888888888888D-01
    8791. 

  8791. <a name="l08727"></a>08727     weight(2) =  0.841721349386809762415796536813D-01
    8792. 

  8792. <a name="l08728"></a>08728     weight(3) =  0.145563668853995128522547654706D+00
    8793. 

  8793. <a name="l08729"></a>08729     weight(4) =  0.196998534826089634656049637969D+00
    8794. 

  8794. <a name="l08730"></a>08730     weight(5) =  0.235003115144985839348633985940D+00
    8795. 

  8795. <a name="l08731"></a>08731     weight(6) =  0.256991338152707776127974253598D+00
    8796. 

  8796. <a name="l08732"></a>08732     weight(7) =  0.261465660552133103438074715743D+00
    8797. 

  8797. <a name="l08733"></a>08733     weight(8) =  0.248121560804009959403073107079D+00
    8798. 

  8798. <a name="l08734"></a>08734     weight(9) =  0.217868879026192438848747482023D+00
    8799. 

  8799. <a name="l08735"></a>08735     weight(10) = 0.172770639313308564306065766966D+00
    8800. 

  8800. <a name="l08736"></a>08736     weight(11) = 0.115907480291738392750341908272D+00
    8801. 

  8801. <a name="l08737"></a>08737     weight(12) = 0.512480992072692974680229451351D-01
    8802. 

  8802. <a name="l08738"></a>08738 
    8803. 

  8803. <a name="l08739"></a>08739   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 13 ) <span class="keyword">then</span>
    8804. 

  8804. <a name="l08740"></a>08740 
    8805. 

  8805. <a name="l08741"></a>08741     xtab(1) =  - 1.0D+00
    8806. 

  8806. <a name="l08742"></a>08742     xtab(2) =  - 0.956875873668299278183813833834D+00
    8807. 

  8807. <a name="l08743"></a>08743     xtab(3) =  - 0.857884202528822035697620310269D+00
    8808. 

  8808. <a name="l08744"></a>08744     xtab(4) =  - 0.709105087529871761580423832811D+00
    8809. 

  8809. <a name="l08745"></a>08745     xtab(5) =  - 0.519197779050454107485205148087D+00
    8810. 

  8810. <a name="l08746"></a>08746     xtab(6) =  - 0.299201300554509985532583446686D+00
    8811. 

  8811. <a name="l08747"></a>08747     xtab(7) =  - 0.619016986256353412578604857936D-01
    8812. 

  8812. <a name="l08748"></a>08748     xtab(8) =    0.178909837597084635021931298881D+00
    8813. 

  8813. <a name="l08749"></a>08749     xtab(9) =    0.409238231474839556754166331248D+00
    8814. 

  8814. <a name="l08750"></a>08750     xtab(10) =   0.615697890940291918017885487543D+00
    8815. 

  8815. <a name="l08751"></a>08751     xtab(11) =   0.786291018233046684731786459135D+00
    8816. 

  8816. <a name="l08752"></a>08752     xtab(12) =   0.911107073689184553949066402429D+00
    8817. 

  8817. <a name="l08753"></a>08753     xtab(13) =   0.982921890023145161262671078244D+00
    8818. 

  8818. <a name="l08754"></a>08754 
    8819. 

  8819. <a name="l08755"></a>08755     weight(1) =  0.118343195266272189349112426036D-01
    8820. 

  8820. <a name="l08756"></a>08756     weight(2) =  0.719024162924955289397537405641D-01
    8821. 

  8821. <a name="l08757"></a>08757     weight(3) =  0.125103834331152358133769287976D+00
    8822. 

  8822. <a name="l08758"></a>08758     weight(4) =  0.171003460470616642463758674512D+00
    8823. 

  8823. <a name="l08759"></a>08759     weight(5) =  0.206960611455877074631132560829D+00
    8824. 

  8824. <a name="l08760"></a>08760     weight(6) =  0.230888862886995434012203758668D+00
    8825. 

  8825. <a name="l08761"></a>08761     weight(7) =  0.241398342287691148630866924129D+00
    8826. 

  8826. <a name="l08762"></a>08762     weight(8) =  0.237878547660712031342685189180D+00
    8827. 

  8827. <a name="l08763"></a>08763     weight(9) =  0.220534229288451464691077164199D+00
    8828. 

  8828. <a name="l08764"></a>08764     weight(10) = 0.190373715559631732254759820746D+00
    8829. 

  8829. <a name="l08765"></a>08765     weight(11) = 0.149150950090000205151491864242D+00
    8830. 

  8830. <a name="l08766"></a>08766     weight(12) = 0.992678068818470859847363877478D-01
    8831. 

  8831. <a name="l08767"></a>08767     weight(13) = 0.437029032679020748288533846051D-01
    8832. 

  8832. <a name="l08768"></a>08768 
    8833. 

  8833. <a name="l08769"></a>08769   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 14 ) <span class="keyword">then</span>
    8834. 

  8834. <a name="l08770"></a>08770 
    8835. 

  8835. <a name="l08771"></a>08771     xtab(1) =  - 1.0D+00
    8836. 

  8836. <a name="l08772"></a>08772     xtab(2) =  - 0.962779269978024297120561244319D+00
    8837. 

  8837. <a name="l08773"></a>08773     xtab(3) =  - 0.877048918201462024795266773531D+00
    8838. 

  8838. <a name="l08774"></a>08774     xtab(4) =  - 0.747389642613378838735429134263D+00
    8839. 

  8839. <a name="l08775"></a>08775     xtab(5) =  - 0.580314056546874971105726664999D+00
    8840. 

  8840. <a name="l08776"></a>08776     xtab(6) =  - 0.384202003439203313794083903375D+00
    8841. 

  8841. <a name="l08777"></a>08777     xtab(7) =  - 0.168887928042680911008441695622D+00
    8842. 

  8842. <a name="l08778"></a>08778     xtab(8) =    0.548312279917645496498107146428D-01
    8843. 

  8843. <a name="l08779"></a>08779     xtab(9) =    0.275737205435522399182637403545D+00
    8844. 

  8844. <a name="l08780"></a>08780     xtab(10) =   0.482752918588474966820418534355D+00
    8845. 

  8845. <a name="l08781"></a>08781     xtab(11) =   0.665497977216884537008955042481D+00
    8846. 

  8846. <a name="l08782"></a>08782     xtab(12) =   0.814809550601994729434217249123D+00
    8847. 

  8847. <a name="l08783"></a>08783     xtab(13) =   0.923203722520643299246334950272D+00
    8848. 

  8848. <a name="l08784"></a>08784     xtab(14) =   0.985270697947821356698617003172D+00
    8849. 

  8849. <a name="l08785"></a>08785 
    8850. 

  8850. <a name="l08786"></a>08786     weight(1) =  0.102040816326530612244897959184D-01
    8851. 

  8851. <a name="l08787"></a>08787     weight(2) =  0.621220169077714601661329164668D-01
    8852. 

  8852. <a name="l08788"></a>08788     weight(3) =  0.108607722744362826826720935229D+00
    8853. 

  8853. <a name="l08789"></a>08789     weight(4) =  0.149620539353121355950520836946D+00
    8854. 

  8854. <a name="l08790"></a>08790     weight(5) =  0.183127002125729654123867302103D+00
    8855. 

  8855. <a name="l08791"></a>08791     weight(6) =  0.207449763335175672668082886489D+00
    8856. 

  8856. <a name="l08792"></a>08792     weight(7) =  0.221369811499570948931671683021D+00
    8857. 

  8857. <a name="l08793"></a>08793     weight(8) =  0.224189348002707794238414632220D+00
    8858. 

  8858. <a name="l08794"></a>08794     weight(9) =  0.215767100604618851381187446115D+00
    8859. 

  8859. <a name="l08795"></a>08795     weight(10) = 0.196525518452982430324613091930D+00
    8860. 

  8860. <a name="l08796"></a>08796     weight(11) = 0.167429727891086278990102277038D+00
    8861. 

  8861. <a name="l08797"></a>08797     weight(12) = 0.129939668737342347807425737146D+00
    8862. 

  8862. <a name="l08798"></a>08798     weight(13) = 0.859405354429804030893077310866D-01
    8863. 

  8863. <a name="l08799"></a>08799     weight(14) = 0.377071632698969142774627282919D-01
    8864. 

