edu.northwestern.at.utils.math.matrix
Class LUDecomposition

java.lang.Object
  edu.northwestern.at.utils.math.matrix.LUDecomposition

public class LUDecomposition
extends java.lang.Object

LUDecomposition of a matrix using Crout/Dolittle algorithm.

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.

This is the JAMA implementation modified for use with our Matrix class.

Constructor Summary

LUDecomposition(Matrix a)
LU Decomposition using Crout/Dolittle algorithm.

Method Summary

double	det() Return determinant of matrix.
double[][]	getDoublePivot() Return pivot permutation vector as a one-dimensional array of doubles.
Matrix	getL() Return lower triangular factor.
int[]	getPivot() Return pivot permutation vector.
Matrix	getPivotMatrix() Return pivot permutation vector .
Matrix	getU() Return upper triangular factor.
boolean	isNonsingular() Is matrix nonsingular?
boolean	isSingular() Is matrix singular?
Matrix	solve(Matrix B) Solve A*X = B .

Methods inherited from class java.lang.Object

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

Constructor Detail

LUDecomposition

public LUDecomposition(Matrix a)

LU Decomposition using Crout/Dolittle algorithm.

Parameters:

a - Rectangular matrix

Method Detail

isNonsingular

public boolean isNonsingular()

Is matrix nonsingular?

Returns:

true if U, and hence A, is nonsingular.

isSingular

public boolean isSingular()

Is matrix singular?

Returns:

true if U, and hence A, is singular.

getL

public Matrix getL()

Return lower triangular factor.

Returns:

The lower triangular factor L.

getU

public Matrix getU()

Return upper triangular factor.

Returns:

The upper triangular factor U .

getPivot

public int[] getPivot()

Return pivot permutation vector.

Returns:

The pivor permutation vector.

getDoublePivot

public double[][] getDoublePivot()

Return pivot permutation vector as a one-dimensional array of doubles.

Returns:

Pivot array as doubles.

getPivotMatrix

public Matrix getPivotMatrix()

Return pivot permutation vector .

Returns:

Pivot permutation vector as a matrix with 1 column.

det

public double det()

Return determinant of matrix.

Returns:

Determinant of matrix which was decomposed.

Throws:

java.lang.IllegalArgumentException - If matrix is not square.

solve

public Matrix solve(Matrix B)

Solve A*X = B .

Parameters:

B - 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.