init
This commit is contained in:
@@ -0,0 +1,250 @@
|
||||
<!DOCTYPE html><html lang="en">
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
|
||||
<meta name="viewport" content="width=device-width; initial-scale=1.0; maximum-scale=1.0; user-scalable=0;">
|
||||
<meta charset="utf-8">
|
||||
<title>PHPExcel classes » \CholeskyDecomposition</title>
|
||||
<meta name="author" content="Mike van Riel">
|
||||
<meta name="description" content="">
|
||||
<link href="../css/template.css" rel="stylesheet" media="all">
|
||||
<script src="../js/jquery-1.7.1.min.js" type="text/javascript"></script><script src="../js/jquery-ui-1.8.2.custom.min.js" type="text/javascript"></script><script src="../js/jquery.mousewheel.min.js" type="text/javascript"></script><script src="../js/bootstrap.js" type="text/javascript"></script><script src="../js/template.js" type="text/javascript"></script><script src="../js/prettify/prettify.min.js" type="text/javascript"></script><link rel="shortcut icon" href="../img/favicon.ico">
|
||||
<link rel="apple-touch-icon" href="../img/apple-touch-icon.png">
|
||||
<link rel="apple-touch-icon" sizes="72x72" href="../img/apple-touch-icon-72x72.png">
|
||||
<link rel="apple-touch-icon" sizes="114x114" href="../img/apple-touch-icon-114x114.png">
|
||||
</head>
|
||||
<body>
|
||||
<div class="navbar navbar-fixed-top">
|
||||
<div class="navbar-inner"><div class="container">
|
||||
<a class="btn btn-navbar" data-toggle="collapse" data-target=".nav-collapse"><span class="icon-bar"></span><span class="icon-bar"></span><span class="icon-bar"></span></a><a class="brand" href="../index.html">PHPExcel classes</a><div class="nav-collapse"><ul class="nav">
|
||||
<li class="dropdown">
|
||||
<a href="#api" class="dropdown-toggle" data-toggle="dropdown">
|
||||
API Documentation <b class="caret"></b></a><ul class="dropdown-menu">
|
||||
<li><a>Packages</a></li>
|
||||
<li><a href="../packages/Default.html"><i class="icon-folder-open"></i> Default</a></li>
|
||||
<li><a href="../packages/JAMA.html"><i class="icon-folder-open"></i> JAMA</a></li>
|
||||
<li><a href="../packages/JAMA%0D%0ACholesky%20decomposition%20class%0D%0AFor%20a%20symmetric,%20positive%20definite%20matrix%20A,%20the%20Cholesky%20decomposition%0D%0Ais%20an%20lower%20triangular%20matrix%20L%20so%20that%20A%20=%20L*L'.html"><i class="icon-folder-open"></i> JAMA
|
||||
Cholesky decomposition class
|
||||
For a symmetric, positive definite matrix A, the Cholesky decomposition
|
||||
is an lower triangular matrix L so that A = L*L'</a></li>
|
||||
<li><a href="../packages/JAMA%0D%0AClass%20to%20obtain%20eigenvalues%20and%20eigenvectors%20of%20a%20real%20matrix.html"><i class="icon-folder-open"></i> JAMA
|
||||
Class to obtain eigenvalues and eigenvectors of a real matrix</a></li>
|
||||
<li><a href="../packages/JAMA%0D%0AError%20handling.html"><i class="icon-folder-open"></i> JAMA
|
||||
Error handling</a></li>
|
||||
<li><a href="../packages/JAMA%0D%0AFor%20an%20m-by-n%20matrix%20A%20with%20m%20>=%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
|
||||
For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n
|
||||
unit lower triangular matrix L, an n-by-n upper triangular matrix U,
|
||||
and a permutation vector piv of length m so that A(piv,:) = L*U</a></li>
|
||||
<li><a href="../packages/JAMA%0D%0AFor%20an%20m-by-n%20matrix%20A%20with%20m%20>=%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
|
||||
For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n
|
||||
orthogonal matrix Q and an n-by-n upper triangular matrix R so that
|
||||
A = Q*R</a></li>
|
||||
<li><a href="../packages/JAMA%0D%0AFor%20an%20m-by-n%20matrix%20A%20with%20m%20>=%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
|
||||
For an m-by-n matrix A with m >= n, the singular value decomposition is
|
||||
an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
|
||||
an n-by-n orthogonal matrix V so that A = U*S*V'</a></li>
|
||||
<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
|
||||
Pythagorean Theorem:
|
||||
a = 3
|
||||
b = 4
|
||||
r = sqrt(square(a) + square(b))
|
||||
r = 5
|
||||
r = sqrt(a^2 + b^2) without under/overflow</a></li>
|
||||
<li><a href="../packages/PHPExcel.html"><i class="icon-folder-open"></i> PHPExcel</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="dropdown" id="charts-menu">
|
||||
<a href="#charts" class="dropdown-toggle" data-toggle="dropdown">
|
||||
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>
|
||||
</li>
|
||||
<li class="dropdown" id="reports-menu">
|
||||
<a href="#reports" class="dropdown-toggle" data-toggle="dropdown">
|
||||
Reports <b class="caret"></b></a><ul class="dropdown-menu">
|
||||
<li><a href="../errors.html"><i class="icon-remove-sign"></i> Errors
|
||||
<span class="label label-info">551</span></a></li>
|
||||
<li><a href="../markers.html"><i class="icon-map-marker"></i> Markers
|
||||
<ul>
|
||||
<li>todo
|
||||
<span class="label label-info">19</span>
|
||||
</li>
|
||||
<li>fixme
|
||||
<span class="label label-info">10</span>
|
||||
</li>
|
||||
</ul></a></li>
|
||||
<li><a href="../deprecated.html"><i class="icon-stop"></i> Deprecated elements
|
||||
<span class="label label-info">12</span></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul></div>
|
||||
</div></div>
|
||||
<div class="go_to_top"><a href="#___" style="color: inherit">Back to top <i class="icon-upload icon-white"></i></a></div>
|
||||
</div>
|
||||
<div id="___" class="container">
|
||||
<noscript><div class="alert alert-warning">
|
||||
Javascript is disabled; several features are only available
|
||||
if Javascript is enabled.
