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

#include <fderivative.h>

Inheritance diagram for GiNaC::fderivative:

Public Member Functions
	fderivative (unsigned ser, unsigned param, const exvector &args)
	Construct derivative with respect to one parameter.

	fderivative (unsigned ser, const paramset &params, const exvector &args)
	Construct derivative with respect to multiple parameters.

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

void	print (const print_context &c, unsigned level=0) const override
	Output to stream.

ex	eval () const override
	Perform automatic non-interruptive term rewriting rules.

ex	series (const relational &r, int order, unsigned options=0) const override
	The series expansion of derivatives falls back to Taylor expansion.

ex	thiscontainer (const exvector &v) const override

ex	thiscontainer (exvector &&v) const override

void	archive (archive_node &n) const override
	Archive the object.

void	read_archive (const archive_node &n, lst &syms) override
	Load (deserialize) the object from an archive node.

const paramset &	derivatives () const
	Expose this object's derivative structure.

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.

unsigned	precedence () const override
	Return relative operator precedence (for parenthezing output).

ex	expand (unsigned options=0) const override
	Expand expression, i.e.

ex	eval () const override
	Perform automatic non-interruptive term rewriting rules.

ex	evalf () const override
	Evaluate object numerically.

ex	eval_ncmul (const exvector &v) const override
	This method is defined to be in line with behavior of function::return_type()

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.

ex	series (const relational &r, int order, unsigned options=0) const override
	Implementation of ex::series for functions.

ex	thiscontainer (const exvector &v) const override

ex	thiscontainer (exvector &&v) const override

ex	conjugate () const override
	Implementation of ex::conjugate for functions.

ex	real_part () const override
	Implementation of ex::real_part for functions.

ex	imag_part () const override
	Implementation of ex::imag_part for functions.

void	archive (archive_node &n) const override
	Archive the object.

void	read_archive (const archive_node &n, lst &syms) override
	Construct object from archive_node.

bool	info (unsigned inf) const override
	Implementation of ex::info for functions.

ex	power (const ex &exp) const

unsigned	get_serial () const

std::string	get_name () const
	Return the print name of the function.

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)

size_t	nops () const override
	Number of operands/members.

ex	op (size_t i) const override
	Return operand/member at position i.

ex &	let_op (size_t i) override
	Return modifiable operand/member at position i.

ex	subs (const exmap &m, unsigned options=0) const override
	Substitute a set of objects by arbitrary expressions.

container &	prepend (const ex &b)
	Add element at front.

container &	append (const ex &b)
	Add element at back.

container &	remove_first ()
	Remove first element.

container &	remove_last ()
	Remove last element.

container &	remove_all ()
	Remove all elements.

container &	sort ()
	Sort elements.

container &	unique ()
	Remove adjacent duplicate elements.

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*.

	basic (const basic &other)

const basic &	operator= (const basic &other)
	basic assignment operator: the other object might be of a derived class.

virtual basic *	duplicate () const
	Create a clone of this object on the heap.

virtual ex	evalm () const
	Evaluate sums, products and integer powers of matrices.

virtual ex	eval_integ () const
	Evaluate integrals, if result is known.

virtual ex	eval_indexed (const basic &i) const
	Perform automatic symbolic evaluations on indexed expression that contains this object as the base expression.

virtual void	dbgprint () const
	Little wrapper around print to be called within a debugger.

virtual void	dbgprinttree () const
	Little wrapper around printtree to be called within a debugger.

virtual ex	operator[] (const ex &index) const

virtual ex	operator[] (size_t i) const

virtual ex &	operator[] (const ex &index)

virtual ex &	operator[] (size_t i)

virtual bool	has (const ex &other, unsigned options=0) const
	Test for occurrence of a pattern.

virtual bool	match (const ex &pattern, exmap &repls) const
	Check whether the expression matches a given pattern.

virtual ex	map (map_function &f) const
	Construct new expression by applying the specified function to all sub-expressions (one level only, not recursively).

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.

virtual int	degree (const ex &s) const
	Return degree of highest power in object s.

virtual int	ldegree (const ex &s) const
	Return degree of lowest power in object s.

virtual ex	coeff (const ex &s, int n=1) const
	Return coefficient of degree n in object s.

virtual ex	collect (const ex &s, bool distributed=false) const
	Sort expanded expression in terms of powers of some object(s).

virtual ex	normal (exmap &repl, exmap &rev_lookup, lst &modifier) const
	Default implementation of ex::normal().

virtual ex	to_rational (exmap &repl) const
	Default implementation of ex::to_rational().

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.

virtual numeric	max_coefficient () const
	Implementation ex::max_coefficient().

virtual exvector	get_free_indices () const
	Return a vector containing the free indices of an expression.

virtual ex	add_indexed (const ex &self, const ex &other) const
	Add two indexed expressions.

virtual ex	scalar_mul_indexed (const ex &self, const numeric &other) const
	Multiply an indexed expression with a scalar.

