def eliminate_redundant_inequalities(A,b):
''' Input format is A x + b <= 0'''
# H-representation: A x + b >= 0
A_plot = Matrix(hstack([-b.reshape((A.shape[0],1)), -A]), number_type=NUMBER_TYPE)
A_plot.rep_type = RepType.INEQUALITY
A_plot.canonicalize()
A_plot = np.array(A_plot)
b_plot, A_plot = -A_plot[:, 0], -A_plot[:, 1:]
return (A_plot, b_plot);
def eliminate_redundant_inequalities(A,b):
# H-representation: A x + b >= 0
A_plot = Matrix(hstack([b.reshape((A.shape[0],1)), -A]), number_type=NUMBER_TYPE)
A_plot.rep_type = RepType.INEQUALITY
A_plot.canonicalize()
A_plot = np.array(A_plot)
b_plot, A_plot = A_plot[:, 0], -A_plot[:, 1:]
return (A_plot, b_plot);
def discard_redundant(self):
"""Remove redundant elements from the credal set
Redundant elements are those that are not vertices of the credal set's
convex hull.
>>> K = CredalSet('abc')
>>> K.add({'a': 1, 'b': 1, 'c': 1})
>>> assert (
... K ==
... CredalSet(
... {PMFunc({'a': '1/3', 'c': '1/3', 'b': '1/3'}),
... PMFunc({'a': 1}), PMFunc({'b': 1}), PMFunc({'c': 1})}
... )
... )
>>> K.discard_redundant()
>>> assert (
... K ==
... CredalSet(
... {PMFunc({'a': 1}), PMFunc({'b': 1}), PMFunc({'c': 1})})
... )
"""
pspace = list(self.pspace())
K = list(self)
mat = Matrix(list([1] + list(p[x] for x in pspace) for p in K),
number_type='fraction')
mat.rep_type = RepType.GENERATOR
lin, red = mat.canonicalize()
for i in red:
self.discard(K[i])
def get_coh_hrep_via_vreps(K, num_type='fraction'):
"""Compute a minimal H-representation for coherence
See Procedure C.1 in my ISIPTA '13 paper “Characterizing coherence,
correcting incoherence”.
"""
vrep = generate_asl_vrep(K, num_type)
hreplist = [Polyhedron(vrep).get_inequalities()]
for i in xrange(len(K)):
vrep = generate_Sasl_vrep(K, i, num_type)
hreplist.append(Polyhedron(vrep).get_inequalities())
constraints = ([list(t) for t in hrep[:]] for hrep in hreplist)
constraintslist = list(chain.from_iterable(constraints))
hrep = Matrix(constraintslist, number_type=num_type)
hrep.rep_type = RepType.INEQUALITY
hrep.canonicalize()
return hrep
