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  26. Cholesky decomposition class

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  27. For a symmetric, positive definite matrix A, the Cholesky decomposition

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  28. is an lower triangular matrix L so that A = L*L'</a></li>
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  29. <li><a href="../packages/JAMA%0D%0AClass%20to%20obtain%20eigenvalues%20and%20eigenvectors%20of%20a%20real%20matrix.html"><i class="icon-folder-open"></i> JAMA

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  30. Class to obtain eigenvalues and eigenvectors of a real matrix</a></li>
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  31. <li><a href="../packages/JAMA%0D%0AError%20handling.html"><i class="icon-folder-open"></i> JAMA

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  32. Error handling</a></li>
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  33. <li><a href="../packages/JAMA%0D%0AFor%20an%20m-by-n%20matrix%20A%20with%20m%20&gt;=%20n,%20the%20LU%20decomposition%20is%20an%20m-by-n%0D%0Aunit%20lower%20triangular%20matrix%20L,%20an%20n-by-n%20upper%20triangular%20matrix%20U,%0D%0Aand%20a%20permutation%20vector%20piv%20of%20length%20m%20so%20that%20A(piv,:)%20=%20L*U.html"><i class="icon-folder-open"></i> JAMA

    34. 

  34. For an m-by-n matrix A with m &gt;= n, the LU decomposition is an m-by-n

    35. 

  35. unit lower triangular matrix L, an n-by-n upper triangular matrix U,

    36. 

  36. and a permutation vector piv of length m so that A(piv,:) = L*U</a></li>
    37. 

  37. <li><a href="../packages/JAMA%0D%0AFor%20an%20m-by-n%20matrix%20A%20with%20m%20&gt;=%20n,%20the%20QR%20decomposition%20is%20an%20m-by-n%0D%0Aorthogonal%20matrix%20Q%20and%20an%20n-by-n%20upper%20triangular%20matrix%20R%20so%20that%0D%0AA%20=%20Q*R.html"><i class="icon-folder-open"></i> JAMA

    38. 

  38. For an m-by-n matrix A with m &gt;= n, the QR decomposition is an m-by-n

    39. 

  39. orthogonal matrix Q and an n-by-n upper triangular matrix R so that

    40. 

  40. A = Q*R</a></li>
    41. 

  41. <li><a href="../packages/JAMA%0D%0AFor%20an%20m-by-n%20matrix%20A%20with%20m%20&gt;=%20n,%20the%20singular%20value%20decomposition%20is%0D%0Aan%20m-by-n%20orthogonal%20matrix%20U,%20an%20n-by-n%20diagonal%20matrix%20S,%20and%0D%0Aan%20n-by-n%20orthogonal%20matrix%20V%20so%20that%20A%20=%20U*S*V'.html"><i class="icon-folder-open"></i> JAMA

    42. 

  42. For an m-by-n matrix A with m &gt;= n, the singular value decomposition is

    43. 

  43. an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and

    44. 

  44. an n-by-n orthogonal matrix V so that A = U*S*V'</a></li>
    45. 

  45. <li><a href="../packages/JAMA%0D%0APythagorean%20Theorem:%0D%0Aa%20=%203%0D%0Ab%20=%204%0D%0Ar%20=%20sqrt(square(a)%20+%20square(b))%0D%0Ar%20=%205%0D%0Ar%20=%20sqrt(a%5E2%20+%20b%5E2)%20without%20under.overflow.html"><i class="icon-folder-open"></i> JAMA

    46. 

  46. Pythagorean Theorem:

    47. 

  47. a = 3

    48. 

  48. b = 4

    49. 

  49. r = sqrt(square(a) + square(b))

    50. 

  50. r = 5

    51. 

  51. r = sqrt(a^2 + b^2) without under/overflow</a></li>
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  57.                                     Charts <b class="caret"></b></a><ul class="dropdown-menu"><li><a href="../graph_class.html"><i class="icon-list-alt"></i> Class hierarchy diagram</a></li></ul>
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  74.                 <span class="label label-info">12</span></a></li>
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  84.                             if Javascript is enabled.
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  85.                         </div></noscript>
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  88. <span class="btn-group visibility" data-toggle="buttons-checkbox"><button class="btn public active" title="Show public elements">Public</button><button class="btn protected" title="Show protected elements">Protected</button><button class="btn private" title="Show private elements">Private</button><button class="btn inherited active" title="Show inherited elements">Inherited</button></span><div class="btn-group view pull-right" data-toggle="buttons-radio">
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  93. <i class="icon-custom icon-method"></i> Methods
    94. 

