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 _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 re_eval(arg,replace_map):
"""
Re-evaluates argument.
:param replace_map: Dictionary.
"""
# Number
if np.isscalar(arg):
return arg
# Constant object
elif type(arg) is cvxpy_obj:
return arg.value
# Scalar variable
elif type(arg) is cvxpy_scalar_var:
if arg in replace_map.keys():
return re_eval(replace_map[arg],replace_map)
else:
return arg
# Scalar param
elif type(arg) is cvxpy_scalar_param:
if arg in replace_map.keys():
return re_eval(replace_map[arg],replace_map)
else:
return arg
# Summation
elif (type(arg) is cvxpy_tree and
arg.item.type == OPERATOR and
arg.item.name == SUMMATION):
new_children = list(map(lambda x:re_eval(x,replace_map),arg.children))
return sum(new_children)
# Multiplication
elif (type(arg) is cvxpy_tree and
arg.item.type == OPERATOR and
arg.item.name == MULTIPLICATION):
child1 = re_eval(arg.children[0],replace_map)
child2 = re_eval(arg.children[1],replace_map)
return child1*child2
# Function
elif (type(arg) is cvxpy_tree and
arg.item.type == FUNCTION):
new_children = list(map(lambda x:re_eval(x,replace_map),arg.children))
return arg.item(new_children)
# Constraint
elif type(arg) is cvxpy_constr:
# Not set membership
if arg.type != BELONGS:
left = re_eval(arg.left ,replace_map)
right= re_eval(arg.right,replace_map)
if arg.type == EQUALS:
return equals(left,right)
elif arg.type == LESS_EQUALS:
return less_equals(left,right)
elif arg.type == GREATER_EQUALS:
return greater_equals(left,right)
else:
raise TypeError('Invalid constraint')
# Set membership
else:
left = re_eval(arg.left,replace_map)
return belongs(left,arg.right)
# Array
elif (type(arg) is cvxpy_array or
type(arg) is cvxpy_var or
type(arg) is cvxpy_param):
(m,n) = arg.shape
new_ar = cvxpy_array(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
new_ar[i,j] = re_eval(arg[i,j],replace_map)
return new_ar
# List
elif (type(arg) is list or
type(arg) is cvxpy_list):
new_list = []
for c in arg:
new_list += [re_eval(c,replace_map)]
return cvxpy_list(new_list)
# Invalid
else:
raise TypeError('Invalid argument')
def re_eval(arg,param_map):
"""
Description
-----------
Replaces parameters found in arg using the param_map
and re-evaluates the resulting object.
Arguments
---------
arg: Argument to be re-evaluated.
param_map: Dictionery that maps the parameters
to objects.
"""
# Number
if(np.isscalar(arg)):
return arg
# Constant object
elif(type(arg) is cvxpy_obj):
return arg.get_value()
# Scalar variable
elif(type(arg) is cvxpy_scalar_var):
return arg
# Scalar param
elif(type(arg) is cvxpy_scalar_param):
return re_eval(param_map[arg],param_map)
# Summation
elif(type(arg) is cvxpy_tree and arg.item.name == '+'):
new_children = map(lambda x:re_eval(x,param_map),arg.children)
return sum(new_children)
# Multiplication
elif(type(arg) is cvxpy_tree and arg.item.name == '*'):
child1 = re_eval(arg.children[0],param_map)
child2 = re_eval(arg.children[1],param_map)
return child1*child2
# Function
elif(type(arg) is cvxpy_tree and arg.item.type == FUNCTION):
new_children = map(lambda x:re_eval(x,param_map),arg.children)
return arg.item(new_children)
# Constraint
elif(type(arg) is cvxpy_constr):
# Not set membership
if(arg.op != 'in'):
left = re_eval(arg.left ,param_map)
right= re_eval(arg.right,param_map)
if(arg.op == '=='):
return equal(left,right)
elif(arg.op == '<='):
return less(left,right)
else:
return greater(left,right)
# Set membership
else:
left = re_eval(arg.left,param_map)
return belongs(left,arg.right)
# Array
elif(type(arg) is cvxpy_expression or
type(arg) is cvxpy_var or
type(arg) is cvxpy_param):
(m,n) = arg.shape
new_exp = cvxpy_expression(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
new_exp[i,j] = re_eval(arg[i,j],param_map)
return new_exp
# List
elif(type(arg) is cvxpy_list):
new_list = cvxpy_list([])
for c in arg:
new_list += cvxpy_list([re_eval(c,param_map)])
return new_list
# Invalid
else:
raise ValueError('Invalid argument')