FieldLUDecomposition (Commons Math 2.2 API)

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- the solve and isNonSingular methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.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

Version:

$Revision: 826627 $ $Date: 2009-10-19 12:27:47 +0200 (lun. 19 oct. 2009) $

See Also:

MathWorld, Wikipedia

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	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