SHOGUN  6.1.3
CRationalApproximation Class Referenceabstract

## Detailed Description

Abstract base class of the rational approximation of a function of a linear operator (A) times vector (v) using Cauchy's integral formula -

$f(\text{A})\text{v}=\oint_{\Gamma}f(z)(z\text{I}-\text{A})^{-1} \text{v}dz$

Computes eigenvalues of linear operator and uses Jacobi elliptic functions and conformal maps [2] for quadrature rule for discretizing the contour integral and computes complex shifts, weights and constant multiplier of the rational approximation of the above expression as

$f(\text{A})\text{v}\approx \eta\text{A}\Im-\left(\sum_{l=1}^{N}\alpha_{l} (\text{A}-\sigma_{l}\text{I})^{-1}\text{v}\right)$

where $$\alpha_{l},\sigma_{l}\in\mathbb{C}$$ are respectively the shifts and weights of the linear systems generated from the rational approximation, and $$\eta\in\mathbb{R}$$ is the constant multiplier, equals to $$\frac{-8K(\lambda_{m}\lambda_{M})^{\frac{1}{4}}}{k\pi N}$$.

The number of shifts is automatically computed based on a previously specified accuracy $$\epsilon$$ using the error bound

$-1.5\left(\log\left( \frac{\lambda_\text{max}}{\lambda_\text{min}}\right)+6.0 \right)\frac{\log(\epsilon)}{2\pi^2}.$

It can also manually be set.

Reference: [1] Aune, E., D. Simpson, and J. Eidsvik (2012). Parameter estimation in high dimensional gaussian distributions. Technical Report Statistics 5/2012, NTNU.

[2] Nicholas Hale, Nicholas J. Higham and Lloyd N. Trefethen (2008). Computing $$A^{\alpha}$$ , $$log(A)$$ and related matrix functions by contour integrals. SIAM Journal of Numerical Analysis, 46:2505-2523

Note: The implementation of compute_weights_shifts_const function has been adapted from KRYLSTAT (Copyright 2011 by Erlend Aune erlen.nosp@m.da@m.nosp@m.ath.n.nosp@m.tnu..nosp@m.no) under GPL2+. See https://github.com/Froskekongen/KRYLSTAT.

Definition at line 63 of file RationalApproximation.h.

Inheritance diagram for CRationalApproximation:
[legend]

## Public Types

typedef rxcpp::subjects::subject< ObservedValueSGSubject

typedef rxcpp::observable< ObservedValue, rxcpp::dynamic_observable< ObservedValue > > SGObservable

typedef rxcpp::subscriber< ObservedValue, rxcpp::observer< ObservedValue, void, void, void, void > > SGSubscriber

## Public Member Functions

CRationalApproximation ()

CRationalApproximation (CLinearOperator< float64_t > *linear_operator, CIndependentComputationEngine *computation_engine, CEigenSolver *eigen_solver, float64_t desired_accuracy, EOperatorFunction function_type)

virtual ~CRationalApproximation ()

virtual void precompute ()

int32_t compute_num_shifts_from_accuracy ()

virtual CJobResultAggregatorsubmit_jobs (SGVector< float64_t > sample)=0

SGVector< complex128_tget_shifts () const

SGVector< complex128_tget_weights () const

float64_t get_constant_multiplier () const

index_t get_num_shifts () const

void set_num_shifts (index_t num_shifts)

virtual const char * get_name () const

CLinearOperator< float64_t > * get_operator () const

int32_t ref ()

int32_t ref_count ()

int32_t unref ()

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)

bool has (const std::string &name) const

template<typename T >
bool has (const Tag< T > &tag) const

template<typename T , typename U = void>
bool has (const std::string &name) const

template<typename T >
void set (const Tag< T > &_tag, const T &value)

template<typename T , typename U = void>
void set (const std::string &name, const T &value)

template<typename T >
get (const Tag< T > &_tag) const

template<typename T , typename U = void>
get (const std::string &name) const

SGObservableget_parameters_observable ()

void subscribe_to_parameters (ParameterObserverInterface *obs)

void list_observable_parameters ()

