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:

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

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

Nested Class Summary

Nested Classes

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

Nested classes/interfaces inherited from interface InvertibleFactor

InvertibleFactor.IdentityFactor<N>

Nested classes/interfaces inherited from interface MatrixDecomposition

MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.Pivoting<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Updatable<N>, MatrixDecomposition.Values<N>

Nested classes/interfaces inherited from interface Provider2D

Provider2D.Condition, Provider2D.Determinant<N>, Provider2D.Eigenpairs, Provider2D.Hermitian, Provider2D.Inverse<M>, Provider2D.Rank, Provider2D.Solution<M>, Provider2D.Symmetric, Provider2D.Trace<N>

Nested classes/interfaces inherited from interface Structure1D

Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback

Nested classes/interfaces inherited from interface Structure2D

Structure2D.IntRowColumn, Structure2D.Logical<S,B>, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R>, Structure2D.Reshapable, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>

Field Summary

Fields

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

Fields inherited from interface MatrixDecomposition

TYPICAL

Method Summary

Modifier and Type	Method	Description
static <N extends 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 Comparable<N>> LDL.Factory<N>	modified(LDL.Factory<N> delegate, N threshold)	Will return a modified LDL decomposition algoritm.
static LDL<Double>	newSparseR064()
default MatrixStore<N>	reconstruct()

Methods inherited from interface DeterminantTask

calculateDeterminant

Methods inherited from interface InverterTask

invert, invert, preallocate

Methods inherited from interface InvertibleFactor

btran, btran, ftran, ftran

Methods inherited from interface LDU

isOrdered

Methods inherited from interface MatrixDecomposition

decompose, isComputed, reset

Methods inherited from interface MatrixDecomposition.Determinant

getDeterminant, toDeterminantProvider

Methods inherited from interface MatrixDecomposition.Hermitian

checkAndDecompose

Methods inherited from interface MatrixDecomposition.Pivoting

decomposeWithoutPivoting, getPivotOrder, getReversePivotOrder, isPivoted

Methods inherited from interface MatrixDecomposition.RankRevealing

countSignificant, getRank, getRankThreshold, isFullRank

Methods inherited from interface MatrixDecomposition.Solver

compute, getInverse, getInverse, getSolution, getSolution, invert, isSolvable, preallocate, solve, toInverseProvider, toSolutionProvider

Methods inherited from interface SolverTask

preallocate, preallocate, solve, solve

Methods inherited from interface Structure2D

count, countColumns, countRows, firstInColumn, firstInRow, getColDim, getMaxDim, getMinDim, getRowDim, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size

Field Details

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<Double> R064

R128

static final LDL.Factory<Quadruple> R128

Method Details

newSparseR064

static LDL<Double> newSparseR064()

equals

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

modified

static <N extends 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 Comparable<N>>