com.rapidminer.operator.learner.functions.kernel.rvm.util
Class SECholeskyDecomposition

java.lang.Object
  com.rapidminer.operator.learner.functions.kernel.rvm.util.SECholeskyDecomposition

public class SECholeskyDecomposition
extends java.lang.Object

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.

Author:

Piotr Kasprzak

Constructor Summary

SECholeskyDecomposition(double[][] A)
Constructors.

SECholeskyDecomposition(Jama.Matrix A)

Method Summary

double	getDetA() Return the determinant of A.
double	getDetL() Return the determinant of L.
double[]	getE_Diagonal() Return the diagonal of error-matrix E with the pivoting still applied.
Jama.Matrix	getE() Return the error-matrix E with pivoting reversed.
double	getENorm() Return the infinity norm of matrix E.
Jama.Matrix	getL() Return the lower triangle matrix factor of the cholesky decomposition.
Jama.Matrix	getPTR() Return the matrix PTR with PTR * (L * L') * PTR' = A + E.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SECholeskyDecomposition

public SECholeskyDecomposition(double[][] A)

Constructors.

Parameters:

A -

SECholeskyDecomposition

public SECholeskyDecomposition(Jama.Matrix A)

Method Detail

getL

public Jama.Matrix getL()

Return the lower triangle matrix factor of the cholesky decomposition.

getPTR

public Jama.Matrix getPTR()

Return the matrix PTR with PTR * (L * L') * PTR' = A + E.

getE_Diagonal

public double[] getE_Diagonal()

Return the diagonal of error-matrix E with the pivoting still applied.

getE

public Jama.Matrix getE()

Return the error-matrix E with pivoting reversed.

getENorm

public double getENorm()

Return the infinity norm of matrix E.

getDetL

public double getDetL()

Return the determinant of L.

getDetA

public double getDetA()

Return the determinant of A.