org.apache.commons.math.linear
Class LUDecompositionImpl

java.lang.Object
  org.apache.commons.math.linear.LUDecompositionImpl

All Implemented Interfaces:

LUDecomposition

public class LUDecompositionImpl
extends java.lang.Object
implements LUDecomposition

Calculates the LUP-decomposition of a square matrix.

The LUP-decomposition of a matrix A consists of three matrices L, U and P that satisfy: PA = LU, L is lower triangular, and U is upper triangular and P is a permutation matrix. All matrices are m×m.

As shown by the presence of the P matrix, this decomposition is implemented using partial pivoting.

Since:

2.0

Version:

$Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $

Nested Class Summary

private static class

LUDecompositionImpl.Solver Specialized solver.

Field Summary

private RealMatrix	cachedL Cached value of L.
private RealMatrix	cachedP Cached value of P.
private RealMatrix	cachedU Cached value of U.
private static double	DEFAULT_TOO_SMALL Default bound to determine effective singularity in LU decomposition
private boolean	even Parity of the permutation associated with the LU decomposition
private double[][]	lu Entries of LU decomposition.
private int[]	pivot Pivot permutation associated with LU decomposition
private boolean	singular Singularity indicator.

Constructor Summary

LUDecompositionImpl(RealMatrix matrix)
Calculates the LU-decomposition of the given matrix.

LUDecompositionImpl(RealMatrix matrix, double singularityThreshold)
Calculates the LU-decomposition of the given matrix.

Method Summary

double	getDeterminant() Return the determinant of the matrix
RealMatrix	getL() Returns the matrix L of the decomposition.
RealMatrix	getP() Returns the P rows permutation matrix.
int[]	getPivot() Returns the pivot permutation vector.
DecompositionSolver	getSolver() Get a solver for finding the A × X = B solution in exact linear sense.
RealMatrix	getU() Returns the matrix U of the decomposition.

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_TOO_SMALL

private static final double DEFAULT_TOO_SMALL

Default bound to determine effective singularity in LU decomposition

See Also:

Constant Field Values

lu

private double[][] lu

Entries of LU decomposition.

pivot

private int[] pivot

Pivot permutation associated with LU decomposition

even

private boolean even

Parity of the permutation associated with the LU decomposition

singular

private boolean singular

Singularity indicator.

cachedL

private RealMatrix cachedL

Cached value of L.

cachedU

private RealMatrix cachedU

Cached value of U.

cachedP

private RealMatrix cachedP

Cached value of P.

Constructor Detail

LUDecompositionImpl

public LUDecompositionImpl(RealMatrix matrix)
                    throws InvalidMatrixException

Calculates the LU-decomposition of the given matrix.

Parameters:

matrix - The matrix to decompose.

Throws:

InvalidMatrixException - if matrix is not square

LUDecompositionImpl

public LUDecompositionImpl(RealMatrix matrix,
                           double singularityThreshold)
                    throws NonSquareMatrixException

Calculates the LU-decomposition of the given matrix.

Parameters:

matrix - The matrix to decompose.

singularityThreshold - threshold (based on partial row norm) under which a matrix is considered singular

Throws:

NonSquareMatrixException - if matrix is not square

Method Detail

getL

public RealMatrix getL()

Returns the matrix L of the decomposition.

L is an lower-triangular matrix

Specified by:

getL in interface LUDecomposition

Returns:

the L matrix (or null if decomposed matrix is singular)

getU

public RealMatrix getU()

Returns the matrix U of the decomposition.

U is an upper-triangular matrix

Specified by:

getU in interface LUDecomposition

Returns:

the U matrix (or null if decomposed matrix is singular)

getP

public RealMatrix getP()

Returns the P rows permutation matrix.

P is a sparse matrix with exactly one element set to 1.0 in each row and each column, all other elements being set to 0.0.

The positions of the 1 elements are given by the pivot permutation vector.

Specified by:

getP in interface LUDecomposition

Returns:

the P rows permutation matrix (or null if decomposed matrix is singular)

See Also:

LUDecomposition.getPivot()

getPivot

public int[] getPivot()

Returns the pivot permutation vector.

Specified by:

getPivot in interface LUDecomposition

Returns:

the pivot permutation vector

See Also:

LUDecomposition.getP()

getDeterminant

public double getDeterminant()

Return the determinant of the matrix

Specified by:

getDeterminant in interface LUDecomposition

Returns:

determinant of the matrix

getSolver

public DecompositionSolver getSolver()

Get a solver for finding the A × X = B solution in exact linear sense.

Specified by:

getSolver in interface LUDecomposition

Returns:

a solver