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- <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 )
- <a name="l00002"></a>00002 <span class="comment">!</span>
- <a name="l00003"></a>00003 <span class="comment">!*******************************************************************************</span>
- <a name="l00004"></a>00004 <span class="comment">!</span>
- <a name="l00005"></a>00005 <span class="comment">!! BASHFORTH_SET sets abscissas and weights for Adams-Bashforth quadrature.</span>
- <a name="l00006"></a>00006 <span class="comment">!</span>
- <a name="l00007"></a>00007 <span class="comment">!</span>
- <a name="l00008"></a>00008 <span class="comment">! Definition:</span>
- <a name="l00009"></a>00009 <span class="comment">!</span>
- <a name="l00010"></a>00010 <span class="comment">! Adams-Bashforth quadrature formulas are normally used in solving</span>
- <a name="l00011"></a>00011 <span class="comment">! ordinary differential equations, and are not really suitable for</span>
- <a name="l00012"></a>00012 <span class="comment">! general quadrature computations. However, an Adams-Bashforth formula</span>
- <a name="l00013"></a>00013 <span class="comment">! is equivalent to approximating the integral of F(Y(X)) between X(M)</span>
- <a name="l00014"></a>00014 <span class="comment">! and X(M+1), using an explicit formula that relies only on known values</span>
- <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>
- <a name="l00016"></a>00016 <span class="comment">! have been included here.</span>
- <a name="l00017"></a>00017 <span class="comment">!</span>
- <a name="l00018"></a>00018 <span class="comment">! Suppose the unknown function is denoted by Y(X), with derivative</span>
- <a name="l00019"></a>00019 <span class="comment">! F(Y(X)), and that approximate values of the function are known at a</span>
- <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>
- <a name="l00021"></a>00021 <span class="comment">! the value Y(X(1)) as Y(1) and so on.</span>
- <a name="l00022"></a>00022 <span class="comment">!</span>
- <a name="l00023"></a>00023 <span class="comment">! Then the solution of the ODE Y'=F(X,Y) at the next point X(M+1) is</span>
- <a name="l00024"></a>00024 <span class="comment">! computed by:</span>
- <a name="l00025"></a>00025 <span class="comment">!</span>
- <a name="l00026"></a>00026 <span class="comment">! Y(M+1) = Y(M) + Integral ( X(M) < X < X(M+1) ) F(Y(X)) dX</span>
- <a name="l00027"></a>00027 <span class="comment">! = Y(M) + H * Sum ( 1 <= I <= N ) W(I) * F(Y(M+1-I)) approximately.</span>
- <a name="l00028"></a>00028 <span class="comment">!</span>
- <a name="l00029"></a>00029 <span class="comment">! In the documentation that follows, we replace F(Y(X)) by F(X).</span>
- <a name="l00030"></a>00030 <span class="comment">!</span>
- <a name="l00031"></a>00031 <span class="comment">! Integration interval:</span>
- <a name="l00032"></a>00032 <span class="comment">!</span>
- <a name="l00033"></a>00033 <span class="comment">! [ 0, 1 ].</span>
- <a name="l00034"></a>00034 <span class="comment">!</span>
- <a name="l00035"></a>00035 <span class="comment">! Weight function:</span>
- <a name="l00036"></a>00036 <span class="comment">!</span>
- <a name="l00037"></a>00037 <span class="comment">! 1.0D+00</span>
- <a name="l00038"></a>00038 <span class="comment">!</span>
- <a name="l00039"></a>00039 <span class="comment">! Integral to approximate:</span>
- <a name="l00040"></a>00040 <span class="comment">!</span>
- <a name="l00041"></a>00041 <span class="comment">! Integral ( 0 <= X <= 1 ) F(X) dX.</span>
- <a name="l00042"></a>00042 <span class="comment">!</span>
- <a name="l00043"></a>00043 <span class="comment">! Approximate integral:</span>
- <a name="l00044"></a>00044 <span class="comment">!</span>
- <a name="l00045"></a>00045 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( 1 - I ),</span>
- <a name="l00046"></a>00046 <span class="comment">!</span>
- <a name="l00047"></a>00047 <span class="comment">! Note:</span>
- <a name="l00048"></a>00048 <span class="comment">!</span>
- <a name="l00049"></a>00049 <span class="comment">! The Adams-Bashforth formulas require equally spaced data.</span>
- <a name="l00050"></a>00050 <span class="comment">!</span>
- <a name="l00051"></a>00051 <span class="comment">! Here is how the formula is applied in the case with non-unit spacing:</span>
- <a name="l00052"></a>00052 <span class="comment">!</span>
- <a name="l00053"></a>00053 <span class="comment">! Integral ( A <= X <= A+H ) F(X) dX =</span>
- <a name="l00054"></a>00054 <span class="comment">! H * Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( A - (I-1)*H ),</span>
- <a name="l00055"></a>00055 <span class="comment">! approximately.</span>
- <a name="l00056"></a>00056 <span class="comment">!</span>
- <a name="l00057"></a>00057 <span class="comment">! The reference lists the second coefficient of the order 8 Adams-Bashforth</span>
- <a name="l00058"></a>00058 <span class="comment">! formula as</span>
- <a name="l00059"></a>00059 <span class="comment">! weight(2) = -1162169.0D+00 / 120960.0D+00</span>
- <a name="l00060"></a>00060 <span class="comment">! but this should be</span>
- <a name="l00061"></a>00061 <span class="comment">! weight(2) = -1152169.0D+00 / 120960.0D+00</span>
- <a name="l00062"></a>00062 <span class="comment">!</span>
- <a name="l00063"></a>00063 <span class="comment">! Reference:</span>
- <a name="l00064"></a>00064 <span class="comment">!</span>
- <a name="l00065"></a>00065 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l00066"></a>00066 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l00067"></a>00067 <span class="comment">! National Bureau of Standards, 1964.</span>
- <a name="l00068"></a>00068 <span class="comment">!</span>
- <a name="l00069"></a>00069 <span class="comment">! Jean Lapidus and John Seinfeld,</span>
- <a name="l00070"></a>00070 <span class="comment">! Numerical Solution of Ordinary Differential Equations,</span>
- <a name="l00071"></a>00071 <span class="comment">! Academic Press, 1971.</span>
- <a name="l00072"></a>00072 <span class="comment">!</span>
- <a name="l00073"></a>00073 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l00074"></a>00074 <span class="comment">! Standard Mathematical Tables and Formulae,</span>
- <a name="l00075"></a>00075 <span class="comment">! 30th Edition,</span>
- <a name="l00076"></a>00076 <span class="comment">! CRC Press, 1996.</span>
- <a name="l00077"></a>00077 <span class="comment">!</span>
- <a name="l00078"></a>00078 <span class="comment">! Modified:</span>
- <a name="l00079"></a>00079 <span class="comment">!</span>
- <a name="l00080"></a>00080 <span class="comment">! 15 September 1998</span>
- <a name="l00081"></a>00081 <span class="comment">!</span>
- <a name="l00082"></a>00082 <span class="comment">! Author:</span>
- <a name="l00083"></a>00083 <span class="comment">!</span>
- <a name="l00084"></a>00084 <span class="comment">! John Burkardt</span>
- <a name="l00085"></a>00085 <span class="comment">!</span>
- <a name="l00086"></a>00086 <span class="comment">! Parameters:</span>
- <a name="l00087"></a>00087 <span class="comment">!</span>
- <a name="l00088"></a>00088 <span class="comment">! Input, integer NORDER, the order of the rule. NORDER should be</span>
- <a name="l00089"></a>00089 <span class="comment">! between 1 and 8.</span>
- <a name="l00090"></a>00090 <span class="comment">!</span>
- <a name="l00091"></a>00091 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l00092"></a>00092 <span class="comment">!</span>
- <a name="l00093"></a>00093 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l00094"></a>00094 <span class="comment">! WEIGHT(1) is the weight at X = 0, WEIGHT(2) the weight at X = -1,</span>
- <a name="l00095"></a>00095 <span class="comment">! and so on. The weights are rational, and should sum to 1. Some</span>
- <a name="l00096"></a>00096 <span class="comment">! weights may be negative.</span>
- <a name="l00097"></a>00097 <span class="comment">!</span>
- <a name="l00098"></a>00098 <span class="keyword">implicit none</span>
- <a name="l00099"></a>00099 <span class="comment">!</span>
- <a name="l00100"></a>00100 <span class="keywordtype">integer</span> norder
- <a name="l00101"></a>00101 <span class="comment">!</span>
- <a name="l00102"></a>00102 <span class="keywordtype">double precision</span> d
- <a name="l00103"></a>00103 <span class="keywordtype">integer</span> i
- <a name="l00104"></a>00104 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l00105"></a>00105 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l00106"></a>00106 <span class="comment">!</span>
- <a name="l00107"></a>00107 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l00108"></a>00108
- <a name="l00109"></a>00109 weight(1) = 1.0D+00
- <a name="l00110"></a>00110
- <a name="l00111"></a>00111 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l00112"></a>00112
- <a name="l00113"></a>00113 d = 2.0D+00
- <a name="l00114"></a>00114
- <a name="l00115"></a>00115 weight(1) = 3.0D+00 / d
- <a name="l00116"></a>00116 weight(2) = - 1.0D+00 / d
- <a name="l00117"></a>00117
- <a name="l00118"></a>00118 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l00119"></a>00119
- <a name="l00120"></a>00120 d = 12.0D+00
- <a name="l00121"></a>00121
- <a name="l00122"></a>00122 weight(1) = 23.0D+00 / d
- <a name="l00123"></a>00123 weight(2) = - 16.0D+00 / d
- <a name="l00124"></a>00124 weight(3) = 5.0D+00 / d
- <a name="l00125"></a>00125
- <a name="l00126"></a>00126 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l00127"></a>00127
- <a name="l00128"></a>00128 d = 24.0D+00
- <a name="l00129"></a>00129
- <a name="l00130"></a>00130 weight(1) = 55.0D+00 / d
- <a name="l00131"></a>00131 weight(2) = - 59.0D+00 / d
- <a name="l00132"></a>00132 weight(3) = 37.0D+00 / d
- <a name="l00133"></a>00133 weight(4) = - 9.0D+00 / d
- <a name="l00134"></a>00134
- <a name="l00135"></a>00135 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l00136"></a>00136
- <a name="l00137"></a>00137 d = 720.0D+00
- <a name="l00138"></a>00138
- <a name="l00139"></a>00139 weight(1) = 1901.0D+00 / d
- <a name="l00140"></a>00140 weight(2) = - 2774.0D+00 / d
- <a name="l00141"></a>00141 weight(3) = 2616.0D+00 / d
- <a name="l00142"></a>00142 weight(4) = - 1274.0D+00 / d
- <a name="l00143"></a>00143 weight(5) = 251.0D+00 / d
- <a name="l00144"></a>00144
- <a name="l00145"></a>00145 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l00146"></a>00146
- <a name="l00147"></a>00147 d = 1440.0D+00
- <a name="l00148"></a>00148
- <a name="l00149"></a>00149 weight(1) = 4277.0D+00 / d
- <a name="l00150"></a>00150 weight(2) = - 7923.0D+00 / d
- <a name="l00151"></a>00151 weight(3) = 9982.0D+00 / d
- <a name="l00152"></a>00152 weight(4) = - 7298.0D+00 / d
- <a name="l00153"></a>00153 weight(5) = 2877.0D+00 / d
- <a name="l00154"></a>00154 weight(6) = - 475.0D+00 / d
- <a name="l00155"></a>00155
- <a name="l00156"></a>00156 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l00157"></a>00157
- <a name="l00158"></a>00158 d = 60480.0D+00
- <a name="l00159"></a>00159
- <a name="l00160"></a>00160 weight(1) = 198721.0D+00 / d
- <a name="l00161"></a>00161 weight(2) = - 447288.0D+00 / d
- <a name="l00162"></a>00162 weight(3) = 705549.0D+00 / d
- <a name="l00163"></a>00163 weight(4) = - 688256.0D+00 / d
- <a name="l00164"></a>00164 weight(5) = 407139.0D+00 / d
- <a name="l00165"></a>00165 weight(6) = - 134472.0D+00 / d
- <a name="l00166"></a>00166 weight(7) = 19087.0D+00 / d
- <a name="l00167"></a>00167
- <a name="l00168"></a>00168 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l00169"></a>00169
- <a name="l00170"></a>00170 d = 120960.0D+00
- <a name="l00171"></a>00171
- <a name="l00172"></a>00172 weight(1) = 434241.0D+00 / d
- <a name="l00173"></a>00173 weight(2) = - 1152169.0D+00 / d
- <a name="l00174"></a>00174 weight(3) = 2183877.0D+00 / d
- <a name="l00175"></a>00175 weight(4) = - 2664477.0D+00 / d
- <a name="l00176"></a>00176 weight(5) = 2102243.0D+00 / d
- <a name="l00177"></a>00177 weight(6) = - 1041723.0D+00 / d
- <a name="l00178"></a>00178 weight(7) = 295767.0D+00 / d
- <a name="l00179"></a>00179 weight(8) = - 36799.0D+00 / d
- <a name="l00180"></a>00180
- <a name="l00181"></a>00181 <span class="keyword">else</span>
- <a name="l00182"></a>00182
- <a name="l00183"></a>00183 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l00184"></a>00184 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'BASHFORTH_SET - Fatal error!'</span>
- <a name="l00185"></a>00185 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l00186"></a>00186 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' Legal values are 1 through 8.'</span>
- <a name="l00187"></a>00187 stop
- <a name="l00188"></a>00188
- <a name="l00189"></a>00189 <span class="keyword">end if</span>
- <a name="l00190"></a>00190
- <a name="l00191"></a>00191 <span class="keyword">do</span> i = 1, norder
- <a name="l00192"></a>00192 xtab(i) = dble ( 1 - i )
- <a name="l00193"></a>00193 <span class="keyword">end do</span>
- <a name="l00194"></a>00194
- <a name="l00195"></a>00195 return
- <a name="l00196"></a>00196 <span class="keyword">end</span>
- <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 )
- <a name="l00198"></a>00198 <span class="comment">!</span>
- <a name="l00199"></a>00199 <span class="comment">!*******************************************************************************</span>
- <a name="l00200"></a>00200 <span class="comment">!</span>
- <a name="l00201"></a>00201 <span class="comment">!! BDF_SET sets weights for backward differentiation ODE weights.</span>
- <a name="l00202"></a>00202 <span class="comment">!</span>
- <a name="l00203"></a>00203 <span class="comment">!</span>
- <a name="l00204"></a>00204 <span class="comment">! Discussion:</span>
- <a name="l00205"></a>00205 <span class="comment">!</span>
- <a name="l00206"></a>00206 <span class="comment">! GAMMA * Y(N+1) = Sum ( 1 <= I <= NORDER ) ALPHA(I) * Y(N+1-I)</span>
- <a name="l00207"></a>00207 <span class="comment">! + dX * BETA * Y'(X(N+1),Y(N+1))</span>
- <a name="l00208"></a>00208 <span class="comment">!</span>
- <a name="l00209"></a>00209 <span class="comment">! This is equivalent to the backward differentiation corrector formulas.</span>
- <a name="l00210"></a>00210 <span class="comment">!</span>
- <a name="l00211"></a>00211 <span class="comment">! Modified:</span>
- <a name="l00212"></a>00212 <span class="comment">!</span>
- <a name="l00213"></a>00213 <span class="comment">! 30 December 1999</span>
- <a name="l00214"></a>00214 <span class="comment">!</span>
- <a name="l00215"></a>00215 <span class="comment">! Author:</span>
- <a name="l00216"></a>00216 <span class="comment">!</span>
- <a name="l00217"></a>00217 <span class="comment">! John Burkardt</span>
- <a name="l00218"></a>00218 <span class="comment">!</span>
- <a name="l00219"></a>00219 <span class="comment">! Parameters:</span>
- <a name="l00220"></a>00220 <span class="comment">!</span>
- <a name="l00221"></a>00221 <span class="comment">! Input, integer NORDER, the order of the rule, between 1 and 6.</span>
- <a name="l00222"></a>00222 <span class="comment">!</span>
- <a name="l00223"></a>00223 <span class="comment">! Output, double precision ALPHA(NORDER), BETA, GAMMA, the weights.</span>
- <a name="l00224"></a>00224 <span class="comment">!</span>
- <a name="l00225"></a>00225 <span class="keyword">implicit none</span>
- <a name="l00226"></a>00226 <span class="comment">!</span>
- <a name="l00227"></a>00227 <span class="keywordtype">integer</span> norder
- <a name="l00228"></a>00228 <span class="comment">!</span>
- <a name="l00229"></a>00229 <span class="keywordtype">double precision</span> alpha(norder)
- <a name="l00230"></a>00230 <span class="keywordtype">double precision</span> beta
- <a name="l00231"></a>00231 <span class="keywordtype">double precision</span> gamma
- <a name="l00232"></a>00232 <span class="comment">!</span>
- <a name="l00233"></a>00233 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l00234"></a>00234 beta = 1.0D+00
- <a name="l00235"></a>00235 gamma = 1.0D+00
- <a name="l00236"></a>00236 alpha(1) = 1.0D+00
- <a name="l00237"></a>00237 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l00238"></a>00238 beta = 2.0D+00
- <a name="l00239"></a>00239 gamma = 3.0D+00
- <a name="l00240"></a>00240 alpha(1) = 4.0D+00
- <a name="l00241"></a>00241 alpha(2) = - 1.0D+00
- <a name="l00242"></a>00242 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l00243"></a>00243 beta = 6.0D+00
- <a name="l00244"></a>00244 gamma = 11.0D+00
- <a name="l00245"></a>00245 alpha(1) = 18.0D+00
- <a name="l00246"></a>00246 alpha(2) = - 9.0D+00
- <a name="l00247"></a>00247 alpha(3) = 2.0D+00
- <a name="l00248"></a>00248 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l00249"></a>00249 beta = 12.0D+00
- <a name="l00250"></a>00250 gamma = 25.0D+00
- <a name="l00251"></a>00251 alpha(1) = 48.0D+00
- <a name="l00252"></a>00252 alpha(2) = - 36.0D+00
- <a name="l00253"></a>00253 alpha(3) = 16.0D+00
- <a name="l00254"></a>00254 alpha(4) = - 3.0D+00
- <a name="l00255"></a>00255 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l00256"></a>00256 beta = 60.0D+00
- <a name="l00257"></a>00257 gamma = 137.0D+00
- <a name="l00258"></a>00258 alpha(1) = 300.0D+00
- <a name="l00259"></a>00259 alpha(2) = - 300.0D+00
- <a name="l00260"></a>00260 alpha(3) = 200.0D+00
- <a name="l00261"></a>00261 alpha(4) = - 75.0D+00
- <a name="l00262"></a>00262 alpha(5) = 12.0D+00
- <a name="l00263"></a>00263 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l00264"></a>00264 beta = 60.0D+00
- <a name="l00265"></a>00265 gamma = 147.0D+00
- <a name="l00266"></a>00266 alpha(1) = 360.0D+00
- <a name="l00267"></a>00267 alpha(2) = - 450.0D+00
- <a name="l00268"></a>00268 alpha(3) = 400.0D+00
- <a name="l00269"></a>00269 alpha(4) = - 225.0D+00
- <a name="l00270"></a>00270 alpha(5) = 72.0D+00
- <a name="l00271"></a>00271 alpha(6) = - 10.0D+00
- <a name="l00272"></a>00272 <span class="keyword">else</span>
- <a name="l00273"></a>00273 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l00274"></a>00274 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'BDF_SET - Fatal error!'</span>
- <a name="l00275"></a>00275 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal order requested = '</span>, norder
- <a name="l00276"></a>00276 stop
- <a name="l00277"></a>00277 <span class="keyword">end if</span>
- <a name="l00278"></a>00278
- <a name="l00279"></a>00279 return
- <a name="l00280"></a>00280 <span class="keyword">end</span>
- <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 )
- <a name="l00282"></a>00282 <span class="comment">!</span>
- <a name="l00283"></a>00283 <span class="comment">!*******************************************************************************</span>
- <a name="l00284"></a>00284 <span class="comment">!</span>
- <a name="l00285"></a>00285 <span class="comment">!! BDFC_SET sets weights for backward differentiation corrector quadrature.</span>
- <a name="l00286"></a>00286 <span class="comment">!</span>
- <a name="l00287"></a>00287 <span class="comment">!</span>
- <a name="l00288"></a>00288 <span class="comment">! Definition:</span>
- <a name="l00289"></a>00289 <span class="comment">!</span>
- <a name="l00290"></a>00290 <span class="comment">! A backward differentiation corrector formula is defined for a set</span>
- <a name="l00291"></a>00291 <span class="comment">! of evenly spaced abscissas X(I) with X(1) = 1 and X(2) = 0. Assuming</span>
- <a name="l00292"></a>00292 <span class="comment">! that the values of the function to be integrated are known at the</span>
- <a name="l00293"></a>00293 <span class="comment">! abscissas, the formula is written in terms of the function value at</span>
- <a name="l00294"></a>00294 <span class="comment">! X(1), and the backward differences at X(1) that approximate the</span>
- <a name="l00295"></a>00295 <span class="comment">! derivatives there.</span>
- <a name="l00296"></a>00296 <span class="comment">!</span>
- <a name="l00297"></a>00297 <span class="comment">! Integration interval:</span>
- <a name="l00298"></a>00298 <span class="comment">!</span>
- <a name="l00299"></a>00299 <span class="comment">! [ 0, 1 ]</span>
- <a name="l00300"></a>00300 <span class="comment">!</span>
- <a name="l00301"></a>00301 <span class="comment">! Weight function:</span>
- <a name="l00302"></a>00302 <span class="comment">!</span>
- <a name="l00303"></a>00303 <span class="comment">! 1.0D+00</span>
- <a name="l00304"></a>00304 <span class="comment">!</span>
- <a name="l00305"></a>00305 <span class="comment">! Integral to approximate:</span>
- <a name="l00306"></a>00306 <span class="comment">!</span>
- <a name="l00307"></a>00307 <span class="comment">! Integral ( 0 <= X <= 1 ) F(X) dX</span>
- <a name="l00308"></a>00308 <span class="comment">!</span>
- <a name="l00309"></a>00309 <span class="comment">! Approximate integral:</span>
- <a name="l00310"></a>00310 <span class="comment">!</span>
- <a name="l00311"></a>00311 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * BD**(I-1) F ( 1 ).</span>
- <a name="l00312"></a>00312 <span class="comment">!</span>
- <a name="l00313"></a>00313 <span class="comment">! Here, "BD**(I-1) F ( 1 )" denotes the (I-1)st backward difference</span>
- <a name="l00314"></a>00314 <span class="comment">! of F at X = 1, using a spacing of 1. In particular,</span>
- <a name="l00315"></a>00315 <span class="comment">!</span>
- <a name="l00316"></a>00316 <span class="comment">! BD**0 F(1) = F(1)</span>
- <a name="l00317"></a>00317 <span class="comment">! BD**1 F(1) = F(1) - F(0)</span>
- <a name="l00318"></a>00318 <span class="comment">! BD**2 F(1) = F(1) - 2 * F(0) + F(-1 )</span>
- <a name="l00319"></a>00319 <span class="comment">!</span>
- <a name="l00320"></a>00320 <span class="comment">! Note:</span>
- <a name="l00321"></a>00321 <span class="comment">!</span>
- <a name="l00322"></a>00322 <span class="comment">! The relationship between a backward difference corrector and the</span>
- <a name="l00323"></a>00323 <span class="comment">! corresponding Adams-Moulton formula may be illustrated for the</span>
- <a name="l00324"></a>00324 <span class="comment">! BDF corrector of order 4:</span>
- <a name="l00325"></a>00325 <span class="comment">!</span>
- <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>
- <a name="l00327"></a>00327 <span class="comment">! = F(1)</span>
- <a name="l00328"></a>00328 <span class="comment">! - 1/2 * ( F(1) - F(0) )</span>
- <a name="l00329"></a>00329 <span class="comment">! - 1/12 * ( F(1) - 2 * F(0) + F(-1) )</span>
- <a name="l00330"></a>00330 <span class="comment">! - 1/24 * ( F(1) - 3 * F(0) + 3 * F(-1) - F(-2) )</span>
- <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>
- <a name="l00332"></a>00332 <span class="comment">!</span>
- <a name="l00333"></a>00333 <span class="comment">! which is the Adams-Moulton formula of order 4.</span>
- <a name="l00334"></a>00334 <span class="comment">! </span>
- <a name="l00335"></a>00335 <span class="comment">! Reference:</span>
- <a name="l00336"></a>00336 <span class="comment">!</span>
- <a name="l00337"></a>00337 <span class="comment">! Simeon Fatunla,</span>
- <a name="l00338"></a>00338 <span class="comment">! Numerical Methods for Initial Value Problems in Ordinary Differential</span>
- <a name="l00339"></a>00339 <span class="comment">! Equations,</span>
- <a name="l00340"></a>00340 <span class="comment">! Academic Press, 1988.</span>
- <a name="l00341"></a>00341 <span class="comment">!</span>
- <a name="l00342"></a>00342 <span class="comment">! Modified:</span>
- <a name="l00343"></a>00343 <span class="comment">!</span>
- <a name="l00344"></a>00344 <span class="comment">! 28 February 2000</span>
- <a name="l00345"></a>00345 <span class="comment">!</span>
- <a name="l00346"></a>00346 <span class="comment">! Author:</span>
- <a name="l00347"></a>00347 <span class="comment">!</span>
- <a name="l00348"></a>00348 <span class="comment">! John Burkardt</span>
- <a name="l00349"></a>00349 <span class="comment">!</span>
- <a name="l00350"></a>00350 <span class="comment">! Parameters:</span>
- <a name="l00351"></a>00351 <span class="comment">!</span>
- <a name="l00352"></a>00352 <span class="comment">! Input, integer NORDER, the order of the rule, which can be</span>
- <a name="l00353"></a>00353 <span class="comment">! any value from 1 to 19.</span>
- <a name="l00354"></a>00354 <span class="comment">!</span>
- <a name="l00355"></a>00355 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l00356"></a>00356 <span class="comment">!</span>
- <a name="l00357"></a>00357 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l00358"></a>00358 <span class="comment">!</span>
- <a name="l00359"></a>00359 <span class="keyword">implicit none</span>
- <a name="l00360"></a>00360 <span class="comment">!</span>
- <a name="l00361"></a>00361 <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxord = 19
- <a name="l00362"></a>00362 <span class="comment">!</span>
- <a name="l00363"></a>00363 <span class="keywordtype">integer</span> norder
- <a name="l00364"></a>00364 <span class="comment">!</span>
- <a name="l00365"></a>00365 <span class="keywordtype">integer</span> i
- <a name="l00366"></a>00366 <span class="keywordtype">double precision</span> w(maxord)
- <a name="l00367"></a>00367 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l00368"></a>00368 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l00369"></a>00369 <span class="comment">!</span>
- <a name="l00370"></a>00370 w(1) = 1.0D+00
- <a name="l00371"></a>00371 w(2) = - 1.0D+00 / 2.0D+00
- <a name="l00372"></a>00372 w(3) = - 1.0D+00 / 12.0D+00
- <a name="l00373"></a>00373 w(4) = - 1.0D+00 / 24.0D+00
- <a name="l00374"></a>00374 w(5) = - 19.0D+00 / 720.0D+00
- <a name="l00375"></a>00375 w(6) = - 3.0D+00 / 160.0D+00
- <a name="l00376"></a>00376 w(7) = - 863.0D+00 / 60480.0D+00
- <a name="l00377"></a>00377 w(8) = - 275.0D+00 / 24792.0D+00
- <a name="l00378"></a>00378 w(9) = - 33953.0D+00 / 3628800.0D+00
- <a name="l00379"></a>00379 w(10) = - 8183.0D+00 / 1036800.0D+00
- <a name="l00380"></a>00380 w(11) = - 3250433.0D+00 / 479001600.0D+00
- <a name="l00381"></a>00381 w(12) = - 4671.0D+00 / 788480.0D+00
- <a name="l00382"></a>00382 w(13) = - 13695779093.0D+00 / 2615348736000.0D+00
- <a name="l00383"></a>00383 w(14) = - 2224234463.0D+00 / 475517952000.0D+00
- <a name="l00384"></a>00384 w(15) = - 132282840127.0D+00 / 31384184832000.0D+00
- <a name="l00385"></a>00385 w(16) = - 2639651053.0D+00 / 689762304000.0D+00
- <a name="l00386"></a>00386 w(17) = 111956703448001.0D+00 / 3201186852864.0D+00
- <a name="l00387"></a>00387 w(18) = 50188465.0D+00 / 15613165568.0D+00
- <a name="l00388"></a>00388 w(19) = 2334028946344463.0D+00 / 786014494949376.0D+00
- <a name="l00389"></a>00389
- <a name="l00390"></a>00390 <span class="keyword">do</span> i = 1, min ( norder, maxord )
- <a name="l00391"></a>00391 weight(i) = w(i)
- <a name="l00392"></a>00392 <span class="keyword">end do</span>
- <a name="l00393"></a>00393
- <a name="l00394"></a>00394 <span class="keyword">do</span> i = 1, norder
- <a name="l00395"></a>00395 xtab(i) = dble ( 2 - i )
- <a name="l00396"></a>00396 <span class="keyword">end do</span>
- <a name="l00397"></a>00397
- <a name="l00398"></a>00398 return
- <a name="l00399"></a>00399 <span class="keyword">end</span>
- <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 )
- <a name="l00401"></a>00401 <span class="comment">!</span>
- <a name="l00402"></a>00402 <span class="comment">!*******************************************************************************</span>
- <a name="l00403"></a>00403 <span class="comment">!</span>
- <a name="l00404"></a>00404 <span class="comment">!! BDFP_SET sets weights for backward differentiation predictor quadrature.</span>
- <a name="l00405"></a>00405 <span class="comment">!</span>
- <a name="l00406"></a>00406 <span class="comment">!</span>
- <a name="l00407"></a>00407 <span class="comment">! Definition:</span>
- <a name="l00408"></a>00408 <span class="comment">!</span>
- <a name="l00409"></a>00409 <span class="comment">! A backward differentiation predictor formula is defined for a set</span>
- <a name="l00410"></a>00410 <span class="comment">! of evenly spaced abscissas X(I) with X(1) = 1 and X(2) = 0. Assuming</span>
- <a name="l00411"></a>00411 <span class="comment">! that the values of the function to be integrated are known at the</span>
- <a name="l00412"></a>00412 <span class="comment">! abscissas, the formula is written in terms of the function value at</span>
- <a name="l00413"></a>00413 <span class="comment">! X(2), and the backward differences at X(2) that approximate the</span>
- <a name="l00414"></a>00414 <span class="comment">! derivatives there. A backward differentiation predictor formula</span>
- <a name="l00415"></a>00415 <span class="comment">! is equivalent to an Adams-Bashforth formula of the same order.</span>
- <a name="l00416"></a>00416 <span class="comment">!</span>
- <a name="l00417"></a>00417 <span class="comment">! Integration interval:</span>
- <a name="l00418"></a>00418 <span class="comment">!</span>
- <a name="l00419"></a>00419 <span class="comment">! [ 0, 1 ]</span>
- <a name="l00420"></a>00420 <span class="comment">!</span>
- <a name="l00421"></a>00421 <span class="comment">! Weight function:</span>
- <a name="l00422"></a>00422 <span class="comment">!</span>
- <a name="l00423"></a>00423 <span class="comment">! 1.0D+00</span>
- <a name="l00424"></a>00424 <span class="comment">!</span>
- <a name="l00425"></a>00425 <span class="comment">! Integral to approximate:</span>
- <a name="l00426"></a>00426 <span class="comment">!</span>
- <a name="l00427"></a>00427 <span class="comment">! Integral ( 0 <= X <= 1 ) F(X) dX</span>
- <a name="l00428"></a>00428 <span class="comment">!</span>
- <a name="l00429"></a>00429 <span class="comment">! Approximate integral:</span>
- <a name="l00430"></a>00430 <span class="comment">!</span>
- <a name="l00431"></a>00431 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * BD**(I-1) F ( 0 ),</span>
- <a name="l00432"></a>00432 <span class="comment">!</span>
- <a name="l00433"></a>00433 <span class="comment">! Here, "BD**(I-1) F ( 0 )" denotes the (I-1)st backward difference</span>
- <a name="l00434"></a>00434 <span class="comment">! of F at X = 0, using a spacing of 1. In particular,</span>
- <a name="l00435"></a>00435 <span class="comment">!</span>
- <a name="l00436"></a>00436 <span class="comment">! BD**0 F(0) = F(0)</span>
- <a name="l00437"></a>00437 <span class="comment">! BD**1 F(0) = F(0) - F(-1)</span>
- <a name="l00438"></a>00438 <span class="comment">! BD**2 F(0) = F(0) - 2 * F(-1) + F(-2 )</span>
- <a name="l00439"></a>00439 <span class="comment">!</span>
- <a name="l00440"></a>00440 <span class="comment">! Note:</span>
- <a name="l00441"></a>00441 <span class="comment">!</span>
- <a name="l00442"></a>00442 <span class="comment">! The relationship between a backward difference predictor and the</span>
- <a name="l00443"></a>00443 <span class="comment">! corresponding Adams-Bashforth formula may be illustrated for the</span>
- <a name="l00444"></a>00444 <span class="comment">! BDF predictor of order 3:</span>
- <a name="l00445"></a>00445 <span class="comment">!</span>
- <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>
- <a name="l00447"></a>00447 <span class="comment">! = F(0)</span>
- <a name="l00448"></a>00448 <span class="comment">! + 1/2 * ( F(0) - F(1) )</span>
- <a name="l00449"></a>00449 <span class="comment">! + 5/12 * ( F(0) - 2 * F(-1) + F(-2) )</span>
- <a name="l00450"></a>00450 <span class="comment">! = 23/12 * F(0) - 16/12 * F(-1) + 5/12 F(-2)</span>
- <a name="l00451"></a>00451 <span class="comment">!</span>
- <a name="l00452"></a>00452 <span class="comment">! which is the Adams-Bashforth formula of order 3.</span>
- <a name="l00453"></a>00453 <span class="comment">! </span>
- <a name="l00454"></a>00454 <span class="comment">! Reference:</span>
- <a name="l00455"></a>00455 <span class="comment">!</span>
- <a name="l00456"></a>00456 <span class="comment">! Simeon Fatunla,</span>
- <a name="l00457"></a>00457 <span class="comment">! Numerical Methods for Initial Value Problems in Ordinary Differential</span>
- <a name="l00458"></a>00458 <span class="comment">! Equations,</span>
- <a name="l00459"></a>00459 <span class="comment">! Academic Press, 1988.</span>
- <a name="l00460"></a>00460 <span class="comment">!</span>
- <a name="l00461"></a>00461 <span class="comment">! Modified:</span>
- <a name="l00462"></a>00462 <span class="comment">!</span>
- <a name="l00463"></a>00463 <span class="comment">! 29 February 2000</span>
- <a name="l00464"></a>00464 <span class="comment">!</span>
- <a name="l00465"></a>00465 <span class="comment">! Author:</span>
- <a name="l00466"></a>00466 <span class="comment">!</span>
- <a name="l00467"></a>00467 <span class="comment">! John Burkardt</span>
- <a name="l00468"></a>00468 <span class="comment">!</span>
- <a name="l00469"></a>00469 <span class="comment">! Parameters:</span>
- <a name="l00470"></a>00470 <span class="comment">!</span>
- <a name="l00471"></a>00471 <span class="comment">! Input, integer NORDER, the order of the rule, which can be</span>
- <a name="l00472"></a>00472 <span class="comment">! any value from 1 to 19.</span>
- <a name="l00473"></a>00473 <span class="comment">!</span>
- <a name="l00474"></a>00474 <span class="comment">! Output, double precision WEIGHT(NORDER), the weight of the rule.</span>
- <a name="l00475"></a>00475 <span class="comment">!</span>
- <a name="l00476"></a>00476 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l00477"></a>00477 <span class="comment">!</span>
- <a name="l00478"></a>00478 <span class="keyword">implicit none</span>
- <a name="l00479"></a>00479 <span class="comment">!</span>
- <a name="l00480"></a>00480 <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxord = 19
- <a name="l00481"></a>00481 <span class="comment">!</span>
- <a name="l00482"></a>00482 <span class="keywordtype">integer</span> norder
- <a name="l00483"></a>00483 <span class="comment">!</span>
- <a name="l00484"></a>00484 <span class="keywordtype">integer</span> i
- <a name="l00485"></a>00485 <span class="keywordtype">double precision</span> w(maxord)
- <a name="l00486"></a>00486 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l00487"></a>00487 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l00488"></a>00488 <span class="comment">!</span>
- <a name="l00489"></a>00489 w(1) = 1.0D+00
- <a name="l00490"></a>00490 w(2) = 1.0D+00 / 2.0D+00
- <a name="l00491"></a>00491 w(3) = 5.0D+00 / 12.0D+00
- <a name="l00492"></a>00492 w(4) = 3.0D+00 / 8.0D+00
- <a name="l00493"></a>00493 w(5) = 251.0D+00 / 720.0D+00
- <a name="l00494"></a>00494 w(6) = 95.0D+00 / 288.0D+00
- <a name="l00495"></a>00495 w(7) = 19087.0D+00 / 60480.0D+00
- <a name="l00496"></a>00496 w(8) = 5257.0D+00 / 17280.0D+00
- <a name="l00497"></a>00497 w(9) = 1070017.0D+00 / 3628800.0D+00
- <a name="l00498"></a>00498 w(10) = 25713.0D+00 / 89600.0D+00
- <a name="l00499"></a>00499 w(11) = 26842253.0D+00 / 95800320.0D+00
- <a name="l00500"></a>00500 w(12) = 4777223.0D+00 / 17418240.0D+00
- <a name="l00501"></a>00501 w(13) = 703604254357.0D+00 / 2615348736000.0D+00
- <a name="l00502"></a>00502 w(14) = 106364763817.0D+00 / 402361344000.0D+00
- <a name="l00503"></a>00503 w(15) = 1166309819657.0D+00 / 4483454976000.0D+00
- <a name="l00504"></a>00504 w(16) = 25221445.0D+00 / 98402304.0D+00
- <a name="l00505"></a>00505 w(17) = 8092989203533249.0D+00 / 3201186852864.0D+00
- <a name="l00506"></a>00506 w(18) = 85455477715379.0D+00 / 34237292544.0D+00
- <a name="l00507"></a>00507 w(19) = 12600467236042756559.0D+00 / 5109094217170944.0D+00
- <a name="l00508"></a>00508
- <a name="l00509"></a>00509 <span class="keyword">do</span> i = 1, min ( norder, maxord )
- <a name="l00510"></a>00510 weight(i) = w(i)
- <a name="l00511"></a>00511 <span class="keyword">end do</span>
- <a name="l00512"></a>00512
- <a name="l00513"></a>00513 <span class="keyword">do</span> i = 1, norder
- <a name="l00514"></a>00514 xtab(i) = dble ( 1 - i )
- <a name="l00515"></a>00515 <span class="keyword">end do</span>
- <a name="l00516"></a>00516
- <a name="l00517"></a>00517 return
- <a name="l00518"></a>00518 <span class="keyword">end</span>
- <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 )
- <a name="l00520"></a>00520 <span class="comment">!</span>
- <a name="l00521"></a>00521 <span class="comment">!*******************************************************************************</span>
- <a name="l00522"></a>00522 <span class="comment">!</span>
- <a name="l00523"></a>00523 <span class="comment">!! BDF_SUM carries out an explicit backward difference quadrature rule for [0,1].</span>
- <a name="l00524"></a>00524 <span class="comment">!</span>
- <a name="l00525"></a>00525 <span class="comment">!</span>
- <a name="l00526"></a>00526 <span class="comment">! Integral to approximate:</span>
- <a name="l00527"></a>00527 <span class="comment">!</span>
- <a name="l00528"></a>00528 <span class="comment">! Integral ( 0 <= X <= 1 ) F(X) dX</span>
- <a name="l00529"></a>00529 <span class="comment">!</span>
- <a name="l00530"></a>00530 <span class="comment">! Formula:</span>
- <a name="l00531"></a>00531 <span class="comment">!</span>
- <a name="l00532"></a>00532 <span class="comment">! RESULT = Sum ( 1 <= I <= NORDER ) WEIGHT(I) * BDF**(I-1) FUNC ( 0 )</span>
- <a name="l00533"></a>00533 <span class="comment">!</span>
- <a name="l00534"></a>00534 <span class="comment">! Note:</span>
- <a name="l00535"></a>00535 <span class="comment">!</span>
- <a name="l00536"></a>00536 <span class="comment">! The integral from 0 to 1 is approximated using data at X = 0,</span>
- <a name="l00537"></a>00537 <span class="comment">! -1, -2, ..., -NORDER+1. This is a form of extrapolation, and</span>
- <a name="l00538"></a>00538 <span class="comment">! the approximation can become poor as NORDER increases.</span>
- <a name="l00539"></a>00539 <span class="comment">!</span>
- <a name="l00540"></a>00540 <span class="comment">! Modified:</span>
- <a name="l00541"></a>00541 <span class="comment">!</span>
- <a name="l00542"></a>00542 <span class="comment">! 26 October 2000</span>
- <a name="l00543"></a>00543 <span class="comment">!</span>
- <a name="l00544"></a>00544 <span class="comment">! Author:</span>
- <a name="l00545"></a>00545 <span class="comment">!</span>
- <a name="l00546"></a>00546 <span class="comment">! John Burkardt</span>
- <a name="l00547"></a>00547 <span class="comment">!</span>
- <a name="l00548"></a>00548 <span class="comment">! Parameters:</span>
- <a name="l00549"></a>00549 <span class="comment">!</span>
- <a name="l00550"></a>00550 <span class="comment">! Input, external FUNC, the name of the FORTRAN function which evaluates</span>
- <a name="l00551"></a>00551 <span class="comment">! the integrand. The function must have the form</span>
- <a name="l00552"></a>00552 <span class="comment">! double precision func ( x ).</span>
- <a name="l00553"></a>00553 <span class="comment">!</span>
- <a name="l00554"></a>00554 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l00555"></a>00555 <span class="comment">!</span>
- <a name="l00556"></a>00556 <span class="comment">! Input, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l00557"></a>00557 <span class="comment">!</span>
- <a name="l00558"></a>00558 <span class="comment">! Input, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l00559"></a>00559 <span class="comment">!</span>
- <a name="l00560"></a>00560 <span class="comment">! Workspace, double precision DIFTAB(NORDER).</span>
- <a name="l00561"></a>00561 <span class="comment">!</span>
- <a name="l00562"></a>00562 <span class="comment">! Output, double precision RESULT, the approximate value of the integral.</span>
- <a name="l00563"></a>00563 <span class="comment">!</span>
- <a name="l00564"></a>00564 <span class="keyword">implicit none</span>
- <a name="l00565"></a>00565 <span class="comment">!</span>
- <a name="l00566"></a>00566 <span class="keywordtype">integer</span> norder
- <a name="l00567"></a>00567 <span class="comment">!</span>
- <a name="l00568"></a>00568 <span class="keywordtype">double precision</span> diftab(norder)
- <a name="l00569"></a>00569 <span class="keywordtype">double precision</span>, <span class="keywordtype">external</span> :: func
- <a name="l00570"></a>00570 <span class="keywordtype">integer</span> i
- <a name="l00571"></a>00571 <span class="keywordtype">integer</span> j
- <a name="l00572"></a>00572 <span class="keywordtype">double precision</span> result
- <a name="l00573"></a>00573 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l00574"></a>00574 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l00575"></a>00575 <span class="comment">!</span>
- <a name="l00576"></a>00576 <span class="keyword">do</span> i = 1, norder
- <a name="l00577"></a>00577 diftab(i) = func ( xtab(i) )
- <a name="l00578"></a>00578 <span class="keyword">end do</span>
- <a name="l00579"></a>00579
- <a name="l00580"></a>00580 <span class="keyword">do</span> i = 2, norder
- <a name="l00581"></a>00581 <span class="keyword">do</span> j = i, norder
- <a name="l00582"></a>00582 diftab(norder+i-j) = ( diftab(norder+i-j-1) - diftab(norder+i-j) )
- <a name="l00583"></a>00583 <span class="keyword">end do</span>
- <a name="l00584"></a>00584 <span class="keyword">end do</span>
- <a name="l00585"></a>00585
- <a name="l00586"></a>00586 result = dot_product ( weight(1:norder), diftab(1:norder) )
- <a name="l00587"></a>00587
- <a name="l00588"></a>00588 return
- <a name="l00589"></a>00589 <span class="keyword">end</span>
- <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 )
- <a name="l00591"></a>00591 <span class="comment">!</span>
- <a name="l00592"></a>00592 <span class="comment">!*******************************************************************************</span>
- <a name="l00593"></a>00593 <span class="comment">!</span>
- <a name="l00594"></a>00594 <span class="comment">!! CHEB_SET sets abscissas and weights for Chebyshev quadrature.</span>
- <a name="l00595"></a>00595 <span class="comment">!</span>
- <a name="l00596"></a>00596 <span class="comment">!</span>
- <a name="l00597"></a>00597 <span class="comment">! Integration interval:</span>
- <a name="l00598"></a>00598 <span class="comment">!</span>
- <a name="l00599"></a>00599 <span class="comment">! [ -1, 1 ]</span>
- <a name="l00600"></a>00600 <span class="comment">!</span>
- <a name="l00601"></a>00601 <span class="comment">! Weight function:</span>
- <a name="l00602"></a>00602 <span class="comment">!</span>
- <a name="l00603"></a>00603 <span class="comment">! 1.0D+00</span>
- <a name="l00604"></a>00604 <span class="comment">!</span>
- <a name="l00605"></a>00605 <span class="comment">! Integral to approximate:</span>
- <a name="l00606"></a>00606 <span class="comment">!</span>
- <a name="l00607"></a>00607 <span class="comment">! Integral ( -1 <= X <= 1 ) F(X) dX</span>
- <a name="l00608"></a>00608 <span class="comment">!</span>
- <a name="l00609"></a>00609 <span class="comment">! Approximate integral:</span>
- <a name="l00610"></a>00610 <span class="comment">!</span>
- <a name="l00611"></a>00611 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l00612"></a>00612 <span class="comment">!</span>
- <a name="l00613"></a>00613 <span class="comment">! Note:</span>
- <a name="l00614"></a>00614 <span class="comment">!</span>
- <a name="l00615"></a>00615 <span class="comment">! The Chebyshev rule is distinguished by using equal weights.</span>
- <a name="l00616"></a>00616 <span class="comment">!</span>
- <a name="l00617"></a>00617 <span class="comment">! Reference:</span>
- <a name="l00618"></a>00618 <span class="comment">!</span>
- <a name="l00619"></a>00619 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l00620"></a>00620 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l00621"></a>00621 <span class="comment">! National Bureau of Standards, 1964.</span>
- <a name="l00622"></a>00622 <span class="comment">!</span>
- <a name="l00623"></a>00623 <span class="comment">! H Engels,</span>
- <a name="l00624"></a>00624 <span class="comment">! Numerical Quadrature and Cubature,</span>
- <a name="l00625"></a>00625 <span class="comment">! Academic Press, 1980.</span>
- <a name="l00626"></a>00626 <span class="comment">!</span>
- <a name="l00627"></a>00627 <span class="comment">! Zdenek Kopal,</span>
- <a name="l00628"></a>00628 <span class="comment">! Numerical Analysis,</span>
- <a name="l00629"></a>00629 <span class="comment">! John Wiley, 1955.</span>
- <a name="l00630"></a>00630 <span class="comment">!</span>
- <a name="l00631"></a>00631 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l00632"></a>00632 <span class="comment">! Standard Mathematical Tables and Formulae,</span>
- <a name="l00633"></a>00633 <span class="comment">! 30th Edition,</span>
- <a name="l00634"></a>00634 <span class="comment">! CRC Press, 1996.</span>
- <a name="l00635"></a>00635 <span class="comment">!</span>
- <a name="l00636"></a>00636 <span class="comment">! Modified:</span>
- <a name="l00637"></a>00637 <span class="comment">!</span>
- <a name="l00638"></a>00638 <span class="comment">! 27 October 2000</span>
- <a name="l00639"></a>00639 <span class="comment">!</span>
- <a name="l00640"></a>00640 <span class="comment">! Author:</span>
- <a name="l00641"></a>00641 <span class="comment">!</span>
- <a name="l00642"></a>00642 <span class="comment">! John Burkardt</span>
- <a name="l00643"></a>00643 <span class="comment">!</span>
- <a name="l00644"></a>00644 <span class="comment">! Parameters:</span>
- <a name="l00645"></a>00645 <span class="comment">!</span>
- <a name="l00646"></a>00646 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l00647"></a>00647 <span class="comment">! NORDER may only have the values 1, 2, 3, 4, 5, 6, 7 or 9.</span>
- <a name="l00648"></a>00648 <span class="comment">! There are NO other Chebyshev rules with real abscissas.</span>
- <a name="l00649"></a>00649 <span class="comment">!</span>
- <a name="l00650"></a>00650 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule,</span>
- <a name="l00651"></a>00651 <span class="comment">! which are symmetric in [-1,1].</span>
- <a name="l00652"></a>00652 <span class="comment">!</span>
- <a name="l00653"></a>00653 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule,</span>
- <a name="l00654"></a>00654 <span class="comment">! which should each equal 2 / NORDER.</span>
- <a name="l00655"></a>00655 <span class="comment">!</span>
- <a name="l00656"></a>00656 <span class="keyword">implicit none</span>
- <a name="l00657"></a>00657 <span class="comment">!</span>
- <a name="l00658"></a>00658 <span class="keywordtype">integer</span> norder
- <a name="l00659"></a>00659 <span class="comment">!</span>
- <a name="l00660"></a>00660 <span class="keywordtype">integer</span> i
- <a name="l00661"></a>00661 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l00662"></a>00662 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l00663"></a>00663 <span class="comment">!</span>
- <a name="l00664"></a>00664 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l00665"></a>00665
- <a name="l00666"></a>00666 xtab(1) = 0.0D+00
- <a name="l00667"></a>00667
- <a name="l00668"></a>00668 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l00669"></a>00669
- <a name="l00670"></a>00670 xtab(1) = - 1.0D+00 / sqrt ( 3.0D+00 )
- <a name="l00671"></a>00671 xtab(2) = 1.0D+00 / sqrt ( 3.0D+00 )
- <a name="l00672"></a>00672
- <a name="l00673"></a>00673 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l00674"></a>00674
- <a name="l00675"></a>00675 xtab(1) = - 1.0D+00 / sqrt ( 2.0D+00 )
- <a name="l00676"></a>00676 xtab(2) = 0.0D+00
- <a name="l00677"></a>00677 xtab(3) = 1.0D+00 / sqrt ( 2.0D+00 )
- <a name="l00678"></a>00678
- <a name="l00679"></a>00679 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l00680"></a>00680
- <a name="l00681"></a>00681 xtab(1) = - sqrt ( ( 1.0D+00 + 2.0D+00/ sqrt ( 5.0D+00 ) ) / 3.0D+00 )
- <a name="l00682"></a>00682 xtab(2) = - sqrt ( ( 1.0D+00 - 2.0D+00/ sqrt ( 5.0D+00 ) ) / 3.0D+00 )
- <a name="l00683"></a>00683 xtab(3) = sqrt ( ( 1.0D+00 - 2.0D+00/ sqrt ( 5.0D+00 ) ) / 3.0D+00 )
- <a name="l00684"></a>00684 xtab(4) = sqrt ( ( 1.0D+00 + 2.0D+00/ sqrt ( 5.0D+00 ) ) / 3.0D+00 )
- <a name="l00685"></a>00685
- <a name="l00686"></a>00686 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l00687"></a>00687
- <a name="l00688"></a>00688 xtab(1) = - sqrt ( ( 5.0D+00 + sqrt ( 11.0D+00) ) / 12.0D+00 )
- <a name="l00689"></a>00689 xtab(2) = - sqrt ( ( 5.0D+00 - sqrt ( 11.0D+00) ) / 12.0D+00 )
- <a name="l00690"></a>00690 xtab(3) = 0.0D+00
- <a name="l00691"></a>00691 xtab(4) = sqrt ( ( 5.0D+00 - sqrt ( 11.0D+00) ) / 12.0D+00 )
- <a name="l00692"></a>00692 xtab(5) = sqrt ( ( 5.0D+00 + sqrt ( 11.0D+00) ) / 12.0D+00 )
- <a name="l00693"></a>00693
- <a name="l00694"></a>00694 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l00695"></a>00695
- <a name="l00696"></a>00696 xtab(1) = - 0.866246818107820591383598D+00
- <a name="l00697"></a>00697 xtab(2) = - 0.422518653761111529118546D+00
- <a name="l00698"></a>00698 xtab(3) = - 0.266635401516704720331534D+00
- <a name="l00699"></a>00699 xtab(4) = 0.266635401516704720331534D+00
- <a name="l00700"></a>00700 xtab(5) = 0.422518653761111529118546D+00
- <a name="l00701"></a>00701 xtab(6) = 0.866246818107820591383598D+00
- <a name="l00702"></a>00702
- <a name="l00703"></a>00703 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l00704"></a>00704
- <a name="l00705"></a>00705 xtab(1) = - 0.883861700758049035704224D+00
- <a name="l00706"></a>00706 xtab(2) = - 0.529656775285156811385048D+00
- <a name="l00707"></a>00707 xtab(3) = - 0.323911810519907637519673D+00
- <a name="l00708"></a>00708 xtab(4) = 0.0D+00
- <a name="l00709"></a>00709 xtab(5) = 0.323911810519907637519673D+00
- <a name="l00710"></a>00710 xtab(6) = 0.529656775285156811385048D+00
- <a name="l00711"></a>00711 xtab(7) = 0.883861700758049035704224D+00
- <a name="l00712"></a>00712
- <a name="l00713"></a>00713 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
- <a name="l00714"></a>00714
- <a name="l00715"></a>00715 xtab(1) = - 0.911589307728434473664949D+00
- <a name="l00716"></a>00716 xtab(2) = - 0.601018655380238071428128D+00
- <a name="l00717"></a>00717 xtab(3) = - 0.528761783057879993260181D+00
- <a name="l00718"></a>00718 xtab(4) = - 0.167906184214803943068031D+00
- <a name="l00719"></a>00719 xtab(5) = 0.0D+00
- <a name="l00720"></a>00720 xtab(6) = 0.167906184214803943068031D+00
- <a name="l00721"></a>00721 xtab(7) = 0.528761783057879993260181D+00
- <a name="l00722"></a>00722 xtab(8) = 0.601018655380238071428128D+00
- <a name="l00723"></a>00723 xtab(9) = 0.911589307728434473664949D+00
- <a name="l00724"></a>00724
- <a name="l00725"></a>00725 <span class="keyword">else</span>
- <a name="l00726"></a>00726
- <a name="l00727"></a>00727 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l00728"></a>00728 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'CHEB_SET - Fatal error!'</span>
- <a name="l00729"></a>00729 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l00730"></a>00730 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' Legal values are 1 through 7, and 9.'</span>
- <a name="l00731"></a>00731 stop
- <a name="l00732"></a>00732
- <a name="l00733"></a>00733 <span class="keyword">end if</span>
- <a name="l00734"></a>00734
- <a name="l00735"></a>00735 weight(1:norder) = 2.0D+00 / dble ( norder )
- <a name="l00736"></a>00736
- <a name="l00737"></a>00737 return
- <a name="l00738"></a>00738 <span class="keyword">end</span>
- <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 )
- <a name="l00740"></a>00740 <span class="comment">!</span>
- <a name="l00741"></a>00741 <span class="comment">!*******************************************************************************</span>
- <a name="l00742"></a>00742 <span class="comment">!</span>
- <a name="l00743"></a>00743 <span class="comment">!! CHEB_TO_SET sets up open Gauss-Chebyshev (first kind) quadrature.</span>
- <a name="l00744"></a>00744 <span class="comment">!</span>
- <a name="l00745"></a>00745 <span class="comment">!</span>
- <a name="l00746"></a>00746 <span class="comment">! Integration interval:</span>
- <a name="l00747"></a>00747 <span class="comment">!</span>
- <a name="l00748"></a>00748 <span class="comment">! [ -1, 1 ]</span>
- <a name="l00749"></a>00749 <span class="comment">!</span>
- <a name="l00750"></a>00750 <span class="comment">! Weight function:</span>
- <a name="l00751"></a>00751 <span class="comment">!</span>
- <a name="l00752"></a>00752 <span class="comment">! 1 / SQRT ( 1 - X**2 )</span>
- <a name="l00753"></a>00753 <span class="comment">!</span>
- <a name="l00754"></a>00754 <span class="comment">! Integral to approximate:</span>
- <a name="l00755"></a>00755 <span class="comment">!</span>
- <a name="l00756"></a>00756 <span class="comment">! Integral ( -1 <= X <= 1 ) F(X) / SQRT ( 1 - X**2 ) dX</span>
- <a name="l00757"></a>00757 <span class="comment">!</span>
- <a name="l00758"></a>00758 <span class="comment">! Approximate integral:</span>
- <a name="l00759"></a>00759 <span class="comment">!</span>
- <a name="l00760"></a>00760 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l00761"></a>00761 <span class="comment">!</span>
- <a name="l00762"></a>00762 <span class="comment">! Precision:</span>
- <a name="l00763"></a>00763 <span class="comment">!</span>
- <a name="l00764"></a>00764 <span class="comment">! If NORDER points are used, then Gauss-Chebyshev quadrature</span>
- <a name="l00765"></a>00765 <span class="comment">! will compute the integral exactly, whenever F(X) is a polynomial</span>
- <a name="l00766"></a>00766 <span class="comment">! of degree 2*NORDER-1 or less.</span>
- <a name="l00767"></a>00767 <span class="comment">!</span>
- <a name="l00768"></a>00768 <span class="comment">! Note:</span>
- <a name="l00769"></a>00769 <span class="comment">!</span>
- <a name="l00770"></a>00770 <span class="comment">! The abscissas of the rule are zeroes of the Chebyshev polynomials</span>
- <a name="l00771"></a>00771 <span class="comment">! of the first kind, T(NORDER)(X).</span>
- <a name="l00772"></a>00772 <span class="comment">!</span>
- <a name="l00773"></a>00773 <span class="comment">! Reference:</span>
- <a name="l00774"></a>00774 <span class="comment">!</span>
- <a name="l00775"></a>00775 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l00776"></a>00776 <span class="comment">! Standard Mathematical Tables and Formulae,</span>
- <a name="l00777"></a>00777 <span class="comment">! 30th Edition,</span>
- <a name="l00778"></a>00778 <span class="comment">! CRC Press, 1996.</span>
- <a name="l00779"></a>00779 <span class="comment">!</span>
- <a name="l00780"></a>00780 <span class="comment">! Modified:</span>
- <a name="l00781"></a>00781 <span class="comment">!</span>
- <a name="l00782"></a>00782 <span class="comment">! 15 September 1998</span>
- <a name="l00783"></a>00783 <span class="comment">!</span>
- <a name="l00784"></a>00784 <span class="comment">! Author:</span>
- <a name="l00785"></a>00785 <span class="comment">!</span>
- <a name="l00786"></a>00786 <span class="comment">! John Burkardt</span>
- <a name="l00787"></a>00787 <span class="comment">!</span>
- <a name="l00788"></a>00788 <span class="comment">! Parameters:</span>
- <a name="l00789"></a>00789 <span class="comment">!</span>
- <a name="l00790"></a>00790 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l00791"></a>00791 <span class="comment">!</span>
- <a name="l00792"></a>00792 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l00793"></a>00793 <span class="comment">!</span>
- <a name="l00794"></a>00794 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule,</span>
- <a name="l00795"></a>00795 <span class="comment">! which are all equal to PI / NORDER.</span>
- <a name="l00796"></a>00796 <span class="comment">!</span>
- <a name="l00797"></a>00797 <span class="keyword">implicit none</span>
- <a name="l00798"></a>00798 <span class="comment">!</span>
- <a name="l00799"></a>00799 <span class="keywordtype">integer</span> norder
- <a name="l00800"></a>00800 <span class="comment">!</span>
- <a name="l00801"></a>00801 <span class="keywordtype">double precision</span> angle
- <a name="l00802"></a>00802 <span class="keywordtype">double precision</span> d_pi
- <a name="l00803"></a>00803 <span class="keywordtype">integer</span> i
- <a name="l00804"></a>00804 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l00805"></a>00805 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l00806"></a>00806 <span class="comment">!</span>
- <a name="l00807"></a>00807 <span class="keyword">do</span> i = 1, norder
- <a name="l00808"></a>00808 angle = dble ( 2 * i - 1 ) * d_pi ( ) / dble ( 2 * norder )
- <a name="l00809"></a>00809 xtab(i) = cos ( angle )
- <a name="l00810"></a>00810 <span class="keyword">end do</span>
- <a name="l00811"></a>00811
- <a name="l00812"></a>00812 weight(1:norder) = d_pi ( ) / dble ( norder )
- <a name="l00813"></a>00813
- <a name="l00814"></a>00814 return
