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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 22:46:13 EDT 2010 --> <META http-equiv="Content-Type" content="text/html; charset=UTF-8"> <TITLE> EigenDecompositionImpl (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="EigenDecompositionImpl (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/EigenDecompositionImpl.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/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear"><B>PREV CLASS</B></A> <A HREF="../../../../../org/apache/commons/math/linear/FieldDecompositionSolver.html" title="interface in org.apache.commons.math.linear"><B>NEXT CLASS</B></A></FONT></TD> <TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2"> <A HREF="../../../../../index.html?org/apache/commons/math/linear/EigenDecompositionImpl.html" target="_top"><B>FRAMES</B></A> <A HREF="EigenDecompositionImpl.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.linear</FONT> <BR> Class EigenDecompositionImpl</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.linear.EigenDecompositionImpl</B> </PRE> <DL> <DT><B>All Implemented Interfaces:</B> <DD><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></DD> </DL> <HR> <DL> <DT><PRE>public class <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.52"><B>EigenDecompositionImpl</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/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></DL> </PRE> <P> Calculates the eigen decomposition of a real <strong>symmetric</strong> matrix. <p> The eigen decomposition of matrix A is a set of two matrices: V and D such that A = V D V<sup>T</sup>. A, V and D are all m × m matrices. </p> <p> As of 2.0, this class supports only <strong>symmetric</strong> matrices, and hence computes only real realEigenvalues. This implies the D matrix returned by <A HREF="../../../../../org/apache/commons/math/linear/EigenDecompositionImpl.html#getD()"><CODE>getD()</CODE></A> is always diagonal and the imaginary values returned <A HREF="../../../../../org/apache/commons/math/linear/EigenDecompositionImpl.html#getImagEigenvalue(int)"><CODE>getImagEigenvalue(int)</CODE></A> and <A HREF="../../../../../org/apache/commons/math/linear/EigenDecompositionImpl.html#getImagEigenvalues()"><CODE>getImagEigenvalues()</CODE></A> are always null. </p> <p> When called with a <A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear"><CODE>RealMatrix</CODE></A> argument, this implementation only uses the upper part of the matrix, the part below the diagonal is not accessed at all. </p> <p> This implementation is based on the paper by A. Drubrulle, R.S. Martin and J.H. Wilkinson 'The Implicit QL Algorithm' in Wilksinson and Reinsch (1971) Handbook for automatic computation, vol. 2, Linear algebra, Springer-Verlag, New-York </p> <P> <P> <DL> <DT><B>Since:</B></DT> <DD>2.0</DD> <DT><B>Version:</B></DT> <DD>$Revision: 912413 $ $Date: 2010-02-21 16:46:12 -0500 (Sun, 21 Feb 2010) $</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/linear/EigenDecompositionImpl.html#EigenDecompositionImpl(double[], double[], double)">EigenDecompositionImpl</A></B>(double[] main, double[] secondary, double splitTolerance)</CODE> <BR> Calculates the eigen decomposition of the symmetric tridiagonal matrix.</TD> </TR> <TR BGCOLOR="white" CLASS="TableRowColor"> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/EigenDecompositionImpl.html#EigenDecompositionImpl(org.apache.commons.math.linear.RealMatrix, double)">EigenDecompositionImpl</A></B>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> matrix, double splitTolerance)</CODE> <BR> Calculates the eigen decomposition of the given symmetric matrix.</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/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/linear/EigenDecompositionImpl.html#getD()">getD</A></B>()</CODE> <BR> Returns the block diagonal matrix D of the decomposition.