Poisson series class. More...

#include <piranha/poisson_series.hpp>

Inheritance diagram for piranha::poisson_series< Cf >:

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Collaboration diagram for piranha::poisson_series< Cf >:

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Public Types
template<typename Cf2 >
using	rebind = poisson_series< Cf2 >
	Series rebind alias.

using	term_type = term< Cf, rtk_monomial >
	Alias for term type.

using	size_type = typename container_type::size_type
	Size type. More...

using	const_iterator = const_iterator_impl
	Const iterator. More...

Public Member Functions
	poisson_series ()=default
	Defaulted default constructor. More...

	poisson_series (const poisson_series &)=default
	Defaulted copy constructor.

	poisson_series (poisson_series &&)=default
	Defaulted move constructor.

	~poisson_series ()
	Trivial destructor.

poisson_series &	operator= (const poisson_series &other)=default
	Copy assignment operator. More...

poisson_series &	operator= (poisson_series &&other)=default
	Move assignment operator. More...

template<typename T = poisson_series>
sin_type< T >	sin () const
	Sine. More...

template<typename T = poisson_series>
cos_type< T >	cos () const
	Cosine. More...

template<typename T = poisson_series>
integrate_type< T >	integrate (const std::string &name) const
	Integration. More...

template<typename T = poisson_series>
ti_type< T >	t_integrate () const
	Time integration. More...

template<typename T = poisson_series>
ti_type< T >	t_integrate (std::vector< std::string > names) const
	Time integration (alternative overload). More...

degree_type< T >	degree () const
	Total degree. More...

pdegree_type< T >	degree (const symbol_fset &names) const
	Partial degree. More...

ldegree_type< T >	ldegree () const
	Total low degree. More...

pldegree_type< T >	ldegree (const symbol_fset &names) const
	Partial low degree. More...

poisson_series< Cf >	truncate_degree (const T &max_degree) const
	Total degree truncation. More...

poisson_series< Cf >	truncate_degree (const T &max_degree, const symbol_fset &names) const
	Partial degree truncation. More...

ipow_subs_type< T >	ipow_subs (const std::string &name, const integer &n, const T &x) const
	Substitution. More...

ipow_subs_type< T >	ipow_subs (const std::string &name, const Int &n, const T &x) const
	Substitution. More...

subs_type< T >	subs (const symbol_fmap< T > &dict) const
	Substitution. More...

t_subs_type< T, U >	t_subs (const std::string &name, const T &c, const U &s) const
	Trigonometric substitution. More...

t_degree_type< T >	t_degree () const
	Trigonometric degree. More...

pt_degree_type< T >	t_degree (const symbol_fset &names) const
	Partial trigonometric degree. More...

t_ldegree_type< T >	t_ldegree () const
	Trigonometric low degree. More...

pt_ldegree_type< T >	t_ldegree (const symbol_fset &names) const
	Partial trigonometric low degree. More...

t_order_type< T >	t_order () const
	Trigonometric order. More...

pt_order_type< T >	t_order (const symbol_fset &names) const
	Partial trigonometric order. More...

t_lorder_type< T >	t_lorder () const
	Trigonometric low order. More...

pt_lorder_type< T >	t_lorder (const symbol_fset &names) const
	Partial trigonometric low order. More...

size_type	size () const
	Series size. More...

bool	empty () const
	Empty test. More...

bool	is_single_coefficient () const
	Test for single-coefficient series. More...

void	insert (T &&term)
	Insert term. More...

void	insert (T &&term)
	Insert generic term with `Sign = true`. More...

poisson_series< Cf >	operator+ () const
	Identity operator. More...

poisson_series< Cf >	operator- () const
	Negation operator. More...

void	negate ()
	Negate series in-place. More...

pow_ret_type< T, U >	pow (const T &x) const
	Exponentiation. More...

partial_type< Series >	partial (const std::string &name) const
	Partial derivative. More...

const_iterator	begin () const
	Begin iterator. More...

const_iterator	end () const
	End iterator. More...

poisson_series< Cf >	filter (std::function< bool(const std::pair< typename term_type::cf_type, poisson_series< Cf > > &)> func) const
	Term filtering. More...

poisson_series< Cf >	transform (std::function< std::pair< typename term_type::cf_type, poisson_series< Cf > >(const std::pair< typename term_type::cf_type, poisson_series< Cf > > &)> func) const
	Term transformation. More...

poisson_series< Cf >	trim () const
	Trim. More...

void	print_tex (std::ostream &os) const
	Print in TeX mode. More...

std::size_t	hash () const
	Hash value. More...

bool	is_identical (const poisson_series< Cf > &other) const
	Check for identical series. More...

const symbol_fset &	get_symbol_set () const
	Symbol set getter. More...

void	set_symbol_set (const symbol_fset &args)
	Symbol set setter. More...

Table-querying methods
Methods to query the properties of the internal container used to store the terms.
sparsity_info_type	table_sparsity () const
	Table sparsity. More...

double	table_load_factor () const
	Table load factor. More...

size_type	table_bucket_count () const
	Table bucket count. More...

Low-level interface
Low-level methods.
container_type &	_container ()
	Get a mutable reference to the container of terms. More...

const container_type &	_container () const
	Get a const reference to the container of terms. More...

Static Public Member Functions
static void	clear_pow_cache ()
	Clear the internal cache of natural powers. More...

static void	register_custom_derivative (const std::string &name, F func)
	Register custom partial derivative. More...

static void	unregister_custom_derivative (const std::string &name)
	Unregister custom partial derivative. More...

static void	unregister_all_custom_derivatives ()
	Unregister all custom partial derivatives. More...