  94.                     <ul>
    95. 

  95. <li class="method public "><a href="#method_clear" title="clear :: Clear the stack"><span class="description">Clear the stack</span><pre>clear()</pre></a></li>
    96. 

  96. <li class="method public "><a href="#method_count" title="count :: Return the number of entries on the stack"><span class="description">Return the number of entries on the stack</span><pre>count()</pre></a></li>
    97. 

  97. <li class="method public "><a href="#method_onStack" title="onStack :: Test to see if a specified entry exists on the stack"><span class="description">Test to see if a specified entry exists on the stack</span><pre>onStack()</pre></a></li>
    98. 

  98. <li class="method public "><a href="#method_pop" title="pop :: Pop the last entry from the stack"><span class="description">Pop the last entry from the stack</span><pre>pop()</pre></a></li>
    99. 

  99. <li class="method public "><a href="#method_push" title="push :: Push a new entry onto the stack"><span class="description">Push a new entry onto the stack</span><pre>push()</pre></a></li>
    100. 

  100. <li class="method public "><a href="#method_showStack" title="showStack :: Return an array of all entries on the stack"><span class="description">Return an array of all entries on the stack</span><pre>showStack()</pre></a></li>
    101. 

  101. </ul>
    102. 

  102. </li>
    103. 

  103. <li class="nav-header">
    104. 

  104. <i class="icon-custom icon-property"></i> Properties
    105. 

  105.                     <ul></ul>
    106. 

  106. </li>
    107. 

  107. <li class="nav-header private">» Private
    108. 

  108.                     <ul><li class="property private "><a href="#property__stack" title="$_stack :: The call stack for calculated cells"><span class="description"></span><pre>$_stack</pre></a></li></ul>
    109. 

  109. </li>
    110. 

  110. </ul>
    111. 

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    112. 

  112. <div class="span8">
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  113. <a id="\PHPExcel_CalcEngine_CyclicReferenceStack"></a><ul class="breadcrumb">
    114. 

  114. <li>
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  115. <a href="../index.html"><i class="icon-custom icon-class"></i></a><span class="divider">\</span>
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  119. <span class="divider">\</span><a href="../classes/PHPExcel_CalcEngine_CyclicReferenceStack.html">PHPExcel_CalcEngine_CyclicReferenceStack</a>
    120. 

  120. </li>
    121. 

  121. </ul>
    122. 

  122. <div class="element class">
    123. 

  123. <p class="short_description">PHPExcel_CalcEngine_CyclicReferenceStack</p>
    124. 

  124. <div class="details">
    125. 

  125. <div class="long_description"></div>
    126. 

  126. <table class="table table-bordered">
    127. 

  127. <tr>
    128. 

  128. <th>category</th>
    129. 

  129. <td>PHPExcel_CalcEngine_CyclicReferenceStack</td>
    130. 

  130. </tr>
    131. 

  131. <tr>
    132. 

  132. <th>package</th>
    133. 

  133. <td><a href="../packages/PHPExcel.Calculation.html">PHPExcel_Calculation</a></td>
    134. 

  134. </tr>
    135. 

  135. <tr>
    136. 

  136. <th>copyright</th>
    137. 

  137. <td>Copyright (c) 2006 - 2013 PHPExcel (http://www.codeplex.com/PHPExcel)</td>
    138. 

  138. </tr>
    139. 

  139. </table>
    140. 

  140. <h3>
    141. 

  141. <i class="icon-custom icon-method"></i> Methods</h3>
    142. 

  142. <a id="method_clear"></a><div class="element clickable method public method_clear" data-toggle="collapse" data-target=".method_clear .collapse">
    143. 

  143. <h2>Clear the stack</h2>
    144. 

  144. <pre>clear() </pre>
    145. 

  145. <div class="labels"></div>
    146. 

  146. <div class="row collapse"><div class="detail-description"><div class="long_description"></div></div></div>
    147. 

  147. </div>
    148. 

  148. <a id="method_count"></a><div class="element clickable method public method_count" data-toggle="collapse" data-target=".method_count .collapse">
    149. 

  149. <h2>Return the number of entries on the stack</h2>
    150. 