- <a name="l00815"></a>00815 <span class="keyword">end</span>
- <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 )
- <a name="l00817"></a>00817 <span class="comment">!</span>
- <a name="l00818"></a>00818 <span class="comment">!*******************************************************************************</span>
- <a name="l00819"></a>00819 <span class="comment">!</span>
- <a name="l00820"></a>00820 <span class="comment">!! CHEB_TC_SET sets up closed Gauss-Chebyshev (first kind) quadrature.</span>
- <a name="l00821"></a>00821 <span class="comment">!</span>
- <a name="l00822"></a>00822 <span class="comment">!</span>
- <a name="l00823"></a>00823 <span class="comment">! Integration interval:</span>
- <a name="l00824"></a>00824 <span class="comment">!</span>
- <a name="l00825"></a>00825 <span class="comment">! [ -1, 1 ]</span>
- <a name="l00826"></a>00826 <span class="comment">!</span>
- <a name="l00827"></a>00827 <span class="comment">! Weight function:</span>
- <a name="l00828"></a>00828 <span class="comment">!</span>
- <a name="l00829"></a>00829 <span class="comment">! 1 / SQRT ( 1 - X**2 )</span>
- <a name="l00830"></a>00830 <span class="comment">!</span>
- <a name="l00831"></a>00831 <span class="comment">! Integral to approximate:</span>
- <a name="l00832"></a>00832 <span class="comment">!</span>
- <a name="l00833"></a>00833 <span class="comment">! Integral ( -1 <= X <= 1 ) F(X) / SQRT ( 1 - X**2 ) dX</span>
- <a name="l00834"></a>00834 <span class="comment">!</span>
- <a name="l00835"></a>00835 <span class="comment">! Approximate integral:</span>
- <a name="l00836"></a>00836 <span class="comment">!</span>
- <a name="l00837"></a>00837 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l00838"></a>00838 <span class="comment">!</span>
- <a name="l00839"></a>00839 <span class="comment">! Precision:</span>
- <a name="l00840"></a>00840 <span class="comment">!</span>
- <a name="l00841"></a>00841 <span class="comment">! If NORDER points are used, then Gauss-Chebyshev quadrature</span>
- <a name="l00842"></a>00842 <span class="comment">! will compute the integral exactly, whenever F(X) is a polynomial</span>
- <a name="l00843"></a>00843 <span class="comment">! of degree 2*NORDER-3 or less.</span>
- <a name="l00844"></a>00844 <span class="comment">!</span>
- <a name="l00845"></a>00845 <span class="comment">! Note:</span>
- <a name="l00846"></a>00846 <span class="comment">!</span>
- <a name="l00847"></a>00847 <span class="comment">! The abscissas include -1 and 1.</span>
- <a name="l00848"></a>00848 <span class="comment">!</span>
- <a name="l00849"></a>00849 <span class="comment">! If the order is doubled, the abscissas of the new rule include</span>
- <a name="l00850"></a>00850 <span class="comment">! all the points of the old rule. This fact can be used to</span>
- <a name="l00851"></a>00851 <span class="comment">! efficiently implement error estimation.</span>
- <a name="l00852"></a>00852 <span class="comment">!</span>
- <a name="l00853"></a>00853 <span class="comment">! Reference:</span>
- <a name="l00854"></a>00854 <span class="comment">!</span>
- <a name="l00855"></a>00855 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l00856"></a>00856 <span class="comment">! Standard Mathematical Tables and Formulae,</span>
- <a name="l00857"></a>00857 <span class="comment">! 30th Edition,</span>
- <a name="l00858"></a>00858 <span class="comment">! CRC Press, 1996.</span>
- <a name="l00859"></a>00859 <span class="comment">!</span>
- <a name="l00860"></a>00860 <span class="comment">! Modified:</span>
- <a name="l00861"></a>00861 <span class="comment">!</span>
- <a name="l00862"></a>00862 <span class="comment">! 15 September 1998</span>
- <a name="l00863"></a>00863 <span class="comment">!</span>
- <a name="l00864"></a>00864 <span class="comment">! Author:</span>
- <a name="l00865"></a>00865 <span class="comment">!</span>
- <a name="l00866"></a>00866 <span class="comment">! John Burkardt</span>
- <a name="l00867"></a>00867 <span class="comment">!</span>
- <a name="l00868"></a>00868 <span class="comment">! Parameters:</span>
- <a name="l00869"></a>00869 <span class="comment">!</span>
- <a name="l00870"></a>00870 <span class="comment">! Input, integer NORDER, the order of the rule, which must be at least 2.</span>
- <a name="l00871"></a>00871 <span class="comment">!</span>
- <a name="l00872"></a>00872 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l00873"></a>00873 <span class="comment">!</span>
- <a name="l00874"></a>00874 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l00875"></a>00875 <span class="comment">! The first and last weights are 0.5 * PI / ( NORDER - 1),</span>
- <a name="l00876"></a>00876 <span class="comment">! and all other weights are PI / ( NORDER - 1 ).</span>
- <a name="l00877"></a>00877 <span class="comment">!</span>
- <a name="l00878"></a>00878 <span class="keyword">implicit none</span>
- <a name="l00879"></a>00879 <span class="comment">!</span>
- <a name="l00880"></a>00880 <span class="keywordtype">integer</span> norder
- <a name="l00881"></a>00881 <span class="comment">!</span>
- <a name="l00882"></a>00882 <span class="keywordtype">double precision</span> angle
- <a name="l00883"></a>00883 <span class="keywordtype">double precision</span> d_pi
- <a name="l00884"></a>00884 <span class="keywordtype">integer</span> i
- <a name="l00885"></a>00885 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l00886"></a>00886 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l00887"></a>00887 <span class="comment">!</span>
- <a name="l00888"></a>00888 <span class="keyword">if</span> ( norder < 2 ) <span class="keyword">then</span>
- <a name="l00889"></a>00889 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l00890"></a>00890 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'CHEB_TC_SET - Fatal error!'</span>
- <a name="l00891"></a>00891 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' NORDER must be at least 2.'</span>
- <a name="l00892"></a>00892 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' The input value was NORDER = '</span>, norder
- <a name="l00893"></a>00893 stop
- <a name="l00894"></a>00894 <span class="keyword">end if</span>
- <a name="l00895"></a>00895
- <a name="l00896"></a>00896 <span class="keyword">do</span> i = 1, norder
- <a name="l00897"></a>00897
- <a name="l00898"></a>00898 angle = dble ( i - 1 ) * d_pi ( ) / dble ( norder - 1 )
- <a name="l00899"></a>00899 xtab(i) = cos ( angle )
- <a name="l00900"></a>00900
- <a name="l00901"></a>00901 <span class="keyword">end do</span>
- <a name="l00902"></a>00902
- <a name="l00903"></a>00903 weight(1) = d_pi ( ) / dble ( 2 * ( norder - 1 ) )
- <a name="l00904"></a>00904 weight(2:norder-1) = d_pi ( ) / dble ( norder - 1 )
- <a name="l00905"></a>00905 weight(norder) = d_pi ( ) / dble ( 2 * ( norder - 1 ) )
- <a name="l00906"></a>00906
- <a name="l00907"></a>00907 return
- <a name="l00908"></a>00908 <span class="keyword">end</span>
- <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 )
- <a name="l00910"></a>00910 <span class="comment">!</span>
- <a name="l00911"></a>00911 <span class="comment">!*******************************************************************************</span>
- <a name="l00912"></a>00912 <span class="comment">!</span>
- <a name="l00913"></a>00913 <span class="comment">!! CHEB_U_SET sets abscissas and weights for Gauss-Chebyshev quadrature.</span>
- <a name="l00914"></a>00914 <span class="comment">!</span>
- <a name="l00915"></a>00915 <span class="comment">!</span>
- <a name="l00916"></a>00916 <span class="comment">! Integration interval:</span>
- <a name="l00917"></a>00917 <span class="comment">!</span>
- <a name="l00918"></a>00918 <span class="comment">! [ -1, 1 ]</span>
- <a name="l00919"></a>00919 <span class="comment">!</span>
- <a name="l00920"></a>00920 <span class="comment">! Weight function:</span>
- <a name="l00921"></a>00921 <span class="comment">!</span>
- <a name="l00922"></a>00922 <span class="comment">! SQRT ( 1 - X**2 )</span>
- <a name="l00923"></a>00923 <span class="comment">!</span>
- <a name="l00924"></a>00924 <span class="comment">! Integral to approximate:</span>
- <a name="l00925"></a>00925 <span class="comment">!</span>
- <a name="l00926"></a>00926 <span class="comment">! Integral ( -1 <= X <= 1 ) SQRT ( 1 - X**2 ) * F(X) dX</span>
- <a name="l00927"></a>00927 <span class="comment">!</span>
- <a name="l00928"></a>00928 <span class="comment">! Approximate integral:</span>
- <a name="l00929"></a>00929 <span class="comment">!</span>
- <a name="l00930"></a>00930 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l00931"></a>00931 <span class="comment">!</span>
- <a name="l00932"></a>00932 <span class="comment">! Precision:</span>
- <a name="l00933"></a>00933 <span class="comment">!</span>
- <a name="l00934"></a>00934 <span class="comment">! If NORDER points are used, then Gauss-Chebyshev quadrature</span>
- <a name="l00935"></a>00935 <span class="comment">! will compute the integral exactly, whenever F(X) is a polynomial</span>
- <a name="l00936"></a>00936 <span class="comment">! of degree 2*NORDER-1 or less.</span>
- <a name="l00937"></a>00937 <span class="comment">!</span>
- <a name="l00938"></a>00938 <span class="comment">! Note:</span>
- <a name="l00939"></a>00939 <span class="comment">!</span>
- <a name="l00940"></a>00940 <span class="comment">! The abscissas are zeroes of the Chebyshev polynomials</span>
- <a name="l00941"></a>00941 <span class="comment">! of the second kind, U(NORDER)(X).</span>
- <a name="l00942"></a>00942 <span class="comment">!</span>
- <a name="l00943"></a>00943 <span class="comment">! Reference:</span>
- <a name="l00944"></a>00944 <span class="comment">!</span>
- <a name="l00945"></a>00945 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l00946"></a>00946 <span class="comment">! Standard Mathematical Tables and Formulae,</span>
- <a name="l00947"></a>00947 <span class="comment">! 30th Edition,</span>
- <a name="l00948"></a>00948 <span class="comment">! CRC Press, 1996.</span>
- <a name="l00949"></a>00949 <span class="comment">!</span>
- <a name="l00950"></a>00950 <span class="comment">! Modified:</span>
- <a name="l00951"></a>00951 <span class="comment">!</span>
- <a name="l00952"></a>00952 <span class="comment">! 15 September 1998</span>
- <a name="l00953"></a>00953 <span class="comment">!</span>
- <a name="l00954"></a>00954 <span class="comment">! Author:</span>
- <a name="l00955"></a>00955 <span class="comment">!</span>
- <a name="l00956"></a>00956 <span class="comment">! John Burkardt</span>
- <a name="l00957"></a>00957 <span class="comment">!</span>
- <a name="l00958"></a>00958 <span class="comment">! Parameters:</span>
- <a name="l00959"></a>00959 <span class="comment">!</span>
- <a name="l00960"></a>00960 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l00961"></a>00961 <span class="comment">!</span>
- <a name="l00962"></a>00962 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l00963"></a>00963 <span class="comment">!</span>
- <a name="l00964"></a>00964 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule,</span>
- <a name="l00965"></a>00965 <span class="comment">! which are all equal to PI / NORDER.</span>
- <a name="l00966"></a>00966 <span class="comment">!</span>
- <a name="l00967"></a>00967 <span class="keyword">implicit none</span>
- <a name="l00968"></a>00968 <span class="comment">!</span>
- <a name="l00969"></a>00969 <span class="keywordtype">integer</span> norder
- <a name="l00970"></a>00970 <span class="comment">!</span>
- <a name="l00971"></a>00971 <span class="keywordtype">double precision</span> angle
- <a name="l00972"></a>00972 <span class="keywordtype">double precision</span> d_pi
- <a name="l00973"></a>00973 <span class="keywordtype">integer</span> i
- <a name="l00974"></a>00974 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l00975"></a>00975 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l00976"></a>00976 <span class="comment">!</span>
- <a name="l00977"></a>00977 <span class="keyword">do</span> i = 1, norder
- <a name="l00978"></a>00978 angle = dble ( i ) * d_pi ( ) / dble ( norder + 1 )
- <a name="l00979"></a>00979 xtab(i) = cos ( angle )
- <a name="l00980"></a>00980 weight(i) = d_pi ( ) * ( sin ( angle ) )**2 / dble ( norder + 1 )
- <a name="l00981"></a>00981 <span class="keyword">end do</span>
- <a name="l00982"></a>00982
- <a name="l00983"></a>00983 return
- <a name="l00984"></a>00984 <span class="keyword">end</span>
- <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 )
- <a name="l00986"></a>00986 <span class="comment">!</span>
- <a name="l00987"></a>00987 <span class="comment">!*******************************************************************************</span>
- <a name="l00988"></a>00988 <span class="comment">!</span>
- <a name="l00989"></a>00989 <span class="comment">!! D_SWAP switches two double precision values.</span>
- <a name="l00990"></a>00990 <span class="comment">!</span>
- <a name="l00991"></a>00991 <span class="comment">!</span>
- <a name="l00992"></a>00992 <span class="comment">! Modified:</span>
- <a name="l00993"></a>00993 <span class="comment">!</span>
- <a name="l00994"></a>00994 <span class="comment">! 01 May 2000</span>
- <a name="l00995"></a>00995 <span class="comment">!</span>
- <a name="l00996"></a>00996 <span class="comment">! Author:</span>
- <a name="l00997"></a>00997 <span class="comment">!</span>
- <a name="l00998"></a>00998 <span class="comment">! John Burkardt</span>
- <a name="l00999"></a>00999 <span class="comment">!</span>
- <a name="l01000"></a>01000 <span class="comment">! Parameters:</span>
- <a name="l01001"></a>01001 <span class="comment">!</span>
- <a name="l01002"></a>01002 <span class="comment">! Input/output, double precision X, Y. On output, the values of X and</span>
- <a name="l01003"></a>01003 <span class="comment">! Y have been interchanged.</span>
- <a name="l01004"></a>01004 <span class="comment">!</span>
- <a name="l01005"></a>01005 <span class="keyword">implicit none</span>
- <a name="l01006"></a>01006 <span class="comment">!</span>
- <a name="l01007"></a>01007 <span class="keywordtype">double precision</span> x
- <a name="l01008"></a>01008 <span class="keywordtype">double precision</span> y
- <a name="l01009"></a>01009 <span class="keywordtype">double precision</span> z
- <a name="l01010"></a>01010 <span class="comment">!</span>
- <a name="l01011"></a>01011 z = x
- <a name="l01012"></a>01012 x = y
- <a name="l01013"></a>01013 y = z
- <a name="l01014"></a>01014
- <a name="l01015"></a>01015 return
- <a name="l01016"></a>01016 <span class="keyword">end</span>
- <a name="l01017"></a><a class="code" href="quadrule_8f90.html#a1196e8a1c04167d129db7f177728d7fc">01017</a> <span class="keyword">function </span>d_pi ( )
- <a name="l01018"></a>01018 <span class="comment">!</span>
- <a name="l01019"></a>01019 <span class="comment">!*******************************************************************************</span>
- <a name="l01020"></a>01020 <span class="comment">!</span>
- <a name="l01021"></a>01021 <span class="comment">!! DPI returns the value of pi as a double precision quantity.</span>
- <a name="l01022"></a>01022 <span class="comment">!</span>
- <a name="l01023"></a>01023 <span class="comment">!</span>
- <a name="l01024"></a>01024 <span class="comment">! Modified:</span>
- <a name="l01025"></a>01025 <span class="comment">!</span>
- <a name="l01026"></a>01026 <span class="comment">! 28 April 2000</span>
- <a name="l01027"></a>01027 <span class="comment">!</span>
- <a name="l01028"></a>01028 <span class="comment">! Author:</span>
- <a name="l01029"></a>01029 <span class="comment">!</span>
- <a name="l01030"></a>01030 <span class="comment">! John Burkardt</span>
- <a name="l01031"></a>01031 <span class="comment">!</span>
- <a name="l01032"></a>01032 <span class="comment">! Parameters:</span>
- <a name="l01033"></a>01033 <span class="comment">!</span>
- <a name="l01034"></a>01034 <span class="comment">! Output, double precision D_PI, the value of pi.</span>
- <a name="l01035"></a>01035 <span class="comment">!</span>
- <a name="l01036"></a>01036 <span class="keyword">implicit none</span>
- <a name="l01037"></a>01037 <span class="comment">!</span>
- <a name="l01038"></a>01038 <span class="keywordtype">double precision</span> d_pi
- <a name="l01039"></a>01039 <span class="comment">!</span>
- <a name="l01040"></a>01040 d_pi = 3.14159265358979323846264338327950288419716939937510D+00
- <a name="l01041"></a>01041
- <a name="l01042"></a>01042 return
- <a name="l01043"></a>01043 <span class="keyword">end</span>
- <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 )
- <a name="l01045"></a>01045 <span class="comment">!</span>
- <a name="l01046"></a>01046 <span class="comment">!*******************************************************************************</span>
- <a name="l01047"></a>01047 <span class="comment">!</span>
- <a name="l01048"></a>01048 <span class="comment">!! DVEC_REVERSE reverses the elements of a double precision vector.</span>
- <a name="l01049"></a>01049 <span class="comment">!</span>
- <a name="l01050"></a>01050 <span class="comment">!</span>
- <a name="l01051"></a>01051 <span class="comment">! Example:</span>
- <a name="l01052"></a>01052 <span class="comment">!</span>
- <a name="l01053"></a>01053 <span class="comment">! Input:</span>
- <a name="l01054"></a>01054 <span class="comment">!</span>
- <a name="l01055"></a>01055 <span class="comment">! N = 5, A = ( 11.0, 12.0, 13.0, 14.0, 15.0D+00 )</span>
- <a name="l01056"></a>01056 <span class="comment">!</span>
- <a name="l01057"></a>01057 <span class="comment">! Output:</span>
- <a name="l01058"></a>01058 <span class="comment">!</span>
- <a name="l01059"></a>01059 <span class="comment">! A = ( 15.0, 14.0, 13.0, 12.0, 11.0D+00 )</span>
- <a name="l01060"></a>01060 <span class="comment">!</span>
- <a name="l01061"></a>01061 <span class="comment">! Modified:</span>
- <a name="l01062"></a>01062 <span class="comment">!</span>
- <a name="l01063"></a>01063 <span class="comment">! 06 October 1998</span>
- <a name="l01064"></a>01064 <span class="comment">!</span>
- <a name="l01065"></a>01065 <span class="comment">! Author:</span>
- <a name="l01066"></a>01066 <span class="comment">!</span>
- <a name="l01067"></a>01067 <span class="comment">! John Burkardt</span>
- <a name="l01068"></a>01068 <span class="comment">!</span>
- <a name="l01069"></a>01069 <span class="comment">! Parameters:</span>
- <a name="l01070"></a>01070 <span class="comment">!</span>
- <a name="l01071"></a>01071 <span class="comment">! Input, integer N, the number of entries in the array.</span>
- <a name="l01072"></a>01072 <span class="comment">!</span>
- <a name="l01073"></a>01073 <span class="comment">! Input/output, double precision A(N), the array to be reversed.</span>
- <a name="l01074"></a>01074 <span class="comment">!</span>
- <a name="l01075"></a>01075 <span class="keyword">implicit none</span>
- <a name="l01076"></a>01076 <span class="comment">!</span>
- <a name="l01077"></a>01077 <span class="keywordtype">integer</span> n
- <a name="l01078"></a>01078 <span class="comment">!</span>
- <a name="l01079"></a>01079 <span class="keywordtype">double precision</span> a(n)
- <a name="l01080"></a>01080 <span class="keywordtype">integer</span> i
- <a name="l01081"></a>01081 <span class="comment">!</span>
- <a name="l01082"></a>01082 <span class="keyword">do</span> i = 1, n/2
- <a name="l01083"></a>01083 call <a class="code" href="quadrule_8f90.html#ab73cf601dce50b6fc79d82a6ee87bb67">d_swap </a>( a(i), a(n+1-i) )
- <a name="l01084"></a>01084 <span class="keyword">end do</span>
- <a name="l01085"></a>01085
- <a name="l01086"></a>01086 return
- <a name="l01087"></a>01087 <span class="keyword">end</span>
- <a name="l01088"></a><a class="code" href="quadrule_8f90.html#a688af4295664e9e84424169e79729a11">01088</a> <span class="keyword">function </span>gamma ( x )
- <a name="l01089"></a>01089 <span class="comment">!</span>
- <a name="l01090"></a>01090 <span class="comment">!*******************************************************************************</span>
- <a name="l01091"></a>01091 <span class="comment">!</span>
- <a name="l01092"></a>01092 <span class="comment">!! GAMMA computes the gamma function using Hastings's approximation.</span>
- <a name="l01093"></a>01093 <span class="comment">!</span>
- <a name="l01094"></a>01094 <span class="comment">!</span>
- <a name="l01095"></a>01095 <span class="comment">! Reference:</span>
- <a name="l01096"></a>01096 <span class="comment">!</span>
- <a name="l01097"></a>01097 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l01098"></a>01098 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l01099"></a>01099 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l01100"></a>01100 <span class="comment">!</span>
- <a name="l01101"></a>01101 <span class="comment">! Modified:</span>
- <a name="l01102"></a>01102 <span class="comment">!</span>
- <a name="l01103"></a>01103 <span class="comment">! 19 September 1998</span>
- <a name="l01104"></a>01104 <span class="comment">!</span>
- <a name="l01105"></a>01105 <span class="comment">! Parameters:</span>
- <a name="l01106"></a>01106 <span class="comment">!</span>
- <a name="l01107"></a>01107 <span class="comment">! Input, double precision X, the argument at which the gamma function</span>
- <a name="l01108"></a>01108 <span class="comment">! is to be evaluated. X must be greater than 0, and less than 70.</span>
- <a name="l01109"></a>01109 <span class="comment">!</span>
- <a name="l01110"></a>01110 <span class="comment">! Output, double precision GAMMA, the gamma function at X.</span>
- <a name="l01111"></a>01111 <span class="comment">!</span>
- <a name="l01112"></a>01112 <span class="keyword">implicit none</span>
- <a name="l01113"></a>01113 <span class="comment">!</span>
- <a name="l01114"></a>01114 <span class="keywordtype">double precision</span> gam
- <a name="l01115"></a>01115 <span class="keywordtype">double precision</span> gamma
- <a name="l01116"></a>01116 <span class="keywordtype">double precision</span> x
- <a name="l01117"></a>01117 <span class="keywordtype">double precision</span> y
- <a name="l01118"></a>01118 <span class="keywordtype">double precision</span> z
- <a name="l01119"></a>01119 <span class="keywordtype">double precision</span> za
- <a name="l01120"></a>01120 <span class="comment">!</span>
- <a name="l01121"></a>01121 gam ( y ) = ((((((( &
- <a name="l01122"></a>01122 0.035868343D+00 * y &
- <a name="l01123"></a>01123 - 0.193527818D+00 ) * y &
- <a name="l01124"></a>01124 + 0.482199394D+00 ) * y &
- <a name="l01125"></a>01125 - 0.756704078D+00 ) * y &
- <a name="l01126"></a>01126 + 0.918206857D+00 ) * y &
- <a name="l01127"></a>01127 - 0.897056937D+00 ) * y &
- <a name="l01128"></a>01128 + 0.988205891D+00 ) * y &
- <a name="l01129"></a>01129 - 0.577191652D+00 ) * y + 1.0D+00
- <a name="l01130"></a>01130
- <a name="l01131"></a>01131 <span class="keyword">if</span> ( x <= 0.0D+00 ) <span class="keyword">then</span>
- <a name="l01132"></a>01132 gamma = 0.0D+00
- <a name="l01133"></a>01133 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l01134"></a>01134 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'GAMMA - Fatal error!'</span>
- <a name="l01135"></a>01135 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' Input argument X <= 0.'</span>
- <a name="l01136"></a>01136 stop
- <a name="l01137"></a>01137 <span class="keyword">end if</span>
- <a name="l01138"></a>01138
- <a name="l01139"></a>01139 <span class="keyword">if</span> ( x >= 70.0D+00 ) <span class="keyword">then</span>
- <a name="l01140"></a>01140 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l01141"></a>01141 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'GAMMA - Fatal error!'</span>
- <a name="l01142"></a>01142 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' Input argument X >= 70.'</span>
- <a name="l01143"></a>01143 stop
- <a name="l01144"></a>01144 <span class="keyword">end if</span>
- <a name="l01145"></a>01145
- <a name="l01146"></a>01146 <span class="keyword">if</span> ( x == 1.0D+00 ) <span class="keyword">then</span>
- <a name="l01147"></a>01147 gamma = 1.0D+00
- <a name="l01148"></a>01148 return
- <a name="l01149"></a>01149 <span class="keyword">end if</span>
- <a name="l01150"></a>01150
- <a name="l01151"></a>01151 <span class="keyword">if</span> ( x <= 1.0D+00 ) <span class="keyword">then</span>
- <a name="l01152"></a>01152 gamma = gam ( x ) / x
- <a name="l01153"></a>01153 return
- <a name="l01154"></a>01154 <span class="keyword">end if</span>
- <a name="l01155"></a>01155
- <a name="l01156"></a>01156 z = x
- <a name="l01157"></a>01157
- <a name="l01158"></a>01158 za = 1.0D+00
- <a name="l01159"></a>01159
- <a name="l01160"></a>01160 <span class="keyword">do</span>
- <a name="l01161"></a>01161
- <a name="l01162"></a>01162 z = z - 1.0D+00
- <a name="l01163"></a>01163
- <a name="l01164"></a>01164 <span class="keyword">if</span> ( z < 1.0D+00 ) <span class="keyword">then</span>
- <a name="l01165"></a>01165 gamma = za * gam ( z )
- <a name="l01166"></a>01166 exit
- <a name="l01167"></a>01167 <span class="keyword">else</span> <span class="keyword">if</span> ( z == 1.0D+00 ) <span class="keyword">then</span>
- <a name="l01168"></a>01168 gamma = za
- <a name="l01169"></a>01169 exit
- <a name="l01170"></a>01170 <span class="keyword">end if</span>
- <a name="l01171"></a>01171
- <a name="l01172"></a>01172 za = za * z
- <a name="l01173"></a>01173
- <a name="l01174"></a>01174 <span class="keyword">end do</span>
- <a name="l01175"></a>01175
- <a name="l01176"></a>01176 return
- <a name="l01177"></a>01177 <span class="keyword">end</span>
- <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 )
- <a name="l01179"></a>01179 <span class="comment">!</span>
- <a name="l01180"></a>01180 <span class="comment">!*******************************************************************************</span>
- <a name="l01181"></a>01181 <span class="comment">!</span>
- <a name="l01182"></a>01182 <span class="comment">!! HERMITE_COM computes the abscissa and weights for Gauss-Hermite quadrature.</span>
- <a name="l01183"></a>01183 <span class="comment">!</span>
- <a name="l01184"></a>01184 <span class="comment">!</span>
- <a name="l01185"></a>01185 <span class="comment">! Discussion:</span>
- <a name="l01186"></a>01186 <span class="comment">!</span>
- <a name="l01187"></a>01187 <span class="comment">! The abscissas are the zeros of the N-th order Hermite polynomial.</span>
- <a name="l01188"></a>01188 <span class="comment">!</span>
- <a name="l01189"></a>01189 <span class="comment">! Integration interval:</span>
- <a name="l01190"></a>01190 <span class="comment">!</span>
- <a name="l01191"></a>01191 <span class="comment">! ( -Infinity, +Infinity )</span>
- <a name="l01192"></a>01192 <span class="comment">!</span>
- <a name="l01193"></a>01193 <span class="comment">! Weight function:</span>
- <a name="l01194"></a>01194 <span class="comment">!</span>
- <a name="l01195"></a>01195 <span class="comment">! EXP ( - X**2 )</span>
- <a name="l01196"></a>01196 <span class="comment">!</span>
- <a name="l01197"></a>01197 <span class="comment">! Integral to approximate:</span>
- <a name="l01198"></a>01198 <span class="comment">!</span>
- <a name="l01199"></a>01199 <span class="comment">! Integral ( -INFINITY < X < +INFINITY ) EXP ( - X**2 ) * F(X) dX</span>
- <a name="l01200"></a>01200 <span class="comment">!</span>
- <a name="l01201"></a>01201 <span class="comment">! Approximate integral:</span>
- <a name="l01202"></a>01202 <span class="comment">!</span>
- <a name="l01203"></a>01203 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l01204"></a>01204 <span class="comment">!</span>
- <a name="l01205"></a>01205 <span class="comment">! Reference:</span>
- <a name="l01206"></a>01206 <span class="comment">!</span>
- <a name="l01207"></a>01207 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l01208"></a>01208 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l01209"></a>01209 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l01210"></a>01210 <span class="comment">!</span>
- <a name="l01211"></a>01211 <span class="comment">! Modified:</span>
- <a name="l01212"></a>01212 <span class="comment">!</span>
- <a name="l01213"></a>01213 <span class="comment">! 19 September 1998</span>
- <a name="l01214"></a>01214 <span class="comment">!</span>
- <a name="l01215"></a>01215 <span class="comment">! Author:</span>
- <a name="l01216"></a>01216 <span class="comment">!</span>
- <a name="l01217"></a>01217 <span class="comment">! John Burkardt</span>
- <a name="l01218"></a>01218 <span class="comment">!</span>
- <a name="l01219"></a>01219 <span class="comment">! Parameters:</span>
- <a name="l01220"></a>01220 <span class="comment">!</span>
- <a name="l01221"></a>01221 <span class="comment">! Input, integer NORDER, the order of the formula to be computed.</span>
- <a name="l01222"></a>01222 <span class="comment">!</span>
- <a name="l01223"></a>01223 <span class="comment">! Output, double precision XTAB(NORDER), the Gauss-Hermite abscissas.</span>
- <a name="l01224"></a>01224 <span class="comment">!</span>
- <a name="l01225"></a>01225 <span class="comment">! Output, double precision WEIGHT(NORDER), the Gauss-Hermite weights.</span>
- <a name="l01226"></a>01226 <span class="comment">!</span>
- <a name="l01227"></a>01227 <span class="keyword">implicit none</span>
- <a name="l01228"></a>01228 <span class="comment">!</span>
- <a name="l01229"></a>01229 <span class="keywordtype">integer</span> norder
- <a name="l01230"></a>01230 <span class="comment">!</span>
- <a name="l01231"></a>01231 <span class="keywordtype">double precision</span> cc
- <a name="l01232"></a>01232 <span class="keywordtype">double precision</span> dp2
- <a name="l01233"></a>01233 <span class="keywordtype">double precision</span> gamma
- <a name="l01234"></a>01234 <span class="keywordtype">integer</span> i
- <a name="l01235"></a>01235 <span class="keywordtype">double precision</span> p1
- <a name="l01236"></a>01236 <span class="keywordtype">double precision</span> s
- <a name="l01237"></a>01237 <span class="keywordtype">double precision</span> temp
- <a name="l01238"></a>01238 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l01239"></a>01239 <span class="keywordtype">double precision</span> x
- <a name="l01240"></a>01240 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l01241"></a>01241 <span class="comment">!</span>
- <a name="l01242"></a>01242 cc = 1.7724538509D+00 * gamma ( dble ( norder ) ) / ( 2.0D+00**( norder - 1 ) )
- <a name="l01243"></a>01243
- <a name="l01244"></a>01244 s = ( 2.0D+00 * dble ( norder ) + 1.0D+00 )**( 1.0D+00 / 6.0D+00 )
- <a name="l01245"></a>01245
- <a name="l01246"></a>01246 <span class="keyword">do</span> i = 1, ( norder + 1 ) / 2
- <a name="l01247"></a>01247
- <a name="l01248"></a>01248 <span class="keyword">if</span> ( i == 1 ) <span class="keyword">then</span>
- <a name="l01249"></a>01249
- <a name="l01250"></a>01250 x = s**3 - 1.85575D+00 / s
- <a name="l01251"></a>01251
- <a name="l01252"></a>01252 <span class="keyword">else</span> <span class="keyword">if</span> ( i == 2 ) <span class="keyword">then</span>
- <a name="l01253"></a>01253
- <a name="l01254"></a>01254 x = x - 1.14D+00 * ( ( dble ( norder ) )**0.426D+00 ) / x
- <a name="l01255"></a>01255
- <a name="l01256"></a>01256 <span class="keyword">else</span> <span class="keyword">if</span> ( i == 3 ) <span class="keyword">then</span>
- <a name="l01257"></a>01257
- <a name="l01258"></a>01258 x = 1.86D+00 * x - 0.86D+00 * xtab(1)
- <a name="l01259"></a>01259
- <a name="l01260"></a>01260 <span class="keyword">else</span> <span class="keyword">if</span> ( i == 4 ) <span class="keyword">then</span>
- <a name="l01261"></a>01261
- <a name="l01262"></a>01262 x = 1.91D+00 * x - 0.91D+00 * xtab(2)
- <a name="l01263"></a>01263
- <a name="l01264"></a>01264 <span class="keyword">else</span>
- <a name="l01265"></a>01265
- <a name="l01266"></a>01266 x = 2.0D+00 * x - xtab(i-2)
- <a name="l01267"></a>01267
- <a name="l01268"></a>01268 <span class="keyword">end if</span>
- <a name="l01269"></a>01269
- <a name="l01270"></a>01270 call <a class="code" href="quadrule_8f90.html#ae9c37528989dee8bb6c51ff8a4626c05">hermite_root </a>( x, norder, dp2, p1 )
- <a name="l01271"></a>01271
- <a name="l01272"></a>01272 xtab(i) = x
- <a name="l01273"></a>01273 weight(i) = ( cc / dp2 ) / p1
- <a name="l01274"></a>01274
- <a name="l01275"></a>01275 xtab(norder-i+1) = - x
- <a name="l01276"></a>01276 weight(norder-i+1) = weight(i)
- <a name="l01277"></a>01277
- <a name="l01278"></a>01278 <span class="keyword">end do</span>
- <a name="l01279"></a>01279 <span class="comment">!</span>
- <a name="l01280"></a>01280 <span class="comment">! Reverse the order of the XTAB values.</span>
- <a name="l01281"></a>01281 <span class="comment">!</span>
- <a name="l01282"></a>01282 call <a class="code" href="quadrule_8f90.html#a7841cf442902dd98d08b6a4d89a9a7bf">dvec_reverse </a>( norder, xtab )
- <a name="l01283"></a>01283
- <a name="l01284"></a>01284 return
- <a name="l01285"></a>01285 <span class="keyword">end</span>
- <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 )
- <a name="l01287"></a>01287 <span class="comment">!</span>
- <a name="l01288"></a>01288 <span class="comment">!*******************************************************************************</span>
- <a name="l01289"></a>01289 <span class="comment">!</span>
- <a name="l01290"></a>01290 <span class="comment">!! HERMITE_RECUR finds the value and derivative of a Hermite polynomial.</span>
- <a name="l01291"></a>01291 <span class="comment">!</span>
- <a name="l01292"></a>01292 <span class="comment">!</span>
- <a name="l01293"></a>01293 <span class="comment">! Reference:</span>
- <a name="l01294"></a>01294 <span class="comment">!</span>
- <a name="l01295"></a>01295 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l01296"></a>01296 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l01297"></a>01297 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l01298"></a>01298 <span class="comment">!</span>
- <a name="l01299"></a>01299 <span class="comment">! Modified:</span>
- <a name="l01300"></a>01300 <span class="comment">!</span>
- <a name="l01301"></a>01301 <span class="comment">! 19 September 1998</span>
- <a name="l01302"></a>01302 <span class="comment">!</span>
- <a name="l01303"></a>01303 <span class="comment">! Parameters:</span>
- <a name="l01304"></a>01304 <span class="comment">!</span>
- <a name="l01305"></a>01305 <span class="comment">! Output, double precision P2, the value of H(NORDER)(X).</span>
- <a name="l01306"></a>01306 <span class="comment">!</span>
- <a name="l01307"></a>01307 <span class="comment">! Output, double precision DP2, the value of H'(NORDER)(X).</span>
- <a name="l01308"></a>01308 <span class="comment">!</span>
- <a name="l01309"></a>01309 <span class="comment">! Output, double precision P1, the value of H(NORDER-1)(X).</span>
- <a name="l01310"></a>01310 <span class="comment">!</span>
- <a name="l01311"></a>01311 <span class="comment">! Input, double precision X, the point at which polynomials are evaluated.</span>
- <a name="l01312"></a>01312 <span class="comment">!</span>
- <a name="l01313"></a>01313 <span class="comment">! Input, integer NORDER, the order of the polynomial to be computed.</span>
- <a name="l01314"></a>01314 <span class="comment">!</span>
- <a name="l01315"></a>01315 <span class="keyword">implicit none</span>
- <a name="l01316"></a>01316 <span class="comment">!</span>
- <a name="l01317"></a>01317 <span class="keywordtype">integer</span> i
- <a name="l01318"></a>01318 <span class="keywordtype">double precision</span> dp0
- <a name="l01319"></a>01319 <span class="keywordtype">double precision</span> dp1
- <a name="l01320"></a>01320 <span class="keywordtype">double precision</span> dp2
- <a name="l01321"></a>01321 <span class="keywordtype">integer</span> norder
- <a name="l01322"></a>01322 <span class="keywordtype">double precision</span> p0
- <a name="l01323"></a>01323 <span class="keywordtype">double precision</span> p1
- <a name="l01324"></a>01324 <span class="keywordtype">double precision</span> p2
- <a name="l01325"></a>01325 <span class="keywordtype">double precision</span> x
- <a name="l01326"></a>01326 <span class="comment">!</span>
- <a name="l01327"></a>01327 p1 = 1.0D+00
- <a name="l01328"></a>01328 dp1 = 0.0D+00
- <a name="l01329"></a>01329
- <a name="l01330"></a>01330 p2 = x
- <a name="l01331"></a>01331 dp2 = 1.0D+00
- <a name="l01332"></a>01332
- <a name="l01333"></a>01333 <span class="keyword">do</span> i = 2, norder
- <a name="l01334"></a>01334
- <a name="l01335"></a>01335 p0 = p1
- <a name="l01336"></a>01336 dp0 = dp1
- <a name="l01337"></a>01337
- <a name="l01338"></a>01338 p1 = p2
- <a name="l01339"></a>01339 dp1 = dp2
- <a name="l01340"></a>01340
- <a name="l01341"></a>01341 p2 = x * p1 - 0.5D+00 * ( dble ( i ) - 1.0D+00 ) * p0
- <a name="l01342"></a>01342 dp2 = x * dp1 + p1 - 0.5D+00 * ( dble ( i ) - 1.0D+00 ) * dp0
- <a name="l01343"></a>01343
- <a name="l01344"></a>01344 <span class="keyword">end do</span>
- <a name="l01345"></a>01345
- <a name="l01346"></a>01346 return
- <a name="l01347"></a>01347 <span class="keyword">end</span>
- <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 )
- <a name="l01349"></a>01349 <span class="comment">!</span>
- <a name="l01350"></a>01350 <span class="comment">!*******************************************************************************</span>
- <a name="l01351"></a>01351 <span class="comment">!</span>
- <a name="l01352"></a>01352 <span class="comment">!! HERMITE_ROOT improves an approximate root of a Hermite polynomial.</span>
- <a name="l01353"></a>01353 <span class="comment">!</span>
- <a name="l01354"></a>01354 <span class="comment">!</span>
- <a name="l01355"></a>01355 <span class="comment">! Reference:</span>
- <a name="l01356"></a>01356 <span class="comment">!</span>
- <a name="l01357"></a>01357 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l01358"></a>01358 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l01359"></a>01359 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l01360"></a>01360 <span class="comment">!</span>
- <a name="l01361"></a>01361 <span class="comment">! Modified:</span>
- <a name="l01362"></a>01362 <span class="comment">!</span>
- <a name="l01363"></a>01363 <span class="comment">! 19 September 1998</span>
- <a name="l01364"></a>01364 <span class="comment">!</span>
- <a name="l01365"></a>01365 <span class="comment">! Parameters:</span>
- <a name="l01366"></a>01366 <span class="comment">!</span>
- <a name="l01367"></a>01367 <span class="comment">! Input/output, double precision X, the approximate root, which</span>
- <a name="l01368"></a>01368 <span class="comment">! should be improved on output.</span>
- <a name="l01369"></a>01369 <span class="comment">!</span>
- <a name="l01370"></a>01370 <span class="comment">! Input, integer NORDER, the order of the Hermite polynomial.</span>
- <a name="l01371"></a>01371 <span class="comment">!</span>
- <a name="l01372"></a>01372 <span class="comment">! Output, double precision DP2, the value of H'(NORDER)(X).</span>
- <a name="l01373"></a>01373 <span class="comment">!</span>
- <a name="l01374"></a>01374 <span class="comment">! Output, double precision P1, the value of H(NORDER-1)(X).</span>
- <a name="l01375"></a>01375 <span class="comment">!</span>
- <a name="l01376"></a>01376 <span class="keyword">implicit none</span>
- <a name="l01377"></a>01377 <span class="comment">!</span>
- <a name="l01378"></a>01378 <span class="keywordtype">double precision</span> d
- <a name="l01379"></a>01379 <span class="keywordtype">double precision</span> dp2
- <a name="l01380"></a>01380 <span class="keywordtype">double precision</span>, <span class="keywordtype">parameter</span> :: eps = 1.0D-12
- <a name="l01381"></a>01381 <span class="keywordtype">integer</span> i
- <a name="l01382"></a>01382 <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxstep = 10
- <a name="l01383"></a>01383 <span class="keywordtype">integer</span> norder
- <a name="l01384"></a>01384 <span class="keywordtype">double precision</span> p1
- <a name="l01385"></a>01385 <span class="keywordtype">double precision</span> p2
- <a name="l01386"></a>01386 <span class="keywordtype">double precision</span> x
- <a name="l01387"></a>01387 <span class="comment">!</span>
- <a name="l01388"></a>01388 <span class="keyword">do</span> i = 1, maxstep
- <a name="l01389"></a>01389
- <a name="l01390"></a>01390 call <a class="code" href="quadrule_8f90.html#a837c192f4116548551a6c0b69465adbb">hermite_recur </a>( p2, dp2, p1, x, norder )
- <a name="l01391"></a>01391
- <a name="l01392"></a>01392 d = p2 / dp2
- <a name="l01393"></a>01393 x = x - d
- <a name="l01394"></a>01394
- <a name="l01395"></a>01395 <span class="keyword">if</span> ( abs ( d ) <= eps * ( abs ( x ) + 1.0D+00 ) ) <span class="keyword">then</span>
- <a name="l01396"></a>01396 return
- <a name="l01397"></a>01397 <span class="keyword">end if</span>
- <a name="l01398"></a>01398
- <a name="l01399"></a>01399 <span class="keyword">end do</span>
- <a name="l01400"></a>01400
- <a name="l01401"></a>01401 return
- <a name="l01402"></a>01402 <span class="keyword">end</span>
- <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 )
- <a name="l01404"></a>01404 <span class="comment">!</span>
- <a name="l01405"></a>01405 <span class="comment">!*******************************************************************************</span>
- <a name="l01406"></a>01406 <span class="comment">!</span>
- <a name="l01407"></a>01407 <span class="comment">!! HERMITE_SET sets abscissas and weights for Hermite quadrature.</span>
- <a name="l01408"></a>01408 <span class="comment">!</span>
- <a name="l01409"></a>01409 <span class="comment">!</span>
- <a name="l01410"></a>01410 <span class="comment">! Integration interval:</span>
- <a name="l01411"></a>01411 <span class="comment">!</span>
- <a name="l01412"></a>01412 <span class="comment">! ( -Infinity, +Infinity )</span>
- <a name="l01413"></a>01413 <span class="comment">!</span>
- <a name="l01414"></a>01414 <span class="comment">! Weight function:</span>
- <a name="l01415"></a>01415 <span class="comment">!</span>
- <a name="l01416"></a>01416 <span class="comment">! EXP ( - X**2 )</span>
- <a name="l01417"></a>01417 <span class="comment">!</span>
- <a name="l01418"></a>01418 <span class="comment">! Integral to approximate:</span>
- <a name="l01419"></a>01419 <span class="comment">!</span>
- <a name="l01420"></a>01420 <span class="comment">! Integral ( -INFINITY < X < +INFINITY ) EXP ( - X**2 ) * F(X) dX</span>
- <a name="l01421"></a>01421 <span class="comment">!</span>
- <a name="l01422"></a>01422 <span class="comment">! Approximate integral:</span>
- <a name="l01423"></a>01423 <span class="comment">!</span>
- <a name="l01424"></a>01424 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) ).</span>
- <a name="l01425"></a>01425 <span class="comment">!</span>
- <a name="l01426"></a>01426 <span class="comment">! Reference:</span>
- <a name="l01427"></a>01427 <span class="comment">!</span>
- <a name="l01428"></a>01428 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l01429"></a>01429 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l01430"></a>01430 <span class="comment">! National Bureau of Standards, 1964.</span>
- <a name="l01431"></a>01431 <span class="comment">!</span>
- <a name="l01432"></a>01432 <span class="comment">! Vladimir Krylov,</span>
- <a name="l01433"></a>01433 <span class="comment">! Approximate Calculation of Integrals,</span>
- <a name="l01434"></a>01434 <span class="comment">! MacMillan, 1962.</span>
- <a name="l01435"></a>01435 <span class="comment">!</span>
- <a name="l01436"></a>01436 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l01437"></a>01437 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l01438"></a>01438 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l01439"></a>01439 <span class="comment">!</span>
- <a name="l01440"></a>01440 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l01441"></a>01441 <span class="comment">! Standard Mathematical Tables and Formulae,</span>
- <a name="l01442"></a>01442 <span class="comment">! 30th Edition,</span>
- <a name="l01443"></a>01443 <span class="comment">! CRC Press, 1996.</span>
- <a name="l01444"></a>01444 <span class="comment">!</span>
- <a name="l01445"></a>01445 <span class="comment">! Modified:</span>
- <a name="l01446"></a>01446 <span class="comment">!</span>
- <a name="l01447"></a>01447 <span class="comment">! 06 December 2000</span>
- <a name="l01448"></a>01448 <span class="comment">!</span>
- <a name="l01449"></a>01449 <span class="comment">! Author:</span>
- <a name="l01450"></a>01450 <span class="comment">!</span>
- <a name="l01451"></a>01451 <span class="comment">! John Burkardt</span>
- <a name="l01452"></a>01452 <span class="comment">!</span>
- <a name="l01453"></a>01453 <span class="comment">! Parameters:</span>
- <a name="l01454"></a>01454 <span class="comment">!</span>
- <a name="l01455"></a>01455 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l01456"></a>01456 <span class="comment">! NORDER must be between 1 and 20, or one of the values</span>
- <a name="l01457"></a>01457 <span class="comment">! 30, 32, 40, 50, 60 or 64.</span>
- <a name="l01458"></a>01458 <span class="comment">!</span>
- <a name="l01459"></a>01459 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule,</span>
- <a name="l01460"></a>01460 <span class="comment">! which are symmetrically placed around 0.</span>
- <a name="l01461"></a>01461 <span class="comment">!</span>
- <a name="l01462"></a>01462 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l01463"></a>01463 <span class="comment">! The weights are positive and symmetric, and should sum</span>
- <a name="l01464"></a>01464 <span class="comment">! to SQRT(PI).</span>
- <a name="l01465"></a>01465 <span class="comment">!</span>
- <a name="l01466"></a>01466 <span class="keyword">implicit none</span>
- <a name="l01467"></a>01467 <span class="comment">!</span>
- <a name="l01468"></a>01468 <span class="keywordtype">integer</span> norder
- <a name="l01469"></a>01469 <span class="comment">!</span>
- <a name="l01470"></a>01470 <span class="keywordtype">double precision</span> d_pi
- <a name="l01471"></a>01471 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l01472"></a>01472 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l01473"></a>01473 <span class="comment">!</span>
- <a name="l01474"></a>01474 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l01475"></a>01475
- <a name="l01476"></a>01476 xtab(1) = 0.0D+00
- <a name="l01477"></a>01477
- <a name="l01478"></a>01478 weight(1) = sqrt ( d_pi ( ) )
- <a name="l01479"></a>01479
- <a name="l01480"></a>01480 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 )<span class="keyword">then</span>
- <a name="l01481"></a>01481
- <a name="l01482"></a>01482 xtab(1) = - 0.707106781186547524400844362105D+00
- <a name="l01483"></a>01483 xtab(2) = 0.707106781186547524400844362105D+00
- <a name="l01484"></a>01484
- <a name="l01485"></a>01485 weight(1) = 0.886226925452758013649083741671D+00
- <a name="l01486"></a>01486 weight(2) = 0.886226925452758013649083741671D+00
- <a name="l01487"></a>01487
- <a name="l01488"></a>01488 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l01489"></a>01489
- <a name="l01490"></a>01490 xtab(1) = - 0.122474487139158904909864203735D+01
- <a name="l01491"></a>01491 xtab(2) = 0.0D+00
- <a name="l01492"></a>01492 xtab(3) = 0.122474487139158904909864203735D+01
- <a name="l01493"></a>01493
- <a name="l01494"></a>01494 weight(1) = 0.295408975150919337883027913890D+00
- <a name="l01495"></a>01495 weight(2) = 0.118163590060367735153211165556D+01
- <a name="l01496"></a>01496 weight(3) = 0.295408975150919337883027913890D+00
- <a name="l01497"></a>01497
- <a name="l01498"></a>01498 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l01499"></a>01499
- <a name="l01500"></a>01500 xtab(1) = - 0.165068012388578455588334111112D+01
- <a name="l01501"></a>01501 xtab(2) = - 0.524647623275290317884060253835D+00
- <a name="l01502"></a>01502 xtab(3) = 0.524647623275290317884060253835D+00
- <a name="l01503"></a>01503 xtab(4) = 0.165068012388578455588334111112D+01
- <a name="l01504"></a>01504
- <a name="l01505"></a>01505 weight(1) = 0.813128354472451771430345571899D-01
- <a name="l01506"></a>01506 weight(2) = 0.804914090005512836506049184481D+00
- <a name="l01507"></a>01507 weight(3) = 0.804914090005512836506049184481D+00
- <a name="l01508"></a>01508 weight(4) = 0.813128354472451771430345571899D-01
- <a name="l01509"></a>01509
- <a name="l01510"></a>01510 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l01511"></a>01511
- <a name="l01512"></a>01512 xtab(1) = - 0.202018287045608563292872408814D+01
- <a name="l01513"></a>01513 xtab(2) = - 0.958572464613818507112770593893D+00
- <a name="l01514"></a>01514 xtab(3) = 0.0D+00
- <a name="l01515"></a>01515 xtab(4) = 0.958572464613818507112770593893D+00
- <a name="l01516"></a>01516 xtab(5) = 0.202018287045608563292872408814D+01
- <a name="l01517"></a>01517
- <a name="l01518"></a>01518 weight(1) = 0.199532420590459132077434585942D-01
- <a name="l01519"></a>01519 weight(2) = 0.393619323152241159828495620852D+00
- <a name="l01520"></a>01520 weight(3) = 0.945308720482941881225689324449D+00
- <a name="l01521"></a>01521 weight(4) = 0.393619323152241159828495620852D+00
- <a name="l01522"></a>01522 weight(5) = 0.199532420590459132077434585942D-01
- <a name="l01523"></a>01523
- <a name="l01524"></a>01524 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l01525"></a>01525
- <a name="l01526"></a>01526 xtab(1) = - 0.235060497367449222283392198706D+01
- <a name="l01527"></a>01527 xtab(2) = - 0.133584907401369694971489528297D+01
- <a name="l01528"></a>01528 xtab(3) = - 0.436077411927616508679215948251D+00
- <a name="l01529"></a>01529 xtab(4) = 0.436077411927616508679215948251D+00
- <a name="l01530"></a>01530 xtab(5) = 0.133584907401369694971489528297D+01
- <a name="l01531"></a>01531 xtab(6) = 0.235060497367449222283392198706D+01
- <a name="l01532"></a>01532
- <a name="l01533"></a>01533 weight(1) = 0.453000990550884564085747256463D-02
- <a name="l01534"></a>01534 weight(2) = 0.157067320322856643916311563508D+00
- <a name="l01535"></a>01535 weight(3) = 0.724629595224392524091914705598D+00
- <a name="l01536"></a>01536 weight(4) = 0.724629595224392524091914705598D+00
- <a name="l01537"></a>01537 weight(5) = 0.157067320322856643916311563508D+00
- <a name="l01538"></a>01538 weight(6) = 0.453000990550884564085747256463D-02
- <a name="l01539"></a>01539
- <a name="l01540"></a>01540 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l01541"></a>01541
- <a name="l01542"></a>01542 xtab(1) = - 0.265196135683523349244708200652D+01
- <a name="l01543"></a>01543 xtab(2) = - 0.167355162876747144503180139830D+01
- <a name="l01544"></a>01544 xtab(3) = - 0.816287882858964663038710959027D+00
- <a name="l01545"></a>01545 xtab(4) = 0.0D+00
- <a name="l01546"></a>01546 xtab(5) = 0.816287882858964663038710959027D+00
- <a name="l01547"></a>01547 xtab(6) = 0.167355162876747144503180139830D+01
- <a name="l01548"></a>01548 xtab(7) = 0.265196135683523349244708200652D+01
- <a name="l01549"></a>01549
- <a name="l01550"></a>01550 weight(1) = 0.971781245099519154149424255939D-03
- <a name="l01551"></a>01551 weight(2) = 0.545155828191270305921785688417D-01
- <a name="l01552"></a>01552 weight(3) = 0.425607252610127800520317466666D+00
- <a name="l01553"></a>01553 weight(4) = 0.810264617556807326764876563813D+00
- <a name="l01554"></a>01554 weight(5) = 0.425607252610127800520317466666D+00
- <a name="l01555"></a>01555 weight(6) = 0.545155828191270305921785688417D-01
- <a name="l01556"></a>01556 weight(7) = 0.971781245099519154149424255939D-03
- <a name="l01557"></a>01557
- <a name="l01558"></a>01558 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l01559"></a>01559
- <a name="l01560"></a>01560 xtab(1) = - 0.293063742025724401922350270524D+01
- <a name="l01561"></a>01561 xtab(2) = - 0.198165675669584292585463063977D+01
- <a name="l01562"></a>01562 xtab(3) = - 0.115719371244678019472076577906D+01
- <a name="l01563"></a>01563 xtab(4) = - 0.381186990207322116854718885584D+00
- <a name="l01564"></a>01564 xtab(5) = 0.381186990207322116854718885584D+00
- <a name="l01565"></a>01565 xtab(6) = 0.115719371244678019472076577906D+01
- <a name="l01566"></a>01566 xtab(7) = 0.198165675669584292585463063977D+01
- <a name="l01567"></a>01567 xtab(8) = 0.293063742025724401922350270524D+01
- <a name="l01568"></a>01568
- <a name="l01569"></a>01569 weight(1) = 0.199604072211367619206090452544D-03
- <a name="l01570"></a>01570 weight(2) = 0.170779830074134754562030564364D-01
- <a name="l01571"></a>01571 weight(3) = 0.207802325814891879543258620286D+00
- <a name="l01572"></a>01572 weight(4) = 0.661147012558241291030415974496D+00
- <a name="l01573"></a>01573 weight(5) = 0.661147012558241291030415974496D+00
- <a name="l01574"></a>01574 weight(6) = 0.207802325814891879543258620286D+00
- <a name="l01575"></a>01575 weight(7) = 0.170779830074134754562030564364D-01
- <a name="l01576"></a>01576 weight(8) = 0.199604072211367619206090452544D-03
- <a name="l01577"></a>01577
- <a name="l01578"></a>01578 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
- <a name="l01579"></a>01579
- <a name="l01580"></a>01580 xtab(1) = - 0.319099320178152760723004779538D+01
- <a name="l01581"></a>01581 xtab(2) = - 0.226658058453184311180209693284D+01
- <a name="l01582"></a>01582 xtab(3) = - 0.146855328921666793166701573925D+01
- <a name="l01583"></a>01583 xtab(4) = - 0.723551018752837573322639864579D+00
- <a name="l01584"></a>01584 xtab(5) = 0.0D+00
- <a name="l01585"></a>01585 xtab(6) = 0.723551018752837573322639864579D+00
- <a name="l01586"></a>01586 xtab(7) = 0.146855328921666793166701573925D+01
- <a name="l01587"></a>01587 xtab(8) = 0.226658058453184311180209693284D+01
- <a name="l01588"></a>01588 xtab(9) = 0.319099320178152760723004779538D+01
- <a name="l01589"></a>01589
- <a name="l01590"></a>01590 weight(1) = 0.396069772632643819045862946425D-04
- <a name="l01591"></a>01591 weight(2) = 0.494362427553694721722456597763D-02
- <a name="l01592"></a>01592 weight(3) = 0.884745273943765732879751147476D-01
- <a name="l01593"></a>01593 weight(4) = 0.432651559002555750199812112956D+00
- <a name="l01594"></a>01594 weight(5) = 0.720235215606050957124334723389D+00
- <a name="l01595"></a>01595 weight(6) = 0.432651559002555750199812112956D+00
- <a name="l01596"></a>01596 weight(7) = 0.884745273943765732879751147476D-01
- <a name="l01597"></a>01597 weight(8) = 0.494362427553694721722456597763D-02
- <a name="l01598"></a>01598 weight(9) = 0.396069772632643819045862946425D-04
- <a name="l01599"></a>01599
- <a name="l01600"></a>01600 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
- <a name="l01601"></a>01601
- <a name="l01602"></a>01602 xtab(1) = - 0.343615911883773760332672549432D+01
- <a name="l01603"></a>01603 xtab(2) = - 0.253273167423278979640896079775D+01
- <a name="l01604"></a>01604 xtab(3) = - 0.175668364929988177345140122011D+01
- <a name="l01605"></a>01605 xtab(4) = - 0.103661082978951365417749191676D+01
- <a name="l01606"></a>01606 xtab(5) = - 0.342901327223704608789165025557D+00
- <a name="l01607"></a>01607 xtab(6) = 0.342901327223704608789165025557D+00
- <a name="l01608"></a>01608 xtab(7) = 0.103661082978951365417749191676D+01
- <a name="l01609"></a>01609 xtab(8) = 0.175668364929988177345140122011D+01
- <a name="l01610"></a>01610 xtab(9) = 0.253273167423278979640896079775D+01
- <a name="l01611"></a>01611 xtab(10) = 0.343615911883773760332672549432D+01
- <a name="l01612"></a>01612
- <a name="l01613"></a>01613 weight(1) = 0.764043285523262062915936785960D-05
- <a name="l01614"></a>01614 weight(2) = 0.134364574678123269220156558585D-02
- <a name="l01615"></a>01615 weight(3) = 0.338743944554810631361647312776D-01
- <a name="l01616"></a>01616 weight(4) = 0.240138611082314686416523295006D+00
- <a name="l01617"></a>01617 weight(5) = 0.610862633735325798783564990433D+00
- <a name="l01618"></a>01618 weight(6) = 0.610862633735325798783564990433D+00
- <a name="l01619"></a>01619 weight(7) = 0.240138611082314686416523295006D+00
- <a name="l01620"></a>01620 weight(8) = 0.338743944554810631361647312776D-01
- <a name="l01621"></a>01621 weight(9) = 0.134364574678123269220156558585D-02
- <a name="l01622"></a>01622 weight(10) = 0.764043285523262062915936785960D-05
- <a name="l01623"></a>01623
- <a name="l01624"></a>01624 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 11 ) <span class="keyword">then</span>
- <a name="l01625"></a>01625
- <a name="l01626"></a>01626 xtab(1) = - 0.366847084655958251845837146485D+01
- <a name="l01627"></a>01627 xtab(2) = - 0.278329009978165177083671870152D+01
- <a name="l01628"></a>01628 xtab(3) = - 0.202594801582575533516591283121D+01
- <a name="l01629"></a>01629 xtab(4) = - 0.132655708449493285594973473558D+01
- <a name="l01630"></a>01630 xtab(5) = - 0.656809566882099765024611575383D+00
- <a name="l01631"></a>01631 xtab(6) = 0.0D+00
- <a name="l01632"></a>01632 xtab(7) = 0.656809566882099765024611575383D+00
