Interface Eigenvalue<N extends java.lang.Comparable<N>>
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- All Superinterfaces:
DeterminantTask<N>
,MatrixDecomposition<N>
,MatrixDecomposition.Determinant<N>
,MatrixDecomposition.Hermitian<N>
,MatrixDecomposition.Ordered<N>
,MatrixDecomposition.Values<N>
,MatrixTask<N>
,Provider2D
,Provider2D.Determinant<N>
,Provider2D.Eigenpairs
,Structure1D
,Structure2D
- All Known Subinterfaces:
Eigenvalue.Generalised<N>
- All Known Implementing Classes:
DynamicEvD
,DynamicEvD.R064
,EigenvalueDecomposition
,GeneralEvD
,GeneralEvD.R064
,GeneralisedEvD
,HermitianEvD
,HermitianEvD.C128
,HermitianEvD.H256
,HermitianEvD.Q128
,HermitianEvD.R064
,HermitianEvD.R128
,RawEigenvalue
,RawEigenvalue.Dynamic
,RawEigenvalue.General
,RawEigenvalue.Symmetric
public interface Eigenvalue<N extends java.lang.Comparable<N>> extends MatrixDecomposition<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.Values<N>, Provider2D.Eigenpairs
[A] = [V][D][V]-1 ([A][V] = [V][D])- [A] = any square matrix.
- [V] = contains the eigenvectors as columns.
- [D] = a diagonal matrix with the eigenvalues on the diagonal (possibly in blocks).
[A] is normal if [A][A]H = [A]H[A], and [A] is normal if and only if there exists a unitary matrix [Q] such that [A] = [Q][D][Q]H. Hermitian matrices are normal.
[V] and [D] can always be calculated in the sense that they will satisfy [A][V] = [V][D], but it is not always possible to calculate [V]-1. (Check the rank and/or the condition number of [V] to determine the validity of [V][D][V]-1.)
The eigenvalues (and their corresponding eigenvectors) of a non-symmetric matrix could be complex.
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Nested Class Summary
Nested Classes Modifier and Type Interface Description static class
Eigenvalue.Eigenpair
static interface
Eigenvalue.Factory<N extends java.lang.Comparable<N>>
static class
Eigenvalue.Generalisation
static interface
Eigenvalue.Generalised<N extends java.lang.Comparable<N>>
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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.Values<N extends java.lang.Comparable<N>>
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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>>
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Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D
Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback
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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>
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Field Summary
Fields Modifier and Type Field Description static Eigenvalue.Factory<ComplexNumber>
C128
static java.util.Comparator<ComplexNumber>
DESCENDING_NORM
Sorts on the norm in descending order.static Eigenvalue.Factory<Quaternion>
H256
static Eigenvalue.Factory<RationalNumber>
Q128
static Eigenvalue.Factory<java.lang.Double>
R064
static Eigenvalue.Factory<Quadruple>
R128
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Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
TYPICAL
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Method Summary
All Methods Static Methods Instance Methods Abstract Methods Default Methods Modifier and Type Method Description private void
copyEigenvector(int index, Array1D<ComplexNumber> destination)
static <N extends java.lang.Comparable<N>>
booleanequals(MatrixStore<N> matrix, Eigenvalue<N> decomposition, NumberContext context)
MatrixStore<N>
getD()
The only requirements on [D] are that it should contain the eigenvalues and that [A][V] = [V][D].default Eigenvalue.Eigenpair
getEigenpair(int index)
default java.util.List<Eigenvalue.Eigenpair>
getEigenpairs()
This list is always ordered in descending eigenvalue order – that's regardless of ifisOrdered()
returns true or false.Array1D<ComplexNumber>
getEigenvalues()
Even for real matrices the eigenvalues (and eigenvectors) are potentially complex numbers.default void
getEigenvalues(double[] realParts, java.util.Optional<double[]> imaginaryParts)
default MatrixStore<ComplexNumber>
getEigenvectors()
ComplexNumber
getTrace()
A matrix' trace is the sum of the diagonal elements.MatrixStore<N>
getV()
The columns of [V] represent the eigenvectors of [A] in the sense that [A][V] = [V][D].boolean
isHermitian()
If [A] is hermitian then [V][D][V]-1 becomes [Q][D][Q]H...boolean
isOrdered()
The eigenvalues in D (and the eigenvectors in V) are not necessarily ordered.default MatrixStore<N>
reconstruct()
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Methods inherited from interface org.ojalgo.matrix.task.DeterminantTask
calculateDeterminant
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
decompose, isComputed, reset
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant
getDeterminant, toDeterminantProvider
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Hermitian
checkAndDecompose
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Values
computeValuesOnly
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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
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Field Detail
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C128
static final Eigenvalue.Factory<ComplexNumber> C128
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DESCENDING_NORM
static final java.util.Comparator<ComplexNumber> DESCENDING_NORM
Sorts on the norm in descending order. If the 2 eigenvalues have equal norm then the usualComplexNumber
sort order is used (reversed).
