org.ojalgo.matrix.decomposition

Interface LDL<N extends Number>

All Superinterfaces:

DeterminantTask<N>, InverterTask<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>, SolverTask<N>, Structure1D, Structure2D

public interface LDL<N extends Number>
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

Author:

apete

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	LDL.Factory<N extends Number>

Nested classes/interfaces inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition

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

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure2D

Structure2D.IntRowColumn, Structure2D.Logical<S extends Structure2D,B extends Structure2D.Logical<S,?>>, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R extends Structure1D>, Structure2D.RowColumnCallback, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>

Nested classes/interfaces inherited from interface org.ojalgo.structure.Structure1D

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

Field Summary

Fields

Modifier and Type	Field and Description
static LDL.Factory<ComplexNumber>	COMPLEX
static LDL.Factory<Double>	PRIMITIVE
static LDL.Factory<Quaternion>	QUATERNION
static LDL.Factory<RationalNumber>	RATIONAL

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

TYPICAL

Method Summary

Modifier and Type	Method and Description
static <N extends Number> 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 Number> LDL<N>	make(Access2D<N> typical)
default MatrixStore<N>	reconstruct()
static <N extends Number> MatrixStore<N>	reconstruct(LDL<N> decomposition) Deprecated. v48 Use reconstruct() instead

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

isOrdered

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Solver

compute, getInverse, getInverse, getSolution, getSolution, isSolvable

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

preallocate, preallocate, solve, solve

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

invert, invert, preallocate, preallocate

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Determinant

getDeterminant

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

calculateDeterminant

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.RankRevealing

countSignificant, getRank, getRankThreshold, isFullRank

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

decompose, isComputed, reset

Methods inherited from interface org.ojalgo.structure.Structure2D

column, column, column, column, column, count, count, countColumns, countRows, index, index, isEmpty, isFat, isScalar, isSquare, isTall, isVector, loopAll, loopColumn, loopColumn, loopDiagonal, loopMatching, loopRow, loopRow, mapperOf, row, row, row, row, row

Methods inherited from interface org.ojalgo.structure.Structure1D

index, loopAll, loopMatching, loopRange, mapper, size

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Hermitian

checkAndCompute, checkAndDecompose

Methods inherited from interface org.ojalgo.matrix.decomposition.MatrixDecomposition.Pivoting

decomposeWithoutPivoting, getPivotOrder, isPivoted

Field Detail

COMPLEX

static final LDL.Factory<ComplexNumber> COMPLEX

PRIMITIVE

static final LDL.Factory<Double> PRIMITIVE

QUATERNION

static final LDL.Factory<Quaternion> QUATERNION

RATIONAL

static final LDL.Factory<RationalNumber> RATIONAL

Method Detail

equals

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

make

static <N extends Number> LDL<N> make(Access2D<N> typical)

reconstruct

@Deprecated
static <N extends Number> MatrixStore<N> reconstruct(LDL<N> decomposition)

Deprecated. v48 Use reconstruct() instead

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 Number>