GiNaC  1.7.8
Public Member Functions | Protected Member Functions | Protected Attributes | List of all members
GiNaC::fderivative Class Reference

This class represents the (abstract) derivative of a symbolic function. More...

#include <fderivative.h>

Inheritance diagram for GiNaC::fderivative:
GiNaC::function GiNaC::container< C > GiNaC::basic GiNaC::container_storage< C > GiNaC::refcounted

Public Member Functions

 fderivative (unsigned ser, unsigned param, const exvector &args)
 Construct derivative with respect to one parameter. More...
 
 fderivative (unsigned ser, const paramset &params, const exvector &args)
 Construct derivative with respect to multiple parameters. More...
 
 fderivative (unsigned ser, const paramset &params, exvector &&v)
 
void print (const print_context &c, unsigned level=0) const override
 Output to stream. More...
 
ex eval () const override
 Perform automatic non-interruptive term rewriting rules. More...
 
ex series (const relational &r, int order, unsigned options=0) const override
 The series expansion of derivatives falls back to Taylor expansion. More...
 
ex thiscontainer (const exvector &v) const override
 
ex thiscontainer (exvector &&v) const override
 
void archive (archive_node &n) const override
 Archive the object. More...
 
void read_archive (const archive_node &n, lst &syms) override
 Load (deserialize) the object from an archive node. More...
 
const paramsetderivatives () const
 Expose this object's derivative structure. More...
 
- Public Member Functions inherited from GiNaC::function
 function (unsigned ser)
 
 function (unsigned ser, const ex &param1)
 
 function (unsigned ser, const ex &param1, const ex &param2)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5, const ex &param6)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5, const ex &param6, const ex &param7)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5, const ex &param6, const ex &param7, const ex &param8)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5, const ex &param6, const ex &param7, const ex &param8, const ex &param9)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5, const ex &param6, const ex &param7, const ex &param8, const ex &param9, const ex &param10)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5, const ex &param6, const ex &param7, const ex &param8, const ex &param9, const ex &param10, const ex &param11)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5, const ex &param6, const ex &param7, const ex &param8, const ex &param9, const ex &param10, const ex &param11, const ex &param12)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5, const ex &param6, const ex &param7, const ex &param8, const ex &param9, const ex &param10, const ex &param11, const ex &param12, const ex &param13)
 
 function (unsigned ser, const ex &param1, const ex &param2, const ex &param3, const ex &param4, const ex &param5, const ex &param6, const ex &param7, const ex &param8, const ex &param9, const ex &param10, const ex &param11, const ex &param12, const ex &param13, const ex &param14)
 
 function (unsigned ser, const exprseq &es)
 
 function (unsigned ser, const exvector &v)
 
 function (unsigned ser, exvector &&v)
 
void print (const print_context &c, unsigned level=0) const override
 Output to stream. More...
 
unsigned precedence () const override
 Return relative operator precedence (for parenthezing output). More...
 
ex expand (unsigned options=0) const override
 Expand expression, i.e. More...
 
ex eval () const override
 Perform automatic non-interruptive term rewriting rules. More...
 
ex evalf () const override
 Evaluate object numerically. More...
 
ex eval_ncmul (const exvector &v) const override
 This method is defined to be in line with behavior of function::return_type() More...
 
unsigned calchash () const override
 Compute the hash value of an object and if it makes sense to store it in the objects status_flags, do so. More...
 
ex series (const relational &r, int order, unsigned options=0) const override
 Implementation of ex::series for functions. More...
 
ex thiscontainer (const exvector &v) const override
 
ex thiscontainer (exvector &&v) const override
 
ex conjugate () const override
 Implementation of ex::conjugate for functions. More...
 
ex real_part () const override
 Implementation of ex::real_part for functions. More...
 
ex imag_part () const override
 Implementation of ex::imag_part for functions. More...
 
void archive (archive_node &n) const override
 Archive the object. More...
 
void read_archive (const archive_node &n, lst &syms) override
 Construct object from archive_node. More...
 
bool info (unsigned inf) const override
 Implementation of ex::info for functions. More...
 
ex power (const ex &exp) const
 
unsigned get_serial () const
 
std::string get_name () const
 Return the print name of the function. More...
 
