fcapy.poset.POSet

class fcapy.poset.POSet(elements: ~typing.Optional[~typing.Collection[~typing.Any]] = None, leq_func: ~typing.Callable[[~typing.Any, ~typing.Any], bool] = <function POSet.<lambda>>, use_cache: bool = True, children_dict: ~typing.Optional[~typing.Dict[int, ~typing.Tuple[int, ...]]] = None)

A class to represent a Partially Ordered Set (POSet)

A POSet (Partially Ordered Set) is a set in which some elements are bigger than the others, some are smaller, and some are incomparable.

Example

A set of elements = [set(), {‘a’}, {‘b’}] with defined leq (less or equal) function = lambda a,b: a in b is a POSet.

set() in {‘a’} = True <=> set()<={‘a’} <=> element #0 is smaller than element #1 set() in {‘b’} = True <=> set()<={‘b’} <=> element #0 is smaller than element #2 {‘a’} in {‘b’} = False and {‘b’} in {‘a’} = False <=> ({‘a’} not <= {‘b’}) and ({‘b’} not <= {‘a’}) <=> element #1 and element #2 are incomparable

__init__(elements: ~typing.Optional[~typing.Collection[~typing.Any]] = None, leq_func: ~typing.Callable[[~typing.Any, ~typing.Any], bool] = <function POSet.<lambda>>, use_cache: bool = True, children_dict: ~typing.Optional[~typing.Dict[int, ~typing.Tuple[int, ...]]] = None)

Construct a POSet based on a set of elements and leq_func defined on this set

Parameters

• elements (list) – A set of elements of POSet of any kind

• leq_func (function (a,b)-> True or False) – A function to compare whether element a` from the POSet is smaller than ``b or not

• use_cache (bool) – A flag whether to save for the output of leq_func and other computations in the cache or not

• children_dict (dict of type {element_i: indexes of the biggest elements smaller than element_i}) – (optional) A dictionary that contains the precomputed relation representing the biggest elements smaller than an element

Methods

__init__([elements, leq_func, use_cache, ...])	Construct a POSet based on a set of elements and leq_func defined on this set
add(element[, fill_up_cache])	Add an element to POSet.
ancestors(element_index)	Return a set of indexes of elements of POSet bigger than element #``element_index``
children(element_index)	Return a set of indexes of the biggest elements smaller than #``element_index``
descendants(element_index)	Return a set of indexes of elements of POSet smaller than element #``element_index``
fill_up_ancestors_cache()	Compute all ancestors of each element in a POSet
fill_up_caches()	Fill up each cache of POSet
fill_up_children_cache()	Compute children of each element in a POSet
fill_up_descendants_cache()	Compute all descendants of each element in a POSet
fill_up_leq_cache()	Compare all the elements of POSet at once
fill_up_parents_cache()	Compute parents of each element in a POSet
index(element)	Returns an index of the element in the list of POSet.elements
infimum([element_indexes])	Alias for self.meet(element_indexes)
join([element_indexes])	Return the smallest element from POSet bigger than all elements from element_indexes
leq_elements(a_index, b_index)	Compare two elements of POSet by their indexes
meet([element_indexes])	Return the biggest element from POSet smaller than all elements from element_indexes
parents(element_index)	Return a set of indexes of the smallest elements bigger than #``element_index``
remove(element)	Remove an element from POSet
supremum([element_indexes])	Alias for self.join(element_indexes)
to_networkx([direction])	Construct networkx.Graph (or DiGraph) based on POSet relations and direction
trace_element(element, direction)	Get the sets of descendants and children (or ancestors and parents) of an element in the POSet

Attributes

ancestors_dict	list`[indexes of all elements bigger than `element_idx]
bottoms	A list of the bottom (the smallest) elements in a POSet
children_dict	list`[indexes of the biggest elements smaller than `element_idx]
descendants_dict	list`[indexes of all elements smaller than `element_idx]
elements	A list of elements of the POSet
leq_func	A function to compare whether element a` from the POSet is smaller than ``b or not
parents_dict	list`[indexes of the smallest elements bigger than `element_idx]
tops	A list of the top (the biggest) elements in a POSet

add(element: Any, fill_up_cache: bool = True)

Add an element to POSet. Automatically fill up the comparison caches if needed

ancestors(element_index: int) → FrozenSet[int]

Return a set of indexes of elements of POSet bigger than element #``element_index``

property ancestors_dict: Dict[int, FrozenSet[int]]

list`[indexes of all elements bigger than `element_idx]

Type

A dictionary of kind {element_idx

property bottoms: List[int]

A list of the bottom (the smallest) elements in a POSet

children(element_index: int) → FrozenSet[int]

Return a set of indexes of the biggest elements smaller than #``element_index``

Element a is a direct sub element of element b if a``<``b and there is no element c such that a``<``c``<``b

property children_dict: Dict[int, FrozenSet[int]]

list`[indexes of the biggest elements smaller than `element_idx]

Type

A dictionary of kind {element_idx

descendants(element_index: int) → FrozenSet[int]

Return a set of indexes of elements of POSet smaller than element #``element_index``

property descendants_dict: Dict[int, FrozenSet[int]]

list`[indexes of all elements smaller than `element_idx]

Type

A dictionary of kind {element_idx

property elements: List[Any]

A list of elements of the POSet

fill_up_ancestors_cache()

Compute all ancestors of each element in a POSet

fill_up_caches()

Fill up each cache of POSet

fill_up_children_cache()

Compute children of each element in a POSet

fill_up_descendants_cache()

Compute all descendants of each element in a POSet

fill_up_leq_cache()

Compare all the elements of POSet at once

fill_up_parents_cache()

Compute parents of each element in a POSet

index(element: Any) → int

Returns an index of the element in the list of POSet.elements

infimum(element_indexes: Optional[Collection[int]] = None) → Optional[int]

Alias for self.meet(element_indexes)

join(element_indexes: Optional[Collection[int]] = None) → Optional[int]

Return the smallest element from POSet bigger than all elements from element_indexes

leq_elements(a_index: int, b_index: int) → bool

Compare two elements of POSet by their indexes

property leq_func: Callable[[Any, Any], bool]

A function to compare whether element a` from the POSet is smaller than ``b or not

meet(element_indexes: Optional[Collection[int]] = None) → Optional[int]

Return the biggest element from POSet smaller than all elements from element_indexes

parents(element_index: int) → FrozenSet[int]

Return a set of indexes of the smallest elements bigger than #``element_index``

Element a is a direct super element of element b if a>``b`` and there is no element c such that a>``c``>``b``

property parents_dict: Dict[int, FrozenSet[int]]

list`[indexes of the smallest elements bigger than `element_idx]

Type

A dictionary of kind {element_idx

remove(element: Any)

Remove an element from POSet

supremum(element_indexes: Optional[Collection[int]] = None) → Optional[int]

Alias for self.join(element_indexes)

to_networkx(direction: str = 'down')

Construct networkx.Graph (or DiGraph) based on POSet relations and direction

property tops: List[int]

A list of the top (the biggest) elements in a POSet

trace_element(element: Any, direction: str) → Tuple[Set[int], Set[int]]

Get the sets of descendants and children (or ancestors and parents) of an element in the POSet

Parameters

• element – An element to compare POSet elements with (not necessary from the POSet itself)

• direction ({'up', 'down'}) – If set ‘up’ then compute all (and direct) descendants of an element, if set ‘down’ then compute all (and direct) ancestors of an element

Returns

• final_elements (set) – A set of children (or parents) of element in the POSet

• traced_elements (set) – A set of descendants (or ancestors) of element in the POSet