- <a name="l01633"></a>01633 xtab(8) = 0.132655708449493285594973473558D+01
- <a name="l01634"></a>01634 xtab(9) = 0.202594801582575533516591283121D+01
- <a name="l01635"></a>01635 xtab(10) = 0.278329009978165177083671870152D+01
- <a name="l01636"></a>01636 xtab(11) = 0.366847084655958251845837146485D+01
- <a name="l01637"></a>01637
- <a name="l01638"></a>01638 weight(1) = 0.143956039371425822033088366032D-05
- <a name="l01639"></a>01639 weight(2) = 0.346819466323345510643413772940D-03
- <a name="l01640"></a>01640 weight(3) = 0.119113954449115324503874202916D-01
- <a name="l01641"></a>01641 weight(4) = 0.117227875167708503381788649308D+00
- <a name="l01642"></a>01642 weight(5) = 0.429359752356125028446073598601D+00
- <a name="l01643"></a>01643 weight(6) = 0.654759286914591779203940657627D+00
- <a name="l01644"></a>01644 weight(7) = 0.429359752356125028446073598601D+00
- <a name="l01645"></a>01645 weight(8) = 0.117227875167708503381788649308D+00
- <a name="l01646"></a>01646 weight(9) = 0.119113954449115324503874202916D-01
- <a name="l01647"></a>01647 weight(10) = 0.346819466323345510643413772940D-03
- <a name="l01648"></a>01648 weight(11) = 0.143956039371425822033088366032D-05
- <a name="l01649"></a>01649
- <a name="l01650"></a>01650 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 12 ) <span class="keyword">then</span>
- <a name="l01651"></a>01651
- <a name="l01652"></a>01652 xtab(1) = - 0.388972489786978191927164274724D+01
- <a name="l01653"></a>01653 xtab(2) = - 0.302063702512088977171067937518D+01
- <a name="l01654"></a>01654 xtab(3) = - 0.227950708050105990018772856942D+01
- <a name="l01655"></a>01655 xtab(4) = - 0.159768263515260479670966277090D+01
- <a name="l01656"></a>01656 xtab(5) = - 0.947788391240163743704578131060D+00
- <a name="l01657"></a>01657 xtab(6) = - 0.314240376254359111276611634095D+00
- <a name="l01658"></a>01658 xtab(7) = 0.314240376254359111276611634095D+00
- <a name="l01659"></a>01659 xtab(8) = 0.947788391240163743704578131060D+00
- <a name="l01660"></a>01660 xtab(9) = 0.159768263515260479670966277090D+01
- <a name="l01661"></a>01661 xtab(10) = 0.227950708050105990018772856942D+01
- <a name="l01662"></a>01662 xtab(11) = 0.302063702512088977171067937518D+01
- <a name="l01663"></a>01663 xtab(12) = 0.388972489786978191927164274724D+01
- <a name="l01664"></a>01664
- <a name="l01665"></a>01665 weight(1) = 0.265855168435630160602311400877D-06
- <a name="l01666"></a>01666 weight(2) = 0.857368704358785865456906323153D-04
- <a name="l01667"></a>01667 weight(3) = 0.390539058462906185999438432620D-02
- <a name="l01668"></a>01668 weight(4) = 0.516079856158839299918734423606D-01
- <a name="l01669"></a>01669 weight(5) = 0.260492310264161129233396139765D+00
- <a name="l01670"></a>01670 weight(6) = 0.570135236262479578347113482275D+00
- <a name="l01671"></a>01671 weight(7) = 0.570135236262479578347113482275D+00
- <a name="l01672"></a>01672 weight(8) = 0.260492310264161129233396139765D+00
- <a name="l01673"></a>01673 weight(9) = 0.516079856158839299918734423606D-01
- <a name="l01674"></a>01674 weight(10) = 0.390539058462906185999438432620D-02
- <a name="l01675"></a>01675 weight(11) = 0.857368704358785865456906323153D-04
- <a name="l01676"></a>01676 weight(12) = 0.265855168435630160602311400877D-06
- <a name="l01677"></a>01677
- <a name="l01678"></a>01678 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 13 ) <span class="keyword">then</span>
- <a name="l01679"></a>01679
- <a name="l01680"></a>01680 xtab(1) = - 0.410133759617863964117891508007D+01
- <a name="l01681"></a>01681 xtab(2) = - 0.324660897837240998812205115236D+01
- <a name="l01682"></a>01682 xtab(3) = - 0.251973568567823788343040913628D+01
- <a name="l01683"></a>01683 xtab(4) = - 0.185310765160151214200350644316D+01
- <a name="l01684"></a>01684 xtab(5) = - 0.122005503659074842622205526637D+01
- <a name="l01685"></a>01685 xtab(6) = - 0.605763879171060113080537108602D+00
- <a name="l01686"></a>01686 xtab(7) = 0.0D+00
- <a name="l01687"></a>01687 xtab(8) = 0.605763879171060113080537108602D+00
- <a name="l01688"></a>01688 xtab(9) = 0.122005503659074842622205526637D+01
- <a name="l01689"></a>01689 xtab(10) = 0.185310765160151214200350644316D+01
- <a name="l01690"></a>01690 xtab(11) = 0.251973568567823788343040913628D+01
- <a name="l01691"></a>01691 xtab(12) = 0.324660897837240998812205115236D+01
- <a name="l01692"></a>01692 xtab(13) = 0.410133759617863964117891508007D+01
- <a name="l01693"></a>01693
- <a name="l01694"></a>01694 weight(1) = 0.482573185007313108834997332342D-07
- <a name="l01695"></a>01695 weight(2) = 0.204303604027070731248669432937D-04
- <a name="l01696"></a>01696 weight(3) = 0.120745999271938594730924899224D-02
- <a name="l01697"></a>01697 weight(4) = 0.208627752961699392166033805050D-01
- <a name="l01698"></a>01698 weight(5) = 0.140323320687023437762792268873D+00
- <a name="l01699"></a>01699 weight(6) = 0.421616296898543221746893558568D+00
- <a name="l01700"></a>01700 weight(7) = 0.604393187921161642342099068579D+00
- <a name="l01701"></a>01701 weight(8) = 0.421616296898543221746893558568D+00
- <a name="l01702"></a>01702 weight(9) = 0.140323320687023437762792268873D+00
- <a name="l01703"></a>01703 weight(10) = 0.208627752961699392166033805050D-01
- <a name="l01704"></a>01704 weight(11) = 0.120745999271938594730924899224D-02
- <a name="l01705"></a>01705 weight(12) = 0.204303604027070731248669432937D-04
- <a name="l01706"></a>01706 weight(13) = 0.482573185007313108834997332342D-07
- <a name="l01707"></a>01707
- <a name="l01708"></a>01708 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 14 ) <span class="keyword">then</span>
- <a name="l01709"></a>01709
- <a name="l01710"></a>01710 xtab(1) = - 0.430444857047363181262129810037D+01
- <a name="l01711"></a>01711 xtab(2) = - 0.346265693360227055020891736115D+01
- <a name="l01712"></a>01712 xtab(3) = - 0.274847072498540256862499852415D+01
- <a name="l01713"></a>01713 xtab(4) = - 0.209518325850771681573497272630D+01
- <a name="l01714"></a>01714 xtab(5) = - 0.147668273114114087058350654421D+01
- <a name="l01715"></a>01715 xtab(6) = - 0.878713787329399416114679311861D+00
- <a name="l01716"></a>01716 xtab(7) = - 0.291745510672562078446113075799D+00
- <a name="l01717"></a>01717 xtab(8) = 0.291745510672562078446113075799D+00
- <a name="l01718"></a>01718 xtab(9) = 0.878713787329399416114679311861D+00
- <a name="l01719"></a>01719 xtab(10) = 0.147668273114114087058350654421D+01
- <a name="l01720"></a>01720 xtab(11) = 0.209518325850771681573497272630D+01
- <a name="l01721"></a>01721 xtab(12) = 0.274847072498540256862499852415D+01
- <a name="l01722"></a>01722 xtab(13) = 0.346265693360227055020891736115D+01
- <a name="l01723"></a>01723 xtab(14) = 0.430444857047363181262129810037D+01
- <a name="l01724"></a>01724
- <a name="l01725"></a>01725 weight(1) = 0.862859116812515794532041783429D-08
- <a name="l01726"></a>01726 weight(2) = 0.471648435501891674887688950105D-05
- <a name="l01727"></a>01727 weight(3) = 0.355092613551923610483661076691D-03
- <a name="l01728"></a>01728 weight(4) = 0.785005472645794431048644334608D-02
- <a name="l01729"></a>01729 weight(5) = 0.685055342234652055387163312367D-01
- <a name="l01730"></a>01730 weight(6) = 0.273105609064246603352569187026D+00
- <a name="l01731"></a>01731 weight(7) = 0.536405909712090149794921296776D+00
- <a name="l01732"></a>01732 weight(8) = 0.536405909712090149794921296776D+00
- <a name="l01733"></a>01733 weight(9) = 0.273105609064246603352569187026D+00
- <a name="l01734"></a>01734 weight(10) = 0.685055342234652055387163312367D-01
- <a name="l01735"></a>01735 weight(11) = 0.785005472645794431048644334608D-02
- <a name="l01736"></a>01736 weight(12) = 0.355092613551923610483661076691D-03
- <a name="l01737"></a>01737 weight(13) = 0.471648435501891674887688950105D-05
- <a name="l01738"></a>01738 weight(14) = 0.862859116812515794532041783429D-08
- <a name="l01739"></a>01739
- <a name="l01740"></a>01740 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
- <a name="l01741"></a>01741
- <a name="l01742"></a>01742 xtab(1) = - 0.449999070730939155366438053053D+01
- <a name="l01743"></a>01743 xtab(2) = - 0.366995037340445253472922383312D+01
- <a name="l01744"></a>01744 xtab(3) = - 0.296716692790560324848896036355D+01
- <a name="l01745"></a>01745 xtab(4) = - 0.232573248617385774545404479449D+01
- <a name="l01746"></a>01746 xtab(5) = - 0.171999257518648893241583152515D+01
- <a name="l01747"></a>01747 xtab(6) = - 0.113611558521092066631913490556D+01
- <a name="l01748"></a>01748 xtab(7) = - 0.565069583255575748526020337198D+00
- <a name="l01749"></a>01749 xtab(8) = 0.0D+00
- <a name="l01750"></a>01750 xtab(9) = 0.565069583255575748526020337198D+00
- <a name="l01751"></a>01751 xtab(10) = 0.113611558521092066631913490556D+01
- <a name="l01752"></a>01752 xtab(11) = 0.171999257518648893241583152515D+01
- <a name="l01753"></a>01753 xtab(12) = 0.232573248617385774545404479449D+01
- <a name="l01754"></a>01754 xtab(13) = 0.296716692790560324848896036355D+01
- <a name="l01755"></a>01755 xtab(14) = 0.366995037340445253472922383312D+01
- <a name="l01756"></a>01756 xtab(15) = 0.449999070730939155366438053053D+01
- <a name="l01757"></a>01757
- <a name="l01758"></a>01758 weight(1) = 0.152247580425351702016062666965D-08
- <a name="l01759"></a>01759 weight(2) = 0.105911554771106663577520791055D-05
- <a name="l01760"></a>01760 weight(3) = 0.100004441232499868127296736177D-03
- <a name="l01761"></a>01761 weight(4) = 0.277806884291277589607887049229D-02
- <a name="l01762"></a>01762 weight(5) = 0.307800338725460822286814158758D-01
- <a name="l01763"></a>01763 weight(6) = 0.158488915795935746883839384960D+00
- <a name="l01764"></a>01764 weight(7) = 0.412028687498898627025891079568D+00
- <a name="l01765"></a>01765 weight(8) = 0.564100308726417532852625797340D+00
- <a name="l01766"></a>01766 weight(9) = 0.412028687498898627025891079568D+00
- <a name="l01767"></a>01767 weight(10) = 0.158488915795935746883839384960D+00
- <a name="l01768"></a>01768 weight(11) = 0.307800338725460822286814158758D-01
- <a name="l01769"></a>01769 weight(12) = 0.277806884291277589607887049229D-02
- <a name="l01770"></a>01770 weight(13) = 0.100004441232499868127296736177D-03
- <a name="l01771"></a>01771 weight(14) = 0.105911554771106663577520791055D-05
- <a name="l01772"></a>01772 weight(15) = 0.152247580425351702016062666965D-08
- <a name="l01773"></a>01773
- <a name="l01774"></a>01774 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
- <a name="l01775"></a>01775
- <a name="l01776"></a>01776 xtab(1) = - 0.468873893930581836468849864875D+01
- <a name="l01777"></a>01777 xtab(2) = - 0.386944790486012269871942409801D+01
- <a name="l01778"></a>01778 xtab(3) = - 0.317699916197995602681399455926D+01
- <a name="l01779"></a>01779 xtab(4) = - 0.254620215784748136215932870545D+01
- <a name="l01780"></a>01780 xtab(5) = - 0.195178799091625397743465541496D+01
- <a name="l01781"></a>01781 xtab(6) = - 0.138025853919888079637208966969D+01
- <a name="l01782"></a>01782 xtab(7) = - 0.822951449144655892582454496734D+00
- <a name="l01783"></a>01783 xtab(8) = - 0.273481046138152452158280401965D+00
- <a name="l01784"></a>01784 xtab(9) = 0.273481046138152452158280401965D+00
- <a name="l01785"></a>01785 xtab(10) = 0.822951449144655892582454496734D+00
- <a name="l01786"></a>01786 xtab(11) = 0.138025853919888079637208966969D+01
- <a name="l01787"></a>01787 xtab(12) = 0.195178799091625397743465541496D+01
- <a name="l01788"></a>01788 xtab(13) = 0.254620215784748136215932870545D+01
- <a name="l01789"></a>01789 xtab(14) = 0.317699916197995602681399455926D+01
- <a name="l01790"></a>01790 xtab(15) = 0.386944790486012269871942409801D+01
- <a name="l01791"></a>01791 xtab(16) = 0.468873893930581836468849864875D+01
- <a name="l01792"></a>01792
- <a name="l01793"></a>01793 weight(1) = 0.265480747401118224470926366050D-09
- <a name="l01794"></a>01794 weight(2) = 0.232098084486521065338749423185D-06
- <a name="l01795"></a>01795 weight(3) = 0.271186009253788151201891432244D-04
- <a name="l01796"></a>01796 weight(4) = 0.932284008624180529914277305537D-03
- <a name="l01797"></a>01797 weight(5) = 0.128803115355099736834642999312D-01
- <a name="l01798"></a>01798 weight(6) = 0.838100413989858294154207349001D-01
- <a name="l01799"></a>01799 weight(7) = 0.280647458528533675369463335380D+00
- <a name="l01800"></a>01800 weight(8) = 0.507929479016613741913517341791D+00
- <a name="l01801"></a>01801 weight(9) = 0.507929479016613741913517341791D+00
- <a name="l01802"></a>01802 weight(10) = 0.280647458528533675369463335380D+00
- <a name="l01803"></a>01803 weight(11) = 0.838100413989858294154207349001D-01
- <a name="l01804"></a>01804 weight(12) = 0.128803115355099736834642999312D-01
- <a name="l01805"></a>01805 weight(13) = 0.932284008624180529914277305537D-03
- <a name="l01806"></a>01806 weight(14) = 0.271186009253788151201891432244D-04
- <a name="l01807"></a>01807 weight(15) = 0.232098084486521065338749423185D-06
- <a name="l01808"></a>01808 weight(16) = 0.265480747401118224470926366050D-09
- <a name="l01809"></a>01809
- <a name="l01810"></a>01810 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 17 ) <span class="keyword">then</span>
- <a name="l01811"></a>01811
- <a name="l01812"></a>01812 xtab(1) = - 0.487134519367440308834927655662D+01
- <a name="l01813"></a>01813 xtab(2) = - 0.406194667587547430689245559698D+01
- <a name="l01814"></a>01814 xtab(3) = - 0.337893209114149408338327069289D+01
- <a name="l01815"></a>01815 xtab(4) = - 0.275776291570388873092640349574D+01
- <a name="l01816"></a>01816 xtab(5) = - 0.217350282666662081927537907149D+01
- <a name="l01817"></a>01817 xtab(6) = - 0.161292431422123133311288254454D+01
- <a name="l01818"></a>01818 xtab(7) = - 0.106764872574345055363045773799D+01
- <a name="l01819"></a>01819 xtab(8) = - 0.531633001342654731349086553718D+00
- <a name="l01820"></a>01820 xtab(9) = 0.0D+00
- <a name="l01821"></a>01821 xtab(10) = 0.531633001342654731349086553718D+00
- <a name="l01822"></a>01822 xtab(11) = 0.106764872574345055363045773799D+01
- <a name="l01823"></a>01823 xtab(12) = 0.161292431422123133311288254454D+01
- <a name="l01824"></a>01824 xtab(13) = 0.217350282666662081927537907149D+01
- <a name="l01825"></a>01825 xtab(14) = 0.275776291570388873092640349574D+01
- <a name="l01826"></a>01826 xtab(15) = 0.337893209114149408338327069289D+01
- <a name="l01827"></a>01827 xtab(16) = 0.406194667587547430689245559698D+01
- <a name="l01828"></a>01828 xtab(17) = 0.487134519367440308834927655662D+01
- <a name="l01829"></a>01829
- <a name="l01830"></a>01830 weight(1) = 0.458057893079863330580889281222D-10
- <a name="l01831"></a>01831 weight(2) = 0.497707898163079405227863353715D-07
- <a name="l01832"></a>01832 weight(3) = 0.711228914002130958353327376218D-05
- <a name="l01833"></a>01833 weight(4) = 0.298643286697753041151336643059D-03
- <a name="l01834"></a>01834 weight(5) = 0.506734995762753791170069495879D-02
- <a name="l01835"></a>01835 weight(6) = 0.409200341495762798094994877854D-01
- <a name="l01836"></a>01836 weight(7) = 0.172648297670097079217645196219D+00
- <a name="l01837"></a>01837 weight(8) = 0.401826469470411956577635085257D+00
- <a name="l01838"></a>01838 weight(9) = 0.530917937624863560331883103379D+00
- <a name="l01839"></a>01839 weight(10) = 0.401826469470411956577635085257D+00
- <a name="l01840"></a>01840 weight(11) = 0.172648297670097079217645196219D+00
- <a name="l01841"></a>01841 weight(12) = 0.409200341495762798094994877854D-01
- <a name="l01842"></a>01842 weight(13) = 0.506734995762753791170069495879D-02
- <a name="l01843"></a>01843 weight(14) = 0.298643286697753041151336643059D-03
- <a name="l01844"></a>01844 weight(15) = 0.711228914002130958353327376218D-05
- <a name="l01845"></a>01845 weight(16) = 0.497707898163079405227863353715D-07
- <a name="l01846"></a>01846 weight(17) = 0.458057893079863330580889281222D-10
- <a name="l01847"></a>01847
- <a name="l01848"></a>01848 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 18 ) <span class="keyword">then</span>
- <a name="l01849"></a>01849
- <a name="l01850"></a>01850 xtab(1) = - 0.504836400887446676837203757885D+01
- <a name="l01851"></a>01851 xtab(2) = - 0.424811787356812646302342016090D+01
- <a name="l01852"></a>01852 xtab(3) = - 0.357376906848626607950067599377D+01
- <a name="l01853"></a>01853 xtab(4) = - 0.296137750553160684477863254906D+01
- <a name="l01854"></a>01854 xtab(5) = - 0.238629908916668600026459301424D+01
- <a name="l01855"></a>01855 xtab(6) = - 0.183553160426162889225383944409D+01
- <a name="l01856"></a>01856 xtab(7) = - 0.130092085838961736566626555439D+01
- <a name="l01857"></a>01857 xtab(8) = - 0.776682919267411661316659462284D+00
- <a name="l01858"></a>01858 xtab(9) = - 0.258267750519096759258116098711D+00
- <a name="l01859"></a>01859 xtab(10) = 0.258267750519096759258116098711D+00
- <a name="l01860"></a>01860 xtab(11) = 0.776682919267411661316659462284D+00
- <a name="l01861"></a>01861 xtab(12) = 0.130092085838961736566626555439D+01
- <a name="l01862"></a>01862 xtab(13) = 0.183553160426162889225383944409D+01
- <a name="l01863"></a>01863 xtab(14) = 0.238629908916668600026459301424D+01
- <a name="l01864"></a>01864 xtab(15) = 0.296137750553160684477863254906D+01
- <a name="l01865"></a>01865 xtab(16) = 0.357376906848626607950067599377D+01
- <a name="l01866"></a>01866 xtab(17) = 0.424811787356812646302342016090D+01
- <a name="l01867"></a>01867 xtab(18) = 0.504836400887446676837203757885D+01
- <a name="l01868"></a>01868
- <a name="l01869"></a>01869 weight(1) = 0.782819977211589102925147471012D-11
- <a name="l01870"></a>01870 weight(2) = 0.104672057957920824443559608435D-07
- <a name="l01871"></a>01871 weight(3) = 0.181065448109343040959702385911D-05
- <a name="l01872"></a>01872 weight(4) = 0.918112686792940352914675407371D-04
- <a name="l01873"></a>01873 weight(5) = 0.188852263026841789438175325426D-02
- <a name="l01874"></a>01874 weight(6) = 0.186400423875446519219315221973D-01
- <a name="l01875"></a>01875 weight(7) = 0.973017476413154293308537234155D-01
- <a name="l01876"></a>01876 weight(8) = 0.284807285669979578595606820713D+00
- <a name="l01877"></a>01877 weight(9) = 0.483495694725455552876410522141D+00
- <a name="l01878"></a>01878 weight(10) = 0.483495694725455552876410522141D+00
- <a name="l01879"></a>01879 weight(11) = 0.284807285669979578595606820713D+00
- <a name="l01880"></a>01880 weight(12) = 0.973017476413154293308537234155D-01
- <a name="l01881"></a>01881 weight(13) = 0.186400423875446519219315221973D-01
- <a name="l01882"></a>01882 weight(14) = 0.188852263026841789438175325426D-02
- <a name="l01883"></a>01883 weight(15) = 0.918112686792940352914675407371D-04
- <a name="l01884"></a>01884 weight(16) = 0.181065448109343040959702385911D-05
- <a name="l01885"></a>01885 weight(17) = 0.104672057957920824443559608435D-07
- <a name="l01886"></a>01886 weight(18) = 0.782819977211589102925147471012D-11
- <a name="l01887"></a>01887
- <a name="l01888"></a>01888 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 19 ) <span class="keyword">then</span>
- <a name="l01889"></a>01889
- <a name="l01890"></a>01890 xtab(1) = - 0.522027169053748216460967142500D+01
- <a name="l01891"></a>01891 xtab(2) = - 0.442853280660377943723498532226D+01
- <a name="l01892"></a>01892 xtab(3) = - 0.376218735196402009751489394104D+01
- <a name="l01893"></a>01893 xtab(4) = - 0.315784881834760228184318034120D+01
- <a name="l01894"></a>01894 xtab(5) = - 0.259113378979454256492128084112D+01
- <a name="l01895"></a>01895 xtab(6) = - 0.204923170985061937575050838669D+01
- <a name="l01896"></a>01896 xtab(7) = - 0.152417061939353303183354859367D+01
- <a name="l01897"></a>01897 xtab(8) = - 0.101036838713431135136859873726D+01
- <a name="l01898"></a>01898 xtab(9) = - 0.503520163423888209373811765050D+00
- <a name="l01899"></a>01899 xtab(10) = 0.0D+00
- <a name="l01900"></a>01900 xtab(11) = 0.503520163423888209373811765050D+00
- <a name="l01901"></a>01901 xtab(12) = 0.101036838713431135136859873726D+01
- <a name="l01902"></a>01902 xtab(13) = 0.152417061939353303183354859367D+01
- <a name="l01903"></a>01903 xtab(14) = 0.204923170985061937575050838669D+01
- <a name="l01904"></a>01904 xtab(15) = 0.259113378979454256492128084112D+01
- <a name="l01905"></a>01905 xtab(16) = 0.315784881834760228184318034120D+01
- <a name="l01906"></a>01906 xtab(17) = 0.376218735196402009751489394104D+01
- <a name="l01907"></a>01907 xtab(18) = 0.442853280660377943723498532226D+01
- <a name="l01908"></a>01908 xtab(19) = 0.522027169053748216460967142500D+01
- <a name="l01909"></a>01909
- <a name="l01910"></a>01910 weight(1) = 0.132629709449851575185289154385D-11
- <a name="l01911"></a>01911 weight(2) = 0.216305100986355475019693077221D-08
- <a name="l01912"></a>01912 weight(3) = 0.448824314722312295179447915594D-06
- <a name="l01913"></a>01913 weight(4) = 0.272091977631616257711941025214D-04
- <a name="l01914"></a>01914 weight(5) = 0.670877521407181106194696282100D-03
- <a name="l01915"></a>01915 weight(6) = 0.798886677772299020922211491861D-02
- <a name="l01916"></a>01916 weight(7) = 0.508103869090520673569908110358D-01
- <a name="l01917"></a>01917 weight(8) = 0.183632701306997074156148485766D+00
- <a name="l01918"></a>01918 weight(9) = 0.391608988613030244504042313621D+00
- <a name="l01919"></a>01919 weight(10) = 0.502974888276186530840731361096D+00
- <a name="l01920"></a>01920 weight(11) = 0.391608988613030244504042313621D+00
- <a name="l01921"></a>01921 weight(12) = 0.183632701306997074156148485766D+00
- <a name="l01922"></a>01922 weight(13) = 0.508103869090520673569908110358D-01
- <a name="l01923"></a>01923 weight(14) = 0.798886677772299020922211491861D-02
- <a name="l01924"></a>01924 weight(15) = 0.670877521407181106194696282100D-03
- <a name="l01925"></a>01925 weight(16) = 0.272091977631616257711941025214D-04
- <a name="l01926"></a>01926 weight(17) = 0.448824314722312295179447915594D-06
- <a name="l01927"></a>01927 weight(18) = 0.216305100986355475019693077221D-08
- <a name="l01928"></a>01928 weight(19) = 0.132629709449851575185289154385D-11
- <a name="l01929"></a>01929
- <a name="l01930"></a>01930 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 20 ) <span class="keyword">then</span>
- <a name="l01931"></a>01931
- <a name="l01932"></a>01932 xtab(1) = - 0.538748089001123286201690041068D+01
- <a name="l01933"></a>01933 xtab(2) = - 0.460368244955074427307767524898D+01
- <a name="l01934"></a>01934 xtab(3) = - 0.394476404011562521037562880052D+01
- <a name="l01935"></a>01935 xtab(4) = - 0.334785456738321632691492452300D+01
- <a name="l01936"></a>01936 xtab(5) = - 0.278880605842813048052503375640D+01
- <a name="l01937"></a>01937 xtab(6) = - 0.225497400208927552308233334473D+01
- <a name="l01938"></a>01938 xtab(7) = - 0.173853771211658620678086566214D+01
- <a name="l01939"></a>01939 xtab(8) = - 0.123407621539532300788581834696D+01
- <a name="l01940"></a>01940 xtab(9) = - 0.737473728545394358705605144252D+00
- <a name="l01941"></a>01941 xtab(10) = - 0.245340708300901249903836530634D+00
- <a name="l01942"></a>01942 xtab(11) = 0.245340708300901249903836530634D+00
- <a name="l01943"></a>01943 xtab(12) = 0.737473728545394358705605144252D+00
- <a name="l01944"></a>01944 xtab(13) = 0.123407621539532300788581834696D+01
- <a name="l01945"></a>01945 xtab(14) = 0.173853771211658620678086566214D+01
- <a name="l01946"></a>01946 xtab(15) = 0.225497400208927552308233334473D+01
- <a name="l01947"></a>01947 xtab(16) = 0.278880605842813048052503375640D+01
- <a name="l01948"></a>01948 xtab(17) = 0.334785456738321632691492452300D+01
- <a name="l01949"></a>01949 xtab(18) = 0.394476404011562521037562880052D+01
- <a name="l01950"></a>01950 xtab(19) = 0.460368244955074427307767524898D+01
- <a name="l01951"></a>01951 xtab(20) = 0.538748089001123286201690041068D+01
- <a name="l01952"></a>01952
- <a name="l01953"></a>01953 weight(1) = 0.222939364553415129252250061603D-12
- <a name="l01954"></a>01954 weight(2) = 0.439934099227318055362885145547D-09
- <a name="l01955"></a>01955 weight(3) = 0.108606937076928169399952456345D-06
- <a name="l01956"></a>01956 weight(4) = 0.780255647853206369414599199965D-05
- <a name="l01957"></a>01957 weight(5) = 0.228338636016353967257145917963D-03
- <a name="l01958"></a>01958 weight(6) = 0.324377334223786183218324713235D-02
- <a name="l01959"></a>01959 weight(7) = 0.248105208874636108821649525589D-01
- <a name="l01960"></a>01960 weight(8) = 0.109017206020023320013755033535D+00
- <a name="l01961"></a>01961 weight(9) = 0.286675505362834129719659706228D+00
- <a name="l01962"></a>01962 weight(10) = 0.462243669600610089650328639861D+00
- <a name="l01963"></a>01963 weight(11) = 0.462243669600610089650328639861D+00
- <a name="l01964"></a>01964 weight(12) = 0.286675505362834129719659706228D+00
- <a name="l01965"></a>01965 weight(13) = 0.109017206020023320013755033535D+00
- <a name="l01966"></a>01966 weight(14) = 0.248105208874636108821649525589D-01
- <a name="l01967"></a>01967 weight(15) = 0.324377334223786183218324713235D-02
- <a name="l01968"></a>01968 weight(16) = 0.228338636016353967257145917963D-03
- <a name="l01969"></a>01969 weight(17) = 0.780255647853206369414599199965D-05
- <a name="l01970"></a>01970 weight(18) = 0.108606937076928169399952456345D-06
- <a name="l01971"></a>01971 weight(19) = 0.439934099227318055362885145547D-09
- <a name="l01972"></a>01972 weight(20) = 0.222939364553415129252250061603D-12
- <a name="l01973"></a>01973
- <a name="l01974"></a>01974 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 30 ) <span class="keyword">then</span>
- <a name="l01975"></a>01975
- <a name="l01976"></a>01976 xtab( 1) = -6.86334529352989158106110835756D+00
- <a name="l01977"></a>01977 xtab( 2) = -6.13827922012393462039499237854D+00
- <a name="l01978"></a>01978 xtab( 3) = -5.53314715156749572511833355558D+00
- <a name="l01979"></a>01979 xtab( 4) = -4.98891896858994394448649710633D+00
- <a name="l01980"></a>01980 xtab( 5) = -4.48305535709251834188703761971D+00
- <a name="l01981"></a>01981 xtab( 6) = -4.00390860386122881522787601332D+00
- <a name="l01982"></a>01982 xtab( 7) = -3.54444387315534988692540090217D+00
- <a name="l01983"></a>01983 xtab( 8) = -3.09997052958644174868873332237D+00
- <a name="l01984"></a>01984 xtab( 9) = -2.66713212453561720057110646422D+00
- <a name="l01985"></a>01985 xtab(10) = -2.24339146776150407247297999483D+00
- <a name="l01986"></a>01986 xtab(11) = -1.82674114360368803883588048351D+00
- <a name="l01987"></a>01987 xtab(12) = -1.41552780019818851194072510555D+00
- <a name="l01988"></a>01988 xtab(13) = -1.00833827104672346180498960870D+00
- <a name="l01989"></a>01989 xtab(14) = -0.603921058625552307778155678757D+00
- <a name="l01990"></a>01990 xtab(15) = -0.201128576548871485545763013244D+00
- <a name="l01991"></a>01991 xtab(16) = 0.201128576548871485545763013244D+00
- <a name="l01992"></a>01992 xtab(17) = 0.603921058625552307778155678757D+00
- <a name="l01993"></a>01993 xtab(18) = 1.00833827104672346180498960870D+00
- <a name="l01994"></a>01994 xtab(19) = 1.41552780019818851194072510555D+00
- <a name="l01995"></a>01995 xtab(20) = 1.82674114360368803883588048351D+00
- <a name="l01996"></a>01996 xtab(21) = 2.24339146776150407247297999483D+00
- <a name="l01997"></a>01997 xtab(22) = 2.66713212453561720057110646422D+00
- <a name="l01998"></a>01998 xtab(23) = 3.09997052958644174868873332237D+00
- <a name="l01999"></a>01999 xtab(24) = 3.54444387315534988692540090217D+00
- <a name="l02000"></a>02000 xtab(25) = 4.00390860386122881522787601332D+00
- <a name="l02001"></a>02001 xtab(26) = 4.48305535709251834188703761971D+00
- <a name="l02002"></a>02002 xtab(27) = 4.98891896858994394448649710633D+00
- <a name="l02003"></a>02003 xtab(28) = 5.53314715156749572511833355558D+00
- <a name="l02004"></a>02004 xtab(29) = 6.13827922012393462039499237854D+00
- <a name="l02005"></a>02005 xtab(30) = 6.86334529352989158106110835756D+00
- <a name="l02006"></a>02006
- <a name="l02007"></a>02007 weight( 1) = 0.290825470013122622941102747365D-20
- <a name="l02008"></a>02008 weight( 2) = 0.281033360275090370876277491534D-16
- <a name="l02009"></a>02009 weight( 3) = 0.287860708054870606219239791142D-13
- <a name="l02010"></a>02010 weight( 4) = 0.810618629746304420399344796173D-11
- <a name="l02011"></a>02011 weight( 5) = 0.917858042437852820850075742492D-09
- <a name="l02012"></a>02012 weight( 6) = 0.510852245077594627738963204403D-07
- <a name="l02013"></a>02013 weight( 7) = 0.157909488732471028834638794022D-05
- <a name="l02014"></a>02014 weight( 8) = 0.293872522892298764150118423412D-04
- <a name="l02015"></a>02015 weight( 9) = 0.348310124318685523420995323183D-03
- <a name="l02016"></a>02016 weight(10) = 0.273792247306765846298942568953D-02
- <a name="l02017"></a>02017 weight(11) = 0.147038297048266835152773557787D-01
- <a name="l02018"></a>02018 weight(12) = 0.551441768702342511680754948183D-01
- <a name="l02019"></a>02019 weight(13) = 0.146735847540890099751693643152D+00
- <a name="l02020"></a>02020 weight(14) = 0.280130930839212667413493211293D+00
- <a name="l02021"></a>02021 weight(15) = 0.386394889541813862555601849165D+00
- <a name="l02022"></a>02022 weight(16) = 0.386394889541813862555601849165D+00
- <a name="l02023"></a>02023 weight(17) = 0.280130930839212667413493211293D+00
- <a name="l02024"></a>02024 weight(18) = 0.146735847540890099751693643152D+00
- <a name="l02025"></a>02025 weight(19) = 0.551441768702342511680754948183D-01
- <a name="l02026"></a>02026 weight(20) = 0.147038297048266835152773557787D-01
- <a name="l02027"></a>02027 weight(21) = 0.273792247306765846298942568953D-02
- <a name="l02028"></a>02028 weight(22) = 0.348310124318685523420995323183D-03
- <a name="l02029"></a>02029 weight(23) = 0.293872522892298764150118423412D-04
- <a name="l02030"></a>02030 weight(24) = 0.157909488732471028834638794022D-05
- <a name="l02031"></a>02031 weight(25) = 0.510852245077594627738963204403D-07
- <a name="l02032"></a>02032 weight(26) = 0.917858042437852820850075742492D-09
- <a name="l02033"></a>02033 weight(27) = 0.810618629746304420399344796173D-11
- <a name="l02034"></a>02034 weight(28) = 0.287860708054870606219239791142D-13
- <a name="l02035"></a>02035 weight(29) = 0.281033360275090370876277491534D-16
- <a name="l02036"></a>02036 weight(30) = 0.290825470013122622941102747365D-20
- <a name="l02037"></a>02037
- <a name="l02038"></a>02038 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 32 ) <span class="keyword">then</span>
- <a name="l02039"></a>02039
- <a name="l02040"></a>02040 xtab( 1) = -7.12581390983D+00
- <a name="l02041"></a>02041 xtab( 2) = -6.40949814927D+00
- <a name="l02042"></a>02042 xtab( 3) = -5.81222594952D+00
- <a name="l02043"></a>02043 xtab( 4) = -5.27555098652D+00
- <a name="l02044"></a>02044 xtab( 5) = -4.77716450350D+00
- <a name="l02045"></a>02045 xtab( 6) = -4.30554795335D+00
- <a name="l02046"></a>02046 xtab( 7) = -3.85375548547D+00
- <a name="l02047"></a>02047 xtab( 8) = -3.41716749282D+00
- <a name="l02048"></a>02048 xtab( 9) = -2.99249082500D+00
- <a name="l02049"></a>02049 xtab(10) = -2.57724953773D+00
- <a name="l02050"></a>02050 xtab(11) = -2.16949918361D+00
- <a name="l02051"></a>02051 xtab(12) = -1.76765410946D+00
- <a name="l02052"></a>02052 xtab(13) = -1.37037641095D+00
- <a name="l02053"></a>02053 xtab(14) = -0.976500463590D+00
- <a name="l02054"></a>02054 xtab(15) = -0.584978765436D+00
- <a name="l02055"></a>02055 xtab(16) = -0.194840741569D+00
- <a name="l02056"></a>02056 xtab(17) = 0.194840741569D+00
- <a name="l02057"></a>02057 xtab(18) = 0.584978765436D+00
- <a name="l02058"></a>02058 xtab(19) = 0.976500463590D+00
- <a name="l02059"></a>02059 xtab(20) = 1.37037641095D+00
- <a name="l02060"></a>02060 xtab(21) = 1.76765410946D+00
- <a name="l02061"></a>02061 xtab(22) = 2.16949918361D+00
- <a name="l02062"></a>02062 xtab(23) = 2.57724953773D+00
- <a name="l02063"></a>02063 xtab(24) = 2.99249082500D+00
- <a name="l02064"></a>02064 xtab(25) = 3.41716749282D+00
- <a name="l02065"></a>02065 xtab(26) = 3.85375548547D+00
- <a name="l02066"></a>02066 xtab(27) = 4.30554795335D+00
- <a name="l02067"></a>02067 xtab(28) = 4.77716450350D+00
- <a name="l02068"></a>02068 xtab(29) = 5.27555098652D+00
- <a name="l02069"></a>02069 xtab(30) = 5.81222594952D+00
- <a name="l02070"></a>02070 xtab(31) = 6.40949814927D+00
- <a name="l02071"></a>02071 xtab(32) = 7.12581390983D+00
- <a name="l02072"></a>02072
- <a name="l02073"></a>02073 weight( 1) = 0.731067642736D-22
- <a name="l02074"></a>02074 weight( 2) = 0.923173653649D-18
- <a name="l02075"></a>02075 weight( 3) = 0.119734401709D-14
- <a name="l02076"></a>02076 weight( 4) = 0.421501021125D-12
- <a name="l02077"></a>02077 weight( 5) = 0.593329146300D-10
- <a name="l02078"></a>02078 weight( 6) = 0.409883216476D-08
- <a name="l02079"></a>02079 weight( 7) = 0.157416779254D-06
- <a name="l02080"></a>02080 weight( 8) = 0.365058512955D-05
- <a name="l02081"></a>02081 weight( 9) = 0.541658406172D-04
- <a name="l02082"></a>02082 weight(10) = 0.536268365526D-03
- <a name="l02083"></a>02083 weight(11) = 0.365489032664D-02
- <a name="l02084"></a>02084 weight(12) = 0.175534288315D-01
- <a name="l02085"></a>02085 weight(13) = 0.604581309557D-01
- <a name="l02086"></a>02086 weight(14) = 0.151269734076D+00
- <a name="l02087"></a>02087 weight(15) = 0.277458142302D+00
- <a name="l02088"></a>02088 weight(16) = 0.375238352592D+00
- <a name="l02089"></a>02089 weight(17) = 0.375238352592D+00
- <a name="l02090"></a>02090 weight(18) = 0.277458142302D+00
- <a name="l02091"></a>02091 weight(19) = 0.151269734076D+00
- <a name="l02092"></a>02092 weight(20) = 0.604581309557D-01
- <a name="l02093"></a>02093 weight(21) = 0.175534288315D-01
- <a name="l02094"></a>02094 weight(22) = 0.365489032664D-02
- <a name="l02095"></a>02095 weight(23) = 0.536268365526D-03
- <a name="l02096"></a>02096 weight(24) = 0.541658406172D-04
- <a name="l02097"></a>02097 weight(25) = 0.365058512955D-05
- <a name="l02098"></a>02098 weight(26) = 0.157416779254D-06
- <a name="l02099"></a>02099 weight(27) = 0.409883216476D-08
- <a name="l02100"></a>02100 weight(28) = 0.593329146300D-10
- <a name="l02101"></a>02101 weight(29) = 0.421501021125D-12
- <a name="l02102"></a>02102 weight(30) = 0.119734401709D-14
- <a name="l02103"></a>02103 weight(31) = 0.923173653649D-18
- <a name="l02104"></a>02104 weight(32) = 0.731067642736D-22
- <a name="l02105"></a>02105
- <a name="l02106"></a>02106 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 40 ) <span class="keyword">then</span>
- <a name="l02107"></a>02107
- <a name="l02108"></a>02108 xtab( 1) = -8.09876113925D+00
- <a name="l02109"></a>02109 xtab( 2) = -7.41158253149D+00
- <a name="l02110"></a>02110 xtab( 3) = -6.84023730525D+00
- <a name="l02111"></a>02111 xtab( 4) = -6.32825535122D+00
- <a name="l02112"></a>02112 xtab( 5) = -5.85409505603D+00
- <a name="l02113"></a>02113 xtab( 6) = -5.40665424797D+00
- <a name="l02114"></a>02114 xtab( 7) = -4.97926097855D+00
- <a name="l02115"></a>02115 xtab( 8) = -4.56750207284D+00
- <a name="l02116"></a>02116 xtab( 9) = -4.16825706683D+00
- <a name="l02117"></a>02117 xtab(10) = -3.77920675344D+00
- <a name="l02118"></a>02118 xtab(11) = -3.39855826586D+00
- <a name="l02119"></a>02119 xtab(12) = -3.02487988390D+00
- <a name="l02120"></a>02120 xtab(13) = -2.65699599844D+00
- <a name="l02121"></a>02121 xtab(14) = -2.29391714188D+00
- <a name="l02122"></a>02122 xtab(15) = -1.93479147228D+00
- <a name="l02123"></a>02123 xtab(16) = -1.57886989493D+00
- <a name="l02124"></a>02124 xtab(17) = -1.22548010905D+00
- <a name="l02125"></a>02125 xtab(18) = -0.874006612357D+00
- <a name="l02126"></a>02126 xtab(19) = -0.523874713832D+00
- <a name="l02127"></a>02127 xtab(20) = -0.174537214598D+00
- <a name="l02128"></a>02128 xtab(21) = 0.174537214598D+00
- <a name="l02129"></a>02129 xtab(22) = 0.523874713832D+00
- <a name="l02130"></a>02130 xtab(23) = 0.874006612357D+00
- <a name="l02131"></a>02131 xtab(24) = 1.22548010905D+00
- <a name="l02132"></a>02132 xtab(25) = 1.57886989493D+00
- <a name="l02133"></a>02133 xtab(26) = 1.93479147228D+00
- <a name="l02134"></a>02134 xtab(27) = 2.29391714188D+00
- <a name="l02135"></a>02135 xtab(28) = 2.65699599844D+00
- <a name="l02136"></a>02136 xtab(29) = 3.02487988390D+00
- <a name="l02137"></a>02137 xtab(30) = 3.39855826586D+00
- <a name="l02138"></a>02138 xtab(31) = 3.77920675344D+00
- <a name="l02139"></a>02139 xtab(32) = 4.16825706683D+00
- <a name="l02140"></a>02140 xtab(33) = 4.56750207284D+00
- <a name="l02141"></a>02141 xtab(34) = 4.97926097855D+00
- <a name="l02142"></a>02142 xtab(35) = 5.40665424797D+00
- <a name="l02143"></a>02143 xtab(36) = 5.85409505603D+00
- <a name="l02144"></a>02144 xtab(37) = 6.32825535122D+00
- <a name="l02145"></a>02145 xtab(38) = 6.84023730525D+00
- <a name="l02146"></a>02146 xtab(39) = 7.41158253149D+00
- <a name="l02147"></a>02147 xtab(40) = 8.09876113925D+00
- <a name="l02148"></a>02148
- <a name="l02149"></a>02149 weight( 1) = 0.259104371384D-28
- <a name="l02150"></a>02150 weight( 2) = 0.854405696375D-24
- <a name="l02151"></a>02151 weight( 3) = 0.256759336540D-20
- <a name="l02152"></a>02152 weight( 4) = 0.198918101211D-17
- <a name="l02153"></a>02153 weight( 5) = 0.600835878947D-15
- <a name="l02154"></a>02154 weight( 6) = 0.880570764518D-13
- <a name="l02155"></a>02155 weight( 7) = 0.715652805267D-11
- <a name="l02156"></a>02156 weight( 8) = 0.352562079135D-09
- <a name="l02157"></a>02157 weight( 9) = 0.112123608322D-07
- <a name="l02158"></a>02158 weight(10) = 0.241114416359D-06
- <a name="l02159"></a>02159 weight(11) = 0.363157615067D-05
- <a name="l02160"></a>02160 weight(12) = 0.393693398108D-04
- <a name="l02161"></a>02161 weight(13) = 0.313853594540D-03
- <a name="l02162"></a>02162 weight(14) = 0.187149682959D-02
- <a name="l02163"></a>02163 weight(15) = 0.846088800823D-02
- <a name="l02164"></a>02164 weight(16) = 0.293125655361D-01
- <a name="l02165"></a>02165 weight(17) = 0.784746058652D-01
- <a name="l02166"></a>02166 weight(18) = 0.163378732713D+00
- <a name="l02167"></a>02167 weight(19) = 0.265728251876D+00
- <a name="l02168"></a>02168 weight(20) = 0.338643277425D+00
- <a name="l02169"></a>02169 weight(21) = 0.338643277425D+00
- <a name="l02170"></a>02170 weight(22) = 0.265728251876D+00
- <a name="l02171"></a>02171 weight(23) = 0.163378732713D+00
- <a name="l02172"></a>02172 weight(24) = 0.784746058652D-01
- <a name="l02173"></a>02173 weight(25) = 0.293125655361D-01
- <a name="l02174"></a>02174 weight(26) = 0.846088800823D-02
- <a name="l02175"></a>02175 weight(27) = 0.187149682959D-02
- <a name="l02176"></a>02176 weight(28) = 0.313853594540D-03
- <a name="l02177"></a>02177 weight(29) = 0.393693398108D-04
- <a name="l02178"></a>02178 weight(30) = 0.363157615067D-05
- <a name="l02179"></a>02179 weight(31) = 0.241114416359D-06
- <a name="l02180"></a>02180 weight(32) = 0.112123608322D-07
- <a name="l02181"></a>02181 weight(33) = 0.352562079135D-09
- <a name="l02182"></a>02182 weight(34) = 0.715652805267D-11
- <a name="l02183"></a>02183 weight(35) = 0.880570764518D-13
- <a name="l02184"></a>02184 weight(36) = 0.600835878947D-15
- <a name="l02185"></a>02185 weight(37) = 0.198918101211D-17
- <a name="l02186"></a>02186 weight(38) = 0.256759336540D-20
- <a name="l02187"></a>02187 weight(39) = 0.854405696375D-24
- <a name="l02188"></a>02188 weight(40) = 0.259104371384D-28
- <a name="l02189"></a>02189
- <a name="l02190"></a>02190 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 50 ) <span class="keyword">then</span>
- <a name="l02191"></a>02191
- <a name="l02192"></a>02192 xtab( 1) = -9.18240695813D+00
- <a name="l02193"></a>02193 xtab( 2) = -8.52277103092D+00
- <a name="l02194"></a>02194 xtab( 3) = -7.97562236821D+00
- <a name="l02195"></a>02195 xtab( 4) = -7.48640942986D+00
- <a name="l02196"></a>02196 xtab( 5) = -7.03432350977D+00
- <a name="l02197"></a>02197 xtab( 6) = -6.60864797386D+00
- <a name="l02198"></a>02198 xtab( 7) = -6.20295251927D+00
- <a name="l02199"></a>02199 xtab( 8) = -5.81299467542D+00
- <a name="l02200"></a>02200 xtab( 9) = -5.43578608722D+00
- <a name="l02201"></a>02201 xtab(10) = -5.06911758492D+00
- <a name="l02202"></a>02202 xtab(11) = -4.71129366617D+00
- <a name="l02203"></a>02203 xtab(12) = -4.36097316045D+00
- <a name="l02204"></a>02204 xtab(13) = -4.01706817286D+00
- <a name="l02205"></a>02205 xtab(14) = -3.67867706252D+00
- <a name="l02206"></a>02206 xtab(15) = -3.34503831394D+00
- <a name="l02207"></a>02207 xtab(16) = -3.01549776957D+00
- <a name="l02208"></a>02208 xtab(17) = -2.68948470227D+00
- <a name="l02209"></a>02209 xtab(18) = -2.36649390430D+00
- <a name="l02210"></a>02210 xtab(19) = -2.04607196869D+00
- <a name="l02211"></a>02211 xtab(20) = -1.72780654752D+00
- <a name="l02212"></a>02212 xtab(21) = -1.41131775490D+00
- <a name="l02213"></a>02213 xtab(22) = -1.09625112896D+00
- <a name="l02214"></a>02214 xtab(23) = -0.782271729555D+00
- <a name="l02215"></a>02215 xtab(24) = -0.469059056678D+00
- <a name="l02216"></a>02216 xtab(25) = -0.156302546889D+00
- <a name="l02217"></a>02217 xtab(26) = 0.156302546889D+00
- <a name="l02218"></a>02218 xtab(27) = 0.469059056678D+00
- <a name="l02219"></a>02219 xtab(28) = 0.782271729555D+00
- <a name="l02220"></a>02220 xtab(29) = 1.09625112896D+00
- <a name="l02221"></a>02221 xtab(30) = 1.41131775490D+00
- <a name="l02222"></a>02222 xtab(31) = 1.72780654752D+00
- <a name="l02223"></a>02223 xtab(32) = 2.04607196869D+00
- <a name="l02224"></a>02224 xtab(33) = 2.36649390430D+00
- <a name="l02225"></a>02225 xtab(34) = 2.68948470227D+00
- <a name="l02226"></a>02226 xtab(35) = 3.01549776957D+00
- <a name="l02227"></a>02227 xtab(36) = 3.34503831394D+00
- <a name="l02228"></a>02228 xtab(37) = 3.67867706252D+00
- <a name="l02229"></a>02229 xtab(38) = 4.01706817286D+00
- <a name="l02230"></a>02230 xtab(39) = 4.36097316045D+00
- <a name="l02231"></a>02231 xtab(40) = 4.71129366617D+00
- <a name="l02232"></a>02232 xtab(41) = 5.06911758492D+00
- <a name="l02233"></a>02233 xtab(42) = 5.43578608722D+00
- <a name="l02234"></a>02234 xtab(43) = 5.81299467542D+00
- <a name="l02235"></a>02235 xtab(44) = 6.20295251927D+00
- <a name="l02236"></a>02236 xtab(45) = 6.60864797386D+00
- <a name="l02237"></a>02237 xtab(46) = 7.03432350977D+00
- <a name="l02238"></a>02238 xtab(47) = 7.48640942986D+00
- <a name="l02239"></a>02239 xtab(48) = 7.97562236821D+00
- <a name="l02240"></a>02240 xtab(49) = 8.52277103092D+00
- <a name="l02241"></a>02241 xtab(50) = 9.18240695813D+00
- <a name="l02242"></a>02242
- <a name="l02243"></a>02243 weight( 1) = 0.183379404857D-36
- <a name="l02244"></a>02244 weight( 2) = 0.167380166790D-31
- <a name="l02245"></a>02245 weight( 3) = 0.121524412340D-27
- <a name="l02246"></a>02246 weight( 4) = 0.213765830835D-24
- <a name="l02247"></a>02247 weight( 5) = 0.141709359957D-21
- <a name="l02248"></a>02248 weight( 6) = 0.447098436530D-19
- <a name="l02249"></a>02249 weight( 7) = 0.774238295702D-17
- <a name="l02250"></a>02250 weight( 8) = 0.809426189344D-15
- <a name="l02251"></a>02251 weight( 9) = 0.546594403180D-13
- <a name="l02252"></a>02252 weight(10) = 0.250665552389D-11
- <a name="l02253"></a>02253 weight(11) = 0.811187736448D-10
- <a name="l02254"></a>02254 weight(12) = 0.190904054379D-08
- <a name="l02255"></a>02255 weight(13) = 0.334679340401D-07
- <a name="l02256"></a>02256 weight(14) = 0.445702996680D-06
- <a name="l02257"></a>02257 weight(15) = 0.458168270794D-05
- <a name="l02258"></a>02258 weight(16) = 0.368401905377D-04
- <a name="l02259"></a>02259 weight(17) = 0.234269892109D-03
- <a name="l02260"></a>02260 weight(18) = 0.118901178175D-02
- <a name="l02261"></a>02261 weight(19) = 0.485326382616D-02
- <a name="l02262"></a>02262 weight(20) = 0.160319410684D-01
- <a name="l02263"></a>02263 weight(21) = 0.430791591566D-01
- <a name="l02264"></a>02264 weight(22) = 0.945489354768D-01
- <a name="l02265"></a>02265 weight(23) = 0.170032455676D+00
- <a name="l02266"></a>02266 weight(24) = 0.251130856331D+00
- <a name="l02267"></a>02267 weight(25) = 0.305085129203D+00
- <a name="l02268"></a>02268 weight(26) = 0.305085129203D+00
- <a name="l02269"></a>02269 weight(27) = 0.251130856331D+00
- <a name="l02270"></a>02270 weight(28) = 0.170032455676D+00
- <a name="l02271"></a>02271 weight(29) = 0.945489354768D-01
- <a name="l02272"></a>02272 weight(30) = 0.430791591566D-01
- <a name="l02273"></a>02273 weight(31) = 0.160319410684D-01
- <a name="l02274"></a>02274 weight(32) = 0.485326382616D-02
- <a name="l02275"></a>02275 weight(33) = 0.118901178175D-02
- <a name="l02276"></a>02276 weight(34) = 0.234269892109D-03
- <a name="l02277"></a>02277 weight(35) = 0.368401905377D-04
- <a name="l02278"></a>02278 weight(36) = 0.458168270794D-05
- <a name="l02279"></a>02279 weight(37) = 0.445702996680D-06
- <a name="l02280"></a>02280 weight(38) = 0.334679340401D-07
- <a name="l02281"></a>02281 weight(39) = 0.190904054379D-08
- <a name="l02282"></a>02282 weight(40) = 0.811187736448D-10
- <a name="l02283"></a>02283 weight(41) = 0.250665552389D-11
- <a name="l02284"></a>02284 weight(42) = 0.546594403180D-13
- <a name="l02285"></a>02285 weight(43) = 0.809426189344D-15
- <a name="l02286"></a>02286 weight(44) = 0.774238295702D-17
- <a name="l02287"></a>02287 weight(45) = 0.447098436530D-19
- <a name="l02288"></a>02288 weight(46) = 0.141709359957D-21
- <a name="l02289"></a>02289 weight(47) = 0.213765830835D-24
- <a name="l02290"></a>02290 weight(48) = 0.121524412340D-27
- <a name="l02291"></a>02291 weight(49) = 0.167380166790D-31
- <a name="l02292"></a>02292 weight(50) = 0.183379404857D-36
- <a name="l02293"></a>02293
- <a name="l02294"></a>02294 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 60 ) <span class="keyword">then</span>
- <a name="l02295"></a>02295
- <a name="l02296"></a>02296 xtab( 1) = -10.1591092462D+00
- <a name="l02297"></a>02297 xtab( 2) = -9.52090367701D+00
- <a name="l02298"></a>02298 xtab( 3) = -8.99239800140D+00
- <a name="l02299"></a>02299 xtab( 4) = -8.52056928412D+00
- <a name="l02300"></a>02300 xtab( 5) = -8.08518865425D+00
- <a name="l02301"></a>02301 xtab( 6) = -7.67583993750D+00
- <a name="l02302"></a>02302 xtab( 7) = -7.28627659440D+00
- <a name="l02303"></a>02303 xtab( 8) = -6.91238153219D+00
- <a name="l02304"></a>02304 xtab( 9) = -6.55125916706D+00
- <a name="l02305"></a>02305 xtab(10) = -6.20077355799D+00
- <a name="l02306"></a>02306 xtab(11) = -5.85929019639D+00
- <a name="l02307"></a>02307 xtab(12) = -5.52552108614D+00
- <a name="l02308"></a>02308 xtab(13) = -5.19842653458D+00
- <a name="l02309"></a>02309 xtab(14) = -4.87715007747D+00
- <a name="l02310"></a>02310 xtab(15) = -4.56097375794D+00
- <a name="l02311"></a>02311 xtab(16) = -4.24928643596D+00
- <a name="l02312"></a>02312 xtab(17) = -3.94156073393D+00
- <a name="l02313"></a>02313 xtab(18) = -3.63733587617D+00
- <a name="l02314"></a>02314 xtab(19) = -3.33620465355D+00
- <a name="l02315"></a>02315 xtab(20) = -3.03780333823D+00
- <a name="l02316"></a>02316 xtab(21) = -2.74180374807D+00
- <a name="l02317"></a>02317 xtab(22) = -2.44790690231D+00
- <a name="l02318"></a>02318 xtab(23) = -2.15583787123D+00
- <a name="l02319"></a>02319 xtab(24) = -1.86534153123D+00
- <a name="l02320"></a>02320 xtab(25) = -1.57617901198D+00
- <a name="l02321"></a>02321 xtab(26) = -1.28812467487D+00
- <a name="l02322"></a>02322 xtab(27) = -1.00096349956D+00
- <a name="l02323"></a>02323 xtab(28) = -0.714488781673D+00
- <a name="l02324"></a>02324 xtab(29) = -0.428500064221D+00
- <a name="l02325"></a>02325 xtab(30) = -0.142801238703D+00
- <a name="l02326"></a>02326 xtab(31) = 0.142801238703D+00
- <a name="l02327"></a>02327 xtab(32) = 0.428500064221D+00
- <a name="l02328"></a>02328 xtab(33) = 0.714488781673D+00
- <a name="l02329"></a>02329 xtab(34) = 1.00096349956D+00
- <a name="l02330"></a>02330 xtab(35) = 1.28812467487D+00
- <a name="l02331"></a>02331 xtab(36) = 1.57617901198D+00
- <a name="l02332"></a>02332 xtab(37) = 1.86534153123D+00
- <a name="l02333"></a>02333 xtab(38) = 2.15583787123D+00
- <a name="l02334"></a>02334 xtab(39) = 2.44790690231D+00
- <a name="l02335"></a>02335 xtab(40) = 2.74180374807D+00
- <a name="l02336"></a>02336 xtab(41) = 3.03780333823D+00
- <a name="l02337"></a>02337 xtab(42) = 3.33620465355D+00
- <a name="l02338"></a>02338 xtab(43) = 3.63733587617D+00
- <a name="l02339"></a>02339 xtab(44) = 3.94156073393D+00
- <a name="l02340"></a>02340 xtab(45) = 4.24928643596D+00
- <a name="l02341"></a>02341 xtab(46) = 4.56097375794D+00
- <a name="l02342"></a>02342 xtab(47) = 4.87715007747D+00
- <a name="l02343"></a>02343 xtab(48) = 5.19842653458D+00
- <a name="l02344"></a>02344 xtab(49) = 5.52552108614D+00
- <a name="l02345"></a>02345 xtab(50) = 5.85929019639D+00
- <a name="l02346"></a>02346 xtab(51) = 6.20077355799D+00
- <a name="l02347"></a>02347 xtab(52) = 6.55125916706D+00
- <a name="l02348"></a>02348 xtab(53) = 6.91238153219D+00
- <a name="l02349"></a>02349 xtab(54) = 7.28627659440D+00
- <a name="l02350"></a>02350 xtab(55) = 7.67583993750D+00
- <a name="l02351"></a>02351 xtab(56) = 8.08518865425D+00
- <a name="l02352"></a>02352 xtab(57) = 8.52056928412D+00
- <a name="l02353"></a>02353 xtab(58) = 8.99239800140D+00
- <a name="l02354"></a>02354 xtab(59) = 9.52090367701D+00
- <a name="l02355"></a>02355 xtab(60) = 10.1591092462D+00
- <a name="l02356"></a>02356
- <a name="l02357"></a>02357 weight( 1) = 0.110958724796D-44
- <a name="l02358"></a>02358 weight( 2) = 0.243974758810D-39
- <a name="l02359"></a>02359 weight( 3) = 0.377162672698D-35
- <a name="l02360"></a>02360 weight( 4) = 0.133255961176D-31
- <a name="l02361"></a>02361 weight( 5) = 0.171557314767D-28
- <a name="l02362"></a>02362 weight( 6) = 0.102940599693D-25
- <a name="l02363"></a>02363 weight( 7) = 0.334575695574D-23
- <a name="l02364"></a>02364 weight( 8) = 0.651256725748D-21
- <a name="l02365"></a>02365 weight( 9) = 0.815364047300D-19
- <a name="l02366"></a>02366 weight(10) = 0.692324790956D-17
- <a name="l02367"></a>02367 weight(11) = 0.415244410968D-15
- <a name="l02368"></a>02368 weight(12) = 0.181662457614D-13
- <a name="l02369"></a>02369 weight(13) = 0.594843051597D-12
- <a name="l02370"></a>02370 weight(14) = 0.148895734905D-10
- <a name="l02371"></a>02371 weight(15) = 0.289935901280D-09
- <a name="l02372"></a>02372 weight(16) = 0.445682277521D-08
- <a name="l02373"></a>02373 weight(17) = 0.547555461926D-07
- <a name="l02374"></a>02374 weight(18) = 0.543351613419D-06
- <a name="l02375"></a>02375 weight(19) = 0.439428693625D-05
- <a name="l02376"></a>02376 weight(20) = 0.291874190415D-04
- <a name="l02377"></a>02377 weight(21) = 0.160277334681D-03
- <a name="l02378"></a>02378 weight(22) = 0.731773556963D-03
- <a name="l02379"></a>02379 weight(23) = 0.279132482894D-02
- <a name="l02380"></a>02380 weight(24) = 0.893217836028D-02
- <a name="l02381"></a>02381 weight(25) = 0.240612727660D-01
- <a name="l02382"></a>02382 weight(26) = 0.547189709320D-01
- <a name="l02383"></a>02383 weight(27) = 0.105298763697D+00
- <a name="l02384"></a>02384 weight(28) = 0.171776156918D+00
- <a name="l02385"></a>02385 weight(29) = 0.237868904958D+00
- <a name="l02386"></a>02386 weight(30) = 0.279853117522D+00
- <a name="l02387"></a>02387 weight(31) = 0.279853117522D+00
- <a name="l02388"></a>02388 weight(32) = 0.237868904958D+00
- <a name="l02389"></a>02389 weight(33) = 0.171776156918D+00
- <a name="l02390"></a>02390 weight(34) = 0.105298763697D+00
- <a name="l02391"></a>02391 weight(35) = 0.547189709320D-01
- <a name="l02392"></a>02392 weight(36) = 0.240612727660D-01
- <a name="l02393"></a>02393 weight(37) = 0.893217836028D-02
- <a name="l02394"></a>02394 weight(38) = 0.279132482894D-02
- <a name="l02395"></a>02395 weight(39) = 0.731773556963D-03
- <a name="l02396"></a>02396 weight(40) = 0.160277334681D-03
- <a name="l02397"></a>02397 weight(41) = 0.291874190415D-04
- <a name="l02398"></a>02398 weight(42) = 0.439428693625D-05
- <a name="l02399"></a>02399 weight(43) = 0.543351613419D-06
- <a name="l02400"></a>02400 weight(44) = 0.547555461926D-07
- <a name="l02401"></a>02401 weight(45) = 0.445682277521D-08
- <a name="l02402"></a>02402 weight(46) = 0.289935901280D-09
- <a name="l02403"></a>02403 weight(47) = 0.148895734905D-10
- <a name="l02404"></a>02404 weight(48) = 0.594843051597D-12
- <a name="l02405"></a>02405 weight(49) = 0.181662457614D-13
- <a name="l02406"></a>02406 weight(50) = 0.415244410968D-15
- <a name="l02407"></a>02407 weight(51) = 0.692324790956D-17
- <a name="l02408"></a>02408 weight(52) = 0.815364047300D-19
- <a name="l02409"></a>02409 weight(53) = 0.651256725748D-21
- <a name="l02410"></a>02410 weight(54) = 0.334575695574D-23
- <a name="l02411"></a>02411 weight(55) = 0.102940599693D-25
- <a name="l02412"></a>02412 weight(56) = 0.171557314767D-28
- <a name="l02413"></a>02413 weight(57) = 0.133255961176D-31
- <a name="l02414"></a>02414 weight(58) = 0.377162672698D-35
- <a name="l02415"></a>02415 weight(59) = 0.243974758810D-39
- <a name="l02416"></a>02416 weight(60) = 0.110958724796D-44
- <a name="l02417"></a>02417
- <a name="l02418"></a>02418 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 64 ) <span class="keyword">then</span>
- <a name="l02419"></a>02419
- <a name="l02420"></a>02420 xtab( 1) = -10.5261231680D+00
- <a name="l02421"></a>02421 xtab( 2) = -9.89528758683D+00
- <a name="l02422"></a>02422 xtab( 3) = -9.37315954965D+00
- <a name="l02423"></a>02423 xtab( 4) = -8.90724909996D+00
- <a name="l02424"></a>02424 xtab( 5) = -8.47752908338D+00
- <a name="l02425"></a>02425 xtab( 6) = -8.07368728501D+00
- <a name="l02426"></a>02426 xtab( 7) = -7.68954016404D+00
- <a name="l02427"></a>02427 xtab( 8) = -7.32101303278D+00
- <a name="l02428"></a>02428 xtab( 9) = -6.96524112055D+00
- <a name="l02429"></a>02429 xtab(10) = -6.62011226264D+00
- <a name="l02430"></a>02430 xtab(11) = -6.28401122877D+00
- <a name="l02431"></a>02431 xtab(12) = -5.95566632680D+00
- <a name="l02432"></a>02432 xtab(13) = -5.63405216435D+00
- <a name="l02433"></a>02433 xtab(14) = -5.31832522463D+00
- <a name="l02434"></a>02434 xtab(15) = -5.00777960220D+00
- <a name="l02435"></a>02435 xtab(16) = -4.70181564741D+00
- <a name="l02436"></a>02436 xtab(17) = -4.39991716823D+00
- <a name="l02437"></a>02437 xtab(18) = -4.10163447457D+00
- <a name="l02438"></a>02438 xtab(19) = -3.80657151395D+00
- <a name="l02439"></a>02439 xtab(20) = -3.51437593574D+00
- <a name="l02440"></a>02440 xtab(21) = -3.22473129199D+00
- <a name="l02441"></a>02441 xtab(22) = -2.93735082300D+00
- <a name="l02442"></a>02442 xtab(23) = -2.65197243543D+00
- <a name="l02443"></a>02443 xtab(24) = -2.36835458863D+00
- <a name="l02444"></a>02444 xtab(25) = -2.08627287988D+00
- <a name="l02445"></a>02445 xtab(26) = -1.80551717147D+00
- <a name="l02446"></a>02446 xtab(27) = -1.52588914021D+00
- <a name="l02447"></a>02447 xtab(28) = -1.24720015694D+00
- <a name="l02448"></a>02448 xtab(29) = -0.969269423071D+00
- <a name="l02449"></a>02449 xtab(30) = -0.691922305810D+00
- <a name="l02450"></a>02450 xtab(31) = -0.414988824121D+00
- <a name="l02451"></a>02451 xtab(32) = -0.138302244987D+00
- <a name="l02452"></a>02452 xtab(33) = 0.138302244987D+00
- <a name="l02453"></a>02453 xtab(34) = 0.414988824121D+00
- <a name="l02454"></a>02454 xtab(35) = 0.691922305810D+00
- <a name="l02455"></a>02455 xtab(36) = 0.969269423071D+00
- <a name="l02456"></a>02456 xtab(37) = 1.24720015694D+00
- <a name="l02457"></a>02457 xtab(38) = 1.52588914021D+00
- <a name="l02458"></a>02458 xtab(39) = 1.80551717147D+00
- <a name="l02459"></a>02459 xtab(40) = 2.08627287988D+00
- <a name="l02460"></a>02460 xtab(41) = 2.36835458863D+00
- <a name="l02461"></a>02461 xtab(42) = 2.65197243543D+00
- <a name="l02462"></a>02462 xtab(43) = 2.93735082300D+00
- <a name="l02463"></a>02463 xtab(44) = 3.22473129199D+00
- <a name="l02464"></a>02464 xtab(45) = 3.51437593574D+00
- <a name="l02465"></a>02465 xtab(46) = 3.80657151395D+00
- <a name="l02466"></a>02466 xtab(47) = 4.10163447457D+00
- <a name="l02467"></a>02467 xtab(48) = 4.39991716823D+00
- <a name="l02468"></a>02468 xtab(49) = 4.70181564741D+00
- <a name="l02469"></a>02469 xtab(50) = 5.00777960220D+00
- <a name="l02470"></a>02470 xtab(51) = 5.31832522463D+00
- <a name="l02471"></a>02471 xtab(52) = 5.63405216435D+00
- <a name="l02472"></a>02472 xtab(53) = 5.95566632680D+00
- <a name="l02473"></a>02473 xtab(54) = 6.28401122877D+00
- <a name="l02474"></a>02474 xtab(55) = 6.62011226264D+00
- <a name="l02475"></a>02475 xtab(56) = 6.96524112055D+00
- <a name="l02476"></a>02476 xtab(57) = 7.32101303278D+00
- <a name="l02477"></a>02477 xtab(58) = 7.68954016404D+00
- <a name="l02478"></a>02478 xtab(59) = 8.07368728501D+00
- <a name="l02479"></a>02479 xtab(60) = 8.47752908338D+00
- <a name="l02480"></a>02480 xtab(61) = 8.90724909996D+00
- <a name="l02481"></a>02481 xtab(62) = 9.37315954965D+00
- <a name="l02482"></a>02482 xtab(63) = 9.89528758683D+00
- <a name="l02483"></a>02483 xtab(64) = 10.5261231680D+00
- <a name="l02484"></a>02484
- <a name="l02485"></a>02485 weight( 1) = 0.553570653584D-48
- <a name="l02486"></a>02486 weight( 2) = 0.167974799010D-42
- <a name="l02487"></a>02487 weight( 3) = 0.342113801099D-38
- <a name="l02488"></a>02488 weight( 4) = 0.155739062462D-34
- <a name="l02489"></a>02489 weight( 5) = 0.254966089910D-31
- <a name="l02490"></a>02490 weight( 6) = 0.192910359546D-28
- <a name="l02491"></a>02491 weight( 7) = 0.786179778889D-26
- <a name="l02492"></a>02492 weight( 8) = 0.191170688329D-23
- <a name="l02493"></a>02493 weight( 9) = 0.298286278427D-21
