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

Class LUDecomposition

java.lang.Object

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

Since:

0.1

Author:

Arthur Zimek

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
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

Constructors

Constructor and Description
LUDecomposition(double[][] LU) LU Decomposition
LUDecomposition(double[][] LU, int m, int n) LU Decomposition

Method Summary

Modifier and Type	Method and Description
double	det() Determinant
double[][]	getL() Return lower triangular factor
int[]	getPivot() Return pivot permutation vector
double[][]	getU() Return upper triangular factor
double[][]	inverse() Find the inverse matrix.
boolean	isNonsingular() Is the matrix nonsingular?
double[]	solve(double[] b) Solve A*X = b
double[][]	solve(double[][] B) Solve A*X = B
double[]	solveInplace(double[] b) Solve A*X = b
private double[][]	solveInplace(double[][] 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(double[][] LU)

LU Decomposition

Parameters:

LU - Rectangular matrix

LUDecomposition

public LUDecomposition(double[][] LU,
                       int m,
                       int n)

LU Decomposition

Parameters:

LU - Rectangular matrix

m - row dimensionality

n - column dimensionality

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

getPivot

public int[] getPivot()

Return pivot permutation vector

Returns:

piv

det

public double det()

Determinant

Returns:

det(A)

Throws:

java.lang.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:

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

java.lang.ArithmeticException - Matrix is singular.

solveInplace

private double[][] solveInplace(double[][] B)

Solve A*X = B

Parameters:

B - A Matrix with as many rows as A and any number of columns.

Returns:

B

Throws:

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

java.lang.ArithmeticException - Matrix is singular.

solve

public double[] solve(double[] b)

Solve A*X = b

Parameters:

b - A column vector with as many rows as A

Returns:

X so that L*U*X = b(piv)

Throws:

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

java.lang.ArithmeticException - Matrix is singular.

solveInplace

public double[] solveInplace(double[] b)

Solve A*X = b

Parameters:

b - A vector

Returns:

b

Throws:

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

java.lang.ArithmeticException - Matrix is singular.

inverse

public double[][] inverse()

Find the inverse matrix.

Returns:

Inverse matrix

Throws:

java.lang.ArithmeticException - Matrix is rank deficient.