Package org.flag4j.linalg.decompositions.lu

Class LU<T extends MatrixMixin<T,?,?,?,?,?,?,?>>

java.lang.Object

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

All Implemented Interfaces:

Decomposition<T>

Direct Known Subclasses:

ComplexLU, RealLU

public abstract class LU<T extends MatrixMixin<T,?,?,?,?,?,?,?>>
extends Object
implements Decomposition<T>

This abstract class specifies methods for computing the LU decomposition of a matrix.

The LU decomposition, decomposes a matrix A into a unit lower triangular matrix L and an upper triangular matrix U such that A=LU.

If partial pivoting is used, the decomposition will also yield a permutation matrix P such that PA=LU.

If full pivoting is used, the decomposition will yield an additional permutation matrix Q such that PAQ=LU.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	LU.Pivoting	Simple enum containing pivoting options for pivoting in LU decomposition.

Field Summary

Fields

Modifier and Type	Field	Description
protected int[]	colSwaps
(package private) final double	DEFAULT_ZERO_PIVOT_TOLERANCE	for determining if pivot value is to be considered zero in LU decomposition with no pivoting.
protected T	LU	Storage for L and U matrices.
protected int	numColSwaps
protected int	numRowSwaps
protected PermutationMatrix	P	Permutation matrix to store row swaps if partial pivoting is used.
final LU.Pivoting	pivotFlag	Flag indicating what pivoting to use.
protected PermutationMatrix	Q	Permutation matrix to store column swaps if full pivoting is used.
protected int[]	rowSwaps
(package private) final double	zeroPivotTol	Tolerance for determining if pivot value is to be considered zero in LU decomposition with no pivoting.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
LU<T>	decompose(T src)	Applies LU decomposition to the source matrix using the pivoting specified in the constructor.
protected abstract void	fullPivot()	Computes the LU decomposition using full/rook pivoting (i.e.
abstract T	getL()	Gets the unit lower triangular matrix of the decomposition.
T	getLU()	Gets the L and U matrices of the decomposition combined in a single matrix.
int	getNumColSwaps()	Gets the number of column swaps used in the last decomposition.
int	getNumRowSwaps()	Gets the number of row swaps used in the last decomposition.
PermutationMatrix	getP()	Gets the row permutation matrix of the decomposition.
PermutationMatrix	getQ()	Gets the column permutation matrix of the decomposition.
abstract T	getU()	Gets the upper triangular matrix of the decomposition.
protected abstract void	initLU(T src)	Initializes the LU matrix by copying the source matrix to decompose.
protected abstract void	noPivot()	Computes the LU decomposition using no pivoting (i.e.
protected abstract void	partialPivot()	Computes the LU decomposition using partial pivoting (i.e.
protected void	swapCols(int colIdx1, int colIdx2)	Tracks the swapping of two columns during gaussian elimination with full pivoting.
protected void	swapRows(int rowIdx1, int rowIdx2)	Tracks the swapping of two rows during gaussian elimination with partial or full pivoting.

Methods inherited from class java.lang.Object

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

Field Details

pivotFlag

public final LU.Pivoting pivotFlag

Flag indicating what pivoting to use.

DEFAULT_ZERO_PIVOT_TOLERANCE

final double DEFAULT_ZERO_PIVOT_TOLERANCE

for determining if pivot value is to be considered zero in LU decomposition with no pivoting.

See Also:

• Constant Field Values

zeroPivotTol

final double zeroPivotTol

Tolerance for determining if pivot value is to be considered zero in LU decomposition with no pivoting.

LU

protected T extends MatrixMixin<T,?,?,?,?,?,?,?> LU

Storage for L and U matrices. Stored in a single matrix

P

protected PermutationMatrix P

Permutation matrix to store row swaps if partial pivoting is used.

Q

protected PermutationMatrix Q

Permutation matrix to store column swaps if full pivoting is used.

numRowSwaps

protected int numRowSwaps

numColSwaps

protected int numColSwaps

rowSwaps

protected int[] rowSwaps

colSwaps

protected int[] colSwaps

Constructor Details

LU

public LU(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.

LU

public LU(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 - Tolerance for considering a pivot to be zero. If a pivot is less than the tolerance in absolute value, then it will be considered zero.

Method Details

decompose

public LU<T> decompose(T src)

Applies LU decomposition to the source matrix using the pivoting specified in the constructor.

Specified by:

decompose in interface Decomposition<T extends MatrixMixin<T,?,?,?,?,?,?,?>>

Parameters:

src - The source matrix to decompose. Not modified.

Returns:

A reference to this decomposer.

initLU

protected abstract void initLU(T src)

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

Parameters:

src - Source matrix to decompose.

noPivot

protected abstract void noPivot()

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

partialPivot

protected abstract void partialPivot()

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

fullPivot

protected abstract void fullPivot()

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

getLU

public T getLU()

Gets the L and U matrices of the decomposition combined in a single matrix.

Returns:

The L and U matrices of the decomposition stored together in a single matrix. The diagonal of L is all ones and is not stored allowing the diagonal of U to be stored along the diagonal of the combined matrix.

getL

public abstract T getL()

Gets the unit lower triangular matrix of the decomposition.

Returns:

The unit lower triangular matrix of the decomposition.

getU

public abstract T getU()

Gets the upper triangular matrix of the decomposition.

Returns:

The upper triangular matrix of the decomposition.

getP

public PermutationMatrix getP()

Gets the row permutation matrix of the decomposition.

Returns:

The row permutation matrix of the decomposition. If no pivoting was used, null will be returned.

getQ

public PermutationMatrix getQ()

Gets the column permutation matrix of the decomposition.

Returns:

The column permutation matrix of the decomposition. If full pivoting was not used, null will be returned.

getNumRowSwaps

public int getNumRowSwaps()

Gets the number of row swaps used in the last decomposition.

Returns:

The number of row swaps used in the last decomposition.

getNumColSwaps

public int getNumColSwaps()

Gets the number of column swaps used in the last decomposition.

Returns:

The number of column swaps used in the last decomposition.

swapRows

protected void swapRows(int rowIdx1,
 int rowIdx2)

Tracks the swapping of two rows during gaussian elimination with partial or full pivoting.

Parameters:

rowIdx1 - First row index in swap.

rowIdx2 - Second row index in swap.

swapCols

protected void swapCols(int colIdx1,
 int colIdx2)

Tracks the swapping of two columns during gaussian elimination with full pivoting.

Parameters:

colIdx1 - First column index in swap.

colIdx2 - Second column index in swap.