def maximize(data, mapping={}, objective=(0, {})):
"""Maximization using the CONEstrip algorithm
.. todo::
document, test more and clean up
"""
E = feasible(data, mapping)
if E == set():
raise ValueError("The linear program is infeasible.")
#print("The linear program is infeasible.")
#return 0
l = sum(len(A) for A in E)
h = Vector(mapping)
goal = (objective[0], Vector(objective[1]))
#print(goal)
coordinates = list(frozenset.union(*(A.domain() for A in E)))
E = [[vector for vector in A] for A in E]
mat = Matrix([[0] + l * [0]], number_type='fraction')
mat.extend([[-h[x]] + [v[x] for A in E for v in A]
for x in coordinates], linear=True) # cone-constraints
mat.extend([[0] + [int(B == A and w == v) for B in E for w in B]
for A in E for v in A]) # mu >= 0
mat.obj_type = LPObjType.MAX
mat.obj_func = tuple([goal[0]] + [goal[1][v] for A in E for v in A])
# (constant, mu)
#print(mat)
lp = LinProg(mat)
lp.solve()
if lp.status == LPStatusType.OPTIMAL:
#print(lp.primal_solution)
return lp.obj_value
elif lp.status == LPStatusType.UNDECIDED:
status = "undecided"
elif lp.status == LPStatusType.INCONSISTENT:
status = "inconsistent"
elif lp.status == LPStatusType.UNBOUNDED:
status = "unbounded"
else:
status = "of unknown status"
raise ValueError("The linear program is " + str(status) + '.')
def feasible(data, mapping=None):
"""Check feasibility using the CONEstrip algorithm
.. todo::
document, test more and clean up
"""
D = set(Polytope(A) for A in data)
if (mapping == None) or all(mapping[x] != 0 for x in mapping):
h = None
else:
h = Vector(mapping)
D.add(Polytope({-h}))
coordinates = list(frozenset.union(*(A.domain() for A in D)))
E = [[vector for vector in A] for A in D]
#print(E)
while (E != []):
k = len(E)
L = [len(A) for A in E]
l = sum(L)
mat = Matrix([[0] + l * [0] + k * [0]], number_type='fraction')
mat.extend([[0] + [v[x] for A in E for v in A] + k * [0]
for x in coordinates],
linear=True) # cone-constraints
mat.extend([[0] + [int(B == A and w == v) for B in E for w in B]
+ k * [0]
for A in E for v in A]) # mu >= 0
mat.extend([[1] + l * [0] + [-int(B == A) for B in E]
for A in E]) # tau <= 1
mat.extend([[0] + l * [0] + [int(B == A) for B in E]
for A in E]) # tau >= 0
mat.extend([[-1] + l * [0] + k * [1]]) # (sum of tau_A) >= 1
mat.extend([[0] + [int(B == A and w == v) for B in E for w in B]
+ [-int(B == A) for B in E]
for A in E for v in A]) # tau_A <= mu_A for all A
if h != None: # mu_{-h} >= 1
mat.extend([[-1] + [int(A == [-h]) for A in E for w in A]
+ k * [0]])
mat.obj_type = LPObjType.MAX
mat.obj_func = tuple([0] + l * [0] + k * [1]) # (constant, mu, tau)
#print(mat)
lp = LinProg(mat)
lp.solve()
if lp.status == LPStatusType.OPTIMAL:
sol = lp.primal_solution # (constant, mu, tau)
tau = sol[l:]
#print(tau)
mu = [sol[sum(L[0:n]):sum(L[0:n]) + L[n]] for n in range(0, k)]
#print(mu)
E = [E[n] for n in range(0, k) if tau[n] == 1]
#print(E)
if all(all(mu[n][m] == 0 for m in range(0, L[n]))
for n in range(0, k) if tau[n] == 0):
E = {Polytope(A) for A in E}
#print(E)
if h != None:
E = E - {Polytope([-h])}
#print(E)
return E
else:
continue
else:
return set()
else:
return set()