de.lmu.ifi.dbs.elki.math.linearalgebra

Class CholeskyDecomposition

java.lang.Object

de.lmu.ifi.dbs.elki.math.linearalgebra.CholeskyDecomposition

public class CholeskyDecomposition
extends java.lang.Object

Cholesky Decomposition. For a symmetric, positive definite matrix A, the Cholesky decomposition is an lower triangular matrix L so that A = L*L^T. If the matrix is not symmetric or positive definite, the constructor returns a partial decomposition and sets an internal flag that may be queried by the isSPD() method.

Since:

0.1

Author:

Arthur Zimek

Field Summary

Fields

Modifier and Type	Field and Description
private boolean	isspd Symmetric and positive definite flag.
private double[][]	L Array for internal storage of decomposition.

Constructor Summary

Constructors

Constructor and Description
CholeskyDecomposition(double[][] A) Cholesky algorithm for symmetric and positive definite matrix.

Method Summary

Modifier and Type	Method and Description
double[][]	getL() Return triangular factor.
boolean	isSPD() Is the matrix symmetric and positive definite?
double[]	solve(double[] b) Solve A*X = b
double[][]	solve(double[][] B) Solve A*X = B
private double[][]	solveL(double[][] X) Solve L*Y = B
double[]	solveLInplace(double[] X) Solve L*X = b, modifying X.
private double[]	solveLtransposed(double[] X) Solve L^T*X = Y
private double[][]	solveLtransposed(double[][] X) Solve L^T*X = Y

Methods inherited from class java.lang.Object

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

Field Detail

L

private double[][] L

Array for internal storage of decomposition.

isspd

private boolean isspd

Symmetric and positive definite flag.

Constructor Detail

CholeskyDecomposition

public CholeskyDecomposition(double[][] A)

Cholesky algorithm for symmetric and positive definite matrix.

Parameters:

A - Square, symmetric matrix.

Method Detail

isSPD

public boolean isSPD()

Is the matrix symmetric and positive definite?

Returns:

true if A is symmetric and positive definite.

getL

public double[][] getL()

Return triangular factor.

Returns:

L

solve

public double[][] solve(double[][] B)

Solve A*X = B

Parameters:

B - A Matrix with as many rows as A and any number of columns.

Returns:

X so that L*L^T*X = B

Throws:

java.lang.IllegalArgumentException - Matrix row dimensions must agree.

java.lang.RuntimeException - Matrix is not symmetric positive definite.

solveL

private double[][] solveL(double[][] X)

Solve L*Y = B

Parameters:

X - Copy of B.

Returns:

X

solveLtransposed

private double[][] solveLtransposed(double[][] X)

Solve L^T*X = Y

Parameters:

X - Solution of L*Y=B

Returns:

X

solve

public double[] solve(double[] b)

Solve A*X = b

Parameters:

b - A column vector with as many rows as A.

Returns:

X so that L*L^T*X = b

Throws:

java.lang.IllegalArgumentException - Matrix row dimensions must agree.

java.lang.RuntimeException - Matrix is not symmetric positive definite.

solveLInplace

public double[] solveLInplace(double[] X)

Solve L*X = b, modifying X.

Parameters:

X - Copy of b.

Returns:

X

solveLtransposed

private double[] solveLtransposed(double[] X)

Solve L^T*X = Y

Parameters:

X - Solution of L*Y=b

Returns:

X