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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <!--NewPage--> <HTML> <HEAD> <!-- Generated by javadoc (build 1.6.0_17) on Sat Mar 27 22:46:15 EDT 2010 --> <META http-equiv="Content-Type" content="text/html; charset=UTF-8"> <TITLE> CorrelatedRandomVectorGenerator (Commons Math 2.1 API) </TITLE> <META NAME="date" CONTENT="2010-03-27"> <LINK REL ="stylesheet" TYPE="text/css" HREF="../../../../../stylesheet.css" TITLE="Style"> <SCRIPT type="text/javascript"> function windowTitle() { if (location.href.indexOf('is-external=true') == -1) { parent.document.title="CorrelatedRandomVectorGenerator (Commons Math 2.1 API)"; } } </SCRIPT> <NOSCRIPT> </NOSCRIPT> </HEAD> <BODY BGCOLOR="white" onload="windowTitle();"> <HR> <!-- ========= START OF TOP NAVBAR ======= --> <A NAME="navbar_top"><!-- --></A> <A HREF="#skip-navbar_top" title="Skip navigation links"></A> <TABLE BORDER="0" WIDTH="100%" CELLPADDING="1" CELLSPACING="0" SUMMARY=""> <TR> <TD COLSPAN=2 BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A NAME="navbar_top_firstrow"><!-- --></A> <TABLE BORDER="0" CELLPADDING="0" CELLSPACING="3" SUMMARY=""> <TR ALIGN="center" VALIGN="top"> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="package-summary.html"><FONT CLASS="NavBarFont1"><B>Package</B></FONT></A> </TD> <TD BGCOLOR="#FFFFFF" CLASS="NavBarCell1Rev"> <FONT CLASS="NavBarFont1Rev"><B>Class</B></FONT> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="class-use/CorrelatedRandomVectorGenerator.html"><FONT CLASS="NavBarFont1"><B>Use</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="package-tree.html"><FONT CLASS="NavBarFont1"><B>Tree</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../deprecated-list.html"><FONT CLASS="NavBarFont1"><B>Deprecated</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../index-all.html"><FONT CLASS="NavBarFont1"><B>Index</B></FONT></A> </TD> <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1"> <A HREF="../../../../../help-doc.html"><FONT CLASS="NavBarFont1"><B>Help</B></FONT></A> </TD> </TR> </TABLE> </TD> <TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM> </EM> </TD> </TR> <TR> <TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2"> <A HREF="../../../../../org/apache/commons/math/random/BitsStreamGenerator.html" title="class in org.apache.commons.math.random"><B>PREV CLASS</B></A> <A HREF="../../../../../org/apache/commons/math/random/EmpiricalDistribution.html" title="interface in org.apache.commons.math.random"><B>NEXT CLASS</B></A></FONT></TD> <TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2"> <A HREF="../../../../../index.html?org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html" target="_top"><B>FRAMES</B></A> <A HREF="CorrelatedRandomVectorGenerator.html" target="_top"><B>NO FRAMES</B></A> <SCRIPT type="text/javascript"> <!-- if(window==top) { document.writeln('<A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>'); } //--> </SCRIPT> <NOSCRIPT> <A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A> </NOSCRIPT> </FONT></TD> </TR> <TR> <TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2"> SUMMARY: NESTED | FIELD | <A HREF="#constructor_summary">CONSTR</A> | <A HREF="#method_summary">METHOD</A></FONT></TD> <TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2"> DETAIL: FIELD | <A HREF="#constructor_detail">CONSTR</A> | <A HREF="#method_detail">METHOD</A></FONT></TD> </TR> </TABLE> <A NAME="skip-navbar_top"></A> <!-- ========= END OF TOP NAVBAR ========= --> <HR> <!-- ======== START OF CLASS DATA ======== --> <H2> <FONT SIZE="-1"> org.apache.commons.math.random</FONT> <BR> Class CorrelatedRandomVectorGenerator</H2> <PRE> <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A> <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math.random.CorrelatedRandomVectorGenerator</B> </PRE> <DL> <DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math.random">RandomVectorGenerator</A></DD> </DL> <HR> <DL> <DT><PRE>public class <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.62"><B>CorrelatedRandomVectorGenerator</B></A><DT>extends <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A><DT>implements <A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math.random">RandomVectorGenerator</A></DL> </PRE> <P> A <A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math.random"><CODE>RandomVectorGenerator</CODE></A> that generates vectors with with correlated components. <p>Random vectors with correlated components are built by combining the uncorrelated components of another random vector in such a way that the resulting correlations are the ones specified by a positive definite covariance matrix.