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graph_utils.py
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graph_utils.py
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import networkx as nx
import numpy as np
from collections import defaultdict
import itertools
import functools
from functools import reduce
import operator
def product(iterable):
return reduce(operator.mul, iterable, 1)
## Graph processing functions
def find_stable_sets(adj_matrix):
n = adj_matrix.shape[0]
I = []
for i in range(0, n):
for j in range(i+1, n):
for k in range(j+1, n):
if not ( adj_matrix[i,j] or adj_matrix[j,k]
or adj_matrix[i,k]):
I.append(set([i,j,k]))
return I
def has_4_ss(adj_matrix):
n = adj_matrix.shape[0]
for i in range(0, n):
for j in range(i+1, n):
for k in range(j+1, n):
for l in range(k+1, n):
if not (adj_matrix[i,j] or adj_matrix[j,k]
or adj_matrix[i,k] or adj_matrix[i,l]
or adj_matrix[j,l] or adj_matrix[k,l]):
return True
def is_copirr(adj_matrix):
n = adj_matrix.shape[0]
# check if it's symmetrical
if (adj_matrix != adj_matrix.T).sum() != 0:
return False
# check if there is no stable set of size 4
if has_4_ss(adj_matrix):
return False
# check alpha critical and alpha covered
for i in range(0, n):
for j in range(i+1, n):
if adj_matrix[i,j]:
adj_matrix[i,j] = adj_matrix[j,i] = 0
if not has_4_ss(adj_matrix):
adj_matrix[i,j] = adj_matrix[j,i] = 1
return False
adj_matrix[i,j] = adj_matrix[j,i] = 1
else:
ok = False
for k in range(n):
if (not adj_matrix[i,k]) and (not adj_matrix[j,k]):
ok = True
if not ok:
return False
return True
## Graph creation
def get_graphs():
ALL_GRAPHS = {}
cycle = np.array([
[1, 0, 0, 1, 1, 0, 0],
[0, 1, 0, 0, 1, 1, 0],
[0, 0, 1, 0, 0, 1, 1],
[1, 0, 0, 1, 0, 0, 1],
[1, 1, 0, 0, 1, 0, 0],
[0, 1, 1, 0, 0, 1, 0],
[0, 0, 1, 1, 0, 0, 1]
])
ALL_GRAPHS['cycle'] = cycle
dupl = np.array([
[1, 0, 0, 1, 1, 0, 0, 1],
[0, 1, 0, 0, 1, 1, 0, 0],
[0, 0, 1, 0, 0, 1, 1, 0],
[1, 0, 0, 1, 0, 0, 1, 1],
[1, 1, 0, 0, 1, 0, 0, 0],
[0, 1, 1, 0, 0, 1, 0, 0],
[0, 0, 1, 1, 0, 0, 1, 1],
[1, 0, 0, 1, 0, 0, 1, 1]
])
ALL_GRAPHS['dupl'] = dupl
zigzag = np.array([
[1, 1, 0, 0, 1, 1, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 1],
[0, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 0],
[1, 0, 0, 1, 1, 0, 0, 1],
[1, 0, 0, 0, 0, 1, 1, 0],
[0, 0, 0, 0, 0, 1, 1, 1],
[0, 1, 0, 0, 1, 0, 1, 1]
])
ALL_GRAPHS['zigzag'] = zigzag
fork = np.array([
[1, 1, 0, 0, 0, 0, 1, 0],
[1, 1, 1, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 1],
[0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 1],
[1, 0, 0, 0, 0, 1, 1, 1],
[0, 0, 1, 0, 0, 1, 1, 1]
])
ALL_GRAPHS['fork'] = fork
big_zig = np.array([
[1, 1, 0, 0, 1, 0, 0, 0, 1],
[1, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 0],
[0, 0, 1, 1, 1, 1, 0, 0, 0],
[1, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1],