  8864. <a name="l08800"></a>08800 
    8865. 

  8865. <a name="l08801"></a>08801   <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
    8866. 

  8866. <a name="l08802"></a>08802 
    8867. 

  8867. <a name="l08803"></a>08803     xtab(1) =  - 1.0D+00
    8868. 

  8868. <a name="l08804"></a>08804     xtab(2) =  - 0.967550468197200476562456018282D+00
    8869. 

  8869. <a name="l08805"></a>08805     xtab(3) =  - 0.892605400120550767066811886849D+00
    8870. 

  8870. <a name="l08806"></a>08806     xtab(4) =  - 0.778685617639031079381743321893D+00
    8871. 

  8871. <a name="l08807"></a>08807     xtab(5) =  - 0.630779478886949283946148437224D+00
    8872. 

  8872. <a name="l08808"></a>08808     xtab(6) =  - 0.455352905778529370872053455981D+00
    8873. 

  8873. <a name="l08809"></a>08809     xtab(7) =  - 0.260073376740807915768961188263D+00
    8874. 

  8874. <a name="l08810"></a>08810     xtab(8) =  - 0.534757226797460641074538896258D-01
    8875. 

  8875. <a name="l08811"></a>08811     xtab(9) =    0.155410685384859484319182024964D+00
    8876. 

  8876. <a name="l08812"></a>08812     xtab(10) =   0.357456512022127651195319205174D+00
    8877. 

  8877. <a name="l08813"></a>08813     xtab(11) =   0.543831458701484016930711802760D+00
    8878. 

  8878. <a name="l08814"></a>08814     xtab(12) =   0.706390264637572540152679669478D+00
    8879. 

  8879. <a name="l08815"></a>08815     xtab(13) =   0.838029000636089631215097384520D+00
    8880. 

  8880. <a name="l08816"></a>08816     xtab(14) =   0.932997190935973719928072142859D+00
    8881. 

  8881. <a name="l08817"></a>08817     xtab(15) =   0.987166478414363086378359071811D+00
    8882. 

  8882. <a name="l08818"></a>08818 
    8883. 

  8883. <a name="l08819"></a>08819     weight(1) =  0.888888888888888888888888888889D-02
    8884. 

  8884. <a name="l08820"></a>08820     weight(2) =  0.542027800486444943382142368018D-01
    8885. 

  8885. <a name="l08821"></a>08821     weight(3) =  0.951295994604808992038477266346D-01
    8886. 

  8886. <a name="l08822"></a>08822     weight(4) =  0.131875462504951632186262157944D+00
    8887. 

  8887. <a name="l08823"></a>08823     weight(5) =  0.162854477303832629448732245828D+00
    8888. 

  8888. <a name="l08824"></a>08824     weight(6) =  0.186715145839450908083795103799D+00
    8889. 

  8889. <a name="l08825"></a>08825     weight(7) =  0.202415187030618429872703310435D+00
    8890. 

  8890. <a name="l08826"></a>08826     weight(8) =  0.209268608147694581430889790306D+00
    8891. 

  8891. <a name="l08827"></a>08827     weight(9) =  0.206975960249553755479027321787D+00
    8892. 

  8892. <a name="l08828"></a>08828     weight(10) = 0.195637503045116116473556617575D+00
    8893. 

  8893. <a name="l08829"></a>08829     weight(11) = 0.175748872642447685670310440476D+00
    8894. 

  8894. <a name="l08830"></a>08830     weight(12) = 0.148179527003467253924682058743D+00
    8895. 

  8895. <a name="l08831"></a>08831     weight(13) = 0.114135203489752753013075582569D+00
    8896. 

  8896. <a name="l08832"></a>08832     weight(14) = 0.751083927605064397329716653914D-01
    8897. 

  8897. <a name="l08833"></a>08833     weight(15) = 0.328643915845935322530428528231D-01
    8898. 

  8898. <a name="l08834"></a>08834 
    8899. 

  8899. <a name="l08835"></a>08835   <span class="keyword">else</span>
    8900. 

  8900. <a name="l08836"></a>08836 
    8901. 

  8901. <a name="l08837"></a>08837     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    8902. 

  8902. <a name="l08838"></a>08838     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;RADAU_SET - Fatal error!&#39;</span>
    8903. 

  8903. <a name="l08839"></a>08839     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Illegal value of NORDER = &#39;</span>, norder
    8904. 

  8904. <a name="l08840"></a>08840     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  Legal values are 1 to 15.&#39;</span>
    8905. 

  8905. <a name="l08841"></a>08841     stop
    8906. 

  8906. <a name="l08842"></a>08842 
    8907. 

  8907. <a name="l08843"></a>08843   <span class="keyword">end if</span>
    8908. 

  8908. <a name="l08844"></a>08844 
    8909. 

  8909. <a name="l08845"></a>08845   return
    8910. 

  8910. <a name="l08846"></a>08846 <span class="keyword">end</span>
    8911. 

  8911. <a name="l08847"></a><a class="code" href="quadrule_8f90.html#aaa549734d177cfe892a84e25e267ee4d">08847</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#aaa549734d177cfe892a84e25e267ee4d">rule_adjust</a> ( a, b, c, d, norder, x, w )
    8912. 

  8912. <a name="l08848"></a>08848 <span class="comment">!</span>
    8913. 

  8913. <a name="l08849"></a>08849 <span class="comment">!*******************************************************************************</span>
    8914. 

  8914. <a name="l08850"></a>08850 <span class="comment">!</span>
    8915. 

  8915. <a name="l08851"></a>08851 <span class="comment">!! RULE_ADJUST maps a quadrature rule from [A,B] to [C,D].</span>
    8916. 

  8916. <a name="l08852"></a>08852 <span class="comment">!</span>
    8917. 

  8917. <a name="l08853"></a>08853 <span class="comment">!</span>
    8918. 

  8918. <a name="l08854"></a>08854 <span class="comment">!  Discussion:</span>
    8919. 

  8919. <a name="l08855"></a>08855 <span class="comment">!</span>
    8920. 

  8920. <a name="l08856"></a>08856 <span class="comment">!    Most quadrature rules are defined on a special interval, like</span>
    8921. 

  8921. <a name="l08857"></a>08857 <span class="comment">!    [-1,1] or [0,1].  To integrate over an interval, the abscissas</span>
    8922. 

  8922. <a name="l08858"></a>08858 <span class="comment">!    and weights must be adjusted.  This can be done on the fly,</span>
    8923. 

  8923. <a name="l08859"></a>08859 <span class="comment">!    or by calling this routine.</span>
    8924. 

  8924. <a name="l08860"></a>08860 <span class="comment">!</span>
    8925. 

  8925. <a name="l08861"></a>08861 <span class="comment">!    If the weight function W(X) is not 1, then the W vector will</span>
    8926. 

  8926. <a name="l08862"></a>08862 <span class="comment">!    require further adjustment by the user.</span>
    8927. 

  8927. <a name="l08863"></a>08863 <span class="comment">!</span>
    8928. 

  8928. <a name="l08864"></a>08864 <span class="comment">!  Modified:</span>
    8929. 

  8929. <a name="l08865"></a>08865 <span class="comment">!</span>
    8930. 

  8930. <a name="l08866"></a>08866 <span class="comment">!    06 December 2000</span>
    8931. 

  8931. <a name="l08867"></a>08867 <span class="comment">!</span>
    8932. 

  8932. <a name="l08868"></a>08868 <span class="comment">!  Author:</span>
    8933. 

  8933. <a name="l08869"></a>08869 <span class="comment">!</span>
    8934. 

  8934. <a name="l08870"></a>08870 <span class="comment">!    John Burkardt</span>
    8935. 

  8935. <a name="l08871"></a>08871 <span class="comment">!</span>
    8936. 

  8936. <a name="l08872"></a>08872 <span class="comment">!  Parameters:</span>
    8937. 

  8937. <a name="l08873"></a>08873 <span class="comment">!</span>
    8938. 

  8938. <a name="l08874"></a>08874 <span class="comment">!    Input, double precision A, B, the endpoints of the definition interval.</span>
    8939. 

  8939. <a name="l08875"></a>08875 <span class="comment">!</span>
    8940. 

