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

Class CholeskyDecomposition

java.lang.Object

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

All Implemented Interfaces:

Serializable

public class CholeskyDecomposition
extends Object
implements Serializable

Cholesky Decomposition.

For a symmetric, positive definite matrix A, the Cholesky decomposition is an lower triangular matrix L so that A = L*L'.

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.

See Also:

Serialized Form

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.
private int	n Row and column dimension (square matrix).

Constructor Summary

Constructors

Constructor and Description
CholeskyDecomposition(Matrix Arg) Cholesky algorithm for symmetric and positive definite matrix.

Method Summary

Methods

Modifier and Type	Method and Description
Matrix	getL() Return triangular factor.
boolean	isSPD() Is the matrix symmetric and positive definite?
Matrix	solve(Matrix B) Solve A*X = B

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.

n

private int n

Row and column dimension (square matrix).

isspd

private boolean isspd

Symmetric and positive definite flag.

Constructor Detail

CholeskyDecomposition

public CholeskyDecomposition(Matrix Arg)

Cholesky algorithm for symmetric and positive definite matrix.

Parameters:

Arg - 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 Matrix getL()

Return triangular factor.

Returns:

L

solve

public Matrix solve(Matrix 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'*X = B

Throws:

IllegalArgumentException - Matrix row dimensions must agree.

RuntimeException - Matrix is not symmetric positive definite.