Module ojalgo

Package org.ojalgo.matrix.decomposition

Interface LDL<N extends java.lang.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<java.util.Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<java.util.Optional<MatrixStore<N>>>, SolverTask<N>, Structure1D, Structure2D

All Known Implementing Classes:

DenseLDL, DenseLDL.C128, DenseLDL.H256, DenseLDL.Q128, DenseLDL.R064, DenseLDL.R128, SparseQDLDL

public interface LDL<N extends java.lang.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

Nested Class Summary

Nested Classes

Modifier and Type	Interface	Description
static interface	LDL.Factory<N extends java.lang.Comparable<N>>
static class	LDL.ModifiedFactory<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.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

Modifier and Type	Field	Description
static LDL.Factory<ComplexNumber>	C128
static LDL.Factory<Quaternion>	H256
static LDL.Factory<RationalNumber>	Q128
static LDL.Factory<java.lang.Double>	R064
static LDL.Factory<Quadruple>	R128

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

TYPICAL

Method Summary

Modifier and Type	Method	Description
static <N extends java.lang.Comparable<N>> boolean	equals(MatrixStore<N> matrix, LDL<N> decomposition, NumberContext context)
MatrixStore<N>	getD()
default MatrixStore<N>	getL()	Must implement either getL() or getR().
default MatrixStore<N>	getR()	Must implement either getL() or getR().
static <N extends java.lang.Comparable<N>> LDL.Factory<N>	modified(LDL.Factory<N> delegate, N threshold)	Will return a modified LDL decomposition algoritm.
static LDL<java.lang.Double>	newSparseR064()
default MatrixStore<N>	reconstruct()

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

calculateDeterminant

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

invert, invert, preallocate

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

btran, btran, ftran, ftran

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

isOrdered

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, getInverse, getInverse, getSolution, getSolution, invert, isSolvable, preallocate, 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

Field Detail

C128

static final LDL.Factory<ComplexNumber> C128

H256

static final LDL.Factory<Quaternion> H256

Q128

static final LDL.Factory<RationalNumber> Q128

R064

static final LDL.Factory<java.lang.Double> R064

R128

static final LDL.Factory<Quadruple> R128

Method Detail

newSparseR064

static LDL<java.lang.Double> newSparseR064()

equals

static <N extends java.lang.Comparable<N>> boolean equals(MatrixStore<N> matrix,
                                                          LDL<N> decomposition,
                                                          NumberContext context)

modified

static <N extends java.lang.Comparable<N>> LDL.Factory<N> modified(LDL.Factory<N> delegate,
                                                                   N threshold)

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.

getD

MatrixStore<N> getD()

getL

default MatrixStore<N> getL()

Must implement either getL() or getR().

getR

default MatrixStore<N> getR()

Must implement either getL() or getR().

reconstruct

default MatrixStore<N> reconstruct()

Specified by:

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