org.apache.commons.math.linear

## Class FieldLUDecompositionImpl<T extends FieldElement<T>>

• java.lang.Object
• org.apache.commons.math.linear.FieldLUDecompositionImpl<T>
• Type Parameters:
`T` - the type of the field elements
All Implemented Interfaces:
FieldLUDecomposition<T>

```public class FieldLUDecompositionImpl<T extends FieldElement<T>>
extends java.lang.Object
implements FieldLUDecomposition<T>```
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.

Since `field elements` do not provide an ordering operator, the permutation matrix is computed here only in order to avoid a zero pivot element, no attempt is done to get the largest pivot element.

Since:
2.0
• ### Constructor Summary

Constructors
Constructor and Description
`FieldLUDecompositionImpl(FieldMatrix<T> matrix)`
Calculates the LU-decomposition of the given matrix.
• ### Method Summary

All Methods
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.
• ### Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Constructor Detail

• #### FieldLUDecompositionImpl

```public FieldLUDecompositionImpl(FieldMatrix<T> matrix)
throws NonSquareMatrixException```
Calculates the LU-decomposition of the given matrix.
Parameters:
`matrix` - The matrix to decompose.
Throws:
`NonSquareMatrixException` - if matrix is not square
• ### Method Detail

• #### getL

`public FieldMatrix<T> getL()`
Returns the matrix L of the decomposition.

L is an lower-triangular matrix

Specified by:
`getL` in interface `FieldLUDecomposition<T extends FieldElement<T>>`
Returns:
the L matrix (or null if decomposed matrix is singular)
• #### getU

`public FieldMatrix<T> getU()`
Returns the matrix U of the decomposition.

U is an upper-triangular matrix

Specified by:
`getU` in interface `FieldLUDecomposition<T extends FieldElement<T>>`
Returns:
the U matrix (or null if decomposed matrix is singular)
• #### getP

`public 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`.

Specified by:
`getP` in interface `FieldLUDecomposition<T extends FieldElement<T>>`
Returns:
the P rows permutation matrix (or null if decomposed matrix is singular)
`FieldLUDecomposition.getPivot()`
• #### getPivot

`public int[] getPivot()`
Returns the pivot permutation vector.
Specified by:
`getPivot` in interface `FieldLUDecomposition<T extends FieldElement<T>>`
Returns:
the pivot permutation vector
`FieldLUDecomposition.getP()`
• #### getDeterminant

`public T getDeterminant()`
Return the determinant of the matrix
Specified by:
`getDeterminant` in interface `FieldLUDecomposition<T extends FieldElement<T>>`
Returns:
determinant of the matrix
• #### getSolver

`public FieldDecompositionSolver<T> getSolver()`
Get a solver for finding the A × X = B solution in exact linear sense.
Specified by:
`getSolver` in interface `FieldLUDecomposition<T extends FieldElement<T>>`
Returns:
a solver