cern.colt.matrix.linalg

Class QRDecomposition

java.lang.Object

cern.colt.matrix.linalg.QRDecomposition

All Implemented Interfaces:

Serializable

public class QRDecomposition
extends Object
implements Serializable

For an m x n matrix A with m >= n, the QR decomposition is an m x n orthogonal matrix Q and an n x 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.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
QRDecomposition(DoubleMatrix2D A) Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Method Summary

Modifier and Type	Method and Description
DoubleMatrix2D	getH() Returns the Householder vectors H.
DoubleMatrix2D	getQ() Generates and returns the (economy-sized) orthogonal factor Q.
DoubleMatrix2D	getR() Returns the upper triangular factor, R.
boolean	hasFullRank() Returns whether the matrix A has full rank.
DoubleMatrix2D	solve(DoubleMatrix2D B) Least squares solution of A*X = B; returns X.
String	toString() Returns a String with (propertyName, propertyValue) pairs.

Methods inherited from class java.lang.Object

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

Constructor Detail

QRDecomposition

public QRDecomposition(DoubleMatrix2D A)

Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Parameters:

A - A rectangular matrix.

Throws:

IllegalArgumentException - if A.rows() < A.columns().

Method Detail

getH

public DoubleMatrix2D getH()

Returns the Householder vectors H.

Returns:

A lower trapezoidal matrix whose columns define the householder reflections.

getQ

public DoubleMatrix2D getQ()

Generates and returns the (economy-sized) orthogonal factor Q.

Returns:

Q

getR

public DoubleMatrix2D getR()

Returns the upper triangular factor, R.

Returns:

R

hasFullRank

public boolean hasFullRank()

Returns whether the matrix A has full rank.

Returns:

true if R, and hence A, has full rank.

solve

public DoubleMatrix2D solve(DoubleMatrix2D B)

Least squares solution of A*X = B; returns X.

Parameters:

B - A matrix with as many rows as A and any number of columns.

Returns:

X that minimizes the two norm of Q*R*X - B.

Throws:

IllegalArgumentException - if B.rows() != A.rows().

IllegalArgumentException - if !this.hasFullRank() (A is rank deficient).

toString

public String toString()

Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example,

rank          : 3
trace         : 0

Overrides:

toString in class Object