fr.cnes.sirius.patrius.math.linear

Class QRDecomposition

java.lang.Object

fr.cnes.sirius.patrius.math.linear.QRDecomposition

All Implemented Interfaces:

Decomposition

public class QRDecomposition
extends Object
implements Decomposition

Calculates the QR-decomposition of a matrix.

The QR-decomposition of a matrix A consists of two matrices Q and R that satisfy: A = QR, Q is orthogonal (Q^TQ = I), and R is upper triangular. If A is m×n, Q is m×m and R m×n.

This class compute the decomposition using Householder reflectors.

For efficiency purposes, the decomposition in packed form is transposed. This allows inner loop to iterate inside rows, which is much more cache-efficient in Java.

This class is based on the class with similar name from the JAMA library, with the following changes:

• a getQT method has been added,
• the solve and isFullRank methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.

This class is up-to-date with commons-math 3.6.1.

Since:

1.2 (changed to concrete class in 3.0)

Version:

$Id: QRDecomposition.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

MathWorld, Wikipedia

Constructor Summary

Constructors

Constructor and Description
QRDecomposition(RealMatrix matrix) Simple constructor.
QRDecomposition(RealMatrix matrix, double inThreshold) Constructor used to set the singularity threshold.
QRDecomposition(RealMatrix matrix, double thresholdIn, boolean parallel) Constructor used to set the singularity threshold and enable parallel computation.

Method Summary

Modifier and Type	Method and Description
static Function<RealMatrix,Decomposition>	decompositionBuilder(double thresholdIn) Builder for decomposition.
static Function<RealMatrix,Decomposition>	decompositionBuilder(double thresholdIn, boolean parallel) Builder for decomposition.
RealMatrix	getH() Returns the Householder reflector vectors.
RealMatrix	getQ() Returns the matrix Q of the decomposition.
RealMatrix	getQT() Returns the transpose of the matrix Q of the decomposition.
RealMatrix	getR() Returns the matrix R of the decomposition.
RealMatrix	getR(boolean compactForm) Returns the matrix R of the decomposition in its compact form (n × n) or in its full form (m × n).
DecompositionSolver	getSolver() Gets a solver for finding the A × X = B solution in exact linear sense.

Methods inherited from class java.lang.Object

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

Constructor Detail

QRDecomposition

public QRDecomposition(RealMatrix matrix)

Simple constructor. The singularity threshold defaults to zero.

The decomposition is directly computed on the input matrix

Parameters:

matrix - The matrix to decompose.

See Also:

QRDecomposition(RealMatrix, double, boolean)

QRDecomposition

public QRDecomposition(RealMatrix matrix,
                       double inThreshold)

Constructor used to set the singularity threshold.

The decomposition is directly computed on the input matrix

Parameters:

matrix - The matrix to decompose.

thresholdIn - Singularity threshold.

See Also:

QRDecomposition(RealMatrix, double, boolean)

QRDecomposition

public QRDecomposition(RealMatrix matrix,
                       double thresholdIn,
                       boolean parallel)

Constructor used to set the singularity threshold and enable parallel computation.

The decomposition is directly computed on the input matrix

Parameters:

matrix - The matrix to decompose.

thresholdIn - Singularity threshold.

parallel - Indicate if a part of the algorithm can be parallelized. It is advised to activate this for big matrices only. Indeed, for small matrices the multi-thread management overload might be disadvantageous.

Method Detail

getR

public RealMatrix getR()

Returns the matrix R of the decomposition. By default, this method returns the full form (n × m) of the matrix R.

R is an upper-triangular matrix

Returns:

the R matrix

getR

public RealMatrix getR(boolean compactForm)

Returns the matrix R of the decomposition in its compact form (n × n) or in its full form (m × n).

R is an upper-triangular matrix

Parameters:

compactForm - if true R dimensions will be n × n, else R dimensions will be m × n

Returns:

the R matrix

getQ

public RealMatrix getQ()

Returns the matrix Q of the decomposition.

Q is an orthogonal matrix

Returns:

the Q matrix

getQT

public RealMatrix getQT()

Returns the transpose of the matrix Q of the decomposition.

Q is an orthogonal matrix

Returns:

the transpose of the Q matrix, Q^T

getH

public RealMatrix getH()

Returns the Householder reflector vectors.

H is a lower trapezoidal matrix whose columns represent each successive Householder reflector vector. This matrix is used to compute Q.

Returns:

a matrix containing the Householder reflector vectors

getSolver

public DecompositionSolver getSolver()

Gets a solver for finding the A × X = B solution in exact linear sense. Get a solver for finding the A × X = B solution in least square sense.

Least Square sense means a solver can be computed for an overdetermined system, (i.e. a system with more equations than unknowns, which corresponds to a tall A matrix with more rows than columns). In any case, if the matrix is singular within the tolerance set at construction, an error will be triggered when the solve method will be called.

Specified by:

getSolver in interface Decomposition

Returns:

a solver

decompositionBuilder

public static Function<RealMatrix,Decomposition> decompositionBuilder(double thresholdIn)

Builder for decomposition.

Parameters:

thresholdIn - Singularity threshold.

Returns:

decomposition

decompositionBuilder

public static Function<RealMatrix,Decomposition> decompositionBuilder(double thresholdIn,
                                                                      boolean parallel)

Builder for decomposition.

Parameters:

thresholdIn - Singularity threshold.

parallel - Indicate if a part of the algorithm can be performed in parallel

Returns:

decomposition