Module ojalgo

Package org.ojalgo.matrix.decomposition

Class SparseLU

java.lang.Object

org.ojalgo.matrix.decomposition.AbstractDecomposition<java.lang.Double,R064Store>

org.ojalgo.matrix.decomposition.SparseLU

All Implemented Interfaces:

LDU<java.lang.Double>, LU<java.lang.Double>, MatrixDecomposition<java.lang.Double>, MatrixDecomposition.Determinant<java.lang.Double>, MatrixDecomposition.Ordered<java.lang.Double>, MatrixDecomposition.Pivoting<java.lang.Double>, MatrixDecomposition.RankRevealing<java.lang.Double>, MatrixDecomposition.Solver<java.lang.Double>, MatrixDecomposition.Updatable<java.lang.Double>, Provider2D, Provider2D.Determinant<java.lang.Double>, Provider2D.Inverse<java.util.Optional<MatrixStore<java.lang.Double>>>, Provider2D.Rank, Provider2D.Solution<java.util.Optional<MatrixStore<java.lang.Double>>>, DeterminantTask<java.lang.Double>, InverterTask<java.lang.Double>, MatrixTask<java.lang.Double>, SolverTask<java.lang.Double>, InvertibleFactor<java.lang.Double>, Structure1D, Structure2D

final class SparseLU
extends AbstractDecomposition<java.lang.Double,R064Store>
implements LU<java.lang.Double>

A sparse, primitive double based, LU decomposition with support for incremental Forrest-Tomlin updates.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
(package private) static class	SparseLU.PermutationEta

Nested classes/interfaces inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor

InvertibleFactor.IdentityFactor<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.LU

LU.Factory<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

MatrixDecomposition.Determinant<N extends java.lang.Comparable<N>>, MatrixDecomposition.EconomySize<N extends java.lang.Comparable<N>>, MatrixDecomposition.Factory<D extends MatrixDecomposition<?>>, MatrixDecomposition.Hermitian<N extends java.lang.Comparable<N>>, MatrixDecomposition.Ordered<N extends java.lang.Comparable<N>>, MatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>, MatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>, MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>, MatrixDecomposition.Updatable<N extends java.lang.Comparable<N>>, MatrixDecomposition.Values<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.Provider2D

Provider2D.Condition, Provider2D.Determinant<N extends java.lang.Comparable<N>>, Provider2D.Eigenpairs, Provider2D.Hermitian, Provider2D.Inverse<M>, Provider2D.Rank, Provider2D.Solution<M>, Provider2D.Symmetric, Provider2D.Trace<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D

Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure2D

Structure2D.IntRowColumn, Structure2D.Logical<S extends Structure2D,B extends Structure2D.Logical<S,B>>, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R extends Structure1D>, Structure2D.Reshapable, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>

Field Summary

Fields

Modifier and Type	Field	Description
private Pivot	myColPivot
private double[]	myDiagU	U diagonal elements
private java.util.List<InvertibleFactor<java.lang.Double>>	myFactors
private RowsSupplier<java.lang.Double>	myL
private Pivot	myPivot
private RowsSupplier<java.lang.Double>	myU
private R064Store	myWorkerColumn
private R064Store	myWorkerRow

Fields inherited from interface org.ojalgo.matrix.decomposition.LU

C128, H256, Q128, R064, R128

Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

TYPICAL

Constructor Summary

Constructors

Constructor	Description
SparseLU()