[0, 0, 1, 0, 0, 0, 1, 1, 1],
[1, 0, 0, 0, 0, 0, 1, 1, 1]
])
ALL_GRAPHS['big_zig'] = big_zig
big_triag = np.array([
[1, 1, 0, 0, 1, 0, 0, 1, 0],
[1, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0, 1],
[0, 0, 1, 1, 1, 1, 0, 0, 0],
[1, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1],
[1, 0, 0, 0, 0, 0, 1, 1, 1],
[0, 0, 1, 0, 0, 0, 1, 1, 1]
])
ALL_GRAPHS['big_triag'] = big_triag
ya_big_triag = np.array([
[1, 1, 0, 0, 0, 0, 1, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 1, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 1],
[0, 0, 1, 1, 1, 0, 0, 0, 1],
[0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 1, 0],
[1, 0, 0, 0, 0, 1, 1, 0, 1],
[0, 1, 1, 0, 0, 1, 0, 1, 1],
[0, 0, 1, 1, 0, 0, 1, 1, 1]
])
ALL_GRAPHS['ya_big_triag'] = ya_big_triag
ya_big_triag_2 = np.array([
[1, 1, 0, 0, 0, 0, 1, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 1],
[0, 0, 1, 1, 1, 0, 0, 0, 1],
[0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 1, 0],
[1, 0, 0, 0, 0, 1, 1, 1, 1],
[0, 0, 1, 0, 0, 1, 1, 1, 1],
[0, 0, 1, 1, 0, 0, 1, 1, 1]
])
ALL_GRAPHS['ya_big_triag_2'] = ya_big_triag_2
tang_triag = np.array([
[1, 1, 0, 0, 0, 1, 0, 0, 1],
[1, 1, 1, 0, 0, 0, 0, 1, 0],
[0, 1, 1, 1, 0, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 1],
[0, 0, 0, 1, 1, 1, 0, 1, 0],
[1, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 0, 0, 1, 1, 1, 1],
[0, 1, 0, 0, 1, 0, 1, 1, 1],
[1, 0, 0, 1, 0, 0, 1, 1, 1]
])
ALL_GRAPHS['tang_triag'] = tang_triag
square = np.array([
[1, 1, 0, 1, 0, 1, 0, 0, 0],
[1, 1, 1, 0, 1, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 1, 0, 0],
[1, 0, 1, 1, 0, 0, 0, 1, 0],
[0, 1, 0, 0, 1, 0, 0, 1, 1],
[1, 0, 0, 0, 0, 1, 1, 0, 1],
[0, 0, 1, 0, 0, 1, 1, 0, 1],
[0, 0, 0, 1, 1, 0, 0, 1, 1],
[0, 0, 0, 0, 1, 1, 1, 1, 1]
])
ALL_GRAPHS['square'] = square
center = np.array([
[1, 1, 0, 0, 0, 0, 0, 1, 0],
[1, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 1, 0, 1],
[0, 0, 1, 1, 1, 0, 0, 1, 1],
[0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 1, 0, 0, 1, 1, 1, 1],
[1, 0, 0, 1, 0, 0, 1, 1, 1],
[0, 0, 1, 1, 0, 0, 1, 1, 1]
])
ALL_GRAPHS['center'] = center
ship = np.array([
[1, 0, 1, 0, 1, 0, 0, 1, 0, 1],
[0, 1, 1, 1, 0, 0, 0, 0, 0, 0],
[1, 1, 1, 0, 0, 1, 1, 0, 0, 0],
[0, 1, 0, 1, 1, 0, 0, 0, 0, 0],
[1, 0, 0, 1, 1, 1, 0, 0, 0, 1],
[0, 0, 1, 0, 1, 1, 1, 0, 1, 0],
[0, 0, 1, 0, 0, 1, 1, 1, 1, 0],
[1, 0, 0, 0, 0, 0, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[1, 0, 0, 0, 1, 0, 0, 1, 1, 1]
])
ALL_GRAPHS['ship'] = ship
sinking_ship = np.array([
[1, 1, 0, 0, 0, 1, 0, 0, 1, 1],
[1, 1, 1, 0, 0, 0, 0, 1, 0, 0],
[0, 1, 1, 1, 0, 0, 1, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 1, 0],
[0, 0, 0, 1, 1, 1, 0, 1, 0, 0],
[1, 0, 0, 0, 1, 1, 1, 0, 0, 1],
[0, 0, 1, 0, 0, 1, 1, 1, 1, 1],
[0, 1, 0, 0, 1, 0, 1, 1, 1, 0],
[1, 0, 0, 1, 0, 0, 1, 1, 1, 1],
[1, 0, 0, 0, 0, 1, 1, 0, 1, 1]
