SHOGUN  4.1.0
CJacobiEllipticFunctions Class Reference

## Detailed Description

Class that contains methods for computing Jacobi elliptic functions related to complex analysis. These functions are inverse of the elliptic integral of first kind, i.e.

$u(k,m)=\int_{0}^{k}\frac{dt}{\sqrt{(1-t^{2})(1-m^{2}t^{2})}} =\int_{0}^{\varphi}\frac{d\theta}{\sqrt{(1-m^{2}sin^{2}\theta)}}$

where $$k=sin\varphi$$, $$t=sin\theta$$ and parameter $$m, 0\le m \le 1$$ is called modulus. Three main Jacobi elliptic functions are defined as $$sn(u,m)=k=sin\theta$$, $$cn(u,m)=cos\theta=\sqrt{1-sn(u,m)^{2}}$$ and $$dn(u,m)=\sqrt{1-m^{2}sn(u,m)^{2}}$$. For $$k=1$$, i.e. $$\varphi=\frac{\pi}{2}$$, $$u(1,m)=K(m)$$ is known as the complete elliptic integral of first kind. Similarly, $$u(1,m'))= K'(m')$$, $$m'=\sqrt{1-m^{2}}$$ is called the complementary complete elliptic integral of first kind. Jacobi functions are double periodic with quardratic periods $$K$$ and $$K'$$.

This class provides two sets of methods for computing $$K,K'$$, and $$sn,cn,dn$$. Useful for computing rational approximation of matrix functions given by Cauchy's integral formula, etc.

Definition at line 55 of file JacobiEllipticFunctions.h.

Inheritance diagram for CJacobiEllipticFunctions:
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## Public Member Functions

virtual const char * get_name () 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="", int32_t param_version=Version::get_version_parameter())

virtual bool load_serializable (CSerializableFile *file, const char *prefix="", int32_t param_version=Version::get_version_parameter())

DynArray< TParameter * > * load_file_parameters (const SGParamInfo *param_info, int32_t file_version, CSerializableFile *file, const char *prefix="")

DynArray< TParameter * > * load_all_file_parameters (int32_t file_version, int32_t current_version, CSerializableFile *file, const char *prefix="")

void map_parameters (DynArray< TParameter * > *param_base, int32_t &base_version, DynArray< const SGParamInfo * > *target_param_infos)

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 ()

## Static Public Member Functions

static void ellipKKp (Real L, Real &K, Real &Kp)

static void ellipJC (Complex u, Real m, Complex &sn, Complex &cn, Complex &dn)

## Public Attributes

SGIOio

Parallelparallel

Versionversion

Parameterm_parameters

Parameterm_model_selection_parameters

Parameterm_gradient_parameters

ParameterMapm_parameter_map

uint32_t m_hash

## Protected Member Functions

virtual TParametermigrate (DynArray< TParameter * > *param_base, const SGParamInfo *target)

virtual void one_to_one_migration_prepare (DynArray< TParameter * > *param_base, const SGParamInfo *target, TParameter *&replacement, TParameter *&to_migrate, char *old_name=NULL)

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)

## 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 1244 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 1361 of file SGObject.cpp.

 CSGObject * deep_copy ( ) const
virtualinherited

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

Definition at line 200 of file SGObject.cpp.

 void ellipJC ( Complex u, Real m, Complex & sn, Complex & cn, Complex & dn )
static

Computes three main Jacobi elliptic functions, $$sn(u,m)$$, $$cn(u,m)$$ and $$dn(u,m)$$ (see class description).

Parameters
 u the elliptic integral of the first kind $$u(k,m)$$ m the modulus parameter, $$0\le m \le 1$$ sn Jacobi elliptic function sn(u,m) cn Jacobi elliptic function cn(u,m) dn Jacobi elliptic function dn(u,m)

Definition at line 58 of file JacobiEllipticFunctions.cpp.

 void ellipKKp ( Real L, Real & K, Real & Kp )
static

Computes the quarter periods (K and K') of Jacobian elliptic functions (see class description).

Parameters
 L K the quarter period (to be computed) on the Real axis Kp the quarter period (to be computed) on the Imaginary axis computed

Definition at line 18 of file JacobiEllipticFunctions.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 1265 of file SGObject.cpp.

 SGIO * get_global_io ( )
inherited

get the io object

Returns
io object

Definition at line 237 of file SGObject.cpp.

 Parallel * get_global_parallel ( )
inherited

get the parallel object

Returns
parallel object

Definition at line 279 of file SGObject.cpp.

 Version * get_global_version ( )
inherited

get the version object

Returns
version object

Definition at line 292 of file SGObject.cpp.

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

Definition at line 1136 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 1160 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 1173 of file SGObject.cpp.

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

Implements CSGObject.

Definition at line 155 of file JacobiEllipticFunctions.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 298 of file SGObject.cpp.

 DynArray< TParameter * > * load_all_file_parameters ( int32_t file_version, int32_t current_version, CSerializableFile * file, const char * prefix = "" )
inherited

maps all parameters of this instance to the provided file version and loads all parameter data from the file into an array, which is sorted (basically calls load_file_parameter(...) for all parameters and puts all results into a sorted array)

Parameters
 file_version parameter version of the file current_version version from which mapping begins (you want to use Version::get_version_parameter() for this in most cases) file file to load from prefix prefix for members
Returns
(sorted) array of created TParameter instances with file data

Definition at line 705 of file SGObject.cpp.