Protected Types
using	container_type = hash_set< term_type >
	Container type for terms.

Protected Attributes
symbol_fset	m_symbol_set
	Symbol set.

container_type	m_container
	Terms container.

Detailed Description

template<typename Cf>
class piranha::poisson_series< Cf >

Poisson series class.

This class represents multivariate Poisson series as collections of multivariate Poisson series terms, in which the trigonometric monomials are represented by piranha::rtk_monomial. Cf represents the ring over which the Poisson series is defined.

This class satisfies the piranha::is_series type trait.

Type requirements

Cf must be suitable for use in piranha::series as first template argument.

Exception safety guarantee

This class provides the same guarantee as the base series type it derives from.

Move semantics

Move semantics is equivalent to the move semantics of the base series type it derives from.

Definition at line 44 of file poisson_series_fwd.hpp.

Member Typedef Documentation

◆ const_iterator

using piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::const_iterator = const_iterator_impl

inherited

Const iterator.

Iterator type that can be used to iterate over the terms of the series. The object returned upon dereferentiation is an std::pair in which the first element is a copy of the coefficient of the term, the second element a single-term instance of Derived constructed from the term's key and a unitary coefficient.

This iterator is an input iterator which additionally offers the multi-pass guarantee.

See also: piranha::series::begin() and piranha::series::end().

Definition at line 1994 of file series.hpp.

◆ size_type

using piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::size_type = typename container_type::size_type

inherited

Size type.

Used to represent the number of terms in the series. Equivalent to piranha::hash_set::size_type.

Definition at line 1981 of file series.hpp.

Constructor & Destructor Documentation

◆ poisson_series()

template<typename Cf >

piranha::poisson_series< Cf >::poisson_series ( )

default

Defaulted default constructor.

Will construct a Poisson series with zero terms.

Member Function Documentation

◆ _container() [1/2]

container_type& piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::_container ( )

inlineinherited

Get a mutable reference to the container of terms.

Returns: a reference to the internal container of terms.

Definition at line 2788 of file series.hpp.

◆ _container() [2/2]

const container_type& piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::_container ( ) const

inlineinherited

Get a const reference to the container of terms.

Returns: a const reference to the internal container of terms.

Definition at line 2796 of file series.hpp.

◆ begin()

const_iterator piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::begin ( ) const

inlineinherited

Begin iterator.

Return an iterator to the first term of the series. The returned iterator will provide, when dereferenced, an std::pair in which the first element is a copy of the coefficient of the term, whereas the second element is a single-term instance of Derived built from the term's key and a unitary coefficient.

Note that terms are stored unordered in the series, hence it is not defined which particular term will be returned by calling this method. The only guarantee is that the iterator can be used to transverse all the series' terms until piranha::series::end() is eventually reached.

Calling any non-const method on the series will invalidate the iterators obtained via piranha::series::begin() and piranha::series::end().

Returns: an iterator to the first term of the series.

Exceptions

unspecified

any exception thrown by:

construction and assignment of piranha::symbol_fset,
insert(),
construction of term, coefficient and key instances.

Definition at line 2504 of file series.hpp.

◆ clear_pow_cache()

static void piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::clear_pow_cache ( )

inlinestaticinherited

Clear the internal cache of natural powers.

This method can be used to clear the cache of natural powers of series maintained by piranha::series::pow().

Exceptions

unspecified any exception thrown by threading primitives.

Definition at line 2371 of file series.hpp.

◆ cos()

template<typename Cf >

template<typename T = poisson_series>

cos_type<T> piranha::poisson_series< Cf >::cos ( ) const

inline

Cosine.

Note: This method is enabled only if piranha::poisson_series::sin() is enabled.

This method works in the same way as piranha::poisson_series::sin().

Returns: the cosine of this.

Exceptions

unspecified any exception thrown by piranha::poisson_series::sin().

Definition at line 606 of file poisson_series.hpp.

◆ degree() [1/2]

degree_type<T> piranha::power_series< ipow_substitutable_series< substitutable_series< t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >, poisson_series< Cf > >, poisson_series< Cf > >, poisson_series< Cf > > , poisson_series< Cf > >::degree ( ) const

inlineinherited

Total degree.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

The degree of the series is the maximum degree of its terms. If the series is empty, zero will be returned.

Returns: the total degree of the series.

Exceptions

std::overflow_error	if the computation results in an overflow.
unspecified	any exception thrown by: the construction of return type, the calculation of the degree of each term, the assignment and less-than operators for the return type.

Definition at line 390 of file power_series.hpp.

◆ degree() [2/2]

pdegree_type<T> piranha::power_series< ipow_substitutable_series< substitutable_series< t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >, poisson_series< Cf > >, poisson_series< Cf > >, poisson_series< Cf > > , poisson_series< Cf > >::degree ( const symbol_fset & names ) const

inlineinherited

Partial degree.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

The partial degree of the series is the maximum partial degree of its terms. If the series is empty, zero will be returned.

Parameters

names names of the variables to be considered in the computation of the degree.

Returns: the partial degree of the series.

Exceptions

std::overflow_error	if the computation results in an overflow.
unspecified	any exception thrown by: the construction of return type, the calculation of the degree of each term, the assignment and less-than operators for the return type.

Definition at line 444 of file power_series.hpp.

◆ empty()

bool piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::empty ( ) const

inlineinherited

Empty test.