- <a name="l02494"></a>02494 weight(10) = 0.315225456649D-19
- <a name="l02495"></a>02495 weight(11) = 0.235188471067D-17
- <a name="l02496"></a>02496 weight(12) = 0.128009339117D-15
- <a name="l02497"></a>02497 weight(13) = 0.521862372645D-14
- <a name="l02498"></a>02498 weight(14) = 0.162834073070D-12
- <a name="l02499"></a>02499 weight(15) = 0.395917776693D-11
- <a name="l02500"></a>02500 weight(16) = 0.761521725012D-10
- <a name="l02501"></a>02501 weight(17) = 0.117361674232D-08
- <a name="l02502"></a>02502 weight(18) = 0.146512531647D-07
- <a name="l02503"></a>02503 weight(19) = 0.149553293672D-06
- <a name="l02504"></a>02504 weight(20) = 0.125834025103D-05
- <a name="l02505"></a>02505 weight(21) = 0.878849923082D-05
- <a name="l02506"></a>02506 weight(22) = 0.512592913577D-04
- <a name="l02507"></a>02507 weight(23) = 0.250983698512D-03
- <a name="l02508"></a>02508 weight(24) = 0.103632909950D-02
- <a name="l02509"></a>02509 weight(25) = 0.362258697852D-02
- <a name="l02510"></a>02510 weight(26) = 0.107560405098D-01
- <a name="l02511"></a>02511 weight(27) = 0.272031289536D-01
- <a name="l02512"></a>02512 weight(28) = 0.587399819634D-01
- <a name="l02513"></a>02513 weight(29) = 0.108498349306D+00
- <a name="l02514"></a>02514 weight(30) = 0.171685842349D+00
- <a name="l02515"></a>02515 weight(31) = 0.232994786062D+00
- <a name="l02516"></a>02516 weight(32) = 0.271377424940D+00
- <a name="l02517"></a>02517 weight(33) = 0.271377424940D+00
- <a name="l02518"></a>02518 weight(34) = 0.232994786062D+00
- <a name="l02519"></a>02519 weight(35) = 0.171685842349D+00
- <a name="l02520"></a>02520 weight(36) = 0.108498349306D+00
- <a name="l02521"></a>02521 weight(37) = 0.587399819634D-01
- <a name="l02522"></a>02522 weight(38) = 0.272031289536D-01
- <a name="l02523"></a>02523 weight(39) = 0.107560405098D-01
- <a name="l02524"></a>02524 weight(40) = 0.362258697852D-02
- <a name="l02525"></a>02525 weight(41) = 0.103632909950D-02
- <a name="l02526"></a>02526 weight(42) = 0.250983698512D-03
- <a name="l02527"></a>02527 weight(43) = 0.512592913577D-04
- <a name="l02528"></a>02528 weight(44) = 0.878849923082D-05
- <a name="l02529"></a>02529 weight(45) = 0.125834025103D-05
- <a name="l02530"></a>02530 weight(46) = 0.149553293672D-06
- <a name="l02531"></a>02531 weight(47) = 0.146512531647D-07
- <a name="l02532"></a>02532 weight(48) = 0.117361674232D-08
- <a name="l02533"></a>02533 weight(49) = 0.761521725012D-10
- <a name="l02534"></a>02534 weight(50) = 0.395917776693D-11
- <a name="l02535"></a>02535 weight(51) = 0.162834073070D-12
- <a name="l02536"></a>02536 weight(52) = 0.521862372645D-14
- <a name="l02537"></a>02537 weight(53) = 0.128009339117D-15
- <a name="l02538"></a>02538 weight(54) = 0.235188471067D-17
- <a name="l02539"></a>02539 weight(55) = 0.315225456649D-19
- <a name="l02540"></a>02540 weight(56) = 0.298286278427D-21
- <a name="l02541"></a>02541 weight(57) = 0.191170688329D-23
- <a name="l02542"></a>02542 weight(58) = 0.786179778889D-26
- <a name="l02543"></a>02543 weight(59) = 0.192910359546D-28
- <a name="l02544"></a>02544 weight(60) = 0.254966089910D-31
- <a name="l02545"></a>02545 weight(61) = 0.155739062462D-34
- <a name="l02546"></a>02546 weight(62) = 0.342113801099D-38
- <a name="l02547"></a>02547 weight(63) = 0.167974799010D-42
- <a name="l02548"></a>02548 weight(64) = 0.553570653584D-48
- <a name="l02549"></a>02549
- <a name="l02550"></a>02550 <span class="keyword">else</span>
- <a name="l02551"></a>02551
- <a name="l02552"></a>02552 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l02553"></a>02553 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'HERMITE_SET - Fatal error!'</span>
- <a name="l02554"></a>02554 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l02555"></a>02555 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' Legal values are 1 to 20,'</span>
- <a name="l02556"></a>02556 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' 30, 32, 40, 50, 60 and 64.'</span>
- <a name="l02557"></a>02557 stop
- <a name="l02558"></a>02558
- <a name="l02559"></a>02559 <span class="keyword">end if</span>
- <a name="l02560"></a>02560
- <a name="l02561"></a>02561 return
- <a name="l02562"></a>02562 <span class="keyword">end</span>
- <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 )
- <a name="l02564"></a>02564 <span class="comment">!</span>
- <a name="l02565"></a>02565 <span class="comment">!*******************************************************************************</span>
- <a name="l02566"></a>02566 <span class="comment">!</span>
- <a name="l02567"></a>02567 <span class="comment">!! JACOBI_COM computes the abscissa and weights for Gauss-Jacobi quadrature.</span>
- <a name="l02568"></a>02568 <span class="comment">!</span>
- <a name="l02569"></a>02569 <span class="comment">!</span>
- <a name="l02570"></a>02570 <span class="comment">! Integration interval:</span>
- <a name="l02571"></a>02571 <span class="comment">!</span>
- <a name="l02572"></a>02572 <span class="comment">! [ -1, 1 ]</span>
- <a name="l02573"></a>02573 <span class="comment">!</span>
- <a name="l02574"></a>02574 <span class="comment">! Weight function:</span>
- <a name="l02575"></a>02575 <span class="comment">!</span>
- <a name="l02576"></a>02576 <span class="comment">! 1.0D+00</span>
- <a name="l02577"></a>02577 <span class="comment">!</span>
- <a name="l02578"></a>02578 <span class="comment">! Integral to approximate:</span>
- <a name="l02579"></a>02579 <span class="comment">!</span>
- <a name="l02580"></a>02580 <span class="comment">! Integral ( -1 <= X <= 1 ) (1+X)**ALPHA * (1-X)**BETA * F(X) dX</span>
- <a name="l02581"></a>02581 <span class="comment">!</span>
- <a name="l02582"></a>02582 <span class="comment">! Approximate integral:</span>
- <a name="l02583"></a>02583 <span class="comment">!</span>
- <a name="l02584"></a>02584 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l02585"></a>02585 <span class="comment">!</span>
- <a name="l02586"></a>02586 <span class="comment">! Reference:</span>
- <a name="l02587"></a>02587 <span class="comment">!</span>
- <a name="l02588"></a>02588 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l02589"></a>02589 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l02590"></a>02590 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l02591"></a>02591 <span class="comment">!</span>
- <a name="l02592"></a>02592 <span class="comment">! Modified:</span>
- <a name="l02593"></a>02593 <span class="comment">!</span>
- <a name="l02594"></a>02594 <span class="comment">! 09 September 2000</span>
- <a name="l02595"></a>02595 <span class="comment">!</span>
- <a name="l02596"></a>02596 <span class="comment">! Parameters:</span>
- <a name="l02597"></a>02597 <span class="comment">!</span>
- <a name="l02598"></a>02598 <span class="comment">! Input, integer NORDER, the order of the quadrature rule to be computed.</span>
- <a name="l02599"></a>02599 <span class="comment">!</span>
- <a name="l02600"></a>02600 <span class="comment">! Output, double precision XTAB(NORDER), the Gauss-Jacobi abscissas.</span>
- <a name="l02601"></a>02601 <span class="comment">!</span>
- <a name="l02602"></a>02602 <span class="comment">! Output, double precision WEIGHT(NORDER), the Gauss-Jacobi weights.</span>
- <a name="l02603"></a>02603 <span class="comment">!</span>
- <a name="l02604"></a>02604 <span class="comment">! Input, double precision ALPHA, BETA, the exponents of (1+X) and</span>
- <a name="l02605"></a>02605 <span class="comment">! (1-X) in the quadrature rule. For simple Gauss-Legendre quadrature,</span>
- <a name="l02606"></a>02606 <span class="comment">! set ALPHA = BETA = 0.0.</span>
- <a name="l02607"></a>02607 <span class="comment">!</span>
- <a name="l02608"></a>02608 <span class="keyword">implicit none</span>
- <a name="l02609"></a>02609 <span class="comment">!</span>
- <a name="l02610"></a>02610 <span class="keywordtype">integer</span> norder
- <a name="l02611"></a>02611 <span class="comment">!</span>
- <a name="l02612"></a>02612 <span class="keywordtype">double precision</span> alpha
- <a name="l02613"></a>02613 <span class="keywordtype">double precision</span> an
- <a name="l02614"></a>02614 <span class="keywordtype">double precision</span> b(norder)
- <a name="l02615"></a>02615 <span class="keywordtype">double precision</span> beta
- <a name="l02616"></a>02616 <span class="keywordtype">double precision</span> bn
- <a name="l02617"></a>02617 <span class="keywordtype">double precision</span> c(norder)
- <a name="l02618"></a>02618 <span class="keywordtype">double precision</span> cc
- <a name="l02619"></a>02619 <span class="keywordtype">double precision</span> delta
- <a name="l02620"></a>02620 <span class="keywordtype">double precision</span> dp2
- <a name="l02621"></a>02621 <span class="keywordtype">double precision</span> log_gamma
- <a name="l02622"></a>02622 <span class="keywordtype">integer</span> i
- <a name="l02623"></a>02623 <span class="keywordtype">double precision</span> p1
- <a name="l02624"></a>02624 <span class="keywordtype">double precision</span> r1
- <a name="l02625"></a>02625 <span class="keywordtype">double precision</span> r2
- <a name="l02626"></a>02626 <span class="keywordtype">double precision</span> r3
- <a name="l02627"></a>02627 <span class="keywordtype">double precision</span> temp
- <a name="l02628"></a>02628 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l02629"></a>02629 <span class="keywordtype">double precision</span> x
- <a name="l02630"></a>02630 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l02631"></a>02631 <span class="comment">!</span>
- <a name="l02632"></a>02632 <span class="comment">! Set the recursion coefficients.</span>
- <a name="l02633"></a>02633 <span class="comment">!</span>
- <a name="l02634"></a>02634 <span class="keyword">do</span> i = 1, norder
- <a name="l02635"></a>02635
- <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>
- <a name="l02637"></a>02637
- <a name="l02638"></a>02638 b(i) = 0.0D+00
- <a name="l02639"></a>02639
- <a name="l02640"></a>02640 <span class="keyword">else</span>
- <a name="l02641"></a>02641
- <a name="l02642"></a>02642 b(i) = ( alpha + beta ) * ( beta - alpha ) / &
- <a name="l02643"></a>02643 ( ( alpha + beta + dble ( 2 * i ) ) &
- <a name="l02644"></a>02644 * ( alpha + beta + dble ( 2 * i - 2 ) ) )
- <a name="l02645"></a>02645
- <a name="l02646"></a>02646 <span class="keyword">end if</span>
- <a name="l02647"></a>02647
- <a name="l02648"></a>02648 <span class="keyword">if</span> ( i == 1 ) <span class="keyword">then</span>
- <a name="l02649"></a>02649
- <a name="l02650"></a>02650 c(i) = 0.0D+00
- <a name="l02651"></a>02651
- <a name="l02652"></a>02652 <span class="keyword">else</span>
- <a name="l02653"></a>02653
- <a name="l02654"></a>02654 c(i) = 4.0D+00 * dble ( i - 1 ) * ( alpha + dble ( i - 1 ) ) &
- <a name="l02655"></a>02655 * ( beta + dble ( i - 1 ) ) &
- <a name="l02656"></a>02656 * ( alpha + beta + dble ( i - 1 ) ) / &
- <a name="l02657"></a>02657 ( ( alpha + beta + dble ( 2 * i - 1 ) ) &
- <a name="l02658"></a>02658 * ( alpha + beta + dble ( 2 * i - 2 ) )**2 &
- <a name="l02659"></a>02659 * ( alpha + beta + dble ( 2 * i - 3 ) ) )
- <a name="l02660"></a>02660
- <a name="l02661"></a>02661 <span class="keyword">end if</span>
- <a name="l02662"></a>02662
- <a name="l02663"></a>02663 <span class="keyword">end do</span>
- <a name="l02664"></a>02664
- <a name="l02665"></a>02665 delta = exp ( log_gamma ( alpha + 1.0D+00 ) + log_gamma ( beta + 1.0D+00) &
- <a name="l02666"></a>02666 + log_gamma ( alpha + beta + 2.0D+00 ) )
- <a name="l02667"></a>02667
- <a name="l02668"></a>02668 cc = delta * 2.0D+00**( alpha + beta + 1.0D+00 ) * product ( c(2:norder) )
- <a name="l02669"></a>02669
- <a name="l02670"></a>02670 <span class="keyword">do</span> i = 1, norder
- <a name="l02671"></a>02671
- <a name="l02672"></a>02672 <span class="keyword">if</span> ( i == 1 ) <span class="keyword">then</span>
- <a name="l02673"></a>02673
- <a name="l02674"></a>02674 an = alpha / dble ( norder )
- <a name="l02675"></a>02675 bn = beta / dble ( norder )
- <a name="l02676"></a>02676
- <a name="l02677"></a>02677 r1 = ( 1.0D+00 + alpha ) * ( 2.78D+00 / ( 4.0D+00+ dble ( norder**2 ) ) &
- <a name="l02678"></a>02678 + 0.768D+00 * an / dble ( norder ) )
- <a name="l02679"></a>02679
- <a name="l02680"></a>02680 r2 = 1.0D+00 + 1.48D+00 * an + 0.96D+00 * bn &
- <a name="l02681"></a>02681 + 0.452D+00 * an**2 + 0.83D+00 * an * bn
- <a name="l02682"></a>02682
- <a name="l02683"></a>02683 x = ( r2 - r1 ) / r2
- <a name="l02684"></a>02684
- <a name="l02685"></a>02685 <span class="keyword">else</span> <span class="keyword">if</span> ( i == 2 ) <span class="keyword">then</span>
- <a name="l02686"></a>02686
- <a name="l02687"></a>02687 r1 = ( 4.1D+00 + alpha ) / &
- <a name="l02688"></a>02688 ( ( 1.0D+00 + alpha ) * ( 1.0D+00 + 0.156D+00 * alpha ) )
- <a name="l02689"></a>02689
- <a name="l02690"></a>02690 r2 = 1.0D+00 + 0.06D+00 * ( dble ( norder ) - 8.0D+00 ) * &
- <a name="l02691"></a>02691 ( 1.0D+00 + 0.12D+00 * alpha ) / dble ( norder )
- <a name="l02692"></a>02692
- <a name="l02693"></a>02693 r3 = 1.0D+00 + 0.012D+00 * beta * &
- <a name="l02694"></a>02694 ( 1.0D+00 + 0.25D+00 * abs ( alpha ) ) / dble ( norder )
- <a name="l02695"></a>02695
- <a name="l02696"></a>02696 x = x - r1 * r2 * r3 * ( 1.0D+00 - x )
- <a name="l02697"></a>02697
- <a name="l02698"></a>02698 <span class="keyword">else</span> <span class="keyword">if</span> ( i == 3 ) <span class="keyword">then</span>
- <a name="l02699"></a>02699
- <a name="l02700"></a>02700 r1 = ( 1.67D+00 + 0.28D+00 * alpha ) / ( 1.0D+00 + 0.37D+00 * alpha )
- <a name="l02701"></a>02701
- <a name="l02702"></a>02702 r2 = 1.0D+00 + 0.22D+00 * ( dble ( norder ) - 8.0D+00 ) / dble ( norder )
- <a name="l02703"></a>02703
- <a name="l02704"></a>02704 r3 = 1.0D+00 + 8.0D+00 * beta / &
- <a name="l02705"></a>02705 ( ( 6.28D+00 + beta ) * dble ( norder**2 ) )
- <a name="l02706"></a>02706
- <a name="l02707"></a>02707 x = x - r1 * r2 * r3 * ( xtab(1) - x )
- <a name="l02708"></a>02708
- <a name="l02709"></a>02709 <span class="keyword">else</span> <span class="keyword">if</span> ( i < norder - 1 ) <span class="keyword">then</span>
- <a name="l02710"></a>02710
- <a name="l02711"></a>02711 x = 3.0D+00 * xtab(i-1) - 3.0D+00 * xtab(i-2) + xtab(i-3)
- <a name="l02712"></a>02712
- <a name="l02713"></a>02713 <span class="keyword">else</span> <span class="keyword">if</span> ( i == norder - 1 ) <span class="keyword">then</span>
- <a name="l02714"></a>02714
- <a name="l02715"></a>02715 r1 = ( 1.0D+00 + 0.235D+00 * beta ) / ( 0.766D+00 + 0.119D+00 * beta )
- <a name="l02716"></a>02716
- <a name="l02717"></a>02717 r2 = 1.0D+00 / ( 1.0D+00 + 0.639D+00 * ( dble ( norder ) - 4.0D+00 ) &
- <a name="l02718"></a>02718 / ( 1.0D+00 + 0.71D+00 * ( dble ( norder ) - 4.0D+00 ) ) )
- <a name="l02719"></a>02719
- <a name="l02720"></a>02720 r3 = 1.0D+00 / ( 1.0D+00 + 20.0D+00 * alpha / ( ( 7.5D+00 + alpha ) * &
- <a name="l02721"></a>02721 dble ( norder**2 ) ) )
- <a name="l02722"></a>02722
- <a name="l02723"></a>02723 x = x + r1 * r2 * r3 * ( x - xtab(i-2) )
- <a name="l02724"></a>02724
- <a name="l02725"></a>02725 <span class="keyword">else</span> <span class="keyword">if</span> ( i == norder ) <span class="keyword">then</span>
- <a name="l02726"></a>02726
- <a name="l02727"></a>02727 r1 = ( 1.0D+00 + 0.37D+00 * beta ) / ( 1.67D+00 + 0.28D+00 * beta )
- <a name="l02728"></a>02728
- <a name="l02729"></a>02729 r2 = 1.0D+00 / &
- <a name="l02730"></a>02730 ( 1.0D+00 + 0.22D+00 * ( dble ( norder ) - 8.0D+00 ) / dble ( norder ) )
- <a name="l02731"></a>02731
- <a name="l02732"></a>02732 r3 = 1.0D+00 / ( 1.0D+00 + 8.0D+00 * alpha / &
- <a name="l02733"></a>02733 ( ( 6.28D+00 + alpha ) * dble ( norder**2 ) ) )
- <a name="l02734"></a>02734
- <a name="l02735"></a>02735 x = x + r1 * r2 * r3 * ( x - xtab(i-2) )
- <a name="l02736"></a>02736
- <a name="l02737"></a>02737 <span class="keyword">end if</span>
- <a name="l02738"></a>02738
- <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 )
- <a name="l02740"></a>02740
- <a name="l02741"></a>02741 xtab(i) = x
- <a name="l02742"></a>02742 weight(i) = cc / ( dp2 * p1 )
- <a name="l02743"></a>02743
- <a name="l02744"></a>02744 <span class="keyword">end do</span>
- <a name="l02745"></a>02745 <span class="comment">!</span>
- <a name="l02746"></a>02746 <span class="comment">! Reverse the order of the XTAB values.</span>
- <a name="l02747"></a>02747 <span class="comment">!</span>
- <a name="l02748"></a>02748 call <a class="code" href="quadrule_8f90.html#a7841cf442902dd98d08b6a4d89a9a7bf">dvec_reverse </a>( norder, xtab )
- <a name="l02749"></a>02749
- <a name="l02750"></a>02750 return
- <a name="l02751"></a>02751 <span class="keyword">end</span>
- <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 )
- <a name="l02753"></a>02753 <span class="comment">!</span>
- <a name="l02754"></a>02754 <span class="comment">!*******************************************************************************</span>
- <a name="l02755"></a>02755 <span class="comment">!</span>
- <a name="l02756"></a>02756 <span class="comment">!! JACOBI_RECUR finds the value and derivative of a Jacobi polynomial.</span>
- <a name="l02757"></a>02757 <span class="comment">!</span>
- <a name="l02758"></a>02758 <span class="comment">!</span>
- <a name="l02759"></a>02759 <span class="comment">! Reference:</span>
- <a name="l02760"></a>02760 <span class="comment">!</span>
- <a name="l02761"></a>02761 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l02762"></a>02762 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l02763"></a>02763 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l02764"></a>02764 <span class="comment">!</span>
- <a name="l02765"></a>02765 <span class="comment">! Modified:</span>
- <a name="l02766"></a>02766 <span class="comment">!</span>
- <a name="l02767"></a>02767 <span class="comment">! 19 September 1998</span>
- <a name="l02768"></a>02768 <span class="comment">!</span>
- <a name="l02769"></a>02769 <span class="comment">! Parameters:</span>
- <a name="l02770"></a>02770 <span class="comment">!</span>
- <a name="l02771"></a>02771 <span class="comment">! Output, double precision P2, the value of J(NORDER)(X).</span>
- <a name="l02772"></a>02772 <span class="comment">!</span>
- <a name="l02773"></a>02773 <span class="comment">! Output, double precision DP2, the value of J'(NORDER)(X).</span>
- <a name="l02774"></a>02774 <span class="comment">!</span>
- <a name="l02775"></a>02775 <span class="comment">! Output, double precision P1, the value of J(NORDER-1)(X).</span>
- <a name="l02776"></a>02776 <span class="comment">!</span>
- <a name="l02777"></a>02777 <span class="comment">! Input, double precision X, the point at which polynomials are evaluated.</span>
- <a name="l02778"></a>02778 <span class="comment">!</span>
- <a name="l02779"></a>02779 <span class="comment">! Input, integer NORDER, the order of the polynomial to be computed.</span>
- <a name="l02780"></a>02780 <span class="comment">!</span>
- <a name="l02781"></a>02781 <span class="comment">! Input, double precision ALPHA, BETA, the exponents of (1+X) and</span>
- <a name="l02782"></a>02782 <span class="comment">! (1-X) in the quadrature rule.</span>
- <a name="l02783"></a>02783 <span class="comment">!</span>
- <a name="l02784"></a>02784 <span class="comment">! Input, double precision B(NORDER), C(NORDER), the recursion</span>
- <a name="l02785"></a>02785 <span class="comment">! coefficients.</span>
- <a name="l02786"></a>02786 <span class="comment">!</span>
- <a name="l02787"></a>02787 <span class="keyword">implicit none</span>
- <a name="l02788"></a>02788 <span class="comment">!</span>
- <a name="l02789"></a>02789 <span class="keywordtype">integer</span> norder
- <a name="l02790"></a>02790 <span class="comment">!</span>
- <a name="l02791"></a>02791 <span class="keywordtype">double precision</span> alpha
- <a name="l02792"></a>02792 <span class="keywordtype">double precision</span> b(norder)
- <a name="l02793"></a>02793 <span class="keywordtype">double precision</span> beta
- <a name="l02794"></a>02794 <span class="keywordtype">double precision</span> c(norder)
- <a name="l02795"></a>02795 <span class="keywordtype">double precision</span> dp0
- <a name="l02796"></a>02796 <span class="keywordtype">double precision</span> dp1
- <a name="l02797"></a>02797 <span class="keywordtype">double precision</span> dp2
- <a name="l02798"></a>02798 <span class="keywordtype">integer</span> i
- <a name="l02799"></a>02799 <span class="keywordtype">double precision</span> p0
- <a name="l02800"></a>02800 <span class="keywordtype">double precision</span> p1
- <a name="l02801"></a>02801 <span class="keywordtype">double precision</span> p2
- <a name="l02802"></a>02802 <span class="keywordtype">double precision</span> x
- <a name="l02803"></a>02803 <span class="comment">!</span>
- <a name="l02804"></a>02804 p1 = 1.0D+00
- <a name="l02805"></a>02805 dp1 = 0.0D+00
- <a name="l02806"></a>02806
- <a name="l02807"></a>02807 p2 = x + ( alpha - beta ) / ( alpha + beta + 2.0D+00 )
- <a name="l02808"></a>02808 dp2 = 1.0D+00
- <a name="l02809"></a>02809
- <a name="l02810"></a>02810 <span class="keyword">do</span> i = 2, norder
- <a name="l02811"></a>02811
- <a name="l02812"></a>02812 p0 = p1
- <a name="l02813"></a>02813 dp0 = dp1
- <a name="l02814"></a>02814
- <a name="l02815"></a>02815 p1 = p2
- <a name="l02816"></a>02816 dp1 = dp2
- <a name="l02817"></a>02817
- <a name="l02818"></a>02818 p2 = ( x - b(i) ) * p1 - c(i) * p0
- <a name="l02819"></a>02819 dp2 = ( x - b(i) ) * dp1 + p1 - c(i) * dp0
- <a name="l02820"></a>02820
- <a name="l02821"></a>02821 <span class="keyword">end do</span>
- <a name="l02822"></a>02822
- <a name="l02823"></a>02823 return
- <a name="l02824"></a>02824 <span class="keyword">end</span>
- <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 )
- <a name="l02826"></a>02826 <span class="comment">!</span>
- <a name="l02827"></a>02827 <span class="comment">!*******************************************************************************</span>
- <a name="l02828"></a>02828 <span class="comment">!</span>
- <a name="l02829"></a>02829 <span class="comment">!! JACOBI_ROOT improves an approximate root of a Jacobi polynomial.</span>
- <a name="l02830"></a>02830 <span class="comment">!</span>
- <a name="l02831"></a>02831 <span class="comment">!</span>
- <a name="l02832"></a>02832 <span class="comment">! Reference:</span>
- <a name="l02833"></a>02833 <span class="comment">!</span>
- <a name="l02834"></a>02834 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l02835"></a>02835 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l02836"></a>02836 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l02837"></a>02837 <span class="comment">!</span>
- <a name="l02838"></a>02838 <span class="comment">! Modified:</span>
- <a name="l02839"></a>02839 <span class="comment">!</span>
- <a name="l02840"></a>02840 <span class="comment">! 09 December 2000</span>
- <a name="l02841"></a>02841 <span class="comment">!</span>
- <a name="l02842"></a>02842 <span class="comment">! Parameters:</span>
- <a name="l02843"></a>02843 <span class="comment">!</span>
- <a name="l02844"></a>02844 <span class="comment">! Input/output, double precision X, the approximate root, which</span>
- <a name="l02845"></a>02845 <span class="comment">! should be improved on output.</span>
- <a name="l02846"></a>02846 <span class="comment">!</span>
- <a name="l02847"></a>02847 <span class="comment">! Input, integer NORDER, the order of the polynomial to be computed.</span>
- <a name="l02848"></a>02848 <span class="comment">!</span>
- <a name="l02849"></a>02849 <span class="comment">! Input, double precision ALPHA, BETA, the exponents of (1+X) and</span>
- <a name="l02850"></a>02850 <span class="comment">! (1-X) in the quadrature rule.</span>
- <a name="l02851"></a>02851 <span class="comment">!</span>
- <a name="l02852"></a>02852 <span class="comment">! Output, double precision DP2, the value of J'(NORDER)(X).</span>
- <a name="l02853"></a>02853 <span class="comment">!</span>
- <a name="l02854"></a>02854 <span class="comment">! Output, double precision P1, the value of J(NORDER-1)(X).</span>
- <a name="l02855"></a>02855 <span class="comment">!</span>
- <a name="l02856"></a>02856 <span class="comment">! Input, double precision B(NORDER), C(NORDER), the recursion coefficients.</span>
- <a name="l02857"></a>02857 <span class="comment">!</span>
- <a name="l02858"></a>02858 <span class="keyword">implicit none</span>
- <a name="l02859"></a>02859 <span class="comment">!</span>
- <a name="l02860"></a>02860 <span class="keywordtype">integer</span> norder
- <a name="l02861"></a>02861 <span class="comment">!</span>
- <a name="l02862"></a>02862 <span class="keywordtype">double precision</span> alpha
- <a name="l02863"></a>02863 <span class="keywordtype">double precision</span> b(norder)
- <a name="l02864"></a>02864 <span class="keywordtype">double precision</span> beta
- <a name="l02865"></a>02865 <span class="keywordtype">double precision</span> c(norder)
- <a name="l02866"></a>02866 <span class="keywordtype">double precision</span> d
- <a name="l02867"></a>02867 <span class="keywordtype">double precision</span> dp2
- <a name="l02868"></a>02868 <span class="keywordtype">double precision</span> eps
- <a name="l02869"></a>02869 <span class="keywordtype">integer</span> i
- <a name="l02870"></a>02870 <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxstep = 10
- <a name="l02871"></a>02871 <span class="keywordtype">double precision</span> p1
- <a name="l02872"></a>02872 <span class="keywordtype">double precision</span> p2
- <a name="l02873"></a>02873 <span class="keywordtype">double precision</span> x
- <a name="l02874"></a>02874 <span class="comment">!</span>
- <a name="l02875"></a>02875 eps = epsilon ( x )
- <a name="l02876"></a>02876
- <a name="l02877"></a>02877 <span class="keyword">do</span> i = 1, maxstep
- <a name="l02878"></a>02878
- <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 )
- <a name="l02880"></a>02880
- <a name="l02881"></a>02881 d = p2 / dp2
- <a name="l02882"></a>02882 x = x - d
- <a name="l02883"></a>02883
- <a name="l02884"></a>02884 <span class="keyword">if</span> ( abs ( d ) <= eps * ( abs ( x ) + 1.0D+00 ) ) <span class="keyword">then</span>
- <a name="l02885"></a>02885 return
- <a name="l02886"></a>02886 <span class="keyword">end if</span>
- <a name="l02887"></a>02887
- <a name="l02888"></a>02888 <span class="keyword">end do</span>
- <a name="l02889"></a>02889
- <a name="l02890"></a>02890 return
- <a name="l02891"></a>02891 <span class="keyword">end</span>
- <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 )
- <a name="l02893"></a>02893 <span class="comment">!</span>
- <a name="l02894"></a>02894 <span class="comment">!*******************************************************************************</span>
- <a name="l02895"></a>02895 <span class="comment">!</span>
- <a name="l02896"></a>02896 <span class="comment">!! KRONROD_SET sets abscissas and weights for Gauss-Kronrod quadrature.</span>
- <a name="l02897"></a>02897 <span class="comment">!</span>
- <a name="l02898"></a>02898 <span class="comment">!</span>
- <a name="l02899"></a>02899 <span class="comment">! Integration interval:</span>
- <a name="l02900"></a>02900 <span class="comment">!</span>
- <a name="l02901"></a>02901 <span class="comment">! [ -1, 1 ]</span>
- <a name="l02902"></a>02902 <span class="comment">!</span>
- <a name="l02903"></a>02903 <span class="comment">! Weight function:</span>
- <a name="l02904"></a>02904 <span class="comment">!</span>
- <a name="l02905"></a>02905 <span class="comment">! 1.0D+00</span>
- <a name="l02906"></a>02906 <span class="comment">!</span>
- <a name="l02907"></a>02907 <span class="comment">! Integral to approximate:</span>
- <a name="l02908"></a>02908 <span class="comment">!</span>
- <a name="l02909"></a>02909 <span class="comment">! Integral ( -1 <= X <= 1 ) F(X) dX</span>
- <a name="l02910"></a>02910 <span class="comment">!</span>
- <a name="l02911"></a>02911 <span class="comment">! Approximate integral:</span>
- <a name="l02912"></a>02912 <span class="comment">!</span>
- <a name="l02913"></a>02913 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l02914"></a>02914 <span class="comment">!</span>
- <a name="l02915"></a>02915 <span class="comment">! Note:</span>
- <a name="l02916"></a>02916 <span class="comment">!</span>
- <a name="l02917"></a>02917 <span class="comment">! A Kronrod rule is used in conjunction with a lower order</span>
- <a name="l02918"></a>02918 <span class="comment">! Gauss rule, and provides an efficient error estimation.</span>
- <a name="l02919"></a>02919 <span class="comment">!</span>
- <a name="l02920"></a>02920 <span class="comment">! The error may be estimated as the difference in the two integral</span>
- <a name="l02921"></a>02921 <span class="comment">! approximations.</span>
- <a name="l02922"></a>02922 <span class="comment">!</span>
- <a name="l02923"></a>02923 <span class="comment">! The efficiency comes about because the Kronrod uses the abscissas</span>
- <a name="l02924"></a>02924 <span class="comment">! of the Gauss rule, thus saving on the number of function evaluations</span>
- <a name="l02925"></a>02925 <span class="comment">! necessary. If the Kronrod rule were replaced by a Gauss rule of</span>
- <a name="l02926"></a>02926 <span class="comment">! the same order, a higher precision integral estimate would be</span>
- <a name="l02927"></a>02927 <span class="comment">! made, but the function would have to be evaluated at many more</span>
- <a name="l02928"></a>02928 <span class="comment">! points.</span>
- <a name="l02929"></a>02929 <span class="comment">!</span>
- <a name="l02930"></a>02930 <span class="comment">! The Gauss Kronrod pair of rules involves an ( NORDER + 1 ) / 2</span>
- <a name="l02931"></a>02931 <span class="comment">! point Gauss-Legendre rule and an NORDER point Kronrod rule.</span>
- <a name="l02932"></a>02932 <span class="comment">! Thus, the 15 point Kronrod rule should be paired with the</span>
- <a name="l02933"></a>02933 <span class="comment">! Gauss-Legendre 7 point rule.</span>
- <a name="l02934"></a>02934 <span class="comment">!</span>
- <a name="l02935"></a>02935 <span class="comment">! Reference:</span>
- <a name="l02936"></a>02936 <span class="comment">!</span>
- <a name="l02937"></a>02937 <span class="comment">! R Piessens, E de Doncker-Kapenger, C Ueberhuber, D Kahaner,</span>
- <a name="l02938"></a>02938 <span class="comment">! QUADPACK, A Subroutine Package for Automatic Integration,</span>
- <a name="l02939"></a>02939 <span class="comment">! Springer Verlag, 1983.</span>
- <a name="l02940"></a>02940 <span class="comment">!</span>
- <a name="l02941"></a>02941 <span class="comment">! Modified:</span>
- <a name="l02942"></a>02942 <span class="comment">!</span>
- <a name="l02943"></a>02943 <span class="comment">! 16 September 1998</span>
- <a name="l02944"></a>02944 <span class="comment">!</span>
- <a name="l02945"></a>02945 <span class="comment">! Author:</span>
- <a name="l02946"></a>02946 <span class="comment">!</span>
- <a name="l02947"></a>02947 <span class="comment">! John Burkardt</span>
- <a name="l02948"></a>02948 <span class="comment">!</span>
- <a name="l02949"></a>02949 <span class="comment">! Parameters:</span>
- <a name="l02950"></a>02950 <span class="comment">!</span>
- <a name="l02951"></a>02951 <span class="comment">! Input, integer NORDER, the order of the rule, which may be</span>
- <a name="l02952"></a>02952 <span class="comment">! 15, 21, 31 or 41, corresponding to Gauss-Legendre rules of</span>
- <a name="l02953"></a>02953 <span class="comment">! order 7, 10, 15 or 20.</span>
- <a name="l02954"></a>02954 <span class="comment">!</span>
- <a name="l02955"></a>02955 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule, which</span>
- <a name="l02956"></a>02956 <span class="comment">! are symmetrically places in [-1,1].</span>
- <a name="l02957"></a>02957 <span class="comment">!</span>
- <a name="l02958"></a>02958 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l02959"></a>02959 <span class="comment">! The weights are positive, symmetric, and should sum to 2.</span>
- <a name="l02960"></a>02960 <span class="comment">!</span>
- <a name="l02961"></a>02961 <span class="keyword">implicit none</span>
- <a name="l02962"></a>02962 <span class="comment">!</span>
- <a name="l02963"></a>02963 <span class="keywordtype">integer</span> norder
- <a name="l02964"></a>02964 <span class="comment">!</span>
- <a name="l02965"></a>02965 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l02966"></a>02966 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l02967"></a>02967 <span class="comment">!</span>
- <a name="l02968"></a>02968 <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
- <a name="l02969"></a>02969
- <a name="l02970"></a>02970 xtab(1) = - 0.9914553711208126D+00
- <a name="l02971"></a>02971 xtab(2) = - 0.9491079123427585D+00
- <a name="l02972"></a>02972 xtab(3) = - 0.8648644233597691D+00
- <a name="l02973"></a>02973 xtab(4) = - 0.7415311855993944D+00
- <a name="l02974"></a>02974 xtab(5) = - 0.5860872354676911D+00
- <a name="l02975"></a>02975 xtab(6) = - 0.4058451513773972D+00
- <a name="l02976"></a>02976 xtab(7) = - 0.2077849550789850D+00
- <a name="l02977"></a>02977 xtab(8) = 0.0D+00
- <a name="l02978"></a>02978 xtab(9) = 0.2077849550789850D+00
- <a name="l02979"></a>02979 xtab(10) = 0.4058451513773972D+00
- <a name="l02980"></a>02980 xtab(11) = 0.5860872354676911D+00
- <a name="l02981"></a>02981 xtab(12) = 0.7415311855993944D+00
- <a name="l02982"></a>02982 xtab(13) = 0.8648644233597691D+00
- <a name="l02983"></a>02983 xtab(14) = 0.9491079123427585D+00
- <a name="l02984"></a>02984 xtab(15) = 0.9914553711208126D+00
- <a name="l02985"></a>02985
- <a name="l02986"></a>02986 weight(1) = 0.2293532201052922D-01
- <a name="l02987"></a>02987 weight(2) = 0.6309209262997855D-01
- <a name="l02988"></a>02988 weight(3) = 0.1047900103222502D+00
- <a name="l02989"></a>02989 weight(4) = 0.1406532597155259D+00
- <a name="l02990"></a>02990 weight(5) = 0.1690047266392679D+00
- <a name="l02991"></a>02991 weight(6) = 0.1903505780647854D+00
- <a name="l02992"></a>02992 weight(7) = 0.2044329400752989D+00
- <a name="l02993"></a>02993 weight(8) = 0.2094821410847278D+00
- <a name="l02994"></a>02994 weight(9) = 0.2044329400752989D+00
- <a name="l02995"></a>02995 weight(10) = 0.1903505780647854D+00
- <a name="l02996"></a>02996 weight(11) = 0.1690047266392679D+00
- <a name="l02997"></a>02997 weight(12) = 0.1406532597155259D+00
- <a name="l02998"></a>02998 weight(13) = 0.1047900103222502D+00
- <a name="l02999"></a>02999 weight(14) = 0.6309209262997855D-01
- <a name="l03000"></a>03000 weight(15) = 0.2293532201052922D-01
- <a name="l03001"></a>03001
- <a name="l03002"></a>03002 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 21 ) <span class="keyword">then</span>
- <a name="l03003"></a>03003
- <a name="l03004"></a>03004 xtab(1) = - 0.9956571630258081D+00
- <a name="l03005"></a>03005 xtab(2) = - 0.9739065285171717D+00
- <a name="l03006"></a>03006 xtab(3) = - 0.9301574913557082D+00
- <a name="l03007"></a>03007 xtab(4) = - 0.8650633666889845D+00
- <a name="l03008"></a>03008 xtab(5) = - 0.7808177265864169D+00
- <a name="l03009"></a>03009 xtab(6) = - 0.6794095682990244D+00
- <a name="l03010"></a>03010 xtab(7) = - 0.5627571346686047D+00
- <a name="l03011"></a>03011 xtab(8) = - 0.4333953941292472D+00
- <a name="l03012"></a>03012 xtab(9) = - 0.2943928627014602D+00
- <a name="l03013"></a>03013 xtab(10) = - 0.1488743389816312D+00
- <a name="l03014"></a>03014 xtab(11) = 0.0D+00
- <a name="l03015"></a>03015 xtab(12) = 0.1488743389816312D+00
- <a name="l03016"></a>03016 xtab(13) = 0.2943928627014602D+00
- <a name="l03017"></a>03017 xtab(14) = 0.4333953941292472D+00
- <a name="l03018"></a>03018 xtab(15) = 0.5627571346686047D+00
- <a name="l03019"></a>03019 xtab(16) = 0.6794095682990244D+00
- <a name="l03020"></a>03020 xtab(17) = 0.7808177265864169D+00
- <a name="l03021"></a>03021 xtab(18) = 0.8650633666889845D+00
- <a name="l03022"></a>03022 xtab(19) = 0.9301574913557082D+00
- <a name="l03023"></a>03023 xtab(20) = 0.9739065285171717D+00
- <a name="l03024"></a>03024 xtab(21) = 0.9956571630258081D+00
- <a name="l03025"></a>03025
- <a name="l03026"></a>03026 weight(1) = 0.1169463886737187D-01
- <a name="l03027"></a>03027 weight(2) = 0.3255816230796473D-01
- <a name="l03028"></a>03028 weight(3) = 0.5475589657435200D-01
- <a name="l03029"></a>03029 weight(4) = 0.7503967481091995D-01
- <a name="l03030"></a>03030 weight(5) = 0.9312545458369761D-01
- <a name="l03031"></a>03031 weight(6) = 0.1093871588022976D+00
- <a name="l03032"></a>03032 weight(7) = 0.1234919762620659D+00
- <a name="l03033"></a>03033 weight(8) = 0.1347092173114733D+00
- <a name="l03034"></a>03034 weight(9) = 0.1427759385770601D+00
- <a name="l03035"></a>03035 weight(10) = 0.1477391049013385D+00
- <a name="l03036"></a>03036 weight(11) = 0.1494455540029169D+00
- <a name="l03037"></a>03037 weight(12) = 0.1477391049013385D+00
- <a name="l03038"></a>03038 weight(13) = 0.1427759385770601D+00
- <a name="l03039"></a>03039 weight(14) = 0.1347092173114733D+00
- <a name="l03040"></a>03040 weight(15) = 0.1234919762620659D+00
- <a name="l03041"></a>03041 weight(16) = 0.1093871588022976D+00
- <a name="l03042"></a>03042 weight(17) = 0.9312545458369761D-01
- <a name="l03043"></a>03043 weight(18) = 0.7503967481091995D-01
- <a name="l03044"></a>03044 weight(19) = 0.5475589657435200D-01
- <a name="l03045"></a>03045 weight(20) = 0.3255816230796473D-01
- <a name="l03046"></a>03046 weight(21) = 0.1169463886737187D-01
- <a name="l03047"></a>03047
- <a name="l03048"></a>03048 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 31 ) <span class="keyword">then</span>
- <a name="l03049"></a>03049
- <a name="l03050"></a>03050 xtab(1) = - 0.9980022986933971D+00
- <a name="l03051"></a>03051 xtab(2) = - 0.9879925180204854D+00
- <a name="l03052"></a>03052 xtab(3) = - 0.9677390756791391D+00
- <a name="l03053"></a>03053 xtab(4) = - 0.9372733924007059D+00
- <a name="l03054"></a>03054 xtab(5) = - 0.8972645323440819D+00
- <a name="l03055"></a>03055 xtab(6) = - 0.8482065834104272D+00
- <a name="l03056"></a>03056 xtab(7) = - 0.7904185014424659D+00
- <a name="l03057"></a>03057 xtab(8) = - 0.7244177313601700D+00
- <a name="l03058"></a>03058 xtab(9) = - 0.6509967412974170D+00
- <a name="l03059"></a>03059 xtab(10) = - 0.5709721726085388D+00
- <a name="l03060"></a>03060 xtab(11) = - 0.4850818636402397D+00
- <a name="l03061"></a>03061 xtab(12) = - 0.3941513470775634D+00
- <a name="l03062"></a>03062 xtab(13) = - 0.2991800071531688D+00
- <a name="l03063"></a>03063 xtab(14) = - 0.2011940939974345D+00
- <a name="l03064"></a>03064 xtab(15) = - 0.1011420669187175D+00
- <a name="l03065"></a>03065 xtab(16) = 0.0D+00
- <a name="l03066"></a>03066 xtab(17) = 0.1011420669187175D+00
- <a name="l03067"></a>03067 xtab(18) = 0.2011940939974345D+00
- <a name="l03068"></a>03068 xtab(19) = 0.2991800071531688D+00
- <a name="l03069"></a>03069 xtab(20) = 0.3941513470775634D+00
- <a name="l03070"></a>03070 xtab(21) = 0.4850818636402397D+00
- <a name="l03071"></a>03071 xtab(22) = 0.5709721726085388D+00
- <a name="l03072"></a>03072 xtab(23) = 0.6509967412974170D+00
- <a name="l03073"></a>03073 xtab(24) = 0.7244177313601700D+00
- <a name="l03074"></a>03074 xtab(25) = 0.7904185014424659D+00
- <a name="l03075"></a>03075 xtab(26) = 0.8482065834104272D+00
- <a name="l03076"></a>03076 xtab(27) = 0.8972645323440819D+00
- <a name="l03077"></a>03077 xtab(28) = 0.9372733924007059D+00
- <a name="l03078"></a>03078 xtab(29) = 0.9677390756791391D+00
- <a name="l03079"></a>03079 xtab(30) = 0.9879925180204854D+00
- <a name="l03080"></a>03080 xtab(31) = 0.9980022986933971D+00
- <a name="l03081"></a>03081
- <a name="l03082"></a>03082 weight(1) = 0.5377479872923349D-02
- <a name="l03083"></a>03083 weight(2) = 0.1500794732931612D-01
- <a name="l03084"></a>03084 weight(3) = 0.2546084732671532D-01
- <a name="l03085"></a>03085 weight(4) = 0.3534636079137585D-01
- <a name="l03086"></a>03086 weight(5) = 0.4458975132476488D-01
- <a name="l03087"></a>03087 weight(6) = 0.5348152469092809D-01
- <a name="l03088"></a>03088 weight(7) = 0.6200956780067064D-01
- <a name="l03089"></a>03089 weight(8) = 0.6985412131872826D-01
- <a name="l03090"></a>03090 weight(9) = 0.7684968075772038D-01
- <a name="l03091"></a>03091 weight(10) = 0.8308050282313302D-01
- <a name="l03092"></a>03092 weight(11) = 0.8856444305621177D-01
- <a name="l03093"></a>03093 weight(12) = 0.9312659817082532D-01
- <a name="l03094"></a>03094 weight(13) = 0.9664272698362368D-01
- <a name="l03095"></a>03095 weight(14) = 0.9917359872179196D-01
- <a name="l03096"></a>03096 weight(15) = 0.1007698455238756D+00
- <a name="l03097"></a>03097 weight(16) = 0.1013300070147915D+00
- <a name="l03098"></a>03098 weight(17) = 0.1007698455238756D+00
- <a name="l03099"></a>03099 weight(18) = 0.9917359872179196D-01
- <a name="l03100"></a>03100 weight(19) = 0.9664272698362368D-01
- <a name="l03101"></a>03101 weight(20) = 0.9312659817082532D-01
- <a name="l03102"></a>03102 weight(21) = 0.8856444305621177D-01
- <a name="l03103"></a>03103 weight(22) = 0.8308050282313302D-01
- <a name="l03104"></a>03104 weight(23) = 0.7684968075772038D-01
- <a name="l03105"></a>03105 weight(24) = 0.6985412131872826D-01
- <a name="l03106"></a>03106 weight(25) = 0.6200956780067064D-01
- <a name="l03107"></a>03107 weight(26) = 0.5348152469092809D-01
- <a name="l03108"></a>03108 weight(27) = 0.4458975132476488D-01
- <a name="l03109"></a>03109 weight(28) = 0.3534636079137585D-01
- <a name="l03110"></a>03110 weight(29) = 0.2546084732671532D-01
- <a name="l03111"></a>03111 weight(30) = 0.1500794732931612D-01
- <a name="l03112"></a>03112 weight(31) = 0.5377479872923349D-02
- <a name="l03113"></a>03113
- <a name="l03114"></a>03114 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 41 ) <span class="keyword">then</span>
- <a name="l03115"></a>03115
- <a name="l03116"></a>03116 xtab(1) = - 0.9988590315882777D+00
- <a name="l03117"></a>03117 xtab(2) = - 0.9931285991850949D+00
- <a name="l03118"></a>03118 xtab(3) = - 0.9815078774502503D+00
- <a name="l03119"></a>03119 xtab(4) = - 0.9639719272779138D+00
- <a name="l03120"></a>03120 xtab(5) = - 0.9408226338317548D+00
- <a name="l03121"></a>03121 xtab(6) = - 0.9122344282513259D+00
- <a name="l03122"></a>03122 xtab(7) = - 0.8782768112522820D+00
- <a name="l03123"></a>03123 xtab(8) = - 0.8391169718222188D+00
- <a name="l03124"></a>03124 xtab(9) = - 0.7950414288375512D+00
- <a name="l03125"></a>03125 xtab(10) = - 0.7463319064601508D+00
- <a name="l03126"></a>03126 xtab(11) = - 0.6932376563347514D+00
- <a name="l03127"></a>03127 xtab(12) = - 0.6360536807265150D+00
- <a name="l03128"></a>03128 xtab(13) = - 0.5751404468197103D+00
- <a name="l03129"></a>03129 xtab(14) = - 0.5108670019508271D+00
- <a name="l03130"></a>03130 xtab(15) = - 0.4435931752387251D+00
- <a name="l03131"></a>03131 xtab(16) = - 0.3737060887154196D+00
- <a name="l03132"></a>03132 xtab(17) = - 0.3016278681149130D+00
- <a name="l03133"></a>03133 xtab(18) = - 0.2277858511416451D+00
- <a name="l03134"></a>03134 xtab(19) = - 0.1526054652409227D+00
- <a name="l03135"></a>03135 xtab(20) = - 0.7652652113349733D-01
- <a name="l03136"></a>03136 xtab(21) = 0.0D+00
- <a name="l03137"></a>03137 xtab(22) = 0.7652652113349733D-01
- <a name="l03138"></a>03138 xtab(23) = 0.1526054652409227D+00
- <a name="l03139"></a>03139 xtab(24) = 0.2277858511416451D+00
- <a name="l03140"></a>03140 xtab(25) = 0.3016278681149130D+00
- <a name="l03141"></a>03141 xtab(26) = 0.3737060887154196D+00
- <a name="l03142"></a>03142 xtab(27) = 0.4435931752387251D+00
- <a name="l03143"></a>03143 xtab(28) = 0.5108670019508271D+00
- <a name="l03144"></a>03144 xtab(29) = 0.5751404468197103D+00
- <a name="l03145"></a>03145 xtab(30) = 0.6360536807265150D+00
- <a name="l03146"></a>03146 xtab(31) = 0.6932376563347514D+00
- <a name="l03147"></a>03147 xtab(32) = 0.7463319064601508D+00
- <a name="l03148"></a>03148 xtab(33) = 0.7950414288375512D+00
- <a name="l03149"></a>03149 xtab(34) = 0.8391169718222188D+00
- <a name="l03150"></a>03150 xtab(35) = 0.8782768112522820D+00
- <a name="l03151"></a>03151 xtab(36) = 0.9122344282513259D+00
- <a name="l03152"></a>03152 xtab(37) = 0.9408226338317548D+00
- <a name="l03153"></a>03153 xtab(38) = 0.9639719272779138D+00
- <a name="l03154"></a>03154 xtab(39) = 0.9815078774502503D+00
- <a name="l03155"></a>03155 xtab(40) = 0.9931285991850949D+00
- <a name="l03156"></a>03156 xtab(41) = 0.9988590315882777D+00
- <a name="l03157"></a>03157
- <a name="l03158"></a>03158 weight(1) = 0.3073583718520532D-02
- <a name="l03159"></a>03159 weight(2) = 0.8600269855642942D-02
- <a name="l03160"></a>03160 weight(3) = 0.1462616925697125D-01
- <a name="l03161"></a>03161 weight(4) = 0.2038837346126652D-01
- <a name="l03162"></a>03162 weight(5) = 0.2588213360495116D-01
- <a name="l03163"></a>03163 weight(6) = 0.3128730677703280D-01
- <a name="l03164"></a>03164 weight(7) = 0.3660016975820080D-01
- <a name="l03165"></a>03165 weight(8) = 0.4166887332797369D-01
- <a name="l03166"></a>03166 weight(9) = 0.4643482186749767D-01
- <a name="l03167"></a>03167 weight(10) = 0.5094457392372869D-01
- <a name="l03168"></a>03168 weight(11) = 0.5519510534828599D-01
- <a name="l03169"></a>03169 weight(12) = 0.5911140088063957D-01
- <a name="l03170"></a>03170 weight(13) = 0.6265323755478117D-01
- <a name="l03171"></a>03171 weight(14) = 0.6583459713361842D-01
- <a name="l03172"></a>03172 weight(15) = 0.6864867292852162D-01
- <a name="l03173"></a>03173 weight(16) = 0.7105442355344407D-01
- <a name="l03174"></a>03174 weight(17) = 0.7303069033278667D-01
- <a name="l03175"></a>03175 weight(18) = 0.7458287540049919D-01
- <a name="l03176"></a>03176 weight(19) = 0.7570449768455667D-01
- <a name="l03177"></a>03177 weight(20) = 0.7637786767208074D-01
- <a name="l03178"></a>03178 weight(21) = 0.7660071191799966D-01
- <a name="l03179"></a>03179 weight(22) = 0.7637786767208074D-01
- <a name="l03180"></a>03180 weight(23) = 0.7570449768455667D-01
- <a name="l03181"></a>03181 weight(24) = 0.7458287540049919D-01
- <a name="l03182"></a>03182 weight(25) = 0.7303069033278667D-01
- <a name="l03183"></a>03183 weight(26) = 0.7105442355344407D-01
- <a name="l03184"></a>03184 weight(27) = 0.6864867292852162D-01
- <a name="l03185"></a>03185 weight(28) = 0.6583459713361842D-01
- <a name="l03186"></a>03186 weight(29) = 0.6265323755478117D-01
- <a name="l03187"></a>03187 weight(30) = 0.5911140088063957D-01
- <a name="l03188"></a>03188 weight(31) = 0.5519510534828599D-01
- <a name="l03189"></a>03189 weight(32) = 0.5094457392372869D-01
- <a name="l03190"></a>03190 weight(33) = 0.4643482186749767D-01
- <a name="l03191"></a>03191 weight(34) = 0.4166887332797369D-01
- <a name="l03192"></a>03192 weight(35) = 0.3660016975820080D-01
- <a name="l03193"></a>03193 weight(36) = 0.3128730677703280D-01
- <a name="l03194"></a>03194 weight(37) = 0.2588213360495116D-01
- <a name="l03195"></a>03195 weight(38) = 0.2038837346126652D-01
- <a name="l03196"></a>03196 weight(39) = 0.1462616925697125D-01
- <a name="l03197"></a>03197 weight(40) = 0.8600269855642942D-02
- <a name="l03198"></a>03198 weight(41) = 0.3073583718520532D-02
- <a name="l03199"></a>03199
- <a name="l03200"></a>03200 <span class="keyword">else</span>
- <a name="l03201"></a>03201
- <a name="l03202"></a>03202 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l03203"></a>03203 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'KRONROD_SET - Fatal error!'</span>
- <a name="l03204"></a>03204 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l03205"></a>03205 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' Legal values are 15, 21, 31 or 41.'</span>
- <a name="l03206"></a>03206 stop
- <a name="l03207"></a>03207
- <a name="l03208"></a>03208 <span class="keyword">end if</span>
- <a name="l03209"></a>03209
- <a name="l03210"></a>03210 return
- <a name="l03211"></a>03211 <span class="keyword">end</span>
- <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 )
- <a name="l03213"></a>03213 <span class="comment">!</span>
- <a name="l03214"></a>03214 <span class="comment">!*******************************************************************************</span>
- <a name="l03215"></a>03215 <span class="comment">!</span>
- <a name="l03216"></a>03216 <span class="comment">!! LAGUERRE_COM computes the abscissa and weights for Gauss-Laguerre quadrature.</span>
- <a name="l03217"></a>03217 <span class="comment">!</span>
- <a name="l03218"></a>03218 <span class="comment">!</span>
- <a name="l03219"></a>03219 <span class="comment">! Discussion:</span>
- <a name="l03220"></a>03220 <span class="comment">!</span>
- <a name="l03221"></a>03221 <span class="comment">! In the simplest case, ALPHA is 0, and we are approximating the</span>
- <a name="l03222"></a>03222 <span class="comment">! integral from 0 to INFINITY of EXP(-X) * F(X). When this is so,</span>
- <a name="l03223"></a>03223 <span class="comment">! it is easy to modify the rule to approximate the integral from</span>
- <a name="l03224"></a>03224 <span class="comment">! A to INFINITY as well.</span>
- <a name="l03225"></a>03225 <span class="comment">!</span>
- <a name="l03226"></a>03226 <span class="comment">! If ALPHA is nonzero, then there is no simple way to extend the</span>
- <a name="l03227"></a>03227 <span class="comment">! rule to approximate the integral from A to INFINITY. The simplest</span>
- <a name="l03228"></a>03228 <span class="comment">! procedures would be to approximate the integral from 0 to A.</span>
- <a name="l03229"></a>03229 <span class="comment">!</span>
- <a name="l03230"></a>03230 <span class="comment">! Integration interval:</span>
- <a name="l03231"></a>03231 <span class="comment">!</span>
- <a name="l03232"></a>03232 <span class="comment">! [ A, +Infinity ) or [ 0, +Infinity )</span>
- <a name="l03233"></a>03233 <span class="comment">!</span>
- <a name="l03234"></a>03234 <span class="comment">! Weight function:</span>
- <a name="l03235"></a>03235 <span class="comment">!</span>
- <a name="l03236"></a>03236 <span class="comment">! EXP ( - X ) or EXP ( - X ) * X**ALPHA</span>
- <a name="l03237"></a>03237 <span class="comment">!</span>
- <a name="l03238"></a>03238 <span class="comment">! Integral to approximate:</span>
- <a name="l03239"></a>03239 <span class="comment">!</span>
- <a name="l03240"></a>03240 <span class="comment">! Integral ( A <= X < +INFINITY ) EXP ( - X ) * F(X) dX</span>
- <a name="l03241"></a>03241 <span class="comment">! or</span>
- <a name="l03242"></a>03242 <span class="comment">! Integral ( 0 <= X < +INFINITY ) EXP ( - X ) * X**ALPHA * F(X) dX</span>
- <a name="l03243"></a>03243 <span class="comment">!</span>
- <a name="l03244"></a>03244 <span class="comment">! Approximate integral:</span>
- <a name="l03245"></a>03245 <span class="comment">!</span>
- <a name="l03246"></a>03246 <span class="comment">! EXP ( - A ) * Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( A+XTAB(I) )</span>
- <a name="l03247"></a>03247 <span class="comment">! or</span>
- <a name="l03248"></a>03248 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l03249"></a>03249 <span class="comment">!</span>
- <a name="l03250"></a>03250 <span class="comment">! Reference:</span>
- <a name="l03251"></a>03251 <span class="comment">!</span>
- <a name="l03252"></a>03252 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l03253"></a>03253 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l03254"></a>03254 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l03255"></a>03255 <span class="comment">!</span>
- <a name="l03256"></a>03256 <span class="comment">! Modified:</span>
- <a name="l03257"></a>03257 <span class="comment">!</span>
- <a name="l03258"></a>03258 <span class="comment">! 15 March 2000</span>
- <a name="l03259"></a>03259 <span class="comment">!</span>
- <a name="l03260"></a>03260 <span class="comment">! Parameters:</span>
- <a name="l03261"></a>03261 <span class="comment">!</span>
- <a name="l03262"></a>03262 <span class="comment">! Input, integer NORDER, the order of the quadrature rule to be computed.</span>
- <a name="l03263"></a>03263 <span class="comment">! NORDER must be at least 1.</span>
- <a name="l03264"></a>03264 <span class="comment">!</span>
- <a name="l03265"></a>03265 <span class="comment">! Output, double precision XTAB(NORDER), the Gauss-Laguerre abscissas.</span>
- <a name="l03266"></a>03266 <span class="comment">!</span>
- <a name="l03267"></a>03267 <span class="comment">! Output, double precision WEIGHT(NORDER), the Gauss-Laguerre weights.</span>
- <a name="l03268"></a>03268 <span class="comment">!</span>
- <a name="l03269"></a>03269 <span class="comment">! Input, double precision ALPHA, the exponent of the X factor.</span>
- <a name="l03270"></a>03270 <span class="comment">! Set ALPHA = 0.0D+00 for the simplest rule.</span>
- <a name="l03271"></a>03271 <span class="comment">! ALPHA must be nonnegative.</span>
- <a name="l03272"></a>03272 <span class="comment">!</span>
- <a name="l03273"></a>03273 <span class="keyword">implicit none</span>
- <a name="l03274"></a>03274 <span class="comment">!</span>
- <a name="l03275"></a>03275 <span class="keywordtype">integer</span> norder
- <a name="l03276"></a>03276 <span class="comment">!</span>
- <a name="l03277"></a>03277 <span class="keywordtype">double precision</span> alpha
- <a name="l03278"></a>03278 <span class="keywordtype">double precision</span> b(norder)
- <a name="l03279"></a>03279 <span class="keywordtype">double precision</span> c(norder)
- <a name="l03280"></a>03280 <span class="keywordtype">double precision</span> cc
- <a name="l03281"></a>03281 <span class="keywordtype">double precision</span> dp2
- <a name="l03282"></a>03282 <span class="keywordtype">double precision</span> gamma
- <a name="l03283"></a>03283 <span class="keywordtype">integer</span> i
- <a name="l03284"></a>03284 <span class="keywordtype">double precision</span> p1
- <a name="l03285"></a>03285 <span class="keywordtype">double precision</span> r1
- <a name="l03286"></a>03286 <span class="keywordtype">double precision</span> r2
- <a name="l03287"></a>03287 <span class="keywordtype">double precision</span> ratio
- <a name="l03288"></a>03288 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l03289"></a>03289 <span class="keywordtype">double precision</span> x
- <a name="l03290"></a>03290 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l03291"></a>03291 <span class="comment">!</span>
- <a name="l03292"></a>03292 <span class="comment">! Set the recursion coefficients.</span>
- <a name="l03293"></a>03293 <span class="comment">!</span>
- <a name="l03294"></a>03294 <span class="keyword">do</span> i = 1, norder
- <a name="l03295"></a>03295 b(i) = ( alpha + dble ( 2 * i - 1 ) )
- <a name="l03296"></a>03296 <span class="keyword">end do</span>
- <a name="l03297"></a>03297
- <a name="l03298"></a>03298 <span class="keyword">do</span> i = 1, norder
- <a name="l03299"></a>03299 c(i) = dble ( i - 1 ) * ( alpha + dble ( i - 1 ) )
- <a name="l03300"></a>03300 <span class="keyword">end do</span>
- <a name="l03301"></a>03301
- <a name="l03302"></a>03302 cc = gamma ( alpha + 1.0D+00 ) * product ( c(2:norder) )
- <a name="l03303"></a>03303
- <a name="l03304"></a>03304 <span class="keyword">do</span> i = 1, norder
- <a name="l03305"></a>03305 <span class="comment">!</span>
- <a name="l03306"></a>03306 <span class="comment">! Compute an estimate for the root.</span>
- <a name="l03307"></a>03307 <span class="comment">!</span>
- <a name="l03308"></a>03308 <span class="keyword">if</span> ( i == 1 ) <span class="keyword">then</span>
- <a name="l03309"></a>03309
- <a name="l03310"></a>03310 x = ( 1.0D+00 + alpha ) * ( 3.0D+00+ 0.92 * alpha ) / &
- <a name="l03311"></a>03311 ( 1.0D+00 + 2.4D+00 * dble ( norder ) + 1.8D+00 * alpha )
- <a name="l03312"></a>03312
- <a name="l03313"></a>03313 <span class="keyword">else</span> <span class="keyword">if</span> ( i == 2 ) <span class="keyword">then</span>
- <a name="l03314"></a>03314
- <a name="l03315"></a>03315 x = x + ( 15.0D+00 + 6.25D+00 * alpha ) / &
- <a name="l03316"></a>03316 ( 1.0D+00 + 0.9D+00 * alpha + 2.5D+00 * dble ( norder ) )
- <a name="l03317"></a>03317
- <a name="l03318"></a>03318 <span class="keyword">else</span>
- <a name="l03319"></a>03319
- <a name="l03320"></a>03320 r1 = ( 1.0D+00 + 2.55D+00 * dble ( i - 2 ) ) / ( 1.9D+00 * dble ( i - 2 ) )
- <a name="l03321"></a>03321
- <a name="l03322"></a>03322 r2 = 1.26D+00 * dble ( i - 2 ) * alpha / &
- <a name="l03323"></a>03323 ( 1.0D+00 + 3.5D+00 * dble ( i - 2 ) )
- <a name="l03324"></a>03324
- <a name="l03325"></a>03325 ratio = ( r1 + r2 ) / ( 1.0D+00 + 0.3D+00 * alpha )
- <a name="l03326"></a>03326
- <a name="l03327"></a>03327 x = x + ratio * ( x - xtab(i-2) )
- <a name="l03328"></a>03328
- <a name="l03329"></a>03329 <span class="keyword">end if</span>
- <a name="l03330"></a>03330 <span class="comment">!</span>
- <a name="l03331"></a>03331 <span class="comment">! Use iteration to find the root.</span>
- <a name="l03332"></a>03332 <span class="comment">!</span>
