com.numericalmethod.suanshu.matrix.doubles.factorization.triangle

Class Cholesky

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.factorization.triangle.Cholesky

All Implemented Interfaces:

java.io.Serializable

public class Cholesky
extends java.lang.Object
implements java.io.Serializable

Cholesky decomposition decomposes a real, symmetric (hence square), and positive definite matrix A into A = L * L^t, where L is a lower triangular matrix. For any real, symmetric, positive definite matrix, there is a unique Cholesky decomposition, such that L's diagonal entries are all positive. This implementation uses the Cholesky-Crout algorithm, which starts from the upper left corner of the matrix L and proceeds to calculate the matrix row by row.

See Also:

Wikipedia: Cholesky decomposition, Serialized Form

Constructor Summary

Constructors

Constructor and Description
Cholesky(Matrix A) Run the Cholesky decomposition on a real, symmetric (hence square), and positive definite matrix.
Cholesky(Matrix A, double epsilon) Run the Cholesky decomposition on a real, symmetric (hence square), and positive definite matrix.

Method Summary

Modifier and Type	Method and Description
LowerTriangularMatrix	L() Get the lower triangular matrix L.
UpperTriangularMatrix	Lt() Get the transpose of the lower triangular matrix, L'.

Methods inherited from class java.lang.Object

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

Constructor Detail

Cholesky

public Cholesky(Matrix A,
                double epsilon)

Run the Cholesky decomposition on a real, symmetric (hence square), and positive definite matrix.

Parameters:

A - a real, symmetric (hence square), and positive definite matrix

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

Throws:

java.lang.IllegalArgumentException - if A is not symmetric

java.lang.RuntimeException - if A is not positive definite matrix

Cholesky

public Cholesky(Matrix A)

Run the Cholesky decomposition on a real, symmetric (hence square), and positive definite matrix.

Parameters:

A - a real, symmetric (hence square), and positive definite matrix

Throws:

java.lang.IllegalArgumentException - if A is not symmetric

java.lang.RuntimeException - if A is not positive definite matrix

Method Detail

L

public LowerTriangularMatrix L()

Get the lower triangular matrix L.

Returns:

L

Lt

public UpperTriangularMatrix Lt()

Get the transpose of the lower triangular matrix, L'. The transpose is upper triangular.

Returns:

L'