Returns: true if size() is nonzero, false otherwise.

Definition at line 2103 of file series.hpp.

◆ end()

const_iterator piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::end ( ) const

inlineinherited

End iterator.

Return an iterator one past the last term of the series. See the documentation of piranha::series::begin() on how the returned iterator can be used.

Returns: an iterator to the end of the series.

Exceptions

unspecified

any exception thrown by:

construction and assignment of piranha::symbol_fset,
insert(),
construction of term, coefficient and key instances.

Definition at line 2523 of file series.hpp.

◆ filter()

poisson_series< Cf > piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::filter ( std::function< bool(const std::pair< typename term_type::cf_type, poisson_series< Cf > > &)> func ) const

inlineinherited

Term filtering.

This method will apply the functor func to each term in the series, and produce a return series containing all terms in this for which func returns true. Terms are passed to func in the format resulting from dereferencing the iterators obtained via piranha::series::begin().

Parameters

func	filtering functor.

Returns: filtered series.

Exceptions

unspecified

any exception thrown by:

the call operator of func,
insert(),
the assignment operator of piranha::symbol_fset,
term, coefficient, key construction.

Definition at line 2547 of file series.hpp.

◆ get_symbol_set()

const symbol_fset& piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::get_symbol_set ( ) const

inlineinherited

Symbol set getter.

Returns: const reference to the piranha::symbol_fset associated to the series.

Definition at line 2762 of file series.hpp.

◆ hash()

std::size_t piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::hash ( ) const

inlineinherited

Hash value.

The hash value for a series is zero if the series is empty, otherwise it is computed by adding the hash values of all terms. This ensures that two identical series in which the terms are stored in different order still produce the same hash value.

Note, however, that the arguments of the series are not considered in the hash value and that, in general, two series that compare equal according to operator==() will not have the same hash value (as the equality operator merges the arguments of two series before actually performing the comparison). Instead of operator==(), is_identical() should be used for storing series as keys in associative containers.

Returns: a hash value for the series.

Exceptions

unspecified any exception thrown by computing the hash of a term.

Definition at line 2730 of file series.hpp.

◆ insert() [1/2]

void piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::insert ( T && term )

inlineinherited

Insert term.

Note: This method is enabled only if the decay type of T is piranha::series::term_type.

This method will insert term into the series using internally piranha::hash_set::insert.

The insertion algorithm proceeds as follows:

if the term is not compatible for insertion, an std::invalid_argument exception is thrown;
if the term is ignorable, the method will return without performing any insertion;
if the term is already in the series, then:
- its coefficient is added (if Sign is true) or subtracted (if Sign is false) to the existing term's coefficient;
- if, after the addition/subtraction the existing term is ignorable, it will be erased;
else:
- the term is inserted into the term container and, if Sign is false, its coefficient is negated.

After any modification to an existing term in the series (e.g., via insertion with negative Sign or via in-place addition or subtraction of existing coefficients), the term will be checked again for compatibility and ignorability, and, in case the term has become incompatible or ignorable, it will be erased from the series.

The exception safety guarantee upon insertion is that the series will be left in an undefined but valid state. Such a guarantee relies on the fact that the addition/subtraction and negation methods of the coefficient type will leave the coefficient in a valid (possibly undefined) state in face of exceptions.

Parameters

term	term to be inserted.

Exceptions

unspecified	any exception thrown by: piranha::hash_set::insert(), piranha::hash_set::find(), piranha::hash_set::erase(), piranha::math::negate(), in-place addition/subtraction on coefficient types.
std::invalid_argument	if `term` is incompatible.

Definition at line 2161 of file series.hpp.

◆ insert() [2/2]

void piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::insert ( T && term )

inlineinherited

Insert generic term with Sign = true.

Note: This method is enabled only if the decay type of T is piranha::series::term_type.

Convenience wrapper for the generic insert() method, with Sign set to true.

Parameters

term	term to be inserted.

Exceptions

unspecified any exception thrown by generic insert().

Definition at line 2177 of file series.hpp.

◆ integrate()

template<typename Cf >

template<typename T = poisson_series>

integrate_type<T> piranha::poisson_series< Cf >::integrate ( const std::string & name ) const

inline

Integration.

Note: This method is enabled only if the algorithm described below is supported by all the involved types.

This method will attempt to compute the antiderivative of the Poisson series term by term using the following procedure:

if the term's monomial does not depend on the integration variable, the integration will be deferred to the coefficient;
otherwise:
- if the coefficient does not depend on the integration variable, the monomial is integrated;
- if the coefficient is a polynomial, a strategy of integration by parts is attempted, its success depending on whether the degree of the polynomial is a non-negative integral value;
- otherwise, an error will be produced.

Parameters

name	integration variable.

Returns: the antiderivative of this with respect to name.

Exceptions

std::invalid_argument if the integration procedure fails.

unspecified

any exception thrown by:

piranha::math::partial(), piranha::math::is_zero(), piranha::math::integrate(), piranha::safe_cast() and piranha::math::negate(),
the assignment operator of piranha::symbol_fset,
term construction,
coefficient construction, assignment and arithmetics,
integration, construction and assignment of the key type,
insert(),
piranha::polynomial::degree(),
series arithmetics.

Definition at line 642 of file poisson_series.hpp.

◆ ipow_subs() [1/2]

ipow_subs_type<T> piranha::ipow_substitutable_series< substitutable_series< t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >, poisson_series< Cf > >, poisson_series< Cf > > , poisson_series< Cf > >::ipow_subs	(	const std::string &	name,
		const integer &	n,
		const T &	x
	)		const

inlineinherited

Substitution.