Method Summary

Modifier and Type	Method	Description
void	btran(PhysicalStore<java.lang.Double> arg)	Backwards-transformation
private void	btranL(int r, PhysicalStore<java.lang.Double> arg)
private void	btranU(int r, PhysicalStore<java.lang.Double> arg)
java.lang.Double	calculateDeterminant(Access2D<?> matrix)
private static Access2D.Sliceable<java.lang.Double>	cast(Access2D.Collectable<java.lang.Double,? super TransformableRegion<java.lang.Double>> matrix)
protected boolean	checkSolvability()
int	countSignificant(double threshold)
boolean	decompose(Access2D.Collectable<java.lang.Double,? super TransformableRegion<java.lang.Double>> matrix)
void	ftran(PhysicalStore<java.lang.Double> arg)	Forward-transformation
private void	ftranInternal(PhysicalStore<java.lang.Double> arg)
private void	ftranL(int r, PhysicalStore<java.lang.Double> arg)
private void	ftranU(PhysicalStore<java.lang.Double> arg, int r)
int	getColDim()
java.lang.Double	getDeterminant()	A matrix' determinant is the product of its eigenvalues.
MatrixStore<java.lang.Double>	getInverse(PhysicalStore<java.lang.Double> preallocated)	Implementing this method is optional.
MatrixStore<java.lang.Double>	getL()
int[]	getPivotOrder()
double	getRankThreshold()
int[]	getReversePivotOrder()
int	getRowDim()
MatrixStore<java.lang.Double>	getSolution(Access2D.Collectable<java.lang.Double,? super PhysicalStore<java.lang.Double>> rhs, PhysicalStore<java.lang.Double> preallocated)	Implementing this method is optional.
MatrixStore<java.lang.Double>	getU()	If updateColumn(int, Access1D.Collectable) or #updateColumn(int, Access1D.Collectable, PhysicalStore) has been invoked, then this is no longer guaranteed to be triangular.
(package private) R064Store	getWorkerColumn(int nbRows)
(package private) R064Store	getWorkerRow(int nbCols)
MatrixStore<java.lang.Double>	invert(Access2D<?> original, PhysicalStore<java.lang.Double> preallocated)	Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface.
boolean	isPivoted()
boolean	isSolvable()	Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever.
PhysicalStore<java.lang.Double>	preallocate(int nbEquations, int nbVariables, int nbSolutions)
(package private) void	reset(Structure2D matrix)
MatrixStore<java.lang.Double>	solve(Access2D<?> body, Access2D<?> rhs, PhysicalStore<java.lang.Double> preallocated)	Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface.
boolean	updateColumn(int specifiedColumn, Access1D.Collectable<java.lang.Double,? super TransformableRegion<java.lang.Double>> newColumn)	The Forrest-Tomlin update algorithm

Methods inherited from class org.ojalgo.matrix.decomposition.AbstractDecomposition

aggregator, applyPivotOrder, applyReverseOrder, collect, computed, function, getDimensionalEpsilon, isAspectRatioNormal, isComputed, makeArray, makeDiagonal, makeEye, makeHouseholder, makeIdentity, makeRotation, makeRotation, makeZero, makeZero, reset, scalar, wrap

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.ojalgo.matrix.task.InverterTask

invert, preallocate

Methods inherited from interface org.ojalgo.matrix.decomposition.LDU

isOrdered

Methods inherited from interface org.ojalgo.matrix.decomposition.LU

getSolution, reconstruct

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

isComputed, reset

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant

toDeterminantProvider

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Pivoting

decomposeWithoutPivoting

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.RankRevealing

getRank, isFullRank

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver

compute, getInverse, invert, preallocate, solve, toInverseProvider, toSolutionProvider

Methods inherited from interface org.ojalgo.matrix.task.SolverTask

preallocate, solve

Methods inherited from interface org.ojalgo.structure.Structure2D

count, countColumns, countRows, firstInColumn, firstInRow, getMaxDim, getMinDim, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size

Field Detail

myColPivot

private Pivot myColPivot

myDiagU

private double[] myDiagU

U diagonal elements

myFactors

private final java.util.List<InvertibleFactor<java.lang.Double>> myFactors

myL

private RowsSupplier<java.lang.Double> myL

myPivot

private final Pivot myPivot

myU

private RowsSupplier<java.lang.Double> myU

myWorkerColumn

private transient R064Store myWorkerColumn

myWorkerRow

private transient R064Store myWorkerRow

Constructor Detail

SparseLU

SparseLU()

Method Detail

cast

private static Access2D.Sliceable<java.lang.Double> cast(Access2D.Collectable<java.lang.Double,? super TransformableRegion<java.lang.Double>> matrix)

btran

public void btran(PhysicalStore<java.lang.Double> arg)

Description copied from interface: InvertibleFactor

Backwards-transformation

Solve [x]^T[A] = [b]^T (equivalent to [A]^T[x] = [b]) by transforming [b] into [x] in-place.

