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.

Since:
2.0
Version:
$Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $
See Also:
MathWorld, Wikipedia

Method Summary
 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


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