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H256
static final Eigenvalue.Factory<Quaternion> H256
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Q128
static final Eigenvalue.Factory<RationalNumber> Q128
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R064
static final Eigenvalue.Factory<java.lang.Double> R064
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R128
static final Eigenvalue.Factory<Quadruple> R128
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Method Detail
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equals
static <N extends java.lang.Comparable<N>> boolean equals(MatrixStore<N> matrix, Eigenvalue<N> decomposition, NumberContext context)
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copyEigenvector
private void copyEigenvector(int index, Array1D<ComplexNumber> destination)
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getD
MatrixStore<N> getD()
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.
- Returns:
- The (block) diagonal eigenvalue matrix.
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getEigenpair
default Eigenvalue.Eigenpair getEigenpair(int index)
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getEigenpairs
default java.util.List<Eigenvalue.Eigenpair> getEigenpairs()
This list is always ordered in descending eigenvalue order – that's regardless of ifisOrdered()
returns true or false.- Specified by:
getEigenpairs
in interfaceProvider2D.Eigenpairs
- See Also:
Provider2D.Eigenpairs.getEigenpairs()
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getEigenvalues
Array1D<ComplexNumber> getEigenvalues()
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 is ordered or not is indicated by the
isOrdered()
method.- Returns:
- The eigenvalues.
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getEigenvalues
default void getEigenvalues(double[] realParts, java.util.Optional<double[]> imaginaryParts)
- Parameters:
realParts
- An array that will receive the real parts of the eigenvaluesimaginaryParts
- An optional array that, if present, will receive the imaginary parts of the eigenvalues
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getEigenvectors
default MatrixStore<ComplexNumber> getEigenvectors()
- Returns:
- A complex valued alternative to
getV()
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getTrace
ComplexNumber getTrace()
A matrix' trace is the sum of the diagonal elements. It is also the sum of the eigenvalues. This method should return the sum of the eigenvalues.- Returns:
- The matrix' trace
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getV
MatrixStore<N> getV()
The columns of [V] represent the eigenvectors of [A] in the sense that [A][V] = [V][D].- Returns:
- The eigenvector matrix.
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isHermitian
boolean isHermitian()
If [A] is hermitian then [V][D][V]-1 becomes [Q][D][Q]H...
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isOrdered
boolean isOrdered()
The eigenvalues in D (and the eigenvectors in V) are not necessarily ordered. This is a property of the algorithm/implementation, not the data.- Specified by:
isOrdered
in interfaceMatrixDecomposition.Ordered<N extends java.lang.Comparable<N>>
- Returns:
- true if they are ordered
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reconstruct
default MatrixStore<N> reconstruct()
- Specified by:
reconstruct
in interfaceMatrixDecomposition<N extends java.lang.Comparable<N>>
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