Note: This method is enabled only if the coefficient and/or key types support integral power substitution, and if the types involved in the substitution support the necessary arithmetic operations to compute the result.

This method will return an object resulting from the substitution of the integral power of the symbol called name in this with the generic object x.

Parameters

name	name of the symbol to be substituted.
n	integral power of the symbol to be substituted.
x	object used for the substitution.

Returns: the result of the substitution.

Exceptions

unspecified

any exception resulting from:

the substitution routines for the coefficients and/or keys,
the computation of the return value,
piranha::series::insert().

Definition at line 224 of file ipow_substitutable_series.hpp.

◆ ipow_subs() [2/2]

ipow_subs_type<T> piranha::ipow_substitutable_series< substitutable_series< t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >, poisson_series< Cf > >, poisson_series< Cf > > , poisson_series< Cf > >::ipow_subs	(	const std::string &	name,
		const Int &	n,
		const T &	x
	)		const

inlineinherited

Substitution.

Note: This method is enabled only if the other ipow_subs() overload is enabled, and Int is a C++ integral type.

This is a convenience method that will call the other ipow_subs() overload after converting n to piranha::integer.

Parameters

name	name of the symbol to be substituted.
n	integral power of the symbol to be substituted.
x	object used for the substitution.

Returns: the result of the substitution.

Exceptions

unspecified any exception resulting from calling the other ipow_subs() overload, or by constructing a piranha::integer from a C++ integral type.

Definition at line 252 of file ipow_substitutable_series.hpp.

◆ is_identical()

bool piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::is_identical ( const poisson_series< Cf > & other ) const

inlineinherited

Check for identical series.

Note: This method is enabled only if Derived is equality-comparable.

This method will return true if the symbol sets of this and other are the same, and other == *this.

Parameters

other argument for the comparison.

Returns: true if this and other are identical, false otherwise.

Exceptions

unspecified any exception thrown by the comparison operator of Derived.

Definition at line 2754 of file series.hpp.

◆ is_single_coefficient()

bool piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::is_single_coefficient ( ) const

inlineinherited

Test for single-coefficient series.

A series is considered to be single-coefficient when it is symbolically equivalent to a coefficient. That is, the series is either empty (in which case it is considered to be equivalent to a coefficient constructed from zero) or consisting of a single term with unitary key (in which case the series is considered equivalent to its only coefficient).

Returns: true in case of single-coefficient series, false otherwise.

Exceptions

unspecified any exception thrown by the is_unitary() method of the key type.

Definition at line 2118 of file series.hpp.

◆ ldegree() [1/2]

ldegree_type<T> piranha::power_series< ipow_substitutable_series< substitutable_series< t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >, poisson_series< Cf > >, poisson_series< Cf > >, poisson_series< Cf > > , poisson_series< Cf > >::ldegree ( ) const

inlineinherited

Total low degree.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

The low degree of the series is the minimum low degree of its terms. If the series is empty, zero will be returned.

Returns: the total low degree of the series.

Exceptions

std::overflow_error	if the computation results in an overflow.
unspecified	any exception thrown by: the construction of return type, the calculation of the low degree of each term, the assignment and less-than operators for the return type.

Definition at line 416 of file power_series.hpp.

◆ ldegree() [2/2]

pldegree_type<T> piranha::power_series< ipow_substitutable_series< substitutable_series< t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >, poisson_series< Cf > >, poisson_series< Cf > >, poisson_series< Cf > > , poisson_series< Cf > >::ldegree ( const symbol_fset & names ) const

inlineinherited

Partial low degree.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

The partial low degree of the series is the minimum partial low degree of its terms. If the series is empty, zero will be returned.

Parameters

names names of the variables to be considered in the computation of the low degree.

Returns: the partial low degree of the series.

Exceptions

std::overflow_error	if the computation results in an overflow.
unspecified	any exception thrown by: the construction of return type, the calculation of the low degree of each term, the assignment and less-than operators for the return type.

Definition at line 475 of file power_series.hpp.

◆ negate()

void piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::negate ( )

inlineinherited

Negate series in-place.

This method will call math::negate() on the coefficients of all terms. In case of exceptions, the basic exception safety guarantee is provided.

If any term becomes ignorable or incompatible after negation, it will be erased from the series.

Exceptions

unspecified any exception thrown by math::negate() on the coefficient type.

Definition at line 2214 of file series.hpp.

◆ operator+()

poisson_series< Cf > piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::operator+ ( ) const

inlineinherited

Identity operator.

Returns: copy of this, cast to Derived.

Exceptions

unspecified any exception thrown by the copy constructor.

Definition at line 2187 of file series.hpp.

◆ operator-()

poisson_series< Cf > piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::operator- ( ) const

inlineinherited

Negation operator.

Returns: a copy of this on which negate() has been called.

Exceptions

unspecified

any exception thrown by:

negate(),
the copy constructor of Derived.

Definition at line 2199 of file series.hpp.

◆ operator=() [1/2]

template<typename Cf >

poisson_series& piranha::poisson_series< Cf >::operator= ( const poisson_series< Cf > & other )

default

Copy assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

Exceptions

unspecified any exception thrown by the assignment operator of the base class.

◆ operator=() [2/2]

template<typename Cf >

poisson_series& piranha::poisson_series< Cf >::operator= ( poisson_series< Cf > && other )

default

Move assignment operator.

