delta_graphs.py¶
from pymwp import DeltaGraph
NODE = Tuple[DELTA, ...]
module-attribute
¶
Graph node type is a variable-length tuple of deltas.
DeltaGraph
¶
Delta Graph is a dictionary representing a weighted graph of tuples of
deltas (also referenced here as a monomial_list, a
Monomials
without its scalar). We will often refer to
tuple of deltas as simple node, but a node with length!
Nodes are "sorted" by this length in order to be compared by chunks of same size.
Weight of edge represents the index where the nodes differ.
We use tuple because we want them to be hashable (as key in dictionary).
Example:
↓
n1 = ( (0,1) , (0,2) , (0,3), (0,4) )
n2 = ( (0,1) , (0,2) , (1,3), (0,4) )
in our graph will have:
n1 <---- 3 ----> n2
or
size = 4 ↓
graph_dict[4][n1][n2] = 3
The graph is symmetric:
graph_dict[4][n2][n1] = 3
This representation will help us simplify the evaluation by removing redundant/irrelevant choices/paths.
Source code in pymwp/delta_graphs.py
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__init__(*init_nodes, degree=3)
¶
Creates a Delta Graph.
Fills a dictionary with nodes of all given initial nodes.
Example:
Create an empty delta graph
dg = DeltaGraph()
Create delta graph with some initial nodes from monomials.
dg = DeltaGraph(mono1, mono2)
Parameters:
Name | Type | Description | Default |
---|---|---|---|
init_nodes |
Optional[Union[Monomial, NODE]]
|
initial list of monomials or nodes (optional). |
()
|
degree |
int
|
degree of a full node [default: 3]. |
3
|
Source code in pymwp/delta_graphs.py
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from_monomial(monomial)
¶
Add monomial's deltas to the delta graph.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
monomial |
Monomial
|
monomial |
required |
Source code in pymwp/delta_graphs.py
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fusion()
¶
Eliminates cliques of same label in a delta graph.
Example:
m1 = ((0, 1), (0, 2))
m2 = ((0, 1), (1, 2))
m3 = ((0, 1), (2, 2), (0, 3))
m4 = ((0, 1), (2, 2), (1, 3))
m5 = ((0, 1), (2, 2), (2, 3))
'''
delta graph:
m1 -- 2 -- m2
m3 -- 3 -- m4
⟍ |
3 3
⟍ |
⟍ |
m5
Looks for cliques (size default 3) at each index.
=> Graph will simplify to: ((0,1)).
'''
Source code in pymwp/delta_graphs.py
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insert_edge(node1, node2, label)
¶
Add an edge of label label
between node1
and node2
If one node does not exist, it's created
Symmetry is also added in the graph.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
node1 |
NODE
|
first node |
required |
node2 |
NODE
|
second node |
required |
label |
int
|
label over the edge |
required |
Source code in pymwp/delta_graphs.py
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insert_node(node)
¶
Insert a node into the graph.
If a node is already in the graph do nothing.
Else compare it with all nodes of same size with node_diff
.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
node |
NODE
|
tuple to insert in the graph |
required |
Source code in pymwp/delta_graphs.py
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is_full(node, size, index)
¶
Check for cliques of same label.
Example:
n3 = ((0, 1), (2, 2), (0, 3))
n4 = ((0, 1), (2, 2), (1, 3))
n5 = ((0, 1), (2, 2), (2, 3))
node = n4
size = 3
index = 3
degree = 3
'''
n3 -- 3 -- n4
⟍ |
3 3
⟍ |
⟍ |
n5
'''
return True
Parameters:
Name | Type | Description | Default |
---|---|---|---|
node |
NODE
|
check for clique around that graph node |
required |
size |
int
|
size of nodes or graph "level" |
required |
index |
int
|
index where to find clique |
required |
Returns:
Type | Description |
---|---|
bool
|
True if there is a clique |
Source code in pymwp/delta_graphs.py
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node_diff(node1, node2, index=None)
staticmethod
¶
Compares two nodes of the same length.
The return value is a tuple representing the result of comparison (boolean) and an index.
The result is True, if and only if both lists differ only on one element regarding the same index. The second return value is the index of the corresponding delta.
Parameters:
Name | Type | Description | Default |
---|---|---|---|
node1 |
NODE
|
first monomial list |
required |
node2 |
NODE
|
second monomial list |
required |
index |
Optional[int]
|
index with to check number of diff |
None
|
Returns:
Name | Type | Description |
---|---|---|
diff |
bool
|
boolean True if the lists differ of one element |
i |
int
|
the index of the delta which differs |
Source code in pymwp/delta_graphs.py
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remove_index(node, index)
staticmethod
¶
Remove delta with given index.
Example:
remove index 4:
((0, 2), (1, 3), (2, 4)) -> ((0, 2), (1, 3))
Parameters:
Name | Type | Description | Default |
---|---|---|---|
node |
NODE
|
monomial list |
required |
index |
int
|
index to remove |
required |
Returns:
Type | Description |
---|---|
NODE
|
a new tuple without deltas with index |
Source code in pymwp/delta_graphs.py
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remove_node(node, index)
¶
Remove given node and neighbors connected with same label.
Also removes edges/labels connected to the node (they no longer exist).
Source code in pymwp/delta_graphs.py
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