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diff --git a/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html new file mode 100644 index 0000000..28adf14 --- /dev/null +++ b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html @@ -0,0 +1,340 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<!-- NewPage --> +<html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<title>RectangularCholeskyDecomposition (Apache Commons Math 3.6.1 API)</title> +<link rel="stylesheet" type="text/css" href="../../../../../stylesheet.css" title="Style"> +</head> +<body> +<script type="text/javascript"><!-- + if (location.href.indexOf('is-external=true') == -1) { + parent.document.title="RectangularCholeskyDecomposition (Apache Commons Math 3.6.1 API)"; + } +//--> +</script> +<noscript> +<div>JavaScript is disabled on your browser.</div> +</noscript> +<!-- ========= START OF TOP NAVBAR ======= --> +<div class="topNav"><a name="navbar_top"> +<!-- --> +</a><a href="#skip-navbar_top" title="Skip navigation links"></a><a name="navbar_top_firstrow"> +<!-- --> +</a> +<ul class="navList" title="Navigation"> +<li><a href="../../../../../overview-summary.html">Overview</a></li> +<li><a href="package-summary.html">Package</a></li> +<li class="navBarCell1Rev">Class</li> +<li><a href="class-use/RectangularCholeskyDecomposition.html">Use</a></li> +<li><a href="package-tree.html">Tree</a></li> +<li><a href="../../../../../deprecated-list.html">Deprecated</a></li> +<li><a href="../../../../../index-all.html">Index</a></li> +<li><a href="../../../../../help-doc.html">Help</a></li> +</ul> +<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> +</div> +<div class="subNav"> +<ul class="navList"> +<li><a href="../../../../../org/apache/commons/math3/linear/RealVectorPreservingVisitor.html" title="interface in org.apache.commons.math3.linear"><span class="strong">Prev Class</span></a></li> +<li><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html" title="class in org.apache.commons.math3.linear"><span class="strong">Next Class</span></a></li> +</ul> +<ul class="navList"> +<li><a href="../../../../../index.html?org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html" target="_top">Frames</a></li> +<li><a href="RectangularCholeskyDecomposition.html" target="_top">No Frames</a></li> +</ul> +<ul class="navList" id="allclasses_navbar_top"> +<li><a href="../../../../../allclasses-noframe.html">All Classes</a></li> +</ul> +<div> +<script type="text/javascript"><!-- + allClassesLink = document.getElementById("allclasses_navbar_top"); + if(window==top) { + allClassesLink.style.display = "block"; + } + else { + allClassesLink.style.display = "none"; + } + //--> +</script> +</div> +<div> +<ul class="subNavList"> +<li>Summary: </li> +<li>Nested | </li> +<li>Field | </li> +<li><a href="#constructor_summary">Constr</a> | </li> +<li><a href="#method_summary">Method</a></li> +</ul> +<ul class="subNavList"> +<li>Detail: </li> +<li>Field | </li> +<li><a href="#constructor_detail">Constr</a> | </li> +<li><a href="#method_detail">Method</a></li> +</ul> +</div> +<a name="skip-navbar_top"> +<!-- --> +</a></div> +<!-- ========= END OF TOP NAVBAR ========= --> +<!-- ======== START OF CLASS DATA ======== --> +<div class="header"> +<div class="subTitle">org.apache.commons.math3.linear</div> +<h2 title="Class RectangularCholeskyDecomposition" class="title">Class RectangularCholeskyDecomposition</h2> +</div> +<div class="contentContainer"> +<ul class="inheritance"> +<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li> +<li> +<ul class="inheritance"> +<li>org.apache.commons.math3.linear.RectangularCholeskyDecomposition</li> +</ul> +</li> +</ul> +<div class="description"> +<ul class="blockList"> +<li class="blockList"> +<hr> +<br> +<pre>public class <span class="strong">RectangularCholeskyDecomposition</span> +extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre> +<div class="block">Calculates the rectangular Cholesky decomposition of a matrix. + <p>The rectangular Cholesky decomposition of a real symmetric positive + semidefinite matrix A consists of a rectangular matrix B with the same + number of rows such that: A is almost equal to BB<sup>T</sup>, depending + on a user-defined tolerance. In a sense, this is the square root of A.</p> + <p>The difference with respect to the regular <a href="../../../../../org/apache/commons/math3/linear/CholeskyDecomposition.html" title="class in org.apache.commons.math3.linear"><code>CholeskyDecomposition</code></a> + is that rows/columns may be permuted (hence the rectangular shape instead + of the traditional triangular shape) and there is a threshold to ignore + small diagonal elements. This is used for example to generate <a href="../../../../../org/apache/commons/math3/random/CorrelatedRandomVectorGenerator.html" title="class in org.apache.commons.math3.random"><code>correlated + random n-dimensions vectors</code></a> in a p-dimension subspace (p < n). + In other words, it allows generating random vectors from a covariance + matrix that is only positive semidefinite, and not positive definite.</p> + <p>Rectangular Cholesky decomposition is <em>not</em> suited for solving + linear systems, so it does not provide any <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear"><code>decomposition solver</code></a>.</p></div> +<dl><dt><span class="strong">Since:</span></dt> + <dd>2.0 (changed to concrete class in 3.0)</dd> +<dt><span class="strong">See Also:</span></dt><dd><a href="http://mathworld.wolfram.com/CholeskyDecomposition.html">MathWorld</a>, +<a href="http://en.wikipedia.org/wiki/Cholesky_decomposition">Wikipedia</a></dd></dl> +</li> +</ul> +</div> +<div class="summary"> +<ul class="blockList"> +<li class="blockList"> +<!-- ======== CONSTRUCTOR SUMMARY ======== --> +<ul class="blockList"> +<li class="blockList"><a name="constructor_summary"> +<!-- --> +</a> +<h3>Constructor Summary</h3> +<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Constructor Summary table, listing constructors, and an explanation"> +<caption><span>Constructors</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colOne" scope="col">Constructor and Description</th> +</tr> +<tr class="altColor"> +<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#RectangularCholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)">RectangularCholeskyDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix)</code> +<div class="block">Decompose a symmetric positive semidefinite matrix.