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

Class LDL

java.lang.Object

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

All Implemented Interfaces:

java.io.Serializable

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

The LDL decomposition decomposes a real and symmetric (hence square) matrix A into A = L * D * L^t. L is a lower triangular matrix. D is a diagonal matrix. Unlike Cholesky decomposition, this decomposition applies to all real and symmetric matrices, whether positive definite or not. Moreover, when A is positive definite the elements of the diagonal matrix D are all positive. In other words, if A is semi/positive/negative definite, so is D. This algorithm eliminates the need to take square roots.

See Also:

Wikipedia: Avoiding taking square roots, Serialized Form

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
DiagonalMatrix	D() Get D the the diagonal matrix in the LDL decomposition.
LowerTriangularMatrix	L() Get L as in the LDL decomposition.
UpperTriangularMatrix	Lt() Get the transpose of L as in the LDL decomposition.

Methods inherited from class java.lang.Object

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

Constructor Detail

LDL

public LDL(Matrix A,
           double epsilon)

Run the LDL decomposition on a real and symmetric (hence square) matrix.

Parameters:

A - a real and symmetric (hence square) matrix

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

Throws:

java.lang.IllegalArgumentException - if A is not symmetric

LDL

public LDL(Matrix A)

Run the LDL decomposition on a real and symmetric (hence square) matrix.

Parameters:

A - a real and symmetric (hence square) matrix

Throws:

java.lang.IllegalArgumentException - if A is not symmetric

Method Detail

L

public LowerTriangularMatrix L()

Get L as in the LDL decomposition.

Returns:

L

Lt

public UpperTriangularMatrix Lt()

Get the transpose of L as in the LDL decomposition. The transpose is upper triangular.

Returns:

L'

D

public DiagonalMatrix D()

Get D the the diagonal matrix in the LDL decomposition.

Returns:

D