org.apache.commons.math.linear

Interface FieldLUDecomposition<T extends FieldElement<T>>

Type Parameters:

T - the type of the field elements

All Known Implementing Classes:

FieldLUDecompositionImpl

public interface FieldLUDecomposition<T extends FieldElement<T>>

An interface to classes that implement an algorithm to calculate the LU-decomposition of a real matrix.

The LU-decomposition of matrix A is a set of three matrices: P, L and U such that P×A = L×U. P is a rows permutation matrix that is used to rearrange the rows of A before so that it can be decomposed. L is a lower triangular matrix with unit diagonal terms and U is an upper triangular matrix.

This interface is based on the class with similar name from the JAMA library.

• a getP method has been added,
• the det method has been renamed as getDeterminant,
• the getDoublePivot method has been removed (but the int based getPivot method has been kept),
• the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.

Since:

2.0

See Also:

MathWorld, Wikipedia

Method Summary

Modifier and Type	Method and Description
T	getDeterminant() Return the determinant of the matrix
FieldMatrix<T>	getL() Returns the matrix L of the decomposition.
FieldMatrix<T>	getP() Returns the P rows permutation matrix.
int[]	getPivot() Returns the pivot permutation vector.
FieldDecompositionSolver<T>	getSolver() Get a solver for finding the A × X = B solution in exact linear sense.
FieldMatrix<T>	getU() Returns the matrix U of the decomposition.

Method Detail

getL

FieldMatrix<T> getL()

Returns the matrix L of the decomposition.

L is an lower-triangular matrix

Returns:

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

getU

FieldMatrix<T> getU()

Returns the matrix U of the decomposition.

U is an upper-triangular matrix

Returns:

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

getP

FieldMatrix<T> 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.

Returns:

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

See Also:

getPivot()

getPivot

int[] getPivot()

Returns the pivot permutation vector.

Returns:

the pivot permutation vector

See Also:

getP()

getDeterminant

T getDeterminant()

Return the determinant of the matrix

Returns:

determinant of the matrix

getSolver

FieldDecompositionSolver<T> getSolver()

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

Returns:

a solver