org.ojalgo.matrix.decomposition

Interface QR<N extends Number>

All Superinterfaces:

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

public interface QR<N extends Number>
extends MatrixDecomposition<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.RankRevealing<N>

QR: [A] = [Q][R] Decomposes [this] into [Q] and [R] where:

• [Q] is an orthogonal matrix (orthonormal columns). It has the same number of rows as [this].
• [R] is a right (upper) triangular matrix. It has the same number of columns as [this].
• [this] = [Q][R]

Note: Either Q or R will be square. The interface does not specify which.

You create instances of (some subclass of) this class by calling one of the static factory methods: RATIONAL, COMPLEX, PRIMITIVE or make(Access2D)

The QR decompostion always exists, even if the matrix does not have full column rank, so the compute method will never fail. The primary use of the QR decomposition is in the least squares solution of overdetermined systems of simultaneous linear equations. This will fail if the matrix does not have full column rank. The rank must be equal to the number of columns.

Author:

apete

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	QR.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 QR.Factory<ComplexNumber>	COMPLEX
static QR.Factory<Double>	PRIMITIVE
static QR.Factory<Quaternion>	QUATERNION
static QR.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, QR<N> decomposition, NumberContext context)
MatrixStore<N>	getQ()
MatrixStore<N>	getR()
default boolean	isOrdered() This is a property of the algorithm/implementation, not the data.
static <N extends Number> QR<N>	make(Access2D<N> typical)
default MatrixStore<N>	reconstruct()
static <N extends Number> MatrixStore<N>	reconstruct(QR<N> decomposition) Deprecated. v48 Use reconstruct() instead

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.EconomySize

isFullSize

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

Field Detail

COMPLEX

static final QR.Factory<ComplexNumber> COMPLEX

PRIMITIVE

static final QR.Factory<Double> PRIMITIVE

QUATERNION

static final QR.Factory<Quaternion> QUATERNION

RATIONAL

static final QR.Factory<RationalNumber> RATIONAL

Method Detail

equals

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

make

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

reconstruct

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

Deprecated. v48 Use reconstruct() instead

getQ

MatrixStore<N> getQ()

getR

MatrixStore<N> getR()

isOrdered

default boolean isOrdered()

Description copied from interface: MatrixDecomposition.Ordered

This is a property of the algorithm/implementation, not the data. Typically relevant for SingularValue, Eigenvalue or any MatrixDecomposition.RankRevealing decomposition.

Specified by:

isOrdered in interface MatrixDecomposition.Ordered<N extends Number>

Returns:

true if the rows/columns of the returned matrix factors are guaranteed some specific order; false if there is no such guarantee.

reconstruct

default MatrixStore<N> reconstruct()

Specified by:

reconstruct in interface MatrixDecomposition<N extends Number>