  8940. <a name="l08876"></a>08876 <span class="comment">!    Input, double precision C, D, the endpoints of the integration interval.</span>
    8941. 

  8941. <a name="l08877"></a>08877 <span class="comment">!</span>
    8942. 

  8942. <a name="l08878"></a>08878 <span class="comment">!    Input, integer NORDER, the number of abscissas and weights.</span>
    8943. 

  8943. <a name="l08879"></a>08879 <span class="comment">!</span>
    8944. 

  8944. <a name="l08880"></a>08880 <span class="comment">!    Input/output, double precision X(NORDER), W(NORDER), the abscissas</span>
    8945. 

  8945. <a name="l08881"></a>08881 <span class="comment">!    and weights.</span>
    8946. 

  8946. <a name="l08882"></a>08882 <span class="comment">!</span>
    8947. 

  8947. <a name="l08883"></a>08883   <span class="keyword">implicit none</span>
    8948. 

  8948. <a name="l08884"></a>08884 <span class="comment">!</span>
    8949. 

  8949. <a name="l08885"></a>08885   <span class="keywordtype">integer</span> norder
    8950. 

  8950. <a name="l08886"></a>08886 <span class="comment">!</span>
    8951. 

  8951. <a name="l08887"></a>08887   <span class="keywordtype">double precision</span> a
    8952. 

  8952. <a name="l08888"></a>08888   <span class="keywordtype">double precision</span> b
    8953. 

  8953. <a name="l08889"></a>08889   <span class="keywordtype">double precision</span> c
    8954. 

  8954. <a name="l08890"></a>08890   <span class="keywordtype">double precision</span> d
    8955. 

  8955. <a name="l08891"></a>08891   <span class="keywordtype">double precision</span> w(norder)
    8956. 

  8956. <a name="l08892"></a>08892   <span class="keywordtype">double precision</span> x(norder)
    8957. 

  8957. <a name="l08893"></a>08893 <span class="comment">!</span>
    8958. 

  8958. <a name="l08894"></a>08894   x(1:norder) = ( ( b - x(1:norder) ) * c + ( x(1:norder) - a ) * d ) &amp;
    8959. 

  8959. <a name="l08895"></a>08895     / ( b - a )
    8960. 

  8960. <a name="l08896"></a>08896 
    8961. 

  8961. <a name="l08897"></a>08897   w(1:norder) = ( ( d - c ) / ( b - a ) ) * w(1:norder)
    8962. 

  8962. <a name="l08898"></a>08898 
    8963. 

  8963. <a name="l08899"></a>08899   return
    8964. 

  8964. <a name="l08900"></a>08900 <span class="keyword">end</span>
    8965. 

  8965. <a name="l08901"></a><a class="code" href="quadrule_8f90.html#adae6ebad1d51cf128e8f0247ef582ac9">08901</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#adae6ebad1d51cf128e8f0247ef582ac9">summer</a> ( func, norder, xtab, weight, result )
    8966. 

  8966. <a name="l08902"></a>08902 <span class="comment">!</span>
    8967. 

  8967. <a name="l08903"></a>08903 <span class="comment">!*******************************************************************************</span>
    8968. 

  8968. <a name="l08904"></a>08904 <span class="comment">!</span>
    8969. 

  8969. <a name="l08905"></a>08905 <span class="comment">!! SUMMER carries out a quadrature rule over a single interval.</span>
    8970. 

  8970. <a name="l08906"></a>08906 <span class="comment">!</span>
    8971. 

  8971. <a name="l08907"></a>08907 <span class="comment">!</span>
    8972. 

  8972. <a name="l08908"></a>08908 <span class="comment">!  Formula:</span>
    8973. 

  8973. <a name="l08909"></a>08909 <span class="comment">!</span>
    8974. 

  8974. <a name="l08910"></a>08910 <span class="comment">!    RESULT = SUM ( 1 &lt;= I &lt;= NORDER ) WEIGHT(I) * FUNC ( XTAB(I) )</span>
    8975. 

  8975. <a name="l08911"></a>08911 <span class="comment">!</span>
    8976. 

  8976. <a name="l08912"></a>08912 <span class="comment">!  Modified:</span>
    8977. 

  8977. <a name="l08913"></a>08913 <span class="comment">!</span>
    8978. 

  8978. <a name="l08914"></a>08914 <span class="comment">!    16 September 1998</span>
    8979. 

  8979. <a name="l08915"></a>08915 <span class="comment">!</span>
    8980. 

  8980. <a name="l08916"></a>08916 <span class="comment">!  Author:</span>
    8981. 

  8981. <a name="l08917"></a>08917 <span class="comment">!</span>
    8982. 

  8982. <a name="l08918"></a>08918 <span class="comment">!    John Burkardt</span>
    8983. 

  8983. <a name="l08919"></a>08919 <span class="comment">!</span>
    8984. 

  8984. <a name="l08920"></a>08920 <span class="comment">!  Parameters:</span>
    8985. 

  8985. <a name="l08921"></a>08921 <span class="comment">!</span>
    8986. 

  8986. <a name="l08922"></a>08922 <span class="comment">!    Input, external FUNC, the name of the FORTRAN function which</span>
    8987. 

  8987. <a name="l08923"></a>08923 <span class="comment">!    evaluates the integrand.  The function must have the form</span>
    8988. 

  8988. <a name="l08924"></a>08924 <span class="comment">!      double precision func ( x ).</span>
    8989. 

  8989. <a name="l08925"></a>08925 <span class="comment">!</span>
    8990. 

  8990. <a name="l08926"></a>08926 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    8991. 

  8991. <a name="l08927"></a>08927 <span class="comment">!</span>
    8992. 

  8992. <a name="l08928"></a>08928 <span class="comment">!    Input, double precision XTAB(NORDER), the abscissas of the rule.</span>
    8993. 

  8993. <a name="l08929"></a>08929 <span class="comment">!</span>
    8994. 

  8994. <a name="l08930"></a>08930 <span class="comment">!    Input, double precision WEIGHT(NORDER), the weights of the rule.</span>
    8995. 

  8995. <a name="l08931"></a>08931 <span class="comment">!</span>
    8996. 

  8996. <a name="l08932"></a>08932 <span class="comment">!    Output, double precision RESULT, the approximate value of the integral.</span>
    8997. 

  8997. <a name="l08933"></a>08933 <span class="comment">!</span>
    8998. 

  8998. <a name="l08934"></a>08934   <span class="keyword">implicit none</span>
    8999. 

  8999. <a name="l08935"></a>08935 <span class="comment">!</span>
    9000. 

  9000. <a name="l08936"></a>08936   <span class="keywordtype">integer</span> norder
    9001. 

  9001. <a name="l08937"></a>08937 <span class="comment">!</span>
    9002. 

  9002. <a name="l08938"></a>08938   <span class="keywordtype">double precision</span>, <span class="keywordtype">external</span> :: func
    9003. 

  9003. <a name="l08939"></a>08939   <span class="keywordtype">integer</span> i
    9004. 

  9004. <a name="l08940"></a>08940   <span class="keywordtype">double precision</span> result
    9005. 

  9005. <a name="l08941"></a>08941   <span class="keywordtype">double precision</span> weight(norder)
    9006. 

  9006. <a name="l08942"></a>08942   <span class="keywordtype">double precision</span> xtab(norder)
    9007. 

  9007. <a name="l08943"></a>08943 <span class="comment">!</span>
    9008. 

  9008. <a name="l08944"></a>08944   <span class="keyword">if</span> ( norder &lt; 1 ) <span class="keyword">then</span>
    9009. 

  9009. <a name="l08945"></a>08945     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    9010. 

  9010. <a name="l08946"></a>08946     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;SUMMER - Fatal error!&#39;</span>
    9011. 

  9011. <a name="l08947"></a>08947     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  NORDER must be at least 1.&#39;</span>
    9012. 

  9012. <a name="l08948"></a>08948     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  The input value was NORDER = &#39;</span>, norder
    9013. 

  9013. <a name="l08949"></a>08949     stop
    9014. 

  9014. <a name="l08950"></a>08950   <span class="keyword">end if</span>
    9015. 

  9015. <a name="l08951"></a>08951 
    9016. 

  9016. <a name="l08952"></a>08952   result = 0.0D+00
    9017. 

