Module ojalgo

Package org.ojalgo.matrix.decomposition

Interface Eigenvalue.Spectral<N extends java.lang.Comparable<N>>

All Superinterfaces:

DeterminantTask<N>, Eigenvalue<N>, InverterTask<N>, InvertibleFactor<N>, MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Values<N>, MatrixTask<N>, Provider2D, Provider2D.Condition, Provider2D.Determinant<N>, Provider2D.Eigenpairs, Provider2D.Inverse<java.util.Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<java.util.Optional<MatrixStore<N>>>, SingularValue<N>, SolverTask<N>, Structure1D, Structure2D

All Known Implementing Classes:

HermitianEvD, HermitianEvD.C128, HermitianEvD.H256, HermitianEvD.Q128, HermitianEvD.R064, HermitianEvD.R128, RawEigenvalue.Symmetric

Enclosing interface:

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

public static interface Eigenvalue.Spectral<N extends java.lang.Comparable<N>>
extends Eigenvalue<N>, SingularValue<N>

“Spectral decomposition” refers specifically to the orthogonal/unitary eigen-decomposition of a normal matrix (most commonly Hermitian / symmetric).

Eigenvalue decomposition of a normal matrix = spectral decomposition.

If, in addition to the matrix being normal, all eigenvalues are real and nonnegative, then the matrix is positive semidefinite, and the decomposition coincides with the SVD. If some eigenvalues are negative, the decomposition is still valid, and can be tweaked to yield a valid SVD by taking absolute values of the eigenvalues and adjusting the signs of the corresponding eigenvectors (on one side).

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.transformation.InvertibleFactor

InvertibleFactor.IdentityFactor<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.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.matrix.decomposition.SingularValue

SingularValue.Factory<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 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

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

C128, H256, Q128, R064, R128

Method Summary

Modifier and Type	Method	Description
boolean	isSPD()	A symmetric (Hermitian) matrix is positive definite if all its eigenvalues are positive.
default MatrixStore<N>	reconstruct()

Methods inherited from interface org.ojalgo.matrix.task.DeterminantTask

calculateDeterminant

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

getD, getEigenpair, getEigenpairs, getEigenvalues, getEigenvalues, getEigenvectors, getTrace, getV, isHermitian, isOrdered

Methods inherited from interface org.ojalgo.matrix.task.InverterTask

invert, invert, preallocate

Methods inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor

btran

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

decompose, isComputed, reset

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

getDeterminant, toDeterminantProvider

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

isFullSize

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

checkAndDecompose

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

countSignificant, getRank, getRankThreshold, isFullRank

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

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

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

computeValuesOnly

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

ftran, getCondition, getCovariance, getD, getFrobeniusNorm, getKyFanNorm, getOperatorNorm, getS, getSingularValues, getSingularValues, getTraceNorm, getU, getV, reconstruct

Methods inherited from interface org.ojalgo.matrix.task.SolverTask

preallocate, preallocate, solve, 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

Method Detail

isSPD

boolean isSPD()

A symmetric (Hermitian) matrix is positive definite if all its eigenvalues are positive.

reconstruct

default MatrixStore<N> reconstruct()

Specified by:

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

Specified by:

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

Specified by:

reconstruct in interface SingularValue<N extends java.lang.Comparable<N>>