Class DenseSingularValue<N extends Comparable<N>>

java.lang.Object

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

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

All Implemented Interfaces:

MatrixDecomposition<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Values<N>, SingularValue<N>, Provider2D, Provider2D.Condition, Provider2D.Inverse<Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<Optional<MatrixStore<N>>>, InverterTask<N>, MatrixTask<N>, SolverTask<N>, InvertibleFactor<N>, Structure1D, Structure2D

Direct Known Subclasses:

DenseSingularValue.C128, DenseSingularValue.H256, DenseSingularValue.Q128, DenseSingularValue.R064, DenseSingularValue.R128

abstract class DenseSingularValue<N extends Comparable<N>>
extends AbstractDecomposition<N, DecompositionStore<N>>
implements SingularValue<N>

Nested Class Summary

Nested Classes

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

Nested classes/interfaces inherited from interface InvertibleFactor

InvertibleFactor.IdentityFactor<N>

Nested classes/interfaces inherited from interface MatrixDecomposition

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

Nested classes/interfaces inherited from interface Provider2D

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

Nested classes/interfaces inherited from interface SingularValue

SingularValue.Factory<N>

Nested classes/interfaces inherited from interface Structure1D

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

Nested classes/interfaces inherited from interface Structure2D

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

Field Summary

Fields

Modifier and Type	Field	Description
private double[]	e
private final DenseBidiagonal<N>	myBidiagonal
private final boolean	myFullSize
private final Structure2D	myInputStructure
private MatrixStore<N>	myInverse
private MatrixStore<N>	myS
private Array1D<Double>	mySingularValues
private boolean	myTransposed
private MatrixStore<N>	myU
private MatrixStore<N>	myV
private boolean	myValuesOnly
private double[]	s
private static final double	TINY	≈ 1.6E-291

Fields inherited from interface MatrixDecomposition

TYPICAL

Fields inherited from interface SingularValue

C128, H256, Q128, R064, R128

Constructor Summary

Constructors

Constructor	Description
DenseSingularValue(PhysicalStore.Factory<N, ? extends DecompositionStore<N>> factory, DenseBidiagonal<N> bidiagonal, boolean fullSize)

Method Summary

Modifier and Type	Method	Description
void	btran(double[] arg)
final void	btran(PhysicalStore<N> arg)	Backwards-transformation
protected boolean	checkSolvability()
protected boolean	compute(Access2D.Collectable<N, ? super TransformableRegion<N>> matrix, boolean valuesOnly, boolean fullSize)
protected boolean	computeBidiagonal(Access2D.Collectable<N, ? super TransformableRegion<N>> matrix, boolean fullSize)
boolean	computeValuesOnly(Access2D.Collectable<N, ? super TransformableRegion<N>> matrix)
int	countSignificant(double threshold)
boolean	decompose(Access2D.Collectable<N, ? super TransformableRegion<N>> matrix)
private static void	doCase1(double[] s, double[] e, int p, int k, RotateRight q2RotR)
private static void	doCase2(double[] s, double[] e, int p, int k, RotateRight mtrxQ1)
private static void	doCase3(double[] s, double[] e, int p, int k, RotateRight q1RotR, RotateRight q2RotR)
private static void	doCase4(double[] s, int k, NegateColumn q2NegCol, ExchangeColumns q1XchgCols, ExchangeColumns q2XchgCols)
protected boolean	doCompute(Access2D.Collectable<N, ? super TransformableRegion<N>> matrix, boolean valuesOnly, boolean fullSize)
void	ftran(double[] arg)
int	getColDim()
double	getCondition()	The condition number.
MatrixStore<N>	getCovariance()
MatrixStore<N>	getD()	Deprecated. Use getS() instead
double	getFrobeniusNorm()	Sometimes also called the Schatten 2-norm or Hilbert-Schmidt norm.
MatrixStore<N>	getInverse()	The output must be a "right inverse" and a "generalised inverse".
MatrixStore<N>	getInverse(PhysicalStore<N> preallocated)	Implementing this method is optional.
private MatrixStore<N>	getInverseOldVersion(DecompositionStore<N> preallocated)
double	getKyFanNorm(int k)	Ky Fan k-norm.
double	getOperatorNorm()
double	getRankThreshold()
int	getRowDim()
MatrixStore<N>	getS()
Array1D<Double>	getSingularValues()
MatrixStore<N>	getSolution(Access2D.Collectable<N, ? super PhysicalStore<N>> rhs, PhysicalStore<N> preallocated)	Implementing this method is optional.
double	getTraceNorm()
MatrixStore<N>	getU()	If [A] is m-by-n and its rank is r, then: The first r columns of [U] span the column space, range or image of [A]. The last m-r columns of [U] span the left nullspace or cokernel of [A]. Calculating the QR decomposition of [A] is a faster alternative.
MatrixStore<N>	getV()	If [A] is m-by-n and its rank is r, then: The first r columns of [V] span the row space or coimage of [A]. The last n-r columns of [V] span the nullspace or kernel of [A]. Calculating the QR decomposition of [A]T is a faster alternative.
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	isFullRank()
boolean	isFullSize()
boolean	isOrdered()	This is a property of the algorithm/implementation, not the data.
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.
protected boolean	isTransposed()
protected MatrixStore<N>	makeD()
protected Array1D<Double>	makeSingularValues()
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)	[A][X]=[B] or [body][return]=[rhs]
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.
(package private) static void	toDiagonal(double[] s, double[] e, RotateRight q1RotR, RotateRight q2RotR, ExchangeColumns q1XchgCols, ExchangeColumns q2XchgCols, NegateColumn q2NegCol)