  9017. <a name="l08953"></a>08953   <span class="keyword">do</span> i = 1, norder
    9018. 

  9018. <a name="l08954"></a>08954     result = result + weight(i) * func ( xtab(i) )
    9019. 

  9019. <a name="l08955"></a>08955   <span class="keyword">end do</span>
    9020. 

  9020. <a name="l08956"></a>08956 
    9021. 

  9021. <a name="l08957"></a>08957   return
    9022. 

  9022. <a name="l08958"></a>08958 <span class="keyword">end</span>
    9023. 

  9023. <a name="l08959"></a><a class="code" href="quadrule_8f90.html#ae2cd4600769ef44fbc01ccd971c0fc73">08959</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#ae2cd4600769ef44fbc01ccd971c0fc73">summer_gk</a> ( func, norderg, weightg, resultg, norderk, xtabk, &amp;
    9024. 

  9024. <a name="l08960"></a>08960   weightk, resultk )
    9025. 

  9025. <a name="l08961"></a>08961 <span class="comment">!</span>
    9026. 

  9026. <a name="l08962"></a>08962 <span class="comment">!*******************************************************************************</span>
    9027. 

  9027. <a name="l08963"></a>08963 <span class="comment">!</span>
    9028. 

  9028. <a name="l08964"></a>08964 <span class="comment">!! SUMMER_GK carries out Gauss-Kronrod quadrature over a single interval.</span>
    9029. 

  9029. <a name="l08965"></a>08965 <span class="comment">!</span>
    9030. 

  9030. <a name="l08966"></a>08966 <span class="comment">!</span>
    9031. 

  9031. <a name="l08967"></a>08967 <span class="comment">!  Note:</span>
    9032. 

  9032. <a name="l08968"></a>08968 <span class="comment">!</span>
    9033. 

  9033. <a name="l08969"></a>08969 <span class="comment">!    The abscissas for the Gauss-Legendre rule of order NORDERG are</span>
    9034. 

  9034. <a name="l08970"></a>08970 <span class="comment">!    not required, since they are assumed to be the even-indexed</span>
    9035. 

  9035. <a name="l08971"></a>08971 <span class="comment">!    entries of the corresponding Kronrod rule.</span>
    9036. 

  9036. <a name="l08972"></a>08972 <span class="comment">!</span>
    9037. 

  9037. <a name="l08973"></a>08973 <span class="comment">!  Modified:</span>
    9038. 

  9038. <a name="l08974"></a>08974 <span class="comment">!</span>
    9039. 

  9039. <a name="l08975"></a>08975 <span class="comment">!    16 September 1998</span>
    9040. 

  9040. <a name="l08976"></a>08976 <span class="comment">!</span>
    9041. 

  9041. <a name="l08977"></a>08977 <span class="comment">!  Author:</span>
    9042. 

  9042. <a name="l08978"></a>08978 <span class="comment">!</span>
    9043. 

  9043. <a name="l08979"></a>08979 <span class="comment">!    John Burkardt</span>
    9044. 

  9044. <a name="l08980"></a>08980 <span class="comment">!</span>
    9045. 

  9045. <a name="l08981"></a>08981 <span class="comment">!  Parameters:</span>
    9046. 

  9046. <a name="l08982"></a>08982 <span class="comment">!</span>
    9047. 

  9047. <a name="l08983"></a>08983 <span class="comment">!    Input, external FUNC, the name of the FORTRAN function which</span>
    9048. 

  9048. <a name="l08984"></a>08984 <span class="comment">!    evaluates the integrand.  The function must have the form</span>
    9049. 

  9049. <a name="l08985"></a>08985 <span class="comment">!      double precision func ( x ).</span>
    9050. 

  9050. <a name="l08986"></a>08986 <span class="comment">!</span>
    9051. 

  9051. <a name="l08987"></a>08987 <span class="comment">!    Input, integer NORDERG, the order of the Gauss-Legendre rule.</span>
    9052. 

  9052. <a name="l08988"></a>08988 <span class="comment">!</span>
    9053. 

  9053. <a name="l08989"></a>08989 <span class="comment">!    Input, double precision WEIGHTG(NORDERG), the weights of the</span>
    9054. 

  9054. <a name="l08990"></a>08990 <span class="comment">!    Gauss-Legendre rule.</span>
    9055. 

  9055. <a name="l08991"></a>08991 <span class="comment">!</span>
    9056. 

  9056. <a name="l08992"></a>08992 <span class="comment">!    Output, double precision RESULTG, the approximate value of the</span>
    9057. 

  9057. <a name="l08993"></a>08993 <span class="comment">!    integral, based on the Gauss-Legendre rule.</span>
    9058. 

  9058. <a name="l08994"></a>08994 <span class="comment">!</span>
    9059. 

  9059. <a name="l08995"></a>08995 <span class="comment">!    Input, integer NORDERK, the order of the Kronrod rule.  NORDERK</span>
    9060. 

  9060. <a name="l08996"></a>08996 <span class="comment">!    must equal 2 * NORDERG + 1.</span>
    9061. 

  9061. <a name="l08997"></a>08997 <span class="comment">!</span>
    9062. 

  9062. <a name="l08998"></a>08998 <span class="comment">!    Input, double precision XTABK(NORDERK), the abscissas of the Kronrod rule.</span>
    9063. 

  9063. <a name="l08999"></a>08999 <span class="comment">!</span>
    9064. 

  9064. <a name="l09000"></a>09000 <span class="comment">!    Input, double precision WEIGHTK(NORDERK), the weights of the Kronrod rule.</span>
    9065. 

  9065. <a name="l09001"></a>09001 <span class="comment">!</span>
    9066. 

  9066. <a name="l09002"></a>09002 <span class="comment">!    Output, double precision RESULTK, the approximate value of the integral,</span>
    9067. 

  9067. <a name="l09003"></a>09003 <span class="comment">!    based on the Kronrod rule.</span>
    9068. 

  9068. <a name="l09004"></a>09004 <span class="comment">!</span>
    9069. 

  9069. <a name="l09005"></a>09005   <span class="keyword">implicit none</span>
    9070. 

  9070. <a name="l09006"></a>09006 <span class="comment">!</span>
    9071. 

  9071. <a name="l09007"></a>09007   <span class="keywordtype">integer</span> norderg
    9072. 

  9072. <a name="l09008"></a>09008   <span class="keywordtype">integer</span> norderk
    9073. 

  9073. <a name="l09009"></a>09009 <span class="comment">!</span>
    9074. 

  9074. <a name="l09010"></a>09010   <span class="keywordtype">double precision</span> fk
    9075. 

  9075. <a name="l09011"></a>09011   <span class="keywordtype">double precision</span>, <span class="keywordtype">external</span> :: func
    9076. 

  9076. <a name="l09012"></a>09012   <span class="keywordtype">integer</span> i
    9077. 

  9077. <a name="l09013"></a>09013   <span class="keywordtype">double precision</span> resultg
    9078. 

  9078. <a name="l09014"></a>09014   <span class="keywordtype">double precision</span> resultk
    9079. 

  9079. <a name="l09015"></a>09015   <span class="keywordtype">double precision</span> weightg(norderg)
    9080. 

  9080. <a name="l09016"></a>09016   <span class="keywordtype">double precision</span> weightk(norderk)
    9081. 

  9081. <a name="l09017"></a>09017   <span class="keywordtype">double precision</span> xtabk(norderk)
    9082. 

  9082. <a name="l09018"></a>09018 <span class="comment">!</span>
    9083. 

  9083. <a name="l09019"></a>09019   <span class="keyword">if</span> ( norderk /= 2 * norderg + 1 ) <span class="keyword">then</span>
    9084. 

  9084. <a name="l09020"></a>09020     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    9085. 

  9085. <a name="l09021"></a>09021     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;SUMMER_GK - Fatal error!&#39;</span>
    9086. 

  9086. <a name="l09022"></a>09022     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  NORDERK must equal 2 * NORDERG + 1.&#39;</span>
    9087. 

  9087. <a name="l09023"></a>09023     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  The input value was NORDERG = &#39;</span>, norderg
    9088. 

  9088. <a name="l09024"></a>09024     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  The input value was NORDERK = &#39;</span>, norderk
    9089. 

  9089. <a name="l09025"></a>09025     stop
    9090. 

