def pm_expand(constr_list):
"""
Description
-----------
Expands functions which are implemented
using partial minimization descriptions.
constr_list: cvxpy_list of constraints.
Arguments
---------
constr_list: cvxpy_list of constraints.
"""
new_list = cvxpy_list([])
for c in constr_list:
if (c.left.type == TREE and c.left.item.type == FUNCTION
and c.left.item.expansion_type == PM):
new_constr = transform(expand(c.left.item._pm_expand(c)))
new_constr = pm_expand(new_constr._get_convex())
new_list += new_constr
elif (c.left.type == EXPRESSION and c.right.type == SET
and c.right.expansion_type == PM):
new_constr = transform(expand(c.right._pm_expand(c)))
new_constr = pm_expand(new_constr._get_convex())
new_list += new_constr
else:
new_list += cvxpy_list([c])
# Return new list
return new_list
def pm_expand(constr_list):
"""
Description
-----------
Expands functions which are implemented
using partial minimization descriptions.
constr_list: cvxpy_list of constraints.
Arguments
---------
constr_list: cvxpy_list of constraints.
"""
new_list = cvxpy_list([])
for c in constr_list:
if(c.left.type == TREE and
c.left.item.type == FUNCTION and
c.left.item.expansion_type == PM):
new_constr = transform(expand(c.left.item._pm_expand(c)))
new_constr = pm_expand(new_constr._get_convex())
new_list += new_constr
elif(c.left.type == EXPRESSION and
c.right.type == SET and
c.right.expansion_type == PM):
new_constr = transform(expand(c.right._pm_expand(c)))
new_constr = pm_expand(new_constr._get_convex())
new_list += new_constr
else:
new_list += cvxpy_list([c])
# Return new list
return new_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 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 __init__(self, action, obj, constr, params, opt, name):
# Function attributes
self.name = name
self.type = FUNCTION
self.atom = False
self.expansion_type = PM
if (action == MINIMIZE):
self.curvature = CONVEX
else:
self.curvature = CONCAVE
# Program attributes
self.lagrange_mul_eq = None
self.action = action
self.obj = obj
self.constr = cvxpy_list(constr)
if (opt != None):
self.options = opt
else:
self.options = {
'SCP_ALG': SCP_ALG_OPT.copy(),
'SCP_SOL': SCP_SOLVER_OPT.copy(),
'REL_SOL': RELAX_SOLVER_OPT.copy(),
'show steps': False,
'quiet': True
}
# Store parameters
param_list = []
for param in params:
if (type(param) is cvxpy_scalar_param):
param_list += [param]
elif (type(param) is cvxpy_param):
(m, n) = param.shape
for i in range(0, m, 1):
for j in range(0, n, 1):
param_list += [param[i, j]]
else:
raise ValueError('Invalid parameter')
self.params = cvxpy_list(param_list)
# Verify parameters
exp_params = self.get_params()
if (len(exp_params) != len(self.params)):
raise ValueError('Parameters do not match')
for x in exp_params:
if (x not in self.params):
raise ValueError('Parameters do not match')
def get_params(self):
l = cvxpy_list([])
for i in range(0,self.shape[0],1):
for j in range(0,self.shape[1],1):
if(not np.isscalar(self[i,j])):
l += self[i,j].get_params()
return l
def __init__(self,object_type,value,name):
"""
Class constructor.
:param object_type: Keyword (See cvxpy.def).
:param value: Number.
:param name: String.
"""
self.type = object_type
self.value = value
self.name = name
self.shape = (1,1)
self.variables = cvxpy_list()
self.parameters = cvxpy_list()
self.T = self
def call_solver(p, quiet):
"""
Calls solver.
:param p: Convex cvxpy_program.
Assumed to be expanded.
:param quiet: Boolean.
"""
# Set printing format for cvxopt sparse matrices
opt.spmatrix_str = opt.printing.spmatrix_str_triplet
# Expand objects defined via partial minimization
constr_list = cvxpy_list(pm_expand(p.constraints))
# Get variables
variables = constr_list.variables
variables.sort()
# Count variables
n = len(variables)
# Create variable-index map
var_to_index = {}
for i in range(0, n, 1):
var_to_index[variables[i]] = i
# Construct objective vector
c = construct_c(p.objective, var_to_index, n, p.action)
# Construct Ax == b
A, b = construct_Ab(constr_list._get_eq(), var_to_index, n)
# Construct Gx <= h
G, h, dim_l, dim_q, dim_s = construct_Gh(constr_list._get_ineq_in(),
var_to_index, n)
# Construct F
F = construct_F(constr_list._get_ineq_in(), var_to_index, n)
# Call cvxopt
solvers.options['maxiters'] = p.options['maxiters']
solvers.options['abstol'] = p.options['abstol']
solvers.options['reltol'] = p.options['reltol']
solvers.options['feastol'] = p.options['feastol']
solvers.options['show_progress'] = not quiet
dims = {'l': dim_l, 'q': dim_q, 's': dim_s}
if F is None:
r = solvers.conelp(c, G, h, dims, A, b)
else:
r = solvers.cpl(c, F, G, h, dims, A, b)
# Store numerical values
if r['status'] != PRIMAL_INFEASIBLE:
for v in variables:
v.value = r['x'][var_to_index[v]]
# Return result
return r
def call_solver(p,quiet):
"""
Calls solver.