  150. <pre>count() : integer</pre>
    151. 

  151. <div class="labels"></div>
    152. 

  152. <div class="row collapse"><div class="detail-description">
    153. 

  153. <div class="long_description"></div>
    154. 

  154. <h3>Returns</h3>
    155. 

  155. <div class="subelement response"><code>integer</code></div>
    156. 

  156. </div></div>
    157. 

  157. </div>
    158. 

  158. <a id="method_onStack"></a><div class="element clickable method public method_onStack" data-toggle="collapse" data-target=".method_onStack .collapse">
    159. 

  159. <h2>Test to see if a specified entry exists on the stack</h2>
    160. 

  160. <pre>onStack(mixed $value) </pre>
    161. 

  161. <div class="labels"></div>
    162. 

  162. <div class="row collapse"><div class="detail-description">
    163. 

  163. <div class="long_description"></div>
    164. 

  164. <h3>Parameters</h3>
    165. 

  165. <div class="subelement argument">
    166. 

  166. <h4>$value</h4>
    167. 

  167. <code>mixed</code><p>The value to test</p></div>
    168. 

  168. </div></div>
    169. 

  169. </div>
    170. 

  170. <a id="method_pop"></a><div class="element clickable method public method_pop" data-toggle="collapse" data-target=".method_pop .collapse">
    171. 

  171. <h2>Pop the last entry from the stack</h2>
    172. 

  172. <pre>pop() : mixed</pre>
    173. 

  173. <div class="labels"></div>
    174. 

  174. <div class="row collapse"><div class="detail-description">
    175. 

  175. <div class="long_description"></div>
    176. 

  176. <h3>Returns</h3>
    177. 

  177. <div class="subelement response"><code>mixed</code></div>
    178. 

  178. </div></div>
    179. 

  179. </div>
    180. 

  180. <a id="method_push"></a><div class="element clickable method public method_push" data-toggle="collapse" data-target=".method_push .collapse">
    181. 

  181. <h2>Push a new entry onto the stack</h2>
    182. 

  182. <pre>push(mixed $value) </pre>
    183. 

  183. <div class="labels"></div>
    184. 

  184. <div class="row collapse"><div class="detail-description">
    185. 

  185. <div class="long_description"></div>
    186. 

  186. <h3>Parameters</h3>
    187. 

  187. <div class="subelement argument">
    188. 

  188. <h4>$value</h4>
    189. 

  189. <code>mixed</code>
    190. 

  190. </div>
    191. 

  191. </div></div>
    192. 

  192. </div>
    193. 

  193. <a id="method_showStack"></a><div class="element clickable method public method_showStack" data-toggle="collapse" data-target=".method_showStack .collapse">
    194. 

  194. <h2>Return an array of all entries on the stack</h2>
    195. 

  195. <pre>showStack() : mixed[]</pre>
    196. 

  196. <div class="labels"></div>
    197. 

  197. <div class="row collapse"><div class="detail-description">
    198. 

  198. <div class="long_description"></div>
    199. 

  199. <h3>Returns</h3>
    200. 

  200. <div class="subelement response"><code>mixed[]</code></div>
    201. 

  201. </div></div>
    202. 

  202. </div>
    203. 

  203. <h3>
    204. 

  204. <i class="icon-custom icon-property"></i> Properties</h3>
    205. 

  205. <a id="property__stack"> </a><div class="element clickable property private property__stack" data-toggle="collapse" data-target=".property__stack .collapse">
    206. 

  206. <h2></h2>
    207. 

  207. <pre>$_stack </pre>
    208. 

  208. <div class="labels"></div>
    209. 

  209. <div class="row collapse"><div class="detail-description"><div class="long_description"><p>@var mixed[]</p></div></div></div>
    210. 

  210. </div>
    211. 

  211. </div>
    212. 

  212. </div>
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  213. </div>
    214. 

  214. </div>
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    216. 

  216.             Template is built using <a href="http://twitter.github.com/bootstrap/">Twitter Bootstrap 2</a> and icons provided by <a href="http://glyphicons.com/">Glyphicons</a>.<br>
    217. 

  217.             Documentation is powered by <a href="http://www.phpdoc.org/">phpDocumentor 2.0.0a12</a> and<br>
    218. 

  218.             generated on 2013-06-02T15:42:47+01:00.<br></footer></div>
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