def var_cone_canon(expr, args):
"""Expand implicit constraints on variable.
"""
# Convert attributes into constraints.
new_attr = expr.attributes.copy()
for key in ['nonneg', 'nonpos', 'symmetric', 'PSD', 'NSD']:
if new_attr[key]:
new_attr[key] = False
if expr.is_symmetric():
n = expr.shape[0]
shape = (n * (n + 1) // 2, 1)
upper_tri = Variable(shape, var_id=expr.id, **new_attr)
fill_coeff = Constant(upper_tri_to_full(n))
full_mat = fill_coeff * upper_tri
obj = reshape(full_mat, (n, n))
else:
obj = Variable(expr.shape, var_id=expr.id, **new_attr)
constr = []
if expr.is_nonneg():
constr.append(obj >= 0)
elif expr.is_nonpos():
constr.append(obj <= 0)
elif expr.attributes['PSD']:
constr.append(obj >> 0)
elif expr.attributes['NSD']:
constr.append(obj << 0)
return (obj, constr)
def apply(self, problem):
if not attributes_present(problem.variables(), CONVEX_ATTRIBUTES):
return problem, ()
# For each unique variable, add constraints.
id2new_var = {}
id2new_obj = {}
id2old_var = {}
constr = []
for var in problem.variables():
if var.id not in id2new_var:
id2old_var[var.id] = var
new_var = False
new_attr = var.attributes.copy()
for key in CONVEX_ATTRIBUTES:
if new_attr[key]:
new_var = True
new_attr[key] = False
if attributes_present([var], SYMMETRIC_ATTRIBUTES):
n = var.shape[0]
shape = (n*(n+1)//2, 1)
upper_tri = Variable(shape, var_id=var.id, **new_attr)
upper_tri.set_variable_of_provenance(var)
id2new_var[var.id] = upper_tri
fill_coeff = Constant(upper_tri_to_full(n))
full_mat = fill_coeff @ upper_tri
obj = reshape(full_mat, (n, n))
elif var.attributes['diag']:
diag_var = Variable(var.shape[0], var_id=var.id, **new_attr)
diag_var.set_variable_of_provenance(var)
id2new_var[var.id] = diag_var
obj = diag(diag_var)
elif new_var:
obj = Variable(var.shape, var_id=var.id, **new_attr)
obj.set_variable_of_provenance(var)
id2new_var[var.id] = obj
else:
obj = var
id2new_var[var.id] = obj
id2new_obj[id(var)] = obj
if var.is_pos() or var.is_nonneg():
constr.append(obj >= 0)
elif var.is_neg() or var.is_nonpos():
constr.append(obj <= 0)
elif var.is_psd():
constr.append(obj >> 0)
elif var.attributes['NSD']:
constr.append(obj << 0)
# Create new problem.
obj = problem.objective.tree_copy(id_objects=id2new_obj)
cons_id_map = {}
for cons in problem.constraints:
constr.append(cons.tree_copy(id_objects=id2new_obj))
cons_id_map[cons.id] = constr[-1].id
inverse_data = (id2new_var, id2old_var, cons_id_map)
return cvxtypes.problem()(obj, constr), inverse_data