])
ALL_GRAPHS['sinking_ship'] = sinking_ship
storm = np.array([
[1, 1, 0, 0, 1, 0, 1, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 1, 0, 1, 0],
[0, 1, 1, 1, 0, 0, 0, 0, 1, 1],
[0, 0, 1, 1, 1, 1, 0, 0, 0, 0],
[1, 0, 0, 1, 1, 0, 0, 0, 0, 1],
[0, 0, 0, 1, 0, 1, 1, 1, 0, 0],
[1, 1, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[0, 1, 1, 0, 0, 0, 0, 1, 1, 1],
[0, 0, 1, 0, 1, 0, 0, 1, 1, 1]
])
ALL_GRAPHS['storm'] = storm
cell = np.array([
[1, 1, 0, 0, 0, 1, 1, 0, 0, 1],
[1, 1, 1, 0, 0, 0, 0, 0, 1, 1],
[0, 1, 1, 1, 0, 0, 0, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 0, 0, 0, 0],
[1, 0, 0, 0, 1, 1, 1, 1, 0, 0],
[1, 0, 0, 0, 0, 1, 1, 1, 0, 1],
[0, 0, 1, 0, 0, 1, 1, 1, 1, 0],
[0, 1, 1, 0, 0, 0, 0, 1, 1, 1],
[1, 1, 0, 0, 0, 0, 1, 0, 1, 1]
])
ALL_GRAPHS['cell'] = cell
rest_of_the_graphs = {
"5": np.array([
[1, 1, 1, 1, 0, 1, 0, 0, 0, 0],
[1, 1, 0, 1, 0, 0, 0, 0, 1, 1],
[1, 0, 1, 0, 1, 0, 0, 1, 0, 1],
[1, 1, 0, 1, 1, 0, 0, 0, 1, 0],
[0, 0, 1, 1, 1, 0, 1, 0, 1, 0],
[1, 0, 0, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 0, 0, 1],
[0, 0, 1, 0, 0, 1, 0, 1, 1, 1],
[0, 1, 0, 1, 1, 0, 0, 1, 1, 0],
[0, 1, 1, 0, 0, 0, 1, 1, 0, 1]
]),
"6": np.array([
[1, 1, 1, 0, 1, 0, 0, 0, 1, 0],
[1, 1, 1, 0, 0, 1, 1, 0, 0, 0],
[1, 1, 1, 1, 0, 0, 0, 0, 0, 1],
[0, 0, 1, 1, 1, 0, 1, 1, 0, 0],
[1, 0, 0, 1, 1, 1, 0, 0, 1, 0],
[0, 1, 0, 0, 1, 1, 1, 0, 0, 1],
[0, 1, 0, 1, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 1, 0, 0, 1, 1, 1, 1],
[1, 0, 0, 0, 1, 0, 0, 1, 1, 1],
[0, 0, 1, 0, 0, 1, 0, 1, 1, 1]
]),
"7": np.array([
[1, 1, 0, 0, 0, 0, 1, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 1, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 1, 1],
[0, 0, 1, 1, 1, 0, 0, 0, 1, 0],
[0, 0, 0, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 1, 0, 1],
[1, 0, 0, 0, 0, 1, 1, 0, 1, 1],
[0, 1, 1, 0, 0, 1, 0, 1, 1, 1],
[0, 0, 1, 1, 0, 0, 1, 1, 1, 1],
[0, 0, 1, 0, 0, 1, 1, 1, 1, 1]
]),
"8": np.array([
[1, 1, 0, 0, 1, 1, 0, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 1, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 1, 1],
[1, 0, 0, 1, 1, 1, 0, 0, 0, 1],
[1, 0, 0, 0, 1, 1, 0, 1, 0, 0],
[0, 1, 0, 0, 0, 0, 1, 1, 0, 1],
[0, 0, 1, 0, 0, 1, 1, 1, 1, 0],
[0, 0, 1, 1, 0, 0, 0, 1, 1, 1],
[0, 0, 0, 1, 1, 0, 1, 0, 1, 1]
]),
"9": np.array([
[1, 1, 0, 0, 1, 0, 1, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 1, 0, 0, 0],
[0, 1, 1, 1, 0, 1, 0, 0, 0, 1],
[0, 0, 1, 1, 1, 0, 0, 0, 1, 1],
[1, 0, 0, 1, 1, 1, 0, 0, 1, 0],
[0, 0, 1, 0, 1, 1, 0, 1, 0, 0],
[1, 1, 0, 0, 0, 0, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[0, 0, 0, 1, 1, 0, 0, 1, 1, 1],
[0, 0, 1, 1, 0, 0, 0, 1, 1, 1]
]),
"10": np.array([
[1, 1, 0, 0, 1, 0, 1, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 1, 0, 1],
[1, 0, 0, 1, 1, 1, 0, 0, 0, 1],
[0, 0, 0, 0, 1, 1, 1, 0, 1, 1],
[1, 0, 0, 0, 0, 1, 1, 1, 1, 0],
