def solve(self, quiet=False, return_status=False):
"""
Solves optimization program using current
parameter values.
"""
# Check DCP
if not self.is_dcp():
raise ValueError('Program is not DCP')
# Create param-value map
replace_map = {}
for param in self.parameters:
if np.isnan(param.value):
raise ValueError('Invalid parameter value: NaN')
else:
replace_map[param] = param.value
# Create new program
new_p = cvxpy_program(self.action, re_eval(self.objective,
replace_map),
re_eval(self.constraints, replace_map), [],
self.options, '')
# Solve new program
obj, valid = solve_prog(new_p, quiet)
if return_status:
return obj, valid
else:
return obj
def solve(self,quiet=False,return_status=False):
"""
Solves optimization program using current
parameter values.
"""
# Check DCP
if not self.is_dcp():
raise ValueError('Program is not DCP')
# Create param-value map
replace_map = {}
for param in self.parameters:
if np.isnan(param.value):
raise ValueError('Invalid parameter value: NaN')
else:
replace_map[param] = param.value
# Create new program
new_p = cvxpy_program(self.action,
re_eval(self.objective,replace_map),
re_eval(self.constraints,replace_map),
[],self.options,'')
# Solve new program
obj,valid = solve_prog(new_p,quiet)
if return_status:
return obj,valid
else:
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 _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 is_dcp(self,args=None):
"""
Description
-----------
Checks if the program follows DCP rules.
If args is None, the check is done on the
body of the program. If args is a list of
arguments, the parameters are replaced
with the arguments and the check is done
on the resulting program. This function
is called with a list of arguments when
cvxpy_tree.is_dcp is executed.
Arguments
---------
args: List of arguments
"""
# No arguments: Check body of program
if(args == None):
if(self.action == MINIMIZE and
not self.obj.is_convex()):
return False
elif(self.action == MAXIMIZE and
not self.obj.is_concave()):
return False
else:
return self.constr.is_dcp()
# Arguments given: Replace parameters and then check
else:
# Check if some argument has parameters
if(len(cvxpy_list(args).get_params()) != 0):
return False
# Create a param-arg map
p_map = {}
for k in range(0,len(args),1):
p_map[self.params[k]] = args[k]
# Re-evaluate
new_p = prog((self.action,re_eval(self.obj,p_map)),
re_eval(self.constr,p_map))
# Check dcp on resulting program
return new_p.is_dcp()
def is_dcp(self, args=None):
"""
Description
-----------
Checks if the program follows DCP rules.
If args is None, the check is done on the
body of the program. If args is a list of
arguments, the parameters are replaced
with the arguments and the check is done
on the resulting program. This function
is called with a list of arguments when
cvxpy_tree.is_dcp is executed.
Arguments
---------
args: List of arguments
"""
# No arguments: Check body of program
if (args == None):
if (self.action == MINIMIZE and not self.obj.is_convex()):
return False
elif (self.action == MAXIMIZE and not self.obj.is_concave()):
return False
else:
return self.constr.is_dcp()
# Arguments given: Replace parameters and then check
else:
# Check if some argument has parameters
if (len(cvxpy_list(args).get_params()) != 0):
return False
# Create a param-arg map
p_map = {}
for k in range(0, len(args), 1):
p_map[self.params[k]] = args[k]
# Re-evaluate
new_p = prog((self.action, re_eval(self.obj, p_map)),
re_eval(self.constr, p_map))
# Check dcp on resulting program
return new_p.is_dcp()
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 _pm_expand(self,constr):
"""
Returns constraints that embed the program into
the parent program.
:param constr: cvxpy_constr of the form
self(args), comparison-type, variable.