 DynArray< TParameter * > * load_file_parameters ( const SGParamInfo * param_info, int32_t file_version, CSerializableFile * file, const char * prefix = "" )
inherited

loads some specified parameters from a file with a specified version The provided parameter info has a version which is recursively mapped until the file parameter version is reached. Note that there may be possibly multiple parameters in the mapping, therefore, a set of TParameter instances is returned

Parameters
 param_info information of parameter file_version parameter version of the file, must be <= provided parameter version file file to load from prefix prefix for members
Returns
new array with TParameter instances with the attached data

Definition at line 546 of file SGObject.cpp.

 bool load_serializable ( CSerializableFile * file, const char * prefix = "", int32_t param_version = Version::get_version_parameter() )
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 param_version (optional) a parameter version different to (this is mainly for testing, better do not use)
Returns
TRUE if done, otherwise FALSE

Definition at line 375 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 1063 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 1058 of file SGObject.cpp.

 void map_parameters ( DynArray< TParameter * > * param_base, int32_t & base_version, DynArray< const SGParamInfo * > * target_param_infos )
inherited

Takes a set of TParameter instances (base) with a certain version and a set of target parameter infos and recursively maps the base level wise to the current version using CSGObject::migrate(...). The base is replaced. After this call, the base version containing parameters should be of same version/type as the initial target parameter infos. Note for this to work, the migrate methods and all the internal parameter mappings have to match

Parameters
 param_base set of TParameter instances that are mapped to the provided target parameter infos base_version version of the parameter base target_param_infos set of SGParamInfo instances that specify the target parameter base

Definition at line 743 of file SGObject.cpp.

 TParameter * migrate ( DynArray< TParameter * > * param_base, const SGParamInfo * target )
protectedvirtualinherited

creates a new TParameter instance, which contains migrated data from the version that is provided. The provided parameter data base is used for migration, this base is a collection of all parameter data of the previous version. Migration is done FROM the data in param_base TO the provided param info Migration is always one version step. Method has to be implemented in subclasses, if no match is found, base method has to be called.

If there is an element in the param_base which equals the target, a copy of the element is returned. This represents the case when nothing has changed and therefore, the migrate method is not overloaded in a subclass

Parameters
 param_base set of TParameter instances to use for migration target parameter info for the resulting TParameter
Returns
a new TParameter instance with migrated data from the base of the type which is specified by the target parameter

Definition at line 950 of file SGObject.cpp.

 void one_to_one_migration_prepare ( DynArray< TParameter * > * param_base, const SGParamInfo * target, TParameter *& replacement, TParameter *& to_migrate, char * old_name = NULL )
protectedvirtualinherited

This method prepares everything for a one-to-one parameter migration. One to one here means that only ONE element of the parameter base is needed for the migration (the one with the same name as the target). Data is allocated for the target (in the type as provided in the target SGParamInfo), and a corresponding new TParameter instance is written to replacement. The to_migrate pointer points to the single needed TParameter instance needed for migration. If a name change happened, the old name may be specified by old_name. In addition, the m_delete_data flag of to_migrate is set to true. So if you want to migrate data, the only thing to do after this call is converting the data in the m_parameter fields. If unsure how to use - have a look into an example for this. (base_migration_type_conversion.cpp for example)

Parameters
 param_base set of TParameter instances to use for migration target parameter info for the resulting TParameter replacement (used as output) here the TParameter instance which is returned by migration is created into to_migrate the only source that is used for migration old_name with this parameter, a name change may be specified

Definition at line 890 of file SGObject.cpp.

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

Definition at line 264 of file SGObject.cpp.

 void print_modsel_params ( )
inherited

prints all parameter registered for model selection and their type

Definition at line 1112 of file SGObject.cpp.

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

prints registered parameters out

Parameters
 prefix prefix for members

Definition at line 310 of file SGObject.cpp.

 bool save_serializable ( CSerializableFile * file, const char * prefix = "", int32_t param_version = Version::get_version_parameter() )
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 param_version (optional) a parameter version different to (this is mainly for testing, better do not use)
Returns
TRUE if done, otherwise FALSE

Definition at line 316 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 1073 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 1068 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 42 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 47 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 52 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 57 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 62 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 67 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 72 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 77 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 82 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 87 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 92 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 97 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 102 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 107 of file SGObject.cpp.

 void set_generic ( )
inherited

Definition at line 112 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 230 of file SGObject.cpp.

 void set_global_parallel ( Parallel * parallel )
inherited

set the parallel object

Parameters
 parallel parallel object to use

Definition at line 243 of file SGObject.cpp.

 void set_global_version ( Version * version )
inherited

set the version object

Parameters
 version version object to use

Definition at line 285 of file SGObject.cpp.

 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 194 of file SGObject.cpp.

 void unset_generic ( )
inherited

unset generic type

this has to be called in classes specializing a template class

Definition at line 305 of file SGObject.cpp.

 void update_parameter_hash ( )
virtualinherited

Updates the hash of current parameter combination

Definition at line 250 of file SGObject.cpp.

## Member Data Documentation

 SGIO* io
inherited

io

Definition at line 496 of file SGObject.h.

 Parameter* m_gradient_parameters
inherited

parameters wrt which we can compute gradients

Definition at line 511 of file SGObject.h.

 uint32_t m_hash
inherited

Hash of parameter values

Definition at line 517 of file SGObject.h.

 Parameter* m_model_selection_parameters
inherited

model selection parameters

Definition at line 508 of file SGObject.h.

 ParameterMap* m_parameter_map
inherited

map for different parameter versions

Definition at line 514 of file SGObject.h.

 Parameter* m_parameters
inherited

parameters

Definition at line 505 of file SGObject.h.

 Parallel* parallel
inherited

parallel

Definition at line 499 of file SGObject.h.

 Version* version
inherited

version

Definition at line 502 of file SGObject.h.

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

SHOGUN Machine Learning Toolbox - Documentation