Package org.ojalgo.matrix.decomposition
Interface LDL<N extends Comparable<N>>
- All Superinterfaces:
DeterminantTask<N>
,InverterTask<N>
,InvertibleFactor<N>
,LDU<N>
,MatrixDecomposition<N>
,MatrixDecomposition.Determinant<N>
,MatrixDecomposition.Hermitian<N>
,MatrixDecomposition.Ordered<N>
,MatrixDecomposition.Pivoting<N>
,MatrixDecomposition.RankRevealing<N>
,MatrixDecomposition.Solver<N>
,MatrixTask<N>
,Provider2D
,Provider2D.Determinant<N>
,Provider2D.Inverse<Optional<MatrixStore<N>>>
,Provider2D.Rank
,Provider2D.Solution<Optional<MatrixStore<N>>>
,SolverTask<N>
,Structure1D
,Structure2D
- All Known Implementing Classes:
LDLDecomposition
,LDLDecomposition.C128
,LDLDecomposition.H256
,LDLDecomposition.Q128
,LDLDecomposition.R064
,LDLDecomposition.R128
public interface LDL<N extends Comparable<N>>
extends LDU<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Pivoting<N>
LDL: [A] = [L][D][L]H (or [R]H[D][R])
[A]H = [A] = [L][D][L]H
If [A] is symmetric (but not necessarily positive definite) then it can be decomposed into [L][D][L] T (or [R]H[D][R]).
- [L] is a unit lower (left) triangular matrix. It has the same dimensions as [this], and ones on the diagonal.
- [D] is a diagonal matrix. It has the same dimensions as [this].
- [this] = [L][D][L]H
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Nested Class Summary
Nested ClassesModifier and TypeInterfaceDescriptionstatic interface
LDL.Factory<N extends Comparable<N>>
static final class
LDL.ModifiedFactory<N extends Comparable<N>>
Nested classes/interfaces inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
InvertibleFactor.IdentityFactor<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.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
FieldsModifier and TypeFieldDescriptionstatic final LDL.Factory
<ComplexNumber> static final LDL.Factory
<Quaternion> static final LDL.Factory
<RationalNumber> static final LDL.Factory
<Double> static final LDL.Factory
<Quadruple> Fields inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition
TYPICAL
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Method Summary
Modifier and TypeMethodDescriptionstatic <N extends Comparable<N>>
booleanequals
(MatrixStore<N> matrix, LDL<N> decomposition, NumberContext context) getD()
default MatrixStore
<N> getL()
default MatrixStore
<N> getR()
static <N extends Comparable<N>>
LDL.Factory<N> modified
(LDL.Factory<N> delegate, N threshold) Will return a modified LDL decomposition algoritm.default MatrixStore
<N> Methods inherited from interface org.ojalgo.matrix.task.DeterminantTask
calculateDeterminant
Methods inherited from interface org.ojalgo.matrix.task.InverterTask
invert, invert, preallocate, preallocate
Methods inherited from interface org.ojalgo.matrix.transformation.InvertibleFactor
btran, 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.Hermitian
checkAndDecompose
Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Pivoting
decomposeWithoutPivoting, getPivotOrder, getReversePivotOrder, isPivoted
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, ftran, ftran, getInverse, getInverse, getSolution, getSolution, invert, isSolvable, solve, toInverseProvider, toSolutionProvider
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
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Field Details
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C128
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H256
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R064
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R128
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Q128
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Method Details
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equals
static <N extends Comparable<N>> boolean equals(MatrixStore<N> matrix, LDL<N> decomposition, NumberContext context) -
modified
Will return a modified LDL decomposition algoritm. It's the Gill, Murray and Wright (GMW) algorithm.The input threshold is the bound on the diagonal values.
The second parameter of the GMW algorithm, that is supposed to cap the magnitude of the elements in the triangular (Cholesky) matrices, is set to something very large. More correctly, it is assumed to be very large and therefore resulting in a negligible contribution to the algorithm.
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getD
MatrixStore<N> getD() -
getL
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getR
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reconstruct
- Specified by:
reconstruct
in interfaceMatrixDecomposition<N extends Comparable<N>>
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