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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>
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Class to obtain eigenvalues and eigenvectors of a real matrix</a></li>
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For an m-by-n matrix A with m &gt;= n, the LU decomposition is an m-by-n
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and a permutation vector piv of length m so that A(piv,:) = L*U</a></li>
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For an m-by-n matrix A with m &gt;= n, the QR decomposition is an m-by-n
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For an m-by-n matrix A with m &gt;= 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>
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<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>
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<i class="icon-custom icon-property"></i> Properties
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<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>
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<span class="divider">\</span><a href="../classes/CholeskyDecomposition.html">CholeskyDecomposition</a>
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<div class="element class">
<p class="short_description"></p>
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<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>
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