- Public Member Functions inherited from GiNaC::container< C >
 container (STLT const &s)
 
 container (STLT &&v)
 
 container (exvector::const_iterator b, exvector::const_iterator e)
 
 container (std::initializer_list< ex > il)
 
 container (const ex &p1) attribute_deprecated
 Deprecatd constructors (prefer initializer list) More...
 
 container (const ex &p1, const ex &p2) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7, const ex &p8) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7, const ex &p8, const ex &p9) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7, const ex &p8, const ex &p9, const ex &p10) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7, const ex &p8, const ex &p9, const ex &p10, const ex &p11) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7, const ex &p8, const ex &p9, const ex &p10, const ex &p11, const ex &p12) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7, const ex &p8, const ex &p9, const ex &p10, const ex &p11, const ex &p12, const ex &p13) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7, const ex &p8, const ex &p9, const ex &p10, const ex &p11, const ex &p12, const ex &p13, const ex &p14) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7, const ex &p8, const ex &p9, const ex &p10, const ex &p11, const ex &p12, const ex &p13, const ex &p14, const ex &p15) attribute_deprecated
 
 container (const ex &p1, const ex &p2, const ex &p3, const ex &p4, const ex &p5, const ex &p6, const ex &p7, const ex &p8, const ex &p9, const ex &p10, const ex &p11, const ex &p12, const ex &p13, const ex &p14, const ex &p15, const ex &p16) attribute_deprecated
 
container_init< ex, STLToperator= (const ex &x) attribute_deprecated
 
size_t nops () const override
 Number of operands/members. More...
 
ex op (size_t i) const override
 Return operand/member at position i. More...
 
exlet_op (size_t i) override
 Return modifiable operand/member at position i. More...
 
ex subs (const exmap &m, unsigned options=0) const override
 Substitute a set of objects by arbitrary expressions. More...
 
containerprepend (const ex &b)
 Add element at front. More...
 
containerappend (const ex &b)
 Add element at back. More...
 
containerremove_first ()
 Remove first element. More...
 
containerremove_last ()
 Remove last element. More...
 
containerremove_all ()
 Remove all elements. More...
 
containersort ()
 Sort elements. More...
 
containerunique ()
 Remove adjacent duplicate elements. More...
 
const_iterator begin () const
 
const_iterator end () const
 
const_reverse_iterator rbegin () const
 
const_reverse_iterator rend () const
 
- Public Member Functions inherited from GiNaC::basic
virtual ~basic ()
 basic destructor, virtual because class ex will delete objects of derived classes via a basic*. More...
 
 basic (const basic &other)
 
const basicoperator= (const basic &other)
 basic assignment operator: the other object might be of a derived class. More...
 
virtual basicduplicate () const
 Create a clone of this object on the heap. More...
 
virtual ex evalm () const
 Evaluate sums, products and integer powers of matrices. More...
 
virtual ex eval_integ () const
 Evaluate integrals, if result is known. More...
 
virtual ex eval_indexed (const basic &i) const
 Perform automatic symbolic evaluations on indexed expression that contains this object as the base expression. More...
 
virtual void dbgprint () const
 Little wrapper around print to be called within a debugger. More...
 
virtual void dbgprinttree () const
 Little wrapper around printtree to be called within a debugger. More...
 
virtual ex operator[] (const ex &index) const
 
virtual ex operator[] (size_t i) const
 
virtual exoperator[] (const ex &index)
 
virtual exoperator[] (size_t i)
 
virtual bool has (const ex &other, unsigned options=0) const
 Test for occurrence of a pattern. More...
 
virtual bool match (const ex &pattern, exmap &repls) const
 Check whether the expression matches a given pattern. More...
 
virtual ex map (map_function &f) const
 Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively). More...
 
virtual void accept (GiNaC::visitor &v) const
 
virtual bool is_polynomial (const ex &var) const
 Check whether this is a polynomial in the given variables. More...
 
virtual int degree (const ex &s) const
 Return degree of highest power in object s. More...
 
virtual int ldegree (const ex &s) const
 Return degree of lowest power in object s. More...
 
virtual ex coeff (const ex &s, int n=1) const
 Return coefficient of degree n in object s. More...
 
virtual ex collect (const ex &s, bool distributed=false) const
 Sort expanded expression in terms of powers of some object(s). More...
 
virtual ex normal (exmap &repl, exmap &rev_lookup) const
 Default implementation of ex::normal(). More...
 
virtual ex to_rational (exmap &repl) const
 Default implementation of ex::to_rational(). More...
 
virtual ex to_polynomial (exmap &repl) const
 
virtual numeric integer_content () const
 
virtual ex smod (const numeric &xi) const
 Apply symmetric modular homomorphism to an expanded multivariate polynomial. More...
 
virtual numeric max_coefficient () const
 Implementation ex::max_coefficient(). More...
 