:param p: Convex cvxpy_program.
Assumed to be expanded.
:param quiet: Boolean.
"""
# Set printing format for cvxopt sparse matrices
opt.spmatrix_str = opt.printing.spmatrix_str_triplet
# Expand objects defined via partial minimization
constr_list = cvxpy_list(pm_expand(p.constraints))
# Get variables
variables = constr_list.variables
variables.sort()
# Count variables
n = len(variables)
# Create variable-index map
var_to_index = {}
for i in range(0,n,1):
var_to_index[variables[i]] = i
# Construct objective vector
c = construct_c(p.objective,var_to_index,n,p.action)
# Construct Ax == b
A,b = construct_Ab(constr_list._get_eq(),var_to_index,n)
# Construct Gx <= h
G,h,dim_l,dim_q,dim_s = construct_Gh(constr_list._get_ineq_in(),
var_to_index,n)
# Construct F
F = construct_F(constr_list._get_ineq_in(),var_to_index,n)
# Call cvxopt
solvers.options['maxiters'] = p.options['maxiters']
solvers.options['abstol'] = p.options['abstol']
solvers.options['reltol'] = p.options['reltol']
solvers.options['feastol'] = p.options['feastol']
solvers.options['show_progress'] = not quiet
dims = {'l':dim_l, 'q':dim_q, 's':dim_s}
if F is None:
r = solvers.conelp(c,G,h,dims,A,b)
else:
r = solvers.cpl(c,F,G,h,dims,A,b)
# Store numerical values
if r['status'] != PRIMAL_INFEASIBLE:
for v in variables:
v.value = r['x'][var_to_index[v]]
# Return result
return r
def _dom_constr(self, args):
"""
Description
-----------
Dummy method to make the program
appear as a function.
"""
return cvxpy_list([])
def _dom_constr(self,args):
"""
Description
-----------
Dummy method to make the program
appear as a function.
"""
return cvxpy_list([])
def __init__(self,action,obj,constr,params,opt,name):
# Function attributes
self.name = name
self.type = FUNCTION
self.atom = False
self.expansion_type = PM
if(action == MINIMIZE):
self.curvature = CONVEX
else:
self.curvature = CONCAVE
# Program attributes
self.lagrange_mul_eq = None
self.action = action
self.obj = obj
self.constr = cvxpy_list(constr)
if(opt != None):
self.options = opt
else:
self.options = {'SCP_ALG':SCP_ALG_OPT.copy(),
'SCP_SOL':SCP_SOLVER_OPT.copy(),
'REL_SOL':RELAX_SOLVER_OPT.copy(),
'show steps':False,'quiet': True}
# Store parameters
param_list = []
for param in params:
if(type(param) is cvxpy_scalar_param):
param_list += [param]
elif(type(param) is cvxpy_param):
(m,n) = param.shape
for i in range(0,m,1):
for j in range(0,n,1):
param_list += [param[i,j]]
else:
raise ValueError('Invalid parameter')
self.params = cvxpy_list(param_list)
# Verify parameters
exp_params = self.get_params()
if(len(exp_params) != len(self.params)):
raise ValueError('Parameters do not match')
for x in exp_params:
if(x not in self.params):
raise ValueError('Parameters do not match')
def __getattribute__(self, name):
# Transpose
if name == 'T':
new_ar = cvxpy_sparray(self.shape[1], self.shape[0])
for i in range(0, self.shape[0], 1):
rowi_indeces = self.rows[i]
rowi_values = self.data[i]
for k in range(0, len(rowi_indeces)):
new_ar[rowi_indeces[k], i] = rowi_values[k]
return new_ar
# Variables
elif name == 'variables':
l = []
for i in range(0, self.shape[0], 1):
for obj in self.data[i]:
if not np.isscalar(obj):
l += obj.variables
return cvxpy_list(set(l))
# Parameters
elif name == 'parameters':
l = []
for i in range(0, self.shape[0], 1):
for obj in self.data[i]:
if not np.isscalar(obj):
l += obj.parameters
return cvxpy_list(set(l))
# Value
elif name == 'value':
mat = cvxpy_spmatrix((self.shape[0], self.shape[1]), np.float64)
for i in range(0, self.shape[0], 1):
rowi_indeces = self.rows[i]
rowi_values = self.data[i]
for k in range(0, len(rowi_indeces)):
if np.isscalar(rowi_values[k]):
mat[i, rowi_indeces[k]] = rowi_values[k]
else:
mat[i, rowi_indeces[k]] = rowi_values[k].value
return mat
# Other attribute
else:
return object.__getattribute__(self, name)
def __getattribute__(self,name):
# Transpose
if name == 'T':
new_ar = cvxpy_sparray(self.shape[1],self.shape[0])
for i in range(0,self.shape[0],1):
rowi_indeces = self.rows[i]
rowi_values = self.data[i]
for k in range(0,len(rowi_indeces)):
new_ar[rowi_indeces[k],i] = rowi_values[k]
return new_ar