- <a name="l03333"></a>03333 call <a class="code" href="quadrule_8f90.html#a50878552a6862bdc03e4e7d904d7b154">laguerre_root </a>( x, norder, alpha, dp2, p1, b, c )
- <a name="l03334"></a>03334 <span class="comment">!</span>
- <a name="l03335"></a>03335 <span class="comment">! Set the abscissa and weight.</span>
- <a name="l03336"></a>03336 <span class="comment">!</span>
- <a name="l03337"></a>03337 xtab(i) = x
- <a name="l03338"></a>03338 weight(i) = ( cc / dp2 ) / p1
- <a name="l03339"></a>03339
- <a name="l03340"></a>03340 <span class="keyword">end do</span>
- <a name="l03341"></a>03341
- <a name="l03342"></a>03342 return
- <a name="l03343"></a>03343 <span class="keyword">end</span>
- <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 )
- <a name="l03345"></a>03345 <span class="comment">!</span>
- <a name="l03346"></a>03346 <span class="comment">!*******************************************************************************</span>
- <a name="l03347"></a>03347 <span class="comment">!</span>
- <a name="l03348"></a>03348 <span class="comment">!! LAGUERRE_RECUR finds the value and derivative of a Laguerre polynomial.</span>
- <a name="l03349"></a>03349 <span class="comment">!</span>
- <a name="l03350"></a>03350 <span class="comment">!</span>
- <a name="l03351"></a>03351 <span class="comment">! Reference:</span>
- <a name="l03352"></a>03352 <span class="comment">!</span>
- <a name="l03353"></a>03353 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l03354"></a>03354 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l03355"></a>03355 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l03356"></a>03356 <span class="comment">!</span>
- <a name="l03357"></a>03357 <span class="comment">! Modified:</span>
- <a name="l03358"></a>03358 <span class="comment">!</span>
- <a name="l03359"></a>03359 <span class="comment">! 19 September 1998</span>
- <a name="l03360"></a>03360 <span class="comment">!</span>
- <a name="l03361"></a>03361 <span class="comment">! Parameters:</span>
- <a name="l03362"></a>03362 <span class="comment">!</span>
- <a name="l03363"></a>03363 <span class="comment">! Output, double precision P2, the value of L(NORDER)(X).</span>
- <a name="l03364"></a>03364 <span class="comment">!</span>
- <a name="l03365"></a>03365 <span class="comment">! Output, double precision DP2, the value of L'(NORDER)(X).</span>
- <a name="l03366"></a>03366 <span class="comment">!</span>
- <a name="l03367"></a>03367 <span class="comment">! Output, double precision P1, the value of L(NORDER-1)(X).</span>
- <a name="l03368"></a>03368 <span class="comment">!</span>
- <a name="l03369"></a>03369 <span class="comment">! Input, double precision X, the point at which polynomials are evaluated.</span>
- <a name="l03370"></a>03370 <span class="comment">!</span>
- <a name="l03371"></a>03371 <span class="comment">! Input, integer NORDER, the order of the polynomial to be computed.</span>
- <a name="l03372"></a>03372 <span class="comment">!</span>
- <a name="l03373"></a>03373 <span class="comment">! Input, double precision ALPHA, the exponent of the X factor in the</span>
- <a name="l03374"></a>03374 <span class="comment">! integrand.</span>
- <a name="l03375"></a>03375 <span class="comment">!</span>
- <a name="l03376"></a>03376 <span class="comment">! Input, double precision B(NORDER), C(NORDER), the recursion</span>
- <a name="l03377"></a>03377 <span class="comment">! coefficients.</span>
- <a name="l03378"></a>03378 <span class="comment">!</span>
- <a name="l03379"></a>03379 <span class="keyword">implicit none</span>
- <a name="l03380"></a>03380 <span class="comment">!</span>
- <a name="l03381"></a>03381 <span class="keywordtype">integer</span> norder
- <a name="l03382"></a>03382 <span class="comment">!</span>
- <a name="l03383"></a>03383 <span class="keywordtype">double precision</span> alpha
- <a name="l03384"></a>03384 <span class="keywordtype">double precision</span> b(norder)
- <a name="l03385"></a>03385 <span class="keywordtype">double precision</span> c(norder)
- <a name="l03386"></a>03386 <span class="keywordtype">double precision</span> dp0
- <a name="l03387"></a>03387 <span class="keywordtype">double precision</span> dp1
- <a name="l03388"></a>03388 <span class="keywordtype">double precision</span> dp2
- <a name="l03389"></a>03389 <span class="keywordtype">integer</span> i
- <a name="l03390"></a>03390 <span class="keywordtype">double precision</span> p0
- <a name="l03391"></a>03391 <span class="keywordtype">double precision</span> p1
- <a name="l03392"></a>03392 <span class="keywordtype">double precision</span> p2
- <a name="l03393"></a>03393 <span class="keywordtype">double precision</span> x
- <a name="l03394"></a>03394 <span class="comment">!</span>
- <a name="l03395"></a>03395 p1 = 1.0D+00
- <a name="l03396"></a>03396 dp1 = 0.0D+00
- <a name="l03397"></a>03397
- <a name="l03398"></a>03398 p2 = x - alpha - 1.0D+00
- <a name="l03399"></a>03399 dp2 = 1.0D+00
- <a name="l03400"></a>03400
- <a name="l03401"></a>03401 <span class="keyword">do</span> i = 2, norder
- <a name="l03402"></a>03402
- <a name="l03403"></a>03403 p0 = p1
- <a name="l03404"></a>03404 dp0 = dp1
- <a name="l03405"></a>03405
- <a name="l03406"></a>03406 p1 = p2
- <a name="l03407"></a>03407 dp1 = dp2
- <a name="l03408"></a>03408
- <a name="l03409"></a>03409 p2 = ( x - b(i) ) * p1 - c(i) * p0
- <a name="l03410"></a>03410 dp2 = ( x - b(i) ) * dp1 + p1 - c(i) * dp0
- <a name="l03411"></a>03411
- <a name="l03412"></a>03412 <span class="keyword">end do</span>
- <a name="l03413"></a>03413
- <a name="l03414"></a>03414 return
- <a name="l03415"></a>03415 <span class="keyword">end</span>
- <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 )
- <a name="l03417"></a>03417 <span class="comment">!</span>
- <a name="l03418"></a>03418 <span class="comment">!*******************************************************************************</span>
- <a name="l03419"></a>03419 <span class="comment">!</span>
- <a name="l03420"></a>03420 <span class="comment">!! LAGUERRE_ROOT improves an approximate root of a Laguerre polynomial.</span>
- <a name="l03421"></a>03421 <span class="comment">!</span>
- <a name="l03422"></a>03422 <span class="comment">!</span>
- <a name="l03423"></a>03423 <span class="comment">! Reference:</span>
- <a name="l03424"></a>03424 <span class="comment">!</span>
- <a name="l03425"></a>03425 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l03426"></a>03426 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l03427"></a>03427 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l03428"></a>03428 <span class="comment">!</span>
- <a name="l03429"></a>03429 <span class="comment">! Modified:</span>
- <a name="l03430"></a>03430 <span class="comment">!</span>
- <a name="l03431"></a>03431 <span class="comment">! 09 December 2000</span>
- <a name="l03432"></a>03432 <span class="comment">!</span>
- <a name="l03433"></a>03433 <span class="comment">! Parameters:</span>
- <a name="l03434"></a>03434 <span class="comment">!</span>
- <a name="l03435"></a>03435 <span class="comment">! Input/output, double precision X, the approximate root, which</span>
- <a name="l03436"></a>03436 <span class="comment">! should be improved on output.</span>
- <a name="l03437"></a>03437 <span class="comment">!</span>
- <a name="l03438"></a>03438 <span class="comment">! Input, integer NORDER, the order of the polynomial to be computed.</span>
- <a name="l03439"></a>03439 <span class="comment">!</span>
- <a name="l03440"></a>03440 <span class="comment">! Input, double precision ALPHA, the exponent of the X factor.</span>
- <a name="l03441"></a>03441 <span class="comment">!</span>
- <a name="l03442"></a>03442 <span class="comment">! Output, double precision DP2, the value of L'(NORDER)(X).</span>
- <a name="l03443"></a>03443 <span class="comment">!</span>
- <a name="l03444"></a>03444 <span class="comment">! Output, double precision P1, the value of L(NORDER-1)(X).</span>
- <a name="l03445"></a>03445 <span class="comment">!</span>
- <a name="l03446"></a>03446 <span class="comment">! Input, double precision B(NORDER), C(NORDER), the recursion coefficients.</span>
- <a name="l03447"></a>03447 <span class="comment">!</span>
- <a name="l03448"></a>03448 <span class="keyword">implicit none</span>
- <a name="l03449"></a>03449 <span class="comment">!</span>
- <a name="l03450"></a>03450 <span class="keywordtype">integer</span> norder
- <a name="l03451"></a>03451 <span class="comment">!</span>
- <a name="l03452"></a>03452 <span class="keywordtype">double precision</span> alpha
- <a name="l03453"></a>03453 <span class="keywordtype">double precision</span> b(norder)
- <a name="l03454"></a>03454 <span class="keywordtype">double precision</span> c(norder)
- <a name="l03455"></a>03455 <span class="keywordtype">double precision</span> d
- <a name="l03456"></a>03456 <span class="keywordtype">double precision</span> dp2
- <a name="l03457"></a>03457 <span class="keywordtype">double precision</span> eps
- <a name="l03458"></a>03458 <span class="keywordtype">integer</span> i
- <a name="l03459"></a>03459 <span class="keywordtype">integer</span>, <span class="keywordtype">parameter</span> :: maxstep = 10
- <a name="l03460"></a>03460 <span class="keywordtype">double precision</span> p1
- <a name="l03461"></a>03461 <span class="keywordtype">double precision</span> p2
- <a name="l03462"></a>03462 <span class="keywordtype">double precision</span> x
- <a name="l03463"></a>03463 <span class="comment">!</span>
- <a name="l03464"></a>03464 eps = epsilon ( x )
- <a name="l03465"></a>03465
- <a name="l03466"></a>03466 <span class="keyword">do</span> i = 1, maxstep
- <a name="l03467"></a>03467
- <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 )
- <a name="l03469"></a>03469
- <a name="l03470"></a>03470 d = p2 / dp2
- <a name="l03471"></a>03471 x = x - d
- <a name="l03472"></a>03472
- <a name="l03473"></a>03473 <span class="keyword">if</span> ( abs ( d ) <= eps * ( abs ( x ) + 1.0D+00 ) ) <span class="keyword">then</span>
- <a name="l03474"></a>03474 return
- <a name="l03475"></a>03475 <span class="keyword">end if</span>
- <a name="l03476"></a>03476
- <a name="l03477"></a>03477 <span class="keyword">end do</span>
- <a name="l03478"></a>03478
- <a name="l03479"></a>03479 return
- <a name="l03480"></a>03480 <span class="keyword">end</span>
- <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 )
- <a name="l03482"></a>03482 <span class="comment">!</span>
- <a name="l03483"></a>03483 <span class="comment">!*******************************************************************************</span>
- <a name="l03484"></a>03484 <span class="comment">!</span>
- <a name="l03485"></a>03485 <span class="comment">!! LAGUERRE_SET sets abscissas and weights for Laguerre quadrature.</span>
- <a name="l03486"></a>03486 <span class="comment">!</span>
- <a name="l03487"></a>03487 <span class="comment">!</span>
- <a name="l03488"></a>03488 <span class="comment">! Integration interval:</span>
- <a name="l03489"></a>03489 <span class="comment">!</span>
- <a name="l03490"></a>03490 <span class="comment">! [ 0, +Infinity )</span>
- <a name="l03491"></a>03491 <span class="comment">!</span>
- <a name="l03492"></a>03492 <span class="comment">! Weight function:</span>
- <a name="l03493"></a>03493 <span class="comment">!</span>
- <a name="l03494"></a>03494 <span class="comment">! EXP ( - X )</span>
- <a name="l03495"></a>03495 <span class="comment">!</span>
- <a name="l03496"></a>03496 <span class="comment">! Integral to approximate:</span>
- <a name="l03497"></a>03497 <span class="comment">!</span>
- <a name="l03498"></a>03498 <span class="comment">! Integral ( 0 <= X < +INFINITY ) EXP ( - X ) * F(X) dX</span>
- <a name="l03499"></a>03499 <span class="comment">!</span>
- <a name="l03500"></a>03500 <span class="comment">! Approximate integral:</span>
- <a name="l03501"></a>03501 <span class="comment">!</span>
- <a name="l03502"></a>03502 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l03503"></a>03503 <span class="comment">!</span>
- <a name="l03504"></a>03504 <span class="comment">! Note:</span>
- <a name="l03505"></a>03505 <span class="comment">!</span>
- <a name="l03506"></a>03506 <span class="comment">! The abscissas are the zeroes of the Laguerre polynomial L(NORDER)(X).</span>
- <a name="l03507"></a>03507 <span class="comment">!</span>
- <a name="l03508"></a>03508 <span class="comment">! Reference:</span>
- <a name="l03509"></a>03509 <span class="comment">!</span>
- <a name="l03510"></a>03510 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l03511"></a>03511 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l03512"></a>03512 <span class="comment">! National Bureau of Standards, 1964.</span>
- <a name="l03513"></a>03513 <span class="comment">!</span>
- <a name="l03514"></a>03514 <span class="comment">! Vladimir Krylov,</span>
- <a name="l03515"></a>03515 <span class="comment">! Approximate Calculation of Integrals,</span>
- <a name="l03516"></a>03516 <span class="comment">! MacMillan, 1962.</span>
- <a name="l03517"></a>03517 <span class="comment">!</span>
- <a name="l03518"></a>03518 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l03519"></a>03519 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l03520"></a>03520 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l03521"></a>03521 <span class="comment">!</span>
- <a name="l03522"></a>03522 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l03523"></a>03523 <span class="comment">! Standard Mathematical Tables and Formulae,</span>
- <a name="l03524"></a>03524 <span class="comment">! 30th Edition,</span>
- <a name="l03525"></a>03525 <span class="comment">! CRC Press, 1996.</span>
- <a name="l03526"></a>03526 <span class="comment">!</span>
- <a name="l03527"></a>03527 <span class="comment">! Modified:</span>
- <a name="l03528"></a>03528 <span class="comment">!</span>
- <a name="l03529"></a>03529 <span class="comment">! 17 September 1998</span>
- <a name="l03530"></a>03530 <span class="comment">!</span>
- <a name="l03531"></a>03531 <span class="comment">! Author:</span>
- <a name="l03532"></a>03532 <span class="comment">!</span>
- <a name="l03533"></a>03533 <span class="comment">! John Burkardt</span>
- <a name="l03534"></a>03534 <span class="comment">!</span>
- <a name="l03535"></a>03535 <span class="comment">! Parameters:</span>
- <a name="l03536"></a>03536 <span class="comment">!</span>
- <a name="l03537"></a>03537 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l03538"></a>03538 <span class="comment">! NORDER must be between 1 and 20.</span>
- <a name="l03539"></a>03539 <span class="comment">!</span>
- <a name="l03540"></a>03540 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l03541"></a>03541 <span class="comment">!</span>
- <a name="l03542"></a>03542 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l03543"></a>03543 <span class="comment">! The weights are positive, and should add to 1.</span>
- <a name="l03544"></a>03544 <span class="comment">!</span>
- <a name="l03545"></a>03545 <span class="keyword">implicit none</span>
- <a name="l03546"></a>03546 <span class="comment">!</span>
- <a name="l03547"></a>03547 <span class="keywordtype">integer</span> norder
- <a name="l03548"></a>03548 <span class="comment">!</span>
- <a name="l03549"></a>03549 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l03550"></a>03550 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l03551"></a>03551 <span class="comment">!</span>
- <a name="l03552"></a>03552 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l03553"></a>03553
- <a name="l03554"></a>03554 xtab(1) = 1.0D+00
- <a name="l03555"></a>03555 weight(1) = 1.0D+00
- <a name="l03556"></a>03556
- <a name="l03557"></a>03557 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l03558"></a>03558
- <a name="l03559"></a>03559 xtab(1) = 0.585786437626904951198311275790D+00
- <a name="l03560"></a>03560 xtab(2) = 0.341421356237309504880168872421D+01
- <a name="l03561"></a>03561
- <a name="l03562"></a>03562 weight(1) = 0.853553390593273762200422181052D+00
- <a name="l03563"></a>03563 weight(2) = 0.146446609406726237799577818948D+00
- <a name="l03564"></a>03564
- <a name="l03565"></a>03565 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l03566"></a>03566
- <a name="l03567"></a>03567 xtab(1) = 0.415774556783479083311533873128D+00
- <a name="l03568"></a>03568 xtab(2) = 0.229428036027904171982205036136D+01
- <a name="l03569"></a>03569 xtab(3) = 0.628994508293747919686641576551D+01
- <a name="l03570"></a>03570
- <a name="l03571"></a>03571 weight(1) = 0.711093009929173015449590191143D+00
- <a name="l03572"></a>03572 weight(2) = 0.278517733569240848801444888457D+00
- <a name="l03573"></a>03573 weight(3) = 0.103892565015861357489649204007D-01
- <a name="l03574"></a>03574
- <a name="l03575"></a>03575 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l03576"></a>03576
- <a name="l03577"></a>03577 xtab(1) = 0.322547689619392311800361943361D+00
- <a name="l03578"></a>03578 xtab(2) = 0.174576110115834657568681671252D+01
- <a name="l03579"></a>03579 xtab(3) = 0.453662029692112798327928538496D+01
- <a name="l03580"></a>03580 xtab(4) = 0.939507091230113312923353644342D+01
- <a name="l03581"></a>03581
- <a name="l03582"></a>03582 weight(1) = 0.603154104341633601635966023818D+00
- <a name="l03583"></a>03583 weight(2) = 0.357418692437799686641492017458D+00
- <a name="l03584"></a>03584 weight(3) = 0.388879085150053842724381681562D-01
- <a name="l03585"></a>03585 weight(4) = 0.539294705561327450103790567621D-03
- <a name="l03586"></a>03586
- <a name="l03587"></a>03587 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l03588"></a>03588
- <a name="l03589"></a>03589 xtab(1) = 0.263560319718140910203061943361D+00
- <a name="l03590"></a>03590 xtab(2) = 0.141340305910651679221840798019D+01
- <a name="l03591"></a>03591 xtab(3) = 0.359642577104072208122318658878D+01
- <a name="l03592"></a>03592 xtab(4) = 0.708581000585883755692212418111D+01
- <a name="l03593"></a>03593 xtab(5) = 0.126408008442757826594332193066D+02
- <a name="l03594"></a>03594
- <a name="l03595"></a>03595 weight(1) = 0.521755610582808652475860928792D+00
- <a name="l03596"></a>03596 weight(2) = 0.398666811083175927454133348144D+00
- <a name="l03597"></a>03597 weight(3) = 0.759424496817075953876533114055D-01
- <a name="l03598"></a>03598 weight(4) = 0.361175867992204845446126257304D-02
- <a name="l03599"></a>03599 weight(5) = 0.233699723857762278911490845516D-04
- <a name="l03600"></a>03600
- <a name="l03601"></a>03601 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l03602"></a>03602
- <a name="l03603"></a>03603 xtab(1) = 0.222846604179260689464354826787D+00
- <a name="l03604"></a>03604 xtab(2) = 0.118893210167262303074315092194D+01
- <a name="l03605"></a>03605 xtab(3) = 0.299273632605931407769132528451D+01
- <a name="l03606"></a>03606 xtab(4) = 0.577514356910451050183983036943D+01
- <a name="l03607"></a>03607 xtab(5) = 0.983746741838258991771554702994D+01
- <a name="l03608"></a>03608 xtab(6) = 0.159828739806017017825457915674D+02
- <a name="l03609"></a>03609
- <a name="l03610"></a>03610 weight(1) = 0.458964673949963593568284877709D+00
- <a name="l03611"></a>03611 weight(2) = 0.417000830772120994113377566193D+00
- <a name="l03612"></a>03612 weight(3) = 0.113373382074044975738706185098D+00
- <a name="l03613"></a>03613 weight(4) = 0.103991974531490748989133028469D-01
- <a name="l03614"></a>03614 weight(5) = 0.261017202814932059479242860001D-03
- <a name="l03615"></a>03615 weight(6) = 0.898547906429621238825292052825D-06
- <a name="l03616"></a>03616
- <a name="l03617"></a>03617 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l03618"></a>03618
- <a name="l03619"></a>03619 xtab(1) = 0.193043676560362413838247885004D+00
- <a name="l03620"></a>03620 xtab(2) = 0.102666489533919195034519944317D+01
- <a name="l03621"></a>03621 xtab(3) = 0.256787674495074620690778622666D+01
- <a name="l03622"></a>03622 xtab(4) = 0.490035308452648456810171437810D+01
- <a name="l03623"></a>03623 xtab(5) = 0.818215344456286079108182755123D+01
- <a name="l03624"></a>03624 xtab(6) = 0.127341802917978137580126424582D+02
- <a name="l03625"></a>03625 xtab(7) = 0.193957278622625403117125820576D+02
- <a name="l03626"></a>03626
- <a name="l03627"></a>03627 weight(1) = 0.409318951701273902130432880018D+00
- <a name="l03628"></a>03628 weight(2) = 0.421831277861719779929281005417D+00
- <a name="l03629"></a>03629 weight(3) = 0.147126348657505278395374184637D+00
- <a name="l03630"></a>03630 weight(4) = 0.206335144687169398657056149642D-01
- <a name="l03631"></a>03631 weight(5) = 0.107401014328074552213195962843D-02
- <a name="l03632"></a>03632 weight(6) = 0.158654643485642012687326223234D-04
- <a name="l03633"></a>03633 weight(7) = 0.317031547899558056227132215385D-07
- <a name="l03634"></a>03634
- <a name="l03635"></a>03635 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l03636"></a>03636
- <a name="l03637"></a>03637 xtab(1) = 0.170279632305100999788861856608D+00
- <a name="l03638"></a>03638 xtab(2) = 0.903701776799379912186020223555D+00
- <a name="l03639"></a>03639 xtab(3) = 0.225108662986613068930711836697D+01
- <a name="l03640"></a>03640 xtab(4) = 0.426670017028765879364942182690D+01
- <a name="l03641"></a>03641 xtab(5) = 0.704590540239346569727932548212D+01
- <a name="l03642"></a>03642 xtab(6) = 0.107585160101809952240599567880D+02
- <a name="l03643"></a>03643 xtab(7) = 0.157406786412780045780287611584D+02
- <a name="l03644"></a>03644 xtab(8) = 0.228631317368892641057005342974D+02
- <a name="l03645"></a>03645
- <a name="l03646"></a>03646 weight(1) = 0.369188589341637529920582839376D+00
- <a name="l03647"></a>03647 weight(2) = 0.418786780814342956076978581333D+00
- <a name="l03648"></a>03648 weight(3) = 0.175794986637171805699659866777D+00
- <a name="l03649"></a>03649 weight(4) = 0.333434922612156515221325349344D-01
- <a name="l03650"></a>03650 weight(5) = 0.279453623522567252493892414793D-02
- <a name="l03651"></a>03651 weight(6) = 0.907650877335821310423850149336D-04
- <a name="l03652"></a>03652 weight(7) = 0.848574671627253154486801830893D-06
- <a name="l03653"></a>03653 weight(8) = 0.104800117487151038161508853552D-08
- <a name="l03654"></a>03654
- <a name="l03655"></a>03655 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
- <a name="l03656"></a>03656
- <a name="l03657"></a>03657 xtab(1) = 0.152322227731808247428107073127D+00
- <a name="l03658"></a>03658 xtab(2) = 0.807220022742255847741419210952D+00
- <a name="l03659"></a>03659 xtab(3) = 0.200513515561934712298303324701D+01
- <a name="l03660"></a>03660 xtab(4) = 0.378347397333123299167540609364D+01
- <a name="l03661"></a>03661 xtab(5) = 0.620495677787661260697353521006D+01
- <a name="l03662"></a>03662 xtab(6) = 0.937298525168757620180971073215D+01
- <a name="l03663"></a>03663 xtab(7) = 0.134662369110920935710978818397D+02
- <a name="l03664"></a>03664 xtab(8) = 0.188335977889916966141498992996D+02
- <a name="l03665"></a>03665 xtab(9) = 0.263740718909273767961410072937D+02
- <a name="l03666"></a>03666
- <a name="l03667"></a>03667 weight(1) = 0.336126421797962519673467717606D+00
- <a name="l03668"></a>03668 weight(2) = 0.411213980423984387309146942793D+00
- <a name="l03669"></a>03669 weight(3) = 0.199287525370885580860575607212D+00
- <a name="l03670"></a>03670 weight(4) = 0.474605627656515992621163600479D-01
- <a name="l03671"></a>03671 weight(5) = 0.559962661079458317700419900556D-02
- <a name="l03672"></a>03672 weight(6) = 0.305249767093210566305412824291D-03
- <a name="l03673"></a>03673 weight(7) = 0.659212302607535239225572284875D-05
- <a name="l03674"></a>03674 weight(8) = 0.411076933034954844290241040330D-07
- <a name="l03675"></a>03675 weight(9) = 0.329087403035070757646681380323D-10
- <a name="l03676"></a>03676
- <a name="l03677"></a>03677 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
- <a name="l03678"></a>03678
- <a name="l03679"></a>03679 xtab(1) = 0.137793470540492430830772505653D+00
- <a name="l03680"></a>03680 xtab(2) = 0.729454549503170498160373121676D+00
- <a name="l03681"></a>03681 xtab(3) = 0.180834290174031604823292007575D+01
- <a name="l03682"></a>03682 xtab(4) = 0.340143369785489951448253222141D+01
- <a name="l03683"></a>03683 xtab(5) = 0.555249614006380363241755848687D+01
- <a name="l03684"></a>03684 xtab(6) = 0.833015274676449670023876719727D+01
- <a name="l03685"></a>03685 xtab(7) = 0.118437858379000655649185389191D+02
- <a name="l03686"></a>03686 xtab(8) = 0.162792578313781020995326539358D+02
- <a name="l03687"></a>03687 xtab(9) = 0.219965858119807619512770901956D+02
- <a name="l03688"></a>03688 xtab(10) = 0.299206970122738915599087933408D+02
- <a name="l03689"></a>03689
- <a name="l03690"></a>03690 weight(1) = 0.308441115765020141547470834678D+00
- <a name="l03691"></a>03691 weight(2) = 0.401119929155273551515780309913D+00
- <a name="l03692"></a>03692 weight(3) = 0.218068287611809421588648523475D+00
- <a name="l03693"></a>03693 weight(4) = 0.620874560986777473929021293135D-01
- <a name="l03694"></a>03694 weight(5) = 0.950151697518110055383907219417D-02
- <a name="l03695"></a>03695 weight(6) = 0.753008388587538775455964353676D-03
- <a name="l03696"></a>03696 weight(7) = 0.282592334959956556742256382685D-04
- <a name="l03697"></a>03697 weight(8) = 0.424931398496268637258657665975D-06
- <a name="l03698"></a>03698 weight(9) = 0.183956482397963078092153522436D-08
- <a name="l03699"></a>03699 weight(10) = 0.991182721960900855837754728324D-12
- <a name="l03700"></a>03700
- <a name="l03701"></a>03701 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 11 ) <span class="keyword">then</span>
- <a name="l03702"></a>03702
- <a name="l03703"></a>03703 xtab(1) = 0.125796442187967522675794577516D+00
- <a name="l03704"></a>03704 xtab(2) = 0.665418255839227841678127839420D+00
- <a name="l03705"></a>03705 xtab(3) = 0.164715054587216930958700321365D+01
- <a name="l03706"></a>03706 xtab(4) = 0.309113814303525495330195934259D+01
- <a name="l03707"></a>03707 xtab(5) = 0.502928440157983321236999508366D+01
- <a name="l03708"></a>03708 xtab(6) = 0.750988786380661681941099714450D+01
- <a name="l03709"></a>03709 xtab(7) = 0.106059509995469677805559216457D+02
- <a name="l03710"></a>03710 xtab(8) = 0.144316137580641855353200450349D+02
- <a name="l03711"></a>03711 xtab(9) = 0.191788574032146786478174853989D+02
- <a name="l03712"></a>03712 xtab(10) = 0.252177093396775611040909447797D+02
- <a name="l03713"></a>03713 xtab(11) = 0.334971928471755372731917259395D+02
- <a name="l03714"></a>03714
- <a name="l03715"></a>03715 weight(1) = 0.284933212894200605056051024724D+00
- <a name="l03716"></a>03716 weight(2) = 0.389720889527849377937553508048D+00
- <a name="l03717"></a>03717 weight(3) = 0.232781831848991333940223795543D+00
- <a name="l03718"></a>03718 weight(4) = 0.765644535461966864008541790132D-01
- <a name="l03719"></a>03719 weight(5) = 0.143932827673506950918639187409D-01
- <a name="l03720"></a>03720 weight(6) = 0.151888084648487306984777640042D-02
- <a name="l03721"></a>03721 weight(7) = 0.851312243547192259720424170600D-04
- <a name="l03722"></a>03722 weight(8) = 0.229240387957450407857683270709D-05
- <a name="l03723"></a>03723 weight(9) = 0.248635370276779587373391491114D-07
- <a name="l03724"></a>03724 weight(10) = 0.771262693369132047028152590222D-10
- <a name="l03725"></a>03725 weight(11) = 0.288377586832362386159777761217D-13
- <a name="l03726"></a>03726
- <a name="l03727"></a>03727 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 12 ) <span class="keyword">then</span>
- <a name="l03728"></a>03728
- <a name="l03729"></a>03729 xtab(1) = 0.115722117358020675267196428240D+00
- <a name="l03730"></a>03730 xtab(2) = 0.611757484515130665391630053042D+00
- <a name="l03731"></a>03731 xtab(3) = 0.151261026977641878678173792687D+01
- <a name="l03732"></a>03732 xtab(4) = 0.283375133774350722862747177657D+01
- <a name="l03733"></a>03733 xtab(5) = 0.459922763941834848460572922485D+01
- <a name="l03734"></a>03734 xtab(6) = 0.684452545311517734775433041849D+01
- <a name="l03735"></a>03735 xtab(7) = 0.962131684245686704391238234923D+01
- <a name="l03736"></a>03736 xtab(8) = 0.130060549933063477203460524294D+02
- <a name="l03737"></a>03737 xtab(9) = 0.171168551874622557281840528008D+02
- <a name="l03738"></a>03738 xtab(10) = 0.221510903793970056699218950837D+02
- <a name="l03739"></a>03739 xtab(11) = 0.284879672509840003125686072325D+02
- <a name="l03740"></a>03740 xtab(12) = 0.370991210444669203366389142764D+02
- <a name="l03741"></a>03741
- <a name="l03742"></a>03742 weight(1) = 0.264731371055443190349738892056D+00
- <a name="l03743"></a>03743 weight(2) = 0.377759275873137982024490556707D+00
- <a name="l03744"></a>03744 weight(3) = 0.244082011319877564254870818274D+00
- <a name="l03745"></a>03745 weight(4) = 0.904492222116809307275054934667D-01
- <a name="l03746"></a>03746 weight(5) = 0.201023811546340965226612867827D-01
- <a name="l03747"></a>03747 weight(6) = 0.266397354186531588105415760678D-02
- <a name="l03748"></a>03748 weight(7) = 0.203231592662999392121432860438D-03
- <a name="l03749"></a>03749 weight(8) = 0.836505585681979874533632766396D-05
- <a name="l03750"></a>03750 weight(9) = 0.166849387654091026116989532619D-06
- <a name="l03751"></a>03751 weight(10) = 0.134239103051500414552392025055D-08
- <a name="l03752"></a>03752 weight(11) = 0.306160163503502078142407718971D-11
- <a name="l03753"></a>03753 weight(12) = 0.814807746742624168247311868103D-15
- <a name="l03754"></a>03754
- <a name="l03755"></a>03755 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 13 ) <span class="keyword">then</span>
- <a name="l03756"></a>03756
- <a name="l03757"></a>03757 xtab(1) = 0.107142388472252310648493376977D+00
- <a name="l03758"></a>03758 xtab(2) = 0.566131899040401853406036347177D+00
- <a name="l03759"></a>03759 xtab(3) = 0.139856433645101971792750259921D+01
- <a name="l03760"></a>03760 xtab(4) = 0.261659710840641129808364008472D+01
- <a name="l03761"></a>03761 xtab(5) = 0.423884592901703327937303389926D+01
- <a name="l03762"></a>03762 xtab(6) = 0.629225627114007378039376523025D+01
- <a name="l03763"></a>03763 xtab(7) = 0.881500194118697804733348868036D+01
- <a name="l03764"></a>03764 xtab(8) = 0.118614035888112425762212021880D+02
- <a name="l03765"></a>03765 xtab(9) = 0.155107620377037527818478532958D+02
- <a name="l03766"></a>03766 xtab(10) = 0.198846356638802283332036594634D+02
- <a name="l03767"></a>03767 xtab(11) = 0.251852638646777580842970297823D+02
- <a name="l03768"></a>03768 xtab(12) = 0.318003863019472683713663283526D+02
- <a name="l03769"></a>03769 xtab(13) = 0.407230086692655795658979667001D+02
- <a name="l03770"></a>03770
- <a name="l03771"></a>03771 weight(1) = 0.247188708429962621346249185964D+00
- <a name="l03772"></a>03772 weight(2) = 0.365688822900521945306717530893D+00
- <a name="l03773"></a>03773 weight(3) = 0.252562420057658502356824288815D+00
- <a name="l03774"></a>03774 weight(4) = 0.103470758024183705114218631672D+00
- <a name="l03775"></a>03775 weight(5) = 0.264327544155616157781587735702D-01
- <a name="l03776"></a>03776 weight(6) = 0.422039604025475276555209292644D-02
- <a name="l03777"></a>03777 weight(7) = 0.411881770472734774892472527082D-03
- <a name="l03778"></a>03778 weight(8) = 0.235154739815532386882897300772D-04
- <a name="l03779"></a>03779 weight(9) = 0.731731162024909910401047197761D-06
- <a name="l03780"></a>03780 weight(10) = 0.110884162570398067979150974759D-07
- <a name="l03781"></a>03781 weight(11) = 0.677082669220589884064621459082D-10
- <a name="l03782"></a>03782 weight(12) = 0.115997995990507606094507145382D-12
- <a name="l03783"></a>03783 weight(13) = 0.224509320389275841599187226865D-16
- <a name="l03784"></a>03784
- <a name="l03785"></a>03785 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 14 ) <span class="keyword">then</span>
- <a name="l03786"></a>03786
- <a name="l03787"></a>03787 xtab(1) = 0.997475070325975745736829452514D-01
- <a name="l03788"></a>03788 xtab(2) = 0.526857648851902896404583451502D+00
- <a name="l03789"></a>03789 xtab(3) = 0.130062912125149648170842022116D+01
- <a name="l03790"></a>03790 xtab(4) = 0.243080107873084463616999751038D+01
- <a name="l03791"></a>03791 xtab(5) = 0.393210282229321888213134366778D+01
- <a name="l03792"></a>03792 xtab(6) = 0.582553621830170841933899983898D+01
- <a name="l03793"></a>03793 xtab(7) = 0.814024014156514503005978046052D+01
- <a name="l03794"></a>03794 xtab(8) = 0.109164995073660188408130510904D+02
- <a name="l03795"></a>03795 xtab(9) = 0.142108050111612886831059780825D+02
- <a name="l03796"></a>03796 xtab(10) = 0.181048922202180984125546272083D+02
- <a name="l03797"></a>03797 xtab(11) = 0.227233816282696248232280886985D+02
- <a name="l03798"></a>03798 xtab(12) = 0.282729817232482056954158923218D+02
- <a name="l03799"></a>03799 xtab(13) = 0.351494436605924265828643121364D+02
- <a name="l03800"></a>03800 xtab(14) = 0.443660817111174230416312423666D+02
- <a name="l03801"></a>03801
- <a name="l03802"></a>03802 weight(1) = 0.231815577144864977840774861104D+00
- <a name="l03803"></a>03803 weight(2) = 0.353784691597543151802331301273D+00
- <a name="l03804"></a>03804 weight(3) = 0.258734610245428085987320561144D+00
- <a name="l03805"></a>03805 weight(4) = 0.115482893556923210087304988673D+00
- <a name="l03806"></a>03806 weight(5) = 0.331920921593373600387499587137D-01
- <a name="l03807"></a>03807 weight(6) = 0.619286943700661021678785967675D-02
- <a name="l03808"></a>03808 weight(7) = 0.739890377867385942425890907080D-03
- <a name="l03809"></a>03809 weight(8) = 0.549071946684169837857331777667D-04
- <a name="l03810"></a>03810 weight(9) = 0.240958576408537749675775256553D-05
- <a name="l03811"></a>03811 weight(10) = 0.580154398167649518088619303904D-07
- <a name="l03812"></a>03812 weight(11) = 0.681931469248497411961562387084D-09
- <a name="l03813"></a>03813 weight(12) = 0.322120775189484793980885399656D-11
- <a name="l03814"></a>03814 weight(13) = 0.422135244051658735159797335643D-14
- <a name="l03815"></a>03815 weight(14) = 0.605237502228918880839870806281D-18
- <a name="l03816"></a>03816
- <a name="l03817"></a>03817 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
- <a name="l03818"></a>03818
- <a name="l03819"></a>03819 xtab(1) = 0.933078120172818047629030383672D-01
- <a name="l03820"></a>03820 xtab(2) = 0.492691740301883908960101791412D+00
- <a name="l03821"></a>03821 xtab(3) = 0.121559541207094946372992716488D+01
- <a name="l03822"></a>03822 xtab(4) = 0.226994952620374320247421741375D+01
- <a name="l03823"></a>03823 xtab(5) = 0.366762272175143727724905959436D+01
- <a name="l03824"></a>03824 xtab(6) = 0.542533662741355316534358132596D+01
- <a name="l03825"></a>03825 xtab(7) = 0.756591622661306786049739555812D+01
- <a name="l03826"></a>03826 xtab(8) = 0.101202285680191127347927394568D+02
- <a name="l03827"></a>03827 xtab(9) = 0.131302824821757235640991204176D+02
- <a name="l03828"></a>03828 xtab(10) = 0.166544077083299578225202408430D+02
- <a name="l03829"></a>03829 xtab(11) = 0.207764788994487667729157175676D+02
- <a name="l03830"></a>03830 xtab(12) = 0.256238942267287801445868285977D+02
- <a name="l03831"></a>03831 xtab(13) = 0.314075191697539385152432196202D+02
- <a name="l03832"></a>03832 xtab(14) = 0.385306833064860094162515167595D+02
- <a name="l03833"></a>03833 xtab(15) = 0.480260855726857943465734308508D+02
- <a name="l03834"></a>03834
- <a name="l03835"></a>03835 weight(1) = 0.218234885940086889856413236448D+00
- <a name="l03836"></a>03836 weight(2) = 0.342210177922883329638948956807D+00
- <a name="l03837"></a>03837 weight(3) = 0.263027577941680097414812275022D+00
- <a name="l03838"></a>03838 weight(4) = 0.126425818105930535843030549378D+00
- <a name="l03839"></a>03839 weight(5) = 0.402068649210009148415854789871D-01
- <a name="l03840"></a>03840 weight(6) = 0.856387780361183836391575987649D-02
- <a name="l03841"></a>03841 weight(7) = 0.121243614721425207621920522467D-02
- <a name="l03842"></a>03842 weight(8) = 0.111674392344251941992578595518D-03
- <a name="l03843"></a>03843 weight(9) = 0.645992676202290092465319025312D-05
- <a name="l03844"></a>03844 weight(10) = 0.222631690709627263033182809179D-06
- <a name="l03845"></a>03845 weight(11) = 0.422743038497936500735127949331D-08
- <a name="l03846"></a>03846 weight(12) = 0.392189726704108929038460981949D-10
- <a name="l03847"></a>03847 weight(13) = 0.145651526407312640633273963455D-12
- <a name="l03848"></a>03848 weight(14) = 0.148302705111330133546164737187D-15
- <a name="l03849"></a>03849 weight(15) = 0.160059490621113323104997812370D-19
- <a name="l03850"></a>03850
- <a name="l03851"></a>03851 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
- <a name="l03852"></a>03852
- <a name="l03853"></a>03853 xtab(1) = 0.876494104789278403601980973401D-01
- <a name="l03854"></a>03854 xtab(2) = 0.462696328915080831880838260664D+00
- <a name="l03855"></a>03855 xtab(3) = 0.114105777483122685687794501811D+01
- <a name="l03856"></a>03856 xtab(4) = 0.212928364509838061632615907066D+01
- <a name="l03857"></a>03857 xtab(5) = 0.343708663389320664523510701675D+01
- <a name="l03858"></a>03858 xtab(6) = 0.507801861454976791292305830814D+01
- <a name="l03859"></a>03859 xtab(7) = 0.707033853504823413039598947080D+01
- <a name="l03860"></a>03860 xtab(8) = 0.943831433639193878394724672911D+01
- <a name="l03861"></a>03861 xtab(9) = 0.122142233688661587369391246088D+02
- <a name="l03862"></a>03862 xtab(10) = 0.154415273687816170767647741622D+02
- <a name="l03863"></a>03863 xtab(11) = 0.191801568567531348546631409497D+02
- <a name="l03864"></a>03864 xtab(12) = 0.235159056939919085318231872752D+02
- <a name="l03865"></a>03865 xtab(13) = 0.285787297428821403675206137099D+02
- <a name="l03866"></a>03866 xtab(14) = 0.345833987022866258145276871778D+02
- <a name="l03867"></a>03867 xtab(15) = 0.419404526476883326354722330252D+02
- <a name="l03868"></a>03868 xtab(16) = 0.517011603395433183643426971197D+02
- <a name="l03869"></a>03869
- <a name="l03870"></a>03870 weight(1) = 0.206151714957800994334273636741D+00
- <a name="l03871"></a>03871 weight(2) = 0.331057854950884165992983098710D+00
- <a name="l03872"></a>03872 weight(3) = 0.265795777644214152599502020650D+00
- <a name="l03873"></a>03873 weight(4) = 0.136296934296377539975547513526D+00
- <a name="l03874"></a>03874 weight(5) = 0.473289286941252189780623392781D-01
- <a name="l03875"></a>03875 weight(6) = 0.112999000803394532312490459701D-01
- <a name="l03876"></a>03876 weight(7) = 0.184907094352631086429176783252D-02
- <a name="l03877"></a>03877 weight(8) = 0.204271915308278460126018338421D-03
- <a name="l03878"></a>03878 weight(9) = 0.148445868739812987713515067551D-04
- <a name="l03879"></a>03879 weight(10) = 0.682831933087119956439559590327D-06
- <a name="l03880"></a>03880 weight(11) = 0.188102484107967321388159920418D-07
- <a name="l03881"></a>03881 weight(12) = 0.286235024297388161963062629156D-09
- <a name="l03882"></a>03882 weight(13) = 0.212707903322410296739033610978D-11
- <a name="l03883"></a>03883 weight(14) = 0.629796700251786778717446214552D-14
- <a name="l03884"></a>03884 weight(15) = 0.505047370003551282040213233303D-17
- <a name="l03885"></a>03885 weight(16) = 0.416146237037285519042648356116D-21
- <a name="l03886"></a>03886
- <a name="l03887"></a>03887 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 17 ) <span class="keyword">then</span>
- <a name="l03888"></a>03888
- <a name="l03889"></a>03889 xtab(1) = 0.826382147089476690543986151980D-01
- <a name="l03890"></a>03890 xtab(2) = 0.436150323558710436375959029847D+00
- <a name="l03891"></a>03891 xtab(3) = 0.107517657751142857732980316755D+01
- <a name="l03892"></a>03892 xtab(4) = 0.200519353164923224070293371933D+01
- <a name="l03893"></a>03893 xtab(5) = 0.323425612404744376157380120696D+01
- <a name="l03894"></a>03894 xtab(6) = 0.477351351370019726480932076262D+01
- <a name="l03895"></a>03895 xtab(7) = 0.663782920536495266541643929703D+01
- <a name="l03896"></a>03896 xtab(8) = 0.884668551116980005369470571184D+01
- <a name="l03897"></a>03897 xtab(9) = 0.114255293193733525869726151469D+02
- <a name="l03898"></a>03898 xtab(10) = 0.144078230374813180021982874959D+02
- <a name="l03899"></a>03899 xtab(11) = 0.178382847307011409290658752412D+02
- <a name="l03900"></a>03900 xtab(12) = 0.217782682577222653261749080522D+02
- <a name="l03901"></a>03901 xtab(13) = 0.263153178112487997766149598369D+02
- <a name="l03902"></a>03902 xtab(14) = 0.315817716804567331343908517497D+02
- <a name="l03903"></a>03903 xtab(15) = 0.377960938374771007286092846663D+02
- <a name="l03904"></a>03904 xtab(16) = 0.453757165339889661829258363215D+02
- <a name="l03905"></a>03905 xtab(17) = 0.553897517898396106640900199790D+02
- <a name="l03906"></a>03906
- <a name="l03907"></a>03907 weight(1) = 0.195332205251770832145927297697D+00
- <a name="l03908"></a>03908 weight(2) = 0.320375357274540281336625631970D+00
- <a name="l03909"></a>03909 weight(3) = 0.267329726357171097238809604160D+00
- <a name="l03910"></a>03910 weight(4) = 0.145129854358758625407426447473D+00
- <a name="l03911"></a>03911 weight(5) = 0.544369432453384577793805803066D-01
- <a name="l03912"></a>03912 weight(6) = 0.143572977660618672917767247431D-01
- <a name="l03913"></a>03913 weight(7) = 0.266282473557277256843236250006D-02
- <a name="l03914"></a>03914 weight(8) = 0.343679727156299920611775097985D-03
- <a name="l03915"></a>03915 weight(9) = 0.302755178378287010943703641131D-04
- <a name="l03916"></a>03916 weight(10) = 0.176851505323167689538081156159D-05
- <a name="l03917"></a>03917 weight(11) = 0.657627288681043332199222748162D-07
- <a name="l03918"></a>03918 weight(12) = 0.146973093215954679034375821888D-08
- <a name="l03919"></a>03919 weight(13) = 0.181691036255544979555476861323D-10
- <a name="l03920"></a>03920 weight(14) = 0.109540138892868740297645078918D-12
- <a name="l03921"></a>03921 weight(15) = 0.261737388222337042155132062413D-15
- <a name="l03922"></a>03922 weight(16) = 0.167293569314615469085022374652D-18
- <a name="l03923"></a>03923 weight(17) = 0.106562631627404278815253271162D-22
- <a name="l03924"></a>03924
- <a name="l03925"></a>03925 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 18 ) <span class="keyword">then</span>
- <a name="l03926"></a>03926
- <a name="l03927"></a>03927 xtab(1) = 0.781691666697054712986747615334D-01
- <a name="l03928"></a>03928 xtab(2) = 0.412490085259129291039101536536D+00
- <a name="l03929"></a>03929 xtab(3) = 0.101652017962353968919093686187D+01
- <a name="l03930"></a>03930 xtab(4) = 0.189488850996976091426727831954D+01
- <a name="l03931"></a>03931 xtab(5) = 0.305435311320265975115241130719D+01
- <a name="l03932"></a>03932 xtab(6) = 0.450420553888989282633795571455D+01
- <a name="l03933"></a>03933 xtab(7) = 0.625672507394911145274209116326D+01
- <a name="l03934"></a>03934 xtab(8) = 0.832782515660563002170470261564D+01
- <a name="l03935"></a>03935 xtab(9) = 0.107379900477576093352179033397D+02
- <a name="l03936"></a>03936 xtab(10) = 0.135136562075550898190863812108D+02
- <a name="l03937"></a>03937 xtab(11) = 0.166893062819301059378183984163D+02
- <a name="l03938"></a>03938 xtab(12) = 0.203107676262677428561313764553D+02
- <a name="l03939"></a>03939 xtab(13) = 0.244406813592837027656442257980D+02
- <a name="l03940"></a>03940 xtab(14) = 0.291682086625796161312980677805D+02
- <a name="l03941"></a>03941 xtab(15) = 0.346279270656601721454012429438D+02
- <a name="l03942"></a>03942 xtab(16) = 0.410418167728087581392948614284D+02
- <a name="l03943"></a>03943 xtab(17) = 0.488339227160865227486586093290D+02
- <a name="l03944"></a>03944 xtab(18) = 0.590905464359012507037157810181D+02
- <a name="l03945"></a>03945
- <a name="l03946"></a>03946 weight(1) = 0.185588603146918805623337752284D+00
- <a name="l03947"></a>03947 weight(2) = 0.310181766370225293649597595713D+00
- <a name="l03948"></a>03948 weight(3) = 0.267866567148536354820854394783D+00
- <a name="l03949"></a>03949 weight(4) = 0.152979747468074906553843082053D+00
- <a name="l03950"></a>03950 weight(5) = 0.614349178609616527076780103487D-01
- <a name="l03951"></a>03951 weight(6) = 0.176872130807729312772600233761D-01
- <a name="l03952"></a>03952 weight(7) = 0.366017976775991779802657207890D-02
- <a name="l03953"></a>03953 weight(8) = 0.540622787007735323128416319257D-03
- <a name="l03954"></a>03954 weight(9) = 0.561696505121423113817929049294D-04
- <a name="l03955"></a>03955 weight(10) = 0.401530788370115755858883625279D-05
- <a name="l03956"></a>03956 weight(11) = 0.191466985667567497969210011321D-06
- <a name="l03957"></a>03957 weight(12) = 0.583609526863159412918086289717D-08
- <a name="l03958"></a>03958 weight(13) = 0.107171126695539012772851317562D-09
- <a name="l03959"></a>03959 weight(14) = 0.108909871388883385562011298291D-11
- <a name="l03960"></a>03960 weight(15) = 0.538666474837830887608094323164D-14
- <a name="l03961"></a>03961 weight(16) = 0.104986597803570340877859934846D-16
- <a name="l03962"></a>03962 weight(17) = 0.540539845163105364356554467358D-20
- <a name="l03963"></a>03963 weight(18) = 0.269165326920102862708377715980D-24
- <a name="l03964"></a>03964
- <a name="l03965"></a>03965 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 19 ) <span class="keyword">then</span>
- <a name="l03966"></a>03966
- <a name="l03967"></a>03967 xtab(1) = 0.741587837572050877131369916024D-01
- <a name="l03968"></a>03968 xtab(2) = 0.391268613319994607337648350299D+00
- <a name="l03969"></a>03969 xtab(3) = 0.963957343997958058624879377130D+00
- <a name="l03970"></a>03970 xtab(4) = 0.179617558206832812557725825252D+01
- <a name="l03971"></a>03971 xtab(5) = 0.289365138187378399116494713237D+01
- <a name="l03972"></a>03972 xtab(6) = 0.426421553962776647436040018167D+01
- <a name="l03973"></a>03973 xtab(7) = 0.591814156164404855815360191408D+01
- <a name="l03974"></a>03974 xtab(8) = 0.786861891533473373105668358176D+01
- <a name="l03975"></a>03975 xtab(9) = 0.101324237168152659251627415800D+02
- <a name="l03976"></a>03976 xtab(10) = 0.127308814638423980045092979656D+02
- <a name="l03977"></a>03977 xtab(11) = 0.156912783398358885454136069861D+02
- <a name="l03978"></a>03978 xtab(12) = 0.190489932098235501532136429732D+02
- <a name="l03979"></a>03979 xtab(13) = 0.228508497608294829323930586693D+02
- <a name="l03980"></a>03980 xtab(14) = 0.271606693274114488789963947149D+02
- <a name="l03981"></a>03981 xtab(15) = 0.320691222518622423224362865906D+02
- <a name="l03982"></a>03982 xtab(16) = 0.377129058012196494770647508283D+02
- <a name="l03983"></a>03983 xtab(17) = 0.443173627958314961196067736013D+02
- <a name="l03984"></a>03984 xtab(18) = 0.523129024574043831658644222420D+02
- <a name="l03985"></a>03985 xtab(19) = 0.628024231535003758413504690673D+02
- <a name="l03986"></a>03986
- <a name="l03987"></a>03987 weight(1) = 0.176768474915912502251035479815D+00
- <a name="l03988"></a>03988 weight(2) = 0.300478143607254379482156807712D+00
- <a name="l03989"></a>03989 weight(3) = 0.267599547038175030772695440648D+00
- <a name="l03990"></a>03990 weight(4) = 0.159913372135580216785512147895D+00
- <a name="l03991"></a>03991 weight(5) = 0.682493799761491134552355368344D-01
- <a name="l03992"></a>03992 weight(6) = 0.212393076065443249244062193091D-01
- <a name="l03993"></a>03993 weight(7) = 0.484162735114839596725013121019D-02
- <a name="l03994"></a>03994 weight(8) = 0.804912747381366766594647138204D-03
- <a name="l03995"></a>03995 weight(9) = 0.965247209315350170843161738801D-04
- <a name="l03996"></a>03996 weight(10) = 0.820730525805103054408982992869D-05
- <a name="l03997"></a>03997 weight(11) = 0.483056672473077253944806671560D-06
- <a name="l03998"></a>03998 weight(12) = 0.190499136112328569993615674552D-07
- <a name="l03999"></a>03999 weight(13) = 0.481668463092806155766936380273D-09
- <a name="l04000"></a>04000 weight(14) = 0.734825883955114437684376840171D-11
- <a name="l04001"></a>04001 weight(15) = 0.620227538757261639893719012423D-13
- <a name="l04002"></a>04002 weight(16) = 0.254143084301542272371866857954D-15
- <a name="l04003"></a>04003 weight(17) = 0.407886129682571235007187465134D-18
- <a name="l04004"></a>04004 weight(18) = 0.170775018759383706100412325084D-21
- <a name="l04005"></a>04005 weight(19) = 0.671506464990818995998969111749D-26
- <a name="l04006"></a>04006
- <a name="l04007"></a>04007 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 20 ) <span class="keyword">then</span>
- <a name="l04008"></a>04008
- <a name="l04009"></a>04009 xtab(1) = 0.705398896919887533666890045842D-01
- <a name="l04010"></a>04010 xtab(2) = 0.372126818001611443794241388761D+00
- <a name="l04011"></a>04011 xtab(3) = 0.916582102483273564667716277074D+00
- <a name="l04012"></a>04012 xtab(4) = 0.170730653102834388068768966741D+01
- <a name="l04013"></a>04013 xtab(5) = 0.274919925530943212964503046049D+01
- <a name="l04014"></a>04014 xtab(6) = 0.404892531385088692237495336913D+01
- <a name="l04015"></a>04015 xtab(7) = 0.561517497086161651410453988565D+01
- <a name="l04016"></a>04016 xtab(8) = 0.745901745367106330976886021837D+01
- <a name="l04017"></a>04017 xtab(9) = 0.959439286958109677247367273428D+01
- <a name="l04018"></a>04018 xtab(10) = 0.120388025469643163096234092989D+02
- <a name="l04019"></a>04019 xtab(11) = 0.148142934426307399785126797100D+02
- <a name="l04020"></a>04020 xtab(12) = 0.179488955205193760173657909926D+02
- <a name="l04021"></a>04021 xtab(13) = 0.214787882402850109757351703696D+02
- <a name="l04022"></a>04022 xtab(14) = 0.254517027931869055035186774846D+02
- <a name="l04023"></a>04023 xtab(15) = 0.299325546317006120067136561352D+02
- <a name="l04024"></a>04024 xtab(16) = 0.350134342404790000062849359067D+02
- <a name="l04025"></a>04025 xtab(17) = 0.408330570567285710620295677078D+02
- <a name="l04026"></a>04026 xtab(18) = 0.476199940473465021399416271529D+02
- <a name="l04027"></a>04027 xtab(19) = 0.558107957500638988907507734445D+02
- <a name="l04028"></a>04028 xtab(20) = 0.665244165256157538186403187915D+02
- <a name="l04029"></a>04029
- <a name="l04030"></a>04030 weight(1) = 0.168746801851113862149223899689D+00
- <a name="l04031"></a>04031 weight(2) = 0.291254362006068281716795323812D+00
- <a name="l04032"></a>04032 weight(3) = 0.266686102867001288549520868998D+00
- <a name="l04033"></a>04033 weight(4) = 0.166002453269506840031469127816D+00
- <a name="l04034"></a>04034 weight(5) = 0.748260646687923705400624639615D-01
- <a name="l04035"></a>04035 weight(6) = 0.249644173092832210728227383234D-01
- <a name="l04036"></a>04036 weight(7) = 0.620255084457223684744754785395D-02
- <a name="l04037"></a>04037 weight(8) = 0.114496238647690824203955356969D-02
- <a name="l04038"></a>04038 weight(9) = 0.155741773027811974779809513214D-03
- <a name="l04039"></a>04039 weight(10) = 0.154014408652249156893806714048D-04
- <a name="l04040"></a>04040 weight(11) = 0.108648636651798235147970004439D-05
- <a name="l04041"></a>04041 weight(12) = 0.533012090955671475092780244305D-07
- <a name="l04042"></a>04042 weight(13) = 0.175798117905058200357787637840D-08
- <a name="l04043"></a>04043 weight(14) = 0.372550240251232087262924585338D-10
- <a name="l04044"></a>04044 weight(15) = 0.476752925157819052449488071613D-12
- <a name="l04045"></a>04045 weight(16) = 0.337284424336243841236506064991D-14
- <a name="l04046"></a>04046 weight(17) = 0.115501433950039883096396247181D-16
- <a name="l04047"></a>04047 weight(18) = 0.153952214058234355346383319667D-19
- <a name="l04048"></a>04048 weight(19) = 0.528644272556915782880273587683D-23
- <a name="l04049"></a>04049 weight(20) = 0.165645661249902329590781908529D-27
- <a name="l04050"></a>04050
- <a name="l04051"></a>04051 <span class="keyword">else</span>
- <a name="l04052"></a>04052
- <a name="l04053"></a>04053 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l04054"></a>04054 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LAGUERRE_SET - Fatal error!'</span>
- <a name="l04055"></a>04055 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l04056"></a>04056 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' Legal values are 1 to 20.'</span>
- <a name="l04057"></a>04057 stop
- <a name="l04058"></a>04058
- <a name="l04059"></a>04059 <span class="keyword">end if</span>
- <a name="l04060"></a>04060
- <a name="l04061"></a>04061 return
- <a name="l04062"></a>04062 <span class="keyword">end</span>
- <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 )
- <a name="l04064"></a>04064 <span class="comment">!</span>
- <a name="l04065"></a>04065 <span class="comment">!*******************************************************************************</span>
- <a name="l04066"></a>04066 <span class="comment">!</span>
- <a name="l04067"></a>04067 <span class="comment">!! LAGUERRE_SUM carries out Laguerre quadrature over [ A, +Infinity ).</span>
- <a name="l04068"></a>04068 <span class="comment">!</span>
- <a name="l04069"></a>04069 <span class="comment">!</span>
- <a name="l04070"></a>04070 <span class="comment">! Discussion:</span>
- <a name="l04071"></a>04071 <span class="comment">!</span>
- <a name="l04072"></a>04072 <span class="comment">! The simplest Laguerre integral to approximate is the</span>
- <a name="l04073"></a>04073 <span class="comment">! integral from 0 to INFINITY of EXP(-X) * F(X). When this is so,</span>
- <a name="l04074"></a>04074 <span class="comment">! it is easy to modify the rule to approximate the integral from</span>
- <a name="l04075"></a>04075 <span class="comment">! A to INFINITY as well.</span>
- <a name="l04076"></a>04076 <span class="comment">!</span>
- <a name="l04077"></a>04077 <span class="comment">! Another common Laguerre integral to approximate is the</span>
- <a name="l04078"></a>04078 <span class="comment">! integral from 0 to Infinity of EXP(-X) * X**ALPHA * F(X).</span>
- <a name="l04079"></a>04079 <span class="comment">! This routine may be used to sum up the terms of the Laguerre</span>
- <a name="l04080"></a>04080 <span class="comment">! rule for such an integral as well. However, if ALPHA is nonzero,</span>
- <a name="l04081"></a>04081 <span class="comment">! then there is no simple way to extend the rule to approximate the</span>
- <a name="l04082"></a>04082 <span class="comment">! integral from A to INFINITY. The simplest procedures would be</span>
- <a name="l04083"></a>04083 <span class="comment">! to approximate the integral from 0 to A.</span>
- <a name="l04084"></a>04084 <span class="comment">!</span>
- <a name="l04085"></a>04085 <span class="comment">! Integration interval:</span>
- <a name="l04086"></a>04086 <span class="comment">!</span>
- <a name="l04087"></a>04087 <span class="comment">! [ A, +Infinity ) or [ 0, +Infinity )</span>
- <a name="l04088"></a>04088 <span class="comment">!</span>
- <a name="l04089"></a>04089 <span class="comment">! Weight function:</span>
- <a name="l04090"></a>04090 <span class="comment">!</span>
- <a name="l04091"></a>04091 <span class="comment">! EXP ( - X ) or EXP ( - X ) * X**ALPHA</span>
- <a name="l04092"></a>04092 <span class="comment">!</span>
- <a name="l04093"></a>04093 <span class="comment">! Integral to approximate:</span>
- <a name="l04094"></a>04094 <span class="comment">!</span>
- <a name="l04095"></a>04095 <span class="comment">! Integral ( A <= X <= +Infinity ) EXP ( -X ) * F(X) dX or</span>
- <a name="l04096"></a>04096 <span class="comment">! Integral ( 0 <= X <= +Infinity ) EXP ( -X ) * X**ALPHA * F(X) dX</span>
- <a name="l04097"></a>04097 <span class="comment">!</span>
- <a name="l04098"></a>04098 <span class="comment">! Approximate integral:</span>
- <a name="l04099"></a>04099 <span class="comment">!</span>
- <a name="l04100"></a>04100 <span class="comment">! EXP ( - A ) * Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) + A ) </span>
- <a name="l04101"></a>04101 <span class="comment">!</span>
- <a name="l04102"></a>04102 <span class="comment">! or</span>
- <a name="l04103"></a>04103 <span class="comment">!</span>
- <a name="l04104"></a>04104 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l04105"></a>04105 <span class="comment">!</span>
- <a name="l04106"></a>04106 <span class="comment">! Reference:</span>
- <a name="l04107"></a>04107 <span class="comment">!</span>
- <a name="l04108"></a>04108 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l04109"></a>04109 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l04110"></a>04110 <span class="comment">! National Bureau of Standards, 1964.</span>
- <a name="l04111"></a>04111 <span class="comment">!</span>
- <a name="l04112"></a>04112 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l04113"></a>04113 <span class="comment">! Standard Mathematical Tables and Formulae,</span>
- <a name="l04114"></a>04114 <span class="comment">! 30th Edition,</span>
- <a name="l04115"></a>04115 <span class="comment">! CRC Press, 1996.</span>
- <a name="l04116"></a>04116 <span class="comment">!</span>
- <a name="l04117"></a>04117 <span class="comment">! Modified:</span>
- <a name="l04118"></a>04118 <span class="comment">!</span>
- <a name="l04119"></a>04119 <span class="comment">! 15 March 2000</span>
- <a name="l04120"></a>04120 <span class="comment">!</span>
- <a name="l04121"></a>04121 <span class="comment">! Author:</span>
- <a name="l04122"></a>04122 <span class="comment">!</span>
- <a name="l04123"></a>04123 <span class="comment">! John Burkardt</span>
- <a name="l04124"></a>04124 <span class="comment">!</span>