virtual exvector get_free_indices () const
 Return a vector containing the free indices of an expression. More...
 
virtual ex add_indexed (const ex &self, const ex &other) const
 Add two indexed expressions. More...
 
virtual ex scalar_mul_indexed (const ex &self, const numeric &other) const
 Multiply an indexed expression with a scalar. More...
 
virtual bool contract_with (exvector::iterator self, exvector::iterator other, exvector &v) const
 Try to contract two indexed expressions that appear in the same product. More...
 
template<class T >
void print_dispatch (const print_context &c, unsigned level) const
 Like print(), but dispatch to the specified class. More...
 
void print_dispatch (const registered_class_info &ri, const print_context &c, unsigned level) const
 Like print(), but dispatch to the specified class. More...
 
ex subs_one_level (const exmap &m, unsigned options) const
 Helper function for subs(). More...
 
ex diff (const symbol &s, unsigned nth=1) const
 Default interface of nth derivative ex::diff(s, n). More...
 
int compare (const basic &other) const
 Compare objects syntactically to establish canonical ordering. More...
 
bool is_equal (const basic &other) const
 Test for syntactic equality. More...
 
const basichold () const
 Stop further evaluation. More...
 
unsigned gethash () const
 
const basicsetflag (unsigned f) const
 Set some status_flags. More...
 
const basicclearflag (unsigned f) const
 Clear some status_flags. More...
 
- Public Member Functions inherited from GiNaC::refcounted
 refcounted () noexcept
 
unsigned int add_reference () noexcept
 
unsigned int remove_reference () noexcept
 
unsigned int get_refcount () const noexcept
 
void set_refcount (unsigned int r) noexcept
 

Protected Member Functions

ex derivative (const symbol &s) const override
 Implementation of ex::diff() for derivatives. More...
 
bool is_equal_same_type (const basic &other) const override
 Returns true if two objects of same type are equal. More...
 
bool match_same_type (const basic &other) const override
 Returns true if the attributes of two objects are similar enough for a match. More...
 
void do_print (const print_context &c, unsigned level) const
 
void do_print_latex (const print_context &c, unsigned level) const
 
void do_print_csrc (const print_csrc &c, unsigned level) const
 
void do_print_tree (const print_tree &c, unsigned level) const
 
- Protected Member Functions inherited from GiNaC::function
ex derivative (const symbol &s) const override
 Implementation of ex::diff() for functions. More...
 
bool is_equal_same_type (const basic &other) const override
 Returns true if two objects of same type are equal. More...
 
bool match_same_type (const basic &other) const override
 Returns true if the attributes of two objects are similar enough for a match. More...
 
unsigned return_type () const override
 
return_type_t return_type_tinfo () const override
 
ex pderivative (unsigned diff_param) const
 
ex expl_derivative (const symbol &s) const
 
bool lookup_remember_table (ex &result) const
 
void store_remember_table (ex const &result) const
 
- Protected Member Functions inherited from GiNaC::container< C >
virtual ex thiscontainer (const STLT &v) const
 Similar to duplicate(), but with a preset sequence. More...
 
virtual ex thiscontainer (STLT &&v) const
 Similar to duplicate(), but with a preset sequence (which gets pilfered). More...
 
virtual void printseq (const print_context &c, char openbracket, char delim, char closebracket, unsigned this_precedence, unsigned upper_precedence=0) const
 Print sequence of contained elements. More...
 
void do_print (const print_context &c, unsigned level) const
 
void do_print_tree (const print_tree &c, unsigned level) const
 
void do_print_python (const print_python &c, unsigned level) const
 
void do_print_python_repr (const print_python_repr &c, unsigned level) const
 
STLT subschildren (const exmap &m, unsigned options=0) const
 
- Protected Member Functions inherited from GiNaC::basic
 basic ()
 
virtual int compare_same_type (const basic &other) const
 Returns order relation between two objects of same type. More...
 
void ensure_if_modifiable () const
 Ensure the object may be modified without hurting others, throws if this is not the case. More...
 
void do_print (const print_context &c, unsigned level) const
 Default output to stream. More...
 
void do_print_tree (const print_tree &c, unsigned level) const
 Tree output to stream. More...
 
void do_print_python_repr (const print_python_repr &c, unsigned level) const
 Python parsable output to stream. More...
 