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#RectangularCholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix,%20double)">RectangularCholeskyDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix, + double small)</code> +<div class="block">Decompose a symmetric positive semidefinite matrix.</div> +</td> +</tr> +</table> +</li> +</ul> +<!-- ========== METHOD SUMMARY =========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_summary"> +<!-- --> +</a> +<h3>Method Summary</h3> +<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation"> +<caption><span>Methods</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colFirst" scope="col">Modifier and Type</th> +<th class="colLast" scope="col">Method and Description</th> +</tr> +<tr class="altColor"> +<td class="colFirst"><code>int</code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRank()">getRank</a></strong>()</code> +<div class="block">Get the rank of the symmetric positive semidefinite matrix.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRootMatrix()">getRootMatrix</a></strong>()</code> +<div class="block">Get the root of the covariance matrix.</div> +</td> +</tr> +</table> +<ul class="blockList"> +<li class="blockList"><a name="methods_inherited_from_class_java.lang.Object"> +<!-- --> +</a> +<h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3> +<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li> +</ul> +</li> +</ul> +</li> +</ul> +</div> +<div class="details"> +<ul class="blockList"> +<li class="blockList"> +<!-- ========= CONSTRUCTOR DETAIL ======== --> +<ul class="blockList"> +<li class="blockList"><a name="constructor_detail"> +<!-- --> +</a> +<h3>Constructor Detail</h3> +<a name="RectangularCholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>RectangularCholeskyDecomposition</h4> +<pre>public RectangularCholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix) + throws <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></pre> +<div class="block">Decompose a symmetric positive semidefinite matrix. + <p> + <b>Note:</b> this constructor follows the linpack method to detect dependent + columns by proceeding with the Cholesky algorithm until a nonpositive diagonal + element is encountered.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Symmetric positive semidefinite matrix.</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if the matrix is not + positive semidefinite.</dd><dt><span class="strong">Since:</span></dt> + <dd>3.1</dd> +<dt><span class="strong">See Also:</span></dt><dd><a href="http://eprints.ma.man.ac.uk/1193/01/covered/MIMS_ep2008_56.pdf"> + Analysis of the Cholesky Decomposition of a Semi-definite Matrix</a></dd></dl> +</li> +</ul> +<a name="RectangularCholeskyDecomposition(org.apache.commons.math3.linear.RealMatrix, double)"> +<!-- --> +</a> +<ul class="blockListLast"> +<li class="blockList"> +<h4>RectangularCholeskyDecomposition</h4> +<pre>public RectangularCholeskyDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> matrix, + double small) + throws <a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></pre> +<div class="block">Decompose a symmetric positive semidefinite matrix.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - Symmetric positive semidefinite matrix.</dd><dd><code>small</code> - Diagonal elements threshold under which columns are + considered to be dependent on previous ones and are discarded.</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../org/apache/commons/math3/linear/NonPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math3.linear">NonPositiveDefiniteMatrixException</a></code> - if the matrix is not + positive semidefinite.</dd></dl> +</li> +</ul> +</li> +</ul> +<!-- ============ METHOD DETAIL ========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_detail"> +<!-- --> +</a> +<h3>Method Detail</h3> +<a name="getRootMatrix()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getRootMatrix</h4> +<pre>public <a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a> getRootMatrix()</pre> +<div class="block">Get the root of the covariance matrix. + The root is the rectangular matrix <code>B</code> such that + the covariance matrix is equal to <code>B.B<sup>T</sup></code></div> +<dl><dt><span class="strong">Returns:</span></dt><dd>root of the square matrix</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRank()"><code>getRank()</code></a></dd></dl> +</li> +</ul> +<a name="getRank()"> +<!-- --> +</a> +<ul class="blockListLast"> +<li class="blockList"> +<h4>getRank</h4> +<pre>public int getRank()</pre> +<div class="block">Get the rank of the symmetric positive semidefinite matrix. + The r is the number of independent rows in the symmetric positive semidefinite + matrix, it is also the number of columns of the rectangular + matrix of the decomposition.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>r of the square matrix.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/RectangularCholeskyDecomposition.html#getRootMatrix()"><code>getRootMatrix()</code></a></dd></dl> +</li> +</ul> +</li> +</ul> +</li> +</ul> +</div> +</div> +<!-- ========= END OF CLASS DATA ========= --> +<!-- ======= START OF BOTTOM NAVBAR ====== --> +<div class="bottomNav"><a name="navbar_bottom"> +<!-- --> +</a><a href="#skip-navbar_bottom" title="Skip navigation links"></a><a name="navbar_bottom_firstrow"> +<!-- --> +</a> +<ul class="navList" title="Navigation"> +<li><a href="../../../../../overview-summary.html">Overview</a></li> +<li><a href="package-summary.html">Package</a></li> +<li class="navBarCell1Rev">Class</li> +<li><a href="class-use/RectangularCholeskyDecomposition.html">Use</a></li> +<li><a href="package-tree.html">Tree</a></li> +<li><a href="../../../../../deprecated-list.html">Deprecated</a></li> +<li><a href="../../../../../index-all.html">Index</a></li> +<li><a href="../../../../../help-doc.html">Help</a></li> 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