def cone_span_to_face(S, eliminate_redundancies=False):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0} if and only if {S^F x <= 0}.
"""
V = hstack([zeros((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays
V_cdd = Matrix(V, number_type=NUMBER_TYPE)
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
H_matrix = P.get_inequalities();
if(eliminate_redundancies):
H_matrix.canonicalize();
H = array(H_matrix);
if(H.shape[1]>1):
b = H[:, 0]
A = H[:, 1:]
else:
b, A = H[:, 0], zeros((H.shape[0],S.shape[0]));
for i in xrange(H.shape[0]):
if b[i] != 0:
raise NotConeSpan(S)
return -A
def face_of_span(S):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0} if and only if {S^F x <= 0}.
"""
V = hstack([zeros((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays
V_cdd = Matrix(V, number_type="float")
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
ineq = P.get_inequalities()
H = array(ineq)
if H.shape == (0,): # H = []
return H
# b, A = H[:, 0], -H[:, 1:] # H matrix is [b, -A]
A = []
for i in xrange(H.shape[0]):
if H[i, 0] != 0: # b should be zero
raise NotConeSpan(S)
elif i not in ineq.lin_set:
A.append(-H[i, 1:])
return array(A)
def cone_span_to_face(S, eliminate_redundancies=False):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0} if and only if {S^F x <= 0}.
"""
V = hstack([ones((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays
V_cdd = Matrix(V, number_type=NUMBER_TYPE)
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
H_matrix = P.get_inequalities()
if (eliminate_redundancies):
H_matrix.canonicalize()
H = array(H_matrix)
if (H.shape[1] > 1):
b = H[:, 0]
A = H[:, 1:]
else:
b, A = H[:, 0], zeros((H.shape[0], S.shape[0]))
#~ for i in xrange(H.shape[0]):
#~ if b[i] != 0:
#~ raise NotConeSpan(S)
return -A, b
def poly_span_to_face(S):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0, sum(z)=1} if and only if {S^F x <= s}.
"""
V = hstack([ones((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays, 1 for vertices
V_cdd = Matrix(V, number_type=NUMBER_TYPE)
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
H = array(P.get_inequalities()) # H-representation: A x + b >= 0
b, A = H[:, 0], H[:, 1:]
return (-A, b)
def poly_span_to_face(S):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0, sum(z)=1} if and only if {S^F x <= s}.
"""
V = hstack([ones((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays, 1 for vertices
V_cdd = Matrix(V, number_type=NUMBER_TYPE)
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
H = array(P.get_inequalities()) # H-representation: A x + b >= 0
b, A = H[:, 0], H[:, 1:]
return (-A,b)
def cone_span_to_face(S, eliminate_redundancies=False):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0} if and only if {S^F x <= 0}.
"""
S = np.asarray(S).squeeze()
V = hstack([zeros((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays
V_cdd = Matrix(V, number_type=NUMBER_TYPE)
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
H_matrix = P.get_inequalities()
if (eliminate_redundancies):
try:
H_matrix.canonicalize()
except:
print "RuntimeError: failed to canonicalize matrix"
H = array(H_matrix)
if (len(H.shape) < 2):
# warnings.warn("[cone_span_to_face] H is a vector rather than a matrix. S:\n"+str(S)+"\nH:\n"+str(H));
# S += 1e-6*np.random.rand(S.shape[0], S.shape[1]);
# V = hstack([zeros((S.shape[1], 1)), S.T])
# V_cdd = Matrix(V, number_type=NUMBER_TYPE)
# V_cdd.rep_type = RepType.GENERATOR
# P = Polyhedron(V_cdd)
# H_matrix = P.get_inequalities();
# H = array(H_matrix);
# if(len(H.shape)<2):
raise ValueError(
"[cone_span_to_face] Cddlib failed to convert cone span to face: H is a vector rather than a matrix. H: "
+ str(H))
if (H.shape[1] > 1):
b = H[:, 0]
A = H[:, 1:]
else:
b, A = H[:, 0], zeros((H.shape[0], S.shape[0]))
for i in xrange(H.shape[0]):
if b[i] != 0:
raise NotConeSpan(S)
return -A
def arbitrary_span_to_face(S, rv):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0} if and only if {S^F x <= f}.
The vector rv specifies whether the corresponding column in S
is a vertex (1) or a ray (0).
"""
V = hstack([rv.reshape((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays
V_cdd = Matrix(V, number_type=NUMBER_TYPE)
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
H = array(P.get_inequalities())
b, A = H[:, 0], H[:, 1:]
return (-A, b)
def arbitrary_span_to_face(S, rv):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0} if and only if {S^F x <= f}.
The vector rv specifies whether the corresponding column in S
is a vertex (1) or a ray (0).
"""
V = hstack([rv.reshape((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays
V_cdd = Matrix(V, number_type=NUMBER_TYPE)
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
H = array(P.get_inequalities())
b, A = H[:, 0], H[:, 1:]
return (-A,b)
def face_of_span(S):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0} if and only if {S^F x <= 0}.
"""
V = hstack([zeros((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays
V_cdd = Matrix(V, number_type=NUMBER_TYPE)
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
H = array(P.get_inequalities())
b, A = H[:, 0], H[:, 1:]
for i in xrange(H.shape[0]):
if b[i] != 0:
raise NotConeSpan(S)
return -A
def face_of_span(S):
"""
Returns the face matrix S^F of the span matrix S,
that is, a matrix such that
{x = S z, z >= 0} if and only if {S^F x <= 0}.
"""
V = hstack([zeros((S.shape[1], 1)), S.T])
# V-representation: first column is 0 for rays
V_cdd = Matrix(V, number_type=NUMBER_TYPE)
V_cdd.rep_type = RepType.GENERATOR
P = Polyhedron(V_cdd)
H = array(P.get_inequalities())
b, A = H[:, 0], H[:, 1:]
for i in xrange(H.shape[0]):
if b[i] != 0:
raise NotConeSpan(S)
return -A