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.

template<class T >
void	print_dispatch (const print_context &c, unsigned level) const
	Like print(), but dispatch to the specified class.

void	print_dispatch (const registered_class_info &ri, const print_context &c, unsigned level) const
	Like print(), but dispatch to the specified class.

ex	subs_one_level (const exmap &m, unsigned options) const
	Helper function for subs().

ex	diff (const symbol &s, unsigned nth=1) const
	Default interface of nth derivative ex::diff(s, n).

int	compare (const basic &other) const
	Compare objects syntactically to establish canonical ordering.

bool	is_equal (const basic &other) const
	Test for syntactic equality.

const basic &	hold () const
	Stop further evaluation.

unsigned	gethash () const

const basic &	setflag (unsigned f) const
	Set some status_flags.

const basic &	clearflag (unsigned f) const
	Clear some status_flags.

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.

bool	is_equal_same_type (const basic &other) const override
	Returns true if two objects of same type are equal.

bool	match_same_type (const basic &other) const override
	Returns true if the attributes of two objects are similar enough for a match.

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.

bool	is_equal_same_type (const basic &other) const override
	Returns true if two objects of same type are equal.

bool	match_same_type (const basic &other) const override
	Returns true if the attributes of two objects are similar enough for a match.

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.

virtual ex	thiscontainer (STLT &&v) const
	Similar to duplicate(), but with a preset sequence (which gets pilfered).

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.

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.

void	ensure_if_modifiable () const
	Ensure the object may be modified without hurting others, throws if this is not the case.

void	do_print (const print_context &c, unsigned level) const
	Default output to stream.

void	do_print_tree (const print_tree &c, unsigned level) const
	Tree output to stream.

void	do_print_python_repr (const print_python_repr &c, unsigned level) const
	Python parsable output to stream.

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 ()

void	reserve (size_t n)

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.

Protected Attributes inherited from GiNaC::function
unsigned	serial

Protected Attributes inherited from GiNaC::basic
unsigned	flags
	of type status_flags

unsigned	hashvalue
	hash value

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.

static std::vector< function_options >	get_registered_functions ()

Static Public Attributes inherited from GiNaC::function
static unsigned	current_serial = 0
	This can be used as a hook for external applications.

Protected Types inherited from GiNaC::container< C >
typedef container_storage< C >::STLT	STLT

Protected Types inherited from GiNaC::container_storage< C >
typedef C< ex >	STLT

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.

static char	get_open_delim ()
	Specialization of container::get_open_delim() for lst.

static char	get_close_delim ()
	Specialization of container::get_close_delim() for lst.

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

ser	Serial number of function
param	Number of parameter with respect to which to take the derivative
args	Arguments of derivative function

Definition at line 48 of file fderivative.cpp.

References parameter_set.

◆ fderivative() [2/3]

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

Construct derivative with respect to multiple parameters.

Parameters

ser	Serial number of function
params	Set of numbers of parameters with respect to which to take the derivative
args	Arguments of derivative function

Definition at line 53 of file fderivative.cpp.

◆ fderivative() [3/3]

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

Definition at line 57 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

c	print context object that describes the output formatting
level	value that is used to identify the precedence or indentation level for placing parentheses and formatting

Reimplemented from GiNaC::basic.

Definition at line 95 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 158 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 173 of file fderivative.cpp.

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

◆ thiscontainer() [1/2]

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

override

Definition at line 178 of file fderivative.cpp.

References parameter_set, and GiNaC::function::serial.

◆ thiscontainer() [2/2]

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

override

Definition at line 183 of file fderivative.cpp.

References 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 80 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 65 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 190 of file fderivative.cpp.

References GiNaC::ex::diff(), 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 215 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 226 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 244 of file fderivative.cpp.

References parameter_set.

◆ do_print()

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

protected

Definition at line 101 of file fderivative.cpp.

References c, GiNaC::container< C >::end(), parameter_set, GiNaC::container< C >::precedence(), GiNaC::function::precedence(), GiNaC::container< C >::printseq(), GiNaC::function::registered_functions(), and GiNaC::function::serial.

◆ do_print_latex()

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

protected

Definition at line 113 of file fderivative.cpp.

References c, GiNaC::container< C >::end(), order, parameter_set, GiNaC::container< C >::precedence(), GiNaC::function::precedence(), GiNaC::container< C >::printseq(), GiNaC::function::registered_functions(), and GiNaC::function::serial.

◆ do_print_csrc()

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

protected

Definition at line 130 of file fderivative.cpp.

References c, GiNaC::container< C >::end(), parameter_set, GiNaC::container< C >::precedence(), GiNaC::function::precedence(), GiNaC::container< C >::printseq(), GiNaC::function::registered_functions(), and GiNaC::function::serial.

◆ do_print_tree()

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

protected

Definition at line 141 of file fderivative.cpp.

References c, GiNaC::container< C >::end(), GiNaC::basic::flags, GiNaC::basic::hashvalue, GiNaC::container< C >::nops(), parameter_set, GiNaC::function::registered_functions(), GiNaC::container_storage< C >::seq, and GiNaC::function::serial.

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(), thiscontainer(), and thiscontainer().

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

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ fderivative() [1/3]

◆ fderivative() [2/3]

◆ fderivative() [3/3]

Member Function Documentation

◆ print()

◆ eval()

◆ series()

◆ thiscontainer() [1/2]

◆ thiscontainer() [2/2]

◆ archive()

◆ read_archive()

◆ derivative()

◆ is_equal_same_type()

◆ match_same_type()

◆ derivatives()

◆ do_print()

◆ do_print_latex()

◆ do_print_csrc()

◆ do_print_tree()

Member Data Documentation

◆ parameter_set