Representations for one-to-one mappings
[Components for Mappings]

Collaboration diagram for Representations for one-to-one mappings:

Classes
struct	GrAL::fail_if_undefined
	Policy to fail when undefined item is queried. More...
struct	GrAL::identity_if_undefined
	Policy to return identity when undefined item is queried. More...
class	GrAL::printer_of_bij_mapping< T1, T2, Policy >
	helper class for custom output of a bijective map More...
class	GrAL::bijective_mapping< T1, T2, Policy >
	Represents a one-to-one mapping T1 -> T2. More...
class	GrAL::inverse_mapping< T1, T2, Policy >
	Represents a mapping T2 --> T1 which is the inverse of some bijective_mapping<T1,T2>. This class has reference semantics with respect to bijective_mapping. More...
class	GrAL::domain_of_bijective_mapping< T1, T2, Policy >
	Represents the domain of definition of a mapping. This class allows STL-style iteration over the items of type T1. More...
class	GrAL::range_of_bijective_mapping< T1, T2, Policy >
	Represents the range (image) of a bijective mapping . This class allows STL-style iteration over the items of type T2. More...
Functions
template<class T1 , class T2 , class Policy >
void	GrAL::write_bm (bijective_mapping< T1, T2, Policy > const &m,::std::ostream &out)
	write a bijective map to ostream
template<class T1 , class T2 , class Policy >
void	GrAL::read_bm (bijective_mapping< T1, T2, Policy > &m,::std::istream &in)
	read a bijective map from istream
template<class T1 , class T2 , class Policy >
printer_of_bij_mapping< T1, T2, Policy >	GrAL::Printer (bijective_mapping< T1, T2, Policy > const &m)
	helper function for custom output of a bijective map

---

Detailed Description

Contents

This module contains class templates for representing bijective mappings:

• class bijective_mapping<T1,T2,Policy> : A one-to-one mapping (short f)
• class inverse_mapping<T1,T2> : Inverse of a bijective_mapping (short inv)
• class domain_of_bijective_mapping<T1,T2>: domain of definition of a bijective mapping (short dom)
• class range_of_bijective_mapping<T1,T2>: range (image) of a bijective mapping. (short ran)
• some helper classes and functions for I/O: read_bm, write_bm, printer_of_bij_mapping, Printer

The extra Policy parameter (which has been omitted for clarity except in the first occurence) permits to control the behaviour of bijective_mapping if evaluated for an item which has not been set explictly. If Policy is fail_if_undefined (the default), than accessing an undefined item is treated as an error. If Policy is identity_if_undefined and T1 == T2 , then the item itself is returned. Thus, simular to partial_mapping, evaluation on an unbounded set of items is possible. However, this policy leads to possibly undetected violations of bijectivity, which would otherwise be detected when the inverse is built. For instance, if we say m[1] = 2 , the mapping m is not bijective any longer because m(1) == 2 || m(2) == 2 , the latter by the implicit identity extension.

Template parameters

(same for bijective_mapping<T1,T2>, inverse_mapping<T1,T2>, domain_of_bijective_mapping<T1,T2>, range_of_bijective_mapping<T1,T2>)

• T1 is Hashable, that is, hash<T1> is defined.
• T1 is Equality Comparable, that is, equal_to<T1> is defined.
• T2 is Assignable and Default Constructible.

Description:

• class bijective_mapping<T1,T2>;
  • the master class with value semantics, giving an interface to a mapping T1 -> T2
  • Template parameters:
    • T1, T2: hash<T> must be defined. (default definitions in STL only for integral types)
  • class printer_of_bij_mapping<T1,T2> is used for output
  • functions read_bm, write_bm are used for I/O
• The other 3 classes have reference semantics with respect to bm:
  • class inverse_mapping<T1,T2>
    • gives a function interface to the inverse (which is really calculated and stored in bm<T1,T2>)
  • class domain_of_bijective_mapping<T1,T2> (dom)
    • gives a set interface to the domain (of definition) of bm;
  • class range_of_bijective_mapping<T1,T2> (ran)
    • gives a set interface to the range (or image) of bm;

Invariants:

• T1 x: inv(f(x)) == x
• T2 y: f(inv(y)) == y
• T1 x: f.defined(x) <=> dom(f).is_member(x)
• T2 y: inv.defined(y) <=> ran(f).is_member(y)
• dom(f).size() == ran(f).size()
• f(* (dom(f).begin() + n) == * (ran(f).begin() + n),

Example:

• see test-bijective.C

See also:

bijective-mapping.h

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Function Documentation

template<class T1 , class T2 , class Policy >

printer_of_bij_mapping<T1,T2,Policy> GrAL::Printer

(

bijective_mapping< T1, T2, Policy > const &

m

)

[inline]

helper function for custom output of a bijective map

Usage:

    bijective_mapping<int,int> bm;
     ...
    cout << Printer(bm) << endl;
    

Definition at line 174 of file bijective-mapping.h.