org.ojalgo.matrix.decomposition

Interface Cholesky<N extends Number>

All Superinterfaces:

DeterminantTask<N>, InverterTask<N>, LDU<N>, MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixTask<N>, SolverTask<N>, Structure1D, Structure2D

public interface Cholesky<N extends Number>
extends LDU<N>, MatrixDecomposition.Hermitian<N>

Cholesky: [A] = [L][L]^H (or [R]^H[R])

[A]^H = [A] = [L][L]^H

If [A] is symmetric and positive definite then the general LU decomposition - [P][L][D][U] - becomes [I][L][D][L]^T (or [I][U]^T[D][U]). [I] can be left out and [D] is normally split in halves and merged with [L] (and/or [U]). We'll express it as [A] = [L][L]^T.

A cholesky decomposition is still/also an LU decomposition where [P][L][D][U] => [L][L]^T.

Author:

apete

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	Cholesky.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 Cholesky.Factory<ComplexNumber>	COMPLEX
static Cholesky.Factory<Double>	PRIMITIVE
static Cholesky.Factory<Quaternion>	QUATERNION
static Cholesky.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, Cholesky<N> decomposition, NumberContext context)
default MatrixStore<N>	getL() Must implement either getL() or getR().
default MatrixStore<N>	getR() Must implement either getL() or getR().
boolean	isSPD() To use the Cholesky decomposition rather than the LU decomposition the matrix must be symmetric and positive definite.
static <N extends Number> Cholesky<N>	make(Access2D<N> typical)
default MatrixStore<N>	reconstruct()
static <N extends Number> MatrixStore<N>	reconstruct(Cholesky<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

Field Detail

COMPLEX

static final Cholesky.Factory<ComplexNumber> COMPLEX

PRIMITIVE

static final Cholesky.Factory<Double> PRIMITIVE

QUATERNION

static final Cholesky.Factory<Quaternion> QUATERNION

RATIONAL

static final Cholesky.Factory<RationalNumber> RATIONAL

Method Detail

equals

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

make

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

reconstruct

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

Deprecated. v48 Use reconstruct() instead

getL

default MatrixStore<N> getL()

Must implement either getL() or getR().

getR

default MatrixStore<N> getR()

Must implement either getL() or getR().

isSPD

boolean isSPD()

To use the Cholesky decomposition rather than the LU decomposition the matrix must be symmetric and positive definite. It is recommended that the decomposition algorithm checks for this during calculation. Possibly the matrix could be assumed to be symmetric (to improve performance) but tests should be made to assure the matrix is positive definite.

Returns:

true if the tests did not fail.

reconstruct

default MatrixStore<N> reconstruct()

Specified by:

reconstruct in interface MatrixDecomposition<N extends Number>