def _pm_expand(self, constr):
# Get objects
v = constr.left
v = vstack([v[i, 0] for i in range(0, v.shape[0])])
n = v.shape[0] - 1
x = vstack([v[0:n, 0]])
y = v[n, 0]
z = variable()
# One element
if n == 1:
return cvxpy_list([greater_equals(x, 0), greater_equals(x, y)])
# Get power of 2 size
m = 0
while np.log2(n + m) % 1 != 0:
m += 1
# Copy elements of x on a list and restrict them
constr_list = []
el_list = []
for i in range(0, n, 1):
el_list += [x[i, 0]]
if (not np.isscalar(x[i, 0]) and type(x[i, 0]) is not cvxpy_obj):
constr_list += [greater_equals(x[i, 0], 0)]
# Construct expansion
for i in range(0, m, 1):
el_list += [z]
while len(el_list) > 2:
new_list = []
for i in range(0, int(len(el_list) / 2)):
x1 = el_list[2 * i]
x2 = el_list[2 * i + 1]
w = variable()
constr_list += [
belongs(vstack((hstack((x1, w)), hstack((w, x2)))),
semidefinite_cone)
]
new_list += [w]
el_list = new_list
x1 = el_list[0]
x2 = el_list[1]
constr_list += [
belongs(vstack((hstack((x1, z)), hstack((z, x2)))),
semidefinite_cone)
]
constr_list += [greater_equals(z, 0), greater_equals(z, y)]
return cvxpy_list(constr_list)
def _pm_expand(self,constr):
# Get objects
v = constr.left
v = vstack([v[i,0] for i in range(0,v.shape[0])])
n = v.shape[0]-1
x = vstack([v[0:n,0]])
y = v[n,0]
z = variable()
# One element
if n==1:
return cvxpy_list([greater_equals(x,0),
greater_equals(x,y)])
# Get power of 2 size
m = 0
while np.log2(n+m) % 1 != 0:
m += 1
# Copy elements of x on a list and restrict them
constr_list = []
el_list = []
for i in range(0,n,1):
el_list+=[x[i,0]]
if (not np.isscalar(x[i,0]) and
type(x[i,0]) is not cvxpy_obj):
constr_list += [greater_equals(x[i,0],0)]
# Construct expansion
for i in range(0,m,1):
el_list += [z]
while len(el_list) > 2:
new_list = []
for i in range(0,int(len(el_list)/2)):
x1 = el_list[2*i]
x2 = el_list[2*i+1]
w = variable()
constr_list += [belongs(vstack((hstack((x1,w)),
hstack((w,x2)))),
semidefinite_cone)]
new_list += [w]
el_list = new_list
x1 = el_list[0]
x2 = el_list[1]
constr_list += [belongs(vstack((hstack((x1,z)),
hstack((z,x2)))),
semidefinite_cone)]
constr_list += [greater_equals(z,0),greater_equals(z,y)]
return cvxpy_list(constr_list)
def __call__(self, *arg):
# Check number of arguments
if len(arg) != 1:
raise ValueError("Invalid number of arguments")
# Extract argument
if type(arg[0]) is list:
x = hstack(arg[0])
else:
x = arg[0]
# Process
if type(x).__name__ in SCALAR_OBJS:
return x
elif type(x).__name__ in ARRAY_OBJS:
(m, n) = x.shape
if m != 1 and n != 1:
raise ValueError("Argument must be 1-Dimensional")
children = []
for i in range(0, m, 1):
for j in range(0, n, 1):
if np.isscalar(x[i, j]):
children += [cvxpy_obj(CONSTANT, x[i, j], str(x[i, j]))]
else:
children += [x[i, j]]
return cvxpy_tree(self, children)
else:
return np.max(x)
def __call__(self, *arg):
# Check number of arguments
if (len(arg) != 1):
raise ValueError('Invalid number of arguments')
# Extract argument
if (type(arg[0]) is list):
x = hstack(arg[0])
else:
x = arg[0]
# Process
if (type(x).__name__ in SCALAR_OBJS):
return x
elif (type(x).__name__ in ARRAY_OBJS):
(m, n) = x.shape
if (m != 1 and n != 1):
raise ValueError('Argument must be 1-Dimensional')
children = []
for i in range(0, m, 1):
for j in range(0, n, 1):
if (np.isscalar(x[i, j])):
children += [
cvxpy_obj(CONSTANT, x[i, j], str(x[i, j]))
]
else:
children += [x[i, j]]
return cvxpy_tree(self, children)
else:
return np.max(x)
def _pm_expand(self,constr):
# Get shape
v = constr.left
n = v.shape[0]-1
x = v[0:n,0]
y = v[n,0]
z = var()
# Get power of 2 size
m = 0
while (np.log2(n+m) % 1 != 0):
m = m + 1
# Copy elements of x on a list and restrict them
constr_list = []
el_list = []
for i in range(0,n,1):
el_list+=[x[i,0]]
if(not np.isscalar(x[i,0]) and
type(x[i,0]) is not cvxpy_obj):
constr_list += [greater(x[i,0],0)]
# Construct expansion
z = var()
for i in range(0,m,1):
el_list += [z]
while(len(el_list) > 2):
new_list = []
for i in range(0,len(el_list)/2):
x1 = el_list[2*i]
x2 = el_list[2*i+1]
w = var()
constr_list += [belongs(vstack((hstack((x1,w)),
hstack((w,x2)))),
sdc(2))]
new_list += [w]
el_list = new_list
x1 = el_list[0]
x2 = el_list[1]
constr_list += [belongs(vstack((hstack((x1,z)),
hstack((z,x2)))),
sdc(2))]
constr_list += [greater(z,0),greater(z,y)]
return cvxpy_list(constr_list)
def _pm_expand(self, constr):
# Get shape
v = constr.left
n = v.shape[0] - 1
x = v[0:n, 0]
y = v[n, 0]
z = var()
# Get power of 2 size
m = 0
while np.log2(n + m) % 1 != 0:
m = m + 1
# Copy elements of x on a list and restrict them
constr_list = []
el_list = []
for i in range(0, n, 1):
el_list += [x[i, 0]]
if not np.isscalar(x[i, 0]) and type(x[i, 0]) is not cvxpy_obj:
constr_list += [greater(x[i, 0], 0)]
# Construct expansion
z = var()
for i in range(0, m, 1):
el_list += [z]
while len(el_list) > 2:
new_list = []
for i in range(0, len(el_list) / 2):
x1 = el_list[2 * i]
x2 = el_list[2 * i + 1]
w = var()
constr_list += [belongs(vstack((hstack((x1, w)), hstack((w, x2)))), sdc(2))]
new_list += [w]
el_list = new_list
x1 = el_list[0]
x2 = el_list[1]
constr_list += [belongs(vstack((hstack((x1, z)), hstack((z, x2)))), sdc(2))]
constr_list += [greater(z, 0), greater(z, y)]
return cvxpy_list(constr_list)
def link_tt_heuristic(link): ff = link.l / link.fd.v q_max = (link.l / link.fd.q_max) * link.v_dens rho_hat = link.fd.rho_max - link.v_dens cong = link.l / link.fd.w * (link.fd.rho_max * quad_over_lin(1.0 , rho_hat) - 1) return cvx_max(hstack([ff, q_max, cong]))