jhplot.math

Class LUDecomposition

java.lang.Object

jhplot.math.LUDecomposition

public class LUDecomposition
extends Object

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. In other words, assuming P the permutation Matrix, P*A = L*U. If m < n, then L is m-by-m and U is m-by-n.

The LU decomposition 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.

Constructor Summary

Constructors

Constructor and Description
LUDecomposition(double[][] A) LU Decomposition

Method Summary

Modifier and Type	Method and Description
double	det() Determinant
double[][]	getL() Return lower triangular factor
double[][]	getP() Return pivot permutation vector
double[][]	getU() Return upper triangular factor
boolean	isNonsingular() Is the matrix nonsingular?
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[][] A)

LU Decomposition

Parameters:

A - Rectangular matrix

Method Detail

isNonsingular

public boolean isNonsingular()

Is the matrix nonsingular?

Returns:

true if U, and hence A, is nonsingular.

getL

public double[][] getL()

Return lower triangular factor

Returns:

L

getU

public double[][] getU()

Return upper triangular factor

Returns:

U

getP

public double[][] getP()

Return pivot permutation vector

Returns:

piv

det

public double det()

Determinant

Returns:

det(A)

Throws:

IllegalArgumentException - Matrix must be square

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:

IllegalArgumentException - Matrix row dimensions must agree.

RuntimeException - Matrix is singular.