X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/25ce908cffca380f930182a77c1e5a4491042a1c..197818714e75c2353ed8b7c9fec653f1212f13ae:/doc/domain.rst?ds=inline diff --git a/doc/domain.rst b/doc/domain.rst index 217acba..06eec6e 100644 --- a/doc/domain.rst +++ b/doc/domain.rst @@ -1,167 +1,180 @@ Domains Module ============== +This module provides classes and functions to deal with polyhedral +domains, i.e. unions of polyhedra. + .. py:class :: Domain - .. py:method:: polyhedra(self) - - Return . - -Domain Properties ------------------ - .. py:method:: symbols(self) - - Returns a list of the symbols used in a set. + This class represents polyhedral domains, i.e. unions of polyhedra. - .. py:method:: dimension(self) + .. py:method:: __new__(cls, *polyhedra) - Returns the number of variables in a set. + Create and return a new domain from a string or a list of polyhedra. - .. py:method:: disjoint(self) + .. attribute:: polyhedra - Returns a set as disjoint. - - .. py:method:: num_parameters(self) - - Returns the total number of parameters, input, output or set dimensions. - - .. py:method:: involves_dims(self, dims) + The tuple of polyhedra which constitute the domain. - Returns true if set depends on given dimensions. - -Unary Properties ----------------- + .. attribute:: symbols + + Returns a tuple of the symbols that exsist in a domain. + + .. attribute:: dimension + + Returns the number of variables that exist in a domain. + .. py:method:: isempty(self) - - Return true is set is an Empty set. + + Return ``True`` is a domain is empty. - .. py:method:: isuniverse(self) + .. py:method:: __bool__(self) - Return true if set is the Universe set. - + Return ``True`` if the domain is non-empty. + + .. py:method:: isuniverse(self) + + Return ``True`` if a domain is the Universe set. + .. py:method:: isbounded(self) - - Return true if set is bounded - .. py:method:: disjoint(self) - - Returns this set as a disjoint set. + Return ``True`` if a domain is bounded. -Binary Properties ------------------ + .. py:method:: make_disjoint(self) + + It is not guarenteed that a domain is disjoint. If it is necessary, this method will return an equivalent domain, whose polyhedra are disjoint. .. py:method:: isdisjoint(self, other) - - Return true if the intersection of two sets results in an Empty set. - + + Return ``True`` if the intersection of *self* and *other* results in an empty set. + .. py:method:: issubset(self, other) - - Returns true if one set contains the other set. + + Test whether every element in a domain is in *other*. .. py:method:: __eq__(self, other) - - Return true if self == other. - + self == other + + Test whether a domain is equal to *other*. + .. py:method:: __lt__(self, other) - - Return true if self < other. - + self < other + + Test whether a domain is a strict subset of *other*. + .. py:method:: __le__(self, other) - - Return true if self <= other. - + self <= other + + Test whether every element in a domain is in *other*. + .. py:method:: __gt__(self, other) - - Return true if self > other. - + self > other + + Test whether a domain is a strict superset of *other*. + .. py:method:: __ge__(self, other) - - Return true if self >= other. - + self >= other -Unary Operations ----------------- + Test whether every element in *other* is in a domain. .. py:method:: complement(self) + ~self + + Return the complementary domain of a domain. + + .. py:method:: coalesce(self) - Return the complement of a set. + Simplify the representation of the domain by trying to combine pairs of + polyhedra into a single polyhedron. + + .. py:method:: detect_equalities(self) + + Simplify the representation of the domain by detecting implicit + equalities. + .. py:method:: simplify(self) - Removes redundant constraints from a set. + Return a new domain without any redundant constraints. - .. py:method:: project(self, dims) - - Return a new set with the given dimensions removed. + .. py:method:: project(self, variables) + + Return a new domain with the given variables removed. .. py:method:: aspolyhedron(self) - - Return polyhedral hull of a set. - - .. py:method:: asdomain(self) - - Return + + Return polyhedral hull of a domain. .. py:method:: sample(self) - - Return a single sample subset of a set. -Binary Operations ------------------ + Return a single sample subset of a domain. - .. py:method:: intersection(self) - - Return the intersection of two sets as a new set. + .. py:method:: intersection(self, other) + __or__ + self | other - .. py:method:: union(self) - - Return the union of two sets as a new set. + Return a new domain with the elements that are common between *self* and *other*. - .. py:method:: __and__(self, other) - - Return the union of two sets as a new set. - - .. py:method:: __or__(self, other) - - Return the intersection of two sets as a new set. - - .. py:method:: __add__(self, other) - - Return the sum of two sets. + .. py:method:: union(self, other) + __and__ + self & other + + Return a new domain with all the elements from *self* and *other*. .. py:method:: difference(self, other) - - Return the difference of two sets. + __sub__ + self - other -Lexiographic Operations ------------------------ + Return a new domain with the elements in a domain that are not in *other* . + + .. py:method:: __add__(self, other) + self + other + + Return the sum of two domains. .. py:method:: lexmin(self) - - Return a new set containing the lexicographic minimum of the elements in the set. - + + Return a new domain containing the lexicographic minimum of the elements in the domain. + .. py:method:: lexmax(self) + + Return a new domain containing the lexicographic maximum of the elements in the domain. + + .. py:method:: subs(self, symbol, expression=None): + + Subsitute symbol by expression in equations and return the resulting + domain. + + .. py:method:: fromstring(cls, string) + + Convert a string into a domain. + + .. py:method:: fromsympy(cls, expr) - Return a new set containing the lexicographic maximum of the elements in the set. + Convert a SymPy expression into a domain. -Plot Properties ---------------- + .. py:method:: tosympy(self) + + Convert a domain into a SymPy expression. + +A 2D or 3D domain can be plotted using the :meth:`plot` method. The points, vertices, and faces of a domain can be inspected using the following functions. .. py:method:: points(self) + + Return a list of the points with integer coordinates contained in a domain as :class:`Points` objects. + + .. py:method:: __contains__(self, point) - Return a list of the points contained in a set. + Return ``True`` if point if contained within the domain. .. py:method:: vertices(self) - - Return a list of the verticies of this set. - + + Return a list of the verticies of a domain. + .. py:method:: faces(self) - - Return a list of the vertices for each face of a set. - + + Return a list of the vertices for each face of a domain. + .. py:method:: plot(self, plot=None, **kwargs) - - Return a plot of the given set. - - - + + Return a plot of the given domain or add a plot to a plot instance, using matplotlib.