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

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.factorization.triangle.LDL

public class LDL
extends java.lang.Object

LDL decomposition decomposes a real and symmetric (hence square) matrix A into

 A = L %*% D %*% Lt
 

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

Constructor Summary

LDL(Matrix A)
Construct an instance of the LDL decomposition.

Method Summary

DiagonalMatrix	D() Get a copy of the diagonal matrix D as in A = L %*% D %*% Lt
LowerTriangularMatrix	L() Get a copy of the lower triangular matrix L as in A = L %*% D %*% Lt
UpperTriangularMatrix	Lt() Get a copy of the transpose of the lower triangular matrix L as in A = L %*% Lt The transpose is upper triangular.

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)

Construct an instance of the LDL decomposition.

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 a copy of the lower triangular matrix L as in A = L %*% D %*% Lt

Returns:

a copy of L

Lt

public UpperTriangularMatrix Lt()

Get a copy of the transpose of the lower triangular matrix L as in A = L %*% Lt

The transpose is upper triangular.

Returns:

a copy of Lt

D

public DiagonalMatrix D()

Get a copy of the diagonal matrix D as in A = L %*% D %*% Lt

Returns:

a copy of D