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 _solve_isolating(self, *args):
"""
Description
-----------
Isolate parameters and then solve program.
Used by linearize method to obtain subgradient.
Arguments must be numbers. A very important
point is that solve_isolating introduces
equality constraints and places them at the
beginning of the constraint list. This is
later used to construct the subgradient.
"""
# Process input
if (len(args) != 0 and type(args[0]) is list):
args = args[0]
# Create argument list
arg_list = []
for arg in args:
if (np.isscalar(arg)):
arg_list += [arg]
elif (type(arg) is cvxpy_matrix):
(m, n) = arg.shape
for i in range(0, m, 1):
for j in range(0, n, 1):
arg_list += [arg[i, j]]
else:
raise ValueError('Arguments must be numeric')
# Check number of arguments
if (len(arg_list) != len(self.params)):
raise ValueError('Invalid number of arguments')
# Isolate parameters
p1_map = {}
new_constr = cvxpy_list([])
for p in self.params:
v = var('v_' + p.name)
p1_map[p] = v
new_constr += cvxpy_list([equal(v, p)])
new_p1 = prog((self.action, re_eval(self.obj, p1_map)),
new_constr + re_eval(self.constr, p1_map), self.params,
self.options, self.name)
# Substitute parameters with arguments
p2_map = {}
for k in range(0, len(arg_list), 1):
p2_map[new_p1.params[k]] = arg_list[k]
new_p2 = prog((new_p1.action, re_eval(new_p1.obj, p2_map)),
re_eval(new_p1.constr, p2_map), [], new_p1.options,
new_p1.name)
# Solve program
obj, lagrange_mul_eq = solve_prog(new_p2)
self.lagrange_mul_eq = lagrange_mul_eq
return obj
def _solve_isolating(self,*args):
"""
Description
-----------
Isolate parameters and then solve program.
Used by linearize method to obtain subgradient.
Arguments must be numbers. A very important
point is that solve_isolating introduces
equality constraints and places them at the
beginning of the constraint list. This is
later used to construct the subgradient.
"""
# Process input
if(len(args) != 0 and type(args[0]) is list):
args = args[0]
# Create argument list
arg_list = []
for arg in args:
if(np.isscalar(arg)):
arg_list += [arg]
elif(type(arg) is cvxpy_matrix):
(m,n) = arg.shape
for i in range(0,m,1):
for j in range(0,n,1):
arg_list += [arg[i,j]]
else:
raise ValueError('Arguments must be numeric')
# Check number of arguments
if(len(arg_list) != len(self.params)):
raise ValueError('Invalid number of arguments')
# Isolate parameters
p1_map = {}
new_constr = cvxpy_list([])
for p in self.params:
v = var('v_'+p.name)
p1_map[p] = v
new_constr += cvxpy_list([equal(v,p)])
new_p1 = prog((self.action,re_eval(self.obj,p1_map)),
new_constr+re_eval(self.constr,p1_map),
self.params, self.options,self.name)
# Substitute parameters with arguments
p2_map = {}
for k in range(0,len(arg_list),1):
p2_map[new_p1.params[k]] = arg_list[k]
new_p2 = prog((new_p1.action,re_eval(new_p1.obj,p2_map)),
re_eval(new_p1.constr,p2_map),
[],new_p1.options,new_p1.name)
# Solve program
obj,lagrange_mul_eq = solve_prog(new_p2)
self.lagrange_mul_eq = lagrange_mul_eq
return obj
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 expand(arg):
# Constant
if(type(arg) is cvxpy_obj):
return arg,cvxpy_list([])
# Scalar variable
elif(type(arg) is cvxpy_scalar_var):
return arg,cvxpy_list([])
# Summation
elif(type(arg) is cvxpy_tree and arg.item.name == '+'):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Expand children
new_children = []
new_constr = cvxpy_list([])
for child in children:
# Multiplication
if(child.type == TREE and
child.item.name == '*'):
child_var,child_constr = expand(child.children[1])
new_children += [child.children[0].data*child_var]
new_constr += child_constr
# Else
else:
child_var,child_constr = expand(child)
new_children += [child_var]
new_constr += child_constr
# Return (Always right side is the new variable)
new_tree = cvxpy_tree(item,new_children)
return v,cvxpy_list([equal(new_tree,v)])+new_constr
# Multiplication
elif(type(arg) is cvxpy_tree and arg.item.name == '*'):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Apply expand to second operand (first is a constant)
child_var,child_constr = expand(children[1])
# Return result (Always right side is the new variable)
new_tree = cvxpy_tree(item,[children[0],child_var])
new_eq = cvxpy_list([equal(new_tree,v)])
new_eq += child_constr
return v,new_eq
# Function
elif(type(arg) is cvxpy_tree and arg.item.type == FUNCTION):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Analyze children
new_children = []
new_constr = cvxpy_list([])
for child in children:
child_var,child_constr = expand(child)
new_children += [child_var]
new_constr += child_constr
# Return (Always right side is the new variable)
new_tree = cvxpy_tree(item,new_children)
new_constr += item._range_constr(v)
new_constr += item._dom_constr(new_children)
return v,cvxpy_list([equal(new_tree,v)])+new_constr
# Constraint
elif(type(arg) is cvxpy_constr):
# Not set membership
if(arg.op != 'in'):
# Apply expand to left and right side
obj1,constr_list1 = expand(arg.left)
obj2,constr_list2 = expand(arg.right)
# Return new constraints
new_constr = cvxpy_constr(obj1,arg.op,obj2)
new_list = cvxpy_list([new_constr])
new_list += constr_list1
new_list += constr_list2
return new_list
# Set membership
else:
obj, constr_list = expand(arg.left)
new_constr = cvxpy_constr(obj,arg.op,arg.right)
return cvxpy_list([new_constr])+constr_list
# Array
elif(type(arg) is cvxpy_expression or
type(arg) is cvxpy_var):
(m,n) = arg.shape
new_list = cvxpy_list([])
new_exp = cvxpy_expression(m,n)
for i in range(0,m,1):
for j in range(0,n,1):
# Number: Upgrade
if(np.isscalar(arg[i,j])):
new_exp[i,j] = cvxpy_obj(CONSTANT,arg[i,j],str(arg[i,j]))
# Not a number
else:
obj,constr_list = expand(arg[i,j])
new_exp[i,j] = obj
new_list += constr_list
return new_exp,new_list
# List of constraints
elif(type(arg) is cvxpy_list):
# Empty list
if(len(arg) == 0):
return cvxpy_list([])
else:
new_list = map(expand,arg)
return reduce(lambda x,y:x+y,new_list)
# Invalid
else:
raise ValueError('Invalid argument')
def expand(arg):
# Constant
if (type(arg) is cvxpy_obj):
return arg, cvxpy_list([])
# Scalar variable
elif (type(arg) is cvxpy_scalar_var):
return arg, cvxpy_list([])
# Summation
elif (type(arg) is cvxpy_tree and arg.item.name == '+'):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Expand children
new_children = []
new_constr = cvxpy_list([])
for child in children:
# Multiplication
if (child.type == TREE and child.item.name == '*'):
child_var, child_constr = expand(child.children[1])
new_children += [child.children[0].data * child_var]
new_constr += child_constr
# Else
else:
child_var, child_constr = expand(child)
new_children += [child_var]
new_constr += child_constr
# Return (Always right side is the new variable)
new_tree = cvxpy_tree(item, new_children)
return v, cvxpy_list([equal(new_tree, v)]) + new_constr
# Multiplication
elif (type(arg) is cvxpy_tree and arg.item.name == '*'):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Apply expand to second operand (first is a constant)
child_var, child_constr = expand(children[1])
# Return result (Always right side is the new variable)
new_tree = cvxpy_tree(item, [children[0], child_var])
new_eq = cvxpy_list([equal(new_tree, v)])
new_eq += child_constr
return v, new_eq
# Function
elif (type(arg) is cvxpy_tree and arg.item.type == FUNCTION):
# Get item and children
item = arg.item
children = arg.children
# New var
v = var()
# Analyze children
new_children = []
new_constr = cvxpy_list([])
for child in children:
child_var, child_constr = expand(child)
new_children += [child_var]
new_constr += child_constr
# Return (Always right side is the new variable)
new_tree = cvxpy_tree(item, new_children)
new_constr += item._range_constr(v)
new_constr += item._dom_constr(new_children)
return v, cvxpy_list([equal(new_tree, v)]) + new_constr
# Constraint
elif (type(arg) is cvxpy_constr):
# Not set membership
if (arg.op != 'in'):
# Apply expand to left and right side
obj1, constr_list1 = expand(arg.left)
obj2, constr_list2 = expand(arg.right)
# Return new constraints
new_constr = cvxpy_constr(obj1, arg.op, obj2)
new_list = cvxpy_list([new_constr])
new_list += constr_list1
new_list += constr_list2
return new_list
# Set membership
else:
obj, constr_list = expand(arg.left)
new_constr = cvxpy_constr(obj, arg.op, arg.right)
return cvxpy_list([new_constr]) + constr_list
# Array
elif (type(arg) is cvxpy_expression or type(arg) is cvxpy_var):
(m, n) = arg.shape
new_list = cvxpy_list([])
new_exp = cvxpy_expression(m, n)
for i in range(0, m, 1):
for j in range(0, n, 1):
# Number: Upgrade
if (np.isscalar(arg[i, j])):
new_exp[i, j] = cvxpy_obj(CONSTANT, arg[i, j],
str(arg[i, j]))
# Not a number
else:
obj, constr_list = expand(arg[i, j])
new_exp[i, j] = obj
new_list += constr_list
return new_exp, new_list
# List of constraints
elif (type(arg) is cvxpy_list):
# Empty list
if (len(arg) == 0):
return cvxpy_list([])
else:
new_list = map(expand, arg)
return reduce(lambda x, y: x + y, new_list)
# Invalid
else:
raise ValueError('Invalid argument')