- Protected Member Functions inherited from GiNaC::container_storage< C >
 container_storage ()
 
 container_storage (size_t n, const ex &e)
 
 container_storage (std::initializer_list< ex > il)
 
template<class In >
 container_storage (In b, In e)
 
void reserve (size_t)
 
 ~container_storage ()
 
template<>
void reserve (size_t n)
 
template<>
void reserve (std::vector< ex > &v, size_t n)
 

Protected Attributes

paramset parameter_set
 Set of parameter numbers with respect to which to take the derivative. More...
 
- Protected Attributes inherited from GiNaC::function
unsigned serial
 
- Protected Attributes inherited from GiNaC::basic
unsigned flags
 of type status_flags More...
 
unsigned hashvalue
 hash value More...
 
- Protected Attributes inherited from GiNaC::container_storage< C >
STLT seq
 

Additional Inherited Members

- Public Types inherited from GiNaC::container< C >
typedef STLT::const_iterator const_iterator
 
typedef STLT::const_reverse_iterator const_reverse_iterator
 
- Static Public Member Functions inherited from GiNaC::function
static unsigned register_new (function_options const &opt)
 
static unsigned find_function (const std::string &name, unsigned nparams)
 Find serial number of function by name and number of parameters. More...
 
static std::vector< function_optionsget_registered_functions ()
 
- Static Public Attributes inherited from GiNaC::function
static unsigned current_serial = 0
 This can be used as a hook for external applications. More...
 
- Protected Types inherited from GiNaC::container< C >
typedef container_storage< C >::STLT STLT
 
- Protected Types inherited from GiNaC::container_storage< C >
typedef C< exSTLT
 
- Static Protected Member Functions inherited from GiNaC::function
static std::vector< function_options > & registered_functions ()
 
- Static Protected Member Functions inherited from GiNaC::container< C >
static unsigned get_default_flags ()
 Specialization of container::get_default_flags() for lst. More...
 
static char get_open_delim ()
 Specialization of container::get_open_delim() for lst. More...
 
static char get_close_delim ()
 Specialization of container::get_close_delim() for lst. More...
 
- Static Protected Member Functions inherited from GiNaC::container_storage< C >
static void reserve (STLT &, size_t)
 

Detailed Description

This class represents the (abstract) derivative of a symbolic function.

It is used to represent the derivatives of functions that do not have a derivative or series expansion procedure defined.

Definition at line 37 of file fderivative.h.

Constructor & Destructor Documentation

◆ fderivative() [1/3]

GiNaC::fderivative::fderivative ( unsigned  ser,
unsigned  param,
const exvector args 
)

Construct derivative with respect to one parameter.

Parameters
serSerial number of function
paramNumber of parameter with respect to which to take the derivative
argsArguments of derivative function

Definition at line 50 of file fderivative.cpp.

References parameter_set.

Referenced by derivative(), and thiscontainer().

◆ fderivative() [2/3]

GiNaC::fderivative::fderivative ( unsigned  ser,
const paramset params,
const exvector args 
)

Construct derivative with respect to multiple parameters.

Parameters
serSerial number of function
paramsSet of numbers of parameters with respect to which to take the derivative
argsArguments of derivative function

Definition at line 55 of file fderivative.cpp.

◆ fderivative() [3/3]

GiNaC::fderivative::fderivative ( unsigned  ser,
const paramset params,
exvector &&  v 
)

Definition at line 59 of file fderivative.cpp.

Member Function Documentation

◆ print()

void GiNaC::fderivative::print ( const print_context c,
unsigned  level = 0 
) const
overridevirtual

Output to stream.

This performs double dispatch on the dynamic type of *this and the dynamic type of the supplied print context.

Parameters
cprint context object that describes the output formatting
levelvalue that is used to identify the precedence or indentation level for placing parentheses and formatting

Reimplemented from GiNaC::basic.

Definition at line 97 of file fderivative.cpp.

References c, and GiNaC::basic::print().

◆ eval()

ex GiNaC::fderivative::eval ( ) const
overridevirtual

Perform automatic non-interruptive term rewriting rules.

Reimplemented from GiNaC::basic.

Definition at line 160 of file fderivative.cpp.

References GiNaC::basic::hold(), parameter_set, GiNaC::function::pderivative(), GiNaC::function::registered_functions(), GiNaC::container_storage< C >::seq, and GiNaC::function::serial.

◆ series()

ex GiNaC::fderivative::series ( const relational r,
int  order,
unsigned  options = 0 
) const
overridevirtual

The series expansion of derivatives falls back to Taylor expansion.

See also
basic::series

Reimplemented from GiNaC::basic.

Definition at line 175 of file fderivative.cpp.

References options, r, and GiNaC::basic::series().

