Package org.apache.commons.math.linear

Class QRDecompositionImpl

java.lang.Object

org.apache.commons.math.linear.QRDecompositionImpl

All Implemented Interfaces:

QRDecomposition

public class QRDecompositionImpl
extends java.lang.Object
implements QRDecomposition

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.

Since:

1.2

See Also:

MathWorld, Wikipedia

Constructor Summary

Constructors

Constructor	Description
QRDecompositionImpl(RealMatrix matrix)	Calculates the QR-decomposition of the given matrix.

Method Summary

Modifier and Type	Method	Description
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

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

Constructor Detail

QRDecompositionImpl

public QRDecompositionImpl(RealMatrix matrix)

Calculates the QR-decomposition of the given matrix.

Parameters:

matrix - The matrix to decompose.

Method Detail

getR

public RealMatrix getR()

Returns the matrix R of the decomposition.

R is an upper-triangular matrix

Specified by:

getR in interface QRDecomposition

Returns:

the R matrix

getQ

public RealMatrix getQ()

Returns the matrix Q of the decomposition.

Q is an orthogonal matrix

Specified by:

getQ in interface QRDecomposition

Returns:

the Q matrix

getQT

public RealMatrix getQT()

Returns the transpose of the matrix Q of the decomposition.

Q is an orthogonal matrix

Specified by:

getQT in interface QRDecomposition

Returns:

the Q matrix

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.

Specified by:

getH in interface QRDecomposition

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.

Specified by:

getSolver in interface QRDecomposition

Returns:

a solver