piranha
0.10

Series class. More...
#include <piranha/series.hpp>
Public Types  
using  term_type = term< Cf, Key > 
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  
series ()=default  
Defaulted default constructor.  
series (const series &)=default  
Defaulted copy constructor. More...  
series (series &&)=default  
Defaulted move constructor.  
template<typename T , typename U = series, generic_ctor_enabler< T, U > = 0>  
series (const T &x)  
Generic constructor. More...  
~series ()  
Trivial destructor.  
series &  operator= (const series &other) 
Copyassignment operator. More...  
series &  operator= (series &&other)=default 
Move assignment operator. More...  
template<typename T , typename U = series, generic_ctor_enabler< T, U > = 0>  
series &  operator= (const T &x) 
Generic assignment operator. More...  
size_type  size () const 
Series size. More...  
bool  empty () const 
Empty test. More...  
bool  is_single_coefficient () const 
Test for singlecoefficient series. More...  
template<bool Sign, typename T , insert_enabler< T > = 0>  
void  insert (T &&term) 
Insert term. More...  
template<typename T , insert_enabler< T > = 0>  
void  insert (T &&term) 
Insert generic term with Sign = true . More...  
Derived  operator+ () const 
Identity operator. More...  
Derived  operator () const 
Negation operator. More...  
void  negate () 
Negate series inplace. More...  
template<typename T , typename U = Derived>  
pow_ret_type< T, U >  pow (const T &x) const 
Exponentiation. More...  
template<typename Series = Derived>  
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...  
Derived  filter (std::function< bool(const std::pair< typename term_type::cf_type, Derived > &)> func) const 
Term filtering. More...  
Derived  transform (std::function< std::pair< typename term_type::cf_type, Derived >(const std::pair< typename term_type::cf_type, Derived > &)> func) const 
Term transformation. More...  
Derived  trim () const 
Trim. More...  
void  print_tex (std::ostream &os) const 
Print in TeX mode. More...  
std::size_t  hash () const 
Hash value. More...  
template<typename T = Derived, is_identical_enabler< T > = 0>  
bool  is_identical (const Derived &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...  
Tablequerying 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...  
Lowlevel interface  
Lowlevel 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  
template<typename T = Derived, is_identical_enabler< T > = 0>  
static void  clear_pow_cache () 
Clear the internal cache of natural powers. More...  
template<typename F , typename Series = Derived, custom_partial_enabler< F, Series > = 0>  
static void  register_custom_derivative (const std::string &name, F func) 
Register custom partial derivative. More...  
template<typename Series = Derived, typename Partial = partial_type<Series>>  
static void  unregister_custom_derivative (const std::string &name) 
Unregister custom partial derivative. More...  
template<typename Series = Derived, typename Partial = partial_type<Series>>  
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.  
Friends  
std::ostream &  operator<< (std::ostream &os, const series &s) 
Overloaded stream operator for piranha::series. More...  
Series class.
This class contains the arithmetic and comparison operator overloads for piranha::series instances via the parent class piranha::series_operators.
Cf
and Key
must be suitable for use in piranha::term.Derived
must derive from piranha::series of Cf
, Key
and Derived
.Derived
must satisfy piranha::is_series.Derived
must satisfy piranha::is_container_element.Unless otherwise specified, this class provides the strong exception safety guarantee for all operations.
Movedfrom series are left in a state equivalent to an empty series.
Definition at line 45 of file series_fwd.hpp.
using piranha::series< Cf, Key, Derived >::const_iterator = const_iterator_impl 
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 singleterm instance of Derived
constructed from the term's key and a unitary coefficient.
This iterator is an input iterator which additionally offers the multipass guarantee.
Definition at line 1994 of file series.hpp.
using piranha::series< Cf, Key, Derived >::size_type = typename container_type::size_type 
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.

default 
Defaulted copy constructor.
unspecified  any exception thrown by the copy constructor of piranha::hash_set. 

inlineexplicit 
Generic constructor.
T
does not derive from the calling piranha::series instance and the algorithm outlined below is supported by the involved types.The generic construction algorithm works as follows:
T
is a series with the same series recursion index as this
, then the symbol set of x
is copied into this
and all terms from x
are inserted into this
. The terms of x
are converted to term_type
via the binary constructor of piranha::term, and the keys of x
are converted to the key type of term_type
via a converting constructor, if available (see piranha::key_is_convertible);T
is less than the recursion index of this:
x
is used to construct a new term as follows:x
is used to construct a coefficient via piranha::convert_to;this
;x  object to construct from. 
unspecified  any exception thrown by:

Definition at line 2033 of file series.hpp.

inline 
Get a mutable reference to the container of terms.
Definition at line 2788 of file series.hpp.

inline 
Get a const reference to the container of terms.
Definition at line 2796 of file series.hpp.

inline 
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 singleterm 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 nonconst method on the series will invalidate the iterators obtained via piranha::series::begin() and piranha::series::end().
unspecified  any exception thrown by:

Definition at line 2504 of file series.hpp.

inlinestatic 
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().
unspecified  any exception thrown by threading primitives. 
Definition at line 2371 of file series.hpp.

inline 
Empty test.
true
if size() is nonzero, false
otherwise. Definition at line 2103 of file series.hpp.

