Class RawQR

java.lang.Object

org.ojalgo.matrix.decomposition.AbstractDecomposition<Double, R064Store>

org.ojalgo.matrix.decomposition.RawDecomposition

org.ojalgo.matrix.decomposition.RawQR

All Implemented Interfaces:

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

final class RawQR
extends RawDecomposition
implements QR<Double>

For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R.

The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.

Nested Class Summary

Nested classes/interfaces inherited from interface InvertibleFactor

InvertibleFactor.IdentityFactor<N>

Nested classes/interfaces inherited from interface MatrixDecomposition

MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Factory<D>, 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 QR

QR.Factory<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
private double[]	myDiagonalR	Array for internal storage of diagonal of R.
private int	myNumberOfHouseholderTransformations

Fields inherited from interface MatrixDecomposition

TYPICAL

Fields inherited from interface QR

C128, H256, Q128, R064, R128

Constructor Summary

Constructors

Constructor	Description
RawQR()	Not recommended to use this constructor directly.

Method Summary

Modifier and Type	Method	Description
void	btran(double[] arg)
void	btran(PhysicalStore<Double> arg)	Backwards-transformation
Double	calculateDeterminant(Access2D<?> matrix)
protected boolean	checkSolvability()
int	countSignificant(double threshold)
boolean	decompose(Access2D.Collectable<Double, ? super TransformableRegion<Double>> matrix)	QR Decomposition, computed by Householder reflections.
private boolean	doDecompose(double[][] data)
private MatrixStore<Double>	doGetInverse(R064Store preallocated)	Makes no use of preallocated at all.
private MatrixStore<Double>	doSolve(R064Store preallocated)
void	ftran(double[] arg)
Double	getDeterminant()	A matrix' determinant is the product of its eigenvalues.
MatrixStore<Double>	getInverse(PhysicalStore<Double> preallocated)	Implementing this method is optional.
RawStore	getQ()	Generate and return the (economy-sized) orthogonal factor
MatrixStore<Double>	getR()	Return the upper triangular factor
double	getRankThreshold()
MatrixStore<Double>	getSolution(Access2D.Collectable<Double, ? super PhysicalStore<Double>> rhs, PhysicalStore<Double> preallocated)	Implementing this method is optional.
MatrixStore<Double>	invert(Access2D<?> original, PhysicalStore<Double> preallocated)	Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface.
boolean	isFullSize()
boolean	isSolvable()	Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever.
PhysicalStore<Double>	preallocate(int nbEquations, int nbVariables, int nbSolutions)
void	reset()	Delete computed results, and resets attributes to default values
MatrixStore<Double>	solve(Access2D<?> body, Access2D<?> rhs, PhysicalStore<Double> preallocated)	Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface.

Methods inherited from class RawDecomposition

checkSymmetry, getColDim, getInternalData, getInternalStore, getRowDim, make, newRawStore, reset, wrap

Methods inherited from class AbstractDecomposition

aggregator, applyPivotOrder, applyReverseOrder, collect, computed, copyColumn, copyRow, function, getDimensionalEpsilon, isAspectRatioNormal, isComputed, makeArray, makeDiagonal, makeEye, makeHouseholder, makeIdentity, makeRotation, makeRotation, makeZero, makeZero, scalar, wrap

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface InverterTask

invert, preallocate

Methods inherited from interface MatrixDecomposition

isComputed

Methods inherited from interface MatrixDecomposition.Determinant

toDeterminantProvider

Methods inherited from interface MatrixDecomposition.RankRevealing

getRank, isFullRank

Methods inherited from interface MatrixDecomposition.Solver

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

Methods inherited from interface QR

ftran, isOrdered, reconstruct, updateColumn

Methods inherited from interface SolverTask

preallocate, 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

myDiagonalR

private double[] myDiagonalR

Array for internal storage of diagonal of R.

myNumberOfHouseholderTransformations

private int myNumberOfHouseholderTransformations

Constructor Details

RawQR

RawQR()

Not recommended to use this constructor directly. Consider using the static factory method

invalid reference

org.ojalgo.matrix.decomposition.QR#make(Access2D)

instead.

Method Details

btran

public void btran(double[] arg)

Specified by:

btran in interface InvertibleFactor<Double>

See Also:

• InvertibleFactor.IdentityFactor.btran(PhysicalStore)

btran

public void btran(PhysicalStore<Double> arg)

Description copied from interface: InvertibleFactor

Backwards-transformation

Solve [x]^T[A] = [b]^T (equivalent to [A]^T[x] = [b]) by transforming [b] into [x] in-place.

Specified by:

btran in interface InvertibleFactor<Double>

Parameters:

arg - [b] transformed into [x]

calculateDeterminant

public Double calculateDeterminant(Access2D<?> matrix)

Specified by:

calculateDeterminant in interface DeterminantTask<Double>

countSignificant

public int countSignificant(double threshold)

Specified by:

countSignificant in interface MatrixDecomposition.RankRevealing<Double>

Parameters:

threshold - Significance limit

Returns:

The number of elements in the diagonal matrix that are greater than the threshold

decompose

public boolean decompose(Access2D.Collectable<Double, ? super TransformableRegion<Double>> matrix)

QR Decomposition, computed by Householder reflections. Structure to access R and the Householder vectors and compute Q.

