def compare(obj1, constraint_type, obj2):
"""
Compares obj1 with obj2.
:param obj1: Left hand side obejct.
:param constraint_type: Keyword (See cvxpy.defs.).
:param obj2: Right hand side object.
"""
# Both scalars
if ((np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS)
and (np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
# Upgrade scalars to cvxpy_obj
if np.isscalar(obj1):
obj1 = cvxpy_obj(CONSTANT, obj1, str(obj1))
if np.isscalar(obj2):
obj2 = cvxpy_obj(CONSTANT, obj2, str(obj2))
# Construct and return constraint
return cvxpy_constr(obj1, constraint_type, obj2)
# Upgrate scalars to arrays
if ((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS)
and (np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
(m, n) = obj1.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] = obj2
obj2 = new_ar
if ((type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS)
and (np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS)):
(m, n) = obj2.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] = obj1
obj1 = new_ar
# Both arrays
if ((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS) and
(type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS)):
constr = []
if obj1.shape != obj2.shape:
raise ValueError('Invalid dimensions')
(m, n) = obj1.shape
for i in range(0, m, 1):
for j in range(0, n, 1):
constr += [compare(obj1[i, j], constraint_type, obj2[i, j])]
return cvxpy_list(constr)
# Invalid arguments
raise TypeError('Objects not comparable')
def compare(obj1,constraint_type,obj2):
"""
Compares obj1 with obj2.
:param obj1: Left hand side obejct.
:param constraint_type: Keyword (See cvxpy.defs.).
:param obj2: Right hand side object.
"""
# Both scalars
if ((np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS) and
(np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
# Upgrade scalars to cvxpy_obj
if np.isscalar(obj1):
obj1 = cvxpy_obj(CONSTANT,obj1,str(obj1))
if np.isscalar(obj2):
obj2 = cvxpy_obj(CONSTANT,obj2,str(obj2))
# Construct and return constraint
return cvxpy_constr(obj1,constraint_type,obj2)
# Upgrate scalars to arrays
if ((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS) and
(np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
(m,n) = obj1.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] = obj2
obj2 = new_ar
if ((type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS) and
(np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS)):
(m,n) = obj2.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] = obj1
obj1 = new_ar
# Both arrays
if ((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS) and
(type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS)):
constr = []
if obj1.shape != obj2.shape:
raise ValueError('Invalid dimensions')
(m,n) = obj1.shape
for i in range(0,m,1):
for j in range(0,n,1):
constr += [compare(obj1[i,j],constraint_type,obj2[i,j])]
return cvxpy_list(constr)
# Invalid arguments
raise TypeError('Objects not comparable')
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 prog(pair, constr=[], params=[], opt=None, name='prog'):
"""
Create an optimization program.
:param pair: (MAXIMIZE or MINIMIZE, objective)
:param constr: List of :class:`cvxpy_constr` or :class:`cvxpy_list`.
:param params: List of :class:`cvxpy_scalar_param` or
:class:`cvxpy_param`. This list must match the number
of parameters present in the program.
:param opt: Dictionary of options.
:param name: Program name string.
:rtype: :class:`cvxpy_program`.
"""
# Parameters
action = pair[0]
obj = pair[1]
# Verify objective
if ((not np.isscalar(obj)) and (not type(obj) is cvxpy_obj)
and type(obj).__name__ not in SCALAR_OBJS):
raise ValueError('Invalid Objective')
# Upgrade numeric objective to scalar object
if (np.isscalar(obj)):
obj = cvxpy_obj(CONSTANT, obj, str(obj))
# Return program
return cvxpy_program(action, obj, constr, params, opt, name)
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 prog(pair,constr=[],params=[],opt=None,name='prog'):
"""
Create an optimization program.
:param pair: (MAXIMIZE or MINIMIZE, objective)
:param constr: List of :class:`cvxpy_constr` or :class:`cvxpy_list`.
:param params: List of :class:`cvxpy_scalar_param` or
:class:`cvxpy_param`. This list must match the number
of parameters present in the program.
:param opt: Dictionary of options.
:param name: Program name string.
:rtype: :class:`cvxpy_program`.
