secholeskydecomposition.html
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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 1.5.0_13) on Mon Jul 14 01:36:31 CEST 2008 --><TITLE>SECholeskyDecomposition (RapidMiner Class Documentation)</TITLE><META NAME="keywords" CONTENT="com.rapidminer.operator.learner.functions.kernel.rvm.util.SECholeskyDecomposition class"><LINK REL ="stylesheet" TYPE="text/css" HREF="../../../../../../../../stylesheet.css" TITLE="Style"><SCRIPT type="text/javascript">function windowTitle(){ parent.document.title="SECholeskyDecomposition (RapidMiner Class Documentation)";}</SCRIPT><NOSCRIPT></NOSCRIPT></HEAD><BODY BGCOLOR="white" onload="windowTitle();"><!-- ========= 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/SECholeskyDecomposition.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"> PREV CLASS NEXT CLASS</FONT></TD><TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2"> <A HREF="../../../../../../../../index.html?com/rapidminer/operator/learner/functions/kernel/rvm/util/SECholeskyDecomposition.html" target="_top"><B>FRAMES</B></A> <A HREF="SECholeskyDecomposition.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">com.rapidminer.operator.learner.functions.kernel.rvm.util</FONT><BR>Class SECholeskyDecomposition</H2><PRE>java.lang.Object <IMG SRC="../../../../../../../../resources/inherit.gif" ALT="extended by "><B>com.rapidminer.operator.learner.functions.kernel.rvm.util.SECholeskyDecomposition</B></PRE><HR><DL><DT><PRE>public class <B>SECholeskyDecomposition</B><DT>extends java.lang.Object</DL></PRE><P>A modified cholesky factorization. Given a n x n matrix A this decomposition produces a matrix L, such that L * L' = A + E, with E being a minimal diagonal matrix making the sum of both matrices positive definite (and regular). In contrast to the standard cholesky decomposition (as implemented in e.g. Jama) the matrix A doesn't have to be regular and positive definite as often happens due to numerical instabilities. The determination of the diagonal elements of E is based on Gerschgorin's circle theorem minimizing ||E||_inf. The a-priori upper bound of ||E||_inf is linear in n; REFERENCES: Robert B. Schnabel and Elizabeth Eskow. 1990. "A New Modified Cholesky Factorization," SIAM Journal of Scientific Statistical Computating, 11, 6: 1136-58. Robert B. Schnabel and Elizabeth Eskow. 1999. "A revised modified Cholesky factorization algorithm," SIAM J. Optim., 9, 4: 1135--1148 (electronic) Jeff Gill and Gary King. 1998. "`Hessian not Invertable.' Help!" manuscript in progress, Harvard University.<P><P><DL><DT><B>Version:</B></DT> <DD>$Id: SECholeskyDecomposition.java,v 1.4 2008/05/09 20:57:26 ingomierswa Exp $</DD><DT><B>Author:</B></DT> <DD>Piotr Kasprzak</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="../../../../../../../../com/rapidminer/operator/learner/functions/kernel/rvm/util/SECholeskyDecomposition.html#SECholeskyDecomposition(double[][])">SECholeskyDecomposition</A></B>(double[][] A)</CODE><BR> Constructors.</TD></TR><TR BGCOLOR="white" CLASS="TableRowColor"><TD><CODE><B><A HREF="../../../../../../../../com/rapidminer/operator/learner/functions/kernel/rvm/util/SECholeskyDecomposition.html#SECholeskyDecomposition(Jama.Matrix)">SECholeskyDecomposition</A></B>(Jama.Matrix A)</CODE><BR> </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> double</CODE></FONT></TD><TD><CODE><B><A HREF="../../../../../../../../com/rapidminer/operator/learner/functions/kernel/rvm/util/SECholeskyDecomposition.html#getDetA()">getDetA</A></B>()</CODE><BR> Return the determinant of A.</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="../../../../../../../../com/rapidminer/operator/learner/functions/kernel/rvm/util/SECholeskyDecomposition.html#getDetL()">getDetL</A></B>()</CODE><BR> Return the determinant of L.</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="../../../../../../../../com/rapidminer/operator/learner/functions/kernel/rvm/util/SECholeskyDecomposition.html#getE_Diagonal()">getE_Diagonal</A></B>()</CODE><BR> Return the diagonal of error-matrix E with the pivoting still applied.</TD></TR><TR BGCOLOR="white" CLASS="TableRowColor"><TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"><CODE> Jama.Matrix</CODE></FONT></TD><TD><CODE><B><A HREF="../../../../../../../../com/rapidminer/operator/learner/functions/kernel/rvm/util/SECholeskyDecomposition.html#getE()">getE</A></B>()</CODE><BR> Return the error-matrix E with pivoting reversed.</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="../../../../../../../../com/rapidminer/operator/learner/functions/kernel/rvm/util/SECholeskyDecomposition.html#getENorm()">getENorm</A></B>()</CODE><BR> Return the infinity norm of matrix E.</TD></TR><TR BGCOLOR="white" CLASS="TableRowColor"><TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1"><CODE> Jama.Matrix</CODE></FONT></TD><TD><CODE><B><A HREF="../../../../../../../../com/rapidminer/operator/learner/functions/kernel/rvm/util/SECholeskyDecomposition.html#getL()">getL</A></B>()</CODE><BR> Return the lower triangle matrix factor of the cholesky decomposition.</TD></TR>⌨️ 快捷键说明
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