SHOGUN  4.1.0
CIterativeShiftedLinearFamilySolver< T, ST > Class Template Referenceabstract

## Detailed Description

### template<class T, class ST = T> class shogun::CIterativeShiftedLinearFamilySolver< T, ST >

abstract template base for CG based solvers to the solution of shifted linear systems of the form $$(A+\sigma)x=b$$ for several values of $$\sigma$$ simultaneously, using only as many matrix-vector operations as the solution of a single system requires. This class adds another interface to the basic iterative linear solver that takes the shifts, $$\sigma$$, and also weights, $$\alpha$$, and returns the summation $$\sum_{i} \alpha_{i}x_{i}$$, where $$x_{i}$$ is the solution of the system $$(A+\sigma_{i})x_{i}=b$$.

Reference: Beat Jegerlehner, Krylov space solvers for shifted linear systems, 1996.

Definition at line 34 of file IterativeShiftedLinearFamilySolver.h.

Inheritance diagram for CIterativeShiftedLinearFamilySolver< T, ST >:
[legend]

## Public Member Functions

CIterativeShiftedLinearFamilySolver ()

CIterativeShiftedLinearFamilySolver (bool store_residuals)

virtual ~CIterativeShiftedLinearFamilySolver ()

virtual SGVector< T > solve (CLinearOperator< T > *A, SGVector< T > b)=0

virtual SGVector< ST > solve_shifted_weighted (CLinearOperator< T > *A, SGVector< T > b, SGVector< ST > shifts, SGVector< ST > weights)=0

virtual const char * get_name () const

void set_iteration_limit (index_t iteration_limit)

const index_t get_iteration_limit () const

void set_relative_tolerence (float64_t relative_tolerence)

const float64_t get_relative_tolerence () const

void set_absolute_tolerence (float64_t absolute_tolerence)

const float64_t get_absolute_tolerence () const

SGVector< float64_tget_residuals () const

virtual CSGObjectshallow_copy () const

virtual CSGObjectdeep_copy () const

virtual bool is_generic (EPrimitiveType *generic) const

template<class T >
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

template<>
void set_generic ()

void unset_generic ()

virtual void print_serializable (const char *prefix="")

virtual bool save_serializable (CSerializableFile *file, const char *prefix="")

virtual bool load_serializable (CSerializableFile *file, const char *prefix="")

void set_global_io (SGIO *io)

SGIOget_global_io ()

void set_global_parallel (Parallel *parallel)

Parallelget_global_parallel ()

void set_global_version (Version *version)

Versionget_global_version ()

SGStringList< char > get_modelsel_names ()

void print_modsel_params ()

char * get_modsel_param_descr (const char *param_name)

index_t get_modsel_param_index (const char *param_name)

void build_gradient_parameter_dictionary (CMap< TParameter *, CSGObject * > *dict)

virtual void update_parameter_hash ()

virtual bool parameter_hash_changed ()

virtual bool equals (CSGObject *other, float64_t accuracy=0.0, bool tolerant=false)

virtual CSGObjectclone ()

## Public Attributes

SGIOio

Parallelparallel

Versionversion

Parameterm_parameters

Parameterm_model_selection_parameters

Parameterm_gradient_parameters

uint32_t m_hash

## Protected Member Functions

void compute_zeta_sh_new (const SGVector< ST > &zeta_sh_old, const SGVector< ST > &zeta_sh_cur, const SGVector< ST > &shifts, const T &beta_old, const T &beta_cur, const T &alpha, SGVector< ST > &zeta_sh_new)

void compute_beta_sh (const SGVector< ST > &zeta_sh_new, const SGVector< ST > &zeta_sh_cur, const T &beta_cur, SGVector< ST > &beta_sh)

void compute_alpha_sh (const SGVector< ST > &zeta_sh_cur, const SGVector< ST > &zeta_sh_old, const SGVector< ST > &beta_sh_old, const T &beta_old, const T &alpha, SGVector< ST > &alpha_sh)

virtual void load_serializable_pre () throw (ShogunException)

virtual void load_serializable_post () throw (ShogunException)

virtual void save_serializable_pre () throw (ShogunException)

virtual void save_serializable_post () throw (ShogunException)

## Protected Attributes

index_t m_max_iteration_limit

float64_t m_relative_tolerence

float64_t m_absolute_tolerence

SGVector< float64_tm_residuals

bool m_store_residuals

## Constructor & Destructor Documentation

 CIterativeShiftedLinearFamilySolver ( )

default constructor

Definition at line 19 of file IterativeShiftedLinearFamilySolver.cpp.