Methods inherited from class 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 Object

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

Methods inherited from interface InverterTask

preallocate

Methods inherited from interface MatrixDecomposition

isComputed

Methods inherited from interface MatrixDecomposition.RankRevealing

getRank

Methods inherited from interface MatrixDecomposition.Solver

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

Methods inherited from interface SingularValue

ftran, getSingularValues, reconstruct, reconstruct

Methods inherited from interface SolverTask

preallocate

Methods inherited from interface Structure2D

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

Field Details

TINY

private static final double TINY

≈ 1.6E-291

e

private double[] e

myBidiagonal

private final DenseBidiagonal<N extends Comparable<N>> myBidiagonal

myFullSize

private final boolean myFullSize

myInputStructure

private final Structure2D myInputStructure

myInverse

private transient MatrixStore<N extends Comparable<N>> myInverse

myS

private transient MatrixStore<N extends Comparable<N>> myS

mySingularValues

private transient Array1D<Double> mySingularValues

myTransposed

private boolean myTransposed

myU

private transient MatrixStore<N extends Comparable<N>> myU

myV

private transient MatrixStore<N extends Comparable<N>> myV

myValuesOnly

private boolean myValuesOnly

s

private double[] s

Constructor Details

DenseSingularValue

DenseSingularValue(PhysicalStore.Factory<N, ? extends DecompositionStore<N>> factory,
 DenseBidiagonal<N> bidiagonal,
 boolean fullSize)

Method Details

doCase1

private static void doCase1(double[] s,
 double[] e,
 int p,
 int k,
 RotateRight q2RotR)

doCase2

private static void doCase2(double[] s,
 double[] e,
 int p,
 int k,
 RotateRight mtrxQ1)

doCase3

private static void doCase3(double[] s,
 double[] e,
 int p,
 int k,
 RotateRight q1RotR,
 RotateRight q2RotR)

doCase4

private static void doCase4(double[] s,
 int k,
 NegateColumn q2NegCol,
 ExchangeColumns q1XchgCols,
 ExchangeColumns q2XchgCols)

toDiagonal

static void toDiagonal(double[] s,
 double[] e,
 RotateRight q1RotR,
 RotateRight q2RotR,
 ExchangeColumns q1XchgCols,
 ExchangeColumns q2XchgCols,
 NegateColumn q2NegCol)

btran

public void btran(double[] arg)

Specified by:

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

See Also:

• InvertibleFactor.IdentityFactor.btran(PhysicalStore)

btran

public final 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]

computeValuesOnly

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

Specified by:

computeValuesOnly in interface MatrixDecomposition.Values<N extends Comparable<N>>

Parameters:

matrix - The matrix to decompose

Returns:

The same as MatrixDecomposition.Solver.compute(Collectable) or MatrixDecomposition.decompose(Collectable) if the instance does not implement MatrixDecomposition.Solver.

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)

getColDim

public int getColDim()

Specified by:

getColDim in interface Structure2D

Returns:

The number of columns

getCondition

public double getCondition()

Description copied from interface: SingularValue

The condition number.

Specified by:

getCondition in interface Provider2D.Condition

Specified by:

getCondition in interface SingularValue<N extends Comparable<N>>

Returns:

The largest singular value divided by the smallest singular value.

getCovariance

public MatrixStore<N> getCovariance()

Specified by:

getCovariance in interface SingularValue<N extends Comparable<N>>

Returns:

[[A]^T[A]]^-1 Where [A] is the original matrix.

getD

@Deprecated
public MatrixStore<N> getD()

Deprecated.

