org.apache.commons.math3.linear
Class QRDecomposition

java.lang.Object
  extended by org.apache.commons.math3.linear.QRDecomposition
Direct Known Subclasses:
RRQRDecomposition

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 (QTQ = 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:

Since:
1.2 (changed to concrete class in 3.0)
Version:
$Id: QRDecomposition.java 1462423 2013-03-29 07:25:18Z luc $
See Also:
MathWorld, Wikipedia

Nested Class Summary
private static class QRDecomposition.Solver
          Specialized solver.
 
Field Summary
private  RealMatrix cachedH
          Cached value of H.
private  RealMatrix cachedQ
          Cached value of Q.
private  RealMatrix cachedQT
          Cached value of QT.
private  RealMatrix cachedR
          Cached value of R.
private  double[][] qrt
          A packed TRANSPOSED representation of the QR decomposition.
private  double[] rDiag
          The diagonal elements of R.
private  double threshold
          Singularity threshold.
 
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
protected  void decompose(double[][] matrix)
          Decompose matrix.
 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.
protected  void performHouseholderReflection(int minor, double[][] matrix)
          Perform Householder reflection for a minor A(minor, minor) of A.
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

qrt

private double[][] qrt
A packed TRANSPOSED representation of the QR decomposition.

The elements BELOW the diagonal are the elements of the UPPER triangular matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors from which an explicit form of Q can be recomputed if desired.


rDiag

private double[] rDiag
The diagonal elements of R.


cachedQ

private RealMatrix cachedQ
Cached value of Q.


cachedQT

private RealMatrix cachedQT
Cached value of QT.


cachedR

private RealMatrix cachedR
Cached value of R.


cachedH

private RealMatrix cachedH
Cached value of H.


threshold

private final double threshold
Singularity threshold.

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

decompose

protected void decompose(double[][] matrix)
Decompose matrix.

Parameters:
matrix - transposed matrix
Since:
3.2

performHouseholderReflection

protected void performHouseholderReflection(int minor,
                                            double[][] matrix)
Perform Householder reflection for a minor A(minor, minor) of A.

Parameters:
minor - minor index
matrix - transposed matrix
Since:
3.2

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, QT

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


Copyright (c) 2003-2013 Apache Software Foundation