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

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

All Implemented Interfaces:

LUDecomposition

public class LU
extends java.lang.Object
implements LUDecomposition

LU decomposition of a matrix.

It decomposes an n x n matrix A so that

 P %*% A == L %*% U
 

where P is an n x n permutation matrix,
L is an n x n lower triangular matrix,
U is an n x n upper triangular matrix

That is,

 P.multiply(A) == L.multiply(U)
 

This decomposition can be used to

1. solve a system of linear equations
2. compute the determinant

See Also:

Wikipedia: LU decomposition

Nested Class Summary

static class

LU.Method the methods available to do the LU decomposition

Constructor Summary

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

LU(Matrix A, LU.Method method, double epsilon)
Construct an instance of the LU decomposition that uses Gaussian Elimination.

Method Summary

LowerTriangularMatrix	L() Get a copy of the lower triangular matrix L as in P %*% A == L %*% U
PermutationMatrix	P() Get a copy of the permutation matrix P as in P %*% A == L %*% U
UpperTriangularMatrix	U() Get a copy of the upper triangular matrix U as in P %*% A == L %*% U

Methods inherited from class java.lang.Object

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

Constructor Detail

LU

public LU(Matrix A,
          LU.Method method,
          double epsilon)

Construct an instance of the LU decomposition that uses Gaussian Elimination.

Parameters:

A - the matrix to be decomposed such that

P %*% A == L %*% U

method - the algorithm to do the LU decomposition

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

LU

public LU(Matrix A)

Construct an instance of the LU decomposition.

Parameters:

A - a matrix

Method Detail

L

public LowerTriangularMatrix L()

Description copied from interface: LUDecomposition

Get a copy of the lower triangular matrix L as in

P %*% A == L %*% U

Specified by:

L in interface LUDecomposition

Returns:

a copy of L

U

public UpperTriangularMatrix U()

Description copied from interface: LUDecomposition

Get a copy of the upper triangular matrix U as in

P %*% A == L %*% U

Specified by:

U in interface LUDecomposition

Returns:

a copy of U

P

public PermutationMatrix P()

Description copied from interface: LUDecomposition

Get a copy of the permutation matrix P as in

P %*% A == L %*% U

Specified by:

P in interface LUDecomposition

Returns:

a copy of P