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

uint32_t m_hash

## Protected Member Functions

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)

template<typename T >
void register_param (Tag< T > &_tag, const T &value)

template<typename T >
void register_param (const std::string &name, const T &value)

bool clone_parameters (CSGObject *other)

void observe (const ObservedValue value)

void register_observable_param (const std::string &name, const SG_OBS_VALUE_TYPE type, const std::string &description)

## Protected Attributes

CEigenSolverm_eigen_solver

SGVector< complex128_tm_shifts

SGVector< complex128_tm_weights

float64_t m_constant_multiplier

int32_t m_num_shifts

float64_t m_desired_accuracy

CLinearOperator< float64_t > * m_linear_operator

CIndependentComputationEnginem_computation_engine

const EOperatorFunction m_function_type

## ◆ SGObservable

 inherited

Definition at line 130 of file SGObject.h.

## ◆ SGSubject

 inherited

Definition at line 127 of file SGObject.h.

## ◆ SGSubscriber

 typedef rxcpp::subscriber< ObservedValue, rxcpp::observer > SGSubscriber
inherited

Definition at line 133 of file SGObject.h.

## ◆ CRationalApproximation() [1/2]

 CRationalApproximation ( )

default constructor

Definition at line 27 of file RationalApproximation.cpp.

## ◆ CRationalApproximation() [2/2]

 CRationalApproximation ( CLinearOperator< float64_t > * linear_operator, CIndependentComputationEngine * computation_engine, CEigenSolver * eigen_solver, float64_t desired_accuracy, EOperatorFunction function_type )

Constructor. Number of shifts will be computed using a specified accuracy.

Parameters
 linear_operator real valued linear operator for this operator function computation_engine engine that computes the independent jobs eigen_solver eigen solver for computing min and max eigenvalues needed for computing shifts, weights and constant multiplier desired_accuracy desired error bound on approximation. Computes the number of shifts automatically function_type operator function type

Definition at line 35 of file RationalApproximation.cpp.

## ◆ ~CRationalApproximation()

 ~CRationalApproximation ( )
virtual

destructor

Definition at line 54 of file RationalApproximation.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 635 of file SGObject.cpp.

## ◆ clone()

 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 734 of file SGObject.cpp.

## ◆ clone_parameters()

 bool clone_parameters ( CSGObject * other )
protectedinherited

Definition at line 759 of file SGObject.cpp.

## ◆ compute_num_shifts_from_accuracy()

 int32_t compute_num_shifts_from_accuracy ( )

Computes the number of shifts from the current set accuracy $$\epsilon$$ using

$-1.5\left(\log\left( \frac{\lambda_\text{max}}{\lambda_\text{min}}\right)+6.0 \right)\frac{\log(\epsilon)}{2\pi^2},$

Returns
number of shift to reach the above error bound

Definition at line 131 of file RationalApproximation.cpp.

## ◆ deep_copy()

 CSGObject * deep_copy ( ) const
virtualinherited

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

Definition at line 232 of file SGObject.cpp.

## ◆ equals()

 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 656 of file SGObject.cpp.

## ◆ get() [1/2]

 T get ( const Tag< T > & _tag ) const
inherited

Getter for a class parameter, identified by a Tag. Throws an exception if the class does not have such a parameter.

Parameters
 _tag name and type information of parameter
Returns
value of the parameter identified by the input tag

Definition at line 381 of file SGObject.h.

## ◆ get() [2/2]

 T get ( const std::string & name ) const
inherited

Getter for a class parameter, identified by a name. Throws an exception if the class does not have such a parameter.

Parameters
 name name of the parameter
Returns
value of the parameter corresponding to the input name and type

Definition at line 404 of file SGObject.h.

## ◆ get_constant_multiplier()

 float64_t get_constant_multiplier ( ) const
Returns
constant multiplier

Definition at line 98 of file RationalApproximation.cpp.

## ◆ get_global_io()

 SGIO * get_global_io ( )
inherited

get the io object

Returns
io object

Definition at line 269 of file SGObject.cpp.

