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PLib::SVDMatrix Class Template Reference

A matrix for the SVD decomposition. More...

#include <matrix/matrixMat.h>

List of all members.

Public Methods
	SVDMatrix ()
	SVDMatrix (const Matrix< T > &A)
int	decompose (const Matrix< T > &A)
void	minMax (T &min_sig, T &max_sig) const
double	q_cond_number (void) const
void	cut_off (const double min_sig)
void	inverseIn (Matrix< T > &inv, double tau=0)
Matrix< T >	inverse (double tau=0)
int	solve (const Matrix< T > &B, Matrix< T > &X, double tau=0)
Public Attributes
const Matrix< T > &	U
const Matrix< T > &	V
const Vector< T > &	sig
Protected Methods
double	left_householder (Matrix< T > &A, const int i)
double	right_householder (Matrix< T > &A, const int i)
double	bidiagonalize (Vector< T > &super_diag, const Matrix< T > &_A)
void	rotate (Matrix< T > &U, const int i, const int j, const double cos_ph, const double sin_ph)
void	rip_through (Vector< T > &super_diag, const int k, const int l, const double eps)
int	get_submatrix_to_work_on (Vector< T > &super_diag, const int k, const double eps)
void	diagonalize (Vector< T > &super_diag, const double eps)
Protected Attributes
int	M
int	N
Matrix< T >	U_
Matrix< T >	V_
Vector< T >	sig_

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Detailed Description

template<class T>
class PLib::SVDMatrix< T >

A matrix for the SVD decomposition.

This matrix was adapted from the Numerical Math Class Library developed by Oleg Kiselyov.

This class can only be used with floating point values (float or double).

The following comments are from Oleg Kiselyov.

Singular Value Decomposition of a rectangular matrix A=U Sig V' where matrices U and V are orthogonal and Sig is a diagonal matrix.

The singular value decomposition is performed by constructing an SVD object from an M*N matrix A with M \ge N (that is, at least as many rows as columns). Note, in case M > N, matrix Sig has to be a M*N diagonal matrix. However, it has only N diagonal elements, which we store in a vector sig.

Algorithm: Bidiagonalization with Householder reflections followed by a modification of a QR-algorithm. For more details, see G.E. Forsythe, M.A. Malcolm, C.B. Moler Computer methods for mathematical computations, Prentice-Hall, 1977. However, in the present implementation, matrices U and V are computed right away rather than delayed until after all Householder reflections.

This code is based for the most part on a Algol68 code I (Oleg Kiselyov) wrote ca. 1987.

Look at the source code for more information about the algorithm.

Author:

Oleg Kiselyov , Philippe Lavoie

Date:

22 Oct. 1997

Definition at line 179 of file matrixMat.h.

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Constructor & Destructor Documentation

template<class T> PLib::SVDMatrix< T >::SVDMatrix (  const Matrix< T > &    A )

Performs the SVD decomposition of A. Performs the SVD decomposition of A. It is not recommended to use this routine has errors from the decomposition routine are discarded Parameters: A  the matrix to decompose Warning: The matrix A must have a number equal or higher of rows than columns. Author: Philippe Lavoie Date: 22 October 1997 Definition at line 796 of file matrixMat.cpp. References decompose.

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Member Function Documentation

template<class T> int PLib::SVDMatrix< T >::decompose (  const Matrix< T > &    A )

Performs the SVD decomposition of A. Performs the SVD decomposition of A. Parameters: A  the matrix to decompose Returns: 1 if the decomposition was succesfull, 0 otherwise. Warning: The matrix A must have a number equal or higher of rows than columns. Author: Philippe Lavoie Date: 22 October 1997 Definition at line 817 of file matrixMat.cpp. References N, sig_, U_, and V_. Referenced by SVDMatrix.

template<class T> Matrix< T > PLib::SVDMatrix< T >::inverse (  double    tau = 0 )

Finds the (pseudo-)inverse of a SVD matrix. Finds the (pseudo-)inverse of a SVD matrix. Parameters: tau  the minimal singular value accepted Warning: The SVD matrix must be valid. Author: Philippe Lavoie Date: 22 October 1997 Definition at line 951 of file matrixMat.cpp. References inverseIn.

template<class T> void PLib::SVDMatrix< T >::inverseIn (  Matrix< T > &    A, double    tau = 0 )

Finds the (pseudo-)inverse of a SVD matrix. Finds the (pseudo-)inverse of a SVD matrix. Parameters: A  the inverse of the SVD matrix tau  the minimal singular value accepted Warning: The SVD matrix must be valid. Author: Philippe Lavoie Date: 22 October 1997 Definition at line 907 of file matrixMat.cpp. References minMax. Referenced by inverse.

template<class T> void PLib::SVDMatrix< T >::minMax (  T &    min_sig, T &    max_sig )  const

Finds the minimal and maximal sigma values. Finds the minimal and maximal sigma values. Parameters: min_sig  the minimal sigma value max_sig  the maximal sigma value Warning: The SVD matrix must be valid. Author: Philippe Lavoie Date: 22 October 1997 Definition at line 862 of file matrixMat.cpp. Referenced by inverseIn, q_cond_number, and solve.

template<class T> double PLib::SVDMatrix< T >::q_cond_number (  void    )  const

Finds the condition number. Finds the condition number which corresponds to the maximal sigma value divided by its minimal value. Returns: The condition number Warning: The SVD matrix must be valid. Author: Philippe Lavoie Date: 22 October 1997 Definition at line 886 of file matrixMat.cpp. References minMax.

template<class T> int PLib::SVDMatrix< T >::solve (  const Matrix< T > &    B, Matrix< T > &    X, double    tau = 0 )

Solves the linear system A X = B. Solves the linear system A X = B. Given A and B it finds the value of X. A is the SVD matrix properly initialized and the only other input parameter is B. Parameters: B  the right hand side of the equation X  the resulting matrix tau  the minimal singular value accepted Returns: 1 if the routine was able to solve the problem, 0 otherwise. Warning: The SVD matrix must be valid and correspond to A. Author: Philippe Lavoie Date: 22 October 1997 Definition at line 977 of file matrixMat.cpp. References minMax.

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The documentation for this class was generated from the following files:

• matrixMat.h
• matrixMat.cpp

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