 CIterativeShiftedLinearFamilySolver ( bool store_residuals )

one arg constructor

Definition at line 26 of file IterativeShiftedLinearFamilySolver.cpp.

 ~CIterativeShiftedLinearFamilySolver ( )
virtual

destructor

Definition at line 32 of file IterativeShiftedLinearFamilySolver.cpp.

## Member Function Documentation

 void build_gradient_parameter_dictionary ( CMap< TParameter *, CSGObject * > * dict )
inherited

Builds a dictionary of all parameters in SGObject as well of those of SGObjects that are parameters of this object. Dictionary maps parameters to the objects that own them.

Parameters
 dict dictionary of parameters to be built.

Definition at line 597 of file SGObject.cpp.

 CSGObject * clone ( )
virtualinherited

Creates a clone of the current object. This is done via recursively traversing all parameters, which corresponds to a deep copy. Calling equals on the cloned object always returns true although none of the memory of both objects overlaps.

Returns
an identical copy of the given object, which is disjoint in memory. NULL if the clone fails. Note that the returned object is SG_REF'ed

Definition at line 714 of file SGObject.cpp.

 void compute_alpha_sh ( const SGVector< ST > & zeta_sh_cur, const SGVector< ST > & zeta_sh_old, const SGVector< ST > & beta_sh_old, const T & beta_old, const T & alpha, SGVector< ST > & alpha_sh )
protected

compute $$\alpha^{\sigma}_{n}$$ as $$\alpha_{n}\frac{\zeta^{\sigma} _{n}\beta^{\sigma}_{n-1}}{\zeta^{\sigma}_{n-1}\beta_{n-1}}$$

Parameters
 zeta_sh_cur $$\zeta^{\sigma}_{n}$$ shifted params zeta_sh_old $$\zeta^{\sigma}_{n-1}$$ shifted params beta_sh_old $$\beta^{\sigma}_{n-1}$$, shifted params beta_old $$\beta_{n-1}$$, non-shifted alpha $$\alpha_{n}$$, non-shifted alpha_sh $$\alpha^{\sigma}_{n}$$, to be computed

Definition at line 79 of file IterativeShiftedLinearFamilySolver.cpp.

 void compute_beta_sh ( const SGVector< ST > & zeta_sh_new, const SGVector< ST > & zeta_sh_cur, const T & beta_cur, SGVector< ST > & beta_sh )
protected

compute $$\beta^{\sigma}_{n}$$ as $$\beta_{n}\frac{\zeta^{\sigma}_{n+1}} {\zeta^{\sigma}_{n}}$$

Parameters
 zeta_sh_new $$\zeta^{\sigma}_{n+1}$$ shifted params zeta_sh_cur $$\zeta^{\sigma}_{n}$$ shifted params beta_cur $$\beta_{n}$$, non-shifted beta_sh $$\beta^{\sigma}_{n}$$, to be computed

Definition at line 59 of file IterativeShiftedLinearFamilySolver.cpp.

 void compute_zeta_sh_new ( const SGVector< ST > & zeta_sh_old, const SGVector< ST > & zeta_sh_cur, const SGVector< ST > & shifts, const T & beta_old, const T & beta_cur, const T & alpha, SGVector< ST > & zeta_sh_new )
protected

compute $$\zeta^{\sigma}_{n+1}$$ as $$\frac{\zeta^{\sigma}_{n} \zeta^{\sigma}_{n-1}\beta_{n-1}}{\beta_{n}\alpha_{n}(\zeta^{\sigma}_{n-1} -\zeta^{\sigma}_{n})+\zeta^{\sigma}_{n-1}\beta_{n-1}(1-\sigma\beta_{n}})$$ [see Jergerlehner, eq 2.44]

Parameters
 zeta_sh_old $$\zeta^{\sigma}_{n-1}$$ shifted params zeta_sh_cur $$\zeta^{\sigma}_{n}$$ shifted params shifts $$\sigma$$ shifts beta_old $$\beta_{n-1}$$, non-shifted beta_cur $$\beta_{n}$$, non-shifted alpha $$\alpha$$ non-shifted zeta_sh_new $$\zeta^{\sigma}_{n+1}$$ to be computed

Definition at line 37 of file IterativeShiftedLinearFamilySolver.cpp.

 CSGObject * deep_copy ( ) const
virtualinherited

A deep copy. All the instance variables will also be copied.