# Variables
elif name == 'variables':
l = []
for i in range(0,self.shape[0],1):
for obj in self.data[i]:
if not np.isscalar(obj):
l += obj.variables
return cvxpy_list(set(l))
# Parameters
elif name == 'parameters':
l = []
for i in range(0,self.shape[0],1):
for obj in self.data[i]:
if not np.isscalar(obj):
l += obj.parameters
return cvxpy_list(set(l))
# Value
elif name == 'value':
mat = cvxpy_spmatrix((self.shape[0],self.shape[1]),np.float64)
for i in range(0,self.shape[0],1):
rowi_indeces = self.rows[i]
rowi_values = self.data[i]
for k in range(0,len(rowi_indeces)):
if np.isscalar(rowi_values[k]):
mat[i,rowi_indeces[k]] = rowi_values[k]
else:
mat[i,rowi_indeces[k]] = rowi_values[k].value
return mat
# Other attribute
else:
return object.__getattribute__(self,name)
def __getattribute__(self,name):
# Parameters
if name == 'parameters':
return cvxpy_list([self])
# Other
else:
return object.__getattribute__(self,name)
def get_params(self):
"""
Description
-----------
Construct a set with the parameters present
in the program.
"""
constr_params = self.constr.get_params()
obj_params = self.obj.get_params()
all_params = constr_params
for v in obj_params:
l1 = map(lambda x: x is v,all_params)
if(len(l1) != 0):
if not reduce(lambda x,y: x or y,l1):
all_params += cvxpy_list([v])
else:
all_params += cvxpy_list([v])
return all_params
def __getattribute__(self,name):
# Variables
if name == 'variables':
return cvxpy_list([self])
# Other
else:
return object.__getattribute__(self,name)
def get_params(self):
"""
Description
-----------
Construct a set with the parameters present
in the program.
"""
constr_params = self.constr.get_params()
obj_params = self.obj.get_params()
all_params = constr_params
for v in obj_params:
l1 = map(lambda x: x is v, all_params)
if (len(l1) != 0):
if not reduce(lambda x, y: x or y, l1):
all_params += cvxpy_list([v])
else:
all_params += cvxpy_list([v])
return all_params
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 __getattribute__(self, name):
# Transpose
if name == 'T':
new_ar = cvxpy_array(self.shape[1], self.shape[0])
for i in range(0, self.shape[0], 1):
for j in range(0, self.shape[1], 1):
new_ar.data[j][i] = self.data[i][j]
return new_ar
# Variables
elif name == 'variables':
l = []
for i in range(0, self.shape[0], 1):
for j in range(0, self.shape[1], 1):
if not np.isscalar(self.data[i][j]):
l += self.data[i][j].variables
return cvxpy_list(set(l))
# Parameters
elif name == 'parameters':
l = []
for i in range(0, self.shape[0], 1):
for j in range(0, self.shape[1], 1):
if not np.isscalar(self.data[i][j]):
l += self.data[i][j].parameters
return cvxpy_list(set(l))
# Value
elif name == 'value':
mat = cvxpy_matrix(np.zeros((self.shape[0], self.shape[1])),
np.float64)
for i in range(0, self.shape[0], 1):
for j in range(0, self.shape[1], 1):
if np.isscalar(self.data[i][j]):
mat[i, j] = self.data[i][j]
else:
mat[i, j] = self.data[i][j].value
return mat
# Other attribute
else:
return object.__getattribute__(self, name)
def __getattribute__(self,name):
# Transpose
if name == 'T':
new_ar = cvxpy_array(self.shape[1],self.shape[0])
for i in range(0,self.shape[0],1):
for j in range(0,self.shape[1],1):
new_ar.data[j][i] = self.data[i][j]
return new_ar
# Variables
elif name == 'variables':
l = []
for i in range(0,self.shape[0],1):
for j in range(0,self.shape[1],1):
if not np.isscalar(self.data[i][j]):
l += self.data[i][j].variables
return cvxpy_list(set(l))
# Parameters
elif name == 'parameters':
l = []
for i in range(0,self.shape[0],1):
for j in range(0,self.shape[1],1):
if not np.isscalar(self.data[i][j]):
l += self.data[i][j].parameters
return cvxpy_list(set(l))
# Value
elif name == 'value':
mat = cvxpy_matrix(np.zeros((self.shape[0],self.shape[1])),np.float64)
for i in range(0,self.shape[0],1):
for j in range(0,self.shape[1],1):
if np.isscalar(self.data[i][j]):
mat[i,j] = self.data[i][j]
else:
mat[i,j] = self.data[i][j].value
return mat
# Other attribute
else:
return object.__getattribute__(self,name)
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: Return the partial minimization
expansion of the function.
