cern.colt.matrix.tdouble.algo.decomposition
Class SparseDoubleQRDecomposition

java.lang.Object
  cern.colt.matrix.tdouble.algo.decomposition.SparseDoubleQRDecomposition

public class SparseDoubleQRDecomposition
extends Object

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. 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.

Author:

Piotr Wendykier (piotr.wendykier@gmail.com)

Constructor Summary

SparseDoubleQRDecomposition(DoubleMatrix2D A, int order)
Constructs and returns a new QR decomposition object; computed by Householder reflections; If m < n then then the QR of A' is computed.

Method Summary

double[]	getBeta() Returns a copy of the beta factors, from the Householder reflections H = I - beta*v*v'.
DoubleMatrix2D	getR() Returns a copy of the upper triangular factor, R.
edu.emory.mathcs.csparsej.tdouble.Dcs_common.Dcss	getSymbolicAnalysis() Returns a copy of the symbolic QR analysis object
DoubleMatrix2D	getV() Returns a copy of the Householder vectors v, from the Householder reflections H = I - beta*v*v'.
boolean	hasFullRank() Returns whether the matrix A has full rank.
void	solve(DoubleMatrix1D b) Solve a least-squares problem (min ||Ax-b||_2, where A is m-by-n with m >= n) or underdetermined system (Ax=b, where m < n).

Methods inherited from class java.lang.Object

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

Constructor Detail

SparseDoubleQRDecomposition

public SparseDoubleQRDecomposition(DoubleMatrix2D A,
                                   int order)

Constructs and returns a new QR decomposition object; computed by Householder reflections; If m < n then then the QR of A' is computed. The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Parameters:

A - A rectangular matrix.

order - ordering option (0 to 3); 0: natural ordering, 1: amd(A+A'), 2: amd(S'*S), 3: amd(A'*A)

Throws:

IllegalArgumentException - if A is not sparse

IllegalArgumentException - if order is not in [0,3]

Method Detail

getV

public DoubleMatrix2D getV()

Returns a copy of the Householder vectors v, from the Householder reflections H = I - beta*v*v'.

Returns:

the Householder vectors.

getBeta

public double[] getBeta()

Returns a copy of the beta factors, from the Householder reflections H = I - beta*v*v'.

Returns:

the beta factors.

getR

public DoubleMatrix2D getR()

Returns a copy of the upper triangular factor, R.

Returns:

R

getSymbolicAnalysis

public edu.emory.mathcs.csparsej.tdouble.Dcs_common.Dcss getSymbolicAnalysis()

Returns a copy of the symbolic QR analysis object

Returns:

symbolic QR analysis

hasFullRank

public boolean hasFullRank()

Returns whether the matrix A has full rank.

Returns:

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

solve

public void solve(DoubleMatrix1D b)

Solve a least-squares problem (min ||Ax-b||_2, where A is m-by-n with m >= n) or underdetermined system (Ax=b, where m < n). Upon return b is overridden with the result x.

Parameters:

b - right-hand side.

Throws:

IllegalArgumentException - if b.size() != max(A.rows(), A.columns()).

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