</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/linear/EigenDecompositionImpl.html#getDeterminant()">getDeterminant</A></B>()</CODE> <BR> Return the determinant of the 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/RealVector.html" title="interface in org.apache.commons.math.linear">RealVector</A></CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/EigenDecompositionImpl.html#getEigenvector(int)">getEigenvector</A></B>(int i)</CODE> <BR> Returns a copy of the i<sup>th</sup> eigenvector of the original 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/linear/EigenDecompositionImpl.html#getImagEigenvalue(int)">getImagEigenvalue</A></B>(int i)</CODE> <BR> Returns the imaginary part of the i<sup>th</sup> eigenvalue of the original 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/linear/EigenDecompositionImpl.html#getImagEigenvalues()">getImagEigenvalues</A></B>()</CODE> <BR> Returns a copy of the imaginary parts of the eigenvalues of the original 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/linear/EigenDecompositionImpl.html#getRealEigenvalue(int)">getRealEigenvalue</A></B>(int i)</CODE> <BR> Returns the real part of the i<sup>th</sup> eigenvalue of the original 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/linear/EigenDecompositionImpl.html#getRealEigenvalues()">getRealEigenvalues</A></B>()</CODE> <BR> Returns a copy of the real parts of the eigenvalues of the original 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/DecompositionSolver.html" title="interface in org.apache.commons.math.linear">DecompositionSolver</A></CODE></FONT></TD> <TD><CODE><B><A HREF="../../../../../org/apache/commons/math/linear/EigenDecompositionImpl.html#getSolver()">getSolver</A></B>()</CODE> <BR> Get a solver for finding the A × X = B solution in exact linear sense.</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/linear/EigenDecompositionImpl.html#getV()">getV</A></B>()</CODE> <BR> Returns the matrix V of the decomposition.</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/linear/EigenDecompositionImpl.html#getVT()">getVT</A></B>()</CODE> <BR> Returns the transpose of the matrix V of the decomposition.</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="EigenDecompositionImpl(org.apache.commons.math.linear.RealMatrix, double)"><!-- --></A><H3> EigenDecompositionImpl</H3> <PRE> public <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.95"><B>EigenDecompositionImpl</B></A>(<A HREF="../../../../../org/apache/commons/math/linear/RealMatrix.html" title="interface in org.apache.commons.math.linear">RealMatrix</A> matrix, double splitTolerance) throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></PRE> <DL> <DD>Calculates the eigen decomposition of the given symmetric matrix. <P> <DL> <DT><B>Parameters:</B><DD><CODE>matrix</CODE> - The <strong>symmetric</strong> matrix to decompose.<DD><CODE>splitTolerance</CODE> - dummy parameter, present for backward compatibility only. <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE> - (wrapping a <A HREF="../../../../../org/apache/commons/math/ConvergenceException.html" title="class in org.apache.commons.math"><CODE>ConvergenceException</CODE></A> if algorithm fails to converge</DL> </DL> <HR> <A NAME="EigenDecompositionImpl(double[], double[], double)"><!-- --></A><H3> EigenDecompositionImpl</H3> <PRE> public <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.119"><B>EigenDecompositionImpl</B></A>(double[] main, double[] secondary, double splitTolerance) throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></PRE> <DL> <DD>Calculates the eigen decomposition of the symmetric tridiagonal matrix. The Householder matrix is assumed to be the identity matrix. <P> <DL> <DT><B>Parameters:</B><DD><CODE>main</CODE> - Main diagonal of the symmetric triadiagonal form<DD><CODE>secondary</CODE> - Secondary of the tridiagonal form<DD><CODE>splitTolerance</CODE> - dummy parameter, present for backward compatibility only. <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE> - (wrapping a <A HREF="../../../../../org/apache/commons/math/ConvergenceException.html" title="class in org.apache.commons.math"><CODE>ConvergenceException</CODE></A> if algorithm fails to converge</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="getV()"><!-- --></A><H3> getV</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/linear/EigenDecompositionImpl.html#line.157"><B>getV</B></A>() throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></PRE> <DL> <DD>Returns the matrix V of the decomposition. <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p> <p>The columns of V are the eigenvectors of the original matrix.</p> <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getV()">getV</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>the V matrix <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE></DL> </DD> </DL> <HR> <A NAME="getD()"><!-- --></A><H3> getD</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/linear/EigenDecompositionImpl.html#line.172"><B>getD</B></A>() throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></PRE> <DL> <DD>Returns the block diagonal matrix D of the decomposition. <p>D is a block diagonal matrix.