Parameters

other the assignment argument.

Returns: a reference to this.

◆ partial()

partial_type<Series> piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::partial ( const std::string & name ) const

inlineinherited

Partial derivative.

Note: This method is enabled only if the coefficient and key are differentiable (i.e., they satisfy the piranha::is_differentiable and piranha::key_is_differentiable type traits), and if the arithmetic operations needed to compute the partial derivative are supported by all the involved types.

This method will return the partial derivative of this with respect to the variable called name. The method will construct the return value from the output of the differentiation methods of coefficient and key, and via arithmetic and/or term insertion operations.

Note that, contrary to the specialisation of piranha::math::partial() for series types, this method will not take into account custom derivatives registered via piranha::series::register_custom_derivative().

Parameters

name	name of the argument with respect to which the derivative will be calculated.

Returns: partial derivative of this with respect to the symbol name.

Exceptions

unspecified

any exception thrown by:

the differentiation methods of coefficient and key,
term construction and insertion,
arithmetic operations on the involved types,
construction of the return type.

Definition at line 2405 of file series.hpp.

◆ pow()

pow_ret_type<T, U> piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::pow ( const T & x ) const

inlineinherited

Exponentiation.

Note: This method is enabled only if the algorithm outlined here is supported by the involved types.

Return this raised to the x-th power. The type of the result is either the calling series type, or the calling series type rebound to the type resulting from the exponentiation of the coefficient of the calling type to the power of x. The exponentiation algorithm proceeds as follows:

if the series is single-coefficient, the result is a single-coefficient series in which the coefficient is the original coefficient (or zero, if the calling series is empty) raised to the power of x;
if x is zero (as established by piranha::math::is_zero()), a series with a single term with unitary key and coefficient constructed from the integer numeral "1" is returned (i.e., any series raised to the power of zero is 1 - including empty series);
if x represents a non-negative integral value, the return value is constructed via repeated multiplications;
otherwise, an exception will be raised.

An internal thread-safe cache of natural powers of series is maintained in order to improve performance during, e.g., substitution operations. This cache can be cleared with clear_pow_cache().

Parameters

x exponent.

Returns: this raised to the power of x.

Exceptions

std::invalid_argument	if exponentiation is computed via repeated series multiplications and `x` does not represent a non-negative integer.
unspecified	any exception thrown by: series, term, coefficient and key construction, insert(), is_single_coefficient(), piranha::math::pow(), piranha::math::is_zero() and piranha::safe_cast(), series multiplication, memory errors in standard containers, threading primitives, hash() or is_identical().

Definition at line 2304 of file series.hpp.

◆ print_tex()

void piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::print_tex ( std::ostream & os ) const

inlineinherited

Print in TeX mode.

Print series to stream os in TeX mode. The representation is constructed in the same way as explained in piranha::series::operator<<(), but using piranha::print_tex_coefficient() and the key's TeX printing method instead of the plain printing functions.

Parameters

os	target stream.

Exceptions

unspecified

any exception thrown by:

piranha::print_tex_coefficient(),
the TeX printing method of the key type,
memory allocation errors in standard containers,
piranha::settings::get_max_term_output(),
streaming to os or to instances of std::ostringstream.

See also: operator<<().

Definition at line 2654 of file series.hpp.

◆ register_custom_derivative()

static void piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::register_custom_derivative	(	const std::string &	name,
		F	func
	)

inlinestaticinherited

Register custom partial derivative.

Note: This method is enabled only if piranha::series::partial() is enabled for Derived, and if F is a type that can be used to construct std::function<partial_type(const Derived &), where partial_type is the type resulting from the partial derivative of Derived.

Register a copy of a callable func associated to the symbol name for use by piranha::math::partial(). func will be used to compute the partial derivative of instances of type Derived with respect to name in place of the default partial differentiation algorithm.

It is safe to call this method from multiple threads.

Parameters

name	symbol for which the custom partial derivative function will be registered.
func	custom partial derivative function.

Exceptions

unspecified

any exception thrown by:

failure(s) in threading primitives,
lookup and insertion operations on std::unordered_map,
construction and move-assignment of std::function.

Definition at line 2432 of file series.hpp.

◆ set_symbol_set()

void piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::set_symbol_set ( const symbol_fset & args )

inlineinherited

Symbol set setter.

Parameters

args	piranha::symbol_fset that will be associated to the series.

Exceptions

std::invalid_argument	if the series is not empty.
unspecified	any exception thrown by the copy assignment operator of piranha::symbol_fset.

Definition at line 2773 of file series.hpp.

◆ sin()

template<typename Cf >

template<typename T = poisson_series>

sin_type<T> piranha::poisson_series< Cf >::sin ( ) const

inline

Sine.

Note: This template method is enabled only if math::sin() can be called on the class from which piranha::poisson_series derives (i.e., only if the default math::sin() implementation for series is appropriate).

In general, this method behaves exactly like the default implementation of piranha::math::sin() for series types. If, however, a polynomial appears in the hierarchy of coefficients, then this method will attempt to extract an integral linear combination of symbolic arguments and use it to construct a Poisson series with a single term, unitary coefficient and the trigonometric key built from the linear combination.

For instance, if the calling Poisson series is

\[ -2x + y, \]

then calling this method will produce the Poisson series

\[ -\sin \left( 2x - y \right). \]

If for any reason it is not possible to extract the linear integral combination, then this method will forward the call to the default implementation of piranha::math::sin() for series types.

Returns: the sine of this.