|
||||
</div></noscript>
|
||||
<div class="row">
|
||||
<div class="span4">
|
||||
<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">
|
||||
<button class="btn details" title="Show descriptions and method names"><i class="icon-list"></i></button><button class="btn simple" title="Show only method names"><i class="icon-align-justify"></i></button>
|
||||
</div>
|
||||
<ul class="side-nav nav nav-list">
|
||||
<li class="nav-header">
|
||||
<i class="icon-custom icon-method"></i> Methods
|
||||
<ul>
|
||||
<li class="method public "><a href="#method___construct" title="__construct :: CholeskyDecomposition"><span class="description">CholeskyDecomposition</span><pre>__construct()</pre></a></li>
|
||||
<li class="method public "><a href="#method_getL" title="getL :: getL"><span class="description">getL</span><pre>getL()</pre></a></li>
|
||||
<li class="method public "><a href="#method_isSPD" title="isSPD :: Is the matrix symmetric and positive definite?"><span class="description">Is the matrix symmetric and positive definite?</span><pre>isSPD()</pre></a></li>
|
||||
<li class="method public "><a href="#method_solve" title="solve :: Solve A*X = B"><span class="description">Solve A*X = B</span><pre>solve()</pre></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="nav-header">
|
||||
<i class="icon-custom icon-property"></i> Properties
|
||||
<ul></ul>
|
||||
</li>
|
||||
<li class="nav-header private">» Private
|
||||
<ul>
|
||||
<li class="property private "><a href="#property_L" title="$L :: Decomposition storage"><span class="description"></span><pre>$L</pre></a></li>
|
||||
<li class="property private "><a href="#property_isspd" title="$isspd :: Symmetric positive definite flag"><span class="description"></span><pre>$isspd</pre></a></li>
|
||||
<li class="property private "><a href="#property_m" title="$m :: Matrix row and column dimension"><span class="description"></span><pre>$m</pre></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
<div class="span8">
|
||||
<a id="\CholeskyDecomposition"></a><ul class="breadcrumb">
|
||||
<li>
|
||||
<a href="../index.html"><i class="icon-custom icon-class"></i></a><span class="divider">\</span>
|
||||
</li>
|
||||
<li><a href="../namespaces/global.html">global</a></li>
|
||||
<li class="active">
|
||||
<span class="divider">\</span><a href="../classes/CholeskyDecomposition.html">CholeskyDecomposition</a>
|
||||
</li>
|
||||
</ul>
|
||||
<div class="element class">
|
||||
<p class="short_description"></p>
|
||||
<div class="details">
|
||||
<div class="long_description"></div>
|
||||
<table class="table table-bordered">
|
||||
<tr>
|
||||
<th>package</th>
|
||||
<td><a href="../packages/JAMA%0D%0ACholesky%20decomposition%20class%0D%0AFor%20a%20symmetric,%20positive%20definite%20matrix%20A,%20the%20Cholesky%20decomposition%0D%0Ais%20an%20lower%20triangular%20matrix%20L%20so%20that%20A%20=%20L*L'.%0D%0AIf%20the%20matrix%20is%20not%20symmetric%20or%20positive%20definite,%20the%20constructor%0D%0Areturns%20a%20partial%20decomposition%20and%20sets%20an%20internal%20flag%20that%20may%0D%0Abe%20queried%20by%20the%20isSPD()%20method..html">JAMA
|
||||
Cholesky decomposition class
|
||||
For a symmetric, positive definite matrix A, the Cholesky decomposition
|
||||
is an lower triangular matrix L so that A = L*L'.
