org.apache.commons.math3.linear
Class QRDecomposition

java.lang.Object
  org.apache.commons.math3.linear.QRDecomposition

public class QRDecomposition
extends Object

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• the solve and isFullRank methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.

Since:

1.2 (changed to concrete class in 3.0)

Version:

$Id: QRDecomposition.java 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

MathWorld, Wikipedia

Constructor Summary

QRDecomposition(RealMatrix matrix)
Calculates the QR-decomposition of the given matrix.

QRDecomposition(RealMatrix matrix, double threshold)
Calculates the QR-decomposition of the given matrix.

Method Summary

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.
DecompositionSolver	getSolver() Get a solver for finding the A × X = B solution in least square 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)

Calculates the QR-decomposition of the given matrix. The singularity threshold defaults to zero.

Parameters:

matrix - The matrix to decompose.

See Also:

QRDecomposition(RealMatrix,double)

QRDecomposition

public QRDecomposition(RealMatrix matrix,
                       double threshold)

Calculates the QR-decomposition of the given matrix.

Parameters:

matrix - The matrix to decompose.

threshold - Singularity threshold.

Method Detail

getR

public RealMatrix getR()

Returns the matrix R of the decomposition.

R is an upper-triangular matrix

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()

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

Returns:

a solver