Exceptions

unspecified

any exception thrown by:

piranha::series::is_single_coefficient(), piranha::series::insert(),
memory allocation errors in standard containers,
the constructors of coefficient, key and term types,
the cast operator of piranha::integer,
piranha::math::negate(),
piranha::math::sin(),
the extraction of a linear combination of integral arguments from the polynomial coefficient.

Definition at line 590 of file poisson_series.hpp.

◆ size()

size_type piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::size ( ) const

inlineinherited

Series size.

Returns: the number of terms in the series.

Definition at line 2095 of file series.hpp.

◆ subs()

subs_type<T> piranha::substitutable_series< t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >, poisson_series< Cf > > , poisson_series< Cf > >::subs ( const symbol_fmap< T > & dict ) const

inlineinherited

Substitution.

Note: This method is enabled only if the coefficient and/or key types support substitution, and if the types involved in the substitution support the necessary arithmetic operations to compute the result. Also, the return type must satisfy piranha::is_returnable, and T must be suitable for use in sm_intersect_idx().

This method will return an object resulting from the substitution in this of the symbols in dict with the mapped values.

Parameters

dict	a dictionary mapping a set of symbols to the values that will be substituted for them.

Returns: the result of the substitution.

Exceptions

unspecified

any exception resulting from:

the substitution routines for the coefficients and/or keys,
the computation of the return value,
piranha::series::insert().

Definition at line 218 of file substitutable_series.hpp.

◆ t_degree() [1/2]

t_degree_type<T> piranha::trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >::t_degree ( ) const

inlineinherited

Trigonometric degree.

Note: This method is enabled only if the requirements outlined in piranha::trigonometric_series are satisfied.

Returns: the total trigonometric degree of the series.

Exceptions

unspecified any exception resulting from the computation and comparison of the degree of the individual terms.

Definition at line 204 of file trigonometric_series.hpp.

◆ t_degree() [2/2]

pt_degree_type<T> piranha::trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >::t_degree ( const symbol_fset & names ) const

inlineinherited

Partial trigonometric degree.

Note: This method is enabled only if the requirements outlined in piranha::trigonometric_series are satisfied.

Parameters

names the names of the variables to be considered in the computation.

Returns: the partial trigonometric degree of the series.

Exceptions

unspecified any exception resulting from the computation and comparison of the degree of the individual terms.

Definition at line 226 of file trigonometric_series.hpp.

◆ t_integrate() [1/2]

template<typename Cf >

template<typename T = poisson_series>

ti_type<T> piranha::poisson_series< Cf >::t_integrate ( ) const

inline

Time integration.

Note

This method is enabled only if:

the coefficient type is an instance of piranha::divisor_series, and
the operations required by the computation of the time integration are supported by all the involved types.

This is a special type of integration in which the trigonometric arguments are considered as linear functions of time, and in which the integration variable is time itself. For instance, if the input series is

\[ \frac{1}{5}z\cos\left( x - y \right), \]

the result of the time integration is

\[ \frac{1}{5}{z}\frac{1}{\left(\nu_{x}-\nu_{y}\right)}\sin{\left({x}-{y}\right)}, \]

where \( \nu_{x} \) and \( \nu_{y} \) are the frequencies associated to \( x \) and \( y \) (that is, it is understood that \( x = \nu_{x}t \) and \( x = \nu_{y}t \)).

This method will throw an error if any term of the calling series has a unitary key (e.g., in the Poisson series \( \frac{1}{5}z \) the only trigonometric key is \( \cos\left( 0 \right) \) and would thus result in a division by zero during a time integration).

Returns: the result of the time integration.

Exceptions

std::invalid_argument	if the calling series has a unitary key.
unspecified	any exception thrown by: memory errors in standard containers, the public interfaces of piranha::symbol_fset, piranha::mp_integer and piranha::series, piranha::math::is_zero(), piranha::math::negate(), the mathematical operations needed to compute the result, piranha::divisor::insert(), construction of the involved types.

Definition at line 710 of file poisson_series.hpp.

◆ t_integrate() [2/2]

template<typename Cf >

template<typename T = poisson_series>

ti_type<T> piranha::poisson_series< Cf >::t_integrate ( std::vector< std::string > names ) const

inline

Time integration (alternative overload).

Note: This method is enabled only if the other overload of piranha::poisson_series::t_integrate() is enabled.

This method operates exactly like the other overload of piranha::poisson_series::t_integrate(), with the difference that the names of the symbols used to represent the frequencies are passed as the names argument, rather than automatically deduced. The names argument must be sorted lexicographically, otherwise an error will be produced. Duplicate entries in names will be removed.

Parameters

names the names of the symbols used to represent the frequencies.

Returns: the result of the time integration.

Exceptions

std::invalid_argument	if the size of `names` is not equal to the size of the symbol set of `this` (after the removal of duplicate entries), or if `names` is not sorted lexicographically.
unspecified	any exception thrown by the other overload.

Definition at line 737 of file poisson_series.hpp.

◆ t_ldegree() [1/2]

t_ldegree_type<T> piranha::trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >::t_ldegree ( ) const

inlineinherited

Trigonometric low degree.

Note: This method is enabled only if the requirements outlined in piranha::trigonometric_series are satisfied.

Returns: the total trigonometric low degree of the series.

Exceptions

unspecified any exception resulting from the computation and comparison of the degree of the individual terms.

Definition at line 248 of file trigonometric_series.hpp.