Specified by:

btran in interface InvertibleFactor<java.lang.Double>

Parameters:

arg - [b] transformed into [x]

calculateDeterminant

public java.lang.Double calculateDeterminant(Access2D<?> matrix)

Specified by:

calculateDeterminant in interface DeterminantTask<java.lang.Double>

countSignificant

public int countSignificant(double threshold)

Specified by:

countSignificant in interface MatrixDecomposition.RankRevealing<java.lang.Double>

Parameters:

threshold - Significance limit

Returns:

The number of elements in the diagonal matrix that are greater than the threshold

decompose

public boolean decompose(Access2D.Collectable<java.lang.Double,? super TransformableRegion<java.lang.Double>> matrix)

Specified by:

decompose in interface MatrixDecomposition<java.lang.Double>

Parameters:

matrix - A matrix to decompose

Returns:

true if decomposition suceeded; false if not

ftran

public void ftran(PhysicalStore<java.lang.Double> arg)

Description copied from interface: InvertibleFactor

Forward-transformation

Solve [A][x] = [b] by transforming [b] into [x] in-place.

Specified by:

ftran in interface InvertibleFactor<java.lang.Double>

Parameters:

arg - [b] transformed into [x]

getColDim

public int getColDim()

Specified by:

getColDim in interface Structure2D

Returns:

The number of columns

getDeterminant

public java.lang.Double getDeterminant()

Description copied from interface: MatrixDecomposition.Determinant

A matrix' determinant is the product of its eigenvalues.

Specified by:

getDeterminant in interface MatrixDecomposition.Determinant<java.lang.Double>

Specified by:

getDeterminant in interface Provider2D.Determinant<java.lang.Double>

Returns:

The matrix' determinant

getInverse

public MatrixStore<java.lang.Double> getInverse(PhysicalStore<java.lang.Double> preallocated)

Description copied from interface: MatrixDecomposition.Solver

Implementing this method is optional.

Exactly how a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling MatrixDecomposition.Solver.getInverse().

Specified by:

getInverse in interface MatrixDecomposition.Solver<java.lang.Double>

Parameters:

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. Use MatrixDecomposition.Solver.preallocate(int, int) or InverterTask.preallocate(Structure2D) to get a suitable instance.

Returns:

The inverse, this is where you get the solution

getL

public MatrixStore<java.lang.Double> getL()

Specified by:

getL in interface LU<java.lang.Double>

getPivotOrder

public int[] getPivotOrder()

Specified by:

getPivotOrder in interface MatrixDecomposition.Pivoting<java.lang.Double>

Returns:

The pivot (row and/or columnn) order

getRankThreshold

public double getRankThreshold()

Specified by:

getRankThreshold in interface MatrixDecomposition.RankRevealing<java.lang.Double>

getReversePivotOrder

public int[] getReversePivotOrder()

Specified by:

getReversePivotOrder in interface MatrixDecomposition.Pivoting<java.lang.Double>

getRowDim

public int getRowDim()

Specified by:

getRowDim in interface Structure2D

Returns:

The number of rows

getSolution

public MatrixStore<java.lang.Double> getSolution(Access2D.Collectable<java.lang.Double,? super PhysicalStore<java.lang.Double>> rhs,
                                                 PhysicalStore<java.lang.Double> preallocated)

Description copied from interface: MatrixDecomposition.Solver

Implementing this method is optional.

Exactly how a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling MatrixDecomposition.Solver.getSolution(Collectable).