</p> <p>The main use for correlated random vector generation is for Monte-Carlo simulation of physical problems with several variables, for example to generate error vectors to be added to a nominal vector. A particularly interesting case is when the generated vector should be drawn from a <a href="http://en.wikipedia.org/wiki/Multivariate_normal_distribution"> Multivariate Normal Distribution</a>. The approach using a Cholesky decomposition is quite usual in this case. However, it cas be extended to other cases as long as the underlying random generator provides <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random"><CODE>normalized values</CODE></A> like <A HREF="../../../../../org/apache/commons/math/random/GaussianRandomGenerator.html" title="class in org.apache.commons.math.random"><CODE>GaussianRandomGenerator</CODE></A> or <A HREF="../../../../../org/apache/commons/math/random/UniformRandomGenerator.html" title="class in org.apache.commons.math.random"><CODE>UniformRandomGenerator</CODE></A>.</p> <p>Sometimes, the covariance matrix for a given simulation is not strictly positive definite. This means that the correlations are not all independent from each other. In this case, however, the non strictly positive elements found during the Cholesky decomposition of the covariance matrix should not be negative either, they should be null. Another non-conventional extension handling this case is used here. Rather than computing <code>C = U<sup>T</sup>.U</code> where <code>C</code> is the covariance matrix and <code>U</code> is an uppertriangular matrix, we compute <code>C = B.B<sup>T</sup></code> where <code>B</code> is a rectangular matrix having more rows than columns. The number of columns of <code>B</code> is the rank of the covariance matrix, and it is the dimension of the uncorrelated random vector that is needed to compute the component of the correlated vector. This class handles this situation automatically.</p> <P> <P> <DL> <DT><B>Since:</B></DT> <DD>1.2</DD> <DT><B>Version:</B></DT> <DD>$Revision: 811827 $ $Date: 2009-09-06 11:32:50 -0400 (Sun, 06 Sep 2009) $</DD> </DL> <HR> <P> <!-- ======== CONSTRUCTOR SUMMARY ======== --> <A NAME="constructor_summary"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2"> <B>Constructor Summary</B></FONT></TH> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#CorrelatedRandomVectorGenerator(double[], org.apache.commons.math.linear.RealMatrix, double, org.apache.commons.math.random.NormalizedRandomGenerator)">CorrelatedRandomVectorGenerator</A></B>(double[] mean, <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> covariance, double small, <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> generator)</CODE> <BR> Simple constructor.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#CorrelatedRandomVectorGenerator(org.apache.commons.math.linear.RealMatrix, double, org.apache.commons.math.random.NormalizedRandomGenerator)">CorrelatedRandomVectorGenerator</A></B>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> covariance, double small, <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> generator)</CODE> <BR> Simple constructor.</TD> </TR> </TABLE> <!-- ========== METHOD SUMMARY =========== --> <A NAME="method_summary"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2"> <B>Method Summary</B></FONT></TH> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A></CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getGenerator()">getGenerator</A></B>()</CODE> <BR> Get the underlying normalized components generator.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> int</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getRank()">getRank</A></B>()</CODE> <BR> Get the rank of the covariance matrix.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A></CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getRootMatrix()">getRootMatrix</A></B>()</CODE> <BR> Get the root of the covariance matrix.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"> <CODE> double[]</CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#nextVector()">nextVector</A></B>()</CODE> <BR> Generate a correlated random vector.</TD> </TR> </TABLE> <A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor"> <TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://java.sun.com/javase/6/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://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD> </TR> </TABLE> <P> <!-- ========= CONSTRUCTOR DETAIL ======== --> <A NAME="constructor_detail"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2"> <B>Constructor Detail</B></FONT></TH> </TR> </TABLE> <A NAME="CorrelatedRandomVectorGenerator(double[], org.apache.commons.math.linear.RealMatrix, double, org.apache.commons.math.random.NormalizedRandomGenerator)"><!-- --></A><H3> CorrelatedRandomVectorGenerator</H3> <PRE> public <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.96"><B>CorrelatedRandomVectorGenerator</B></A>(double[] mean, <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> covariance, double small, <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> generator) throws <A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A>, <A HREF="../../../../../org/apache/commons/math/DimensionMismatchException.html" title="class in org.apache.commons.math">DimensionMismatchException</A></PRE> <DL> <DD>Simple constructor. <p>Build a correlated random vector generator from its mean vector and covariance matrix.