Package org.ojalgo.matrix.decomposition
Class GeneralEvD.R064
- java.lang.Object
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- org.ojalgo.matrix.decomposition.AbstractDecomposition<N>
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- org.ojalgo.matrix.decomposition.GenericDecomposition<N>
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- org.ojalgo.matrix.decomposition.EigenvalueDecomposition<N>
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- org.ojalgo.matrix.decomposition.GeneralEvD<java.lang.Double>
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- org.ojalgo.matrix.decomposition.GeneralEvD.R064
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- All Implemented Interfaces:
Eigenvalue<java.lang.Double>
,MatrixDecomposition<java.lang.Double>
,MatrixDecomposition.Determinant<java.lang.Double>
,MatrixDecomposition.Hermitian<java.lang.Double>
,MatrixDecomposition.Ordered<java.lang.Double>
,MatrixDecomposition.Values<java.lang.Double>
,Provider2D
,Provider2D.Determinant<java.lang.Double>
,Provider2D.Eigenpairs
,DeterminantTask<java.lang.Double>
,MatrixTask<java.lang.Double>
,Structure1D
,Structure2D
- Enclosing class:
- GeneralEvD<N extends java.lang.Comparable<N>>
static final class GeneralEvD.R064 extends GeneralEvD<java.lang.Double>
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
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Nested classes/interfaces inherited from class org.ojalgo.matrix.decomposition.GeneralEvD
GeneralEvD.R064
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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>>
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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.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.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
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Fields inherited from interface org.ojalgo.matrix.decomposition.Eigenvalue
C128, DESCENDING_NORM, H256, Q128, R064, R128
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Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
TYPICAL
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Constructor Summary
Constructors Constructor Description R064()
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Method Summary
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Methods inherited from class org.ojalgo.matrix.decomposition.GeneralEvD
checkAndDecompose, checkSolvability, doDecompose, getDeterminant, getInverse, getInverse, getTrace, isHermitian, isOrdered, makeD, makeEigenvalues, makeInverse, makeV
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Methods inherited from class org.ojalgo.matrix.decomposition.EigenvalueDecomposition
calculateDeterminant, computeValuesOnly, decompose, getColDim, getD, getEigenvalues, getMaxDim, getMinDim, getRowDim, getV, reset, setD, setEigenvalues, setV, sort
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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
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Methods inherited from class org.ojalgo.matrix.decomposition.AbstractDecomposition
computed, countColumns, countRows, getDimensionalEpsilon, isAspectRatioNormal, isComputed, isSolvable
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface org.ojalgo.matrix.decomposition.Eigenvalue
getEigenpair, getEigenpairs, getEigenvalues, getEigenvectors, reconstruct
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
isComputed
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Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant
toDeterminantProvider
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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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