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 transform(constr_list):
"""
Description
-----------
Transforms nonlinear equality constraints
to equivalent form involving two inequalities.
Arguments
---------
constr_list: cvxpy_list of constraints in
expanded form so that all nonlinear constraints
are equalities.
"""
# New list
new_list = cvxpy_list([])
# Transform
for constr in constr_list:
# Function
if (constr.left.type == TREE and constr.left.item.type == FUNCTION):
# Get function
fn = constr.left.item
# Get equivalent transformation
new_constr = cvxpy_list([
less(constr.left, constr.right),
greater(constr.left, constr.right)
])
# Append
new_list += cvxpy_list(new_constr)
# Not a function
else:
# Append
new_list += cvxpy_list([constr])
# Return transformed list
return new_list
def transform(constr_list):
"""
Description
-----------
Transforms nonlinear equality constraints
to equivalent form involving two inequalities.
Arguments
---------
constr_list: cvxpy_list of constraints in
expanded form so that all nonlinear constraints
are equalities.
"""
# New list
new_list = cvxpy_list([])
# Transform
for constr in constr_list:
# Function
if(constr.left.type == TREE and
constr.left.item.type == FUNCTION):
# Get function
fn = constr.left.item
# Get equivalent transformation
new_constr = cvxpy_list([less(constr.left,constr.right),
greater(constr.left,constr.right)])
# Append
new_list += cvxpy_list(new_constr)
# Not a function
else:
# Append
new_list += cvxpy_list([constr])
# Return transformed list
return new_list
def _pm_expand(self,constr):
"""
Description
-----------
Given the constraint, which must be in the form
self(args) operator variable, the parameters
are replaced with arguments and then the
partial minimization description of the program
is merged with the constraint.
Argument
--------
constr: cvxpy_constr of the form self(args)
operator variable.
"""
# Get arguments
args = constr.left.children
# Create arg-param map by position
p_map = {}
for k in range(0,len(args),1):
p_map[self.params[k]] = args[k]
# Create new program
new_p = prog((self.action,re_eval(self.obj,p_map)),
re_eval(self.constr,p_map),[],
self.options,self.name)
# Expand partial minimization
right = constr.right
new_constr = []
if(self.curvature == CONVEX):
new_constr += [less(new_p.obj,right)]
else:
new_constr += [greater(new_p.obj,right)]
new_constr += new_p.constr
# Return constraints
return cvxpy_list(new_constr)
def _pm_expand(self, constr):
"""
Description
-----------
Given the constraint, which must be in the form
self(args) operator variable, the parameters
are replaced with arguments and then the
partial minimization description of the program
is merged with the constraint.
Argument
--------
constr: cvxpy_constr of the form self(args)
operator variable.
"""
# Get arguments
args = constr.left.children
# Create arg-param map by position
p_map = {}
for k in range(0, len(args), 1):
p_map[self.params[k]] = args[k]
# Create new program
new_p = prog((self.action, re_eval(self.obj, p_map)),
re_eval(self.constr, p_map), [], self.options, self.name)
# Expand partial minimization
right = constr.right
new_constr = []
if (self.curvature == CONVEX):
new_constr += [less(new_p.obj, right)]
else:
new_constr += [greater(new_p.obj, right)]
new_constr += new_p.constr
# Return constraints
return cvxpy_list(new_constr)
def _range_constr(self, v):
return cvxpy_list([greater(v,0)])
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')
def _range_constr(self, v):
return cvxpy_list([greater(v, 0)])
def _dom_constr(self,args):
arg = args[0]
return cvxpy_list([greater(arg,0)])
def _dom_constr(self, args):
arg = args[0]
return cvxpy_list([greater(arg, 0)])
