lti::singularValueDecomp< T > Class Template Reference

Singular Value Decomposition. More...

#include <ltiSVD.h>

Inheritance diagram for lti::singularValueDecomp< T >:

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Collaboration diagram for lti::singularValueDecomp< T >:

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List of all members.

Classes
class	parameters
	the parameters for the class More...
Public Member Functions
	singularValueDecomp ()
	singularValueDecomp (const parameters &params)
	singularValueDecomp (bool sort)
	singularValueDecomp (const singularValueDecomp< T > &other)
virtual	~singularValueDecomp ()
virtual const char *	getTypeName () const
singularValueDecomp &	copy (const singularValueDecomp &other)
virtual functor *	clone () const
const parameters &	getParameters () const
bool	decomposition (matrix< T > &src, vector< T > &w, matrix< T > &v) const
virtual bool	apply (matrix< T > &src, vector< T > &w, matrix< T > &v) const
virtual bool	apply (const matrix< T > &src, matrix< T > &u, vector< T > &w, matrix< T > &v) const

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Detailed Description

template<class T>
class lti::singularValueDecomp< T >

Singular Value Decomposition.

The functor will take a matrix A and compute its singular value decomposition, consisting of three matrices U, W, and V, with A=U*W*V' (where V' denotes the transpose of V). U is a column-orthonormal matrix, W is a diagonal matrix with the singular values on the diagonal, and V is a orthonormal matrix. Those columns of V whose corresponding entries in W are zero are the basis of A's null space.

You can find more theoretical information about a similar algorithm in W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery: Numerical Recipes in C, 2nd edition, Cambridge University Press, 1992.

Only instantiations of floating point types makes sense (i.e. for T double or float). If you want the singular values and corresponding singular vectors to be sorted, you have to set parameters::sort to true.

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Constructor & Destructor Documentation

template<class T>

lti::singularValueDecomp< T >::singularValueDecomp

(

)

default constructor

template<class T>

lti::singularValueDecomp< T >::singularValueDecomp

(

const parameters &

params

)

default constructor with parameters

template<class T>

lti::singularValueDecomp< T >::singularValueDecomp

(

bool

sort

)

constructor.

Sets parameters::sort to the given value.

template<class T>

lti::singularValueDecomp< T >::singularValueDecomp

(

const singularValueDecomp< T > &

other

)

copy constructor

template<class T>

virtual lti::singularValueDecomp< T >::~singularValueDecomp

(

)

[virtual]

destructor

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Member Function Documentation

template<class T>

virtual bool lti::singularValueDecomp< T >::apply	(	const matrix< T > &	src,
		matrix< T > &	u,
		vector< T > &	w,
		matrix< T > &	v
	)			const [virtual]

OnCopy version of Singular Value Decomposition.

Parameters:

	src	matrix<T> with the source matrix
	u	the U matrix
	w	vector<T> with the singular values, sorted descendingly if parameters::sort is true. The elements of this vector constitute the diagonal of the W matrix.
	v	the V matrix

Returns:

true is the decomposition was successfull, false if an error occured

Reimplemented in lti::fastSVD< T >.

template<class T>

virtual bool lti::singularValueDecomp< T >::apply	(	matrix< T > &	src,
		vector< T > &	w,
		matrix< T > &	v
	)			const [virtual]

OnPlace version of Singular Value Decomposition.

Parameters:

	src	matrix<T> with the source matrix, will also contain the U matrix after the function has returned.
	w	vector<T> with the singular values, sorted descendingly if parameters::sort is true. The elements of this vector constitute the diagonal of the W matrix.
	v	the V matrix

Returns:

true is the decomposition was successfull, false if an error occured

Reimplemented in lti::fastSVD< T >.

template<class T>

virtual functor* lti::singularValueDecomp< T >::clone

(

)

const [virtual]

returns a pointer to a clone of this functor.

Implements lti::functor.

Reimplemented in lti::fastSVD< T >.

template<class T>

singularValueDecomp& lti::singularValueDecomp< T >::copy

(

const singularValueDecomp< T > &

other

)

copy data of "other" functor.

Parameters:

other

the functor to be copied

Returns:

a reference to this functor object

Reimplemented from lti::functor.

template<class T>

bool lti::singularValueDecomp< T >::decomposition	(	matrix< T > &	src,
		vector< T > &	w,
		matrix< T > &	v
	)			const

OnPlace version of Singular Value Decomposition.

Singular Value Decomposition means that a m*n-matrix A is decomposed into three matrices U,W,V, such that A = U*W*V'. U is m*n, W is a diagonal matrix with n elements (which is implemented as vector), V is a n*n-matrix. Note that the function returns V, not V'.

Parameters:

	src	matrix<T> with the source matrix, will also contain the U matrix after the function has returned. If src is a m*n matrix, U will also be of size m*n
	w	vector<T> with the singular values, sorted descendingly The elements of this vector constitute the diagonal of the W matrix.
	v	the V matrix

Returns:

true is the decomposition was successfull, false if an error occured

template<class T>

const parameters& lti::singularValueDecomp< T >::getParameters

(

)

const

returns used parameters

Reimplemented from lti::functor.

Reimplemented in lti::fastSVD< T >.

template<class T>

virtual const char* lti::singularValueDecomp< T >::getTypeName

(

)

const [virtual]

returns the name of this type ("singularValueDecomp")

Reimplemented from lti::linearAlgebraFunctor.

Reimplemented in lti::fastSVD< T >.

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

• ltiSVD.h