Module ojalgo

Package org.ojalgo.matrix.decomposition

Class DenseQR<N extends Comparable<N>>

java.lang.Object

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

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

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

All Implemented Interfaces:

MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Updatable<N>, QR<N>, Provider2D, Provider2D.Determinant<N>, Provider2D.Inverse<Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<Optional<MatrixStore<N>>>, DeterminantTask<N>, InverterTask<N>, MatrixTask<N>, SolverTask<N>, InvertibleFactor<N>, Structure1D, Structure2D

Direct Known Subclasses:

DenseQR.C128, DenseQR.H256, DenseQR.Q128, DenseQR.R064, DenseQR.R128

abstract class DenseQR<N extends Comparable<N>>
extends InPlaceDecomposition<N>
implements QR<N>

Nested Class Summary

Nested Classes

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

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

InvertibleFactor.IdentityFactor<N extends Comparable<N>>

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

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

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

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

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

QR.Factory<N extends 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 final boolean	myFullSize
private int	myNumberOfHouseholderTransformations

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

TYPICAL

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

C128, H256, Q128, R064, R128

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	DenseQR(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory, boolean fullSize)

Method Summary

Modifier and Type	Method	Description
void	btran(double[] arg)
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)
void	ftran(double[] arg)
N	getDeterminant()	A matrix' determinant is the product of its eigenvalues.
MatrixStore<N>	getInverse(PhysicalStore<N> preallocated)	Implementing this method is optional.
protected DecompositionStore<N>	getL()
MatrixStore<N>	getQ()
MatrixStore<N>	getR()
double	getRankThreshold()
MatrixStore<N>	getSolution(Access2D.Collectable<N,? super PhysicalStore<N>> rhs, PhysicalStore<N> preallocated)	Solve [A]*[X]=[B] by first solving [Q]*[Y]=[B] and then [R]*[X]=[Y].
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	isFullSize()
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)
void	reset()	Delete computed results, and resets attributes to default values
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.

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, copyColumn, copyRow, function, getDimensionalEpsilon, isAspectRatioNormal, isComputed, makeArray, makeDiagonal, makeEye, makeHouseholder, makeIdentity, makeRotation, makeRotation, makeZero, makeZero, 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.MatrixDecomposition

isComputed

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, getSolution, invert, preallocate, solve, toInverseProvider, toSolutionProvider

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

ftran, isOrdered, reconstruct, updateColumn

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 Details

myFullSize

private final boolean myFullSize

myNumberOfHouseholderTransformations

private int myNumberOfHouseholderTransformations

Constructor Details

DenseQR

protected DenseQR(PhysicalStore.Factory<N,? extends DecompositionStore<N>> factory,
 boolean fullSize)

Method Details

btran

public void btran(double[] arg)

Specified by:

btran in interface InvertibleFactor<N extends Comparable<N>>

See Also:

• InvertibleFactor.IdentityFactor.btran(PhysicalStore)

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 Comparable<N>>

Parameters:

arg - [b] transformed into [x]

calculateDeterminant

public N calculateDeterminant(Access2D<?> matrix)

Specified by:

calculateDeterminant in interface DeterminantTask<N extends Comparable<N>>

countSignificant

public int countSignificant(double threshold)

Specified by:

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

Parameters:

matrix - A matrix to decompose

Returns:

true if decomposition suceeded; false if not

ftran

public void ftran(double[] arg)

Specified by:

ftran in interface InvertibleFactor<N extends Comparable<N>>

See Also:

• InvertibleFactor.IdentityFactor.ftran(PhysicalStore)

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 Comparable<N>>

Specified by:

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

Overrides:

getInverse in class InPlaceDecomposition<N extends 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

getQ

public MatrixStore<N> getQ()

Specified by:

getQ in interface QR<N extends Comparable<N>>

getR

public MatrixStore<N> getR()

Specified by:

getR in interface QR<N extends Comparable<N>>

getRankThreshold

public double getRankThreshold()

Specified by:

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

getSolution

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

Solve [A]*[X]=[B] by first solving [Q]*[Y]=[B] and then [R]*[X]=[Y]. [X] minimises the 2-norm of [Q]*[R]*[X]-[B].

Specified by:

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

Parameters:

rhs - The right hand side [B]

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] "preallocated" is used to form the results, but the solution is in the returned MatrixStore.

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 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 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.

Returns:

The inverse

Throws:

RecoverableCondition - TODO

isFullSize

public boolean isFullSize()

Specified by:

isFullSize in interface MatrixDecomposition.EconomySize<N extends Comparable<N>>

Returns:

True if it will generate a full sized decomposition.

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 Comparable<N>>

Overrides:

isSolvable in class AbstractDecomposition<N extends Comparable<N>,DecompositionStore<N extends 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 Comparable<N>>

reset

public void reset()

Description copied from interface: MatrixDecomposition

Delete computed results, and resets attributes to default values

Specified by:

reset in interface MatrixDecomposition<N extends Comparable<N>>

Overrides:

reset in class AbstractDecomposition<N extends Comparable<N>,DecompositionStore<N extends 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 Comparable<N>>

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/ /correct solution.

Returns:

The solution

Throws:

RecoverableCondition

checkSolvability

protected boolean checkSolvability()

Overrides:

checkSolvability in class AbstractDecomposition<N extends Comparable<N>,DecompositionStore<N extends Comparable<N>>>

getL

protected DecompositionStore<N> getL()

Returns:

L as in R^T.