cern.colt.matrix.tdcomplex.algo.decomposition

Class SparseDComplexQRDecomposition

java.lang.Object

cern.colt.matrix.tdcomplex.algo.decomposition.SparseDComplexQRDecomposition

public class SparseDComplexQRDecomposition
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

Constructors

Constructor and Description
SparseDComplexQRDecomposition(DComplexMatrix2D 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

Methods

Modifier and Type	Method and Description
double[]	getBeta() Returns a copy of the beta factors, from the Householder reflections H = I - beta*v*v'.
DComplexMatrix2D	getR() Returns a copy of the upper triangular factor, R.
edu.emory.mathcs.csparsej.tdcomplex.DZcs_common.DZcss	getSymbolicAnalysis() Returns a copy of the symbolic QR analysis object
DComplexMatrix2D	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(DComplexMatrix1D 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

SparseDComplexQRDecomposition

public SparseDComplexQRDecomposition(DComplexMatrix2D 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 DComplexMatrix2D 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 DComplexMatrix2D getR()

Returns a copy of the upper triangular factor, R.

Returns:

R

getSymbolicAnalysis

public edu.emory.mathcs.csparsej.tdcomplex.DZcs_common.DZcss 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(DComplexMatrix1D 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).