Specified by:

getSolution in interface MatrixDecomposition.Solver<java.lang.Double>

Parameters:

rhs - The Right Hand Side, wont be modfied

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. Use SolverTask.preallocate(int, int, int) or SolverTask.preallocate(Structure2D, Structure2D) to get a suitable instance.

Returns:

The solution

getU

public MatrixStore<java.lang.Double> getU()

If updateColumn(int, Access1D.Collectable) or #updateColumn(int, Access1D.Collectable, PhysicalStore) has been invoked, then this is no longer guaranteed to be triangular.

Specified by:

getU in interface LU<java.lang.Double>

See Also:

MatrixDecomposition.Pivoting.getPivotOrder(), LU.getL()

invert

public MatrixStore<java.lang.Double> invert(Access2D<?> original,
                                            PhysicalStore<java.lang.Double> preallocated)
                                     throws RecoverableCondition

Description copied from interface: InverterTask

Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling InverterTask.invert(Access2D).

Use InverterTask.preallocate(Structure2D) to obtain a suitbale preallocated.

Specified by:

invert in interface InverterTask<java.lang.Double>

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution.

Returns:

The inverse

Throws:

RecoverableCondition - TODO

isPivoted

public boolean isPivoted()

Specified by:

isPivoted in interface MatrixDecomposition.Pivoting<java.lang.Double>

Returns:

true if any pivoting was actually done

isSolvable

public boolean isSolvable()

Description copied from interface: MatrixDecomposition.Solver

Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever. It's that in combination with the specific decomposition algorithm's capabilities.

Specified by:

isSolvable in interface MatrixDecomposition.Solver<java.lang.Double>

Overrides:

isSolvable in class AbstractDecomposition<java.lang.Double,R064Store>

Returns:

true if this matrix decomposition is in a state to be able to deliver an inverse or an equation system solution (with some degree of numerical stability).

preallocate

public PhysicalStore<java.lang.Double> preallocate(int nbEquations,
                                                   int nbVariables,
                                                   int nbSolutions)

Specified by:

preallocate in interface SolverTask<java.lang.Double>

solve

public MatrixStore<java.lang.Double> solve(Access2D<?> body,
                                           Access2D<?> rhs,
                                           PhysicalStore<java.lang.Double> preallocated)
                                    throws RecoverableCondition

Description copied from interface: SolverTask

Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling SolverTask.solve(Access2D, Access2D).

Use SolverTask.preallocate(Structure2D, Structure2D) to obtain a suitbale preallocated.

Specified by:

solve in interface SolverTask<java.lang.Double>

rhs - The Right Hand Side, wont be modfied

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/ /correct solution.

Returns:

The solution

Throws:

RecoverableCondition

updateColumn

public boolean updateColumn(int specifiedColumn,
                            Access1D.Collectable<java.lang.Double,? super TransformableRegion<java.lang.Double>> newColumn)

The Forrest-Tomlin update algorithm

Specified by:

updateColumn in interface MatrixDecomposition.Updatable<java.lang.Double>

Parameters:

specifiedColumn - The index of the column, in the original matrix, to replace

newColumn - The new column values

Returns:

true if update was successful, false if not.

btranL

private void btranL(int r,
                    PhysicalStore<java.lang.Double> arg)

btranU

private void btranU(int r,
                    PhysicalStore<java.lang.Double> arg)

ftranInternal

private void ftranInternal(PhysicalStore<java.lang.Double> arg)

ftranL

private void ftranL(int r,
                    PhysicalStore<java.lang.Double> arg)

ftranU

private void ftranU(PhysicalStore<java.lang.Double> arg,
                    int r)

checkSolvability

protected boolean checkSolvability()

Overrides:

checkSolvability in class AbstractDecomposition<java.lang.Double,R064Store>

getWorkerColumn

R064Store getWorkerColumn(int nbRows)

getWorkerRow

R064Store getWorkerRow(int nbCols)

reset

void reset(Structure2D matrix)