  9090. <a name="l09026"></a>09026   <span class="keyword">end if</span>
    9091. 

  9091. <a name="l09027"></a>09027 
    9092. 

  9092. <a name="l09028"></a>09028   resultg = 0.0D+00
    9093. 

  9093. <a name="l09029"></a>09029   resultk = 0.0D+00
    9094. 

  9094. <a name="l09030"></a>09030 
    9095. 

  9095. <a name="l09031"></a>09031   <span class="keyword">do</span> i = 1, norderk
    9096. 

  9096. <a name="l09032"></a>09032 
    9097. 

  9097. <a name="l09033"></a>09033     fk = func ( xtabk(i) )
    9098. 

  9098. <a name="l09034"></a>09034 
    9099. 

  9099. <a name="l09035"></a>09035     resultk = resultk + weightk(i) * fk
    9100. 

  9100. <a name="l09036"></a>09036 
    9101. 

  9101. <a name="l09037"></a>09037     <span class="keyword">if</span> ( mod ( i, 2 ) == 0 )<span class="keyword">then</span>
    9102. 

  9102. <a name="l09038"></a>09038       resultg = resultg + weightg(i/2) * fk
    9103. 

  9103. <a name="l09039"></a>09039     <span class="keyword">end if</span>
    9104. 

  9104. <a name="l09040"></a>09040 
    9105. 

  9105. <a name="l09041"></a>09041   <span class="keyword">end do</span>
    9106. 

  9106. <a name="l09042"></a>09042 
    9107. 

  9107. <a name="l09043"></a>09043   return
    9108. 

  9108. <a name="l09044"></a>09044 <span class="keyword">end</span>
    9109. 

  9109. <a name="l09045"></a><a class="code" href="quadrule_8f90.html#a268ec8eaa9ed225402666340aecb03d4">09045</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a268ec8eaa9ed225402666340aecb03d4">sum_sub</a> ( func, a, b, nsub, norder, xlo, xhi, xtab, weight, result )
    9110. 

  9110. <a name="l09046"></a>09046 <span class="comment">!</span>
    9111. 

  9111. <a name="l09047"></a>09047 <span class="comment">!*******************************************************************************</span>
    9112. 

  9112. <a name="l09048"></a>09048 <span class="comment">!</span>
    9113. 

  9113. <a name="l09049"></a>09049 <span class="comment">!! SUM_SUB carries out a composite quadrature rule.</span>
    9114. 

  9114. <a name="l09050"></a>09050 <span class="comment">!</span>
    9115. 

  9115. <a name="l09051"></a>09051 <span class="comment">!</span>
    9116. 

  9116. <a name="l09052"></a>09052 <span class="comment">!  Discussion:</span>
    9117. 

  9117. <a name="l09053"></a>09053 <span class="comment">!</span>
    9118. 

  9118. <a name="l09054"></a>09054 <span class="comment">!    SUM_SUB assumes the original rule was written for [XLO,XHI].</span>
    9119. 

  9119. <a name="l09055"></a>09055 <span class="comment">!</span>
    9120. 

  9120. <a name="l09056"></a>09056 <span class="comment">!  Integration interval:</span>
    9121. 

  9121. <a name="l09057"></a>09057 <span class="comment">!</span>
    9122. 

  9122. <a name="l09058"></a>09058 <span class="comment">!    [ A, B ]</span>
    9123. 

  9123. <a name="l09059"></a>09059 <span class="comment">!</span>
    9124. 

  9124. <a name="l09060"></a>09060 <span class="comment">!  Integral to approximate:</span>
    9125. 

  9125. <a name="l09061"></a>09061 <span class="comment">!</span>
    9126. 

  9126. <a name="l09062"></a>09062 <span class="comment">!    Integral ( A &lt;= X &lt;= B ) F(X) dX</span>
    9127. 

  9127. <a name="l09063"></a>09063 <span class="comment">!</span>
    9128. 

  9128. <a name="l09064"></a>09064 <span class="comment">!  Modified:</span>
    9129. 

  9129. <a name="l09065"></a>09065 <span class="comment">!</span>
    9130. 

  9130. <a name="l09066"></a>09066 <span class="comment">!    06 December 2000</span>
    9131. 

  9131. <a name="l09067"></a>09067 <span class="comment">!</span>
    9132. 

  9132. <a name="l09068"></a>09068 <span class="comment">!  Author:</span>
    9133. 

  9133. <a name="l09069"></a>09069 <span class="comment">!</span>
    9134. 

  9134. <a name="l09070"></a>09070 <span class="comment">!    John Burkardt</span>
    9135. 

  9135. <a name="l09071"></a>09071 <span class="comment">!</span>
    9136. 

  9136. <a name="l09072"></a>09072 <span class="comment">!  Parameters:</span>
    9137. 

  9137. <a name="l09073"></a>09073 <span class="comment">!</span>
    9138. 

  9138. <a name="l09074"></a>09074 <span class="comment">!    Input, external FUNC, the name of the FORTRAN function which</span>
    9139. 

  9139. <a name="l09075"></a>09075 <span class="comment">!    evaluates the integrand.  The function must have the form</span>
    9140. 

  9140. <a name="l09076"></a>09076 <span class="comment">!      double precision func ( x ).</span>
    9141. 

  9141. <a name="l09077"></a>09077 <span class="comment">!</span>
    9142. 

  9142. <a name="l09078"></a>09078 <span class="comment">!    Input, double precision A, B, the lower and upper limits of integration.</span>
    9143. 

  9143. <a name="l09079"></a>09079 <span class="comment">!</span>
    9144. 

  9144. <a name="l09080"></a>09080 <span class="comment">!    Input, integer NSUB, the number of equal subintervals into</span>
    9145. 

  9145. <a name="l09081"></a>09081 <span class="comment">!    which the finite interval (A,B) is to be subdivided for</span>
    9146. 

  9146. <a name="l09082"></a>09082 <span class="comment">!    higher accuracy.  NSUB must be at least 1.</span>
    9147. 

  9147. <a name="l09083"></a>09083 <span class="comment">!</span>
    9148. 

  9148. <a name="l09084"></a>09084 <span class="comment">!    Input, integer NORDER, the order of the rule.</span>
    9149. 

  9149. <a name="l09085"></a>09085 <span class="comment">!    NORDER must be at least 1.</span>
    9150. 

  9150. <a name="l09086"></a>09086 <span class="comment">!</span>
    9151. 

  9151. <a name="l09087"></a>09087 <span class="comment">!    Input, double precision XLO, XHI, the left and right endpoints of</span>
    9152. 

  9152. <a name="l09088"></a>09088 <span class="comment">!    the interval over which the quadrature rule was defined.</span>
    9153. 

  9153. <a name="l09089"></a>09089 <span class="comment">!</span>
    9154. 

  9154. <a name="l09090"></a>09090 <span class="comment">!    Input, double precision XTAB(NORDER), the abscissas of a quadrature</span>
    9155. 

  9155. <a name="l09091"></a>09091 <span class="comment">!    rule for the interval [XLO,XHI].</span>
    9156. 

  9156. <a name="l09092"></a>09092 <span class="comment">!</span>
    9157. 

  9157. <a name="l09093"></a>09093 <span class="comment">!    Input, double precision WEIGHT(NORDER), the weights of the quadrature rule.</span>
    9158. 

  9158. <a name="l09094"></a>09094 <span class="comment">!</span>
    9159. 

  9159. <a name="l09095"></a>09095 <span class="comment">!    Output, double precision RESULT, the approximate value of the integral.</span>
    9160. 

  9160. <a name="l09096"></a>09096 <span class="comment">!</span>
    9161. 

  9161. <a name="l09097"></a>09097   <span class="keyword">implicit none</span>
    9162. 

  9162. <a name="l09098"></a>09098 <span class="comment">!</span>
    9163. 

  9163. <a name="l09099"></a>09099   <span class="keywordtype">integer</span> norder
    9164. 

  9164. <a name="l09100"></a>09100 <span class="comment">!</span>
    9165. 

  9165. <a name="l09101"></a>09101   <span class="keywordtype">double precision</span> a
    9166. 

  9166. <a name="l09102"></a>09102   <span class="keywordtype">double precision</span> a_sub
    9167. 

