org.ojalgo.matrix.decomposition

Interface Tridiagonal<N extends Number>

All Superinterfaces:

MatrixDecomposition<N>

public interface Tridiagonal<N extends Number>
extends MatrixDecomposition<N>

Tridiagonal: [A] = [Q][D][Q]^H Any square symmetric (hermitian) matrix [A] can be factorized by similarity transformations into the form, [A]=[Q][D][Q]^-1 where [Q] is an orthogonal (unitary) matrix and [D] is a real symmetric tridiagonal matrix. Note that [D] can/should be made real even when [A] has complex elements. Since [Q] is orthogonal (unitary) [Q]^-1 = [Q]^H and when it is real [Q]^H = [Q]^T.

Author:

apete

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	Tridiagonal.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.RankRevealing<N extends Number>, MatrixDecomposition.Solver<N extends Number>, MatrixDecomposition.Values<N extends Number>

Field Summary

Fields

Modifier and Type	Field and Description
static Tridiagonal.Factory<BigDecimal>	BIG
static Tridiagonal.Factory<ComplexNumber>	COMPLEX
static Tridiagonal.Factory<Double>	PRIMITIVE
static Tridiagonal.Factory<Quaternion>	QUATERNION
static Tridiagonal.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, Tridiagonal<N> decomposition, NumberContext context)
MatrixStore<N>	getD()
MatrixStore<N>	getQ()
static <N extends Number> Tridiagonal<N>	make(Access2D<N> typical)
default MatrixStore<N>	reconstruct()
static <N extends Number> MatrixStore<N>	reconstruct(Tridiagonal<N> decomposition)

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

decompose, isComputed, reset

Field Detail

BIG

static final Tridiagonal.Factory<BigDecimal> BIG

COMPLEX

static final Tridiagonal.Factory<ComplexNumber> COMPLEX

PRIMITIVE

static final Tridiagonal.Factory<Double> PRIMITIVE

QUATERNION

static final Tridiagonal.Factory<Quaternion> QUATERNION

RATIONAL

static final Tridiagonal.Factory<RationalNumber> RATIONAL

Method Detail

make

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

equals

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

reconstruct

static <N extends Number> MatrixStore<N> reconstruct(Tridiagonal<N> decomposition)

getD

MatrixStore<N> getD()

getQ

MatrixStore<N> getQ()

reconstruct

default MatrixStore<N> reconstruct()

Specified by:

reconstruct in interface MatrixDecomposition<N extends Number>