- <a name="l04125"></a>04125 <span class="comment">! Parameters:</span>
- <a name="l04126"></a>04126 <span class="comment">!</span>
- <a name="l04127"></a>04127 <span class="comment">! Input, external FUNC, the name of the FORTRAN function which</span>
- <a name="l04128"></a>04128 <span class="comment">! evaluates the integrand. The function must have the form</span>
- <a name="l04129"></a>04129 <span class="comment">! double precision func ( x ).</span>
- <a name="l04130"></a>04130 <span class="comment">!</span>
- <a name="l04131"></a>04131 <span class="comment">! Input, double precision A, the beginning of the integration interval.</span>
- <a name="l04132"></a>04132 <span class="comment">!</span>
- <a name="l04133"></a>04133 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l04134"></a>04134 <span class="comment">!</span>
- <a name="l04135"></a>04135 <span class="comment">! Input, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l04136"></a>04136 <span class="comment">!</span>
- <a name="l04137"></a>04137 <span class="comment">! Input, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l04138"></a>04138 <span class="comment">!</span>
- <a name="l04139"></a>04139 <span class="comment">! Output, double precision RESULT, the approximate value of the integral.</span>
- <a name="l04140"></a>04140 <span class="comment">!</span>
- <a name="l04141"></a>04141 <span class="keyword">implicit none</span>
- <a name="l04142"></a>04142 <span class="comment">!</span>
- <a name="l04143"></a>04143 <span class="keywordtype">integer</span> norder
- <a name="l04144"></a>04144 <span class="comment">!</span>
- <a name="l04145"></a>04145 <span class="keywordtype">double precision</span> a
- <a name="l04146"></a>04146 <span class="keywordtype">double precision</span>, <span class="keywordtype">external</span> :: func
- <a name="l04147"></a>04147 <span class="keywordtype">integer</span> i
- <a name="l04148"></a>04148 <span class="keywordtype">double precision</span> result
- <a name="l04149"></a>04149 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l04150"></a>04150 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l04151"></a>04151 <span class="comment">!</span>
- <a name="l04152"></a>04152 <span class="keyword">if</span> ( norder < 1 ) <span class="keyword">then</span>
- <a name="l04153"></a>04153 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l04154"></a>04154 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LAGUERRE_SUM - Fatal error!'</span>
- <a name="l04155"></a>04155 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Nonpositive NORDER = '</span>, norder
- <a name="l04156"></a>04156 stop
- <a name="l04157"></a>04157 <span class="keyword">end if</span>
- <a name="l04158"></a>04158
- <a name="l04159"></a>04159 result = 0.0D+00
- <a name="l04160"></a>04160 <span class="keyword">do</span> i = 1, norder
- <a name="l04161"></a>04161 result = result + weight(i) * func ( xtab(i) + a )
- <a name="l04162"></a>04162 <span class="keyword">end do</span>
- <a name="l04163"></a>04163 result = exp ( - a ) * result
- <a name="l04164"></a>04164
- <a name="l04165"></a>04165 return
- <a name="l04166"></a>04166 <span class="keyword">end</span>
- <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 )
- <a name="l04168"></a>04168 <span class="comment">!</span>
- <a name="l04169"></a>04169 <span class="comment">!*******************************************************************************</span>
- <a name="l04170"></a>04170 <span class="comment">!</span>
- <a name="l04171"></a>04171 <span class="comment">!! LEGENDRE_COM computes abscissas and weights for Gauss-Legendre quadrature.</span>
- <a name="l04172"></a>04172 <span class="comment">!</span>
- <a name="l04173"></a>04173 <span class="comment">!</span>
- <a name="l04174"></a>04174 <span class="comment">! Integration interval:</span>
- <a name="l04175"></a>04175 <span class="comment">!</span>
- <a name="l04176"></a>04176 <span class="comment">! [ -1, 1 ]</span>
- <a name="l04177"></a>04177 <span class="comment">!</span>
- <a name="l04178"></a>04178 <span class="comment">! Weight function:</span>
- <a name="l04179"></a>04179 <span class="comment">!</span>
- <a name="l04180"></a>04180 <span class="comment">! 1.0D+00</span>
- <a name="l04181"></a>04181 <span class="comment">!</span>
- <a name="l04182"></a>04182 <span class="comment">! Integral to approximate:</span>
- <a name="l04183"></a>04183 <span class="comment">!</span>
- <a name="l04184"></a>04184 <span class="comment">! Integral ( -1 <= X <= 1 ) F(X) dX</span>
- <a name="l04185"></a>04185 <span class="comment">!</span>
- <a name="l04186"></a>04186 <span class="comment">! Approximate integral:</span>
- <a name="l04187"></a>04187 <span class="comment">!</span>
- <a name="l04188"></a>04188 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l04189"></a>04189 <span class="comment">!</span>
- <a name="l04190"></a>04190 <span class="comment">! Modified:</span>
- <a name="l04191"></a>04191 <span class="comment">!</span>
- <a name="l04192"></a>04192 <span class="comment">! 16 September 1998</span>
- <a name="l04193"></a>04193 <span class="comment">!</span>
- <a name="l04194"></a>04194 <span class="comment">! Parameters:</span>
- <a name="l04195"></a>04195 <span class="comment">!</span>
- <a name="l04196"></a>04196 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l04197"></a>04197 <span class="comment">! NORDER must be greater than 0.</span>
- <a name="l04198"></a>04198 <span class="comment">!</span>
- <a name="l04199"></a>04199 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l04200"></a>04200 <span class="comment">!</span>
- <a name="l04201"></a>04201 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l04202"></a>04202 <span class="comment">! The weights are positive, symmetric, and should sum to 2.</span>
- <a name="l04203"></a>04203 <span class="comment">!</span>
- <a name="l04204"></a>04204 <span class="keyword">implicit none</span>
- <a name="l04205"></a>04205 <span class="comment">!</span>
- <a name="l04206"></a>04206 <span class="keywordtype">integer</span> norder
- <a name="l04207"></a>04207 <span class="comment">!</span>
- <a name="l04208"></a>04208 <span class="keywordtype">double precision</span> d1
- <a name="l04209"></a>04209 <span class="keywordtype">double precision</span> d2pn
- <a name="l04210"></a>04210 <span class="keywordtype">double precision</span> d3pn
- <a name="l04211"></a>04211 <span class="keywordtype">double precision</span> d4pn
- <a name="l04212"></a>04212 <span class="keywordtype">double precision</span> dp
- <a name="l04213"></a>04213 <span class="keywordtype">double precision</span> d_pi
- <a name="l04214"></a>04214 <span class="keywordtype">double precision</span> dpn
- <a name="l04215"></a>04215 <span class="keywordtype">double precision</span> e1
- <a name="l04216"></a>04216 <span class="keywordtype">double precision</span> fx
- <a name="l04217"></a>04217 <span class="keywordtype">double precision</span> h
- <a name="l04218"></a>04218 <span class="keywordtype">integer</span> i
- <a name="l04219"></a>04219 <span class="keywordtype">integer</span> iback
- <a name="l04220"></a>04220 <span class="keywordtype">integer</span> k
- <a name="l04221"></a>04221 <span class="keywordtype">integer</span> m
- <a name="l04222"></a>04222 <span class="keywordtype">integer</span> mp1mi
- <a name="l04223"></a>04223 <span class="keywordtype">integer</span> ncopy
- <a name="l04224"></a>04224 <span class="keywordtype">integer</span> nmove
- <a name="l04225"></a>04225 <span class="keywordtype">double precision</span> p
- <a name="l04226"></a>04226 <span class="keywordtype">double precision</span> pk
- <a name="l04227"></a>04227 <span class="keywordtype">double precision</span> pkm1
- <a name="l04228"></a>04228 <span class="keywordtype">double precision</span> pkp1
- <a name="l04229"></a>04229 <span class="keywordtype">double precision</span> t
- <a name="l04230"></a>04230 <span class="keywordtype">double precision</span> u
- <a name="l04231"></a>04231 <span class="keywordtype">double precision</span> v
- <a name="l04232"></a>04232 <span class="keywordtype">double precision</span> x0
- <a name="l04233"></a>04233 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l04234"></a>04234 <span class="keywordtype">double precision</span> xtemp
- <a name="l04235"></a>04235 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l04236"></a>04236 <span class="comment">!</span>
- <a name="l04237"></a>04237 <span class="keyword">if</span> ( norder < 1 ) <span class="keyword">then</span>
- <a name="l04238"></a>04238 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l04239"></a>04239 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LEGENDRE_COM - Fatal error!'</span>
- <a name="l04240"></a>04240 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l04241"></a>04241 stop
- <a name="l04242"></a>04242 <span class="keyword">end if</span>
- <a name="l04243"></a>04243
- <a name="l04244"></a>04244 e1 = dble ( norder * ( norder + 1 ) )
- <a name="l04245"></a>04245
- <a name="l04246"></a>04246 m = ( norder + 1 ) / 2
- <a name="l04247"></a>04247
- <a name="l04248"></a>04248 <span class="keyword">do</span> i = 1, ( norder + 1 ) / 2
- <a name="l04249"></a>04249
- <a name="l04250"></a>04250 mp1mi = m + 1 - i
- <a name="l04251"></a>04251 t = dble ( 4 * i - 1 ) * d_pi ( ) / dble ( 4 * norder + 2 )
- <a name="l04252"></a>04252 x0 = cos(t) * ( 1.0D+00 - ( 1.0D+00 - 1.0D+00 / dble ( norder ) ) &
- <a name="l04253"></a>04253 / dble ( 8 * norder**2 ) )
- <a name="l04254"></a>04254
- <a name="l04255"></a>04255 pkm1 = 1.0D+00
- <a name="l04256"></a>04256 pk = x0
- <a name="l04257"></a>04257
- <a name="l04258"></a>04258 <span class="keyword">do</span> k = 2, norder
- <a name="l04259"></a>04259 pkp1 = 2.0D+00 * x0 * pk - pkm1 - ( x0 * pk - pkm1 ) / dble ( k )
- <a name="l04260"></a>04260 pkm1 = pk
- <a name="l04261"></a>04261 pk = pkp1
- <a name="l04262"></a>04262 <span class="keyword">end do</span>
- <a name="l04263"></a>04263
- <a name="l04264"></a>04264 d1 = dble ( norder ) * ( pkm1 - x0 * pk )
- <a name="l04265"></a>04265
- <a name="l04266"></a>04266 dpn = d1 / ( 1.0D+00 - x0**2 )
- <a name="l04267"></a>04267
- <a name="l04268"></a>04268 d2pn = ( 2.0D+00 * x0 * dpn - e1 * pk ) / ( 1.0D+00 - x0**2 )
- <a name="l04269"></a>04269
- <a name="l04270"></a>04270 d3pn = ( 4.0D+00 * x0 * d2pn + ( 2.0D+00 - e1 ) * dpn ) &
- <a name="l04271"></a>04271 / ( 1.0D+00 - x0**2 )
- <a name="l04272"></a>04272
- <a name="l04273"></a>04273 d4pn = ( 6.0D+00 * x0 * d3pn + ( 6.0D+00 - e1 ) * d2pn ) / &
- <a name="l04274"></a>04274 ( 1.0D+00 - x0**2 )
- <a name="l04275"></a>04275
- <a name="l04276"></a>04276 u = pk / dpn
- <a name="l04277"></a>04277 v = d2pn / dpn
- <a name="l04278"></a>04278 <span class="comment">!</span>
- <a name="l04279"></a>04279 <span class="comment">! Initial approximation H:</span>
- <a name="l04280"></a>04280 <span class="comment">!</span>
- <a name="l04281"></a>04281 h = - u * ( 1.0D+00 + 0.5D+00 * u * ( v + u * ( v**2 - d3pn / &
- <a name="l04282"></a>04282 ( 3.0D+00 * dpn ) ) ) )
- <a name="l04283"></a>04283 <span class="comment">!</span>
- <a name="l04284"></a>04284 <span class="comment">! Refine H using one step of Newton's method:</span>
- <a name="l04285"></a>04285 <span class="comment">!</span>
- <a name="l04286"></a>04286 p = pk + h * ( dpn + 0.5D+00 * h * ( d2pn + h / 3.0D+00 &
- <a name="l04287"></a>04287 * ( d3pn + 0.25D+00 * h * d4pn ) ) )
- <a name="l04288"></a>04288
- <a name="l04289"></a>04289 dp = dpn + h * ( d2pn + 0.5D+00 * h * ( d3pn + h * d4pn / 3.0D+00 ) )
- <a name="l04290"></a>04290
- <a name="l04291"></a>04291 h = h - p / dp
- <a name="l04292"></a>04292
- <a name="l04293"></a>04293 xtemp = x0 + h
- <a name="l04294"></a>04294
- <a name="l04295"></a>04295 xtab(mp1mi) = xtemp
- <a name="l04296"></a>04296
- <a name="l04297"></a>04297 fx = d1 - h * e1 * ( pk + 0.5D+00 * h * ( dpn + h / 3.0D+00 &
- <a name="l04298"></a>04298 * ( d2pn + 0.25D+00 * h * ( d3pn + 0.2D+00 * h * d4pn ) ) ) )
- <a name="l04299"></a>04299
- <a name="l04300"></a>04300 weight(mp1mi) = 2.0D+00 * ( 1.0D+00 - xtemp**2 ) / fx**2
- <a name="l04301"></a>04301
- <a name="l04302"></a>04302 <span class="keyword">end do</span>
- <a name="l04303"></a>04303
- <a name="l04304"></a>04304 <span class="keyword">if</span> ( mod ( norder, 2 ) == 1 ) <span class="keyword">then</span>
- <a name="l04305"></a>04305 xtab(1) = 0.0D+00
- <a name="l04306"></a>04306 <span class="keyword">end if</span>
- <a name="l04307"></a>04307 <span class="comment">!</span>
- <a name="l04308"></a>04308 <span class="comment">! Shift the data up.</span>
- <a name="l04309"></a>04309 <span class="comment">!</span>
- <a name="l04310"></a>04310 nmove = ( norder + 1 ) / 2
- <a name="l04311"></a>04311 ncopy = norder - nmove
- <a name="l04312"></a>04312
- <a name="l04313"></a>04313 <span class="keyword">do</span> i = 1, nmove
- <a name="l04314"></a>04314 iback = norder + 1 - i
- <a name="l04315"></a>04315 xtab(iback) = xtab(iback-ncopy)
- <a name="l04316"></a>04316 weight(iback) = weight(iback-ncopy)
- <a name="l04317"></a>04317 <span class="keyword">end do</span>
- <a name="l04318"></a>04318 <span class="comment">!</span>
- <a name="l04319"></a>04319 <span class="comment">! Reflect values for the negative abscissas.</span>
- <a name="l04320"></a>04320 <span class="comment">!</span>
- <a name="l04321"></a>04321 <span class="keyword">do</span> i = 1, norder - nmove
- <a name="l04322"></a>04322 xtab(i) = - xtab(norder+1-i)
- <a name="l04323"></a>04323 weight(i) = weight(norder+1-i)
- <a name="l04324"></a>04324 <span class="keyword">end do</span>
- <a name="l04325"></a>04325
- <a name="l04326"></a>04326 return
- <a name="l04327"></a>04327 <span class="keyword">end</span>
- <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 )
- <a name="l04329"></a>04329 <span class="comment">!</span>
- <a name="l04330"></a>04330 <span class="comment">!*******************************************************************************</span>
- <a name="l04331"></a>04331 <span class="comment">!</span>
- <a name="l04332"></a>04332 <span class="comment">!! LEGENDRE_RECUR finds the value and derivative of a Legendre polynomial.</span>
- <a name="l04333"></a>04333 <span class="comment">!</span>
- <a name="l04334"></a>04334 <span class="comment">!</span>
- <a name="l04335"></a>04335 <span class="comment">! Reference:</span>
- <a name="l04336"></a>04336 <span class="comment">!</span>
- <a name="l04337"></a>04337 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l04338"></a>04338 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l04339"></a>04339 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l04340"></a>04340 <span class="comment">!</span>
- <a name="l04341"></a>04341 <span class="comment">! Modified:</span>
- <a name="l04342"></a>04342 <span class="comment">!</span>
- <a name="l04343"></a>04343 <span class="comment">! 19 September 1998</span>
- <a name="l04344"></a>04344 <span class="comment">!</span>
- <a name="l04345"></a>04345 <span class="comment">! Parameters:</span>
- <a name="l04346"></a>04346 <span class="comment">!</span>
- <a name="l04347"></a>04347 <span class="comment">! Output, double precision P2, the value of P(NORDER)(X).</span>
- <a name="l04348"></a>04348 <span class="comment">!</span>
- <a name="l04349"></a>04349 <span class="comment">! Output, double precision DP2, the value of P'(NORDER)(X).</span>
- <a name="l04350"></a>04350 <span class="comment">!</span>
- <a name="l04351"></a>04351 <span class="comment">! Output, double precision P1, the value of P(NORDER-1)(X).</span>
- <a name="l04352"></a>04352 <span class="comment">!</span>
- <a name="l04353"></a>04353 <span class="comment">! Input, double precision X, the point at which polynomials are evaluated.</span>
- <a name="l04354"></a>04354 <span class="comment">!</span>
- <a name="l04355"></a>04355 <span class="comment">! Input, integer NORDER, the order of the polynomial to be computed.</span>
- <a name="l04356"></a>04356 <span class="comment">!</span>
- <a name="l04357"></a>04357 <span class="keyword">implicit none</span>
- <a name="l04358"></a>04358 <span class="comment">!</span>
- <a name="l04359"></a>04359 <span class="keywordtype">integer</span> norder
- <a name="l04360"></a>04360 <span class="comment">!</span>
- <a name="l04361"></a>04361 <span class="keywordtype">double precision</span> dp0
- <a name="l04362"></a>04362 <span class="keywordtype">double precision</span> dp1
- <a name="l04363"></a>04363 <span class="keywordtype">double precision</span> dp2
- <a name="l04364"></a>04364 <span class="keywordtype">integer</span> i
- <a name="l04365"></a>04365 <span class="keywordtype">double precision</span> p0
- <a name="l04366"></a>04366 <span class="keywordtype">double precision</span> p1
- <a name="l04367"></a>04367 <span class="keywordtype">double precision</span> p2
- <a name="l04368"></a>04368 <span class="keywordtype">double precision</span> x
- <a name="l04369"></a>04369 <span class="comment">!</span>
- <a name="l04370"></a>04370 p1 = 1.0D+00
- <a name="l04371"></a>04371 dp1 = 0.0D+00
- <a name="l04372"></a>04372
- <a name="l04373"></a>04373 p2 = x
- <a name="l04374"></a>04374 dp2 = 1.0D+00
- <a name="l04375"></a>04375
- <a name="l04376"></a>04376 <span class="keyword">do</span> i = 2, norder
- <a name="l04377"></a>04377
- <a name="l04378"></a>04378 p0 = p1
- <a name="l04379"></a>04379 dp0 = dp1
- <a name="l04380"></a>04380
- <a name="l04381"></a>04381 p1 = p2
- <a name="l04382"></a>04382 dp1 = dp2
- <a name="l04383"></a>04383
- <a name="l04384"></a>04384 p2 = ( dble ( 2 * i - 1 ) * x * p1 - dble ( i - 1 ) * p0 ) / dble ( i )
- <a name="l04385"></a>04385
- <a name="l04386"></a>04386 dp2 = ( dble ( 2 * i - 1 ) * ( p1 + x * dp1 ) - dble ( i - 1 ) * dp0 ) &
- <a name="l04387"></a>04387 / dble ( i )
- <a name="l04388"></a>04388
- <a name="l04389"></a>04389 <span class="keyword">end do</span>
- <a name="l04390"></a>04390
- <a name="l04391"></a>04391 return
- <a name="l04392"></a>04392 <span class="keyword">end</span>
- <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 )
- <a name="l04394"></a>04394 <span class="comment">!</span>
- <a name="l04395"></a>04395 <span class="comment">!*******************************************************************************</span>
- <a name="l04396"></a>04396 <span class="comment">!</span>
- <a name="l04397"></a>04397 <span class="comment">!! LEGENDRE_SET sets abscissas and weights for Gauss-Legendre quadrature.</span>
- <a name="l04398"></a>04398 <span class="comment">!</span>
- <a name="l04399"></a>04399 <span class="comment">!</span>
- <a name="l04400"></a>04400 <span class="comment">! Integration interval:</span>
- <a name="l04401"></a>04401 <span class="comment">!</span>
- <a name="l04402"></a>04402 <span class="comment">! [ -1, 1 ]</span>
- <a name="l04403"></a>04403 <span class="comment">!</span>
- <a name="l04404"></a>04404 <span class="comment">! Weight function:</span>
- <a name="l04405"></a>04405 <span class="comment">!</span>
- <a name="l04406"></a>04406 <span class="comment">! 1.0D+00</span>
- <a name="l04407"></a>04407 <span class="comment">!</span>
- <a name="l04408"></a>04408 <span class="comment">! Integral to approximate:</span>
- <a name="l04409"></a>04409 <span class="comment">!</span>
- <a name="l04410"></a>04410 <span class="comment">! Integral ( -1 <= X <= 1 ) F(X) dX</span>
- <a name="l04411"></a>04411 <span class="comment">!</span>
- <a name="l04412"></a>04412 <span class="comment">! Approximate integral:</span>
- <a name="l04413"></a>04413 <span class="comment">!</span>
- <a name="l04414"></a>04414 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l04415"></a>04415 <span class="comment">!</span>
- <a name="l04416"></a>04416 <span class="comment">! Precision:</span>
- <a name="l04417"></a>04417 <span class="comment">!</span>
- <a name="l04418"></a>04418 <span class="comment">! The quadrature rule will integrate exactly all polynomials up to</span>
- <a name="l04419"></a>04419 <span class="comment">! X**(2*NORDER-1).</span>
- <a name="l04420"></a>04420 <span class="comment">!</span>
- <a name="l04421"></a>04421 <span class="comment">! Note:</span>
- <a name="l04422"></a>04422 <span class="comment">!</span>
- <a name="l04423"></a>04423 <span class="comment">! The abscissas of the rule are the zeroes of the Legendre polynomial</span>
- <a name="l04424"></a>04424 <span class="comment">! P(NORDER)(X).</span>
- <a name="l04425"></a>04425 <span class="comment">!</span>
- <a name="l04426"></a>04426 <span class="comment">! The integral produced by a Gauss-Legendre rule is equal to the</span>
- <a name="l04427"></a>04427 <span class="comment">! integral of the unique polynomial of degree NORDER-1 which</span>
- <a name="l04428"></a>04428 <span class="comment">! agrees with the function at the NORDER abscissas of the rule.</span>
- <a name="l04429"></a>04429 <span class="comment">!</span>
- <a name="l04430"></a>04430 <span class="comment">! Reference:</span>
- <a name="l04431"></a>04431 <span class="comment">!</span>
- <a name="l04432"></a>04432 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l04433"></a>04433 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l04434"></a>04434 <span class="comment">! National Bureau of Standards, 1964.</span>
- <a name="l04435"></a>04435 <span class="comment">!</span>
- <a name="l04436"></a>04436 <span class="comment">! Vladimir Krylov,</span>
- <a name="l04437"></a>04437 <span class="comment">! Approximate Calculation of Integrals,</span>
- <a name="l04438"></a>04438 <span class="comment">! MacMillan, 1962.</span>
- <a name="l04439"></a>04439 <span class="comment">!</span>
- <a name="l04440"></a>04440 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l04441"></a>04441 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l04442"></a>04442 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l04443"></a>04443 <span class="comment">!</span>
- <a name="l04444"></a>04444 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l04445"></a>04445 <span class="comment">! Standard Mathematical Tables and Formulae,</span>
- <a name="l04446"></a>04446 <span class="comment">! 30th Edition,</span>
- <a name="l04447"></a>04447 <span class="comment">! CRC Press, 1996.</span>
- <a name="l04448"></a>04448 <span class="comment">!</span>
- <a name="l04449"></a>04449 <span class="comment">! Modified:</span>
- <a name="l04450"></a>04450 <span class="comment">!</span>
- <a name="l04451"></a>04451 <span class="comment">! 18 December 2000</span>
- <a name="l04452"></a>04452 <span class="comment">!</span>
- <a name="l04453"></a>04453 <span class="comment">! Author:</span>
- <a name="l04454"></a>04454 <span class="comment">!</span>
- <a name="l04455"></a>04455 <span class="comment">! John Burkardt</span>
- <a name="l04456"></a>04456 <span class="comment">!</span>
- <a name="l04457"></a>04457 <span class="comment">! Parameters:</span>
- <a name="l04458"></a>04458 <span class="comment">!</span>
- <a name="l04459"></a>04459 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l04460"></a>04460 <span class="comment">! NORDER must be between 1 and 20, 32 or 64.</span>
- <a name="l04461"></a>04461 <span class="comment">!</span>
- <a name="l04462"></a>04462 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l04463"></a>04463 <span class="comment">!</span>
- <a name="l04464"></a>04464 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l04465"></a>04465 <span class="comment">! The weights are positive, symmetric and should sum to 2.</span>
- <a name="l04466"></a>04466 <span class="comment">!</span>
- <a name="l04467"></a>04467 <span class="keyword">implicit none</span>
- <a name="l04468"></a>04468 <span class="comment">!</span>
- <a name="l04469"></a>04469 <span class="keywordtype">integer</span> norder
- <a name="l04470"></a>04470 <span class="comment">!</span>
- <a name="l04471"></a>04471 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l04472"></a>04472 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l04473"></a>04473 <span class="comment">!</span>
- <a name="l04474"></a>04474 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l04475"></a>04475
- <a name="l04476"></a>04476 xtab(1) = 0.0D+00
- <a name="l04477"></a>04477
- <a name="l04478"></a>04478 weight(1) = 2.0D+00
- <a name="l04479"></a>04479
- <a name="l04480"></a>04480 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l04481"></a>04481
- <a name="l04482"></a>04482 xtab(1) = - 0.577350269189625764509148780502D+00
- <a name="l04483"></a>04483 xtab(2) = 0.577350269189625764509148780502D+00
- <a name="l04484"></a>04484
- <a name="l04485"></a>04485 weight(1) = 1.0D+00
- <a name="l04486"></a>04486 weight(2) = 1.0D+00
- <a name="l04487"></a>04487
- <a name="l04488"></a>04488 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l04489"></a>04489
- <a name="l04490"></a>04490 xtab(1) = - 0.774596669241483377035853079956D+00
- <a name="l04491"></a>04491 xtab(2) = 0.0D+00
- <a name="l04492"></a>04492 xtab(3) = 0.774596669241483377035853079956D+00
- <a name="l04493"></a>04493
- <a name="l04494"></a>04494 weight(1) = 5.0D+00 / 9.0D+00
- <a name="l04495"></a>04495 weight(2) = 8.0D+00 / 9.0D+00
- <a name="l04496"></a>04496 weight(3) = 5.0D+00 / 9.0D+00
- <a name="l04497"></a>04497
- <a name="l04498"></a>04498 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l04499"></a>04499
- <a name="l04500"></a>04500 xtab(1) = - 0.861136311594052575223946488893D+00
- <a name="l04501"></a>04501 xtab(2) = - 0.339981043584856264802665759103D+00
- <a name="l04502"></a>04502 xtab(3) = 0.339981043584856264802665759103D+00
- <a name="l04503"></a>04503 xtab(4) = 0.861136311594052575223946488893D+00
- <a name="l04504"></a>04504
- <a name="l04505"></a>04505 weight(1) = 0.347854845137453857373063949222D+00
- <a name="l04506"></a>04506 weight(2) = 0.652145154862546142626936050778D+00
- <a name="l04507"></a>04507 weight(3) = 0.652145154862546142626936050778D+00
- <a name="l04508"></a>04508 weight(4) = 0.347854845137453857373063949222D+00
- <a name="l04509"></a>04509
- <a name="l04510"></a>04510 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l04511"></a>04511
- <a name="l04512"></a>04512 xtab(1) = - 0.906179845938663992797626878299D+00
- <a name="l04513"></a>04513 xtab(2) = - 0.538469310105683091036314420700D+00
- <a name="l04514"></a>04514 xtab(3) = 0.0D+00
- <a name="l04515"></a>04515 xtab(4) = 0.538469310105683091036314420700D+00
- <a name="l04516"></a>04516 xtab(5) = 0.906179845938663992797626878299D+00
- <a name="l04517"></a>04517
- <a name="l04518"></a>04518 weight(1) = 0.236926885056189087514264040720D+00
- <a name="l04519"></a>04519 weight(2) = 0.478628670499366468041291514836D+00
- <a name="l04520"></a>04520 weight(3) = 0.568888888888888888888888888889D+00
- <a name="l04521"></a>04521 weight(4) = 0.478628670499366468041291514836D+00
- <a name="l04522"></a>04522 weight(5) = 0.236926885056189087514264040720D+00
- <a name="l04523"></a>04523
- <a name="l04524"></a>04524 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l04525"></a>04525
- <a name="l04526"></a>04526 xtab(1) = - 0.932469514203152027812301554494D+00
- <a name="l04527"></a>04527 xtab(2) = - 0.661209386466264513661399595020D+00
- <a name="l04528"></a>04528 xtab(3) = - 0.238619186083196908630501721681D+00
- <a name="l04529"></a>04529 xtab(4) = 0.238619186083196908630501721681D+00
- <a name="l04530"></a>04530 xtab(5) = 0.661209386466264513661399595020D+00
- <a name="l04531"></a>04531 xtab(6) = 0.932469514203152027812301554494D+00
- <a name="l04532"></a>04532
- <a name="l04533"></a>04533 weight(1) = 0.171324492379170345040296142173D+00
- <a name="l04534"></a>04534 weight(2) = 0.360761573048138607569833513838D+00
- <a name="l04535"></a>04535 weight(3) = 0.467913934572691047389870343990D+00
- <a name="l04536"></a>04536 weight(4) = 0.467913934572691047389870343990D+00
- <a name="l04537"></a>04537 weight(5) = 0.360761573048138607569833513838D+00
- <a name="l04538"></a>04538 weight(6) = 0.171324492379170345040296142173D+00
- <a name="l04539"></a>04539
- <a name="l04540"></a>04540 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l04541"></a>04541
- <a name="l04542"></a>04542 xtab(1) = - 0.949107912342758524526189684048D+00
- <a name="l04543"></a>04543 xtab(2) = - 0.741531185599394439863864773281D+00
- <a name="l04544"></a>04544 xtab(3) = - 0.405845151377397166906606412077D+00
- <a name="l04545"></a>04545 xtab(4) = 0.0D+00
- <a name="l04546"></a>04546 xtab(5) = 0.405845151377397166906606412077D+00
- <a name="l04547"></a>04547 xtab(6) = 0.741531185599394439863864773281D+00
- <a name="l04548"></a>04548 xtab(7) = 0.949107912342758524526189684048D+00
- <a name="l04549"></a>04549
- <a name="l04550"></a>04550 weight(1) = 0.129484966168869693270611432679D+00
- <a name="l04551"></a>04551 weight(2) = 0.279705391489276667901467771424D+00
- <a name="l04552"></a>04552 weight(3) = 0.381830050505118944950369775489D+00
- <a name="l04553"></a>04553 weight(4) = 0.417959183673469387755102040816D+00
- <a name="l04554"></a>04554 weight(5) = 0.381830050505118944950369775489D+00
- <a name="l04555"></a>04555 weight(6) = 0.279705391489276667901467771424D+00
- <a name="l04556"></a>04556 weight(7) = 0.129484966168869693270611432679D+00
- <a name="l04557"></a>04557
- <a name="l04558"></a>04558 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l04559"></a>04559
- <a name="l04560"></a>04560 xtab(1) = - 0.960289856497536231683560868569D+00
- <a name="l04561"></a>04561 xtab(2) = - 0.796666477413626739591553936476D+00
- <a name="l04562"></a>04562 xtab(3) = - 0.525532409916328985817739049189D+00
- <a name="l04563"></a>04563 xtab(4) = - 0.183434642495649804939476142360D+00
- <a name="l04564"></a>04564 xtab(5) = 0.183434642495649804939476142360D+00
- <a name="l04565"></a>04565 xtab(6) = 0.525532409916328985817739049189D+00
- <a name="l04566"></a>04566 xtab(7) = 0.796666477413626739591553936476D+00
- <a name="l04567"></a>04567 xtab(8) = 0.960289856497536231683560868569D+00
- <a name="l04568"></a>04568
- <a name="l04569"></a>04569 weight(1) = 0.101228536290376259152531354310D+00
- <a name="l04570"></a>04570 weight(2) = 0.222381034453374470544355994426D+00
- <a name="l04571"></a>04571 weight(3) = 0.313706645877887287337962201987D+00
- <a name="l04572"></a>04572 weight(4) = 0.362683783378361982965150449277D+00
- <a name="l04573"></a>04573 weight(5) = 0.362683783378361982965150449277D+00
- <a name="l04574"></a>04574 weight(6) = 0.313706645877887287337962201987D+00
- <a name="l04575"></a>04575 weight(7) = 0.222381034453374470544355994426D+00
- <a name="l04576"></a>04576 weight(8) = 0.101228536290376259152531354310D+00
- <a name="l04577"></a>04577
- <a name="l04578"></a>04578 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
- <a name="l04579"></a>04579
- <a name="l04580"></a>04580 xtab(1) = - 0.968160239507626089835576202904D+00
- <a name="l04581"></a>04581 xtab(2) = - 0.836031107326635794299429788070D+00
- <a name="l04582"></a>04582 xtab(3) = - 0.613371432700590397308702039341D+00
- <a name="l04583"></a>04583 xtab(4) = - 0.324253423403808929038538014643D+00
- <a name="l04584"></a>04584 xtab(5) = 0.0D+00
- <a name="l04585"></a>04585 xtab(6) = 0.324253423403808929038538014643D+00
- <a name="l04586"></a>04586 xtab(7) = 0.613371432700590397308702039341D+00
- <a name="l04587"></a>04587 xtab(8) = 0.836031107326635794299429788070D+00
- <a name="l04588"></a>04588 xtab(9) = 0.968160239507626089835576202904D+00
- <a name="l04589"></a>04589
- <a name="l04590"></a>04590 weight(1) = 0.812743883615744119718921581105D-01
- <a name="l04591"></a>04591 weight(2) = 0.180648160694857404058472031243D+00
- <a name="l04592"></a>04592 weight(3) = 0.260610696402935462318742869419D+00
- <a name="l04593"></a>04593 weight(4) = 0.312347077040002840068630406584D+00
- <a name="l04594"></a>04594 weight(5) = 0.330239355001259763164525069287D+00
- <a name="l04595"></a>04595 weight(6) = 0.312347077040002840068630406584D+00
- <a name="l04596"></a>04596 weight(7) = 0.260610696402935462318742869419D+00
- <a name="l04597"></a>04597 weight(8) = 0.180648160694857404058472031243D+00
- <a name="l04598"></a>04598 weight(9) = 0.812743883615744119718921581105D-01
- <a name="l04599"></a>04599
- <a name="l04600"></a>04600 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 10 ) <span class="keyword">then</span>
- <a name="l04601"></a>04601
- <a name="l04602"></a>04602 xtab(1) = - 0.973906528517171720077964012084D+00
- <a name="l04603"></a>04603 xtab(2) = - 0.865063366688984510732096688423D+00
- <a name="l04604"></a>04604 xtab(3) = - 0.679409568299024406234327365115D+00
- <a name="l04605"></a>04605 xtab(4) = - 0.433395394129247190799265943166D+00
- <a name="l04606"></a>04606 xtab(5) = - 0.148874338981631210884826001130D+00
- <a name="l04607"></a>04607 xtab(6) = 0.148874338981631210884826001130D+00
- <a name="l04608"></a>04608 xtab(7) = 0.433395394129247190799265943166D+00
- <a name="l04609"></a>04609 xtab(8) = 0.679409568299024406234327365115D+00
- <a name="l04610"></a>04610 xtab(9) = 0.865063366688984510732096688423D+00
- <a name="l04611"></a>04611 xtab(10) = 0.973906528517171720077964012084D+00
- <a name="l04612"></a>04612
- <a name="l04613"></a>04613 weight(1) = 0.666713443086881375935688098933D-01
- <a name="l04614"></a>04614 weight(2) = 0.149451349150580593145776339658D+00
- <a name="l04615"></a>04615 weight(3) = 0.219086362515982043995534934228D+00
- <a name="l04616"></a>04616 weight(4) = 0.269266719309996355091226921569D+00
- <a name="l04617"></a>04617 weight(5) = 0.295524224714752870173892994651D+00
- <a name="l04618"></a>04618 weight(6) = 0.295524224714752870173892994651D+00
- <a name="l04619"></a>04619 weight(7) = 0.269266719309996355091226921569D+00
- <a name="l04620"></a>04620 weight(8) = 0.219086362515982043995534934228D+00
- <a name="l04621"></a>04621 weight(9) = 0.149451349150580593145776339658D+00
- <a name="l04622"></a>04622 weight(10) = 0.666713443086881375935688098933D-01
- <a name="l04623"></a>04623
- <a name="l04624"></a>04624 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 11 ) <span class="keyword">then</span>
- <a name="l04625"></a>04625
- <a name="l04626"></a>04626 xtab(1) = - 0.978228658146056992803938001123D+00
- <a name="l04627"></a>04627 xtab(2) = - 0.887062599768095299075157769304D+00
- <a name="l04628"></a>04628 xtab(3) = - 0.730152005574049324093416252031D+00
- <a name="l04629"></a>04629 xtab(4) = - 0.519096129206811815925725669459D+00
- <a name="l04630"></a>04630 xtab(5) = - 0.269543155952344972331531985401D+00
- <a name="l04631"></a>04631 xtab(6) = 0.0D+00
- <a name="l04632"></a>04632 xtab(7) = 0.269543155952344972331531985401D+00
- <a name="l04633"></a>04633 xtab(8) = 0.519096129206811815925725669459D+00
- <a name="l04634"></a>04634 xtab(9) = 0.730152005574049324093416252031D+00
- <a name="l04635"></a>04635 xtab(10) = 0.887062599768095299075157769304D+00
- <a name="l04636"></a>04636 xtab(11) = 0.978228658146056992803938001123D+00
- <a name="l04637"></a>04637
- <a name="l04638"></a>04638 weight(1) = 0.556685671161736664827537204425D-01
- <a name="l04639"></a>04639 weight(2) = 0.125580369464904624634694299224D+00
- <a name="l04640"></a>04640 weight(3) = 0.186290210927734251426097641432D+00
- <a name="l04641"></a>04641 weight(4) = 0.233193764591990479918523704843D+00
- <a name="l04642"></a>04642 weight(5) = 0.262804544510246662180688869891D+00
- <a name="l04643"></a>04643 weight(6) = 0.272925086777900630714483528336D+00
- <a name="l04644"></a>04644 weight(7) = 0.262804544510246662180688869891D+00
- <a name="l04645"></a>04645 weight(8) = 0.233193764591990479918523704843D+00
- <a name="l04646"></a>04646 weight(9) = 0.186290210927734251426097641432D+00
- <a name="l04647"></a>04647 weight(10) = 0.125580369464904624634694299224D+00
- <a name="l04648"></a>04648 weight(11) = 0.556685671161736664827537204425D-01
- <a name="l04649"></a>04649
- <a name="l04650"></a>04650 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 12 ) <span class="keyword">then</span>
- <a name="l04651"></a>04651
- <a name="l04652"></a>04652 xtab(1) = - 0.981560634246719250690549090149D+00
- <a name="l04653"></a>04653 xtab(2) = - 0.904117256370474856678465866119D+00
- <a name="l04654"></a>04654 xtab(3) = - 0.769902674194304687036893833213D+00
- <a name="l04655"></a>04655 xtab(4) = - 0.587317954286617447296702418941D+00
- <a name="l04656"></a>04656 xtab(5) = - 0.367831498998180193752691536644D+00
- <a name="l04657"></a>04657 xtab(6) = - 0.125233408511468915472441369464D+00
- <a name="l04658"></a>04658 xtab(7) = 0.125233408511468915472441369464D+00
- <a name="l04659"></a>04659 xtab(8) = 0.367831498998180193752691536644D+00
- <a name="l04660"></a>04660 xtab(9) = 0.587317954286617447296702418941D+00
- <a name="l04661"></a>04661 xtab(10) = 0.769902674194304687036893833213D+00
- <a name="l04662"></a>04662 xtab(11) = 0.904117256370474856678465866119D+00
- <a name="l04663"></a>04663 xtab(12) = 0.981560634246719250690549090149D+00
- <a name="l04664"></a>04664
- <a name="l04665"></a>04665 weight(1) = 0.471753363865118271946159614850D-01
- <a name="l04666"></a>04666 weight(2) = 0.106939325995318430960254718194D+00
- <a name="l04667"></a>04667 weight(3) = 0.160078328543346226334652529543D+00
- <a name="l04668"></a>04668 weight(4) = 0.203167426723065921749064455810D+00
- <a name="l04669"></a>04669 weight(5) = 0.233492536538354808760849898925D+00
- <a name="l04670"></a>04670 weight(6) = 0.249147045813402785000562436043D+00
- <a name="l04671"></a>04671 weight(7) = 0.249147045813402785000562436043D+00
- <a name="l04672"></a>04672 weight(8) = 0.233492536538354808760849898925D+00
- <a name="l04673"></a>04673 weight(9) = 0.203167426723065921749064455810D+00
- <a name="l04674"></a>04674 weight(10) = 0.160078328543346226334652529543D+00
- <a name="l04675"></a>04675 weight(11) = 0.106939325995318430960254718194D+00
- <a name="l04676"></a>04676 weight(12) = 0.471753363865118271946159614850D-01
- <a name="l04677"></a>04677
- <a name="l04678"></a>04678 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 13 ) <span class="keyword">then</span>
- <a name="l04679"></a>04679
- <a name="l04680"></a>04680 xtab(1) = - 0.984183054718588149472829448807D+00
- <a name="l04681"></a>04681 xtab(2) = - 0.917598399222977965206547836501D+00
- <a name="l04682"></a>04682 xtab(3) = - 0.801578090733309912794206489583D+00
- <a name="l04683"></a>04683 xtab(4) = - 0.642349339440340220643984606996D+00
- <a name="l04684"></a>04684 xtab(5) = - 0.448492751036446852877912852128D+00
- <a name="l04685"></a>04685 xtab(6) = - 0.230458315955134794065528121098D+00
- <a name="l04686"></a>04686 xtab(7) = 0.0D+00
- <a name="l04687"></a>04687 xtab(8) = 0.230458315955134794065528121098D+00
- <a name="l04688"></a>04688 xtab(9) = 0.448492751036446852877912852128D+00
- <a name="l04689"></a>04689 xtab(10) = 0.642349339440340220643984606996D+00
- <a name="l04690"></a>04690 xtab(11) = 0.801578090733309912794206489583D+00
- <a name="l04691"></a>04691 xtab(12) = 0.917598399222977965206547836501D+00
- <a name="l04692"></a>04692 xtab(13) = 0.984183054718588149472829448807D+00
- <a name="l04693"></a>04693
- <a name="l04694"></a>04694 weight(1) = 0.404840047653158795200215922010D-01
- <a name="l04695"></a>04695 weight(2) = 0.921214998377284479144217759538D-01
- <a name="l04696"></a>04696 weight(3) = 0.138873510219787238463601776869D+00
- <a name="l04697"></a>04697 weight(4) = 0.178145980761945738280046691996D+00
- <a name="l04698"></a>04698 weight(5) = 0.207816047536888502312523219306D+00
- <a name="l04699"></a>04699 weight(6) = 0.226283180262897238412090186040D+00
- <a name="l04700"></a>04700 weight(7) = 0.232551553230873910194589515269D+00
- <a name="l04701"></a>04701 weight(8) = 0.226283180262897238412090186040D+00
- <a name="l04702"></a>04702 weight(9) = 0.207816047536888502312523219306D+00
- <a name="l04703"></a>04703 weight(10) = 0.178145980761945738280046691996D+00
- <a name="l04704"></a>04704 weight(11) = 0.138873510219787238463601776869D+00
- <a name="l04705"></a>04705 weight(12) = 0.921214998377284479144217759538D-01
- <a name="l04706"></a>04706 weight(13) = 0.404840047653158795200215922010D-01
- <a name="l04707"></a>04707
- <a name="l04708"></a>04708 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 14 ) <span class="keyword">then</span>
- <a name="l04709"></a>04709
- <a name="l04710"></a>04710 xtab(1) = - 0.986283808696812338841597266704D+00
- <a name="l04711"></a>04711 xtab(2) = - 0.928434883663573517336391139378D+00
- <a name="l04712"></a>04712 xtab(3) = - 0.827201315069764993189794742650D+00
- <a name="l04713"></a>04713 xtab(4) = - 0.687292904811685470148019803019D+00
- <a name="l04714"></a>04714 xtab(5) = - 0.515248636358154091965290718551D+00
- <a name="l04715"></a>04715 xtab(6) = - 0.319112368927889760435671824168D+00
- <a name="l04716"></a>04716 xtab(7) = - 0.108054948707343662066244650220D+00
- <a name="l04717"></a>04717 xtab(8) = 0.108054948707343662066244650220D+00
- <a name="l04718"></a>04718 xtab(9) = 0.319112368927889760435671824168D+00
- <a name="l04719"></a>04719 xtab(10) = 0.515248636358154091965290718551D+00
- <a name="l04720"></a>04720 xtab(11) = 0.687292904811685470148019803019D+00
- <a name="l04721"></a>04721 xtab(12) = 0.827201315069764993189794742650D+00
- <a name="l04722"></a>04722 xtab(13) = 0.928434883663573517336391139378D+00
- <a name="l04723"></a>04723 xtab(14) = 0.986283808696812338841597266704D+00
- <a name="l04724"></a>04724
- <a name="l04725"></a>04725 weight(1) = 0.351194603317518630318328761382D-01
- <a name="l04726"></a>04726 weight(2) = 0.801580871597602098056332770629D-01
- <a name="l04727"></a>04727 weight(3) = 0.121518570687903184689414809072D+00
- <a name="l04728"></a>04728 weight(4) = 0.157203167158193534569601938624D+00
- <a name="l04729"></a>04729 weight(5) = 0.185538397477937813741716590125D+00
- <a name="l04730"></a>04730 weight(6) = 0.205198463721295603965924065661D+00
- <a name="l04731"></a>04731 weight(7) = 0.215263853463157790195876443316D+00
- <a name="l04732"></a>04732 weight(8) = 0.215263853463157790195876443316D+00
- <a name="l04733"></a>04733 weight(9) = 0.205198463721295603965924065661D+00
- <a name="l04734"></a>04734 weight(10) = 0.185538397477937813741716590125D+00
- <a name="l04735"></a>04735 weight(11) = 0.157203167158193534569601938624D+00
- <a name="l04736"></a>04736 weight(12) = 0.121518570687903184689414809072D+00
- <a name="l04737"></a>04737 weight(13) = 0.801580871597602098056332770629D-01
- <a name="l04738"></a>04738 weight(14) = 0.351194603317518630318328761382D-01
- <a name="l04739"></a>04739
- <a name="l04740"></a>04740 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 15 ) <span class="keyword">then</span>
- <a name="l04741"></a>04741
- <a name="l04742"></a>04742 xtab(1) = - 0.987992518020485428489565718587D+00
- <a name="l04743"></a>04743 xtab(2) = - 0.937273392400705904307758947710D+00
- <a name="l04744"></a>04744 xtab(3) = - 0.848206583410427216200648320774D+00
- <a name="l04745"></a>04745 xtab(4) = - 0.724417731360170047416186054614D+00
- <a name="l04746"></a>04746 xtab(5) = - 0.570972172608538847537226737254D+00
- <a name="l04747"></a>04747 xtab(6) = - 0.394151347077563369897207370981D+00
- <a name="l04748"></a>04748 xtab(7) = - 0.201194093997434522300628303395D+00
- <a name="l04749"></a>04749 xtab(8) = 0.0D+00
- <a name="l04750"></a>04750 xtab(9) = 0.201194093997434522300628303395D+00
- <a name="l04751"></a>04751 xtab(10) = 0.394151347077563369897207370981D+00
- <a name="l04752"></a>04752 xtab(11) = 0.570972172608538847537226737254D+00
- <a name="l04753"></a>04753 xtab(12) = 0.724417731360170047416186054614D+00
- <a name="l04754"></a>04754 xtab(13) = 0.848206583410427216200648320774D+00
- <a name="l04755"></a>04755 xtab(14) = 0.937273392400705904307758947710D+00
- <a name="l04756"></a>04756 xtab(15) = 0.987992518020485428489565718587D+00
- <a name="l04757"></a>04757
- <a name="l04758"></a>04758 weight(1) = 0.307532419961172683546283935772D-01
- <a name="l04759"></a>04759 weight(2) = 0.703660474881081247092674164507D-01
- <a name="l04760"></a>04760 weight(3) = 0.107159220467171935011869546686D+00
- <a name="l04761"></a>04761 weight(4) = 0.139570677926154314447804794511D+00
- <a name="l04762"></a>04762 weight(5) = 0.166269205816993933553200860481D+00
- <a name="l04763"></a>04763 weight(6) = 0.186161000015562211026800561866D+00
- <a name="l04764"></a>04764 weight(7) = 0.198431485327111576456118326444D+00
- <a name="l04765"></a>04765 weight(8) = 0.202578241925561272880620199968D+00
- <a name="l04766"></a>04766 weight(9) = 0.198431485327111576456118326444D+00
- <a name="l04767"></a>04767 weight(10) = 0.186161000015562211026800561866D+00
- <a name="l04768"></a>04768 weight(11) = 0.166269205816993933553200860481D+00
- <a name="l04769"></a>04769 weight(12) = 0.139570677926154314447804794511D+00
- <a name="l04770"></a>04770 weight(13) = 0.107159220467171935011869546686D+00
- <a name="l04771"></a>04771 weight(14) = 0.703660474881081247092674164507D-01
- <a name="l04772"></a>04772 weight(15) = 0.307532419961172683546283935772D-01
- <a name="l04773"></a>04773
- <a name="l04774"></a>04774 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
- <a name="l04775"></a>04775
- <a name="l04776"></a>04776 xtab(1) = - 0.989400934991649932596154173450D+00
- <a name="l04777"></a>04777 xtab(2) = - 0.944575023073232576077988415535D+00
- <a name="l04778"></a>04778 xtab(3) = - 0.865631202387831743880467897712D+00
- <a name="l04779"></a>04779 xtab(4) = - 0.755404408355003033895101194847D+00
- <a name="l04780"></a>04780 xtab(5) = - 0.617876244402643748446671764049D+00
- <a name="l04781"></a>04781 xtab(6) = - 0.458016777657227386342419442984D+00
- <a name="l04782"></a>04782 xtab(7) = - 0.281603550779258913230460501460D+00
- <a name="l04783"></a>04783 xtab(8) = - 0.950125098376374401853193354250D-01
- <a name="l04784"></a>04784 xtab(9) = 0.950125098376374401853193354250D-01
- <a name="l04785"></a>04785 xtab(10) = 0.281603550779258913230460501460D+00
- <a name="l04786"></a>04786 xtab(11) = 0.458016777657227386342419442984D+00
- <a name="l04787"></a>04787 xtab(12) = 0.617876244402643748446671764049D+00
- <a name="l04788"></a>04788 xtab(13) = 0.755404408355003033895101194847D+00
- <a name="l04789"></a>04789 xtab(14) = 0.865631202387831743880467897712D+00
- <a name="l04790"></a>04790 xtab(15) = 0.944575023073232576077988415535D+00
- <a name="l04791"></a>04791 xtab(16) = 0.989400934991649932596154173450D+00
- <a name="l04792"></a>04792
- <a name="l04793"></a>04793 weight(1) = 0.271524594117540948517805724560D-01
- <a name="l04794"></a>04794 weight(2) = 0.622535239386478928628438369944D-01
- <a name="l04795"></a>04795 weight(3) = 0.951585116824927848099251076022D-01
- <a name="l04796"></a>04796 weight(4) = 0.124628971255533872052476282192D+00
- <a name="l04797"></a>04797 weight(5) = 0.149595988816576732081501730547D+00
- <a name="l04798"></a>04798 weight(6) = 0.169156519395002538189312079030D+00
- <a name="l04799"></a>04799 weight(7) = 0.182603415044923588866763667969D+00
- <a name="l04800"></a>04800 weight(8) = 0.189450610455068496285396723208D+00
- <a name="l04801"></a>04801 weight(9) = 0.189450610455068496285396723208D+00
- <a name="l04802"></a>04802 weight(10) = 0.182603415044923588866763667969D+00
- <a name="l04803"></a>04803 weight(11) = 0.169156519395002538189312079030D+00
- <a name="l04804"></a>04804 weight(12) = 0.149595988816576732081501730547D+00
- <a name="l04805"></a>04805 weight(13) = 0.124628971255533872052476282192D+00
- <a name="l04806"></a>04806 weight(14) = 0.951585116824927848099251076022D-01
- <a name="l04807"></a>04807 weight(15) = 0.622535239386478928628438369944D-01
- <a name="l04808"></a>04808 weight(16) = 0.271524594117540948517805724560D-01
- <a name="l04809"></a>04809
- <a name="l04810"></a>04810 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 17 ) <span class="keyword">then</span>
- <a name="l04811"></a>04811
- <a name="l04812"></a>04812 xtab(1) = - 0.990575475314417335675434019941D+00
- <a name="l04813"></a>04813 xtab(2) = - 0.950675521768767761222716957896D+00
- <a name="l04814"></a>04814 xtab(3) = - 0.880239153726985902122955694488D+00
- <a name="l04815"></a>04815 xtab(4) = - 0.781514003896801406925230055520D+00
- <a name="l04816"></a>04816 xtab(5) = - 0.657671159216690765850302216643D+00
- <a name="l04817"></a>04817 xtab(6) = - 0.512690537086476967886246568630D+00
- <a name="l04818"></a>04818 xtab(7) = - 0.351231763453876315297185517095D+00
- <a name="l04819"></a>04819 xtab(8) = - 0.178484181495847855850677493654D+00
- <a name="l04820"></a>04820 xtab(9) = 0.0D+00
- <a name="l04821"></a>04821 xtab(10) = 0.178484181495847855850677493654D+00
- <a name="l04822"></a>04822 xtab(11) = 0.351231763453876315297185517095D+00
- <a name="l04823"></a>04823 xtab(12) = 0.512690537086476967886246568630D+00
- <a name="l04824"></a>04824 xtab(13) = 0.657671159216690765850302216643D+00
- <a name="l04825"></a>04825 xtab(14) = 0.781514003896801406925230055520D+00
- <a name="l04826"></a>04826 xtab(15) = 0.880239153726985902122955694488D+00
- <a name="l04827"></a>04827 xtab(16) = 0.950675521768767761222716957896D+00
- <a name="l04828"></a>04828 xtab(17) = 0.990575475314417335675434019941D+00
- <a name="l04829"></a>04829
- <a name="l04830"></a>04830 weight(1) = 0.241483028685479319601100262876D-01
- <a name="l04831"></a>04831 weight(2) = 0.554595293739872011294401653582D-01
- <a name="l04832"></a>04832 weight(3) = 0.850361483171791808835353701911D-01
- <a name="l04833"></a>04833 weight(4) = 0.111883847193403971094788385626D+00
- <a name="l04834"></a>04834 weight(5) = 0.135136368468525473286319981702D+00
- <a name="l04835"></a>04835 weight(6) = 0.154045761076810288081431594802D+00
- <a name="l04836"></a>04836 weight(7) = 0.168004102156450044509970663788D+00
- <a name="l04837"></a>04837 weight(8) = 0.176562705366992646325270990113D+00
- <a name="l04838"></a>04838 weight(9) = 0.179446470356206525458265644262D+00
- <a name="l04839"></a>04839 weight(10) = 0.176562705366992646325270990113D+00
- <a name="l04840"></a>04840 weight(11) = 0.168004102156450044509970663788D+00
- <a name="l04841"></a>04841 weight(12) = 0.154045761076810288081431594802D+00
- <a name="l04842"></a>04842 weight(13) = 0.135136368468525473286319981702D+00
- <a name="l04843"></a>04843 weight(14) = 0.111883847193403971094788385626D+00
- <a name="l04844"></a>04844 weight(15) = 0.850361483171791808835353701911D-01
- <a name="l04845"></a>04845 weight(16) = 0.554595293739872011294401653582D-01
- <a name="l04846"></a>04846 weight(17) = 0.241483028685479319601100262876D-01
- <a name="l04847"></a>04847
- <a name="l04848"></a>04848 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 18 ) <span class="keyword">then</span>
- <a name="l04849"></a>04849
- <a name="l04850"></a>04850 xtab(1) = - 0.991565168420930946730016004706D+00
- <a name="l04851"></a>04851 xtab(2) = - 0.955823949571397755181195892930D+00
- <a name="l04852"></a>04852 xtab(3) = - 0.892602466497555739206060591127D+00
- <a name="l04853"></a>04853 xtab(4) = - 0.803704958972523115682417455015D+00
- <a name="l04854"></a>04854 xtab(5) = - 0.691687043060353207874891081289D+00
- <a name="l04855"></a>04855 xtab(6) = - 0.559770831073947534607871548525D+00
- <a name="l04856"></a>04856 xtab(7) = - 0.411751161462842646035931793833D+00
- <a name="l04857"></a>04857 xtab(8) = - 0.251886225691505509588972854878D+00
- <a name="l04858"></a>04858 xtab(9) = - 0.847750130417353012422618529358D-01
- <a name="l04859"></a>04859 xtab(10) = 0.847750130417353012422618529358D-01
- <a name="l04860"></a>04860 xtab(11) = 0.251886225691505509588972854878D+00
- <a name="l04861"></a>04861 xtab(12) = 0.411751161462842646035931793833D+00
- <a name="l04862"></a>04862 xtab(13) = 0.559770831073947534607871548525D+00
- <a name="l04863"></a>04863 xtab(14) = 0.691687043060353207874891081289D+00
- <a name="l04864"></a>04864 xtab(15) = 0.803704958972523115682417455015D+00
- <a name="l04865"></a>04865 xtab(16) = 0.892602466497555739206060591127D+00
- <a name="l04866"></a>04866 xtab(17) = 0.955823949571397755181195892930D+00
- <a name="l04867"></a>04867 xtab(18) = 0.991565168420930946730016004706D+00
- <a name="l04868"></a>04868
- <a name="l04869"></a>04869 weight(1) = 0.216160135264833103133427102665D-01
- <a name="l04870"></a>04870 weight(2) = 0.497145488949697964533349462026D-01
- <a name="l04871"></a>04871 weight(3) = 0.764257302548890565291296776166D-01
- <a name="l04872"></a>04872 weight(4) = 0.100942044106287165562813984925D+00
- <a name="l04873"></a>04873 weight(5) = 0.122555206711478460184519126800D+00
- <a name="l04874"></a>04874 weight(6) = 0.140642914670650651204731303752D+00
- <a name="l04875"></a>04875 weight(7) = 0.154684675126265244925418003836D+00
- <a name="l04876"></a>04876 weight(8) = 0.164276483745832722986053776466D+00
- <a name="l04877"></a>04877 weight(9) = 0.169142382963143591840656470135D+00
- <a name="l04878"></a>04878 weight(10) = 0.169142382963143591840656470135D+00
- <a name="l04879"></a>04879 weight(11) = 0.164276483745832722986053776466D+00
- <a name="l04880"></a>04880 weight(12) = 0.154684675126265244925418003836D+00
- <a name="l04881"></a>04881 weight(13) = 0.140642914670650651204731303752D+00
- <a name="l04882"></a>04882 weight(14) = 0.122555206711478460184519126800D+00
- <a name="l04883"></a>04883 weight(15) = 0.100942044106287165562813984925D+00
- <a name="l04884"></a>04884 weight(16) = 0.764257302548890565291296776166D-01
- <a name="l04885"></a>04885 weight(17) = 0.497145488949697964533349462026D-01
- <a name="l04886"></a>04886 weight(18) = 0.216160135264833103133427102665D-01
- <a name="l04887"></a>04887
- <a name="l04888"></a>04888 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 19 ) <span class="keyword">then</span>
- <a name="l04889"></a>04889
- <a name="l04890"></a>04890 xtab(1) = - 0.992406843843584403189017670253D+00
- <a name="l04891"></a>04891 xtab(2) = - 0.960208152134830030852778840688D+00
- <a name="l04892"></a>04892 xtab(3) = - 0.903155903614817901642660928532D+00
- <a name="l04893"></a>04893 xtab(4) = - 0.822714656537142824978922486713D+00
- <a name="l04894"></a>04894 xtab(5) = - 0.720966177335229378617095860824D+00
- <a name="l04895"></a>04895 xtab(6) = - 0.600545304661681023469638164946D+00
- <a name="l04896"></a>04896 xtab(7) = - 0.464570741375960945717267148104D+00
- <a name="l04897"></a>04897 xtab(8) = - 0.316564099963629831990117328850D+00
- <a name="l04898"></a>04898 xtab(9) = - 0.160358645640225375868096115741D+00
- <a name="l04899"></a>04899 xtab(10) = 0.0D+00
- <a name="l04900"></a>04900 xtab(11) = 0.160358645640225375868096115741D+00
- <a name="l04901"></a>04901 xtab(12) = 0.316564099963629831990117328850D+00
- <a name="l04902"></a>04902 xtab(13) = 0.464570741375960945717267148104D+00
- <a name="l04903"></a>04903 xtab(14) = 0.600545304661681023469638164946D+00
- <a name="l04904"></a>04904 xtab(15) = 0.720966177335229378617095860824D+00
- <a name="l04905"></a>04905 xtab(16) = 0.822714656537142824978922486713D+00
- <a name="l04906"></a>04906 xtab(17) = 0.903155903614817901642660928532D+00
- <a name="l04907"></a>04907 xtab(18) = 0.960208152134830030852778840688D+00
- <a name="l04908"></a>04908 xtab(19) = 0.992406843843584403189017670253D+00
- <a name="l04909"></a>04909
- <a name="l04910"></a>04910 weight(1) = 0.194617882297264770363120414644D-01
- <a name="l04911"></a>04911 weight(2) = 0.448142267656996003328381574020D-01
- <a name="l04912"></a>04912 weight(3) = 0.690445427376412265807082580060D-01
- <a name="l04913"></a>04913 weight(4) = 0.914900216224499994644620941238D-01
- <a name="l04914"></a>04914 weight(5) = 0.111566645547333994716023901682D+00
- <a name="l04915"></a>04915 weight(6) = 0.128753962539336227675515784857D+00
- <a name="l04916"></a>04916 weight(7) = 0.142606702173606611775746109442D+00
- <a name="l04917"></a>04917 weight(8) = 0.152766042065859666778855400898D+00
- <a name="l04918"></a>04918 weight(9) = 0.158968843393954347649956439465D+00
- <a name="l04919"></a>04919 weight(10) = 0.161054449848783695979163625321D+00
- <a name="l04920"></a>04920 weight(11) = 0.158968843393954347649956439465D+00
- <a name="l04921"></a>04921 weight(12) = 0.152766042065859666778855400898D+00
- <a name="l04922"></a>04922 weight(13) = 0.142606702173606611775746109442D+00
- <a name="l04923"></a>04923 weight(14) = 0.128753962539336227675515784857D+00
- <a name="l04924"></a>04924 weight(15) = 0.111566645547333994716023901682D+00
- <a name="l04925"></a>04925 weight(16) = 0.914900216224499994644620941238D-01
- <a name="l04926"></a>04926 weight(17) = 0.690445427376412265807082580060D-01
- <a name="l04927"></a>04927 weight(18) = 0.448142267656996003328381574020D-01
- <a name="l04928"></a>04928 weight(19) = 0.194617882297264770363120414644D-01
- <a name="l04929"></a>04929
- <a name="l04930"></a>04930 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 20 ) <span class="keyword">then</span>
- <a name="l04931"></a>04931
- <a name="l04932"></a>04932 xtab(1) = - 0.993128599185094924786122388471D+00
- <a name="l04933"></a>04933 xtab(2) = - 0.963971927277913791267666131197D+00
- <a name="l04934"></a>04934 xtab(3) = - 0.912234428251325905867752441203D+00
- <a name="l04935"></a>04935 xtab(4) = - 0.839116971822218823394529061702D+00
- <a name="l04936"></a>04936 xtab(5) = - 0.746331906460150792614305070356D+00
- <a name="l04937"></a>04937 xtab(6) = - 0.636053680726515025452836696226D+00
