Package org.flag4j.linalg.decompositions.lu

Class RealLU

java.lang.Object

org.flag4j.linalg.decompositions.lu.LU<Matrix>

org.flag4j.linalg.decompositions.lu.RealLU

All Implemented Interfaces:

Decomposition<Matrix>

public final class RealLU
extends LU<Matrix>

This class provides methods for computing the LU decomposition of a real dense matrix.

The following decompositions are provided: A=LU, PA=LU, and PAQ=LU.

Nested Class Summary

Nested classes/interfaces inherited from class org.flag4j.linalg.decompositions.lu.LU

LU.Pivoting

Field Summary

Fields inherited from class org.flag4j.linalg.decompositions.lu.LU

colSwaps, DEFAULT_ZERO_PIVOT_TOLERANCE, LU, numColSwaps, numRowSwaps, P, pivotFlag, Q, rowSwaps, zeroPivotTol

Constructor Summary

Constructors

Constructor	Description
RealLU()	Constructs a LU decomposer to decompose the specified matrix using partial pivoting.
RealLU(int pivoting)	Constructs a LU decomposer to decompose the specified matrix.
RealLU(int pivoting, double zeroPivotTol)	Constructs a LU decomposer to decompose the specified matrix.

Method Summary

Modifier and Type	Method	Description
private void	computeRows(int j)	Helper method which computes rows in the gaussian elimination algorithm.
protected void	fullPivot()	Computes the LU decomposition using full/rook pivoting (i.e.
Matrix	getL()	Gets the unit lower triangular matrix of the decomposition.
Matrix	getU()	Gets the upper triangular matrix of the decomposition.
protected void	initLU(Matrix src)	Initializes the LU matrix by copying the source matrix to decompose.
private int	maxColIndex(int j)	Computes the max absolute value in a column so that the row is >= j.
private int[]	maxIndex(int startIndex)	Computes maximum absolute value in sub portion of LU matrix below and right of startIndex, startIndex.
protected void	noPivot()	Computes the LU decomposition using no pivoting (i.e.
protected void	partialPivot()	Computes the LU decomposition using partial pivoting (i.e.

Methods inherited from class org.flag4j.linalg.decompositions.lu.LU

decompose, getLU, getNumColSwaps, getNumRowSwaps, getP, getQ, swapCols, swapRows

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

RealLU

public RealLU()

Constructs a LU decomposer to decompose the specified matrix using partial pivoting.

RealLU

public RealLU(int pivoting)

Constructs a LU decomposer to decompose the specified matrix.

Parameters:

pivoting - Pivoting to use. If pivoting is 2, full pivoting will be used. If pivoting is 1, partial pivoting will be used. If pivoting is any other value, no pivoting will be used.

RealLU

public RealLU(int pivoting,
 double zeroPivotTol)

Constructs a LU decomposer to decompose the specified matrix.

Parameters:

pivoting - Pivoting to use. If pivoting is 2, full pivoting will be used. If pivoting is 1, partial pivoting will be used. If pivoting is any other value, no pivoting will be used.

zeroPivotTol - Value for determining if a zero pivot value is detected when computing the LU decomposition with no pivoting. If a pivot value (value along the principle diagonal of U) is within this tolerance from zero, then an exception will be thrown if solving with no pivoting.

Method Details

initLU

protected void initLU(Matrix src)

Initializes the LU matrix by copying the source matrix to decompose.

Specified by:

initLU in class LU<Matrix>

Parameters:

src - Source matrix to decompose.

noPivot

protected void noPivot()

Computes the LU decomposition using no pivoting (i.e. rows and columns are not swapped).

Specified by:

noPivot in class LU<Matrix>

partialPivot

protected void partialPivot()

Computes the LU decomposition using partial pivoting (i.e. row swapping).

Specified by:

partialPivot in class LU<Matrix>

fullPivot

protected void fullPivot()

Computes the LU decomposition using full/rook pivoting (i.e. row and column swapping).

Specified by:

fullPivot in class LU<Matrix>

computeRows

private void computeRows(int j)

Helper method which computes rows in the gaussian elimination algorithm.

Parameters:

j - Column for which to compute values to the right of.

maxColIndex

private int maxColIndex(int j)

Computes the max absolute value in a column so that the row is >= j.

Parameters:

j - column index.

Returns:

The index of the maximum absolute value in the specified column such that the row is >= j.

maxIndex

private int[] maxIndex(int startIndex)

Computes maximum absolute value in sub portion of LU matrix below and right of startIndex, startIndex.

Parameters:

startIndex - Top left index of row and column of sub matrix.

Returns:

Index of maximum absolute value in specified sub matrix.

getL

public Matrix getL()

Gets the unit lower triangular matrix of the decomposition.

Specified by:

getL in class LU<Matrix>

Returns:

The lower triangular matrix of the decomposition.

getU

public Matrix getU()

Gets the upper triangular matrix of the decomposition.

Specified by:

getU in class LU<Matrix>

Returns:

The lower triangular matrix of the decomposition.