[0, 0, 1, 1, 0, 0, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[0, 0, 0, 1, 1, 1, 0, 0, 1, 1]
]),
"11": np.array([
[1, 1, 0, 0, 0, 1, 0, 1, 1, 0],
[1, 1, 1, 0, 0, 0, 0, 0, 1, 0],
[0, 1, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 0, 1],
[0, 0, 0, 1, 1, 1, 1, 0, 0, 1],
[1, 0, 0, 0, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 1, 1, 1, 1, 0, 1],
[1, 0, 0, 0, 0, 1, 1, 1, 1, 0],
[1, 1, 0, 0, 0, 0, 0, 1, 1, 1],
[0, 0, 0, 1, 1, 0, 1, 0, 1, 1]
]),
"12": np.array([
[1, 1, 0, 0, 1, 1, 0, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 1, 1, 0],
[0, 1, 1, 1, 0, 0, 0, 0, 1, 1],
[0, 0, 1, 1, 1, 0, 0, 0, 1, 1],
[1, 0, 0, 1, 1, 1, 0, 0, 0, 0],
[1, 0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 0, 1],
[0, 1, 0, 0, 0, 0, 1, 1, 1, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 1, 0],
[0, 0, 1, 1, 0, 0, 1, 0, 0, 1]
]),
"13": np.array([
[1, 1, 0, 0, 1, 1, 0, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 1, 1, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 1, 1],
[1, 0, 0, 1, 1, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 1, 1, 0, 1, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 0, 1],
[0, 1, 1, 0, 0, 0, 1, 1, 0, 0],
[0, 1, 1, 1, 0, 1, 0, 0, 1, 1],
[0, 0, 0, 1, 1, 0, 1, 0, 1, 1]
]),
"14": np.array([
[1, 1, 0, 0, 1, 1, 0, 1, 0, 0],
[1, 1, 1, 0, 0, 0, 1, 0, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 1, 0],
[1, 0, 0, 1, 1, 1, 0, 0, 0, 0],
[1, 0, 0, 0, 1, 1, 0, 1, 0, 1],
[0, 1, 0, 0, 0, 0, 1, 0, 0, 1],
[1, 0, 1, 0, 0, 1, 0, 1, 1, 1],
[0, 0, 1, 1, 0, 0, 0, 1, 1, 1],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]
]),
"15": np.array([
[1, 1, 0, 0, 1, 1, 0, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 1, 0, 0],
[0, 1, 1, 1, 0, 0, 0, 0, 1, 0],
[0, 0, 1, 1, 1, 0, 0, 0, 1, 1],
[1, 0, 0, 1, 1, 1, 0, 0, 0, 1],
[1, 0, 0, 0, 1, 1, 1, 0, 1, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1],
[0, 1, 0, 0, 0, 0, 1, 1, 0, 1],
[0, 0, 1, 1, 0, 1, 1, 0, 1, 0],
[0, 0, 0, 1, 1, 0, 1, 1, 0, 1]
]),
"16": np.array([
[1, 1, 1, 1, 0, 0, 0, 1, 0, 0],
[1, 1, 1, 0, 0, 0, 1, 0, 0, 1],
[1, 1, 1, 1, 1, 0, 0, 0, 0, 0],
[1, 0, 1, 1, 1, 1, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 1, 0, 0, 1, 1, 1, 1, 0, 0],
[1, 0, 0, 0, 0, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 1, 1],
[0, 1, 0, 0, 0, 0, 0, 0, 1, 1]
]),
"anti_3": np.array([[1., 1., 1., 0., 0., 0., 0., 0., 0., 1., 1.],
[1., 1., 1., 1., 0., 0., 0., 0., 0., 0., 1.],
[1., 1., 1., 1., 1., 0., 0., 0., 0., 0., 0.],
[0., 1., 1., 1., 1., 1., 0., 0., 0., 0., 0.],
[0., 0., 1., 1., 1., 1., 1., 0., 0., 0., 0.],
[0., 0., 0., 1., 1., 1., 1., 1., 0., 0., 0.],
[0., 0., 0., 0., 1., 1., 1., 1., 1., 0., 0.],
[0., 0., 0., 0., 0., 1., 1., 1., 1., 1., 0.],
[0., 0., 0., 0., 0., 0., 1., 1., 1., 1., 1.],
[1., 0., 0., 0., 0., 0., 0., 1., 1., 1., 1.],
[1., 1., 0., 0., 0., 0., 0., 0., 1., 1., 1.]])
