Catalano.Math.Decompositions

Class LUDecomposition

java.lang.Object

Catalano.Math.Decompositions.LUDecomposition

All Implemented Interfaces:

java.io.Serializable

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

LU Decomposition.

For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.

The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
LUDecomposition(double[][] matrix) Initializes a new instance of the LUDecomposition class.

Method Summary

Modifier and Type	Method and Description
double	determinant() Calculate the determinant.
double[]	getDoublePivot() Get the pivot permutation vector as double type.
double[][]	getL() Get the Lower triangular factor.
int[]	getPivot() Get the pivot permutation vector.
double[][]	getU() Get the Upper triangular factor.
double[][]	inverse() Matrix inverse or pseudoinverse.
boolean	isNonsingular() Check if the matrix is non singular.
double[][]	solve(double[][] B) Solve A*X = B

Methods inherited from class java.lang.Object

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

Constructor Detail

LUDecomposition

public LUDecomposition(double[][] matrix)

Initializes a new instance of the LUDecomposition class.

Parameters:

matrix - Matrix.

Method Detail

isNonsingular

public boolean isNonsingular()

Check if the matrix is non singular.

Returns:

True if U, and hence A, is nonsingular.

inverse

public double[][] inverse()

Matrix inverse or pseudoinverse.

Returns:

Matrix inverse.

getL

public double[][] getL()

Get the Lower triangular factor.

Returns:

L.

getU

public double[][] getU()

Get the Upper triangular factor.

Returns:

U.

getPivot

public int[] getPivot()

Get the pivot permutation vector.

Returns:

Pivot.

getDoublePivot

public double[] getDoublePivot()

Get the pivot permutation vector as double type.

Returns:

Pivot.

determinant

public double determinant()

Calculate the determinant.

Returns:

Determinant.

solve

public double[][] solve(double[][] 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*U*X = B(piv,:)

Throws:

java.lang.IllegalArgumentException - Matrix row dimensions must agree.

java.lang.RuntimeException - Matrix is singular.