org.ejml.interfaces.decomposition

Interface LUDecomposition<T extends Matrix>

All Superinterfaces:

DecompositionInterface<T>

All Known Implementing Classes:

LUDecompositionAlt_D64, LUDecompositionBase_D64

public interface LUDecomposition<T extends Matrix>
extends DecompositionInterface<T>

LU Decomposition refactors the original matrix such that:

P^T*L*U = A

where P is a pivot matrix, L is a lower triangular matrix, U is an upper triangular matrix and A is the original matrix.

LU Decomposition is useful since once the decomposition has been performed linear equations can be quickly solved and the original matrix A inverted. Different algorithms can be selected to perform the decomposition, all will have the same end result.

To use this class first specify the size of the matrix that will be decomposed by it in the constructor. Only square m by m matrices can be decomposed. Then to decompose a matrix call DecompositionInterface.decompose(T). If it encounters any problems an exception will be thrown. After that all the other functions will be available for solving and inverting matrices.

Method Summary

Methods

Modifier and Type	Method and Description
Complex64F	computeDeterminant() Computes the matrix's determinant using the LU decomposition.
T	getLower(T lower) Returns the L matrix from the decomposition.
T	getPivot(T pivot) For numerical stability there are often row interchanges.
T	getUpper(T upper) Returns the U matrix from the decomposition.
boolean	isSingular() Returns true if the decomposition detected a singular matrix.

Methods inherited from interface org.ejml.interfaces.decomposition.DecompositionInterface

decompose, inputModified

Method Detail

getLower

T getLower(T lower)

Returns the L matrix from the decomposition. Should only be called after DecompositionInterface.decompose(org.ejml.data.Matrix) has been called.

If parameter 'lower' is not null, then that matrix is used to store the L matrix. Otherwise a new matrix is created.

Parameters:

lower - Storage for T matrix. If null then a new matrix is returned. Modified.

Returns:

The L matrix.

getUpper

T getUpper(T upper)

Returns the U matrix from the decomposition. Should only be called after DecompositionInterface.decompose(org.ejml.data.Matrix) has been called.

If parameter 'upper' is not null, then that matrix is used to store the U matrix. Otherwise a new matrix is created.

Parameters:

upper - Storage for U matrix. If null then a new matrix is returned. Modified.

Returns:

The U matrix.

getPivot

T getPivot(T pivot)

For numerical stability there are often row interchanges. This computes a pivot matrix that will undo those changes.

Parameters:

pivot - Storage for the pivot matrix. If null then a new matrix is returned. Modified.

Returns:

The pivot matrix.

isSingular

boolean isSingular()

Returns true if the decomposition detected a singular matrix. This check will not work 100% of the time due to machine precision issues.

Returns:

True if the matrix is singular and false if it is not.

computeDeterminant

Complex64F computeDeterminant()

Computes the matrix's determinant using the LU decomposition.

Returns:

The determinant.