◆ thiscontainer() [1/2]

ex GiNaC::fderivative::thiscontainer ( const exvector v) const
override

Definition at line 180 of file fderivative.cpp.

References fderivative(), parameter_set, and GiNaC::function::serial.

◆ thiscontainer() [2/2]

ex GiNaC::fderivative::thiscontainer ( exvector &&  v) const
override

Definition at line 185 of file fderivative.cpp.

References fderivative(), parameter_set, and GiNaC::function::serial.

◆ archive()

void GiNaC::fderivative::archive ( archive_node n) const
overridevirtual

Archive the object.

Reimplemented from GiNaC::container< C >.

Definition at line 82 of file fderivative.cpp.

References GiNaC::container< C >::end(), n, and parameter_set.

◆ read_archive()

void GiNaC::fderivative::read_archive ( const archive_node n,
lst syms 
)
overridevirtual

Load (deserialize) the object from an archive node.

Construct object from archive_node.

Note
This method is essentially a constructor. However, constructors can't be virtual. So, if unarchiving routines are implemented as constructors one would need to define such a constructor in every class, even if all it does is simply calling constructor of a superclass.

Reimplemented from GiNaC::container< C >.

Definition at line 67 of file fderivative.cpp.

References n, and parameter_set.

◆ derivative()

ex GiNaC::fderivative::derivative ( const symbol s) const
overrideprotectedvirtual

Implementation of ex::diff() for derivatives.

It applies the chain rule.

See also
ex::diff

Reimplemented from GiNaC::basic.

Definition at line 192 of file fderivative.cpp.

References fderivative(), GiNaC::ex::is_zero(), parameter_set, GiNaC::container_storage< C >::seq, and GiNaC::function::serial.

◆ is_equal_same_type()

bool GiNaC::fderivative::is_equal_same_type ( const basic other) const
overrideprotectedvirtual

Returns true if two objects of same type are equal.

Normally needs not be reimplemented as long as it wasn't overwritten by some parent class, since it just calls compare_same_type(). The reason why this function exists is that sometimes it is easier to determine equality than an order relation and then it can be overridden.

Reimplemented from GiNaC::container< C >.

Definition at line 217 of file fderivative.cpp.

References GINAC_ASSERT, and parameter_set.

◆ match_same_type()

bool GiNaC::fderivative::match_same_type ( const basic other) const
overrideprotectedvirtual

Returns true if the attributes of two objects are similar enough for a match.

This function must not match subexpressions (this is already done by basic::match()). Only attributes not accessible by op() should be compared. This is also the reason why this function doesn't take the wildcard replacement list from match() as an argument: only subexpressions are subject to wildcard matches. Also, this function only needs to be implemented for container classes because is_equal_same_type() is automatically used instead of match_same_type() if nops() == 0.

See also
basic::match

Reimplemented from GiNaC::basic.

Definition at line 228 of file fderivative.cpp.

References GINAC_ASSERT, and parameter_set.

◆ derivatives()

const paramset & GiNaC::fderivative::derivatives ( ) const

Expose this object's derivative structure.

Parameter numbers occurring more than once stand for repeated differentiation with respect to that parameter. If a symbolic function f(x,y) is differentiated with respect to x, this method will return {0}. If f(x,y) is differentiated twice with respect to y, it will return {1,1}. (This corresponds to the way this object is printed.)

Returns
multiset of function's parameter numbers that are abstractly differentiated.

Definition at line 246 of file fderivative.cpp.

References parameter_set.

◆ do_print()

void GiNaC::fderivative::do_print ( const print_context c,
unsigned  level 
) const
protected

◆ do_print_latex()

void GiNaC::fderivative::do_print_latex ( const print_context c,
unsigned  level 
) const
protected

◆ do_print_csrc()

void GiNaC::fderivative::do_print_csrc ( const print_csrc c,
unsigned  level 
) const
protected

◆ do_print_tree()

void GiNaC::fderivative::do_print_tree ( const print_tree c,
unsigned  level 
) const
protected

Member Data Documentation

◆ parameter_set

paramset GiNaC::fderivative::parameter_set
protected

Set of parameter numbers with respect to which to take the derivative.

Definition at line 85 of file fderivative.h.

Referenced by archive(), derivative(), derivatives(), do_print(), do_print_csrc(), do_print_latex(), do_print_tree(), eval(), fderivative(), is_equal_same_type(), match_same_type(), read_archive(), and thiscontainer().


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

This page is part of the GiNaC developer's reference. It was generated automatically by doxygen. For an introduction, see the tutorial.