- <a name="l04938"></a>04938 xtab(7) = - 0.510867001950827098004364050955D+00
- <a name="l04939"></a>04939 xtab(8) = - 0.373706088715419560672548177025D+00
- <a name="l04940"></a>04940 xtab(9) = - 0.227785851141645078080496195369D+00
- <a name="l04941"></a>04941 xtab(10) = - 0.765265211334973337546404093988D-01
- <a name="l04942"></a>04942 xtab(11) = 0.765265211334973337546404093988D-01
- <a name="l04943"></a>04943 xtab(12) = 0.227785851141645078080496195369D+00
- <a name="l04944"></a>04944 xtab(13) = 0.373706088715419560672548177025D+00
- <a name="l04945"></a>04945 xtab(14) = 0.510867001950827098004364050955D+00
- <a name="l04946"></a>04946 xtab(15) = 0.636053680726515025452836696226D+00
- <a name="l04947"></a>04947 xtab(16) = 0.746331906460150792614305070356D+00
- <a name="l04948"></a>04948 xtab(17) = 0.839116971822218823394529061702D+00
- <a name="l04949"></a>04949 xtab(18) = 0.912234428251325905867752441203D+00
- <a name="l04950"></a>04950 xtab(19) = 0.963971927277913791267666131197D+00
- <a name="l04951"></a>04951 xtab(20) = 0.993128599185094924786122388471D+00
- <a name="l04952"></a>04952
- <a name="l04953"></a>04953 weight(1) = 0.176140071391521183118619623519D-01
- <a name="l04954"></a>04954 weight(2) = 0.406014298003869413310399522749D-01
- <a name="l04955"></a>04955 weight(3) = 0.626720483341090635695065351870D-01
- <a name="l04956"></a>04956 weight(4) = 0.832767415767047487247581432220D-01
- <a name="l04957"></a>04957 weight(5) = 0.101930119817240435036750135480D+00
- <a name="l04958"></a>04958 weight(6) = 0.118194531961518417312377377711D+00
- <a name="l04959"></a>04959 weight(7) = 0.131688638449176626898494499748D+00
- <a name="l04960"></a>04960 weight(8) = 0.142096109318382051329298325067D+00
- <a name="l04961"></a>04961 weight(9) = 0.149172986472603746787828737002D+00
- <a name="l04962"></a>04962 weight(10) = 0.152753387130725850698084331955D+00
- <a name="l04963"></a>04963 weight(11) = 0.152753387130725850698084331955D+00
- <a name="l04964"></a>04964 weight(12) = 0.149172986472603746787828737002D+00
- <a name="l04965"></a>04965 weight(13) = 0.142096109318382051329298325067D+00
- <a name="l04966"></a>04966 weight(14) = 0.131688638449176626898494499748D+00
- <a name="l04967"></a>04967 weight(15) = 0.118194531961518417312377377711D+00
- <a name="l04968"></a>04968 weight(16) = 0.101930119817240435036750135480D+00
- <a name="l04969"></a>04969 weight(17) = 0.832767415767047487247581432220D-01
- <a name="l04970"></a>04970 weight(18) = 0.626720483341090635695065351870D-01
- <a name="l04971"></a>04971 weight(19) = 0.406014298003869413310399522749D-01
- <a name="l04972"></a>04972 weight(20) = 0.176140071391521183118619623519D-01
- <a name="l04973"></a>04973
- <a name="l04974"></a>04974 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 32 ) <span class="keyword">then</span>
- <a name="l04975"></a>04975
- <a name="l04976"></a>04976 xtab(1) = - 0.997263861849481563544981128665D+00
- <a name="l04977"></a>04977 xtab(2) = - 0.985611511545268335400175044631D+00
- <a name="l04978"></a>04978 xtab(3) = - 0.964762255587506430773811928118D+00
- <a name="l04979"></a>04979 xtab(4) = - 0.934906075937739689170919134835D+00
- <a name="l04980"></a>04980 xtab(5) = - 0.896321155766052123965307243719D+00
- <a name="l04981"></a>04981 xtab(6) = - 0.849367613732569970133693004968D+00
- <a name="l04982"></a>04982 xtab(7) = - 0.794483795967942406963097298970D+00
- <a name="l04983"></a>04983 xtab(8) = - 0.732182118740289680387426665091D+00
- <a name="l04984"></a>04984 xtab(9) = - 0.663044266930215200975115168663D+00
- <a name="l04985"></a>04985 xtab(10) = - 0.587715757240762329040745476402D+00
- <a name="l04986"></a>04986 xtab(11) = - 0.506899908932229390023747474378D+00
- <a name="l04987"></a>04987 xtab(12) = - 0.421351276130635345364119436172D+00
- <a name="l04988"></a>04988 xtab(13) = - 0.331868602282127649779916805730D+00
- <a name="l04989"></a>04989 xtab(14) = - 0.239287362252137074544603209166D+00
- <a name="l04990"></a>04990 xtab(15) = - 0.144471961582796493485186373599D+00
- <a name="l04991"></a>04991 xtab(16) = - 0.483076656877383162348125704405D-01
- <a name="l04992"></a>04992 xtab(17) = 0.483076656877383162348125704405D-01
- <a name="l04993"></a>04993 xtab(18) = 0.144471961582796493485186373599D+00
- <a name="l04994"></a>04994 xtab(19) = 0.239287362252137074544603209166D+00
- <a name="l04995"></a>04995 xtab(20) = 0.331868602282127649779916805730D+00
- <a name="l04996"></a>04996 xtab(21) = 0.421351276130635345364119436172D+00
- <a name="l04997"></a>04997 xtab(22) = 0.506899908932229390023747474378D+00
- <a name="l04998"></a>04998 xtab(23) = 0.587715757240762329040745476402D+00
- <a name="l04999"></a>04999 xtab(24) = 0.663044266930215200975115168663D+00
- <a name="l05000"></a>05000 xtab(25) = 0.732182118740289680387426665091D+00
- <a name="l05001"></a>05001 xtab(26) = 0.794483795967942406963097298970D+00
- <a name="l05002"></a>05002 xtab(27) = 0.849367613732569970133693004968D+00
- <a name="l05003"></a>05003 xtab(28) = 0.896321155766052123965307243719D+00
- <a name="l05004"></a>05004 xtab(29) = 0.934906075937739689170919134835D+00
- <a name="l05005"></a>05005 xtab(30) = 0.964762255587506430773811928118D+00
- <a name="l05006"></a>05006 xtab(31) = 0.985611511545268335400175044631D+00
- <a name="l05007"></a>05007 xtab(32) = 0.997263861849481563544981128665D+00
- <a name="l05008"></a>05008
- <a name="l05009"></a>05009 weight(1) = 0.701861000947009660040706373885D-02
- <a name="l05010"></a>05010 weight(2) = 0.162743947309056706051705622064D-01
- <a name="l05011"></a>05011 weight(3) = 0.253920653092620594557525897892D-01
- <a name="l05012"></a>05012 weight(4) = 0.342738629130214331026877322524D-01
- <a name="l05013"></a>05013 weight(5) = 0.428358980222266806568786466061D-01
- <a name="l05014"></a>05014 weight(6) = 0.509980592623761761961632446895D-01
- <a name="l05015"></a>05015 weight(7) = 0.586840934785355471452836373002D-01
- <a name="l05016"></a>05016 weight(8) = 0.658222227763618468376500637069D-01
- <a name="l05017"></a>05017 weight(9) = 0.723457941088485062253993564785D-01
- <a name="l05018"></a>05018 weight(10) = 0.781938957870703064717409188283D-01
- <a name="l05019"></a>05019 weight(11) = 0.833119242269467552221990746043D-01
- <a name="l05020"></a>05020 weight(12) = 0.876520930044038111427714627518D-01
- <a name="l05021"></a>05021 weight(13) = 0.911738786957638847128685771116D-01
- <a name="l05022"></a>05022 weight(14) = 0.938443990808045656391802376681D-01
- <a name="l05023"></a>05023 weight(15) = 0.956387200792748594190820022041D-01
- <a name="l05024"></a>05024 weight(16) = 0.965400885147278005667648300636D-01
- <a name="l05025"></a>05025 weight(17) = 0.965400885147278005667648300636D-01
- <a name="l05026"></a>05026 weight(18) = 0.956387200792748594190820022041D-01
- <a name="l05027"></a>05027 weight(19) = 0.938443990808045656391802376681D-01
- <a name="l05028"></a>05028 weight(20) = 0.911738786957638847128685771116D-01
- <a name="l05029"></a>05029 weight(21) = 0.876520930044038111427714627518D-01
- <a name="l05030"></a>05030 weight(22) = 0.833119242269467552221990746043D-01
- <a name="l05031"></a>05031 weight(23) = 0.781938957870703064717409188283D-01
- <a name="l05032"></a>05032 weight(24) = 0.723457941088485062253993564785D-01
- <a name="l05033"></a>05033 weight(25) = 0.658222227763618468376500637069D-01
- <a name="l05034"></a>05034 weight(26) = 0.586840934785355471452836373002D-01
- <a name="l05035"></a>05035 weight(27) = 0.509980592623761761961632446895D-01
- <a name="l05036"></a>05036 weight(28) = 0.428358980222266806568786466061D-01
- <a name="l05037"></a>05037 weight(29) = 0.342738629130214331026877322524D-01
- <a name="l05038"></a>05038 weight(30) = 0.253920653092620594557525897892D-01
- <a name="l05039"></a>05039 weight(31) = 0.162743947309056706051705622064D-01
- <a name="l05040"></a>05040 weight(32) = 0.701861000947009660040706373885D-02
- <a name="l05041"></a>05041
- <a name="l05042"></a>05042 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 64 ) <span class="keyword">then</span>
- <a name="l05043"></a>05043
- <a name="l05044"></a>05044 xtab(1) = - 0.999305041735772139456905624346D+00
- <a name="l05045"></a>05045 xtab(2) = - 0.996340116771955279346924500676D+00
- <a name="l05046"></a>05046 xtab(3) = - 0.991013371476744320739382383443D+00
- <a name="l05047"></a>05047 xtab(4) = - 0.983336253884625956931299302157D+00
- <a name="l05048"></a>05048 xtab(5) = - 0.973326827789910963741853507352D+00
- <a name="l05049"></a>05049 xtab(6) = - 0.961008799652053718918614121897D+00
- <a name="l05050"></a>05050 xtab(7) = - 0.946411374858402816062481491347D+00
- <a name="l05051"></a>05051 xtab(8) = - 0.929569172131939575821490154559D+00
- <a name="l05052"></a>05052 xtab(9) = - 0.910522137078502805756380668008D+00
- <a name="l05053"></a>05053 xtab(10) = - 0.889315445995114105853404038273D+00
- <a name="l05054"></a>05054 xtab(11) = - 0.865999398154092819760783385070D+00
- <a name="l05055"></a>05055 xtab(12) = - 0.840629296252580362751691544696D+00
- <a name="l05056"></a>05056 xtab(13) = - 0.813265315122797559741923338086D+00
- <a name="l05057"></a>05057 xtab(14) = - 0.783972358943341407610220525214D+00
- <a name="l05058"></a>05058 xtab(15) = - 0.752819907260531896611863774886D+00
- <a name="l05059"></a>05059 xtab(16) = - 0.719881850171610826848940217832D+00
- <a name="l05060"></a>05060 xtab(17) = - 0.685236313054233242563558371031D+00
- <a name="l05061"></a>05061 xtab(18) = - 0.648965471254657339857761231993D+00
- <a name="l05062"></a>05062 xtab(19) = - 0.611155355172393250248852971019D+00
- <a name="l05063"></a>05063 xtab(20) = - 0.571895646202634034283878116659D+00
- <a name="l05064"></a>05064 xtab(21) = - 0.531279464019894545658013903544D+00
- <a name="l05065"></a>05065 xtab(22) = - 0.489403145707052957478526307022D+00
- <a name="l05066"></a>05066 xtab(23) = - 0.446366017253464087984947714759D+00
- <a name="l05067"></a>05067 xtab(24) = - 0.402270157963991603695766771260D+00
- <a name="l05068"></a>05068 xtab(25) = - 0.357220158337668115950442615046D+00
- <a name="l05069"></a>05069 xtab(26) = - 0.311322871990210956157512698560D+00
- <a name="l05070"></a>05070 xtab(27) = - 0.264687162208767416373964172510D+00
- <a name="l05071"></a>05071 xtab(28) = - 0.217423643740007084149648748989D+00
- <a name="l05072"></a>05072 xtab(29) = - 0.169644420423992818037313629748D+00
- <a name="l05073"></a>05073 xtab(30) = - 0.121462819296120554470376463492D+00
- <a name="l05074"></a>05074 xtab(31) = - 0.729931217877990394495429419403D-01
- <a name="l05075"></a>05075 xtab(32) = - 0.243502926634244325089558428537D-01
- <a name="l05076"></a>05076 xtab(33) = 0.243502926634244325089558428537D-01
- <a name="l05077"></a>05077 xtab(34) = 0.729931217877990394495429419403D-01
- <a name="l05078"></a>05078 xtab(35) = 0.121462819296120554470376463492D+00
- <a name="l05079"></a>05079 xtab(36) = 0.169644420423992818037313629748D+00
- <a name="l05080"></a>05080 xtab(37) = 0.217423643740007084149648748989D+00
- <a name="l05081"></a>05081 xtab(38) = 0.264687162208767416373964172510D+00
- <a name="l05082"></a>05082 xtab(39) = 0.311322871990210956157512698560D+00
- <a name="l05083"></a>05083 xtab(40) = 0.357220158337668115950442615046D+00
- <a name="l05084"></a>05084 xtab(41) = 0.402270157963991603695766771260D+00
- <a name="l05085"></a>05085 xtab(42) = 0.446366017253464087984947714759D+00
- <a name="l05086"></a>05086 xtab(43) = 0.489403145707052957478526307022D+00
- <a name="l05087"></a>05087 xtab(44) = 0.531279464019894545658013903544D+00
- <a name="l05088"></a>05088 xtab(45) = 0.571895646202634034283878116659D+00
- <a name="l05089"></a>05089 xtab(46) = 0.611155355172393250248852971019D+00
- <a name="l05090"></a>05090 xtab(47) = 0.648965471254657339857761231993D+00
- <a name="l05091"></a>05091 xtab(48) = 0.685236313054233242563558371031D+00
- <a name="l05092"></a>05092 xtab(49) = 0.719881850171610826848940217832D+00
- <a name="l05093"></a>05093 xtab(50) = 0.752819907260531896611863774886D+00
- <a name="l05094"></a>05094 xtab(51) = 0.783972358943341407610220525214D+00
- <a name="l05095"></a>05095 xtab(52) = 0.813265315122797559741923338086D+00
- <a name="l05096"></a>05096 xtab(53) = 0.840629296252580362751691544696D+00
- <a name="l05097"></a>05097 xtab(54) = 0.865999398154092819760783385070D+00
- <a name="l05098"></a>05098 xtab(55) = 0.889315445995114105853404038273D+00
- <a name="l05099"></a>05099 xtab(56) = 0.910522137078502805756380668008D+00
- <a name="l05100"></a>05100 xtab(57) = 0.929569172131939575821490154559D+00
- <a name="l05101"></a>05101 xtab(58) = 0.946411374858402816062481491347D+00
- <a name="l05102"></a>05102 xtab(59) = 0.961008799652053718918614121897D+00
- <a name="l05103"></a>05103 xtab(60) = 0.973326827789910963741853507352D+00
- <a name="l05104"></a>05104 xtab(61) = 0.983336253884625956931299302157D+00
- <a name="l05105"></a>05105 xtab(62) = 0.991013371476744320739382383443D+00
- <a name="l05106"></a>05106 xtab(63) = 0.996340116771955279346924500676D+00
- <a name="l05107"></a>05107 xtab(64) = 0.999305041735772139456905624346D+00
- <a name="l05108"></a>05108
- <a name="l05109"></a>05109 weight(1) = 0.178328072169643294729607914497D-02
- <a name="l05110"></a>05110 weight(2) = 0.414703326056246763528753572855D-02
- <a name="l05111"></a>05111 weight(3) = 0.650445796897836285611736039998D-02
- <a name="l05112"></a>05112 weight(4) = 0.884675982636394772303091465973D-02
- <a name="l05113"></a>05113 weight(5) = 0.111681394601311288185904930192D-01
- <a name="l05114"></a>05114 weight(6) = 0.134630478967186425980607666860D-01
- <a name="l05115"></a>05115 weight(7) = 0.157260304760247193219659952975D-01
- <a name="l05116"></a>05116 weight(8) = 0.179517157756973430850453020011D-01
- <a name="l05117"></a>05117 weight(9) = 0.201348231535302093723403167285D-01
- <a name="l05118"></a>05118 weight(10) = 0.222701738083832541592983303842D-01
- <a name="l05119"></a>05119 weight(11) = 0.243527025687108733381775504091D-01
- <a name="l05120"></a>05120 weight(12) = 0.263774697150546586716917926252D-01
- <a name="l05121"></a>05121 weight(13) = 0.283396726142594832275113052002D-01
- <a name="l05122"></a>05122 weight(14) = 0.302346570724024788679740598195D-01
- <a name="l05123"></a>05123 weight(15) = 0.320579283548515535854675043479D-01
- <a name="l05124"></a>05124 weight(16) = 0.338051618371416093915654821107D-01
- <a name="l05125"></a>05125 weight(17) = 0.354722132568823838106931467152D-01
- <a name="l05126"></a>05126 weight(18) = 0.370551285402400460404151018096D-01
- <a name="l05127"></a>05127 weight(19) = 0.385501531786156291289624969468D-01
- <a name="l05128"></a>05128 weight(20) = 0.399537411327203413866569261283D-01
- <a name="l05129"></a>05129 weight(21) = 0.412625632426235286101562974736D-01
- <a name="l05130"></a>05130 weight(22) = 0.424735151236535890073397679088D-01
- <a name="l05131"></a>05131 weight(23) = 0.435837245293234533768278609737D-01
- <a name="l05132"></a>05132 weight(24) = 0.445905581637565630601347100309D-01
- <a name="l05133"></a>05133 weight(25) = 0.454916279274181444797709969713D-01
- <a name="l05134"></a>05134 weight(26) = 0.462847965813144172959532492323D-01
- <a name="l05135"></a>05135 weight(27) = 0.469681828162100173253262857546D-01
- <a name="l05136"></a>05136 weight(28) = 0.475401657148303086622822069442D-01
- <a name="l05137"></a>05137 weight(29) = 0.479993885964583077281261798713D-01
- <a name="l05138"></a>05138 weight(30) = 0.483447622348029571697695271580D-01
- <a name="l05139"></a>05139 weight(31) = 0.485754674415034269347990667840D-01
- <a name="l05140"></a>05140 weight(32) = 0.486909570091397203833653907347D-01
- <a name="l05141"></a>05141 weight(33) = 0.486909570091397203833653907347D-01
- <a name="l05142"></a>05142 weight(34) = 0.485754674415034269347990667840D-01
- <a name="l05143"></a>05143 weight(35) = 0.483447622348029571697695271580D-01
- <a name="l05144"></a>05144 weight(36) = 0.479993885964583077281261798713D-01
- <a name="l05145"></a>05145 weight(37) = 0.475401657148303086622822069442D-01
- <a name="l05146"></a>05146 weight(38) = 0.469681828162100173253262857546D-01
- <a name="l05147"></a>05147 weight(39) = 0.462847965813144172959532492323D-01
- <a name="l05148"></a>05148 weight(40) = 0.454916279274181444797709969713D-01
- <a name="l05149"></a>05149 weight(41) = 0.445905581637565630601347100309D-01
- <a name="l05150"></a>05150 weight(42) = 0.435837245293234533768278609737D-01
- <a name="l05151"></a>05151 weight(43) = 0.424735151236535890073397679088D-01
- <a name="l05152"></a>05152 weight(44) = 0.412625632426235286101562974736D-01
- <a name="l05153"></a>05153 weight(45) = 0.399537411327203413866569261283D-01
- <a name="l05154"></a>05154 weight(46) = 0.385501531786156291289624969468D-01
- <a name="l05155"></a>05155 weight(47) = 0.370551285402400460404151018096D-01
- <a name="l05156"></a>05156 weight(48) = 0.354722132568823838106931467152D-01
- <a name="l05157"></a>05157 weight(49) = 0.338051618371416093915654821107D-01
- <a name="l05158"></a>05158 weight(50) = 0.320579283548515535854675043479D-01
- <a name="l05159"></a>05159 weight(51) = 0.302346570724024788679740598195D-01
- <a name="l05160"></a>05160 weight(52) = 0.283396726142594832275113052002D-01
- <a name="l05161"></a>05161 weight(53) = 0.263774697150546586716917926252D-01
- <a name="l05162"></a>05162 weight(54) = 0.243527025687108733381775504091D-01
- <a name="l05163"></a>05163 weight(55) = 0.222701738083832541592983303842D-01
- <a name="l05164"></a>05164 weight(56) = 0.201348231535302093723403167285D-01
- <a name="l05165"></a>05165 weight(57) = 0.179517157756973430850453020011D-01
- <a name="l05166"></a>05166 weight(58) = 0.157260304760247193219659952975D-01
- <a name="l05167"></a>05167 weight(59) = 0.134630478967186425980607666860D-01
- <a name="l05168"></a>05168 weight(60) = 0.111681394601311288185904930192D-01
- <a name="l05169"></a>05169 weight(61) = 0.884675982636394772303091465973D-02
- <a name="l05170"></a>05170 weight(62) = 0.650445796897836285611736039998D-02
- <a name="l05171"></a>05171 weight(63) = 0.414703326056246763528753572855D-02
- <a name="l05172"></a>05172 weight(64) = 0.178328072169643294729607914497D-02
- <a name="l05173"></a>05173
- <a name="l05174"></a>05174 <span class="keyword">else</span>
- <a name="l05175"></a>05175
- <a name="l05176"></a>05176 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l05177"></a>05177 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LEGENDRE_SET - Fatal error!'</span>
- <a name="l05178"></a>05178 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l05179"></a>05179 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' Legal values are 1 to 20, 32 or 64.'</span>
- <a name="l05180"></a>05180 stop
- <a name="l05181"></a>05181
- <a name="l05182"></a>05182 <span class="keyword">end if</span>
- <a name="l05183"></a>05183
- <a name="l05184"></a>05184 return
- <a name="l05185"></a>05185 <span class="keyword">end</span>
- <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 )
- <a name="l05187"></a>05187 <span class="comment">!</span>
- <a name="l05188"></a>05188 <span class="comment">!*******************************************************************************</span>
- <a name="l05189"></a>05189 <span class="comment">!</span>
- <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>
- <a name="l05191"></a>05191 <span class="comment">!</span>
- <a name="l05192"></a>05192 <span class="comment">!</span>
- <a name="l05193"></a>05193 <span class="comment">! Integration interval:</span>
- <a name="l05194"></a>05194 <span class="comment">!</span>
- <a name="l05195"></a>05195 <span class="comment">! [ -PI/2, PI/2 ]</span>
- <a name="l05196"></a>05196 <span class="comment">!</span>
- <a name="l05197"></a>05197 <span class="comment">! Weight function:</span>
- <a name="l05198"></a>05198 <span class="comment">!</span>
- <a name="l05199"></a>05199 <span class="comment">! COS(X) * F(X)</span>
- <a name="l05200"></a>05200 <span class="comment">!</span>
- <a name="l05201"></a>05201 <span class="comment">! Integral to approximate:</span>
- <a name="l05202"></a>05202 <span class="comment">!</span>
- <a name="l05203"></a>05203 <span class="comment">! Integral ( -PI/2 <= X <= PI/2 ) COS(X) * F(X) dX</span>
- <a name="l05204"></a>05204 <span class="comment">!</span>
- <a name="l05205"></a>05205 <span class="comment">! Approximate integral:</span>
- <a name="l05206"></a>05206 <span class="comment">!</span>
- <a name="l05207"></a>05207 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l05208"></a>05208 <span class="comment">!</span>
- <a name="l05209"></a>05209 <span class="comment">! Discussion:</span>
- <a name="l05210"></a>05210 <span class="comment">!</span>
- <a name="l05211"></a>05211 <span class="comment">! The same rule can be used to approximate</span>
- <a name="l05212"></a>05212 <span class="comment">!</span>
- <a name="l05213"></a>05213 <span class="comment">! Integral ( 0 <= X <= PI ) SIN(X) * F(X) dX</span>
- <a name="l05214"></a>05214 <span class="comment">!</span>
- <a name="l05215"></a>05215 <span class="comment">! as</span>
- <a name="l05216"></a>05216 <span class="comment">!</span>
- <a name="l05217"></a>05217 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) + PI/2 )</span>
- <a name="l05218"></a>05218 <span class="comment">!</span>
- <a name="l05219"></a>05219 <span class="comment">! Reference:</span>
- <a name="l05220"></a>05220 <span class="comment">!</span>
- <a name="l05221"></a>05221 <span class="comment">! Gwynne Evans,</span>
- <a name="l05222"></a>05222 <span class="comment">! Practical Numerical Integration,</span>
- <a name="l05223"></a>05223 <span class="comment">! Wiley, 1993, QA299.3E93, page 310.</span>
- <a name="l05224"></a>05224 <span class="comment">!</span>
- <a name="l05225"></a>05225 <span class="comment">! Modified:</span>
- <a name="l05226"></a>05226 <span class="comment">!</span>
- <a name="l05227"></a>05227 <span class="comment">! 23 November 2000</span>
- <a name="l05228"></a>05228 <span class="comment">!</span>
- <a name="l05229"></a>05229 <span class="comment">! Author:</span>
- <a name="l05230"></a>05230 <span class="comment">!</span>
- <a name="l05231"></a>05231 <span class="comment">! John Burkardt</span>
- <a name="l05232"></a>05232 <span class="comment">!</span>
- <a name="l05233"></a>05233 <span class="comment">! Parameters:</span>
- <a name="l05234"></a>05234 <span class="comment">!</span>
- <a name="l05235"></a>05235 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l05236"></a>05236 <span class="comment">! NORDER must be between 1, 2, 4, 8 or 16.</span>
- <a name="l05237"></a>05237 <span class="comment">!</span>
- <a name="l05238"></a>05238 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l05239"></a>05239 <span class="comment">!</span>
- <a name="l05240"></a>05240 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l05241"></a>05241 <span class="comment">!</span>
- <a name="l05242"></a>05242 <span class="keyword">implicit none</span>
- <a name="l05243"></a>05243 <span class="comment">!</span>
- <a name="l05244"></a>05244 <span class="keywordtype">integer</span> norder
- <a name="l05245"></a>05245 <span class="comment">!</span>
- <a name="l05246"></a>05246 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l05247"></a>05247 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l05248"></a>05248 <span class="comment">!</span>
- <a name="l05249"></a>05249 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l05250"></a>05250
- <a name="l05251"></a>05251 xtab(1) = 0.0D+00
- <a name="l05252"></a>05252
- <a name="l05253"></a>05253 weight(1) = 2.0D+00
- <a name="l05254"></a>05254
- <a name="l05255"></a>05255 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l05256"></a>05256
- <a name="l05257"></a>05257 xtab(1) = - 0.68366739008990304094D+00
- <a name="l05258"></a>05258 xtab(2) = 0.68366739008990304094D+00
- <a name="l05259"></a>05259
- <a name="l05260"></a>05260 weight(1) = 1.0D+00
- <a name="l05261"></a>05261 weight(2) = 1.0D+00
- <a name="l05262"></a>05262
- <a name="l05263"></a>05263 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l05264"></a>05264
- <a name="l05265"></a>05265 xtab(1) = - 1.1906765638948557415D+00
- <a name="l05266"></a>05266 xtab(2) = - 0.43928746686001514756D+00
- <a name="l05267"></a>05267 xtab(3) = 0.43928746686001514756D+00
- <a name="l05268"></a>05268 xtab(4) = 1.1906765638948557415D+00
- <a name="l05269"></a>05269
- <a name="l05270"></a>05270 weight(1) = 0.22407061812762016065D+00
- <a name="l05271"></a>05271 weight(2) = 0.77592938187237983935D+00
- <a name="l05272"></a>05272 weight(3) = 0.77592938187237983935D+00
- <a name="l05273"></a>05273 weight(4) = 0.22407061812762016065D+00
- <a name="l05274"></a>05274
- <a name="l05275"></a>05275 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l05276"></a>05276
- <a name="l05277"></a>05277 xtab(1) = - 1.4414905401823575701D+00
- <a name="l05278"></a>05278 xtab(2) = - 1.1537256454567275850D+00
- <a name="l05279"></a>05279 xtab(3) = - 0.74346864787549244989D+00
- <a name="l05280"></a>05280 xtab(4) = - 0.25649650741623123020D+00
- <a name="l05281"></a>05281 xtab(5) = 0.25649650741623123020D+00
- <a name="l05282"></a>05282 xtab(6) = 0.74346864787549244989D+00
- <a name="l05283"></a>05283 xtab(7) = 1.1537256454567275850D+00
- <a name="l05284"></a>05284 xtab(8) = 1.4414905401823575701D+00
- <a name="l05285"></a>05285
- <a name="l05286"></a>05286 weight(1) = 0.027535633513767011149D+00
- <a name="l05287"></a>05287 weight(2) = 0.14420409203022750950D+00
- <a name="l05288"></a>05288 weight(3) = 0.33626447785280459621D+00
- <a name="l05289"></a>05289 weight(4) = 0.49199579660320088314D+00
- <a name="l05290"></a>05290 weight(5) = 0.49199579660320088314D+00
- <a name="l05291"></a>05291 weight(6) = 0.33626447785280459621D+00
- <a name="l05292"></a>05292 weight(7) = 0.14420409203022750950D+00
- <a name="l05293"></a>05293 weight(8) = 0.027535633513767011149D+00
- <a name="l05294"></a>05294
- <a name="l05295"></a>05295 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
- <a name="l05296"></a>05296
- <a name="l05297"></a>05297 xtab( 1) = - 1.5327507132362304779D+00
- <a name="l05298"></a>05298 xtab( 2) = - 1.4446014873666514608D+00
- <a name="l05299"></a>05299 xtab( 3) = - 1.3097818904452936698D+00
- <a name="l05300"></a>05300 xtab( 4) = - 1.1330068786005003695D+00
- <a name="l05301"></a>05301 xtab( 5) = - 0.92027786206637096497D+00
- <a name="l05302"></a>05302 xtab( 6) = - 0.67861108097560545347D+00
- <a name="l05303"></a>05303 xtab( 7) = - 0.41577197673418943962D+00
- <a name="l05304"></a>05304 xtab( 8) = - 0.14003444424696773778D+00
- <a name="l05305"></a>05305 xtab( 9) = 0.14003444424696773778D+00
- <a name="l05306"></a>05306 xtab(10) = 0.41577197673418943962D+00
- <a name="l05307"></a>05307 xtab(11) = 0.67861108097560545347D+00
- <a name="l05308"></a>05308 xtab(12) = 0.92027786206637096497D+00
- <a name="l05309"></a>05309 xtab(13) = 1.1330068786005003695D+00
- <a name="l05310"></a>05310 xtab(14) = 1.3097818904452936698D+00
- <a name="l05311"></a>05311 xtab(15) = 1.4446014873666514608D+00
- <a name="l05312"></a>05312 xtab(16) = 1.5327507132362304779D+00
- <a name="l05313"></a>05313
- <a name="l05314"></a>05314 weight( 1) = 0.0024194677567615628193D+00
- <a name="l05315"></a>05315 weight( 2) = 0.014115268156854008264D+00
- <a name="l05316"></a>05316 weight( 3) = 0.040437893946503669410D+00
- <a name="l05317"></a>05317 weight( 4) = 0.083026647573217742131D+00
- <a name="l05318"></a>05318 weight( 5) = 0.13834195526951273359D+00
- <a name="l05319"></a>05319 weight( 6) = 0.19741148870253455567D+00
- <a name="l05320"></a>05320 weight( 7) = 0.24763632094635522403D+00
- <a name="l05321"></a>05321 weight( 8) = 0.27661095764826050408D+00
- <a name="l05322"></a>05322 weight( 9) = 0.27661095764826050408D+00
- <a name="l05323"></a>05323 weight(10) = 0.24763632094635522403D+00
- <a name="l05324"></a>05324 weight(11) = 0.19741148870253455567D+00
- <a name="l05325"></a>05325 weight(12) = 0.13834195526951273359D+00
- <a name="l05326"></a>05326 weight(13) = 0.083026647573217742131D+00
- <a name="l05327"></a>05327 weight(14) = 0.040437893946503669410D+00
- <a name="l05328"></a>05328 weight(15) = 0.014115268156854008264D+00
- <a name="l05329"></a>05329 weight(16) = 0.0024194677567615628193D+00
- <a name="l05330"></a>05330
- <a name="l05331"></a>05331 <span class="keyword">else</span>
- <a name="l05332"></a>05332
- <a name="l05333"></a>05333 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l05334"></a>05334 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LEGENDRE_SET_COS - Fatal error!'</span>
- <a name="l05335"></a>05335 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l05336"></a>05336 stop
- <a name="l05337"></a>05337
- <a name="l05338"></a>05338 <span class="keyword">end if</span>
- <a name="l05339"></a>05339
- <a name="l05340"></a>05340 return
- <a name="l05341"></a>05341 <span class="keyword">end</span>
- <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 )
- <a name="l05343"></a>05343 <span class="comment">!</span>
- <a name="l05344"></a>05344 <span class="comment">!*******************************************************************************</span>
- <a name="l05345"></a>05345 <span class="comment">!</span>
- <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>
- <a name="l05347"></a>05347 <span class="comment">!</span>
- <a name="l05348"></a>05348 <span class="comment">!</span>
- <a name="l05349"></a>05349 <span class="comment">! Integration interval:</span>
- <a name="l05350"></a>05350 <span class="comment">!</span>
- <a name="l05351"></a>05351 <span class="comment">! [ 0, PI/2 ]</span>
- <a name="l05352"></a>05352 <span class="comment">!</span>
- <a name="l05353"></a>05353 <span class="comment">! Weight function:</span>
- <a name="l05354"></a>05354 <span class="comment">!</span>
- <a name="l05355"></a>05355 <span class="comment">! COS(X) * F(X)</span>
- <a name="l05356"></a>05356 <span class="comment">!</span>
- <a name="l05357"></a>05357 <span class="comment">! Integral to approximate:</span>
- <a name="l05358"></a>05358 <span class="comment">!</span>
- <a name="l05359"></a>05359 <span class="comment">! Integral ( 0 <= X <= PI/2 ) COS(X) * F(X) dX</span>
- <a name="l05360"></a>05360 <span class="comment">!</span>
- <a name="l05361"></a>05361 <span class="comment">! Approximate integral:</span>
- <a name="l05362"></a>05362 <span class="comment">!</span>
- <a name="l05363"></a>05363 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l05364"></a>05364 <span class="comment">!</span>
- <a name="l05365"></a>05365 <span class="comment">! Discussion:</span>
- <a name="l05366"></a>05366 <span class="comment">!</span>
- <a name="l05367"></a>05367 <span class="comment">! The same rule can be used to approximate</span>
- <a name="l05368"></a>05368 <span class="comment">!</span>
- <a name="l05369"></a>05369 <span class="comment">! Integral ( 0 <= X <= PI/2 ) SIN(X) * F(X) dX</span>
- <a name="l05370"></a>05370 <span class="comment">!</span>
- <a name="l05371"></a>05371 <span class="comment">! as</span>
- <a name="l05372"></a>05372 <span class="comment">!</span>
- <a name="l05373"></a>05373 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( PI/2 - XTAB(I) )</span>
- <a name="l05374"></a>05374 <span class="comment">!</span>
- <a name="l05375"></a>05375 <span class="comment">! Reference:</span>
- <a name="l05376"></a>05376 <span class="comment">!</span>
- <a name="l05377"></a>05377 <span class="comment">! Gwynne Evans,</span>
- <a name="l05378"></a>05378 <span class="comment">! Practical Numerical Integration,</span>
- <a name="l05379"></a>05379 <span class="comment">! Wiley, 1993, QA299.3E93, page 311.</span>
- <a name="l05380"></a>05380 <span class="comment">!</span>
- <a name="l05381"></a>05381 <span class="comment">! Modified:</span>
- <a name="l05382"></a>05382 <span class="comment">!</span>
- <a name="l05383"></a>05383 <span class="comment">! 24 November 2000</span>
- <a name="l05384"></a>05384 <span class="comment">!</span>
- <a name="l05385"></a>05385 <span class="comment">! Author:</span>
- <a name="l05386"></a>05386 <span class="comment">!</span>
- <a name="l05387"></a>05387 <span class="comment">! John Burkardt</span>
- <a name="l05388"></a>05388 <span class="comment">!</span>
- <a name="l05389"></a>05389 <span class="comment">! Parameters:</span>
- <a name="l05390"></a>05390 <span class="comment">!</span>
- <a name="l05391"></a>05391 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l05392"></a>05392 <span class="comment">! NORDER must be between 2, 4, 8 or 16.</span>
- <a name="l05393"></a>05393 <span class="comment">!</span>
- <a name="l05394"></a>05394 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l05395"></a>05395 <span class="comment">!</span>
- <a name="l05396"></a>05396 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l05397"></a>05397 <span class="comment">!</span>
- <a name="l05398"></a>05398 <span class="keyword">implicit none</span>
- <a name="l05399"></a>05399 <span class="comment">!</span>
- <a name="l05400"></a>05400 <span class="keywordtype">integer</span> norder
- <a name="l05401"></a>05401 <span class="comment">!</span>
- <a name="l05402"></a>05402 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l05403"></a>05403 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l05404"></a>05404 <span class="comment">!</span>
- <a name="l05405"></a>05405 <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l05406"></a>05406
- <a name="l05407"></a>05407 xtab(1) = 0.26587388056307823382D+00
- <a name="l05408"></a>05408 xtab(2) = 1.0351526093171315182D+00
- <a name="l05409"></a>05409
- <a name="l05410"></a>05410 weight(1) = 0.60362553280827113087D+00
- <a name="l05411"></a>05411 weight(2) = 0.39637446719172886913D+00
- <a name="l05412"></a>05412
- <a name="l05413"></a>05413 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l05414"></a>05414
- <a name="l05415"></a>05415 xtab(1) = 0.095669389196858636773D+00
- <a name="l05416"></a>05416 xtab(2) = 0.45240902327067096554D+00
- <a name="l05417"></a>05417 xtab(3) = 0.93185057672024082424D+00
- <a name="l05418"></a>05418 xtab(4) = 1.3564439599666466230D+00
- <a name="l05419"></a>05419
- <a name="l05420"></a>05420 weight( 1) = 0.23783071419515504517D+00
- <a name="l05421"></a>05421 weight( 2) = 0.40265695523581253512D+00
- <a name="l05422"></a>05422 weight( 3) = 0.28681737948564715225D+00
- <a name="l05423"></a>05423 weight( 4) = 0.072694951083385267446D+00
- <a name="l05424"></a>05424
- <a name="l05425"></a>05425 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l05426"></a>05426
- <a name="l05427"></a>05427 xtab(1) = 0.029023729768913933432D+00
- <a name="l05428"></a>05428 xtab(2) = 0.14828524404581819442D+00
- <a name="l05429"></a>05429 xtab(3) = 0.34531111151664787488D+00
- <a name="l05430"></a>05430 xtab(4) = 0.59447696797658360178D+00
- <a name="l05431"></a>05431 xtab(5) = 0.86538380686123504827D+00
- <a name="l05432"></a>05432 xtab(6) = 1.1263076093187456632D+00
- <a name="l05433"></a>05433 xtab(7) = 1.3470150460281258016D+00
- <a name="l05434"></a>05434 xtab(8) = 1.5015603622059195568D+00
- <a name="l05435"></a>05435
- <a name="l05436"></a>05436 weight( 1) = 0.073908998095117384985D+00
- <a name="l05437"></a>05437 weight( 2) = 0.16002993702338006099D+00
- <a name="l05438"></a>05438 weight( 3) = 0.21444434341803549108D+00
- <a name="l05439"></a>05439 weight( 4) = 0.21979581268851903339D+00
- <a name="l05440"></a>05440 weight( 5) = 0.17581164478209568886D+00
- <a name="l05441"></a>05441 weight( 6) = 0.10560448025308322171D+00
- <a name="l05442"></a>05442 weight( 7) = 0.042485497299217201089D+00
- <a name="l05443"></a>05443 weight( 8) = 0.0079192864405519178899D+00
- <a name="l05444"></a>05444
- <a name="l05445"></a>05445 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
- <a name="l05446"></a>05446
- <a name="l05447"></a>05447 xtab( 1) = 0.0080145034906295973494D+00
- <a name="l05448"></a>05448 xtab( 2) = 0.041893031354246254797D+00
- <a name="l05449"></a>05449 xtab( 3) = 0.10149954486757579459D+00
- <a name="l05450"></a>05450 xtab( 4) = 0.18463185923836617507D+00
- <a name="l05451"></a>05451 xtab( 5) = 0.28826388487760574589D+00
- <a name="l05452"></a>05452 xtab( 6) = 0.40870579076464794191D+00
- <a name="l05453"></a>05453 xtab( 7) = 0.54176054986913847463D+00
- <a name="l05454"></a>05454 xtab( 8) = 0.68287636658719416893D+00
- <a name="l05455"></a>05455 xtab( 9) = 0.82729287620416833520D+00
- <a name="l05456"></a>05456 xtab(10) = 0.97018212594829367065D+00
- <a name="l05457"></a>05457 xtab(11) = 1.1067865150286247873D+00
- <a name="l05458"></a>05458 xtab(12) = 1.2325555697227748824D+00
- <a name="l05459"></a>05459 xtab(13) = 1.3432821921580721861D+00
- <a name="l05460"></a>05460 xtab(14) = 1.4352370549295032923D+00
- <a name="l05461"></a>05461 xtab(15) = 1.5052970876794669248D+00
- <a name="l05462"></a>05462 xtab(16) = 1.5510586944086135769D+00
- <a name="l05463"></a>05463
- <a name="l05464"></a>05464 weight( 1) = 0.020528714977215248902D+00
- <a name="l05465"></a>05465 weight( 2) = 0.046990919853597958123D+00
- <a name="l05466"></a>05466 weight( 3) = 0.071441021312218541698D+00
- <a name="l05467"></a>05467 weight( 4) = 0.092350338329243052271D+00
- <a name="l05468"></a>05468 weight( 5) = 0.10804928026816236935D+00
- <a name="l05469"></a>05469 weight( 6) = 0.11698241243306261791D+00
- <a name="l05470"></a>05470 weight( 7) = 0.11812395361762037649D+00
- <a name="l05471"></a>05471 weight( 8) = 0.11137584940420091049D+00
- <a name="l05472"></a>05472 weight( 9) = 0.097778236145946543110D+00
- <a name="l05473"></a>05473 weight(10) = 0.079418758985944482077D+00
- <a name="l05474"></a>05474 weight(11) = 0.059039620053768691402D+00
- <a name="l05475"></a>05475 weight(12) = 0.039458876783728165671D+00
- <a name="l05476"></a>05476 weight(13) = 0.022987785677206847531D+00
- <a name="l05477"></a>05477 weight(14) = 0.011010405600421536861D+00
- <a name="l05478"></a>05478 weight(15) = 0.0038123928030499915653D+00
- <a name="l05479"></a>05479 weight(16) = 0.00065143375461266656171D+00
- <a name="l05480"></a>05480
- <a name="l05481"></a>05481 <span class="keyword">else</span>
- <a name="l05482"></a>05482
- <a name="l05483"></a>05483 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l05484"></a>05484 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LEGENDRE_SET_COS2 - Fatal error!'</span>
- <a name="l05485"></a>05485 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l05486"></a>05486 stop
- <a name="l05487"></a>05487
- <a name="l05488"></a>05488 <span class="keyword">end if</span>
- <a name="l05489"></a>05489
- <a name="l05490"></a>05490 return
- <a name="l05491"></a>05491 <span class="keyword">end</span>
- <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 )
- <a name="l05493"></a>05493 <span class="comment">!</span>
- <a name="l05494"></a>05494 <span class="comment">!*******************************************************************************</span>
- <a name="l05495"></a>05495 <span class="comment">!</span>
- <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>
- <a name="l05497"></a>05497 <span class="comment">!</span>
- <a name="l05498"></a>05498 <span class="comment">!</span>
- <a name="l05499"></a>05499 <span class="comment">! Integration interval:</span>
- <a name="l05500"></a>05500 <span class="comment">!</span>
- <a name="l05501"></a>05501 <span class="comment">! [ 0, 1 ]</span>
- <a name="l05502"></a>05502 <span class="comment">!</span>
- <a name="l05503"></a>05503 <span class="comment">! Weight function:</span>
- <a name="l05504"></a>05504 <span class="comment">!</span>
- <a name="l05505"></a>05505 <span class="comment">! - LOG(X) * F(X)</span>
- <a name="l05506"></a>05506 <span class="comment">!</span>
- <a name="l05507"></a>05507 <span class="comment">! Integral to approximate:</span>
- <a name="l05508"></a>05508 <span class="comment">!</span>
- <a name="l05509"></a>05509 <span class="comment">! Integral ( 0 <= X <= 1 ) - LOG(X) * F(X) dX</span>
- <a name="l05510"></a>05510 <span class="comment">!</span>
- <a name="l05511"></a>05511 <span class="comment">! Approximate integral:</span>
- <a name="l05512"></a>05512 <span class="comment">!</span>
- <a name="l05513"></a>05513 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l05514"></a>05514 <span class="comment">!</span>
- <a name="l05515"></a>05515 <span class="comment">! Reference:</span>
- <a name="l05516"></a>05516 <span class="comment">!</span>
- <a name="l05517"></a>05517 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l05518"></a>05518 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l05519"></a>05519 <span class="comment">! National Bureau of Standards, 1964, page 920.</span>
- <a name="l05520"></a>05520 <span class="comment">!</span>
- <a name="l05521"></a>05521 <span class="comment">! Gwynne Evans,</span>
- <a name="l05522"></a>05522 <span class="comment">! Practical Numerical Integration,</span>
- <a name="l05523"></a>05523 <span class="comment">! Wiley, 1993, QA299.3E93, page 309.</span>
- <a name="l05524"></a>05524 <span class="comment">!</span>
- <a name="l05525"></a>05525 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l05526"></a>05526 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l05527"></a>05527 <span class="comment">! Prentice Hall, 1966.</span>
- <a name="l05528"></a>05528 <span class="comment">!</span>
- <a name="l05529"></a>05529 <span class="comment">! Modified:</span>
- <a name="l05530"></a>05530 <span class="comment">!</span>
- <a name="l05531"></a>05531 <span class="comment">! 05 December 2000</span>
- <a name="l05532"></a>05532 <span class="comment">!</span>
- <a name="l05533"></a>05533 <span class="comment">! Author:</span>
- <a name="l05534"></a>05534 <span class="comment">!</span>
- <a name="l05535"></a>05535 <span class="comment">! John Burkardt</span>
- <a name="l05536"></a>05536 <span class="comment">!</span>
- <a name="l05537"></a>05537 <span class="comment">! Parameters:</span>
- <a name="l05538"></a>05538 <span class="comment">!</span>
- <a name="l05539"></a>05539 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l05540"></a>05540 <span class="comment">! NORDER must be between 1 through 8, or 16.</span>
- <a name="l05541"></a>05541 <span class="comment">!</span>
- <a name="l05542"></a>05542 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l05543"></a>05543 <span class="comment">!</span>
- <a name="l05544"></a>05544 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l05545"></a>05545 <span class="comment">!</span>
- <a name="l05546"></a>05546 <span class="keyword">implicit none</span>
- <a name="l05547"></a>05547 <span class="comment">!</span>
- <a name="l05548"></a>05548 <span class="keywordtype">integer</span> norder
- <a name="l05549"></a>05549 <span class="comment">!</span>
- <a name="l05550"></a>05550 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l05551"></a>05551 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l05552"></a>05552 <span class="comment">!</span>
- <a name="l05553"></a>05553 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l05554"></a>05554
- <a name="l05555"></a>05555 xtab(1) = 0.25D+00
- <a name="l05556"></a>05556
- <a name="l05557"></a>05557 weight(1) = 1.0D+00
- <a name="l05558"></a>05558
- <a name="l05559"></a>05559 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l05560"></a>05560
- <a name="l05561"></a>05561 xtab(1) = 0.112008806166976182957205488948D+00
- <a name="l05562"></a>05562 xtab(2) = 0.602276908118738102757080225338D+00
- <a name="l05563"></a>05563
- <a name="l05564"></a>05564 weight(1) = 0.718539319030384440665510200891D+00
- <a name="l05565"></a>05565 weight(2) = 0.281460680969615559334489799109D+00
- <a name="l05566"></a>05566
- <a name="l05567"></a>05567 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l05568"></a>05568
- <a name="l05569"></a>05569 xtab(1) = 0.0638907930873254049961166031363D+00
- <a name="l05570"></a>05570 xtab(2) = 0.368997063715618765546197645857D+00
- <a name="l05571"></a>05571 xtab(3) = 0.766880303938941455423682659817D+00
- <a name="l05572"></a>05572
- <a name="l05573"></a>05573 weight(1) = 0.513404552232363325129300497567D+00
- <a name="l05574"></a>05574 weight(2) = 0.391980041201487554806287180966D+00
- <a name="l05575"></a>05575 weight(3) = 0.0946154065661491200644123214672D+00
- <a name="l05576"></a>05576
- <a name="l05577"></a>05577 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l05578"></a>05578
- <a name="l05579"></a>05579 xtab(1) = 0.0414484801993832208033213101564D+00
- <a name="l05580"></a>05580 xtab(2) = 0.245274914320602251939675759523D+00
- <a name="l05581"></a>05581 xtab(3) = 0.556165453560275837180184354376D+00
- <a name="l05582"></a>05582 xtab(4) = 0.848982394532985174647849188085D+00
- <a name="l05583"></a>05583
- <a name="l05584"></a>05584 weight(1) = 0.383464068145135124850046522343D+00
- <a name="l05585"></a>05585 weight(2) = 0.386875317774762627336008234554D+00
- <a name="l05586"></a>05586 weight(3) = 0.190435126950142415361360014547D+00
- <a name="l05587"></a>05587 weight(4) = 0.0392254871299598324525852285552D+00
- <a name="l05588"></a>05588
- <a name="l05589"></a>05589 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l05590"></a>05590
- <a name="l05591"></a>05591 xtab(1) = 0.0291344721519720533037267621154D+00
- <a name="l05592"></a>05592 xtab(2) = 0.173977213320897628701139710829D+00
- <a name="l05593"></a>05593 xtab(3) = 0.411702520284902043174931924646D+00
- <a name="l05594"></a>05594 xtab(4) = 0.677314174582820380701802667998D+00
- <a name="l05595"></a>05595 xtab(5) = 0.894771361031008283638886204455D+00
- <a name="l05596"></a>05596
- <a name="l05597"></a>05597 weight(1) = 0.297893471782894457272257877888D+00
- <a name="l05598"></a>05598 weight(2) = 0.349776226513224180375071870307D+00
- <a name="l05599"></a>05599 weight(3) = 0.234488290044052418886906857943D+00
- <a name="l05600"></a>05600 weight(4) = 0.0989304595166331469761807114404D+00
- <a name="l05601"></a>05601 weight(5) = 0.0189115521431957964895826824218D+00
- <a name="l05602"></a>05602
- <a name="l05603"></a>05603 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l05604"></a>05604
- <a name="l05605"></a>05605 xtab(1) = 0.0216340058441169489956958558537D+00
- <a name="l05606"></a>05606 xtab(2) = 0.129583391154950796131158505009D+00
- <a name="l05607"></a>05607 xtab(3) = 0.314020449914765508798248188420D+00
- <a name="l05608"></a>05608 xtab(4) = 0.538657217351802144548941893993D+00
- <a name="l05609"></a>05609 xtab(5) = 0.756915337377402852164544156139D+00
- <a name="l05610"></a>05610 xtab(6) = 0.922668851372120237333873231507D+00
- <a name="l05611"></a>05611
- <a name="l05612"></a>05612 weight(1) = 0.238763662578547569722268303330D+00
- <a name="l05613"></a>05613 weight(2) = 0.308286573273946792969383109211D+00
- <a name="l05614"></a>05614 weight(3) = 0.245317426563210385984932540188D+00
- <a name="l05615"></a>05615 weight(4) = 0.142008756566476685421345576030D+00
- <a name="l05616"></a>05616 weight(5) = 0.0554546223248862900151353549662D+00
- <a name="l05617"></a>05617 weight(6) = 0.0101689586929322758869351162755D+00
- <a name="l05618"></a>05618
- <a name="l05619"></a>05619 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l05620"></a>05620
- <a name="l05621"></a>05621 xtab(1) = 0.0167193554082585159416673609320D+00
- <a name="l05622"></a>05622 xtab(2) = 0.100185677915675121586885031757D+00
- <a name="l05623"></a>05623 xtab(3) = 0.246294246207930599046668547239D+00
- <a name="l05624"></a>05624 xtab(4) = 0.433463493257033105832882482601D+00
- <a name="l05625"></a>05625 xtab(5) = 0.632350988047766088461805812245D+00
- <a name="l05626"></a>05626 xtab(6) = 0.811118626740105576526226796782D+00
- <a name="l05627"></a>05627 xtab(7) = 0.940848166743347721760134113379D+00
- <a name="l05628"></a>05628
- <a name="l05629"></a>05629 weight(1) = 0.196169389425248207525427377585D+00
- <a name="l05630"></a>05630 weight(2) = 0.270302644247272982145271719533D+00
- <a name="l05631"></a>05631 weight(3) = 0.239681873007690948308072785252D+00
- <a name="l05632"></a>05632 weight(4) = 0.165775774810432906560869687736D+00
- <a name="l05633"></a>05633 weight(5) = 0.0889432271376579644357238403458D+00
- <a name="l05634"></a>05634 weight(6) = 0.0331943043565710670254494111034D+00
- <a name="l05635"></a>05635 weight(7) = 0.00593278701512592399918517844468D+00
- <a name="l05636"></a>05636
- <a name="l05637"></a>05637 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l05638"></a>05638
- <a name="l05639"></a>05639 xtab(1) = 0.0133202441608924650122526725243D+00
- <a name="l05640"></a>05640 xtab(2) = 0.0797504290138949384098277291424D+00
- <a name="l05641"></a>05641 xtab(3) = 0.197871029326188053794476159516D+00
- <a name="l05642"></a>05642 xtab(4) = 0.354153994351909419671463603538D+00
- <a name="l05643"></a>05643 xtab(5) = 0.529458575234917277706149699996D+00
- <a name="l05644"></a>05644 xtab(6) = 0.701814529939099963837152670310D+00
- <a name="l05645"></a>05645 xtab(7) = 0.849379320441106676048309202301D+00
- <a name="l05646"></a>05646 xtab(8) = 0.953326450056359788767379678514D+00
- <a name="l05647"></a>05647
- <a name="l05648"></a>05648 weight(1) = 0.164416604728002886831472568326D+00
- <a name="l05649"></a>05649 weight(2) = 0.237525610023306020501348561960D+00
- <a name="l05650"></a>05650 weight(3) = 0.226841984431919126368780402936D+00
- <a name="l05651"></a>05651 weight(4) = 0.175754079006070244988056212006D+00
- <a name="l05652"></a>05652 weight(5) = 0.112924030246759051855000442086D+00
- <a name="l05653"></a>05653 weight(6) = 0.0578722107177820723985279672940D+00
- <a name="l05654"></a>05654 weight(7) = 0.0209790737421329780434615241150D+00
- <a name="l05655"></a>05655 weight(8) = 0.00368640710402761901335232127647D+00
- <a name="l05656"></a>05656
- <a name="l05657"></a>05657 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 16 ) <span class="keyword">then</span>
- <a name="l05658"></a>05658
- <a name="l05659"></a>05659 xtab( 1) = 0.00389783448711591592405360527037D+00
- <a name="l05660"></a>05660 xtab( 2) = 0.0230289456168732398203176309848D+00
- <a name="l05661"></a>05661 xtab( 3) = 0.0582803983062404123483532298394D+00
- <a name="l05662"></a>05662 xtab( 4) = 0.108678365091054036487713613051D+00
- <a name="l05663"></a>05663 xtab( 5) = 0.172609454909843937760843776232D+00
- <a name="l05664"></a>05664 xtab( 6) = 0.247937054470578495147671753047D+00
- <a name="l05665"></a>05665 xtab( 7) = 0.332094549129917155984755859320D+00
- <a name="l05666"></a>05666 xtab( 8) = 0.422183910581948600115088366745D+00
- <a name="l05667"></a>05667 xtab( 9) = 0.515082473381462603476277704052D+00
- <a name="l05668"></a>05668 xtab(10) = 0.607556120447728724086384921709D+00
- <a name="l05669"></a>05669 xtab(11) = 0.696375653228214061156318166581D+00
- <a name="l05670"></a>05670 xtab(12) = 0.778432565873265405203868167732D+00
- <a name="l05671"></a>05671 xtab(13) = 0.850850269715391083233822761319D+00
- <a name="l05672"></a>05672 xtab(14) = 0.911086857222271905418818994060D+00
- <a name="l05673"></a>05673 xtab(15) = 0.957025571703542157591520509383D+00
- <a name="l05674"></a>05674 xtab(16) = 0.987047800247984476758697436516D+00
- <a name="l05675"></a>05675
- <a name="l05676"></a>05676 weight( 1) = 0.0607917100435912328511733871235D+00
- <a name="l05677"></a>05677 weight( 2) = 0.102915677517582144387691736210D+00
- <a name="l05678"></a>05678 weight( 3) = 0.122355662046009193557547513197D+00
- <a name="l05679"></a>05679 weight( 4) = 0.127569246937015988717042209239D+00
- <a name="l05680"></a>05680 weight( 5) = 0.123013574600070915423123365137D+00
- <a name="l05681"></a>05681 weight( 6) = 0.111847244855485722621848903429D+00
- <a name="l05682"></a>05682 weight( 7) = 0.0965963851521243412529681650802D+00
- <a name="l05683"></a>05683 weight( 8) = 0.0793566643514731387824416770520D+00
- <a name="l05684"></a>05684 weight( 9) = 0.0618504945819652070951360853113D+00
- <a name="l05685"></a>05685 weight(10) = 0.0454352465077266686288299526509D+00
- <a name="l05686"></a>05686 weight(11) = 0.0310989747515818064092528627927D+00
- <a name="l05687"></a>05687 weight(12) = 0.0194597659273608420780860268669D+00
- <a name="l05688"></a>05688 weight(13) = 0.0107762549632055256455393162159D+00
- <a name="l05689"></a>05689 weight(14) = 0.00497254289008764171250524951646D+00
- <a name="l05690"></a>05690 weight(15) = 0.00167820111005119451503546419059D+00
- <a name="l05691"></a>05691 weight(16) = 0.000282353764668436321778085987413D+00
- <a name="l05692"></a>05692
- <a name="l05693"></a>05693 <span class="keyword">else</span>
- <a name="l05694"></a>05694
- <a name="l05695"></a>05695 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l05696"></a>05696 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LEGENDRE_SET_LOG - Fatal error!'</span>
- <a name="l05697"></a>05697 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l05698"></a>05698 stop
- <a name="l05699"></a>05699
- <a name="l05700"></a>05700 <span class="keyword">end if</span>
- <a name="l05701"></a>05701
- <a name="l05702"></a>05702 return
- <a name="l05703"></a>05703 <span class="keyword">end</span>
- <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 )
- <a name="l05705"></a>05705 <span class="comment">!</span>
- <a name="l05706"></a>05706 <span class="comment">!*******************************************************************************</span>
- <a name="l05707"></a>05707 <span class="comment">!</span>
- <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>
- <a name="l05709"></a>05709 <span class="comment">!</span>
- <a name="l05710"></a>05710 <span class="comment">!</span>
- <a name="l05711"></a>05711 <span class="comment">! Integration interval:</span>
- <a name="l05712"></a>05712 <span class="comment">!</span>
- <a name="l05713"></a>05713 <span class="comment">! [ 0, 1 ]</span>
- <a name="l05714"></a>05714 <span class="comment">!</span>
- <a name="l05715"></a>05715 <span class="comment">! Weight function:</span>
- <a name="l05716"></a>05716 <span class="comment">!</span>
- <a name="l05717"></a>05717 <span class="comment">! SQRT ( X )</span>
- <a name="l05718"></a>05718 <span class="comment">!</span>
- <a name="l05719"></a>05719 <span class="comment">! Integral to approximate:</span>
- <a name="l05720"></a>05720 <span class="comment">!</span>
- <a name="l05721"></a>05721 <span class="comment">! Integral ( 0 <= X <= 1 ) SQRT ( X ) * F(X) dX =</span>
- <a name="l05722"></a>05722 <span class="comment">! Integral ( 0 <= Y <= 1 ) 2 * Y**2 * F(Y**2) dY.</span>
- <a name="l05723"></a>05723 <span class="comment">! (using Y = SQRT(X) )</span>
- <a name="l05724"></a>05724 <span class="comment">!</span>
- <a name="l05725"></a>05725 <span class="comment">! Approximate integral:</span>
- <a name="l05726"></a>05726 <span class="comment">!</span>
- <a name="l05727"></a>05727 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l05728"></a>05728 <span class="comment">!</span>
- <a name="l05729"></a>05729 <span class="comment">! Reference:</span>
- <a name="l05730"></a>05730 <span class="comment">!</span>
- <a name="l05731"></a>05731 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l05732"></a>05732 <span class="comment">! CRC Standard Mathematical Tables and Formulae,</span>
- <a name="l05733"></a>05733 <span class="comment">! CRC Press, 30th Edition, 2000, page 696.</span>
- <a name="l05734"></a>05734 <span class="comment">!</span>
- <a name="l05735"></a>05735 <span class="comment">! Modified:</span>
- <a name="l05736"></a>05736 <span class="comment">!</span>
- <a name="l05737"></a>05737 <span class="comment">! 23 January 2001</span>
- <a name="l05738"></a>05738 <span class="comment">!</span>
- <a name="l05739"></a>05739 <span class="comment">! Author:</span>
- <a name="l05740"></a>05740 <span class="comment">!</span>
- <a name="l05741"></a>05741 <span class="comment">! John Burkardt</span>
- <a name="l05742"></a>05742 <span class="comment">!</span>
- <a name="l05743"></a>05743 <span class="comment">! Parameters:</span>
- <a name="l05744"></a>05744 <span class="comment">!</span>
- <a name="l05745"></a>05745 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l05746"></a>05746 <span class="comment">!</span>
- <a name="l05747"></a>05747 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l05748"></a>05748 <span class="comment">!</span>
- <a name="l05749"></a>05749 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l05750"></a>05750 <span class="comment">!</span>
- <a name="l05751"></a>05751 <span class="keyword">implicit none</span>
- <a name="l05752"></a>05752 <span class="comment">!</span>
- <a name="l05753"></a>05753 <span class="keywordtype">integer</span> norder
- <a name="l05754"></a>05754 <span class="comment">!</span>
- <a name="l05755"></a>05755 <span class="keywordtype">integer</span> norder2
- <a name="l05756"></a>05756 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l05757"></a>05757 <span class="keywordtype">double precision</span> xtab2(2*norder+1)
- <a name="l05758"></a>05758 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l05759"></a>05759 <span class="keywordtype">double precision</span> weight2(2*norder+1)
- <a name="l05760"></a>05760 <span class="comment">!</span>
- <a name="l05761"></a>05761 norder2 = 2 * norder + 1
- <a name="l05762"></a>05762
