Package org.ojalgo.matrix.decomposition
Class GeneralEvD.R064
java.lang.Object
- All Implemented Interfaces:
Eigenvalue<Double>
,MatrixDecomposition<Double>
,MatrixDecomposition.Determinant<Double>
,MatrixDecomposition.Hermitian<Double>
,MatrixDecomposition.Ordered<Double>
,MatrixDecomposition.Values<Double>
,Provider2D
,Provider2D.Determinant<Double>
,Provider2D.Eigenpairs
,DeterminantTask<Double>
,MatrixTask<Double>
,Structure1D
,Structure2D
- Enclosing class:
GeneralEvD<N extends Comparable<N>>
Eigenvalues and eigenvectors of a real matrix.
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.times(D.times(V.transpose())) and V.times(V.transpose()) equals the identity matrix.
If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond().
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Nested Class Summary
Nested classes/interfaces inherited from class org.ojalgo.matrix.decomposition.GeneralEvD
GeneralEvD.R064
Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.Eigenvalue
Eigenvalue.Eigenpair, Eigenvalue.Factory<N extends Comparable<N>>, Eigenvalue.Generalisation, Eigenvalue.Generalised<N extends Comparable<N>>
Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
MatrixDecomposition.Determinant<N extends Comparable<N>>, MatrixDecomposition.EconomySize<N extends Comparable<N>>, MatrixDecomposition.Factory<D extends MatrixDecomposition<?>>, MatrixDecomposition.Hermitian<N extends Comparable<N>>, MatrixDecomposition.Ordered<N extends Comparable<N>>, MatrixDecomposition.Pivoting<N extends Comparable<N>>, MatrixDecomposition.RankRevealing<N extends Comparable<N>>, MatrixDecomposition.Solver<N extends Comparable<N>>, MatrixDecomposition.Values<N extends Comparable<N>>
Nested classes/interfaces inherited from interface org.ojalgo.matrix.Provider2D
Provider2D.Condition, Provider2D.Determinant<N extends Comparable<N>>, Provider2D.Eigenpairs, Provider2D.Hermitian, Provider2D.Inverse<M>, Provider2D.Rank, Provider2D.Solution<M>, Provider2D.Symmetric, Provider2D.Trace<N extends 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
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Constructor Summary
Constructors -
Method Summary
Methods inherited from class org.ojalgo.matrix.decomposition.GeneralEvD
checkAndDecompose, checkSolvability, doDecompose, getDeterminant, getInverse, getInverse, getTrace, isHermitian, isOrdered, makeD, makeEigenvalues, makeInverse, makeV
Methods inherited from class org.ojalgo.matrix.decomposition.EigenvalueDecomposition
calculateDeterminant, computeValuesOnly, decompose, getColDim, getD, getEigenvalues, getMaxDim, getMinDim, getRowDim, getV, reset, setD, setEigenvalues, setV, sort
Methods inherited from class org.ojalgo.matrix.decomposition.GenericDecomposition
aggregator, allocate, collect, copy, function, makeArray, makeDiagonal, makeEye, makeHouseholder, makeIdentity, makeRotation, makeRotation, makeZero, makeZero, scalar, wrap
Methods inherited from class org.ojalgo.matrix.decomposition.AbstractDecomposition
computed, countColumns, countRows, getDimensionalEpsilon, isAspectRatioNormal, isComputed, isSolvable
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, reconstruct
Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
isComputed
Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant
toDeterminantProvider
Methods inherited from interface org.ojalgo.structure.Structure2D
count, countColumns, countRows, firstInColumn, firstInRow, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size
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Constructor Details
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R064
R064()
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