"""
# Get arguments
args = constr.left.children
# Create argument reference list
args_ref = self._get_expanded_objects(self.formals)
# Check number of arguments
if len(args) != len(args_ref):
raise TypeError("Invalid number of arguments")
# Create map and new program
replace_map = {}
for k in range(0,len(args),1):
replace_map[args_ref[k]] = args[k]
new_p = cvxpy_program(self.action,
re_eval(self.objective,replace_map),
re_eval(self.constraints,replace_map),
[],self.options,'')
# Embed
right = constr.right
new_constr = []
if self.action == MINIMIZE:
new_constr += [compare(new_p.objective,LESS_EQUALS,right)]
else:
new_constr += [compare(new_p.objective,GREATER_EQUALS,right)]
new_constr += new_p.constraints
# Return constraints
return new_constr
def is_dcp(self,args=None):
"""
Determines if program is DCP-compliant.
:param args: List of scalar arguments.
"""
# No arguments: Check body of program
if args == None:
if (self.action == MINIMIZE and
not self.objective.is_convex()):
return False
elif (self.action == MAXIMIZE and
not self.objective.is_concave()):
return False
else:
return self.constraints.is_dcp()
# Arguments given: Replace arguments and then check
else:
# Create reference list of arguments
args_ref = self._get_expanded_objects(self.formals)
# Check number of arguments
if len(args) != len(args_ref):
raise TypeError('Invalid number of arguments')
# Create map and new program
replace_map = {}
for k in range(0,len(args),1):
replace_map[args_ref[k]] = args[k]
new_p = cvxpy_program(self.action,
re_eval(self.objective,replace_map),
re_eval(self.constraints,replace_map),
[],self.options,'')
# Check dcp on resulting program
return new_p.is_dcp()
def _pm_expand(self, constr):
"""
Returns constraints that embed the program into
the parent program.
:param constr: cvxpy_constr of the form
self(args), comparison-type, variable.
"""
# Get arguments
args = constr.left.children
# Create argument reference list
args_ref = self._get_expanded_objects(self.formals)
# Check number of arguments
if len(args) != len(args_ref):
raise TypeError("Invalid number of arguments")
# Create map and new program
replace_map = {}
for k in range(0, len(args), 1):
replace_map[args_ref[k]] = args[k]
new_p = cvxpy_program(self.action, re_eval(self.objective,
replace_map),
re_eval(self.constraints, replace_map), [],
self.options, '')
# Embed
right = constr.right
new_constr = []
if self.action == MINIMIZE:
new_constr += [compare(new_p.objective, LESS_EQUALS, right)]
else:
new_constr += [compare(new_p.objective, GREATER_EQUALS, right)]
new_constr += new_p.constraints
# Return constraints
return new_constr
def is_dcp(self, args=None):
"""
Determines if program is DCP-compliant.
:param args: List of scalar arguments.
"""
# No arguments: Check body of program
if args == None:
if (self.action == MINIMIZE and not self.objective.is_convex()):
return False
elif (self.action == MAXIMIZE and not self.objective.is_concave()):
return False
else:
return self.constraints.is_dcp()
# Arguments given: Replace arguments and then check
else:
# Create reference list of arguments
args_ref = self._get_expanded_objects(self.formals)
# Check number of arguments
if len(args) != len(args_ref):
raise TypeError('Invalid number of arguments')
# Create map and new program
replace_map = {}
for k in range(0, len(args), 1):
replace_map[args_ref[k]] = args[k]
new_p = cvxpy_program(self.action,
re_eval(self.objective, replace_map),
re_eval(self.constraints, replace_map), [],
self.options, '')
# Check dcp on resulting program
return new_p.is_dcp()
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):
"""
Invokes program.
:param args: List of arguments.