Definition at line 198 of file SGObject.cpp.

 bool equals ( CSGObject * other, float64_t accuracy = 0.0, bool tolerant = false )
virtualinherited

Recursively compares the current SGObject to another one. Compares all registered numerical parameters, recursion upon complex (SGObject) parameters. Does not compare pointers!

May be overwritten but please do with care! Should not be necessary in most cases.

Parameters
 other object to compare with accuracy accuracy to use for comparison (optional) tolerant allows linient check on float equality (within accuracy)
Returns
true if all parameters were equal, false if not

Definition at line 618 of file SGObject.cpp.

 const float64_t get_absolute_tolerence ( ) const
inherited
Returns
absolute tolerence

Definition at line 83 of file IterativeLinearSolver.h.

 SGIO * get_global_io ( )
inherited

get the io object

Returns
io object

Definition at line 235 of file SGObject.cpp.

 Parallel * get_global_parallel ( )
inherited

get the parallel object

Returns
parallel object

Definition at line 277 of file SGObject.cpp.

 Version * get_global_version ( )
inherited

get the version object

Returns
version object

Definition at line 290 of file SGObject.cpp.

 const index_t get_iteration_limit ( ) const
inherited
Returns
maximum iteration limit

Definition at line 59 of file IterativeLinearSolver.h.

 SGStringList< char > get_modelsel_names ( )
inherited
Returns
vector of names of all parameters which are registered for model selection

Definition at line 498 of file SGObject.cpp.

 char * get_modsel_param_descr ( const char * param_name )
inherited

Returns description of a given parameter string, if it exists. SG_ERROR otherwise

Parameters
 param_name name of the parameter
Returns
description of the parameter

Definition at line 522 of file SGObject.cpp.

 index_t get_modsel_param_index ( const char * param_name )
inherited

Returns index of model selection parameter with provided index

Parameters
 param_name name of model selection parameter
Returns
index of model selection parameter with provided name, -1 if there is no such

Definition at line 535 of file SGObject.cpp.

 virtual const char* get_name ( ) const
virtual
Returns
object name

Reimplemented from CIterativeLinearSolver< T, T >.

Reimplemented in CCGMShiftedFamilySolver.

Definition at line 72 of file IterativeShiftedLinearFamilySolver.h.

 const float64_t get_relative_tolerence ( ) const
inherited
Returns
relative tolerence

Definition at line 71 of file IterativeLinearSolver.h.

 SGVector get_residuals ( ) const
inherited
Returns
the residuals

Definition at line 89 of file IterativeLinearSolver.h.

 bool is_generic ( EPrimitiveType * generic ) const
virtualinherited

If the SGSerializable is a class template then TRUE will be returned and GENERIC is set to the type of the generic.

Parameters
 generic set to the type of the generic if returning TRUE
Returns
TRUE if a class template.

Definition at line 296 of file SGObject.cpp.

 bool load_serializable ( CSerializableFile * file, const char * prefix = "" )
virtualinherited

Load this object from file. If it will fail (returning FALSE) then this object will contain inconsistent data and should not be used!

Parameters
 file where to load from prefix prefix for members
Returns
TRUE if done, otherwise FALSE

Definition at line 369 of file SGObject.cpp.

 void load_serializable_post ( ) throw ( ShogunException )
protectedvirtualinherited

Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_POST is called.

Exceptions
 ShogunException will be thrown if an error occurs.

Definition at line 426 of file SGObject.cpp.

 void load_serializable_pre ( ) throw ( ShogunException )
protectedvirtualinherited

Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::LOAD_SERIALIZABLE_PRE is called.

Exceptions
 ShogunException will be thrown if an error occurs.

Definition at line 421 of file SGObject.cpp.

 bool parameter_hash_changed ( )
virtualinherited
Returns
whether parameter combination has changed since last update

Definition at line 262 of file SGObject.cpp.

 void print_modsel_params ( )
inherited

prints all parameter registered for model selection and their type

Definition at line 474 of file SGObject.cpp.

 void print_serializable ( const char * prefix = "" )
virtualinherited

prints registered parameters out

Parameters
 prefix prefix for members

Definition at line 308 of file SGObject.cpp.

 bool save_serializable ( CSerializableFile * file, const char * prefix = "" )
virtualinherited

Save this object to file.

Parameters
 file where to save the object; will be closed during returning if PREFIX is an empty string. prefix prefix for members
Returns
TRUE if done, otherwise FALSE

Definition at line 314 of file SGObject.cpp.

 void save_serializable_post ( ) throw ( ShogunException )
protectedvirtualinherited

Can (optionally) be overridden to post-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_POST is called.

