Module ojalgo

Package org.ojalgo.matrix.decomposition

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

java.lang.Object

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

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

All Implemented Interfaces:

Eigenvalue<N>, MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.Values<N>, Provider2D, Provider2D.Determinant<N>, Provider2D.Eigenpairs, DeterminantTask<N>, MatrixTask<N>, Structure1D, Structure2D

Direct Known Subclasses:

DynamicEvD, GeneralEvD, GeneralisedEvD, HermitianEvD

abstract class DenseEigenvalue<N extends java.lang.Comparable<N>>
extends AbstractDecomposition<N,DecompositionStore<N>>
implements Eigenvalue<N>

Nested Class Summary

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

Eigenvalue.Eigenpair, Eigenvalue.Factory<N extends java.lang.Comparable<N>>, Eigenvalue.Generalisation, Eigenvalue.Generalised<N extends java.lang.Comparable<N>>, Eigenvalue.Spectral<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 MatrixStore<N>	myD
private Array1D<ComplexNumber>	myEigenvalues
private int	mySquareDim
private MatrixStore<N>	myV
private boolean	myValuesOnly

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

C128, DESCENDING_NORM, H256, Q128, R064, R128

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

TYPICAL

Constructor Summary

Constructors

Constructor	Description
DenseEigenvalue(PhysicalStore.Factory<N,? extends DecompositionStore<N>> aFactory)

Method Summary

Modifier and Type	Method	Description
N	calculateDeterminant(Access2D<?> matrix)
boolean	computeValuesOnly(Access2D.Collectable<N,? super TransformableRegion<N>> matrix)
boolean	decompose(Access2D.Collectable<N,? super TransformableRegion<N>> matrix)
private boolean	decompose(Access2D.Collectable<N,? super TransformableRegion<N>> matrix, boolean valuesOnly)
protected abstract boolean	doDecompose(Access2D.Collectable<N,? super TransformableRegion<N>> matrix, boolean valuesOnly)
int	getColDim()
MatrixStore<N>	getD()	The only requirements on [D] are that it should contain the eigenvalues and that [A][V] = [V][D].
Array1D<ComplexNumber>	getEigenvalues()	Even for real matrices the eigenvalues (and eigenvectors) are potentially complex numbers.
int	getMaxDim()
int	getMinDim()
int	getRowDim()
MatrixStore<N>	getV()	The columns of [V] represent the eigenvectors of [A] in the sense that [A][V] = [V][D].
(package private) boolean	isValuesOnly()
protected abstract MatrixStore<N>	makeD()
protected abstract Array1D<ComplexNumber>	makeEigenvalues()
protected abstract MatrixStore<N>	makeV()
void	reset()	Delete computed results, and resets attributes to default values
(package private) void	setD(MatrixStore<N> newD)
(package private) void	setEigenvalues(Array1D<ComplexNumber> eigenvalues)
(package private) void	setV(MatrixStore<N> newV)

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

aggregator, applyPivotOrder, applyReverseOrder, checkSolvability, collect, computed, function, getDimensionalEpsilon, isAspectRatioNormal, isComputed, isSolvable, 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.decomposition.Eigenvalue

getEigenpair, getEigenpairs, getEigenvalues, getEigenvectors, getTrace, isHermitian, isOrdered, reconstruct

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

isComputed

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

getDeterminant, toDeterminantProvider

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

checkAndDecompose

Methods inherited from interface org.ojalgo.structure.Structure2D

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

Field Detail

myD

private MatrixStore<N extends java.lang.Comparable<N>> myD

myEigenvalues

private Array1D<ComplexNumber> myEigenvalues

mySquareDim

private int mySquareDim

myV

private MatrixStore<N extends java.lang.Comparable<N>> myV

myValuesOnly

private boolean myValuesOnly

Constructor Detail

DenseEigenvalue

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

Method Detail

calculateDeterminant

public N calculateDeterminant(Access2D<?> matrix)

Specified by:

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

computeValuesOnly

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

Specified by:

computeValuesOnly in interface MatrixDecomposition.Values<N extends java.lang.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.

decompose

public final 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

getColDim

public int getColDim()

Specified by:

getColDim in interface Structure2D

Returns:

The number of columns

getD

public final MatrixStore<N> getD()

Description copied from interface: Eigenvalue

The only requirements on [D] are that it should contain the eigenvalues and that [A][V] = [V][D]. The ordering of the eigenvalues is not specified.

• If [A] is real and symmetric then [D] is (purely) diagonal with real eigenvalues.
• If [A] is real but not symmetric then [D] is block-diagonal with real eigenvalues in 1-by-1 blocks and complex eigenvalues in 2-by-2 blocks.
• If [A] is complex then [D] is (purely) diagonal with complex eigenvalues.

Specified by:

getD in interface Eigenvalue<N extends java.lang.Comparable<N>>

Returns:

The (block) diagonal eigenvalue matrix.

getEigenvalues

public final Array1D<ComplexNumber> getEigenvalues()

Description copied from interface: Eigenvalue

Even for real matrices the eigenvalues (and eigenvectors) are potentially complex numbers. Typically they need to be expressed as complex numbers when [A] is not symmetric.

The values should be in the same order as the matrices "V" and "D", and if they are ordered or not is indicated by the Eigenvalue.isOrdered() method.

Specified by:

getEigenvalues in interface Eigenvalue<N extends java.lang.Comparable<N>>

Returns:

The eigenvalues.

getMaxDim

public int getMaxDim()

Specified by:

getMaxDim in interface Structure2D

getMinDim

public int getMinDim()

Specified by:

getMinDim in interface Structure2D

getRowDim

public int getRowDim()

Specified by:

getRowDim in interface Structure2D

Returns:

The number of rows

getV

public final MatrixStore<N> getV()

Description copied from interface: Eigenvalue

The columns of [V] represent the eigenvectors of [A] in the sense that [A][V] = [V][D].

Specified by:

getV in interface Eigenvalue<N extends java.lang.Comparable<N>>

Returns:

The eigenvector matrix.

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 java.lang.Comparable<N>>

Overrides:

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

decompose

private final boolean decompose(Access2D.Collectable<N,? super TransformableRegion<N>> matrix,
                                boolean valuesOnly)

doDecompose

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

makeD

protected abstract MatrixStore<N> makeD()

makeEigenvalues

protected abstract Array1D<ComplexNumber> makeEigenvalues()

makeV

protected abstract MatrixStore<N> makeV()

isValuesOnly

boolean isValuesOnly()

setD

final void setD(MatrixStore<N> newD)

setEigenvalues

final void setEigenvalues(Array1D<ComplexNumber> eigenvalues)

setV

final void setV(MatrixStore<N> newV)