org.ojalgo.matrix.decomposition
Class SingularValueDecomposition<N extends Number & Comparable<N>>

java.lang.Object
  org.ojalgo.matrix.decomposition.SingularValueDecomposition<N>

All Implemented Interfaces:

MatrixDecomposition<N>, SingularValue<N>

public abstract class SingularValueDecomposition<N extends Number & Comparable<N>>
extends Object
implements SingularValue<N>

You create instances of (some subclass of) this class by calling one of the static factory methods: makeBig(), makeComplex(), makePrimitive(), makeAlternative() or makeJama().

Author:

apete

Method Summary

boolean	compute(Access2D<?> aMtrx)
boolean	compute(Access2D<?> aMtrx, boolean singularValuesOnly)
boolean	equals(MatrixDecomposition<N> aDecomp, NumberContext aCntxt)
boolean	equals(Object someObj)
double	getCondition() The condition number.
MatrixStore<N>	getD()
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(DecompositionStore<N> preallocated) Implementiong this method is optional.
double	getKyFanNorm(int k) Ky Fan k-norm.
double	getOperatorNorm()
MatrixStore<N>	getQ1()
MatrixStore<N>	getQ2()
int	getRank() Effective numerical matrix rank.
Array1D<Double>	getSingularValues()
double	getTraceNorm()
boolean	isAspectRatioNormal()
boolean	isComputed()
static <N extends Number> SingularValue<N>	make(Access2D<N> aTypical)
static SingularValue<Double>	makeAlternative()
static SingularValue<BigDecimal>	makeBig()
static SingularValue<ComplexNumber>	makeComplex()
static SingularValue<Double>	makeJama()
static SingularValue<Double>	makePrimitive()
MatrixStore<N>	reconstruct()
void	reset() Delete computed results, and resets attributes to default values
MatrixStore<N>	solve(MatrixStore<N> aRHS) [A][X]=[B] or [this][return]=[aRHS]
MatrixStore<N>	solve(MatrixStore<N> aRHS, DecompositionStore<N> preallocated) Implementiong this method is optional.

Methods inherited from class java.lang.Object

getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

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

isOrdered

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

equals, equals, isComputed, isFullSize, isSolvable

Method Detail

make

public static final <N extends Number> SingularValue<N> make(Access2D<N> aTypical)

makeAlternative

public static final SingularValue<Double> makeAlternative()

makeBig

public static final SingularValue<BigDecimal> makeBig()

makeComplex

public static final SingularValue<ComplexNumber> makeComplex()

makeJama

public static final SingularValue<Double> makeJama()

makePrimitive

public static final SingularValue<Double> makePrimitive()

compute

public final boolean compute(Access2D<?> aMtrx)

Specified by:

compute in interface MatrixDecomposition<N extends Number & Comparable<N>>

Parameters:

aMtrx - A matrix to decompose

Returns:

true if the computation suceeded; false if not

compute

public boolean compute(Access2D<?> aMtrx,
                       boolean singularValuesOnly)

Specified by:

compute in interface SingularValue<N extends Number & Comparable<N>>

Parameters:

aMtrx - A matrix to decompose

singularValuesOnly - No need to calculate eigenvectors

Returns:

true/false if the computation succeeded or not

getCondition

public final double getCondition()

Description copied from interface: SingularValue

The condition number.

Specified by:

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

Returns:

The largest singular value divided by the smallest singular value.

getD

public final MatrixStore<N> getD()

Specified by:

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

Returns:

The diagonal matrix of singular values.

getFrobeniusNorm

public final 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 Number & Comparable<N>>

Returns:

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

getInverse

public final MatrixStore<N> getInverse()

Description copied from interface: MatrixDecomposition

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

Specified by:

getInverse in interface MatrixDecomposition<N extends Number & Comparable<N>>

See Also:

BasicMatrix.invert()

getInverse

public final MatrixStore<N> getInverse(DecompositionStore<N> preallocated)

Description copied from interface: MatrixDecomposition

Implementiong 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.getInverse().

Specified by:

getInverse in interface MatrixDecomposition<N extends Number & 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

getKyFanNorm

public final 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 Number & Comparable<N>>

Parameters:

k - The number of singular values to add up.

Returns:

The sum of the k largest singular values.

getOperatorNorm

public final double getOperatorNorm()

Specified by:

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

Returns:

2-norm

getQ1

public final MatrixStore<N> getQ1()

Specified by:

getQ1 in interface SingularValue<N extends Number & Comparable<N>>

getQ2

public final MatrixStore<N> getQ2()

Specified by:

getQ2 in interface SingularValue<N extends Number & Comparable<N>>

getRank

public final int getRank()

Description copied from interface: SingularValue

Effective numerical matrix rank.

Specified by:

getRank in interface SingularValue<N extends Number & Comparable<N>>

Returns:

The number of nonnegligible singular values.

getSingularValues

public final Array1D<Double> getSingularValues()

Specified by:

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

Returns:

The singular values ordered in descending order.

getTraceNorm

public final double getTraceNorm()

Specified by:

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

isAspectRatioNormal

public final boolean isAspectRatioNormal()

reconstruct

public MatrixStore<N> reconstruct()

Specified by:

reconstruct in interface MatrixDecomposition<N extends Number & 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 Number & Comparable<N>>

solve

public MatrixStore<N> solve(MatrixStore<N> aRHS)

Description copied from interface: MatrixDecomposition

[A][X]=[B] or [this][return]=[aRHS]

Specified by:

solve in interface MatrixDecomposition<N extends Number & Comparable<N>>

solve

public MatrixStore<N> solve(MatrixStore<N> aRHS,
                            DecompositionStore<N> preallocated)

Description copied from interface: MatrixDecomposition

Implementiong 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.solve(MatrixStore).

Specified by:

solve in interface MatrixDecomposition<N extends Number & Comparable<N>>

Parameters:

aRHS - 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.

Returns:

The solution

equals

public final boolean equals(MatrixDecomposition<N> aDecomp,
                            NumberContext aCntxt)

Specified by:

equals in interface MatrixDecomposition<N extends Number>

equals

public boolean equals(Object someObj)

Overrides:

equals in class Object

isComputed

public final boolean isComputed()

Specified by:

isComputed in interface MatrixDecomposition<N extends Number>

Returns:

true if computation has been attemped; false if not.

See Also:

MatrixDecomposition.compute(Access2D), MatrixDecomposition.isSolvable()