## ◆ get_global_parallel()

 Parallel * get_global_parallel ( )
inherited

get the parallel object

Returns
parallel object

Definition at line 311 of file SGObject.cpp.

## ◆ get_global_version()

 Version * get_global_version ( )
inherited

get the version object

Returns
version object

Definition at line 324 of file SGObject.cpp.

## ◆ get_modelsel_names()

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

Definition at line 536 of file SGObject.cpp.

## ◆ get_modsel_param_descr()

 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 560 of file SGObject.cpp.

## ◆ get_modsel_param_index()

 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 573 of file SGObject.cpp.

## ◆ get_name()

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

Reimplemented from COperatorFunction< float64_t >.

Reimplemented in CLogRationalApproximationIndividual, and CLogRationalApproximationCGM.

Definition at line 142 of file RationalApproximation.h.

## ◆ get_num_shifts()

 index_t get_num_shifts ( ) const
Returns
number of shifts

Definition at line 103 of file RationalApproximation.cpp.

## ◆ get_operator()

 CLinearOperator* get_operator ( ) const
inherited
Returns
the operator

Definition at line 81 of file OperatorFunction.h.

## ◆ get_parameters_observable()

 SGObservable* get_parameters_observable ( )
inherited

Get parameters observable

Returns
RxCpp observable

Definition at line 415 of file SGObject.h.

## ◆ get_shifts()

 SGVector< complex128_t > get_shifts ( ) const
Returns
shifts

Definition at line 88 of file RationalApproximation.cpp.

## ◆ get_weights()

 SGVector< complex128_t > get_weights ( ) const
Returns
weights

Definition at line 93 of file RationalApproximation.cpp.

## ◆ has() [1/3]

 bool has ( const std::string & name ) const
inherited

Checks if object has a class parameter identified by a name.

Parameters
 name name of the parameter
Returns
true if the parameter exists with the input name

Definition at line 304 of file SGObject.h.

## ◆ has() [2/3]

 bool has ( const Tag< T > & tag ) const
inherited

Checks if object has a class parameter identified by a Tag.

Parameters
 tag tag of the parameter containing name and type information
Returns
true if the parameter exists with the input tag

Definition at line 315 of file SGObject.h.

## ◆ has() [3/3]

 bool has ( const std::string & name ) const
inherited

Checks if a type exists for a class parameter identified by a name.

Parameters
 name name of the parameter
Returns
true if the parameter exists with the input name and type

Definition at line 326 of file SGObject.h.

## ◆ is_generic()

 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 330 of file SGObject.cpp.

## ◆ list_observable_parameters()

 void list_observable_parameters ( )
inherited

Print to stdout a list of observable parameters

Definition at line 878 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 403 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 460 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 455 of file SGObject.cpp.

## ◆ observe()

 void observe ( const ObservedValue value )
protectedinherited

Observe a parameter value and emit them to observer.

Parameters
 value Observed parameter's value

Definition at line 828 of file SGObject.cpp.

## ◆ parameter_hash_changed()

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

Definition at line 296 of file SGObject.cpp.

## ◆ precompute()

 void precompute ( )
virtual

precompute method that computes extremal eigenvalues using the eigensolver and then computes complex shifts, weights and constant multiplier coming from rational approximation of operator function times vector

Automatically computes the number of shifts if they have not been specified or are zero using set_shifts_from_accuracy().

Implements COperatorFunction< float64_t >.

Definition at line 113 of file RationalApproximation.cpp.

## ◆ print_modsel_params()

 void print_modsel_params ( )
inherited

prints all parameter registered for model selection and their type

Definition at line 512 of file SGObject.cpp.

## ◆ print_serializable()

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

prints registered parameters out

Parameters
 prefix prefix for members

Definition at line 342 of file SGObject.cpp.

## ◆ ref()

 int32_t ref ( )
inherited

increase reference counter

Returns
reference count

Definition at line 186 of file SGObject.cpp.

## ◆ ref_count()

 int32_t ref_count ( )
inherited

display reference counter

Returns
reference count

Definition at line 193 of file SGObject.cpp.

