Package org.jscience.mathematics.vector

Class LUDecomposition<F extends Field<F>>

java.lang.Object

org.jscience.mathematics.vector.LUDecomposition<F>

public final class LUDecomposition<F extends Field<F>>
extends java.lang.Object

This class represents the decomposition of a matrix A into a product of a lower and upper triangular matrices, L and U respectively, such as A = P·L·U with P a permutation matrix.

This decomposition is typically used to resolve linear systems of equations (Gaussian elimination) or to calculate the determinant of a square Matrix (O(m³)).

Numerical stability is guaranteed through pivoting if the Field elements are numbers For others elements types, numerical stability can be ensured by setting the context-local pivot comparator (see setPivotComparator(java.util.Comparator<org.jscience.mathematics.structure.Field>)).

Pivoting can be disabled by setting the pivot comparator to null (P is then the matrix identity).

Version:

3.3, January 2, 2007

Author:

Jean-Marie Dautelle

See Also:

Wikipedia: LU decomposition

Field Summary

Fields

Modifier and Type	Field	Description
static java.util.Comparator<Field>	NUMERIC_COMPARATOR	Holds the default comparator for pivoting.

Method Summary

Modifier and Type	Method	Description
F	determinant()	Returns the determinant of the Matrix having this decomposition.
DenseMatrix<F>	getLower(F zero, F one)	Returns the lower matrix decomposition (L) with diagonal elements equal to the multiplicative identity for F.
DenseMatrix<F>	getLU()	Returns the lower/upper decomposition in one single matrix.
SparseMatrix<F>	getPermutation(F zero, F one)	Returns the permutation matrix (P).
static java.util.Comparator<Field>	getPivotComparator()	Returns the local comparator used for pivoting or null if pivoting is not performed (default NUMERIC_COMPARATOR).
javolution.util.FastTable<javolution.util.Index>	getPivots()	Returns the pivots elements of this decomposition.
DenseMatrix<F>	getUpper(F zero)	Returns the upper matrix decomposition (U).
DenseMatrix<F>	inverse()	Returns the solution X of the equation: A * X = Identity with this = A.lu() using back and forward substitutions.
static void	setPivotComparator(java.util.Comparator<Field> cmp)	Sets the local comparator used for pivoting or null to disable pivoting.
DenseMatrix<F>	solve(Matrix<F> B)	Returns the solution X of the equation: A * X = B with this = A.lu() using back and forward substitutions.
static <F extends Field<F>> LUDecomposition<F>	valueOf(Matrix<F> source)	Returns the lower/upper decomposition of the specified matrix.

Methods inherited from class java.lang.Object

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

Field Detail

NUMERIC_COMPARATOR

public static final java.util.Comparator<Field> NUMERIC_COMPARATOR

Holds the default comparator for pivoting.

Method Detail

valueOf

public static <F extends Field<F>> LUDecomposition<F> valueOf(Matrix<F> source)

Returns the lower/upper decomposition of the specified matrix.

Parameters:

source - the matrix for which the decomposition is calculated.

Returns:

the lower/upper decomposition of the specified matrix.

Throws:

DimensionException - if the specified matrix is not square.

setPivotComparator

public static void setPivotComparator(java.util.Comparator<Field> cmp)

Sets the local comparator used for pivoting or null to disable pivoting.

Parameters:

cmp - the comparator for pivoting or null.

getPivotComparator

public static java.util.Comparator<Field> getPivotComparator()

Returns the local comparator used for pivoting or null if pivoting is not performed (default NUMERIC_COMPARATOR).

Returns:

the comparator for pivoting or null.

solve

public DenseMatrix<F> solve(Matrix<F> B)

Returns the solution X of the equation: A * X = B with this = A.lu() using back and forward substitutions.

Parameters:

B - the input matrix.

Returns:

the solution X = (1 / A) * B.

Throws:

DimensionException - if the dimensions do not match.

inverse

public DenseMatrix<F> inverse()

Returns the solution X of the equation: A * X = Identity with this = A.lu() using back and forward substitutions.

Returns:

this.solve(Identity)

determinant

public F determinant()

Returns the determinant of the Matrix having this decomposition.

Returns:

the determinant of the matrix source.

getLower

public DenseMatrix<F> getLower(F zero,
                               F one)

Returns the lower matrix decomposition (L) with diagonal elements equal to the multiplicative identity for F.

Parameters:

zero - the additive identity for F.

one - the multiplicative identity for F.

Returns:

the lower matrix.

getUpper

public DenseMatrix<F> getUpper(F zero)

Returns the upper matrix decomposition (U).

Parameters:

zero - the additive identity for F.

Returns:

the upper matrix.

getPermutation

public SparseMatrix<F> getPermutation(F zero,
                                      F one)

Returns the permutation matrix (P).

Parameters:

zero - the additive identity for F.

one - the multiplicative identity for F.

Returns:

the permutation matrix.

getLU

public DenseMatrix<F> getLU()

Returns the lower/upper decomposition in one single matrix.

Returns:

the lower/upper matrix merged in a single matrix.

getPivots

public javolution.util.FastTable<javolution.util.Index> getPivots()

Returns the pivots elements of this decomposition.

Returns:

the row indices after permutation.