Use getS() instead

Specified by:

getD in interface SingularValue<N extends Comparable<N>>

Returns:

The diagonal matrix of singular values.

getFrobeniusNorm

public double getFrobeniusNorm()

Description copied from interface: SingularValue

Sometimes also called the Schatten 2-norm or Hilbert-Schmidt norm.

Specified by:

getFrobeniusNorm in interface SingularValue<N extends Comparable<N>>

Returns:

The square root of the sum of squares of the singular values.

getInverse

public MatrixStore<N> getInverse()

Description copied from interface: MatrixDecomposition.Solver

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

Specified by:

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

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>>

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

getKyFanNorm

public double getKyFanNorm(int k)

Description copied from interface: SingularValue

Ky Fan k-norm.

The first Ky Fan k-norm is the operator norm (the largest singular value), and the last is called the trace norm (the sum of all singular values).

Specified by:

getKyFanNorm in interface SingularValue<N extends Comparable<N>>

Parameters:

k - The number of singular values to add up.

Returns:

The sum of the k largest singular values.

getOperatorNorm

public double getOperatorNorm()

Specified by:

getOperatorNorm in interface SingularValue<N extends Comparable<N>>

Returns:

2-norm

getRankThreshold

public double getRankThreshold()

Specified by:

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

getRowDim

public int getRowDim()

Specified by:

getRowDim in interface Structure2D

Returns:

The number of rows

getS

public MatrixStore<N> getS()

Specified by:

getS in interface SingularValue<N extends Comparable<N>>

Returns:

The diagonal matrix of singular values.

getSingularValues

public Array1D<Double> getSingularValues()

Specified by:

getSingularValues in interface SingularValue<N extends Comparable<N>>

Returns:

The singular values ordered in descending order.

getSolution

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

Specified by:

getSolution in interface MatrixDecomposition.Solver<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/final/correct solution. Use SolverTask.preallocate(int, int, int) or SolverTask.preallocate(Structure2D, Structure2D) to get a suitable instance.

Returns:

The solution

getTraceNorm

public double getTraceNorm()

Specified by:

getTraceNorm in interface SingularValue<N extends Comparable<N>>

getU

public MatrixStore<N> getU()

Description copied from interface: SingularValue

If [A] is m-by-n and its rank is r, then:

• The first r columns of [U] span the column space, range or image of [A].
• The last m-r columns of [U] span the left nullspace or cokernel of [A].

Calculating the QR decomposition of [A] is a faster alternative.

Specified by:

getU in interface SingularValue<N extends Comparable<N>>

getV

public MatrixStore<N> getV()

Description copied from interface: SingularValue

If [A] is m-by-n and its rank is r, then:

• The first r columns of [V] span the row space or coimage of [A].
• The last n-r columns of [V] span the nullspace or kernel of [A].

Calculating the QR decomposition of [A]^T is a faster alternative.

Specified by:

getV in interface SingularValue<N extends Comparable<N>>

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

isFullRank

public boolean isFullRank()

Specified by:

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

Returns:

true if the rank is equal to the minimum of the row and column dimensions; false if not

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.

isOrdered

public boolean isOrdered()

Description copied from interface: MatrixDecomposition.Ordered

This is a property of the algorithm/implementation, not the data. Typically relevant for SingularValue, Eigenvalue or any MatrixDecomposition.RankRevealing decomposition.

Specified by:

isOrdered in interface MatrixDecomposition.Ordered<N extends Comparable<N>>

Returns:

true if the rows/columns of the returned matrix factors are guaranteed some specific order; false if there is no such guarantee.

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)
                     throws RecoverableCondition

Description copied from interface: SolverTask

[A][X]=[B] or [body][return]=[rhs]

Specified by:

solve in interface SolverTask<N extends Comparable<N>>

Throws:

RecoverableCondition

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

getInverseOldVersion

private MatrixStore<N> getInverseOldVersion(DecompositionStore<N> preallocated)

checkSolvability

protected boolean checkSolvability()

Overrides:

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

compute

protected boolean compute(Access2D.Collectable<N, ? super TransformableRegion<N>> matrix,
 boolean valuesOnly,
 boolean fullSize)

computeBidiagonal

protected boolean computeBidiagonal(Access2D.Collectable<N, ? super TransformableRegion<N>> matrix,
 boolean fullSize)

doCompute

protected boolean doCompute(Access2D.Collectable<N, ? super TransformableRegion<N>> matrix,
 boolean valuesOnly,
 boolean fullSize)

isTransposed

protected boolean isTransposed()

makeD

protected MatrixStore<N> makeD()

makeSingularValues

protected Array1D<Double> makeSingularValues()