  9167. <a name="l09103"></a>09103   <span class="keywordtype">double precision</span> b
    9168. 

  9168. <a name="l09104"></a>09104   <span class="keywordtype">double precision</span> b_sub
    9169. 

  9169. <a name="l09105"></a>09105   <span class="keywordtype">double precision</span>, <span class="keywordtype">external</span> :: func
    9170. 

  9170. <a name="l09106"></a>09106   <span class="keywordtype">double precision</span> h
    9171. 

  9171. <a name="l09107"></a>09107   <span class="keywordtype">integer</span> i
    9172. 

  9172. <a name="l09108"></a>09108   <span class="keywordtype">integer</span> j
    9173. 

  9173. <a name="l09109"></a>09109   <span class="keywordtype">integer</span> nsub
    9174. 

  9174. <a name="l09110"></a>09110   <span class="keywordtype">double precision</span> quad_sub
    9175. 

  9175. <a name="l09111"></a>09111   <span class="keywordtype">double precision</span> result
    9176. 

  9176. <a name="l09112"></a>09112   <span class="keywordtype">double precision</span> result_sub
    9177. 

  9177. <a name="l09113"></a>09113   <span class="keywordtype">double precision</span> x
    9178. 

  9178. <a name="l09114"></a>09114   <span class="keywordtype">double precision</span> xhi
    9179. 

  9179. <a name="l09115"></a>09115   <span class="keywordtype">double precision</span> xlo
    9180. 

  9180. <a name="l09116"></a>09116   <span class="keywordtype">double precision</span> xmid
    9181. 

  9181. <a name="l09117"></a>09117   <span class="keywordtype">double precision</span> xtab(norder)
    9182. 

  9182. <a name="l09118"></a>09118   <span class="keywordtype">double precision</span> volume
    9183. 

  9183. <a name="l09119"></a>09119   <span class="keywordtype">double precision</span> volume_sub
    9184. 

  9184. <a name="l09120"></a>09120   <span class="keywordtype">double precision</span> weight(norder)
    9185. 

  9185. <a name="l09121"></a>09121 <span class="comment">!</span>
    9186. 

  9186. <a name="l09122"></a>09122   <span class="keyword">if</span> ( a == b ) <span class="keyword">then</span>
    9187. 

  9187. <a name="l09123"></a>09123     result = 0.0D+00
    9188. 

  9188. <a name="l09124"></a>09124     return
    9189. 

  9189. <a name="l09125"></a>09125   <span class="keyword">end if</span>
    9190. 

  9190. <a name="l09126"></a>09126 
    9191. 

  9191. <a name="l09127"></a>09127   <span class="keyword">if</span> ( norder &lt; 1 ) <span class="keyword">then</span>
    9192. 

  9192. <a name="l09128"></a>09128     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    9193. 

  9193. <a name="l09129"></a>09129     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;SUM_SUB - Fatal error!&#39;</span>
    9194. 

  9194. <a name="l09130"></a>09130     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Nonpositive value of NORDER = &#39;</span>, norder
    9195. 

  9195. <a name="l09131"></a>09131     stop
    9196. 

  9196. <a name="l09132"></a>09132   <span class="keyword">end if</span>
    9197. 

  9197. <a name="l09133"></a>09133 
    9198. 

  9198. <a name="l09134"></a>09134   <span class="keyword">if</span> ( nsub &lt; 1 ) <span class="keyword">then</span>
    9199. 

  9199. <a name="l09135"></a>09135     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    9200. 

  9200. <a name="l09136"></a>09136     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;SUM_SUB - Fatal error!&#39;</span>
    9201. 

  9201. <a name="l09137"></a>09137     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  Nonpositive value of NSUB = &#39;</span>, nsub
    9202. 

  9202. <a name="l09138"></a>09138     stop
    9203. 

  9203. <a name="l09139"></a>09139   <span class="keyword">end if</span>
    9204. 

  9204. <a name="l09140"></a>09140 
    9205. 

  9205. <a name="l09141"></a>09141   <span class="keyword">if</span> ( xlo == xhi ) <span class="keyword">then</span>
    9206. 

  9206. <a name="l09142"></a>09142     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    9207. 

  9207. <a name="l09143"></a>09143     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;SUM_SUB - Fatal error!&#39;</span>
    9208. 

  9208. <a name="l09144"></a>09144     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  XLO = XHI.&#39;</span>
    9209. 

  9209. <a name="l09145"></a>09145     stop
    9210. 

  9210. <a name="l09146"></a>09146   <span class="keyword">end if</span>
    9211. 

  9211. <a name="l09147"></a>09147 
    9212. 

  9212. <a name="l09148"></a>09148   volume = 0.0D+00
    9213. 

  9213. <a name="l09149"></a>09149   result = 0.0D+00
    9214. 

  9214. <a name="l09150"></a>09150 
    9215. 

  9215. <a name="l09151"></a>09151   <span class="keyword">do</span> j = 1, nsub
    9216. 

  9216. <a name="l09152"></a>09152 
    9217. 

  9217. <a name="l09153"></a>09153     a_sub = ( dble ( nsub - j + 1 ) * a + dble ( j - 1 ) * b ) / dble ( nsub )
    9218. 

  9218. <a name="l09154"></a>09154     b_sub = ( dble ( nsub - j )     * a + dble ( j )     * b ) / dble ( nsub )
    9219. 

  9219. <a name="l09155"></a>09155 
    9220. 

  9220. <a name="l09156"></a>09156     quad_sub = 0.0D+00
    9221. 

  9221. <a name="l09157"></a>09157     <span class="keyword">do</span> i = 1, norder
    9222. 

  9222. <a name="l09158"></a>09158       x = ( ( xhi - xtab(i) ) * a_sub + ( xtab(i) - xlo ) * b_sub ) &amp;
    9223. 

  9223. <a name="l09159"></a>09159         / ( xhi - xlo )
    9224. 

  9224. <a name="l09160"></a>09160       quad_sub = quad_sub + weight(i) * func ( x )
    9225. 

  9225. <a name="l09161"></a>09161     <span class="keyword">end do</span>
    9226. 

  9226. <a name="l09162"></a>09162 
    9227. 

  9227. <a name="l09163"></a>09163     volume_sub = ( b - a ) / ( ( xhi - xlo ) * dble ( nsub ) )
    9228. 

  9228. <a name="l09164"></a>09164     result_sub = quad_sub * volume_sub
    9229. 

  9229. <a name="l09165"></a>09165 
    9230. 

  9230. <a name="l09166"></a>09166     volume = volume + volume_sub
    9231. 

  9231. <a name="l09167"></a>09167     result = result + result_sub
    9232. 

  9232. <a name="l09168"></a>09168 
    9233. 

  9233. <a name="l09169"></a>09169   <span class="keyword">end do</span>
    9234. 

  9234. <a name="l09170"></a>09170 
    9235. 

  9235. <a name="l09171"></a>09171   return
    9236. 

  9236. <a name="l09172"></a>09172 <span class="keyword">end</span>
    9237. 

  9237. <a name="l09173"></a><a class="code" href="quadrule_8f90.html#a423ae8e8d1445586d8ba40e7a7e0d5f4">09173</a> <span class="keyword">subroutine </span><a class="code" href="quadrule_8f90.html#a423ae8e8d1445586d8ba40e7a7e0d5f4">sum_sub_gk</a> ( func, a, b, nsub, norderg, weightg, resultg, norderk, &amp;
    9238. 

  9238. <a name="l09174"></a>09174   xtabk, weightk, resultk, error )
    9239. 

  9239. <a name="l09175"></a>09175 <span class="comment">!</span>
    9240. 

  9240. <a name="l09176"></a>09176 <span class="comment">!*******************************************************************************</span>
    9241. 

  9241. <a name="l09177"></a>09177 <span class="comment">!</span>
    9242. 

  9242. <a name="l09178"></a>09178 <span class="comment">!! SUM_SUB_GK carries out a composite Gauss-Kronrod rule.</span>
    9243. 

  9243. <a name="l09179"></a>09179 <span class="comment">!</span>
    9244. 

  9244. <a name="l09180"></a>09180 <span class="comment">!</span>
    9245. 

  9245. <a name="l09181"></a>09181 <span class="comment">!  Integration interval:</span>
    9246. 