inline 
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.
unspecified  any exception thrown by:

Definition at line 2523 of file series.hpp.

inline 
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().
func  filtering functor. 
unspecified  any exception thrown by:

Definition at line 2547 of file series.hpp.

inline 
Symbol set getter.
Definition at line 2762 of file series.hpp.

inline 
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.
unspecified  any exception thrown by computing the hash of a term. 
Definition at line 2730 of file series.hpp.

inline 
Insert term.
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:
std::invalid_argument
exception is thrown;Sign
is true
) or subtracted (if Sign
is false
) to the existing term's coefficient;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 inplace 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.
term  term to be inserted. 
unspecified  any exception thrown by:

std::invalid_argument  if term is incompatible. 
Definition at line 2161 of file series.hpp.

inline 
Insert generic term with Sign = true
.
T
is piranha::series::term_type.Convenience wrapper for the generic insert() method, with Sign
set to true
.
term  term to be inserted. 
unspecified  any exception thrown by generic insert(). 
Definition at line 2177 of file series.hpp.

inline 
Check for identical series.
Derived
is equalitycomparable.This method will return true
if the symbol sets of this
and other
are the same, and other == *this
.
other  argument for the comparison. 
true
if this
and other
are identical, false
otherwise.unspecified  any exception thrown by the comparison operator of Derived . 
Definition at line 2754 of file series.hpp.

inline 
Test for singlecoefficient series.
A series is considered to be singlecoefficient 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).
true
in case of singlecoefficient series, false
otherwise.unspecified  any exception thrown by the is_unitary() method of the key type. 
Definition at line 2118 of file series.hpp.

inline 
Negate series inplace.
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.
unspecified  any exception thrown by math::negate() on the coefficient type. 
Definition at line 2214 of file series.hpp.

inline 
Identity operator.
this
, cast to Derived
.unspecified  any exception thrown by the copy constructor. 
Definition at line 2187 of file series.hpp.

inline 
Negation operator.
this
on which negate() has been called.unspecified  any exception thrown by:

Definition at line 2199 of file series.hpp.

inline 
Copyassignment operator.
other  assignment argument. 
this
.unspecified  any exception thrown by the copy constructor. 
Definition at line 2055 of file series.hpp.

default 
Move assignment operator.
other  the assignment argument. 
this
.

inline 
Generic assignment operator.
x
is enabled.Generic assignment is equivalent to assignment to a piranha::series constructed via the generic constructor.
x  assignment argument. 
this
.unspecified  any exception thrown by the generic constructor. 
Definition at line 2085 of file series.hpp.

inline 
Partial derivative.
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().
name  name of the argument with respect to which the derivative will be calculated. 
this
with respect to the symbol name
.unspecified  any exception thrown by:

Definition at line 2405 of file series.hpp.

inline 
Exponentiation.
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:
x
;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);x
represents a nonnegative integral value, the return value is constructed via repeated multiplications;An internal threadsafe 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().
x  exponent. 
this
raised to the power of x
.std::invalid_argument  if exponentiation is computed via repeated series multiplications and x does not represent a nonnegative integer. 
unspecified  any exception thrown by:

Definition at line 2304 of file series.hpp.

inline 
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.
os  target stream. 
unspecified  any exception thrown by:

Definition at line 2654 of file series.hpp.

inlinestatic 
Register custom partial derivative.
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.
name  symbol for which the custom partial derivative function will be registered. 
func  custom partial derivative function. 
unspecified  any exception thrown by:

Definition at line 2432 of file series.hpp.

inline 
Symbol set setter.
args  piranha::symbol_fset that will be associated to the series. 
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.

inline 

inline 
Table bucket count.
Definition at line 2263 of file series.hpp.

inline 
Table load factor.
Will call piranha::hash_set::load_factor() on the internal terms container and return the result.
Definition at line 2255 of file series.hpp.

inline 
Table sparsity.
Will call piranha::hash_set::evaluate_sparsity() on the internal terms container and return the result.
unspecified  any exception thrown by piranha::hash_set::evaluate_sparsity(). 
Definition at line 2244 of file series.hpp.

inline 
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
.
func  transforming functor. 
unspecified  any exception thrown by:

Definition at line 2585 of file series.hpp.

inline 
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.
this
.unspecified  any exception thrown by:

Definition at line 2619 of file series.hpp.

inlinestatic 
Unregister all custom partial derivatives.
Derived
.Will unregister all custom derivatives currently registered via register_custom_derivative(). It is safe to call this method from multiple threads.
unspecified  any exception thrown by failure(s) in threading primitives. 
Definition at line 2478 of file series.hpp.

inlinestatic 
Unregister custom partial derivative.
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 noop.
It is safe to call this method from multiple threads.
name  symbol for which the custom partial derivative function will be unregistered. 
unspecified  any exception thrown by:

Definition at line 2459 of file series.hpp.

friend 
Overloaded stream operator for piranha::series.
Will direct to stream a humanreadable representation of the series.
The humanreadable representation of the series is built as follows:
print()
method;The following additional transformations take place on the printed output:
Note that the print order of the terms will be undefined.
os  target stream. 
s  piranha::series argument. 
os
.unspecified  any exception thrown by:

Definition at line 2699 of file series.hpp.