de.lmu.ifi.dbs.elki.math.linearalgebra
Class LUDecomposition

java.lang.Object
  de.lmu.ifi.dbs.elki.math.linearalgebra.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

Field Summary

private double[][]	LU Array for internal storage of decomposition.
private int	m Row and column dimensions, and pivot sign.
private int	n Row and column dimensions, and pivot sign.
private int[]	piv Internal storage of pivot vector.
private int	pivsign Row and column dimensions, and pivot sign.
private static long	serialVersionUID Serial version

Constructor Summary

LUDecomposition(Matrix A)
LU Decomposition

Method Summary

double	det() Determinant
double[]	getDoublePivot() Return pivot permutation vector as a one-dimensional double array
Matrix	getL() Return lower triangular factor
int[]	getPivot() Return pivot permutation vector
Matrix	getU() Return upper triangular factor
boolean	isNonsingular() Is the matrix nonsingular?
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

Field Detail

serialVersionUID

private static final long serialVersionUID

Serial version

See Also:

Constant Field Values

LU

private double[][] LU

Array for internal storage of decomposition.

m

private int m

Row and column dimensions, and pivot sign.

n

private int n

Row and column dimensions, and pivot sign.

pivsign

private int pivsign

Row and column dimensions, and pivot sign.

piv

private int[] piv

Internal storage of pivot vector.

Constructor Detail

LUDecomposition

public LUDecomposition(Matrix 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 Matrix getL()

Return lower triangular factor

Returns:

L

getU

public Matrix getU()

Return upper triangular factor

Returns:

U

getPivot

public int[] getPivot()

Return pivot permutation vector

Returns:

piv

getDoublePivot

public double[] getDoublePivot()

Return pivot permutation vector as a one-dimensional double array

Returns:

(double) piv

det

public double det()

Determinant

Returns:

det(A)

Throws:

IllegalArgumentException - Matrix must be square

solve

public Matrix solve(Matrix 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.