  9246. <a name="l09182"></a>09182 <span class="comment">!</span>
    9247. 

  9247. <a name="l09183"></a>09183 <span class="comment">!    [ A, B ]</span>
    9248. 

  9248. <a name="l09184"></a>09184 <span class="comment">!</span>
    9249. 

  9249. <a name="l09185"></a>09185 <span class="comment">!  Integral to approximate:</span>
    9250. 

  9250. <a name="l09186"></a>09186 <span class="comment">!</span>
    9251. 

  9251. <a name="l09187"></a>09187 <span class="comment">!    Integral ( A &lt;= X &lt;= B ) F(X) dX</span>
    9252. 

  9252. <a name="l09188"></a>09188 <span class="comment">!</span>
    9253. 

  9253. <a name="l09189"></a>09189 <span class="comment">!  Approximate integral:</span>
    9254. 

  9254. <a name="l09190"></a>09190 <span class="comment">!</span>
    9255. 

  9255. <a name="l09191"></a>09191 <span class="comment">!    H = ( B - A ) / NSUB</span>
    9256. 

  9256. <a name="l09192"></a>09192 <span class="comment">!    XMID(J) = A + 0.5 * H * REAL ( 2 * J - 1 )</span>
    9257. 

  9257. <a name="l09193"></a>09193 <span class="comment">!</span>
    9258. 

  9258. <a name="l09194"></a>09194 <span class="comment">!    Sum ( 1 &lt;= J &lt;= NSUB )</span>
    9259. 

  9259. <a name="l09195"></a>09195 <span class="comment">!      Sum ( 1 &lt;= I &lt;= NORDERK )</span>
    9260. 

  9260. <a name="l09196"></a>09196 <span class="comment">!        WEIGHTK(I) * F ( XMID(J) + 0.5 * H * XTABK(I) )</span>
    9261. 

  9261. <a name="l09197"></a>09197 <span class="comment">!</span>
    9262. 

  9262. <a name="l09198"></a>09198 <span class="comment">!  Note:</span>
    9263. 

  9263. <a name="l09199"></a>09199 <span class="comment">!</span>
    9264. 

  9264. <a name="l09200"></a>09200 <span class="comment">!    The Gauss-Legendre weights should be computed by LEGCOM or LEGSET.</span>
    9265. 

  9265. <a name="l09201"></a>09201 <span class="comment">!    The Kronrod abscissas and weights should be computed by KRONSET.</span>
    9266. 

  9266. <a name="l09202"></a>09202 <span class="comment">!</span>
    9267. 

  9267. <a name="l09203"></a>09203 <span class="comment">!    The orders of the Gauss-Legendre and Kronrod rules must satisfy</span>
    9268. 

  9268. <a name="l09204"></a>09204 <span class="comment">!    NORDERK = 2 * NORDERG + 1.</span>
    9269. 

  9269. <a name="l09205"></a>09205 <span class="comment">!</span>
    9270. 

  9270. <a name="l09206"></a>09206 <span class="comment">!    The Kronrod rule uses the abscissas of the Gauss-Legendre rule,</span>
    9271. 

  9271. <a name="l09207"></a>09207 <span class="comment">!    plus more points, resulting in an efficient and higher order estimate.</span>
    9272. 

  9272. <a name="l09208"></a>09208 <span class="comment">!</span>
    9273. 

  9273. <a name="l09209"></a>09209 <span class="comment">!    The difference between the Gauss-Legendre and Kronrod estimates</span>
    9274. 

  9274. <a name="l09210"></a>09210 <span class="comment">!    is taken as an estimate of the error in the approximation to the</span>
    9275. 

  9275. <a name="l09211"></a>09211 <span class="comment">!    integral.</span>
    9276. 

  9276. <a name="l09212"></a>09212 <span class="comment">!</span>
    9277. 

  9277. <a name="l09213"></a>09213 <span class="comment">!  Modified:</span>
    9278. 

  9278. <a name="l09214"></a>09214 <span class="comment">!</span>
    9279. 

  9279. <a name="l09215"></a>09215 <span class="comment">!    15 September 1998</span>
    9280. 

  9280. <a name="l09216"></a>09216 <span class="comment">!</span>
    9281. 

  9281. <a name="l09217"></a>09217 <span class="comment">!  Author:</span>
    9282. 

  9282. <a name="l09218"></a>09218 <span class="comment">!</span>
    9283. 

  9283. <a name="l09219"></a>09219 <span class="comment">!    John Burkardt</span>
    9284. 

  9284. <a name="l09220"></a>09220 <span class="comment">!</span>
    9285. 

  9285. <a name="l09221"></a>09221 <span class="comment">!  Parameters:</span>
    9286. 

  9286. <a name="l09222"></a>09222 <span class="comment">!</span>
    9287. 

  9287. <a name="l09223"></a>09223 <span class="comment">!    Input, external FUNC, the name of the FORTRAN function which</span>
    9288. 

  9288. <a name="l09224"></a>09224 <span class="comment">!    evaluates the integrand.  The function must have the form</span>
    9289. 

  9289. <a name="l09225"></a>09225 <span class="comment">!      double precision func ( x ).</span>
    9290. 

  9290. <a name="l09226"></a>09226 <span class="comment">!</span>
    9291. 

  9291. <a name="l09227"></a>09227 <span class="comment">!    Input, double precision A, B, the lower and upper limits of integration.</span>
    9292. 

  9292. <a name="l09228"></a>09228 <span class="comment">!</span>
    9293. 

  9293. <a name="l09229"></a>09229 <span class="comment">!    Input, integer NSUB, the number of equal subintervals into</span>
    9294. 

  9294. <a name="l09230"></a>09230 <span class="comment">!    which the finite interval (A,B) is to be subdivided for</span>
    9295. 

  9295. <a name="l09231"></a>09231 <span class="comment">!    higher accuracy.  NSUB must be at least 1.</span>
    9296. 

  9296. <a name="l09232"></a>09232 <span class="comment">!</span>
    9297. 

  9297. <a name="l09233"></a>09233 <span class="comment">!    Input, integer NORDERG, the order of the Gauss-Legendre rule.</span>
    9298. 

  9298. <a name="l09234"></a>09234 <span class="comment">!    NORDERG must be at least 1.</span>
    9299. 

  9299. <a name="l09235"></a>09235 <span class="comment">!</span>
    9300. 

  9300. <a name="l09236"></a>09236 <span class="comment">!    Input, double precision WEIGHTG(NORDERG), the weights of the</span>
    9301. 

  9301. <a name="l09237"></a>09237 <span class="comment">!    Gauss-Legendre rule.</span>
    9302. 

  9302. <a name="l09238"></a>09238 <span class="comment">!</span>
    9303. 

  9303. <a name="l09239"></a>09239 <span class="comment">!    Output, double precision RESULTG, the approximate value of the</span>
    9304. 

  9304. <a name="l09240"></a>09240 <span class="comment">!    integral based on the Gauss-Legendre rule.</span>
    9305. 

  9305. <a name="l09241"></a>09241 <span class="comment">!</span>
    9306. 

  9306. <a name="l09242"></a>09242 <span class="comment">!    Input, integer NORDERK, the order of the Kronrod rule.</span>
    9307. 

  9307. <a name="l09243"></a>09243 <span class="comment">!    NORDERK must be at least 1.</span>
    9308. 

  9308. <a name="l09244"></a>09244 <span class="comment">!</span>
    9309. 

  9309. <a name="l09245"></a>09245 <span class="comment">!    Input, double precision XTABK(NORDERK), the abscissas of the</span>
    9310. 

  9310. <a name="l09246"></a>09246 <span class="comment">!    Kronrod rule.</span>
    9311. 

  9311. <a name="l09247"></a>09247 <span class="comment">!</span>
    9312. 

  9312. <a name="l09248"></a>09248 <span class="comment">!    Input, double precision WEIGHTK(NORDERK), the weights of the</span>
    9313. 

  9313. <a name="l09249"></a>09249 <span class="comment">!    Kronrod rule.</span>
    9314. 

  9314. <a name="l09250"></a>09250 <span class="comment">!</span>
    9315. 

  9315. <a name="l09251"></a>09251 <span class="comment">!    Output, double precision RESULTK, the approximate value of the</span>
    9316. 