</p> <p>Real eigenvalues are on the diagonal while complex values are on 2x2 blocks { {real +imaginary}, {-imaginary, real} }.</p> <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getD()">getD</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>the D matrix <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE><DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getRealEigenvalues()"><CODE>EigenDecomposition.getRealEigenvalues()</CODE></A>, <A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getImagEigenvalues()"><CODE>EigenDecomposition.getImagEigenvalues()</CODE></A></DL> </DD> </DL> <HR> <A NAME="getVT()"><!-- --></A><H3> getVT</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/linear/EigenDecompositionImpl.html#line.181"><B>getVT</B></A>() throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></PRE> <DL> <DD>Returns the transpose of the matrix V of the decomposition. <p>V is an orthogonal matrix, i.e. its transpose is also its inverse.</p> <p>The columns of V are the eigenvectors of the original matrix.</p> <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getVT()">getVT</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>the transpose of the V matrix <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE></DL> </DD> </DL> <HR> <A NAME="getRealEigenvalues()"><!-- --></A><H3> getRealEigenvalues</H3> <PRE> public double[] <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.197"><B>getRealEigenvalues</B></A>() throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></PRE> <DL> <DD>Returns a copy of the real parts of the eigenvalues of the original matrix. <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getRealEigenvalues()">getRealEigenvalues</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>a copy of the real parts of the eigenvalues of the original matrix <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE><DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getD()"><CODE>EigenDecomposition.getD()</CODE></A>, <A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getRealEigenvalue(int)"><CODE>EigenDecomposition.getRealEigenvalue(int)</CODE></A>, <A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getImagEigenvalues()"><CODE>EigenDecomposition.getImagEigenvalues()</CODE></A></DL> </DD> </DL> <HR> <A NAME="getRealEigenvalue(int)"><!-- --></A><H3> getRealEigenvalue</H3> <PRE> public double <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.202"><B>getRealEigenvalue</B></A>(int i) throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/ArrayIndexOutOfBoundsException.html?is-external=true" title="class or interface in java.lang">ArrayIndexOutOfBoundsException</A></PRE> <DL> <DD>Returns the real part of the i<sup>th</sup> eigenvalue of the original matrix. <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getRealEigenvalue(int)">getRealEigenvalue</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Parameters:</B><DD><CODE>i</CODE> - index of the eigenvalue (counting from 0) <DT><B>Returns:</B><DD>real part of the i<sup>th</sup> eigenvalue of the original matrix <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE> <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/ArrayIndexOutOfBoundsException.html?is-external=true" title="class or interface in java.lang">ArrayIndexOutOfBoundsException</A></CODE><DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getD()"><CODE>EigenDecomposition.getD()</CODE></A>, <A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getRealEigenvalues()"><CODE>EigenDecomposition.getRealEigenvalues()</CODE></A>, <A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getImagEigenvalue(int)"><CODE>EigenDecomposition.getImagEigenvalue(int)</CODE></A></DL> </DD> </DL> <HR> <A NAME="getImagEigenvalues()"><!-- --></A><H3> getImagEigenvalues</H3> <PRE> public double[] <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.208"><B>getImagEigenvalues</B></A>() throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></PRE> <DL> <DD>Returns a copy of the imaginary parts of the eigenvalues of the original matrix. <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getImagEigenvalues()">getImagEigenvalues</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>a copy of the imaginary parts of the eigenvalues of the original matrix <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE><DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getD()"><CODE>EigenDecomposition.getD()</CODE></A>, <A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getImagEigenvalue(int)"><CODE>EigenDecomposition.getImagEigenvalue(int)</CODE></A>, <A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getRealEigenvalues()"><CODE>EigenDecomposition.getRealEigenvalues()</CODE></A></DL> </DD> </DL> <HR> <A NAME="getImagEigenvalue(int)"><!