Exceptions
 ShogunException will be thrown if an error occurs.

Reimplemented in CKernel.

Definition at line 436 of file SGObject.cpp.

 void save_serializable_pre ( ) throw ( ShogunException )
protectedvirtualinherited

Can (optionally) be overridden to pre-initialize some member variables which are not PARAMETER::ADD'ed. Make sure that at first the overridden method BASE_CLASS::SAVE_SERIALIZABLE_PRE is called.

Exceptions
 ShogunException will be thrown if an error occurs.

Definition at line 431 of file SGObject.cpp.

 void set_absolute_tolerence ( float64_t absolute_tolerence )
inherited

set absolute tolerence

Definition at line 77 of file IterativeLinearSolver.h.

 void set_generic ( )
inherited

Definition at line 41 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 46 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 51 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 56 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 61 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 66 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 71 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 76 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 81 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 86 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 91 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 96 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 101 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 106 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 111 of file SGObject.cpp.

 void set_generic ( )
inherited

set generic type to T

 void set_global_io ( SGIO * io )
inherited

set the io object

Parameters
 io io object to use

Definition at line 228 of file SGObject.cpp.

 void set_global_parallel ( Parallel * parallel )
inherited

set the parallel object

Parameters
 parallel parallel object to use

Definition at line 241 of file SGObject.cpp.

 void set_global_version ( Version * version )
inherited

set the version object

Parameters
 version version object to use

Definition at line 283 of file SGObject.cpp.

 void set_iteration_limit ( index_t iteration_limit )
inherited

set maximum iteration limit

Definition at line 48 of file IterativeLinearSolver.h.

 void set_relative_tolerence ( float64_t relative_tolerence )
inherited

set relative tolerence

Definition at line 65 of file IterativeLinearSolver.h.

 CSGObject * shallow_copy ( ) const
virtualinherited

A shallow copy. All the SGObject instance variables will be simply assigned and SG_REF-ed.

Reimplemented in CGaussianKernel.

Definition at line 192 of file SGObject.cpp.

 virtual SGVector solve ( CLinearOperator< T > * A, SGVector< T > b )
pure virtual

abstract solve method for solving real linear systems which computes the solution for non-shifted linear system in CG iteration

Parameters
 A the linear operator of the system b the vector of the system
Returns
the solution vector

Implements CIterativeLinearSolver< T, T >.

Implemented in CCGMShiftedFamilySolver.

 virtual SGVector solve_shifted_weighted ( CLinearOperator< T > * A, SGVector< T > b, SGVector< ST > shifts, SGVector< ST > weights )
pure virtual

abstract method that solves the shifted family of linear systems, multiples each solution vector with a weight, computes a summation over all the shifts and returns the final solution vector

Parameters
 A the linear operator of the system b the vector of the system shifts the shifts of the shifted system weights the weights to be multiplied with each solution for each shift

Implemented in CCGMShiftedFamilySolver.

 void unset_generic ( )
inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 303 of file SGObject.cpp.

 void update_parameter_hash ( )
virtualinherited

Updates the hash of current parameter combination

Definition at line 248 of file SGObject.cpp.

## Member Data Documentation

 SGIO* io
inherited

io

Definition at line 369 of file SGObject.h.

 float64_t m_absolute_tolerence
protectedinherited

absolute tolerence

Definition at line 109 of file IterativeLinearSolver.h.

 Parameter* m_gradient_parameters
inherited

parameters wrt which we can compute gradients

Definition at line 384 of file SGObject.h.

 uint32_t m_hash
inherited

Hash of parameter values

Definition at line 387 of file SGObject.h.

 index_t m_max_iteration_limit
protectedinherited

iteration limit for conjugate gradient

Definition at line 103 of file IterativeLinearSolver.h.

 Parameter* m_model_selection_parameters
inherited

model selection parameters

Definition at line 381 of file SGObject.h.

 Parameter* m_parameters
inherited

parameters

Definition at line 378 of file SGObject.h.

 float64_t m_relative_tolerence
protectedinherited

relative tolerence

Definition at line 106 of file IterativeLinearSolver.h.

 SGVector m_residuals
protectedinherited

the residuals

Definition at line 112 of file IterativeLinearSolver.h.

 bool m_store_residuals
protectedinherited

whether to store the residuals

Definition at line 115 of file IterativeLinearSolver.h.

 Parallel* parallel
inherited

parallel

Definition at line 372 of file SGObject.h.

 Version* version
inherited

version

Definition at line 375 of file SGObject.h.

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

SHOGUN Machine Learning Toolbox - Documentation