org.ojalgo.matrix.decomposition

Interface Tridiagonal<N extends Comparable<N>>

All Superinterfaces:

MatrixDecomposition<N>, Structure1D, Structure2D

public interface Tridiagonal<N extends Comparable<N>>
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 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

Field Summary

Fields

Modifier and Type	Field and Description
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 Comparable<N>> boolean	equals(MatrixStore<N> matrix, Tridiagonal<N> decomposition, NumberContext context)
MatrixStore<N>	getD()
MatrixStore<N>	getQ()
default MatrixStore<N>	reconstruct()

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

Field Detail

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

equals

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

getD

MatrixStore<N> getD()

getQ

MatrixStore<N> getQ()

reconstruct

default MatrixStore<N> reconstruct()

Specified by:

reconstruct in interface MatrixDecomposition<N extends Comparable<N>>