## ◆ register_observable_param()

 void register_observable_param ( const std::string & name, const SG_OBS_VALUE_TYPE type, const std::string & description )
protectedinherited

Register which params this object can emit.

Parameters
 name the param name type the param type description a user oriented description

Definition at line 871 of file SGObject.cpp.

## ◆ register_param() [1/2]

 void register_param ( Tag< T > & _tag, const T & value )
protectedinherited

Registers a class parameter which is identified by a tag. This enables the parameter to be modified by set() and retrieved by get(). Parameters can be registered in the constructor of the class.

Parameters
 _tag name and type information of parameter value value of the parameter

Definition at line 472 of file SGObject.h.

## ◆ register_param() [2/2]

 void register_param ( const std::string & name, const T & value )
protectedinherited

Registers a class parameter which is identified by a name. This enables the parameter to be modified by set() and retrieved by get(). Parameters can be registered in the constructor of the class.

Parameters
 name name of the parameter value value of the parameter along with type information

Definition at line 485 of file SGObject.h.

## ◆ save_serializable()

 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 348 of file SGObject.cpp.

## ◆ save_serializable_post()

 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 470 of file SGObject.cpp.

## ◆ save_serializable_pre()

 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 465 of file SGObject.cpp.

## ◆ set() [1/2]

 void set ( const Tag< T > & _tag, const T & value )
inherited

Setter for a class parameter, identified by a Tag. Throws an exception if the class does not have such a parameter.

Parameters
 _tag name and type information of parameter value value of the parameter

Definition at line 342 of file SGObject.h.

## ◆ set() [2/2]

 void set ( const std::string & name, const T & value )
inherited

Setter for a class parameter, identified by a name. Throws an exception if the class does not have such a parameter.

Parameters
 name name of the parameter value value of the parameter along with type information

Definition at line 368 of file SGObject.h.

## ◆ set_generic() [1/16]

 void set_generic ( )
inherited

Definition at line 73 of file SGObject.cpp.

## ◆ set_generic() [2/16]

 void set_generic ( )
inherited

Definition at line 78 of file SGObject.cpp.

## ◆ set_generic() [3/16]

 void set_generic ( )
inherited

Definition at line 83 of file SGObject.cpp.

## ◆ set_generic() [4/16]

 void set_generic ( )
inherited

Definition at line 88 of file SGObject.cpp.

## ◆ set_generic() [5/16]

 void set_generic ( )
inherited

Definition at line 93 of file SGObject.cpp.

## ◆ set_generic() [6/16]

 void set_generic ( )
inherited

Definition at line 98 of file SGObject.cpp.

## ◆ set_generic() [7/16]

 void set_generic ( )
inherited

Definition at line 103 of file SGObject.cpp.

## ◆ set_generic() [8/16]

 void set_generic ( )
inherited

Definition at line 108 of file SGObject.cpp.

## ◆ set_generic() [9/16]

 void set_generic ( )
inherited

Definition at line 113 of file SGObject.cpp.

## ◆ set_generic() [10/16]

 void set_generic ( )
inherited

Definition at line 118 of file SGObject.cpp.

## ◆ set_generic() [11/16]

 void set_generic ( )
inherited

Definition at line 123 of file SGObject.cpp.

## ◆ set_generic() [12/16]

 void set_generic ( )
inherited

Definition at line 128 of file SGObject.cpp.

## ◆ set_generic() [13/16]

 void set_generic ( )
inherited

Definition at line 133 of file SGObject.cpp.

## ◆ set_generic() [14/16]

 void set_generic ( )
inherited

Definition at line 138 of file SGObject.cpp.

## ◆ set_generic() [15/16]

 void set_generic ( )
inherited

Definition at line 143 of file SGObject.cpp.

## ◆ set_generic() [16/16]

 void set_generic ( )
inherited

set generic type to T

## ◆ set_global_io()

 void set_global_io ( SGIO * io )
inherited

set the io object

Parameters
 io io object to use

Definition at line 262 of file SGObject.cpp.

## ◆ set_global_parallel()

 void set_global_parallel ( Parallel * parallel )
inherited

set the parallel object

Parameters
 parallel parallel object to use

Definition at line 275 of file SGObject.cpp.