}
for x in rest_of_the_graphs:
ALL_GRAPHS[x] = rest_of_the_graphs[x]
return ALL_GRAPHS
## Functions for building equalities+inequalities systems for specific graphs
def build_triple_equalities(I, n):
# Give numbers to all cells in a matrix
var_matr = np.ones([n,n], dtype=np.int)*(-1)
num_params = int((n*(n-1))/2)
c = 0
for i in range(n):
for j in range(i+1, n):
var_matr[i][j] = c
var_matr[j][i] = c
c += 1
# Now make equalities
param_eq = []
for ss in I:
s = ss.copy()
i, j, k = s.pop(), s.pop(), s.pop()
param_eq.append([var_matr[i,j], var_matr[i,k], var_matr[j,k]])
# And put them in a matrix
A = []
for p in param_eq:
ai = np.zeros(num_params)
ai[p[0]] = ai[p[1]] = ai[p[2]] = 1
A.append(ai)
return A, var_matr, num_params
def total_num_of_combinations(I, var_matr, num_params, only_nonequivalent=True):
# Find parametrizations for elements of a matrix that correspond to an edge
variants = defaultdict(list)
for x in range(len(I)):
for y in range(x+1, len(I)):
if len(I[x].intersection(I[y])) == 2:
inter = I[x].intersection(I[y])
i = I[x].difference(I[y]).pop()
j = inter.pop()
k = inter.pop()
l = I[y].difference(I[x]).pop()
variants[var_matr[i,l]].append([var_matr[i,j], var_matr[j,k], var_matr[k,l]])
if only_nonequivalent:
return product([2**(len(var)-1) for element, var in variants.items()])
else:
return product([2**(len(var)) for element, var in variants.items()])
def one_param_iterator(k):
for x in itertools.product([-1,1], repeat=k-1):
yield (1,) + x
def build_variance_equalities_iterator(I, var_matr, num_params, only_nonequivalent=True):
# Find parametrizations for elements of a matrix that correspond to an edge
variants = defaultdict(list)
for x in range(len(I)):
for y in range(x+1, len(I)):
if len(I[x].intersection(I[y])) == 2:
inter = I[x].intersection(I[y])
i = I[x].difference(I[y]).pop()
j = inter.pop()
k = inter.pop()
l = I[y].difference(I[x]).pop()
variants[var_matr[i,l]].append([var_matr[i,j], var_matr[j,k], var_matr[k,l]])
variant_keys = list(variants.keys())
# Give away equalities that represent different module openings
if only_nonequivalent:
comb_iter = itertools.product(*[one_param_iterator(len(variants[x])) for x in variant_keys])
else:
comb_iter = itertools.product(*[itertools.product([-1,1], repeat=len(variants[x])) for x in variant_keys])
for p in comb_iter:
perm = functools.reduce(lambda x, y: x+y, p)
A = []; b = []
c = 0
openings = defaultdict(list)
for edge_key in variant_keys:
var = variants[edge_key]
for k in range(len(var)):
ai = np.zeros(num_params)
ai[edge_key] = 1
bi = 0
if perm[c] == 1:
ai[var[k]] = -1; bi = 0
openings[edge_key].append((var[k], 1))
elif perm[c] == -1:
ai[var[k]] = 1; bi = 2
openings[edge_key].append((var[k], -1))
c += 1
A.append(ai)
b.append(bi)
yield A, b, openings
def build_inequalities(num_params):
B = np.concatenate([np.identity(num_params), -1*np.identity(num_params)])
c = np.array([1 for _ in range(num_params)] + [0 for _ in range(num_params)])
return B, c