"""
# Get arguments reference
args_ref = self._get_expanded_objects(self.formals)
# Internal call
if len(args) == 1 and type(args[0]) is list:
# Get list of arguments
args_list = args[0]
# Check number of arguments
if len(args_list) != len(args_ref):
raise TypeError('Invalid number of arguments')
# User call
else:
# Check number of arguments
if len(args) != len(self.formals):
raise TypeError('Invalid number of arguments')
# Check syntax
for i in range(0,len(args),1):
if (np.isscalar(args[i]) or
type(args[i]).__name__ in SCALAR_OBJS):
if self.formals[i].shape != (1,1):
raise ValueError('Invalid argument shape')
elif (type(args[i]) is cvxpy_matrix or
type(args[i]).__name__ in ARRAY_OBJS):
if self.formals[i].shape != args[i].shape:
raise ValueError('Invalid argument shape')
else:
raise TypeError('Invalid argument')
# Expand arguments
args_list = self._get_expanded_objects(args)
# Verify values
for i in range(0,len(args_ref)):
if np.isscalar(args_list[i]) and np.isnan(args_list[i]):
raise ValueError('Invalid argument value: NaN')
# Upgrade scalars to objects
args_upgraded = self._upgrade_scalars(args_list)
# Verify replacements
for i in range(0,len(args_ref)):
if (len(args_upgraded[i].variables) != 0 and
type(args_ref[i]) is not cvxpy_scalar_var):
raise TypeError('Invalid replacement')
# All numeric
if all(list(map(lambda x: type(x) is cvxpy_obj,args_upgraded))):
# Create map and new program
replace_map = {}
for i in range(0,len(args_ref),1):
replace_map[args_ref[i]] = args_upgraded[i]
new_p = cvxpy_program(self.action,
re_eval(self.objective,replace_map),
re_eval(self.constraints,replace_map),
[],self.options,'')
# Solve
obj,valid = new_p.solve(quiet=True,return_status=True)
if not valid:
raise ValueError('Unable to compute value')
else:
return obj
# Not all numeric
else:
# Return expression tree
return cvxpy_tree(self,args_upgraded)
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):
"""
Invokes program.
:param args: List of arguments.
"""
# Get arguments reference
args_ref = self._get_expanded_objects(self.formals)
# Internal call
if len(args) == 1 and type(args[0]) is list:
# Get list of arguments
args_list = args[0]
# Check number of arguments
if len(args_list) != len(args_ref):
raise TypeError('Invalid number of arguments')
# User call
else:
# Check number of arguments
if len(args) != len(self.formals):
raise TypeError('Invalid number of arguments')
# Check syntax
for i in range(0, len(args), 1):
if (np.isscalar(args[i])
or type(args[i]).__name__ in SCALAR_OBJS):
if self.formals[i].shape != (1, 1):
raise ValueError('Invalid argument shape')
elif (type(args[i]) is cvxpy_matrix
or type(args[i]).__name__ in ARRAY_OBJS):
if self.formals[i].shape != args[i].shape:
raise ValueError('Invalid argument shape')
else:
raise TypeError('Invalid argument')
# Expand arguments
args_list = self._get_expanded_objects(args)
# Verify values
for i in range(0, len(args_ref)):
if np.isscalar(args_list[i]) and np.isnan(args_list[i]):
raise ValueError('Invalid argument value: NaN')
# Upgrade scalars to objects
args_upgraded = self._upgrade_scalars(args_list)
# Verify replacements
for i in range(0, len(args_ref)):
if (len(args_upgraded[i].variables) != 0
and type(args_ref[i]) is not cvxpy_scalar_var):
raise TypeError('Invalid replacement')
# All numeric
if all(list(map(lambda x: type(x) is cvxpy_obj, args_upgraded))):
# Create map and new program
replace_map = {}
for i in range(0, len(args_ref), 1):
replace_map[args_ref[i]] = args_upgraded[i]
new_p = cvxpy_program(self.action,
re_eval(self.objective, replace_map),
re_eval(self.constraints, replace_map), [],
self.options, '')
# Solve
obj, valid = new_p.solve(quiet=True, return_status=True)
if not valid:
raise ValueError('Unable to compute value')
else:
return obj
# Not all numeric
else:
# Return expression tree
return cvxpy_tree(self, args_upgraded)