Interface QR<N extends Comparable<N>>

All Superinterfaces:

DeterminantTask<N>, InverterTask<N>, InvertibleFactor<N>, MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Updatable<N>, MatrixTask<N>, Provider2D, Provider2D.Determinant<N>, Provider2D.Inverse<Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<Optional<MatrixStore<N>>>, SolverTask<N>, Structure1D, Structure2D

All Known Implementing Classes:

DenseQR, DenseQR.C128, DenseQR.H256, DenseQR.Q128, DenseQR.R064, DenseQR.R128, RawQR

public interface QR<N extends Comparable<N>>
extends MatrixDecomposition.Updatable<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: Q128, C128,

invalid reference

#PRIMITIVE

or

invalid reference

#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.

Nested Class Summary

Nested Classes

Modifier and Type	Interface	Description
static interface	QR.Factory<N extends Comparable<N>>

Nested classes/interfaces inherited from interface InvertibleFactor

InvertibleFactor.IdentityFactor<N>

Nested classes/interfaces inherited from interface MatrixDecomposition

MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.Pivoting<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Updatable<N>, MatrixDecomposition.Values<N>

Nested classes/interfaces inherited from interface Provider2D

Provider2D.Condition, Provider2D.Determinant<N>, Provider2D.Eigenpairs, Provider2D.Hermitian, Provider2D.Inverse<M>, Provider2D.Rank, Provider2D.Solution<M>, Provider2D.Symmetric, Provider2D.Trace<N>

Nested classes/interfaces inherited from interface Structure1D

Structure1D.BasicMapper<T>, Structure1D.IndexMapper<T>, Structure1D.IntIndex, Structure1D.LongIndex, Structure1D.LoopCallback

Nested classes/interfaces inherited from interface Structure2D

Structure2D.IntRowColumn, Structure2D.Logical<S,B>, Structure2D.LongRowColumn, Structure2D.ReducibleTo1D<R>, Structure2D.Reshapable, Structure2D.RowColumnKey<R,C>, Structure2D.RowColumnMapper<R,C>

Field Summary

Fields

Modifier and Type	Field	Description
static final QR.Factory<ComplexNumber>	C128
static final QR.Factory<Quaternion>	H256
static final QR.Factory<RationalNumber>	Q128
static final QR.Factory<Double>	R064
static final QR.Factory<Quadruple>	R128

Fields inherited from interface MatrixDecomposition

TYPICAL

Method Summary

Modifier and Type	Method	Description
static <N extends Comparable<N>> boolean	equals(MatrixStore<N> matrix, QR<N> decomposition, NumberContext context)
default void	ftran(PhysicalStore<N> arg)	Forward-transformation
MatrixStore<N>	getQ()
MatrixStore<N>	getR()
default boolean	isOrdered()	This is a property of the algorithm/implementation, not the data.
default MatrixStore<N>	reconstruct()
default boolean	updateColumn(int columnIndex, Access1D.Collectable<N, ? super TransformableRegion<N>> newColumn)	Updates the decomposition when a column in the original matrix is replaced.

Methods inherited from interface DeterminantTask

calculateDeterminant

Methods inherited from interface InverterTask

invert, invert, preallocate

Methods inherited from interface InvertibleFactor

btran, btran, ftran

Methods inherited from interface MatrixDecomposition

decompose, isComputed, reset

Methods inherited from interface MatrixDecomposition.Determinant

getDeterminant, toDeterminantProvider

Methods inherited from interface MatrixDecomposition.EconomySize

isFullSize

Methods inherited from interface MatrixDecomposition.RankRevealing

countSignificant, getRank, getRankThreshold, isFullRank

Methods inherited from interface MatrixDecomposition.Solver

compute, getInverse, getInverse, getSolution, getSolution, invert, isSolvable, preallocate, solve, toInverseProvider, toSolutionProvider

Methods inherited from interface SolverTask

preallocate, preallocate, solve, solve

Methods inherited from interface Structure2D

count, countColumns, countRows, firstInColumn, firstInRow, getColDim, getMaxDim, getMinDim, getRowDim, isEmpty, isFat, isScalar, isSquare, isTall, isVector, limitOfColumn, limitOfRow, size

Field Details

C128

static final QR.Factory<ComplexNumber> C128

H256

static final QR.Factory<Quaternion> H256

Q128

static final QR.Factory<RationalNumber> Q128

R064

static final QR.Factory<Double> R064

R128

static final QR.Factory<Quadruple> R128

Method Details

equals

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

ftran

default void ftran(PhysicalStore<N> arg)

Description copied from interface: InvertibleFactor

Forward-transformation

Solve [A][x] = [b] by transforming [b] into [x] in-place.

Specified by:

ftran in interface InvertibleFactor<N extends Comparable<N>>

Parameters:

arg - [b] transformed into [x]

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 Comparable<N>>

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 Comparable<N>>

updateColumn

default boolean updateColumn(int columnIndex,
 Access1D.Collectable<N, ? super TransformableRegion<N>> newColumn)

Description copied from interface: MatrixDecomposition.Updatable

Updates the decomposition when a column in the original matrix is replaced.

This method can only be called after an initial decomposition has been calculated.

If the updatable decomposition is a MatrixDecomposition.Solver then this method should only return true if MatrixDecomposition.Solver.isSolvable() is true after the update.

Specified by:

updateColumn in interface MatrixDecomposition.Updatable<N extends Comparable<N>>

Parameters:

columnIndex - The index of the column, in the original matrix, to replace

newColumn - The new column values

Returns:

true if update was successful, false if not.