de.gsi.math.matrix

Class LUDecomposition

java.lang.Object

de.gsi.math.matrix.LUDecomposition

All Implemented Interfaces:

Serializable

public class LUDecomposition
extends Object
implements 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(MatrixD A) LU Decomposition

Method Summary

Modifier and Type	Method and Description
double	det() Determinant
double[]	getDoublePivot() Return pivot permutation vector as a one-dimensional double array
MatrixD	getL() Return lower triangular factor
int[]	getPivot() Return pivot permutation vector
MatrixD	getU() Return upper triangular factor
boolean	isNonsingular() Is the matrix nonsingular?
MatrixD	solve(MatrixD 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(MatrixD A)

LU Decomposition

Parameters:

A - Rectangular matrix Structure to access L, U and piv.

Method Detail

det

public double det()

Determinant

Returns:

det(A)

Throws:

IllegalArgumentException - Matrix must be square

getDoublePivot

public double[] getDoublePivot()

Return pivot permutation vector as a one-dimensional double array

Returns:

(double) piv

getL

public MatrixD getL()

Return lower triangular factor

Returns:

L

getPivot

public int[] getPivot()

Return pivot permutation vector

Returns:

piv

getU

public MatrixD getU()

Return upper triangular factor

Returns:

U

isNonsingular

public boolean isNonsingular()

Is the matrix nonsingular?

Returns:

true if U, and hence A, is nonsingular.

solve

public MatrixD solve(MatrixD 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.