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 CSGObject *	shallow_copy () const

virtual CSGObject *	deep_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)

SGIO *	get_global_io ()

void	set_global_parallel (Parallel *parallel)

Parallel *	get_global_parallel ()

void	set_global_version (Version *version)

Version *	get_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 CSGObject *	clone ()

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
SGIO *	io

Parallel *	parallel

Version *	version

Parameter *	m_parameters

Parameter *	m_model_selection_parameters

Parameter *	m_gradient_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)

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.

CSGObject * deep_copy ( ) const

virtualinherited

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

Definition at line 198 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 618 of file SGObject.cpp.

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.

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

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 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.

Reimplemented in CKernel, CWeightedDegreePositionStringKernel, CList, CAlphabet, CLinearHMM, CGaussianKernel, CInverseMultiQuadricKernel, CCircularKernel, and CExponentialKernel.

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.

Reimplemented in CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.

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.

Reimplemented in CKernel, CDynamicArray< T >, CDynamicArray< float64_t >, CDynamicArray< float32_t >, CDynamicArray< int32_t >, CDynamicArray< char >, CDynamicArray< bool >, and CDynamicObjectArray.

Definition at line 431 of file SGObject.cpp.

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.

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.

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.

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.

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.

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:

Detailed Description

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Member Function Documentation

Member Data Documentation