Module ojalgo

Package org.ojalgo.matrix.decomposition

Class DenseLU<N extends java.lang.Comparable<N>>

java.lang.Object

org.ojalgo.matrix.decomposition.AbstractDecomposition<N,DecompositionStore<N>>

org.ojalgo.matrix.decomposition.InPlaceDecomposition<N>

org.ojalgo.matrix.decomposition.DenseLU<N>

All Implemented Interfaces:

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

Direct Known Subclasses:

DenseLU.C128, DenseLU.H256, DenseLU.Q128, DenseLU.R064, DenseLU.R128

abstract class DenseLU<N extends java.lang.Comparable<N>>
extends InPlaceDecomposition<N>
implements LU<N>

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
(package private) static class	DenseLU.C128
(package private) static class	DenseLU.H256
(package private) static class	DenseLU.Q128
(package private) static class	DenseLU.R064
(package private) static class	DenseLU.R128

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 Pivot	myPivot
private PhysicalStore<N>	myWorkerColumn
private PhysicalStore<N>	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

Modifier	Constructor	Description
protected	DenseLU(PhysicalStore.Factory<N,? extends DecompositionStore<N>> aFactory)

Method Summary

Modifier and Type	Method	Description
void	btran(PhysicalStore<N> arg)	Backwards-transformation
N	calculateDeterminant(Access2D<?> matrix)
protected boolean	checkSolvability()
int	countSignificant(double threshold)
boolean	decompose(Access2D.Collectable<N,? super TransformableRegion<N>> matrix)
boolean	decomposeWithoutPivoting(Access2D.Collectable<N,? super TransformableRegion<N>> matrix)	The normal MatrixDecomposition.decompose(Access2D.Collectable) method must handle cases where pivoting is necessary.
private boolean	doDecompose(Access2D.Collectable<N,? super PhysicalStore<N>> matrix, boolean pivoting)
void	ftran(PhysicalStore<N> arg)	Forward-transformation
N	getDeterminant()	A matrix' determinant is the product of its eigenvalues.
MatrixStore<N>	getInverse(PhysicalStore<N> preallocated)	Implementing this method is optional.
MatrixStore<N>	getL()
int[]	getPivotOrder()
double	getRankThreshold()
(package private) int[]	getReducedPivots()
int[]	getReversePivotOrder()
MatrixStore<N>	getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs, PhysicalStore<N> preallocated)	Solves [this][X] = [rhs] by first solving
MatrixStore<N>	getU()	http://en.wikipedia.org/wiki/Row_echelon_form This is the same as [D][U].
(package private) PhysicalStore<N>	getWorkerColumn(int nbRows)
(package private) PhysicalStore<N>	getWorkerRow(int nbCols)
MatrixStore<N>	invert(Access2D<?> original)	The output must be a "right inverse" and a "generalised inverse".
MatrixStore<N>	invert(Access2D<?> original, PhysicalStore<N> 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<N>	preallocate(int nbEquations, int nbVariables, int nbSolutions)
MatrixStore<N>	solve(Access2D<?> body, Access2D<?> rhs, PhysicalStore<N> preallocated)	Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface.
boolean	updateColumn(int columnIndex, Access1D.Collectable<N,? super TransformableRegion<N>> newColumn)	Updates the decomposition when a column in the original matrix is replaced.

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

getColDim, getInPlace, getInverse, getRowDim, setInPlace

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

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.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, getColDim, getMaxDim, getMinDim, getRowDim, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size

Field Detail

myColPivot

private Pivot myColPivot

myPivot

private final Pivot myPivot

myWorkerColumn

private transient PhysicalStore<N extends java.lang.Comparable<N>> myWorkerColumn

myWorkerRow

private transient PhysicalStore<N extends java.lang.Comparable<N>> myWorkerRow

Constructor Detail

DenseLU

protected DenseLU(PhysicalStore.Factory<N,? extends DecompositionStore<N>> aFactory)

Method Detail

btran

public void btran(PhysicalStore<N> 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<N extends java.lang.Comparable<N>>

Parameters:

arg - [b] transformed into [x]

calculateDeterminant

public N calculateDeterminant(Access2D<?> matrix)

Specified by:

calculateDeterminant in interface DeterminantTask<N extends java.lang.Comparable<N>>

countSignificant

public int countSignificant(double threshold)

Specified by:

countSignificant in interface MatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>

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<N,? super TransformableRegion<N>> matrix)

Specified by:

decompose in interface MatrixDecomposition<N extends java.lang.Comparable<N>>

Parameters:

matrix - A matrix to decompose

Returns:

true if decomposition suceeded; false if not

decomposeWithoutPivoting

public boolean decomposeWithoutPivoting(Access2D.Collectable<N,? super TransformableRegion<N>> matrix)

Description copied from interface: MatrixDecomposition.Pivoting

The normal MatrixDecomposition.decompose(Access2D.Collectable) method must handle cases where pivoting is necessary. If you know that pivoting is not needed you may call this method instead - it may be faster. Implementing this method, to actually decompose without pivoting, is optional. The default implementation simply calls MatrixDecomposition.decompose(Access2D.Collectable).