|
||||
If the matrix is not symmetric or positive definite, the constructor
|
||||
returns a partial decomposition and sets an internal flag that may
|
||||
be queried by the isSPD() method.</a></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<th>author</th>
|
||||
<td><a href="">Paul Meagher</a></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<th>author</th>
|
||||
<td><a href="">Michael Bommarito</a></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<th>version</th>
|
||||
<td>1.2</td>
|
||||
</tr>
|
||||
</table>
|
||||
<h3>
|
||||
<i class="icon-custom icon-method"></i> Methods</h3>
|
||||
<a id="method___construct"></a><div class="element clickable method public method___construct" data-toggle="collapse" data-target=".method___construct .collapse">
|
||||
<h2>CholeskyDecomposition</h2>
|
||||
<pre>__construct(mixed $A) </pre>
|
||||
<div class="labels"></div>
|
||||
<div class="row collapse"><div class="detail-description">
|
||||
<div class="long_description"><p>Class constructor - decomposes symmetric positive definite matrix</p></div>
|
||||
<h3>Parameters</h3>
|
||||
<div class="subelement argument">
|
||||
<h4>$A</h4>
|
||||
<code>mixed</code><p>Matrix square symmetric positive definite matrix</p></div>
|
||||
</div></div>
|
||||
</div>
|
||||
<a id="method_getL"></a><div class="element clickable method public method_getL" data-toggle="collapse" data-target=".method_getL .collapse">
|
||||
<h2>getL</h2>
|
||||
<pre>getL() : \Matrix</pre>
|
||||
<div class="labels"></div>
|
||||
<div class="row collapse"><div class="detail-description">
|
||||
<div class="long_description"><p>Return triangular factor.</p></div>
|
||||
<h3>Returns</h3>
|
||||
<div class="subelement response">
|
||||
<code>\Matrix</code>Lower triangular matrix</div>
|
||||
</div></div>
|
||||
</div>
|
||||
<a id="method_isSPD"></a><div class="element clickable method public method_isSPD" data-toggle="collapse" data-target=".method_isSPD .collapse">
|
||||
<h2>Is the matrix symmetric and positive definite?</h2>
|
||||
<pre>isSPD() : boolean</pre>
|
||||
<div class="labels"></div>
|
||||
<div class="row collapse"><div class="detail-description">
|
||||
<div class="long_description"></div>
|
||||
<h3>Returns</h3>
|
||||
<div class="subelement response"><code>boolean</code></div>
|
||||
</div></div>
|
||||
</div>
|
||||
<a id="method_solve"></a><div class="element clickable method public method_solve" data-toggle="collapse" data-target=".method_solve .collapse">
|
||||
<h2>Solve A*X = B</h2>
|
||||
<pre>solve($B) : \Matrix</pre>
|
||||
<div class="labels"></div>
|
||||
<div class="row collapse"><div class="detail-description">
|
||||
<div class="long_description"></div>
|
||||
<h3>Parameters</h3>
|
||||
<div class="subelement argument">
|
||||
<h4>$B</h4><p>Row-equal matrix</p>
|
||||
</div>
|
||||
<h3>Returns</h3>
|
||||
<div class="subelement response">
|
||||
<code>\Matrix</code>L * L' * X = B</div>
|
||||
</div></div>
|
||||
</div>
|
||||
<h3>
|
||||
<i class="icon-custom icon-property"></i> Properties</h3>
|
||||
<a id="property_L"> </a><div class="element clickable property private property_L" data-toggle="collapse" data-target=".property_L .collapse">
|
||||
<h2></h2>
|
||||
<pre>$L : array</pre>
|
||||
<div class="labels"></div>
|
||||
<div class="row collapse"><div class="detail-description">
|
||||
<div class="long_description"></div>
|
||||
<table class="table table-bordered"><tr>
|
||||
<th>access</th>
|
||||
<td>private</td>
|
||||
</tr></table>
|
||||
</div></div>
|
||||
</div>
|
||||
<a id="property_isspd"> </a><div class="element clickable property private property_isspd" data-toggle="collapse" data-target=".property_isspd .collapse">
|
||||
<h2></h2>
|
||||
<pre>$isspd : boolean</pre>
|
||||
<div class="labels"></div>
|
||||
<div class="row collapse"><div class="detail-description">
|
||||
<div class="long_description"></div>
|
||||
<table class="table table-bordered"><tr>
|
||||
<th>access</th>
|
||||
<td>private</td>
|
||||
</tr></table>
|
||||
</div></div>
|
||||
</div>
|
||||
<a id="property_m"> </a><div class="element clickable property private property_m" data-toggle="collapse" data-target=".property_m .collapse">
|
||||
<h2></h2>
|
||||
<pre>$m : int</pre>
|
||||
<div class="labels"></div>
|
||||
<div class="row collapse"><div class="detail-description">
|
||||
<div class="long_description"></div>
|
||||
<table class="table table-bordered"><tr>
|
||||
<th>access</th>
|
||||
<td>private</td>
|
||||
</tr></table>
|
||||
</div></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="row"><footer class="span12">
|
||||
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>
|
||||
Documentation is powered by <a href="http://www.phpdoc.org/">phpDocumentor 2.0.0a12</a> and<br>
|
||||
generated on 2014-03-02T15:27:36Z.<br></footer></div>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
Reference in New Issue
Block a user