  9316. <a name="l09252"></a>09252 <span class="comment">!    integral based on the Kronrod rule.</span>
    9317. 

  9317. <a name="l09253"></a>09253 <span class="comment">!</span>
    9318. 

  9318. <a name="l09254"></a>09254 <span class="comment">!    Output, double precision ERROR, an estimate of the approximation</span>
    9319. 

  9319. <a name="l09255"></a>09255 <span class="comment">!    error.  This is computed by taking the sum of the absolute values of</span>
    9320. 

  9320. <a name="l09256"></a>09256 <span class="comment">!    the differences between the Gauss-Legendre and Kronrod rules</span>
    9321. 

  9321. <a name="l09257"></a>09257 <span class="comment">!    over each subinterval.  This is usually a good estimate of</span>
    9322. 

  9322. <a name="l09258"></a>09258 <span class="comment">!    the error in the value RESULTG.  The error in the Kronrod</span>
    9323. 

  9323. <a name="l09259"></a>09259 <span class="comment">!    estimate RESULTK is usually much smaller.</span>
    9324. 

  9324. <a name="l09260"></a>09260 <span class="comment">!</span>
    9325. 

  9325. <a name="l09261"></a>09261   <span class="keyword">implicit none</span>
    9326. 

  9326. <a name="l09262"></a>09262 <span class="comment">!</span>
    9327. 

  9327. <a name="l09263"></a>09263   <span class="keywordtype">integer</span> norderg
    9328. 

  9328. <a name="l09264"></a>09264   <span class="keywordtype">integer</span> norderk
    9329. 

  9329. <a name="l09265"></a>09265 <span class="comment">!</span>
    9330. 

  9330. <a name="l09266"></a>09266   <span class="keywordtype">double precision</span> a
    9331. 

  9331. <a name="l09267"></a>09267   <span class="keywordtype">double precision</span> b
    9332. 

  9332. <a name="l09268"></a>09268   <span class="keywordtype">double precision</span> error
    9333. 

  9333. <a name="l09269"></a>09269   <span class="keywordtype">double precision</span> fk
    9334. 

  9334. <a name="l09270"></a>09270   <span class="keywordtype">double precision</span>, <span class="keywordtype">external</span> :: func
    9335. 

  9335. <a name="l09271"></a>09271   <span class="keywordtype">double precision</span> h
    9336. 

  9336. <a name="l09272"></a>09272   <span class="keywordtype">integer</span> i
    9337. 

  9337. <a name="l09273"></a>09273   <span class="keywordtype">integer</span> j
    9338. 

  9338. <a name="l09274"></a>09274   <span class="keywordtype">integer</span> nsub
    9339. 

  9339. <a name="l09275"></a>09275   <span class="keywordtype">double precision</span> partg
    9340. 

  9340. <a name="l09276"></a>09276   <span class="keywordtype">double precision</span> partk
    9341. 

  9341. <a name="l09277"></a>09277   <span class="keywordtype">double precision</span> resultg
    9342. 

  9342. <a name="l09278"></a>09278   <span class="keywordtype">double precision</span> resultk
    9343. 

  9343. <a name="l09279"></a>09279   <span class="keywordtype">double precision</span> x
    9344. 

  9344. <a name="l09280"></a>09280   <span class="keywordtype">double precision</span> xmid
    9345. 

  9345. <a name="l09281"></a>09281   <span class="keywordtype">double precision</span> xtabk(norderk)
    9346. 

  9346. <a name="l09282"></a>09282   <span class="keywordtype">double precision</span> weightg(norderg)
    9347. 

  9347. <a name="l09283"></a>09283   <span class="keywordtype">double precision</span> weightk(norderk)
    9348. 

  9348. <a name="l09284"></a>09284 <span class="comment">!</span>
    9349. 

  9349. <a name="l09285"></a>09285   resultg = 0.0D+00
    9350. 

  9350. <a name="l09286"></a>09286   resultk = 0.0D+00
    9351. 

  9351. <a name="l09287"></a>09287   error = 0
    9352. 

  9352. <a name="l09288"></a>09288 
    9353. 

  9353. <a name="l09289"></a>09289   <span class="keyword">if</span> ( a == b ) <span class="keyword">then</span>
    9354. 

  9354. <a name="l09290"></a>09290     return
    9355. 

  9355. <a name="l09291"></a>09291   <span class="keyword">end if</span>
    9356. 

  9356. <a name="l09292"></a>09292 
    9357. 

  9357. <a name="l09293"></a>09293   <span class="keyword">if</span> ( norderk /= 2 * norderg + 1 ) <span class="keyword">then</span>
    9358. 

  9358. <a name="l09294"></a>09294     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39; &#39;</span>
    9359. 

  9359. <a name="l09295"></a>09295     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;SUM_SUB_GK - Fatal error!&#39;</span>
    9360. 

  9360. <a name="l09296"></a>09296     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a)&#39;</span> ) <span class="stringliteral">&#39;  NORDERK must equal 2 * NORDERG + 1.&#39;</span>
    9361. 

  9361. <a name="l09297"></a>09297     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  The input value was NORDERG = &#39;</span>, norderg
    9362. 

  9362. <a name="l09298"></a>09298     <span class="keyword">write</span> ( *, <span class="stringliteral">&#39;(a,i6)&#39;</span> ) <span class="stringliteral">&#39;  The input value was NORDERK = &#39;</span>, norderk
    9363. 

  9363. <a name="l09299"></a>09299     stop
    9364. 

  9364. <a name="l09300"></a>09300   <span class="keyword">end if</span>
    9365. 

  9365. <a name="l09301"></a>09301 
    9366. 

  9366. <a name="l09302"></a>09302   h = ( b - a ) / dble ( nsub )
    9367. 

  9367. <a name="l09303"></a>09303 
    9368. 

  9368. <a name="l09304"></a>09304   <span class="keyword">do</span> j = 1, nsub
    9369. 

  9369. <a name="l09305"></a>09305 
    9370. 

  9370. <a name="l09306"></a>09306     xmid = a + 0.5D0 * h * dble ( 2 * j - 1 )
    9371. 

  9371. <a name="l09307"></a>09307 
    9372. 

  9372. <a name="l09308"></a>09308     partg = 0.0D+00
    9373. 

  9373. <a name="l09309"></a>09309     partk = 0.0D+00
    9374. 

  9374. <a name="l09310"></a>09310 
    9375. 

  9375. <a name="l09311"></a>09311     <span class="keyword">do</span> i = 1, norderk
    9376. 

  9376. <a name="l09312"></a>09312 
    9377. 

  9377. <a name="l09313"></a>09313       x = xmid + 0.5D0 * h * xtabk(i)
    9378. 

  9378. <a name="l09314"></a>09314       fk = func ( x )
    9379. 

  9379. <a name="l09315"></a>09315       partk = partk + 0.5D0 * h * weightk(i) * fk
    9380. 

  9380. <a name="l09316"></a>09316 
    9381. 

  9381. <a name="l09317"></a>09317       <span class="keyword">if</span> ( mod ( i, 2 ) == 0 ) <span class="keyword">then</span>
    9382. 

  9382. <a name="l09318"></a>09318         partg = partg + 0.5D0 * h * weightg(i/2) * fk
    9383. 

  9383. <a name="l09319"></a>09319       <span class="keyword">end if</span>
    9384. 

  9384. <a name="l09320"></a>09320 
    9385. 

  9385. <a name="l09321"></a>09321     <span class="keyword">end do</span>
    9386. 

  9386. <a name="l09322"></a>09322 
    9387. 

  9387. <a name="l09323"></a>09323     resultg = resultg + partg
    9388. 

  9388. <a name="l09324"></a>09324     resultk = resultk + partk
    9389. 

  9389. <a name="l09325"></a>09325     error = error + abs ( partk - partg )
    9390. 

  9390. <a name="l09326"></a>09326 
    9391. 

  9391. <a name="l09327"></a>09327   <span class="keyword">end do</span>
    9392. 

  9392. <a name="l09328"></a>09328 
    9393. 

  9393. <a name="l09329"></a>09329   return
    9394. 

  9394. <a name="l09330"></a>09330 <span class="keyword">end</span>
    9395. 

  9395. </pre></div></div>
    9396. 

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    9397. 

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    9399. 

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    9402. 

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    9412. 

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