</p> <P> <DL> <DT><B>Parameters:</B><DD><CODE>mean</CODE> - expected mean values for all components<DD><CODE>covariance</CODE> - covariance matrix<DD><CODE>small</CODE> - diagonal elements threshold under which column are considered to be dependent on previous ones and are discarded<DD><CODE>generator</CODE> - underlying generator for uncorrelated normalized components <DT><B>Throws:</B> <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</A></CODE> - if there is a dimension mismatch between the mean vector and the covariance matrix <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></CODE> - if the covariance matrix is not strictly positive definite <DD><CODE><A HREF="../../../../../org/apache/commons/math/DimensionMismatchException.html" title="class in org.apache.commons.math">DimensionMismatchException</A></CODE> - if the mean and covariance arrays dimensions don't match</DL> </DL> <HR> <A NAME="CorrelatedRandomVectorGenerator(org.apache.commons.math.linear.RealMatrix, double, org.apache.commons.math.random.NormalizedRandomGenerator)"><!-- --></A><H3> CorrelatedRandomVectorGenerator</H3> <PRE> public <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.125"><B>CorrelatedRandomVectorGenerator</B></A>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> covariance, double small, <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> generator) throws <A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></PRE> <DL> <DD>Simple constructor. <p>Build a null mean random correlated vector generator from its covariance matrix.</p> <P> <DL> <DT><B>Parameters:</B><DD><CODE>covariance</CODE> - covariance matrix<DD><CODE>small</CODE> - diagonal elements threshold under which column are considered to be dependent on previous ones and are discarded<DD><CODE>generator</CODE> - underlying generator for uncorrelated normalized components <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/NotPositiveDefiniteMatrixException.html" title="class in org.apache.commons.math.linear">NotPositiveDefiniteMatrixException</A></CODE> - if the covariance matrix is not strictly positive definite</DL> </DL> <!-- ============ METHOD DETAIL ========== --> <A NAME="method_detail"><!-- --></A> <TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""> <TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"> <TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2"> <B>Method Detail</B></FONT></TH> </TR> </TABLE> <A NAME="getGenerator()"><!-- --></A><H3> getGenerator</H3> <PRE> public <A HREF="../../../../../org/apache/commons/math/random/NormalizedRandomGenerator.html" title="interface in org.apache.commons.math.random">NormalizedRandomGenerator</A> <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.145"><B>getGenerator</B></A>()</PRE> <DL> <DD>Get the underlying normalized components generator. <P> <DD><DL> </DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>underlying uncorrelated components generator</DL> </DD> </DL> <HR> <A NAME="getRootMatrix()"><!-- --></A><H3> getRootMatrix</H3> <PRE> public <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.155"><B>getRootMatrix</B></A>()</PRE> <DL> <DD>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> <P> <DD><DL> </DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>root of the square matrix<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getRank()"><CODE>getRank()</CODE></A></DL> </DD> </DL> <HR> <A NAME="getRank()"><!-- --></A><H3> getRank</H3> <PRE> public int <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.166"><B>getRank</B></A>()</PRE> <DL> <DD>Get the rank of the covariance matrix. The rank is the number of independent rows in the covariance matrix, it is also the number of columns of the rectangular matrix of the decomposition. <P> <DD><DL> </DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>rank of the square matrix.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#getRootMatrix()"><CODE>getRootMatrix()</CODE></A></DL> </DD> </DL> <HR> <A NAME="nextVector()"><!-- --></A><H3> nextVector</H3> <PRE> public double[] <A HREF="../../../../../src-html/org/apache/commons/math/random/CorrelatedRandomVectorGenerator.html#line.283"><B>nextVector</B></A>()</PRE> <DL> <DD>Generate a correlated random vector. <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html#nextVector()">nextVector</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/random/RandomVectorGenerator.html" title="interface in org.apache.commons.math.random">RandomVectorGenerator</A></CODE></DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>a random vector as an array of double. 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