## ◆ set_global_version()

 void set_global_version ( Version * version )
inherited

set the version object

Parameters
 version version object to use

Definition at line 317 of file SGObject.cpp.

## ◆ set_num_shifts()

 void set_num_shifts ( index_t num_shifts )
Parameters
 num_shifts number of shifts

Definition at line 108 of file RationalApproximation.cpp.

## ◆ shallow_copy()

 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 226 of file SGObject.cpp.

## ◆ submit_jobs()

 virtual CJobResultAggregator* submit_jobs ( SGVector< float64_t > sample )
pure virtual

abstract method that creates a job result aggregator, then creates a number of jobs based on its implementation, attaches the aggregator with all those jobs, hands over the responsility of those to the computation engine and then returns the aggregator for collecting the job results

Parameters
 sample the vector for which new computation job(s) are to be created
Returns
the array of generated independent jobs

Implements COperatorFunction< float64_t >.

Implemented in CLogRationalApproximationIndividual, and CLogRationalApproximationCGM.

## ◆ subscribe_to_parameters()

 void subscribe_to_parameters ( ParameterObserverInterface * obs )
inherited

Subscribe a parameter observer to watch over params

Definition at line 811 of file SGObject.cpp.

## ◆ unref()

 int32_t unref ( )
inherited

decrement reference counter and deallocate object if refcount is zero before or after decrementing it

Returns
reference count

Definition at line 200 of file SGObject.cpp.

## ◆ unset_generic()

 void unset_generic ( )
inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 337 of file SGObject.cpp.

## ◆ update_parameter_hash()

 void update_parameter_hash ( )
virtualinherited

Updates the hash of current parameter combination

Definition at line 282 of file SGObject.cpp.

## ◆ io

 SGIO* io
inherited

io

Definition at line 600 of file SGObject.h.

## ◆ m_computation_engine

 CIndependentComputationEngine* m_computation_engine
protectedinherited

the computation engine

Definition at line 115 of file OperatorFunction.h.

## ◆ m_constant_multiplier

 float64_t m_constant_multiplier
protected

constant multiplier

Definition at line 158 of file RationalApproximation.h.

## ◆ m_desired_accuracy

 float64_t m_desired_accuracy
protected

desired accuracy from which number of shifts might be computed

Definition at line 164 of file RationalApproximation.h.

## ◆ m_eigen_solver

 CEigenSolver* m_eigen_solver
protected

the eigen solver for computing extremal eigenvalues

Definition at line 149 of file RationalApproximation.h.

## ◆ m_function_type

 const EOperatorFunction m_function_type
protectedinherited

the linear operator function type

Definition at line 118 of file OperatorFunction.h.

inherited

parameters wrt which we can compute gradients

Definition at line 615 of file SGObject.h.

## ◆ m_hash

 uint32_t m_hash
inherited

Hash of parameter values

Definition at line 618 of file SGObject.h.

## ◆ m_linear_operator

 CLinearOperator* m_linear_operator
protectedinherited

the linear operator

Definition at line 112 of file OperatorFunction.h.

## ◆ m_model_selection_parameters

 Parameter* m_model_selection_parameters
inherited

model selection parameters

Definition at line 612 of file SGObject.h.

## ◆ m_num_shifts

 int32_t m_num_shifts
protected

number of shifts

Definition at line 161 of file RationalApproximation.h.

## ◆ m_parameters

 Parameter* m_parameters
inherited

parameters

Definition at line 609 of file SGObject.h.

## ◆ m_shifts

 SGVector m_shifts
protected

complex shifts in the systems coming from rational approximation

Definition at line 152 of file RationalApproximation.h.

## ◆ m_weights

 SGVector m_weights
protected

complex weights in the systems coming from rational approximation

Definition at line 155 of file RationalApproximation.h.

## ◆ parallel

 Parallel* parallel
inherited

parallel

Definition at line 603 of file SGObject.h.

## ◆ version

 Version* version
inherited

version

Definition at line 606 of file SGObject.h.

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

SHOGUN Machine Learning Toolbox - Documentation