Used to construct and work with singular value decompositions. More...

#include <rw/lapack/sv.h>

Inheritance diagram for RWSVDecomp< TypeT, SVDCalc >:

Public Types
typedef rw_numeric_traits< TypeT >::norm_type	norm_type

Public Member Functions
	RWSVDecomp ()

	RWSVDecomp (const RWSVDecomp< TypeT, SVDCalc > &A)

	RWSVDecomp (const RWGenMat< TypeT > &A, norm_type tol=0)

unsigned	cols () const

void	factor (const RWGenMat< TypeT > &A, norm_type tol=0)

bool	fail () const

bool	good () const

const RWMathVec< TypeT >	leftVector (int i) const

const RWGenMat< TypeT >	leftVectors () const

unsigned	numLeftVectors () const

unsigned	numRightVectors () const

RWSVDecomp< TypeT, SVDCalc > &	operator= (const RWSVDecomp< TypeT, SVDCalc > &x)

unsigned	rank () const

const RWMathVec< TypeT >	rightVector (int i) const

const RWGenMat< TypeT >	rightVectors () const

unsigned	rows () const

norm_type	singularValue (int i) const

const RWMathVec< norm_type >	singularValues () const

void	truncate (norm_type tol)

Detailed Description

template<class TypeT, class SVDCalc>
class RWSVDecomp< TypeT, SVDCalc >

A singular value decomposition is a representation of a matrix A of the form:

\[ A = UEV' \]

where U and V are orthogonal, and E is diagonal. The entries along the diagonal of E are the singular values; the columns of U are the left singular vectors, and the columns of V are the right singular vectors.

The class RWSVDecomp is used to construct and work with singular value decompositions. The singular values are always ordered smallest to largest with this class. You may need more control over the computation of the decomposition than is provided by this class. For example, if you don't need all the singular vectors, you can use the SV decomposition server class, RWSVServer, to do the construction.

The template parameter <SVDCalc> determines the algorithm used by the RWSVDecomp class to compute the singular value decomposition and must implement the following method:

Note: For greater flexibility, the user can implement this method, or the Linear Algebra Module provides two classes to perform this function — RWSVDCalc and RWSVDDivConqCalc. Please see their descriptions for more information.

bool computeSVD(const RWGenMat<T>&   A,
                      RWGenMat<T>&   U,
                      RWGenMat<T>&  VT,
                      RWMathVec<norm_type>&  sigma,
                      norm_type  tolerance,
                  int numLeftVectors = -1,
                  int numRightVectors = -1);

where norm_type is a typedef for rw_numeric_traits<T>::norm_type.

Parameters:

A - The input matrix for which the singular value decomposition is being computed.

U - The output matrix of left singular victors (the columns of U are the left singular vectors).

VT - The output matrix of right singular victors (the rows of VT are the right singular victors).

sigma - The output vector of singular values in descending order.

tolerance - The input singular values with magnitude less than tolerance will be set to zero.

numLeftVectors - The input number of left vectors to compute. If the number is less than zero, the default number of vectors will be computed (it is up to the developer to determine what the default is).

numRightVectors - The input number of right vectors to compute. If the number is less than zero, the default number of vectors will be computed (it is up to the developer to determine what the default is).

The return value is true if the decomposition was successfully computed.

Synopsis: #include <rw/lapack/sv.h>

#include <rw/lapack/svddccalc.h>

RWGenMat<double> A;

.

.

.

RWSVDecomp<double,RWSVDDivConqCalc<double> >sv(A);

Example: #include <rw/iostream>

#include <rw/lapack/sv.h>

#include <rw/lapack/svddccalc.h>

int main()

{

RWGenMat<double> A;

std::cin >> A;

RWSVDecomp<double, RWSVDDivConqCalc<double> >

sv(A);

std::cout << "Input matrix: " << A << std::endl;

std::cout << "singular values: " <<

sv.singularValues() << std::endl;

std::cout << "left vectors: " << sv.leftVectors()

<< std::endl;

std::cout << "right vectors: " << sv.rightVectors()

<< std::endl;

return 0;

}