◆ t_ldegree() [2/2]

pt_ldegree_type<T> piranha::trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >::t_ldegree ( const symbol_fset & names ) const

inlineinherited

Partial trigonometric low degree.

Note: This method is enabled only if the requirements outlined in piranha::trigonometric_series are satisfied.

Parameters

names the names of the variables to be considered in the computation.

Returns: the partial trigonometric low degree of the series.

Exceptions

unspecified any exception resulting from the computation and comparison of the degree of the individual terms.

Definition at line 270 of file trigonometric_series.hpp.

◆ t_lorder() [1/2]

t_lorder_type<T> piranha::trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >::t_lorder ( ) const

inlineinherited

Trigonometric low order.

Note: This method is enabled only if the requirements outlined in piranha::trigonometric_series are satisfied.

Returns: the total trigonometric low order of the series.

Exceptions

unspecified any exception resulting from the computation and comparison of the order of the individual terms.

Definition at line 335 of file trigonometric_series.hpp.

◆ t_lorder() [2/2]

pt_lorder_type<T> piranha::trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >::t_lorder ( const symbol_fset & names ) const

inlineinherited

Partial trigonometric low order.

Note: This method is enabled only if the requirements outlined in piranha::trigonometric_series are satisfied.

Parameters

names the names of the variables to be considered in the computation.

Returns: the partial trigonometric low order of the series.

Exceptions

unspecified any exception resulting from the computation and comparison of the order of the individual terms.

Definition at line 357 of file trigonometric_series.hpp.

◆ t_order() [1/2]

t_order_type<T> piranha::trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >::t_order ( ) const

inlineinherited

Trigonometric order.

Note: This method is enabled only if the requirements outlined in piranha::trigonometric_series are satisfied.

Returns: the total trigonometric order of the series.

Exceptions

unspecified any exception resulting from the computation and comparison of the order of the individual terms.

Definition at line 292 of file trigonometric_series.hpp.

◆ t_order() [2/2]

pt_order_type<T> piranha::trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >::t_order ( const symbol_fset & names ) const

inlineinherited

Partial trigonometric order.

Note: This method is enabled only if the requirements outlined in piranha::trigonometric_series are satisfied.

Parameters

names the names of the variables to be considered in the computation.

Returns: the partial trigonometric order of the series.

Exceptions

unspecified any exception resulting from the computation and comparison of the order of the individual terms.

Definition at line 314 of file trigonometric_series.hpp.

◆ t_subs()

t_subs_type<T, U> piranha::t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > > , poisson_series< Cf > >::t_subs	(	const std::string &	name,
		const T &	c,
		const U &	s
	)		const

inlineinherited

Trigonometric substitution.

Note: This method is available only if the requirements outlined in piranha::t_substitutable_series are satisfied.

Trigonometric substitution is the substitution of the cosine and sine of name for c and s.

Parameters

name	name of the symbol that will be subject to substitution.
c	cosine of `name`.
s	sine of `name`.

Returns: the result of the trigonometric substitution.

Exceptions

unspecified

any exception resulting from:

construction of the return type,
the assignment operator of piranha::symbol_fset,
term construction,
arithmetics on the intermediary values needed to compute the return value,
piranha::series::insert(),
the substitution methods of coefficient and key.

Definition at line 219 of file t_substitutable_series.hpp.

◆ table_bucket_count()

size_type piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::table_bucket_count ( ) const

inlineinherited

Table bucket count.

Returns: the bucket count of the internal container.

Definition at line 2263 of file series.hpp.

◆ table_load_factor()

double piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::table_load_factor ( ) const

inlineinherited

Table load factor.

Will call piranha::hash_set::load_factor() on the internal terms container and return the result.

Returns: the load factor of the internal container.

Definition at line 2255 of file series.hpp.

◆ table_sparsity()

sparsity_info_type piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::table_sparsity ( ) const

inlineinherited

Table sparsity.

Will call piranha::hash_set::evaluate_sparsity() on the internal terms container and return the result.

Returns: the output of piranha::hash_set::evaluate_sparsity().

Exceptions

unspecified any exception thrown by piranha::hash_set::evaluate_sparsity().

Definition at line 2244 of file series.hpp.

◆ transform()

poisson_series< Cf > piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::transform ( std::function< std::pair< typename term_type::cf_type, poisson_series< Cf > >(const std::pair< typename term_type::cf_type, poisson_series< Cf > > &)> func ) const

inlineinherited

Term transformation.

This method will apply the functor func to each term in the series, and will use the return value of the functor to construct a new series. Terms are passed to func in the same format resulting from dereferencing the iterators obtained via piranha::series::begin(), and func is expected to produce a return value of the same type.

The return series is first initialised as an empty series. For each input term t, the return value of func is used to construct a new temporary series from the multiplication of t.first and t.second. Each temporary series is then added to the return value series.

This method requires the coefficient type to be multipliable by Derived.

Parameters

func	transforming functor.

Returns: transformed series.

Exceptions

unspecified

any exception thrown by:

the call operator of func,
insert(),
the assignment operator of piranha::symbol_fset,
term, coefficient, key construction,
series multiplication and addition.

Definition at line 2585 of file series.hpp.

◆ trim()

poisson_series< Cf > piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::trim ( ) const

inlineinherited

Trim.

This method will return a series mathematically equivalent to this in which discardable arguments have been removed from the internal set of symbols. Which symbols are removed depends on the trimming method trim_identify() of the key type (e.g., in a polynomial a symbol can be discarded if its exponent is zero in all monomials).