- <a name="l05763"></a>05763 call <a class="code" href="quadrule_8f90.html#a68e328951e712e3b7e2bc9f6dcf8fc6a">legendre_set </a>( norder2, xtab2, weight2 )
- <a name="l05764"></a>05764
- <a name="l05765"></a>05765 xtab(1:norder) = xtab2(norder+2:2*norder+1)**2
- <a name="l05766"></a>05766 weight(1:norder) = 2.0D+00 * weight2(norder+2:2*norder+1) * xtab(1:norder)
- <a name="l05767"></a>05767
- <a name="l05768"></a>05768 return
- <a name="l05769"></a>05769 <span class="keyword">end</span>
- <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 )
- <a name="l05771"></a>05771 <span class="comment">!</span>
- <a name="l05772"></a>05772 <span class="comment">!*******************************************************************************</span>
- <a name="l05773"></a>05773 <span class="comment">!</span>
- <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>
- <a name="l05775"></a>05775 <span class="comment">!</span>
- <a name="l05776"></a>05776 <span class="comment">!</span>
- <a name="l05777"></a>05777 <span class="comment">! Integration interval:</span>
- <a name="l05778"></a>05778 <span class="comment">!</span>
- <a name="l05779"></a>05779 <span class="comment">! [ 0, 1 ]</span>
- <a name="l05780"></a>05780 <span class="comment">!</span>
- <a name="l05781"></a>05781 <span class="comment">! Weight function:</span>
- <a name="l05782"></a>05782 <span class="comment">!</span>
- <a name="l05783"></a>05783 <span class="comment">! 1 / SQRT ( X )</span>
- <a name="l05784"></a>05784 <span class="comment">!</span>
- <a name="l05785"></a>05785 <span class="comment">! Integral to approximate:</span>
- <a name="l05786"></a>05786 <span class="comment">!</span>
- <a name="l05787"></a>05787 <span class="comment">! Integral ( 0 <= X <= 1 ) F(X) / SQRT ( X ) dX</span>
- <a name="l05788"></a>05788 <span class="comment">!</span>
- <a name="l05789"></a>05789 <span class="comment">! Approximate integral:</span>
- <a name="l05790"></a>05790 <span class="comment">!</span>
- <a name="l05791"></a>05791 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l05792"></a>05792 <span class="comment">!</span>
- <a name="l05793"></a>05793 <span class="comment">! Reference:</span>
- <a name="l05794"></a>05794 <span class="comment">!</span>
- <a name="l05795"></a>05795 <span class="comment">! Daniel Zwillinger, editor,</span>
- <a name="l05796"></a>05796 <span class="comment">! CRC Standard Mathematical Tables and Formulae,</span>
- <a name="l05797"></a>05797 <span class="comment">! CRC Press, 30th Edition, 2000, page 696.</span>
- <a name="l05798"></a>05798 <span class="comment">!</span>
- <a name="l05799"></a>05799 <span class="comment">! Modified:</span>
- <a name="l05800"></a>05800 <span class="comment">!</span>
- <a name="l05801"></a>05801 <span class="comment">! 21 January 2001</span>
- <a name="l05802"></a>05802 <span class="comment">!</span>
- <a name="l05803"></a>05803 <span class="comment">! Author:</span>
- <a name="l05804"></a>05804 <span class="comment">!</span>
- <a name="l05805"></a>05805 <span class="comment">! John Burkardt</span>
- <a name="l05806"></a>05806 <span class="comment">!</span>
- <a name="l05807"></a>05807 <span class="comment">! Parameters:</span>
- <a name="l05808"></a>05808 <span class="comment">!</span>
- <a name="l05809"></a>05809 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l05810"></a>05810 <span class="comment">!</span>
- <a name="l05811"></a>05811 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l05812"></a>05812 <span class="comment">!</span>
- <a name="l05813"></a>05813 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l05814"></a>05814 <span class="comment">!</span>
- <a name="l05815"></a>05815 <span class="keyword">implicit none</span>
- <a name="l05816"></a>05816 <span class="comment">!</span>
- <a name="l05817"></a>05817 <span class="keywordtype">integer</span> norder
- <a name="l05818"></a>05818 <span class="comment">!</span>
- <a name="l05819"></a>05819 <span class="keywordtype">integer</span> norder2
- <a name="l05820"></a>05820 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l05821"></a>05821 <span class="keywordtype">double precision</span> xtab2(2*norder+1)
- <a name="l05822"></a>05822 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l05823"></a>05823 <span class="keywordtype">double precision</span> weight2(2*norder+1)
- <a name="l05824"></a>05824 <span class="comment">!</span>
- <a name="l05825"></a>05825 norder2 = 2 * norder + 1
- <a name="l05826"></a>05826
- <a name="l05827"></a>05827 call <a class="code" href="quadrule_8f90.html#a68e328951e712e3b7e2bc9f6dcf8fc6a">legendre_set </a>( norder2, xtab2, weight2 )
- <a name="l05828"></a>05828
- <a name="l05829"></a>05829 xtab(1:norder) = xtab2(norder+2:2*norder+1)**2
- <a name="l05830"></a>05830 weight(1:norder) = 2.0D+00 * weight2(norder+2:2*norder+1)
- <a name="l05831"></a>05831
- <a name="l05832"></a>05832 return
- <a name="l05833"></a>05833 <span class="keyword">end</span>
- <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 )
- <a name="l05835"></a>05835 <span class="comment">!</span>
- <a name="l05836"></a>05836 <span class="comment">!*******************************************************************************</span>
- <a name="l05837"></a>05837 <span class="comment">!</span>
- <a name="l05838"></a>05838 <span class="comment">!! LEGENDRE_SET_X0_01 sets a Gauss-Legendre rule for F(X) on [0,1].</span>
- <a name="l05839"></a>05839 <span class="comment">!</span>
- <a name="l05840"></a>05840 <span class="comment">!</span>
- <a name="l05841"></a>05841 <span class="comment">! Integration interval:</span>
- <a name="l05842"></a>05842 <span class="comment">!</span>
- <a name="l05843"></a>05843 <span class="comment">! [ 0, 1 ]</span>
- <a name="l05844"></a>05844 <span class="comment">!</span>
- <a name="l05845"></a>05845 <span class="comment">! Weight function:</span>
- <a name="l05846"></a>05846 <span class="comment">!</span>
- <a name="l05847"></a>05847 <span class="comment">! 1.0D+00</span>
- <a name="l05848"></a>05848 <span class="comment">!</span>
- <a name="l05849"></a>05849 <span class="comment">! Integral to approximate:</span>
- <a name="l05850"></a>05850 <span class="comment">!</span>
- <a name="l05851"></a>05851 <span class="comment">! Integral ( 0 <= X <= 1 ) F(X) dX</span>
- <a name="l05852"></a>05852 <span class="comment">!</span>
- <a name="l05853"></a>05853 <span class="comment">! Approximate integral:</span>
- <a name="l05854"></a>05854 <span class="comment">!</span>
- <a name="l05855"></a>05855 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l05856"></a>05856 <span class="comment">!</span>
- <a name="l05857"></a>05857 <span class="comment">! Reference:</span>
- <a name="l05858"></a>05858 <span class="comment">!</span>
- <a name="l05859"></a>05859 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l05860"></a>05860 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l05861"></a>05861 <span class="comment">! National Bureau of Standards, 1964, page 921.</span>
- <a name="l05862"></a>05862 <span class="comment">!</span>
- <a name="l05863"></a>05863 <span class="comment">! Modified:</span>
- <a name="l05864"></a>05864 <span class="comment">!</span>
- <a name="l05865"></a>05865 <span class="comment">! 18 November 2000</span>
- <a name="l05866"></a>05866 <span class="comment">!</span>
- <a name="l05867"></a>05867 <span class="comment">! Author:</span>
- <a name="l05868"></a>05868 <span class="comment">!</span>
- <a name="l05869"></a>05869 <span class="comment">! John Burkardt</span>
- <a name="l05870"></a>05870 <span class="comment">!</span>
- <a name="l05871"></a>05871 <span class="comment">! Parameters:</span>
- <a name="l05872"></a>05872 <span class="comment">!</span>
- <a name="l05873"></a>05873 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l05874"></a>05874 <span class="comment">! NORDER must be between 1 and 8.</span>
- <a name="l05875"></a>05875 <span class="comment">!</span>
- <a name="l05876"></a>05876 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l05877"></a>05877 <span class="comment">!</span>
- <a name="l05878"></a>05878 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l05879"></a>05879 <span class="comment">!</span>
- <a name="l05880"></a>05880 <span class="keyword">implicit none</span>
- <a name="l05881"></a>05881 <span class="comment">!</span>
- <a name="l05882"></a>05882 <span class="keywordtype">integer</span> norder
- <a name="l05883"></a>05883 <span class="comment">!</span>
- <a name="l05884"></a>05884 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l05885"></a>05885 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l05886"></a>05886 <span class="comment">!</span>
- <a name="l05887"></a>05887 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l05888"></a>05888
- <a name="l05889"></a>05889 xtab(1) = 0.5D+00
- <a name="l05890"></a>05890
- <a name="l05891"></a>05891 weight(1) = 1.0D+00
- <a name="l05892"></a>05892
- <a name="l05893"></a>05893 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l05894"></a>05894
- <a name="l05895"></a>05895 xtab(1) = 0.2113248654D+00
- <a name="l05896"></a>05896 xtab(2) = 0.7886751346D+00
- <a name="l05897"></a>05897
- <a name="l05898"></a>05898 weight(1) = 0.5D+00
- <a name="l05899"></a>05899 weight(2) = 0.5D+00
- <a name="l05900"></a>05900
- <a name="l05901"></a>05901 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l05902"></a>05902
- <a name="l05903"></a>05903 xtab(1) = 0.1127016654D+00
- <a name="l05904"></a>05904 xtab(2) = 0.5000000000D+00
- <a name="l05905"></a>05905 xtab(3) = 0.8872983346D+00
- <a name="l05906"></a>05906
- <a name="l05907"></a>05907 weight(1) = 5.0D+00 / 18.0D+00
- <a name="l05908"></a>05908 weight(2) = 8.0D+00 / 18.0D+00
- <a name="l05909"></a>05909 weight(3) = 5.0D+00 / 18.0D+00
- <a name="l05910"></a>05910
- <a name="l05911"></a>05911 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l05912"></a>05912
- <a name="l05913"></a>05913 xtab(1) = 0.0694318442D+00
- <a name="l05914"></a>05914 xtab(2) = 0.3300094782D+00
- <a name="l05915"></a>05915 xtab(3) = 0.6699905218D+00
- <a name="l05916"></a>05916 xtab(4) = 0.9305681558D+00
- <a name="l05917"></a>05917
- <a name="l05918"></a>05918 weight(1) = 0.1739274226D+00
- <a name="l05919"></a>05919 weight(2) = 0.3260725774D+00
- <a name="l05920"></a>05920 weight(3) = 0.3260725774D+00
- <a name="l05921"></a>05921 weight(4) = 0.1739274226D+00
- <a name="l05922"></a>05922
- <a name="l05923"></a>05923 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l05924"></a>05924
- <a name="l05925"></a>05925 xtab(1) = 0.0469100770D+00
- <a name="l05926"></a>05926 xtab(2) = 0.2307653449D+00
- <a name="l05927"></a>05927 xtab(3) = 0.5000000000D+00
- <a name="l05928"></a>05928 xtab(4) = 0.7692346551D+00
- <a name="l05929"></a>05929 xtab(5) = 0.9530899230D+00
- <a name="l05930"></a>05930
- <a name="l05931"></a>05931 weight(1) = 0.1184634425D+00
- <a name="l05932"></a>05932 weight(2) = 0.2393143352D+00
- <a name="l05933"></a>05933 weight(3) = 0.2844444444D+00
- <a name="l05934"></a>05934 weight(4) = 0.2393143352D+00
- <a name="l05935"></a>05935 weight(5) = 0.1184634425D+00
- <a name="l05936"></a>05936
- <a name="l05937"></a>05937 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l05938"></a>05938
- <a name="l05939"></a>05939 xtab(1) = 0.0337652429D+00
- <a name="l05940"></a>05940 xtab(2) = 0.1693953068D+00
- <a name="l05941"></a>05941 xtab(3) = 0.3806904070D+00
- <a name="l05942"></a>05942 xtab(4) = 0.6193095930D+00
- <a name="l05943"></a>05943 xtab(5) = 0.8306046932D+00
- <a name="l05944"></a>05944 xtab(6) = 0.9662347571D+00
- <a name="l05945"></a>05945
- <a name="l05946"></a>05946 weight(1) = 0.0856622462D+00
- <a name="l05947"></a>05947 weight(2) = 0.1803807865D+00
- <a name="l05948"></a>05948 weight(3) = 0.2339569673D+00
- <a name="l05949"></a>05949 weight(4) = 0.2339569673D+00
- <a name="l05950"></a>05950 weight(5) = 0.1803807865D+00
- <a name="l05951"></a>05951 weight(6) = 0.0856622462D+00
- <a name="l05952"></a>05952
- <a name="l05953"></a>05953 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l05954"></a>05954
- <a name="l05955"></a>05955 xtab(1) = 0.0254460438D+00
- <a name="l05956"></a>05956 xtab(2) = 0.1292344072D+00
- <a name="l05957"></a>05957 xtab(3) = 0.2970774243D+00
- <a name="l05958"></a>05958 xtab(4) = 0.5000000000D+00
- <a name="l05959"></a>05959 xtab(5) = 0.7029225757D+00
- <a name="l05960"></a>05960 xtab(6) = 0.8707655928D+00
- <a name="l05961"></a>05961 xtab(7) = 0.9745539562D+00
- <a name="l05962"></a>05962
- <a name="l05963"></a>05963 weight(1) = 0.0647424831D+00
- <a name="l05964"></a>05964 weight(2) = 0.1398526957D+00
- <a name="l05965"></a>05965 weight(3) = 0.1909150253D+00
- <a name="l05966"></a>05966 weight(4) = 0.2089795918D+00
- <a name="l05967"></a>05967 weight(5) = 0.1909150253D+00
- <a name="l05968"></a>05968 weight(6) = 0.1398526957D+00
- <a name="l05969"></a>05969 weight(7) = 0.0647424831D+00
- <a name="l05970"></a>05970
- <a name="l05971"></a>05971 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l05972"></a>05972
- <a name="l05973"></a>05973 xtab(1) = 0.0198550718D+00
- <a name="l05974"></a>05974 xtab(2) = 0.1016667613D+00
- <a name="l05975"></a>05975 xtab(3) = 0.2372337950D+00
- <a name="l05976"></a>05976 xtab(4) = 0.4082826788D+00
- <a name="l05977"></a>05977 xtab(5) = 0.5917173212D+00
- <a name="l05978"></a>05978 xtab(6) = 0.7627662050D+00
- <a name="l05979"></a>05979 xtab(7) = 0.8983332387D+00
- <a name="l05980"></a>05980 xtab(8) = 0.9801449282D+00
- <a name="l05981"></a>05981
- <a name="l05982"></a>05982 weight(1) = 0.0506142681D+00
- <a name="l05983"></a>05983 weight(2) = 0.1111905172D+00
- <a name="l05984"></a>05984 weight(3) = 0.1568533229D+00
- <a name="l05985"></a>05985 weight(4) = 0.1813418917D+00
- <a name="l05986"></a>05986 weight(5) = 0.1813418917D+00
- <a name="l05987"></a>05987 weight(6) = 0.1568533229D+00
- <a name="l05988"></a>05988 weight(7) = 0.1111905172D+00
- <a name="l05989"></a>05989 weight(8) = 0.0506142681D+00
- <a name="l05990"></a>05990
- <a name="l05991"></a>05991 <span class="keyword">else</span>
- <a name="l05992"></a>05992
- <a name="l05993"></a>05993 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l05994"></a>05994 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LEGENDRE_SET_X0_01 - Fatal error!'</span>
- <a name="l05995"></a>05995 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l05996"></a>05996 stop
- <a name="l05997"></a>05997
- <a name="l05998"></a>05998 <span class="keyword">end if</span>
- <a name="l05999"></a>05999
- <a name="l06000"></a>06000 return
- <a name="l06001"></a>06001 <span class="keyword">end</span>
- <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 )
- <a name="l06003"></a>06003 <span class="comment">!</span>
- <a name="l06004"></a>06004 <span class="comment">!*******************************************************************************</span>
- <a name="l06005"></a>06005 <span class="comment">!</span>
- <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>
- <a name="l06007"></a>06007 <span class="comment">!</span>
- <a name="l06008"></a>06008 <span class="comment">!</span>
- <a name="l06009"></a>06009 <span class="comment">! Integration interval:</span>
- <a name="l06010"></a>06010 <span class="comment">!</span>
- <a name="l06011"></a>06011 <span class="comment">! [ -1, 1 ]</span>
- <a name="l06012"></a>06012 <span class="comment">!</span>
- <a name="l06013"></a>06013 <span class="comment">! Weight function:</span>
- <a name="l06014"></a>06014 <span class="comment">!</span>
- <a name="l06015"></a>06015 <span class="comment">! 1 + X</span>
- <a name="l06016"></a>06016 <span class="comment">!</span>
- <a name="l06017"></a>06017 <span class="comment">! Integral to approximate:</span>
- <a name="l06018"></a>06018 <span class="comment">!</span>
- <a name="l06019"></a>06019 <span class="comment">! Integral ( -1 <= X <= 1 ) ( 1 + X ) * F(X) dX</span>
- <a name="l06020"></a>06020 <span class="comment">!</span>
- <a name="l06021"></a>06021 <span class="comment">! Approximate integral:</span>
- <a name="l06022"></a>06022 <span class="comment">!</span>
- <a name="l06023"></a>06023 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l06024"></a>06024 <span class="comment">!</span>
- <a name="l06025"></a>06025 <span class="comment">! Reference:</span>
- <a name="l06026"></a>06026 <span class="comment">!</span>
- <a name="l06027"></a>06027 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l06028"></a>06028 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l06029"></a>06029 <span class="comment">! Prentice Hall, 1966, Table #3.</span>
- <a name="l06030"></a>06030 <span class="comment">!</span>
- <a name="l06031"></a>06031 <span class="comment">! Modified:</span>
- <a name="l06032"></a>06032 <span class="comment">!</span>
- <a name="l06033"></a>06033 <span class="comment">! 18 December 2000</span>
- <a name="l06034"></a>06034 <span class="comment">!</span>
- <a name="l06035"></a>06035 <span class="comment">! Author:</span>
- <a name="l06036"></a>06036 <span class="comment">!</span>
- <a name="l06037"></a>06037 <span class="comment">! John Burkardt</span>
- <a name="l06038"></a>06038 <span class="comment">!</span>
- <a name="l06039"></a>06039 <span class="comment">! Parameters:</span>
- <a name="l06040"></a>06040 <span class="comment">!</span>
- <a name="l06041"></a>06041 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l06042"></a>06042 <span class="comment">! NORDER must be between 1 and 9.</span>
- <a name="l06043"></a>06043 <span class="comment">!</span>
- <a name="l06044"></a>06044 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l06045"></a>06045 <span class="comment">!</span>
- <a name="l06046"></a>06046 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l06047"></a>06047 <span class="comment">!</span>
- <a name="l06048"></a>06048 <span class="keyword">implicit none</span>
- <a name="l06049"></a>06049 <span class="comment">!</span>
- <a name="l06050"></a>06050 <span class="keywordtype">integer</span> norder
- <a name="l06051"></a>06051 <span class="comment">!</span>
- <a name="l06052"></a>06052 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l06053"></a>06053 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l06054"></a>06054 <span class="comment">!</span>
- <a name="l06055"></a>06055 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l06056"></a>06056
- <a name="l06057"></a>06057 xtab(1) = 0.333333333333333333333333333333D+00
- <a name="l06058"></a>06058
- <a name="l06059"></a>06059 weight(1) = 2.0D+00
- <a name="l06060"></a>06060
- <a name="l06061"></a>06061 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l06062"></a>06062
- <a name="l06063"></a>06063 xtab(1) = -0.289897948556635619639456814941D+00
- <a name="l06064"></a>06064 xtab(2) = 0.689897948556635619639456814941D+00
- <a name="l06065"></a>06065
- <a name="l06066"></a>06066 weight(1) = 0.727834473024091322422523991699D+00
- <a name="l06067"></a>06067 weight(2) = 1.27216552697590867757747600830D+00
- <a name="l06068"></a>06068
- <a name="l06069"></a>06069 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l06070"></a>06070
- <a name="l06071"></a>06071 xtab(1) = -0.575318923521694112050483779752D+00
- <a name="l06072"></a>06072 xtab(2) = 0.181066271118530578270147495862D+00
- <a name="l06073"></a>06073 xtab(3) = 0.822824080974592105208907712461D+00
- <a name="l06074"></a>06074
- <a name="l06075"></a>06075 weight(1) = 0.279307919605816490135525088716D+00
- <a name="l06076"></a>06076 weight(2) = 0.916964425438344986775682378225D+00
- <a name="l06077"></a>06077 weight(3) = 0.803727654955838523088792533058D+00
- <a name="l06078"></a>06078
- <a name="l06079"></a>06079 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l06080"></a>06080
- <a name="l06081"></a>06081 xtab(1) = -0.720480271312438895695825837750D+00
- <a name="l06082"></a>06082 xtab(2) = -0.167180864737833640113395337326D+00
- <a name="l06083"></a>06083 xtab(3) = 0.446313972723752344639908004629D+00
- <a name="l06084"></a>06084 xtab(4) = 0.885791607770964635613757614892D+00
- <a name="l06085"></a>06085
- <a name="l06086"></a>06086 weight(1) = 0.124723883800032328695500588386D+00
- <a name="l06087"></a>06087 weight(2) = 0.519390190432929763305824811559D+00
- <a name="l06088"></a>06088 weight(3) = 0.813858272041085443165617903743D+00
- <a name="l06089"></a>06089 weight(4) = 0.542027653725952464833056696312D+00
- <a name="l06090"></a>06090
- <a name="l06091"></a>06091 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l06092"></a>06092
- <a name="l06093"></a>06093 xtab(1) = -0.802929828402347147753002204224D+00
- <a name="l06094"></a>06094 xtab(2) = -0.390928546707272189029229647442D+00
- <a name="l06095"></a>06095 xtab(3) = 0.124050379505227711989974959990D+00
- <a name="l06096"></a>06096 xtab(4) = 0.603973164252783654928415726409D+00
- <a name="l06097"></a>06097 xtab(5) = 0.920380285897062515318386619813D+00
- <a name="l06098"></a>06098
- <a name="l06099"></a>06099 weight(1) = 0.0629916580867691047411692662740D+00
- <a name="l06100"></a>06100 weight(2) = 0.295635480290466681402532877367D+00
- <a name="l06101"></a>06101 weight(3) = 0.585547948338679234792151477424D+00
- <a name="l06102"></a>06102 weight(4) = 0.668698552377478261966702492391D+00
- <a name="l06103"></a>06103 weight(5) = 0.387126360906606717097443886545D+00
- <a name="l06104"></a>06104
- <a name="l06105"></a>06105 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l06106"></a>06106
- <a name="l06107"></a>06107 xtab(1) = -0.853891342639482229703747931639D+00
- <a name="l06108"></a>06108 xtab(2) = -0.538467724060109001833766720231D+00
- <a name="l06109"></a>06109 xtab(3) = -0.117343037543100264162786683611D+00
- <a name="l06110"></a>06110 xtab(4) = 0.326030619437691401805894055838D+00
- <a name="l06111"></a>06111 xtab(5) = 0.703842800663031416300046295008D+00
- <a name="l06112"></a>06112 xtab(6) = 0.941367145680430216055899446174D+00
- <a name="l06113"></a>06113
- <a name="l06114"></a>06114 weight(1) = 0.0349532072544381270240692132496D+00
- <a name="l06115"></a>06115 weight(2) = 0.175820662202035902032706497222D+00
- <a name="l06116"></a>06116 weight(3) = 0.394644603562621056482338042193D+00
- <a name="l06117"></a>06117 weight(4) = 0.563170215152795712476307356284D+00
- <a name="l06118"></a>06118 weight(5) = 0.542169988926074467362761586552D+00
- <a name="l06119"></a>06119 weight(6) = 0.289241322902034734621817304499D+00
- <a name="l06120"></a>06120
- <a name="l06121"></a>06121 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l06122"></a>06122
- <a name="l06123"></a>06123 xtab(1) = -0.887474878926155707068695617935D+00
- <a name="l06124"></a>06124 xtab(2) = -0.639518616526215270024840114382D+00
- <a name="l06125"></a>06125 xtab(3) = -0.294750565773660725252184459658D+00
- <a name="l06126"></a>06126 xtab(4) = 0.0943072526611107660028971153047D+00
- <a name="l06127"></a>06127 xtab(5) = 0.468420354430821063046421216613D+00
- <a name="l06128"></a>06128 xtab(6) = 0.770641893678191536180719525865D+00
- <a name="l06129"></a>06129 xtab(7) = 0.955041227122575003782349000858D+00
- <a name="l06130"></a>06130
- <a name="l06131"></a>06131 weight(1) = 0.0208574488112296163587654972151D+00
- <a name="l06132"></a>06132 weight(2) = 0.109633426887493901777324193433D+00
- <a name="l06133"></a>06133 weight(3) = 0.265538785861965879934591955055D+00
- <a name="l06134"></a>06134 weight(4) = 0.428500262783494679963649011999D+00
- <a name="l06135"></a>06135 weight(5) = 0.509563589198353307674937943100D+00
- <a name="l06136"></a>06136 weight(6) = 0.442037032763498409684482945478D+00
- <a name="l06137"></a>06137 weight(7) = 0.223869453693964204606248453720D+00
- <a name="l06138"></a>06138
- <a name="l06139"></a>06139 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l06140"></a>06140
- <a name="l06141"></a>06141 xtab(1) = -0.910732089420060298533757956283D+00
- <a name="l06142"></a>06142 xtab(2) = -0.711267485915708857029562959544D+00
- <a name="l06143"></a>06143 xtab(3) = -0.426350485711138962102627520502D+00
- <a name="l06144"></a>06144 xtab(4) = -0.0903733696068532980645444599064D+00
- <a name="l06145"></a>06145 xtab(5) = 0.256135670833455395138292079035D+00
- <a name="l06146"></a>06146 xtab(6) = 0.571383041208738483284917464837D+00
- <a name="l06147"></a>06147 xtab(7) = 0.817352784200412087992517083851D+00
- <a name="l06148"></a>06148 xtab(8) = 0.964440169705273096373589797925D+00
- <a name="l06149"></a>06149
- <a name="l06150"></a>06150 weight(1) = 0.0131807657689951954189692640444D+00
- <a name="l06151"></a>06151 weight(2) = 0.0713716106239448335742111888042D+00
- <a name="l06152"></a>06152 weight(3) = 0.181757278018795592332221684383D+00
- <a name="l06153"></a>06153 weight(4) = 0.316798397969276640481632757440D+00
- <a name="l06154"></a>06154 weight(5) = 0.424189437743720042818124385645D+00
- <a name="l06155"></a>06155 weight(6) = 0.450023197883549464687088394417D+00
- <a name="l06156"></a>06156 weight(7) = 0.364476094545494505382889847132D+00
- <a name="l06157"></a>06157 weight(8) = 0.178203217446223725304862478136D+00
- <a name="l06158"></a>06158
- <a name="l06159"></a>06159 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
- <a name="l06160"></a>06160
- <a name="l06161"></a>06161 xtab(1) = -0.927484374233581078117671398464D+00
- <a name="l06162"></a>06162 xtab(2) = -0.763842042420002599615429776011D+00
- <a name="l06163"></a>06163 xtab(3) = -0.525646030370079229365386614293D+00
- <a name="l06164"></a>06164 xtab(4) = -0.236234469390588049278459503207D+00
- <a name="l06165"></a>06165 xtab(5) = 0.0760591978379781302337137826389D+00
- <a name="l06166"></a>06166 xtab(6) = 0.380664840144724365880759065541D+00
- <a name="l06167"></a>06167 xtab(7) = 0.647766687674009436273648507855D+00
- <a name="l06168"></a>06168 xtab(8) = 0.851225220581607910728163628088D+00
- <a name="l06169"></a>06169 xtab(9) = 0.971175180702246902734346518378D+00
- <a name="l06170"></a>06170
- <a name="l06171"></a>06171 weight(1) = 0.00872338834309252349019620448007D+00
- <a name="l06172"></a>06172 weight(2) = 0.0482400171391415162069086091476D+00
- <a name="l06173"></a>06173 weight(3) = 0.127219285964216005046760427743D+00
- <a name="l06174"></a>06174 weight(4) = 0.233604781180660442262926091607D+00
- <a name="l06175"></a>06175 weight(5) = 0.337433287379681397577000079834D+00
- <a name="l06176"></a>06176 weight(6) = 0.401235236773473158616600898930D+00
- <a name="l06177"></a>06177 weight(7) = 0.394134968689382820640692081477D+00
- <a name="l06178"></a>06178 weight(8) = 0.304297020437232650320317215016D+00
- <a name="l06179"></a>06179 weight(9) = 0.145112014093119485838598391765D+00
- <a name="l06180"></a>06180
- <a name="l06181"></a>06181 <span class="keyword">else</span>
- <a name="l06182"></a>06182
- <a name="l06183"></a>06183 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l06184"></a>06184 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LEGENDRE_SET_X1 - Fatal error!'</span>
- <a name="l06185"></a>06185 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal input value of NORDER = '</span>, norder
- <a name="l06186"></a>06186 stop
- <a name="l06187"></a>06187
- <a name="l06188"></a>06188 <span class="keyword">end if</span>
- <a name="l06189"></a>06189
- <a name="l06190"></a>06190 return
- <a name="l06191"></a>06191 <span class="keyword">end</span>
- <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 )
- <a name="l06193"></a>06193 <span class="comment">!</span>
- <a name="l06194"></a>06194 <span class="comment">!*******************************************************************************</span>
- <a name="l06195"></a>06195 <span class="comment">!</span>
- <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>
- <a name="l06197"></a>06197 <span class="comment">!</span>
- <a name="l06198"></a>06198 <span class="comment">!</span>
- <a name="l06199"></a>06199 <span class="comment">! Integration interval:</span>
- <a name="l06200"></a>06200 <span class="comment">!</span>
- <a name="l06201"></a>06201 <span class="comment">! [ 0, 1 ]</span>
- <a name="l06202"></a>06202 <span class="comment">!</span>
- <a name="l06203"></a>06203 <span class="comment">! Weight function:</span>
- <a name="l06204"></a>06204 <span class="comment">!</span>
- <a name="l06205"></a>06205 <span class="comment">! X</span>
- <a name="l06206"></a>06206 <span class="comment">!</span>
- <a name="l06207"></a>06207 <span class="comment">! Integral to approximate:</span>
- <a name="l06208"></a>06208 <span class="comment">!</span>
- <a name="l06209"></a>06209 <span class="comment">! Integral ( 0 <= X <= 1 ) X * F(X) dX</span>
- <a name="l06210"></a>06210 <span class="comment">!</span>
- <a name="l06211"></a>06211 <span class="comment">! Approximate integral:</span>
- <a name="l06212"></a>06212 <span class="comment">!</span>
- <a name="l06213"></a>06213 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l06214"></a>06214 <span class="comment">!</span>
- <a name="l06215"></a>06215 <span class="comment">! Reference:</span>
- <a name="l06216"></a>06216 <span class="comment">!</span>
- <a name="l06217"></a>06217 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l06218"></a>06218 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l06219"></a>06219 <span class="comment">! National Bureau of Standards, 1964, page 921.</span>
- <a name="l06220"></a>06220 <span class="comment">!</span>
- <a name="l06221"></a>06221 <span class="comment">! Modified:</span>
- <a name="l06222"></a>06222 <span class="comment">!</span>
- <a name="l06223"></a>06223 <span class="comment">! 18 November 2000</span>
- <a name="l06224"></a>06224 <span class="comment">!</span>
- <a name="l06225"></a>06225 <span class="comment">! Author:</span>
- <a name="l06226"></a>06226 <span class="comment">!</span>
- <a name="l06227"></a>06227 <span class="comment">! John Burkardt</span>
- <a name="l06228"></a>06228 <span class="comment">!</span>
- <a name="l06229"></a>06229 <span class="comment">! Parameters:</span>
- <a name="l06230"></a>06230 <span class="comment">!</span>
- <a name="l06231"></a>06231 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l06232"></a>06232 <span class="comment">! NORDER must be between 1 and 8.</span>
- <a name="l06233"></a>06233 <span class="comment">!</span>
- <a name="l06234"></a>06234 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l06235"></a>06235 <span class="comment">!</span>
- <a name="l06236"></a>06236 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l06237"></a>06237 <span class="comment">!</span>
- <a name="l06238"></a>06238 <span class="keyword">implicit none</span>
- <a name="l06239"></a>06239 <span class="comment">!</span>
- <a name="l06240"></a>06240 <span class="keywordtype">integer</span> norder
- <a name="l06241"></a>06241 <span class="comment">!</span>
- <a name="l06242"></a>06242 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l06243"></a>06243 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l06244"></a>06244 <span class="comment">!</span>
- <a name="l06245"></a>06245 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l06246"></a>06246
- <a name="l06247"></a>06247 xtab(1) = 0.6666666667D+00
- <a name="l06248"></a>06248
- <a name="l06249"></a>06249 weight(1) = 0.5000000000D+00
- <a name="l06250"></a>06250
- <a name="l06251"></a>06251 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l06252"></a>06252
- <a name="l06253"></a>06253 xtab(1) = 0.3550510257D+00
- <a name="l06254"></a>06254 xtab(2) = 0.8449489743D+00
- <a name="l06255"></a>06255
- <a name="l06256"></a>06256 weight(1) = 0.1819586183D+00
- <a name="l06257"></a>06257 weight(2) = 0.3180413817D+00
- <a name="l06258"></a>06258
- <a name="l06259"></a>06259 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l06260"></a>06260
- <a name="l06261"></a>06261 xtab(1) = 0.2123405382D+00
- <a name="l06262"></a>06262 xtab(2) = 0.5905331356D+00
- <a name="l06263"></a>06263 xtab(3) = 0.9114120405D+00
- <a name="l06264"></a>06264
- <a name="l06265"></a>06265 weight(1) = 0.0698269799D+00
- <a name="l06266"></a>06266 weight(2) = 0.2292411064D+00
- <a name="l06267"></a>06267 weight(3) = 0.2009319137D+00
- <a name="l06268"></a>06268
- <a name="l06269"></a>06269 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l06270"></a>06270
- <a name="l06271"></a>06271 xtab(1) = 0.1397598643D+00
- <a name="l06272"></a>06272 xtab(2) = 0.4164095676D+00
- <a name="l06273"></a>06273 xtab(3) = 0.7231569864D+00
- <a name="l06274"></a>06274 xtab(4) = 0.9428958039D+00
- <a name="l06275"></a>06275
- <a name="l06276"></a>06276 weight(1) = 0.0311809710D+00
- <a name="l06277"></a>06277 weight(2) = 0.1298475476D+00
- <a name="l06278"></a>06278 weight(3) = 0.2034645680D+00
- <a name="l06279"></a>06279 weight(4) = 0.1355069134D+00
- <a name="l06280"></a>06280
- <a name="l06281"></a>06281 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l06282"></a>06282
- <a name="l06283"></a>06283 xtab(1) = 0.0985350858D+00
- <a name="l06284"></a>06284 xtab(2) = 0.3045357266D+00
- <a name="l06285"></a>06285 xtab(3) = 0.5620251898D+00
- <a name="l06286"></a>06286 xtab(4) = 0.8019865821D+00
- <a name="l06287"></a>06287 xtab(5) = 0.9601901429D+00
- <a name="l06288"></a>06288
- <a name="l06289"></a>06289 weight(1) = 0.0157479145D+00
- <a name="l06290"></a>06290 weight(2) = 0.0739088701D+00
- <a name="l06291"></a>06291 weight(3) = 0.1463888701D+00
- <a name="l06292"></a>06292 weight(4) = 0.1671746381D+00
- <a name="l06293"></a>06293 weight(5) = 0.0967815902D+00
- <a name="l06294"></a>06294
- <a name="l06295"></a>06295 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l06296"></a>06296
- <a name="l06297"></a>06297 xtab(1) = 0.0730543287D+00
- <a name="l06298"></a>06298 xtab(2) = 0.2307661380D+00
- <a name="l06299"></a>06299 xtab(3) = 0.4413284812D+00
- <a name="l06300"></a>06300 xtab(4) = 0.6630153097D+00
- <a name="l06301"></a>06301 xtab(5) = 0.8519214003D+00
- <a name="l06302"></a>06302 xtab(6) = 0.9706835728D+00
- <a name="l06303"></a>06303
- <a name="l06304"></a>06304 weight(1) = 0.0087383108D+00
- <a name="l06305"></a>06305 weight(2) = 0.0439551656D+00
- <a name="l06306"></a>06306 weight(3) = 0.0986611509D+00
- <a name="l06307"></a>06307 weight(4) = 0.1407925538D+00
- <a name="l06308"></a>06308 weight(5) = 0.1355424972D+00
- <a name="l06309"></a>06309 weight(6) = 0.0723103307D+00
- <a name="l06310"></a>06310
- <a name="l06311"></a>06311 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l06312"></a>06312
- <a name="l06313"></a>06313 xtab(1) = 0.0562625605D+00
- <a name="l06314"></a>06314 xtab(2) = 0.1802406917D+00
- <a name="l06315"></a>06315 xtab(3) = 0.3526247171D+00
- <a name="l06316"></a>06316 xtab(4) = 0.5471536263D+00
- <a name="l06317"></a>06317 xtab(5) = 0.7342101772D+00
- <a name="l06318"></a>06318 xtab(6) = 0.8853209468D+00
- <a name="l06319"></a>06319 xtab(7) = 0.9775206136D+00
- <a name="l06320"></a>06320
- <a name="l06321"></a>06321 weight(1) = 0.0052143622D+00
- <a name="l06322"></a>06322 weight(2) = 0.0274083567D+00
- <a name="l06323"></a>06323 weight(3) = 0.0663846965D+00
- <a name="l06324"></a>06324 weight(4) = 0.1071250657D+00
- <a name="l06325"></a>06325 weight(5) = 0.1273908973D+00
- <a name="l06326"></a>06326 weight(6) = 0.1105092582D+00
- <a name="l06327"></a>06327 weight(7) = 0.0559673634D+00
- <a name="l06328"></a>06328
- <a name="l06329"></a>06329 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l06330"></a>06330
- <a name="l06331"></a>06331 xtab(1) = 0.0446339553D+00
- <a name="l06332"></a>06332 xtab(2) = 0.1443662570D+00
- <a name="l06333"></a>06333 xtab(3) = 0.2868247571D+00
- <a name="l06334"></a>06334 xtab(4) = 0.4548133152D+00
- <a name="l06335"></a>06335 xtab(5) = 0.6280678354D+00
- <a name="l06336"></a>06336 xtab(6) = 0.7856915206D+00
- <a name="l06337"></a>06337 xtab(7) = 0.9086763921D+00
- <a name="l06338"></a>06338 xtab(8) = 0.9822200849D+00
- <a name="l06339"></a>06339
- <a name="l06340"></a>06340 weight(1) = 0.0032951914D+00
- <a name="l06341"></a>06341 weight(2) = 0.0178429027D+00
- <a name="l06342"></a>06342 weight(3) = 0.0454393195D+00
- <a name="l06343"></a>06343 weight(4) = 0.0791995995D+00
- <a name="l06344"></a>06344 weight(5) = 0.1060473594D+00
- <a name="l06345"></a>06345 weight(6) = 0.1125057995D+00
- <a name="l06346"></a>06346 weight(7) = 0.0911190236D+00
- <a name="l06347"></a>06347 weight(8) = 0.0445508044D+00
- <a name="l06348"></a>06348
- <a name="l06349"></a>06349 <span class="keyword">else</span>
- <a name="l06350"></a>06350
- <a name="l06351"></a>06351 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l06352"></a>06352 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LEGENDRE_SET_X1_01 - Fatal error!'</span>
- <a name="l06353"></a>06353 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal value of NORDER = '</span>, norder
- <a name="l06354"></a>06354 stop
- <a name="l06355"></a>06355
- <a name="l06356"></a>06356 <span class="keyword">end if</span>
- <a name="l06357"></a>06357
- <a name="l06358"></a>06358 return
- <a name="l06359"></a>06359 <span class="keyword">end</span>
- <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 )
- <a name="l06361"></a>06361 <span class="comment">!</span>
- <a name="l06362"></a>06362 <span class="comment">!*******************************************************************************</span>
- <a name="l06363"></a>06363 <span class="comment">!</span>
- <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>
- <a name="l06365"></a>06365 <span class="comment">!</span>
- <a name="l06366"></a>06366 <span class="comment">!</span>
- <a name="l06367"></a>06367 <span class="comment">! Integration interval:</span>
- <a name="l06368"></a>06368 <span class="comment">!</span>
- <a name="l06369"></a>06369 <span class="comment">! [ -1, 1 ]</span>
- <a name="l06370"></a>06370 <span class="comment">!</span>
- <a name="l06371"></a>06371 <span class="comment">! Weight function:</span>
- <a name="l06372"></a>06372 <span class="comment">!</span>
- <a name="l06373"></a>06373 <span class="comment">! ( 1 + X )**2</span>
- <a name="l06374"></a>06374 <span class="comment">!</span>
- <a name="l06375"></a>06375 <span class="comment">! Integral to approximate:</span>
- <a name="l06376"></a>06376 <span class="comment">!</span>
- <a name="l06377"></a>06377 <span class="comment">! Integral ( -1 <= X <= 1 ) ( 1 + X )**2 * F(X) dX</span>
- <a name="l06378"></a>06378 <span class="comment">!</span>
- <a name="l06379"></a>06379 <span class="comment">! Approximate integral:</span>
- <a name="l06380"></a>06380 <span class="comment">!</span>
- <a name="l06381"></a>06381 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l06382"></a>06382 <span class="comment">!</span>
- <a name="l06383"></a>06383 <span class="comment">! Reference:</span>
- <a name="l06384"></a>06384 <span class="comment">!</span>
- <a name="l06385"></a>06385 <span class="comment">! Arthur Stroud and Don Secrest,</span>
- <a name="l06386"></a>06386 <span class="comment">! Gaussian Quadrature Formulas,</span>
- <a name="l06387"></a>06387 <span class="comment">! Prentice Hall, 1966, Table #3.</span>
- <a name="l06388"></a>06388 <span class="comment">!</span>
- <a name="l06389"></a>06389 <span class="comment">! Modified:</span>
- <a name="l06390"></a>06390 <span class="comment">!</span>
- <a name="l06391"></a>06391 <span class="comment">! 18 December 2000</span>
- <a name="l06392"></a>06392 <span class="comment">!</span>
- <a name="l06393"></a>06393 <span class="comment">! Author:</span>
- <a name="l06394"></a>06394 <span class="comment">!</span>
- <a name="l06395"></a>06395 <span class="comment">! John Burkardt</span>
- <a name="l06396"></a>06396 <span class="comment">!</span>
- <a name="l06397"></a>06397 <span class="comment">! Parameters:</span>
- <a name="l06398"></a>06398 <span class="comment">!</span>
- <a name="l06399"></a>06399 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l06400"></a>06400 <span class="comment">! NORDER must be between 1 and 9.</span>
- <a name="l06401"></a>06401 <span class="comment">!</span>
- <a name="l06402"></a>06402 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l06403"></a>06403 <span class="comment">!</span>
- <a name="l06404"></a>06404 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l06405"></a>06405 <span class="comment">!</span>
- <a name="l06406"></a>06406 <span class="keyword">implicit none</span>
- <a name="l06407"></a>06407 <span class="comment">!</span>
- <a name="l06408"></a>06408 <span class="keywordtype">integer</span> norder
- <a name="l06409"></a>06409 <span class="comment">!</span>
- <a name="l06410"></a>06410 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l06411"></a>06411 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l06412"></a>06412 <span class="comment">!</span>
- <a name="l06413"></a>06413 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l06414"></a>06414
- <a name="l06415"></a>06415 xtab(1) = 0.5D+00
- <a name="l06416"></a>06416
- <a name="l06417"></a>06417 weight(1) = 2.66666666666666666666666666666D+00
- <a name="l06418"></a>06418
- <a name="l06419"></a>06419 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l06420"></a>06420
- <a name="l06421"></a>06421 xtab(1) = -0.0883036880224505775998524725910D+00
- <a name="l06422"></a>06422 xtab(2) = 0.754970354689117244266519139258D+00
- <a name="l06423"></a>06423
- <a name="l06424"></a>06424 weight(1) = 0.806287056638603444666851075928D+00
- <a name="l06425"></a>06425 weight(2) = 1.86037961002806322199981559074D+00
- <a name="l06426"></a>06426
- <a name="l06427"></a>06427 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l06428"></a>06428
- <a name="l06429"></a>06429 xtab(1) = -0.410004419776996766244796955168D+00
- <a name="l06430"></a>06430 xtab(2) = 0.305992467923296230556472913192D+00
- <a name="l06431"></a>06431 xtab(3) = 0.854011951853700535688324041976D+00
- <a name="l06432"></a>06432
- <a name="l06433"></a>06433 weight(1) = 0.239605624068645584091811926047D+00
- <a name="l06434"></a>06434 weight(2) = 1.16997015407892817602809616291D+00
- <a name="l06435"></a>06435 weight(3) = 1.25709088851909290654675857771D+00
- <a name="l06436"></a>06436
- <a name="l06437"></a>06437 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l06438"></a>06438
- <a name="l06439"></a>06439 xtab(1) = -0.591702835793545726606755921586D+00
- <a name="l06440"></a>06440 xtab(2) = -0.0340945902087350046811467387661D+00
- <a name="l06441"></a>06441 xtab(3) = 0.522798524896275389882037174551D+00
- <a name="l06442"></a>06442 xtab(4) = 0.902998901106005341405865485802D+00
- <a name="l06443"></a>06443
- <a name="l06444"></a>06444 weight(1) = 0.0828179259993445222751812523731D+00
- <a name="l06445"></a>06445 weight(2) = 0.549071097383384602539010760334D+00
- <a name="l06446"></a>06446 weight(3) = 1.14767031839371367238662411421D+00
- <a name="l06447"></a>06447 weight(4) = 0.887107324890223869465850539752D+00
- <a name="l06448"></a>06448
- <a name="l06449"></a>06449 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l06450"></a>06450
- <a name="l06451"></a>06451 xtab(1) = -0.702108425894032836232448374820D+00
- <a name="l06452"></a>06452 xtab(2) = -0.268666945261773544694327777841D+00
- <a name="l06453"></a>06453 xtab(3) = 0.220227225868961343518209179230D+00
- <a name="l06454"></a>06454 xtab(4) = 0.653039358456608553790815164028D+00
- <a name="l06455"></a>06455 xtab(5) = 0.930842120163569816951085142737D+00
- <a name="l06456"></a>06456
- <a name="l06457"></a>06457 weight(1) = 0.0329106016247920636689299329544D+00
- <a name="l06458"></a>06458 weight(2) = 0.256444805783695354037991444453D+00
- <a name="l06459"></a>06459 weight(3) = 0.713601289772720001490035944563D+00
- <a name="l06460"></a>06460 weight(4) = 1.00959169519929190423066348132D+00
- <a name="l06461"></a>06461 weight(5) = 0.654118274286167343239045863379D+00
- <a name="l06462"></a>06462
- <a name="l06463"></a>06463 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l06464"></a>06464
- <a name="l06465"></a>06465 xtab(1) = -0.773611232355123732602532012021D+00
- <a name="l06466"></a>06466 xtab(2) = -0.431362254623427837535325249187D+00
- <a name="l06467"></a>06467 xtab(3) = -0.0180728263295041680220798103354D+00
- <a name="l06468"></a>06468 xtab(4) = 0.395126163954217534500188844163D+00
- <a name="l06469"></a>06469 xtab(5) = 0.736872116684029732026178298518D+00
- <a name="l06470"></a>06470 xtab(6) = 0.948190889812665614490712786006D+00
- <a name="l06471"></a>06471
- <a name="l06472"></a>06472 weight(1) = 0.0146486064549543818622276447204D+00
- <a name="l06473"></a>06473 weight(2) = 0.125762377479560410622810097040D+00
- <a name="l06474"></a>06474 weight(3) = 0.410316569036929681761034600615D+00
- <a name="l06475"></a>06475 weight(4) = 0.756617493988329628546336413760D+00
- <a name="l06476"></a>06476 weight(5) = 0.859011997894245060846045458784D+00
- <a name="l06477"></a>06477 weight(6) = 0.500309621812647503028212451747D+00
- <a name="l06478"></a>06478
- <a name="l06479"></a>06479 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 7 ) <span class="keyword">then</span>
- <a name="l06480"></a>06480
- <a name="l06481"></a>06481 xtab(1) = -0.822366333126005527278634734418D+00
- <a name="l06482"></a>06482 xtab(2) = -0.547034493182875002223997992852D+00
- <a name="l06483"></a>06483 xtab(3) = -0.200043026557985860387937545780D+00
- <a name="l06484"></a>06484 xtab(4) = 0.171995710805880507163425502299D+00
- <a name="l06485"></a>06485 xtab(5) = 0.518891747903884926692601716998D+00
- <a name="l06486"></a>06486 xtab(6) = 0.793821941703901970495546427988D+00
- <a name="l06487"></a>06487 xtab(7) = 0.959734452453198985538996625765D+00
- <a name="l06488"></a>06488
- <a name="l06489"></a>06489 weight(1) = 0.00714150426951365443207221475404D+00
- <a name="l06490"></a>06490 weight(2) = 0.0653034050584375560578544725498D+00
- <a name="l06491"></a>06491 weight(3) = 0.235377690316228918725962815880D+00
- <a name="l06492"></a>06492 weight(4) = 0.505171029671130381676271523850D+00
- <a name="l06493"></a>06493 weight(5) = 0.733870426238362032891332767175D+00
- <a name="l06494"></a>06494 weight(6) = 0.725590596901489156295739839779D+00
- <a name="l06495"></a>06495 weight(7) = 0.394212014211504966587433032679D+00
- <a name="l06496"></a>06496
- <a name="l06497"></a>06497 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 8 ) <span class="keyword">then</span>
- <a name="l06498"></a>06498
- <a name="l06499"></a>06499 xtab(1) = -0.857017929919813794402037235698D+00
- <a name="l06500"></a>06500 xtab(2) = -0.631543407166567521509503573952D+00
- <a name="l06501"></a>06501 xtab(3) = -0.339104543648722903660229021109D+00
- <a name="l06502"></a>06502 xtab(4) = -0.0111941563689783438801237300122D+00
- <a name="l06503"></a>06503 xtab(5) = 0.316696017045595559454075475675D+00
- <a name="l06504"></a>06504 xtab(6) = 0.609049663022520165351466780939D+00
- <a name="l06505"></a>06505 xtab(7) = 0.834198765028697794599267293239D+00
- <a name="l06506"></a>06506 xtab(8) = 0.967804480896157932935972899807D+00
- <a name="l06507"></a>06507
- <a name="l06508"></a>06508 weight(1) = 0.00374814227227757804631954025851D+00
- <a name="l06509"></a>06509 weight(2) = 0.0357961737041152639660521680263D+00
- <a name="l06510"></a>06510 weight(3) = 0.137974910241879862433949246199D+00
- <a name="l06511"></a>06511 weight(4) = 0.326515411108352185491692769217D+00
- <a name="l06512"></a>06512 weight(5) = 0.547577467373226177976217604887D+00
- <a name="l06513"></a>06513 weight(6) = 0.682278153375510121675529810121D+00
- <a name="l06514"></a>06514 weight(7) = 0.614544746137780998436053880546D+00
- <a name="l06515"></a>06515 weight(8) = 0.318231662453524478640851647411D+00
- <a name="l06516"></a>06516
- <a name="l06517"></a>06517 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 9 ) <span class="keyword">then</span>
- <a name="l06518"></a>06518
- <a name="l06519"></a>06519 xtab(1) = -0.882491728426548422828684254270D+00
- <a name="l06520"></a>06520 xtab(2) = -0.694873684026474640346360850039D+00
- <a name="l06521"></a>06521 xtab(3) = -0.446537143480670863635920316400D+00
- <a name="l06522"></a>06522 xtab(4) = -0.159388112702326252531544826624D+00
- <a name="l06523"></a>06523 xtab(5) = 0.141092709224374414981503995427D+00
- <a name="l06524"></a>06524 xtab(6) = 0.428217823321559204544020866175D+00
- <a name="l06525"></a>06525 xtab(7) = 0.676480966471850715860378175342D+00
- <a name="l06526"></a>06526 xtab(8) = 0.863830940812464825046988286026D+00
- <a name="l06527"></a>06527 xtab(9) = 0.973668228805771018909618924364D+00
- <a name="l06528"></a>06528
- <a name="l06529"></a>06529 weight(1) = 0.00209009877215570354392734918986D+00
- <a name="l06530"></a>06530 weight(2) = 0.0205951891648697848186537272448D+00
- <a name="l06531"></a>06531 weight(3) = 0.0832489326348178964194106978875D+00
- <a name="l06532"></a>06532 weight(4) = 0.210746247220398685903797568021D+00
- <a name="l06533"></a>06533 weight(5) = 0.388325022916052063676224499399D+00
- <a name="l06534"></a>06534 weight(6) = 0.554275165518437673725822282791D+00
- <a name="l06535"></a>06535 weight(7) = 0.621388553284444032628761363828D+00
- <a name="l06536"></a>06536 weight(8) = 0.523916296267173054255512857631D+00
- <a name="l06537"></a>06537 weight(9) = 0.262081160888317771694556320674D+00
- <a name="l06538"></a>06538
- <a name="l06539"></a>06539 <span class="keyword">else</span>
- <a name="l06540"></a>06540
- <a name="l06541"></a>06541 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">' '</span>
- <a name="l06542"></a>06542 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a)'</span> ) <span class="stringliteral">'LEGENDRE_SET_X2 - Fatal error!'</span>
- <a name="l06543"></a>06543 <span class="keyword">write</span> ( *, <span class="stringliteral">'(a,i6)'</span> ) <span class="stringliteral">' Illegal input value of NORDER = '</span>, norder
- <a name="l06544"></a>06544 stop
- <a name="l06545"></a>06545
- <a name="l06546"></a>06546 <span class="keyword">end if</span>
- <a name="l06547"></a>06547
- <a name="l06548"></a>06548 return
- <a name="l06549"></a>06549 <span class="keyword">end</span>
- <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 )
- <a name="l06551"></a>06551 <span class="comment">!</span>
- <a name="l06552"></a>06552 <span class="comment">!*******************************************************************************</span>
- <a name="l06553"></a>06553 <span class="comment">!</span>
- <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>
- <a name="l06555"></a>06555 <span class="comment">!</span>
- <a name="l06556"></a>06556 <span class="comment">!</span>
- <a name="l06557"></a>06557 <span class="comment">! Integration interval:</span>
- <a name="l06558"></a>06558 <span class="comment">!</span>
- <a name="l06559"></a>06559 <span class="comment">! [ 0, 1 ]</span>
- <a name="l06560"></a>06560 <span class="comment">!</span>
- <a name="l06561"></a>06561 <span class="comment">! Weight function:</span>
- <a name="l06562"></a>06562 <span class="comment">!</span>
- <a name="l06563"></a>06563 <span class="comment">! X**2</span>
- <a name="l06564"></a>06564 <span class="comment">!</span>
- <a name="l06565"></a>06565 <span class="comment">! Integral to approximate:</span>
- <a name="l06566"></a>06566 <span class="comment">!</span>
- <a name="l06567"></a>06567 <span class="comment">! Integral ( 0 <= X <= 1 ) X*X * F(X) dX</span>
- <a name="l06568"></a>06568 <span class="comment">!</span>
- <a name="l06569"></a>06569 <span class="comment">! Approximate integral:</span>
- <a name="l06570"></a>06570 <span class="comment">!</span>
- <a name="l06571"></a>06571 <span class="comment">! Sum ( 1 <= I <= NORDER ) WEIGHT(I) * F ( XTAB(I) )</span>
- <a name="l06572"></a>06572 <span class="comment">!</span>
- <a name="l06573"></a>06573 <span class="comment">! Reference:</span>
- <a name="l06574"></a>06574 <span class="comment">!</span>
- <a name="l06575"></a>06575 <span class="comment">! Abramowitz and Stegun,</span>
- <a name="l06576"></a>06576 <span class="comment">! Handbook of Mathematical Functions,</span>
- <a name="l06577"></a>06577 <span class="comment">! National Bureau of Standards, 1964, page 921.</span>
- <a name="l06578"></a>06578 <span class="comment">!</span>
- <a name="l06579"></a>06579 <span class="comment">! Modified:</span>
- <a name="l06580"></a>06580 <span class="comment">!</span>
- <a name="l06581"></a>06581 <span class="comment">! 18 November 2000</span>
- <a name="l06582"></a>06582 <span class="comment">!</span>
- <a name="l06583"></a>06583 <span class="comment">! Author:</span>
- <a name="l06584"></a>06584 <span class="comment">!</span>
- <a name="l06585"></a>06585 <span class="comment">! John Burkardt</span>
- <a name="l06586"></a>06586 <span class="comment">!</span>
- <a name="l06587"></a>06587 <span class="comment">! Parameters:</span>
- <a name="l06588"></a>06588 <span class="comment">!</span>
- <a name="l06589"></a>06589 <span class="comment">! Input, integer NORDER, the order of the rule.</span>
- <a name="l06590"></a>06590 <span class="comment">! NORDER must be between 1 and 8.</span>
- <a name="l06591"></a>06591 <span class="comment">!</span>
- <a name="l06592"></a>06592 <span class="comment">! Output, double precision XTAB(NORDER), the abscissas of the rule.</span>
- <a name="l06593"></a>06593 <span class="comment">!</span>
- <a name="l06594"></a>06594 <span class="comment">! Output, double precision WEIGHT(NORDER), the weights of the rule.</span>
- <a name="l06595"></a>06595 <span class="comment">!</span>
- <a name="l06596"></a>06596 <span class="keyword">implicit none</span>
- <a name="l06597"></a>06597 <span class="comment">!</span>
- <a name="l06598"></a>06598 <span class="keywordtype">integer</span> norder
- <a name="l06599"></a>06599 <span class="comment">!</span>
- <a name="l06600"></a>06600 <span class="keywordtype">double precision</span> xtab(norder)
- <a name="l06601"></a>06601 <span class="keywordtype">double precision</span> weight(norder)
- <a name="l06602"></a>06602 <span class="comment">!</span>
- <a name="l06603"></a>06603 <span class="keyword">if</span> ( norder == 1 ) <span class="keyword">then</span>
- <a name="l06604"></a>06604
- <a name="l06605"></a>06605 xtab(1) = 0.75D+00
- <a name="l06606"></a>06606
- <a name="l06607"></a>06607 weight(1) = 1.0D+00 / 3.0D+00
- <a name="l06608"></a>06608
- <a name="l06609"></a>06609 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 2 ) <span class="keyword">then</span>
- <a name="l06610"></a>06610
- <a name="l06611"></a>06611 xtab(1) = 0.4558481560D+00
- <a name="l06612"></a>06612 xtab(2) = 0.8774851773D+00
- <a name="l06613"></a>06613
- <a name="l06614"></a>06614 weight(1) = 0.1007858821D+00
- <a name="l06615"></a>06615 weight(2) = 0.2325474513D+00
- <a name="l06616"></a>06616
- <a name="l06617"></a>06617 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 3 ) <span class="keyword">then</span>
- <a name="l06618"></a>06618
- <a name="l06619"></a>06619 xtab(1) = 0.2949977901D+00
- <a name="l06620"></a>06620 xtab(2) = 0.6529962340D+00
- <a name="l06621"></a>06621 xtab(3) = 0.9270059759D+00
- <a name="l06622"></a>06622
- <a name="l06623"></a>06623 weight(1) = 0.0299507030D+00
- <a name="l06624"></a>06624 weight(2) = 0.1462462693D+00
- <a name="l06625"></a>06625 weight(3) = 0.1571363611D+00
- <a name="l06626"></a>06626
- <a name="l06627"></a>06627 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 4 ) <span class="keyword">then</span>
- <a name="l06628"></a>06628
- <a name="l06629"></a>06629 xtab(1) = 0.2041485821D+00
- <a name="l06630"></a>06630 xtab(2) = 0.4829527049D+00
- <a name="l06631"></a>06631 xtab(3) = 0.7613992624D+00
- <a name="l06632"></a>06632 xtab(4) = 0.9514994506D+00
- <a name="l06633"></a>06633
- <a name="l06634"></a>06634 weight(1) = 0.0103522408D+00
- <a name="l06635"></a>06635 weight(2) = 0.0686338872D+00
- <a name="l06636"></a>06636 weight(3) = 0.1434587898D+00
- <a name="l06637"></a>06637 weight(4) = 0.1108884156D+00
- <a name="l06638"></a>06638
- <a name="l06639"></a>06639 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 5 ) <span class="keyword">then</span>
- <a name="l06640"></a>06640
- <a name="l06641"></a>06641 xtab(1) = 0.1489457871D+00
- <a name="l06642"></a>06642 xtab(2) = 0.3656665274D+00
- <a name="l06643"></a>06643 xtab(3) = 0.6101136129D+00
- <a name="l06644"></a>06644 xtab(4) = 0.8265196792D+00
- <a name="l06645"></a>06645 xtab(5) = 0.9654210601D+00
- <a name="l06646"></a>06646
- <a name="l06647"></a>06647 weight(1) = 0.0041138252D+00
- <a name="l06648"></a>06648 weight(2) = 0.0320556007D+00
- <a name="l06649"></a>06649 weight(3) = 0.0892001612D+00
- <a name="l06650"></a>06650 weight(4) = 0.1261989619D+00
- <a name="l06651"></a>06651 weight(5) = 0.0817647843D+00
- <a name="l06652"></a>06652
- <a name="l06653"></a>06653 <span class="keyword">else</span> <span class="keyword">if</span> ( norder == 6 ) <span class="keyword">then</span>
- <a name="l06654"></a>06654
- <a name="l06655"></a>06655 xtab(1) = 0.1131943838D+00
- <a name="l06656"></a>06656 xtab(2) = 0.2843188727D+00
- <a name="l06657"></a>06657 xtab(3) = 0.4909635868D+00
- <a name="l06658"></a>06658 xtab(4) = 0.6975630820D+00
- <a name="l06659"></a>06659 xtab(5) = 0.8684360583D+00
- <a name="l06660"></a>06660 xtab(6) = 0.9740954449D+00
- <a name="l06661"></a>06661
- <a name="l06662"></a>06662 weight(1) = 0.0018310758D+00
- <a name="l06663"></a>06663 weight(2) = 0.0157202972D+00
- <a name="l06664"></a>06664