"""
# Parameters
action = pair[0]
obj = pair[1]
# Verify objective
if((not np.isscalar(obj)) and
(not type(obj) is cvxpy_obj) and
type(obj).__name__ not in SCALAR_OBJS):
raise ValueError('Invalid Objective')
# Upgrade numeric objective to scalar object
if(np.isscalar(obj)):
obj = cvxpy_obj(CONSTANT,obj,str(obj))
# Return program
return cvxpy_program(action,obj,constr,params,opt,name)
def compare(obj1, op, obj2):
# Both scalars
if ((np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS)
and (np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
# Upgrade scalars to cvxpy_obj
if (np.isscalar(obj1)):
obj1 = cvxpy_obj(CONSTANT, obj1, str(obj1))
if (np.isscalar(obj2)):
obj2 = cvxpy_obj(CONSTANT, obj2, str(obj2))
# Construct and return constraint
return cvxpy_constr(obj1, op, obj2)
# Upgrate scalars to arrays
if ((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS)
and (np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
(m, n) = obj1.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] = obj2
obj2 = new_exp
if ((type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS)
and (np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS)):
(m, n) = obj2.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] = obj1
obj1 = new_exp
# Both arrays
if ((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS) and
(type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS)):
constr = []
if (obj1.shape != obj2.shape):
raise ValueError('Invalid dimensions')
(m, n) = obj1.shape
for i in range(0, m, 1):
for j in range(0, n, 1):
constr += [compare(obj1[i, j], op, obj2[i, j])]
return cvxpy_list(constr)
# Invalid arguments
raise ValueError('Objects not comparable')
def compare(obj1,op,obj2):
# Both scalars
if((np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS) and
(np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
# Upgrade scalars to cvxpy_obj
if(np.isscalar(obj1)):
obj1 = cvxpy_obj(CONSTANT,obj1,str(obj1))
if(np.isscalar(obj2)):
obj2 = cvxpy_obj(CONSTANT,obj2,str(obj2))
# Construct and return constraint
return cvxpy_constr(obj1,op,obj2)
# Upgrate scalars to arrays
if((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS) and
(np.isscalar(obj2) or type(obj2).__name__ in SCALAR_OBJS)):
(m,n) = obj1.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] = obj2
obj2 = new_exp
if((type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS) and
(np.isscalar(obj1) or type(obj1).__name__ in SCALAR_OBJS)):
(m,n) = obj2.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] = obj1
obj1 = new_exp
# Both arrays
if((type(obj1) is cvxpy_matrix or type(obj1).__name__ in ARRAY_OBJS) and
(type(obj2) is cvxpy_matrix or type(obj2).__name__ in ARRAY_OBJS)):
constr = []
if(obj1.shape != obj2.shape):
raise ValueError('Invalid dimensions')
(m,n) = obj1.shape
for i in range(0,m,1):
for j in range(0,n,1):
constr += [compare(obj1[i,j],op,obj2[i,j])]
return cvxpy_list(constr)
# Invalid arguments
raise ValueError('Objects not comparable')
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')
def __call__(self, *args):
"""
Description
-----------
Call program with specified arguments.
Parameters are substituted with arguments.
If all arguments are numeric, the resulting
optimization program is solved. If some
arguments are object, a tree is returned.
Arguments
---------
args: List of arguments.
(Can be numbers or objects)
"""
# 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) or type(arg).__name__ in SCALAR_OBJS):
arg_list += [arg]
elif (type(arg) is cvxpy_matrix
or type(arg).__name__ in ARRAY_OBJS):
(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('Invalid argument type')
# Check number of arguments
if (len(arg_list) != len(self.params)):
raise ValueError('Invalid argument syntax')
# Solve if numeric
if (len(arg_list) == 0
or reduce(lambda x, y: x and y,
map(lambda x: np.isscalar(x), arg_list))):
# Substitute parameters with arguments
p1_map = {}
for k in range(0, len(arg_list), 1):
p1_map[self.params[k]] = arg_list[k]
new_p = prog((self.action, re_eval(self.obj, p1_map)),
re_eval(self.constr, p1_map), [], self.options,
self.name)
# Solve program
obj, lagrange_mul_eq = solve_prog(new_p)
return obj
# Upgrade numbers to objects
for i in range(0, len(arg_list), 1):
if (np.isscalar(arg_list[i])):
arg_list[i] = cvxpy_obj(CONSTANT, arg_list[i],
str(arg_list[i]))
# Return tree
return cvxpy_tree(self, arg_list)
def __call__(self,*args):
"""
Description
-----------
Call program with specified arguments.
Parameters are substituted with arguments.
If all arguments are numeric, the resulting
optimization program is solved. If some
arguments are object, a tree is returned.
Arguments
---------
args: List of arguments.
(Can be numbers or objects)
"""
# 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) or
type(arg).__name__ in SCALAR_OBJS):
arg_list += [arg]
elif(type(arg) is cvxpy_matrix or
type(arg).__name__ in ARRAY_OBJS):
(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('Invalid argument type')
# Check number of arguments
if(len(arg_list) != len(self.params)):
raise ValueError('Invalid argument syntax')
# Solve if numeric
if(len(arg_list) == 0 or
reduce(lambda x,y: x and y,
map(lambda x: np.isscalar(x),arg_list))):
# Substitute parameters with arguments
p1_map = {}
for k in range(0,len(arg_list),1):
p1_map[self.params[k]] = arg_list[k]
new_p = prog((self.action,re_eval(self.obj,p1_map)),
re_eval(self.constr,p1_map),[],
self.options,self.name)
# Solve program
obj,lagrange_mul_eq = solve_prog(new_p)
return obj
# Upgrade numbers to objects
for i in range(0,len(arg_list),1):
if(np.isscalar(arg_list[i])):
arg_list[i] = cvxpy_obj(CONSTANT,
arg_list[i],
str(arg_list[i]))
# Return tree
return cvxpy_tree(self,arg_list)