Specified by:

decompose in interface MatrixDecomposition<Double>

Parameters:

matrix - Rectangular matrix

Returns:

true if decomposition suceeded; false if not

ftran

public void ftran(double[] arg)

Specified by:

ftran in interface InvertibleFactor<Double>

See Also:

• InvertibleFactor.IdentityFactor.ftran(PhysicalStore)

getDeterminant

public Double getDeterminant()

Description copied from interface: MatrixDecomposition.Determinant

A matrix' determinant is the product of its eigenvalues.

Specified by:

getDeterminant in interface MatrixDecomposition.Determinant<Double>

Specified by:

getDeterminant in interface Provider2D.Determinant<Double>

Returns:

The matrix' determinant

getInverse

public MatrixStore<Double> getInverse(PhysicalStore<Double> preallocated)

Description copied from interface: MatrixDecomposition.Solver

Implementing this method is optional.

Exactly how a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling MatrixDecomposition.Solver.getInverse().

Specified by:

getInverse in interface MatrixDecomposition.Solver<Double>

Parameters:

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. Use MatrixDecomposition.Solver.preallocate(int, int) or InverterTask.preallocate(Structure2D) to get a suitable instance.

Returns:

The inverse, this is where you get the solution

getQ

public RawStore getQ()

Generate and return the (economy-sized) orthogonal factor

Specified by:

getQ in interface QR<Double>

Returns:

Q

getR

public MatrixStore<Double> getR()

Return the upper triangular factor

Specified by:

getR in interface QR<Double>

Returns:

R

getRankThreshold

public double getRankThreshold()

Specified by:

getRankThreshold in interface MatrixDecomposition.RankRevealing<Double>

getSolution

public MatrixStore<Double> getSolution(Access2D.Collectable<Double, ? super PhysicalStore<Double>> rhs,
 PhysicalStore<Double> preallocated)

Description copied from interface: MatrixDecomposition.Solver

Implementing this method is optional.

Exactly how a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling MatrixDecomposition.Solver.getSolution(Collectable).

Specified by:

getSolution in interface MatrixDecomposition.Solver<Double>

Parameters:

rhs - The Right Hand Side, wont be modfied

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution. Use SolverTask.preallocate(int, int, int) or SolverTask.preallocate(Structure2D, Structure2D) to get a suitable instance.

Returns:

The solution

invert

public MatrixStore<Double> invert(Access2D<?> original,
 PhysicalStore<Double> preallocated)
                           throws RecoverableCondition

Description copied from interface: InverterTask

Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling InverterTask.invert(Access2D).

Use InverterTask.preallocate(Structure2D) to obtain a suitbale preallocated.

Specified by:

invert in interface InverterTask<Double>

Parameters:

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/final/correct solution.

Returns:

The inverse

Throws:

RecoverableCondition - TODO

isFullSize

public boolean isFullSize()

Specified by:

isFullSize in interface MatrixDecomposition.EconomySize<Double>

Returns:

True if it will generate a full sized decomposition.

isSolvable

public boolean isSolvable()

Description copied from interface: MatrixDecomposition.Solver

Please note that producing a pseudoinverse and/or a least squares solution is ok! The return value, of this method, is not an indication of if the decomposed matrix is square, has full rank, is postive definite or whatever. It's that in combination with the specific decomposition algorithm's capabilities.

Specified by:

isSolvable in interface MatrixDecomposition.Solver<Double>

Overrides:

isSolvable in class AbstractDecomposition<Double, R064Store>

Returns:

true if this matrix decomposition is in a state to be able to deliver an inverse or an equation system solution (with some degree of numerical stability).

preallocate

public PhysicalStore<Double> preallocate(int nbEquations,
 int nbVariables,
 int nbSolutions)

Specified by:

preallocate in interface SolverTask<Double>

reset

public void reset()

Description copied from interface: MatrixDecomposition

Delete computed results, and resets attributes to default values

Specified by:

reset in interface MatrixDecomposition<Double>

Overrides:

reset in class AbstractDecomposition<Double, R064Store>

solve

public MatrixStore<Double> solve(Access2D<?> body,
 Access2D<?> rhs,
 PhysicalStore<Double> preallocated)
                          throws RecoverableCondition

Description copied from interface: SolverTask

Exactly how (if at all) a specific implementation makes use of preallocated is not specified by this interface. It must be documented for each implementation.

Should produce the same results as calling SolverTask.solve(Access2D, Access2D).

Use SolverTask.preallocate(Structure2D, Structure2D) to obtain a suitbale preallocated.

Specified by:

solve in interface SolverTask<Double>

Parameters:

rhs - The Right Hand Side, wont be modfied

preallocated - Preallocated memory for the results, possibly some intermediate results. You must assume this is modified, but you cannot assume it will contain the full/ /correct solution.

Returns:

The solution

Throws:

RecoverableCondition

doDecompose

private boolean doDecompose(double[][] data)

doGetInverse

private MatrixStore<Double> doGetInverse(R064Store preallocated)

Makes no use of preallocated at all. Simply delegates to MatrixDecomposition.Solver.getInverse().

doSolve

private MatrixStore<Double> doSolve(R064Store preallocated)

checkSolvability

protected boolean checkSolvability()

Overrides:

checkSolvability in class AbstractDecomposition<Double, R064Store>