org.ojalgo.matrix.decomposition

Interface LDL<N extends Comparable<N>>

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>, Provider2D, Provider2D.Determinant<N>, Provider2D.Inverse<Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<Optional<MatrixStore<N>>>, SolverTask<N>, Structure1D, Structure2D

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

Author:

apete

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	LDL.Factory<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.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.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

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>>

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 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().
default MatrixStore<N>	reconstruct()

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, invert, isSolvable, solve, toInverseProvider, toSolutionProvider

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, toDeterminantProvider

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, firstInColumn, firstInColumn, firstInColumn, firstInRow, firstInRow, firstInRow, getColDim, getMaxDim, getMinDim, getRowDim, index, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfColumn, limitOfColumn, limitOfRow, limitOfRow, limitOfRow, 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, toIntIndexes

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

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

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>>