Specified by:

decomposeWithoutPivoting in interface MatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>

ftran

public void ftran(PhysicalStore<N> 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<N extends java.lang.Comparable<N>>

Parameters:

arg - [b] transformed into [x]

getDeterminant

public N getDeterminant()

Description copied from interface: MatrixDecomposition.Determinant

A matrix' determinant is the product of its eigenvalues.

Specified by:

getDeterminant in interface MatrixDecomposition.Determinant<N extends java.lang.Comparable<N>>

Specified by:

getDeterminant in interface Provider2D.Determinant<N extends java.lang.Comparable<N>>

Returns:

The matrix' determinant

getInverse

public MatrixStore<N> getInverse(PhysicalStore<N> 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<N extends java.lang.Comparable<N>>

Overrides:

getInverse in class InPlaceDecomposition<N extends java.lang.Comparable<N>>

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<N> getL()

Specified by:

getL in interface LU<N extends java.lang.Comparable<N>>

getPivotOrder

public int[] getPivotOrder()

Specified by:

getPivotOrder in interface MatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>

Returns:

The pivot (row and/or columnn) order

getRankThreshold

public double getRankThreshold()

Specified by:

getRankThreshold in interface MatrixDecomposition.RankRevealing<N extends java.lang.Comparable<N>>

getReversePivotOrder

public int[] getReversePivotOrder()

Specified by:

getReversePivotOrder in interface MatrixDecomposition.Pivoting<N extends java.lang.Comparable<N>>

getSolution

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

Solves [this][X] = [rhs] by first solving

 [L][Y] = [rhs]
 

and then

 [U][X] = [Y]
 

Specified by:

getSolution in interface MatrixDecomposition.Solver<N extends java.lang.Comparable<N>>

Parameters:

rhs - The right hand side

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:

[X] The solution will be written to "preallocated" and then returned.

getU

public MatrixStore<N> getU()

Description copied from interface: LU

http://en.wikipedia.org/wiki/Row_echelon_form

This is the same as [D][U]. Together with the pivotOrder and [L] this constitutes an alternative, more compact, way to express the decomposition.

Specified by:

getU in interface LU<N extends java.lang.Comparable<N>>

See Also:

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

invert

public MatrixStore<N> invert(Access2D<?> original)
                      throws RecoverableCondition

Description copied from interface: InverterTask

The output must be a "right inverse" and a "generalised inverse".

Specified by:

invert in interface InverterTask<N extends java.lang.Comparable<N>>

Throws:

RecoverableCondition

invert

public MatrixStore<N> invert(Access2D<?> original,
                             PhysicalStore<N> 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<N extends java.lang.Comparable<N>>

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

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

Overrides:

isSolvable in class AbstractDecomposition<N extends java.lang.Comparable<N>,DecompositionStore<N extends java.lang.Comparable<N>>>

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<N> preallocate(int nbEquations,
                                    int nbVariables,
                                    int nbSolutions)

Specified by:

preallocate in interface SolverTask<N extends java.lang.Comparable<N>>

solve

public MatrixStore<N> solve(Access2D<?> body,
                            Access2D<?> rhs,
                            PhysicalStore<N> 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<N extends java.lang.Comparable<N>>

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 columnIndex,
                            Access1D.Collectable<N,? super TransformableRegion<N>> newColumn)

Description copied from interface: MatrixDecomposition.Updatable

Updates the decomposition when a column in the original matrix is replaced.

This method can only be called after an initial decomposition has been calculated.

If the updatable decomposition is a MatrixDecomposition.Solver then this method should only return true if MatrixDecomposition.Solver.isSolvable() is true after the update.

Specified by:

updateColumn in interface MatrixDecomposition.Updatable<N extends java.lang.Comparable<N>>

Parameters:

columnIndex - 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.

doDecompose

private boolean doDecompose(Access2D.Collectable<N,? super PhysicalStore<N>> matrix,
                            boolean pivoting)

checkSolvability

protected boolean checkSolvability()

Overrides:

checkSolvability in class AbstractDecomposition<N extends java.lang.Comparable<N>,DecompositionStore<N extends java.lang.Comparable<N>>>

getReducedPivots

int[] getReducedPivots()

getWorkerColumn

PhysicalStore<N> getWorkerColumn(int nbRows)

getWorkerRow

PhysicalStore<N> getWorkerRow(int nbCols)