If the coefficient type is an instance of piranha::series, trim() will be called recursively on the coefficients while building the return value.

Returns: trimmed version of this.

Exceptions

unspecified

any exception thrown by:

piranha::safe_cast(),
operations on piranha::symbol_fset,
the trimming methods of coefficient and/or key,
insert(),
term, coefficient and key type construction.

Definition at line 2619 of file series.hpp.

◆ truncate_degree() [1/2]

poisson_series< Cf > piranha::power_series< ipow_substitutable_series< substitutable_series< t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >, poisson_series< Cf > >, poisson_series< Cf > >, poisson_series< Cf > > , poisson_series< Cf > >::truncate_degree ( const T & max_degree ) const

inlineinherited

Total degree truncation.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

This method can be used to eliminate the parts of a series whose degree is greater than max_degree. This includes the elimination of whole terms, but also the recursive truncation of coefficients via the piranha::math::truncate_degree() function, if supported by the coefficient. It must be noted that, in general, this method is not guaranteed to eliminate all the parts whose degree is greater than max_degree (in particular, in the current implementation there is no truncation implemented for keys - a key is kept as-is or completely eliminated).

Parameters

max_degree maximum allowed total degree.

Returns: the truncated counterpart of this.

Exceptions

unspecified

any exception thrown by:

piranha::math::truncate_degree(), if used,
the constructor of the term type,
the computation and comparison of degree types,
piranha::series::insert().

Definition at line 510 of file power_series.hpp.

◆ truncate_degree() [2/2]

poisson_series< Cf > piranha::power_series< ipow_substitutable_series< substitutable_series< t_substitutable_series< trigonometric_series< series< Cf, rtk_monomial, poisson_series< Cf > > >, poisson_series< Cf > >, poisson_series< Cf > >, poisson_series< Cf > > , poisson_series< Cf > >::truncate_degree	(	const T &	max_degree,
		const symbol_fset &	names
	)		const

inlineinherited

Partial degree truncation.

Note: This method is available only if the requisites outlined in piranha::power_series are satisfied.

This method is equivalent to the other overload, the only difference being that the partial degree is considered in the computation.

Parameters

max_degree	maximum allowed partial degree.
names	names of the variables to be considered in the computation of the partial degree.

Returns: the truncated counterpart of this.

Exceptions

unspecified

any exception thrown by:

piranha::math::truncate_degree(), if used,
the constructor of the term type,
the computation and comparison of degree types,
piranha::series::insert().

Definition at line 543 of file power_series.hpp.

◆ unregister_all_custom_derivatives()

static void piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::unregister_all_custom_derivatives ( )

inlinestaticinherited

Unregister all custom partial derivatives.

Note: This method is enabled only if piranha::series::partial() is enabled for Derived.

Will unregister all custom derivatives currently registered via register_custom_derivative(). It is safe to call this method from multiple threads.

Exceptions

unspecified any exception thrown by failure(s) in threading primitives.

Definition at line 2478 of file series.hpp.

◆ unregister_custom_derivative()

static void piranha::series< Cf, rtk_monomial , poisson_series< Cf > >::unregister_custom_derivative ( const std::string & name )

inlinestaticinherited

Unregister custom partial derivative.

Note: This method is enabled only if piranha::series::partial() is enabled for Derived.

Unregister the custom partial derivative function associated to the symbol name. If no custom partial derivative was previously registered using register_custom_derivative(), calling this function will be a no-op.

It is safe to call this method from multiple threads.

Parameters

name	symbol for which the custom partial derivative function will be unregistered.

Exceptions

unspecified

any exception thrown by:

failure(s) in threading primitives,
lookup and erase operations on std::unordered_map.

Definition at line 2459 of file series.hpp.

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Types

Protected Attributes

Detailed Description

template<typename Cf> class piranha::poisson_series< Cf >

Type requirements

Exception safety guarantee

Move semantics

Member Typedef Documentation

◆ const_iterator

◆ size_type

Constructor & Destructor Documentation

◆ poisson_series()

Member Function Documentation

◆ _container() [1/2]

◆ _container() [2/2]

◆ begin()

◆ clear_pow_cache()

◆ cos()

◆ degree() [1/2]

◆ degree() [2/2]

◆ empty()

◆ end()

◆ filter()

◆ get_symbol_set()

◆ hash()

◆ insert() [1/2]

◆ insert() [2/2]

◆ integrate()

◆ ipow_subs() [1/2]

◆ ipow_subs() [2/2]

◆ is_identical()

◆ is_single_coefficient()

◆ ldegree() [1/2]

◆ ldegree() [2/2]

◆ negate()

◆ operator+()

◆ operator-()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ partial()

◆ pow()

◆ print_tex()

◆ register_custom_derivative()

◆ set_symbol_set()

◆ sin()

◆ size()

◆ subs()

◆ t_degree() [1/2]

◆ t_degree() [2/2]

◆ t_integrate() [1/2]

◆ t_integrate() [2/2]

◆ t_ldegree() [1/2]

◆ t_ldegree() [2/2]

◆ t_lorder() [1/2]

◆ t_lorder() [2/2]

◆ t_order() [1/2]

◆ t_order() [2/2]

◆ t_subs()

◆ table_bucket_count()

◆ table_load_factor()

◆ table_sparsity()

◆ transform()

◆ trim()

◆ truncate_degree() [1/2]

◆ truncate_degree() [2/2]

◆ unregister_all_custom_derivatives()

◆ unregister_custom_derivative()

template<typename Cf>
class piranha::poisson_series< Cf >