-- --></A><H3> getImagEigenvalue</H3> <PRE> public double <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.213"><B>getImagEigenvalue</B></A>(int i) throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/ArrayIndexOutOfBoundsException.html?is-external=true" title="class or interface in java.lang">ArrayIndexOutOfBoundsException</A></PRE> <DL> <DD>Returns the imaginary part of the i<sup>th</sup> eigenvalue of the original matrix. <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getImagEigenvalue(int)">getImagEigenvalue</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Parameters:</B><DD><CODE>i</CODE> - index of the eigenvalue (counting from 0) <DT><B>Returns:</B><DD>imaginary part of the i<sup>th</sup> eigenvalue of the original matrix <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE> <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/ArrayIndexOutOfBoundsException.html?is-external=true" title="class or interface in java.lang">ArrayIndexOutOfBoundsException</A></CODE><DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getD()"><CODE>EigenDecomposition.getD()</CODE></A>, <A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getImagEigenvalues()"><CODE>EigenDecomposition.getImagEigenvalues()</CODE></A>, <A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getRealEigenvalue(int)"><CODE>EigenDecomposition.getRealEigenvalue(int)</CODE></A></DL> </DD> </DL> <HR> <A NAME="getEigenvector(int)"><!-- --></A><H3> getEigenvector</H3> <PRE> public <A HREF="../../../../../org/apache/commons/math/linear/RealVector.html" title="interface in org.apache.commons.math.linear">RealVector</A> <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.219"><B>getEigenvector</B></A>(int i) throws <A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A>, <A HREF="http://java.sun.com/javase/6/docs/api/java/lang/ArrayIndexOutOfBoundsException.html?is-external=true" title="class or interface in java.lang">ArrayIndexOutOfBoundsException</A></PRE> <DL> <DD>Returns a copy of the i<sup>th</sup> eigenvector of the original matrix. <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getEigenvector(int)">getEigenvector</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Parameters:</B><DD><CODE>i</CODE> - index of the eigenvector (counting from 0) <DT><B>Returns:</B><DD>copy of the i<sup>th</sup> eigenvector of the original matrix <DT><B>Throws:</B> <DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/InvalidMatrixException.html" title="class in org.apache.commons.math.linear">InvalidMatrixException</A></CODE> <DD><CODE><A HREF="http://java.sun.com/javase/6/docs/api/java/lang/ArrayIndexOutOfBoundsException.html?is-external=true" title="class or interface in java.lang">ArrayIndexOutOfBoundsException</A></CODE><DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getD()"><CODE>EigenDecomposition.getD()</CODE></A></DL> </DD> </DL> <HR> <A NAME="getDeterminant()"><!-- --></A><H3> getDeterminant</H3> <PRE> public double <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.228"><B>getDeterminant</B></A>()</PRE> <DL> <DD>Return the determinant of the matrix <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getDeterminant()">getDeterminant</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>determinant of the matrix</DL> </DD> </DL> <HR> <A NAME="getSolver()"><!-- --></A><H3> getSolver</H3> <PRE> public <A HREF="../../../../../org/apache/commons/math/linear/DecompositionSolver.html" title="interface in org.apache.commons.math.linear">DecompositionSolver</A> <A HREF="../../../../../src-html/org/apache/commons/math/linear/EigenDecompositionImpl.html#line.237"><B>getSolver</B></A>()</PRE> <DL> <DD>Get a solver for finding the A × X = B solution in exact linear sense. <P> <DD><DL> <DT><B>Specified by:</B><DD><CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html#getSolver()">getSolver</A></CODE> in interface <CODE><A HREF="../../../../../org/apache/commons/math/linear/EigenDecomposition.html" title="interface in org.apache.commons.math.linear">EigenDecomposition</A></CODE></DL> </DD> <DD><DL> <DT><B>Returns:</B><DD>a solver</DL> </DD> </DL> 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