Argument constr: The constraint to be
replaced. It is assumed to be in expanded
format so the right hand side is a variable.
"""
arg = constr.left.children[0]
right = constr.right
return cvxpy_list([less(-right, arg), less(arg, right)])
def _pm_expand(self,constr):
"""
Description: Return the partial minimization
expansion of the function.
Argument constr: The constraint to be
replaced. It is assumed to be in expanded
format so the right hand side is a variable.
"""
arg = constr.left.children[0]
right = constr.right
return cvxpy_list([less(-right,arg),
less(arg,right)])
def __getattribute__(self,name):
# Variables
if name == 'variables':
l = list(map(lambda x: x.variables,self.children))
return cvxpy_list(set(reduce(lambda x,y:x+y,l,[])))
# Parameters
elif name == 'parameters':
l = list(map(lambda x: x.parameters,self.children))
return cvxpy_list(set(reduce(lambda x,y:x+y,l,[])))
# Value
elif name == 'value':
# Summation
if (self.item.type == OPERATOR and
self.item.name == SUMMATION):
return np.sum(list(map(lambda x:x.value,self.children)))
# Multiplication
elif (self.item.type == OPERATOR and
self.item.name == MULTIPLICATION):
return self.children[0].value*self.children[1].value
# Function
elif self.item.type == FUNCTION:
return self.item(list(map(lambda x: x.value,self.children)))
# Error
else:
raise TypeError('Invalid tree item')
# Other
else:
return object.__getattribute__(self,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 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):
# 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 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
-----------
Return the partial minimization
expansion of the function.
Argument
--------
constr: The constraint to be replaced.
It is assumed the constraint was expanded
and transformed so that the right hand side
is a variable.
"""
new_list = []
for arg in constr.left.children:
if type(arg) is cvxpy_obj:
arg = arg.get_value()
new_list += [less(arg, constr.right)]
return cvxpy_list(new_list)
def _pm_expand(self, constr):
"""
Description
-----------
Return the partial minimization
expansion of the function.
Argument
--------
constr: The constraint to be replaced.
It is assumed the constraint was expanded
and transformed so that the right hand side
is a variable.
"""
new_list = []
for arg in constr.left.children:
if (type(arg) is cvxpy_obj):
arg = arg.get_value()
new_list += [less(arg, constr.right)]
return cvxpy_list(new_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):
"""
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 is_affine(self):
"""
Determines if tree is an affine expression.
"""
# Summation
if (self.item.type == OPERATOR and
self.item.name == SUMMATION):
return all(list(map(lambda x: x.is_affine(),self.children)))
# Multiplication
elif (self.item.type == OPERATOR and
self.item.name == MULTIPLICATION):
ob2 = self.children[1]
return ob2.is_affine()
# Function
elif self.item.type == FUNCTION:
return len(cvxpy_list(self.children).variables) == 0
# Error
else:
raise TypeError('Invalid tree item')
def get_vars(self):
return cvxpy_list([])
def _range_constr(self, v):
return cvxpy_list([greater(v, 0)])
def _dom_constr(self, args):
return cvxpy_list([])
def _range_constr(self, v):
return cvxpy_list([])
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 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 get_params(self):
return cvxpy_list([])
def _dom_constr(self, args):
return cvxpy_list([])
def get_params(self):
l = map(lambda x: x.get_params(),self.children)
if(len(l) != 0):
return reduce(lambda x,y:x+y,l)
else:
return cvxpy_list([])
def _range_constr(self, v):
return cvxpy_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')