def __add__(self, other):
"""The sum of two expressions.
"""
return types.add_expr()([self, other])
def get_separable_problems(problem):
"""Return a list of separable problems whose sum is the original one.
Parameters
----------
problem : Problem
A problem that consists of separable (sub)problems.
Returns
-------
List
A list of problems which are separable whose sum is the original one.
"""
# obj_terms contains the terms in the objective functions. We have to
# deal with the special case where the objective function is not a sum.
if isinstance(problem.objective.args[0], types.add_expr()):
obj_terms = problem.objective.args[0].args
else:
obj_terms = [problem.objective.args[0]]
# Remove constant terms, which will be appended to the first separable
# problem.
constant_terms = [term for term in obj_terms if term.is_constant()]
obj_terms = [term for term in obj_terms if not term.is_constant()]
constraints = problem.constraints
num_obj_terms = len(obj_terms)
num_terms = len(obj_terms) + len(constraints)
# Objective terms and constraints are indexed from 0 to num_terms - 1.
var_sets = [frozenset(func.variables()) for func in obj_terms + constraints
]
all_vars = frozenset().union(*var_sets)
adj_matrix = dok_matrix((num_terms, num_terms), dtype=bool)
for var in all_vars:
# Find all functions that contain this variable
term_ids = [i for i, var_set in enumerate(var_sets) if var in var_set]
# Add an edge between any two objetive terms/constraints sharing
# this variable.
if len(term_ids) > 1:
for i, j in itertools.combinations(term_ids, 2):
adj_matrix[i, j] = adj_matrix[j, i] = True
num_components, labels = csgraph.connected_components(adj_matrix,
directed=False)
# After splitting, construct subproblems from appropriate objective
# terms and constraints.
term_ids_per_subproblem = [[] for _ in range(num_components)]
for i, label in enumerate(labels):
term_ids_per_subproblem[label].append(i)
problem_list = []
for index in range(num_components):
terms = [obj_terms[i] for i in term_ids_per_subproblem[index]
if i < num_obj_terms]
# If we just call sum, we'll have an extra 0 in the objective.
obj = sum(terms[1:], terms[0]) if terms else Constant(0)
constrs = [constraints[i - num_obj_terms]
for i in term_ids_per_subproblem[index]
if i >= num_obj_terms]
problem_list.append(Problem(problem.objective.copy([obj]), constrs))
# Append constant terms to the first separable problem.
if constant_terms:
# Avoid adding an extra 0 in the objective
sum_constant_terms = sum(constant_terms[1:], constant_terms[0])
if problem_list:
problem_list[0].objective.args[0] += sum_constant_terms
else:
problem_list.append(Problem(problem.objective.copy(
[sum_constant_terms])))
return problem_list
def __add__(self, other):
"""The sum of two expressions.
"""
return types.add_expr()([self, other])
def get_separable_problems(problem):
"""Return a list of separable problems whose sum is the original one.
Parameters
----------
problem : Problem
A problem that consists of separable (sub)problems.
Returns
-------
List
A list of problems which are separable whose sum is the original one.
"""
# obj_terms contains the terms in the objective functions. We have to
# deal with the special case where the objective function is not a sum.
if isinstance(problem.objective.args[0], types.add_expr()):
obj_terms = problem.objective.args[0].args
else:
obj_terms = [problem.objective.args[0]]
# Remove constant terms, which will be appended to the first separable
# problem.
constant_terms = [term for term in obj_terms if term.is_constant()]
obj_terms = [term for term in obj_terms if not term.is_constant()]
constraints = problem.constraints
num_obj_terms = len(obj_terms)
num_terms = len(obj_terms) + len(constraints)
# Objective terms and constraints are indexed from 0 to num_terms - 1.
var_sets = [
frozenset(func.variables()) for func in obj_terms + constraints
]
all_vars = frozenset().union(*var_sets)
adj_matrix = dok_matrix((num_terms, num_terms), dtype=bool)
for var in all_vars:
# Find all functions that contain this variable
term_ids = [i for i, var_set in enumerate(var_sets) if var in var_set]
# Add an edge between any two objetive terms/constraints sharing
# this variable.
if len(term_ids) > 1:
for i, j in itertools.combinations(term_ids, 2):
adj_matrix[i, j] = adj_matrix[j, i] = True
num_components, labels = csgraph.connected_components(adj_matrix,
directed=False)
# After splitting, construct subproblems from appropriate objective
# terms and constraints.
term_ids_per_subproblem = [[] for _ in range(num_components)]
for i, label in enumerate(labels):
term_ids_per_subproblem[label].append(i)
problem_list = []
for index in range(num_components):
terms = [
obj_terms[i] for i in term_ids_per_subproblem[index]
if i < num_obj_terms
]
# If we just call sum, we'll have an extra 0 in the objective.
obj = sum(terms[1:], terms[0]) if terms else Constant(0)
constrs = [
constraints[i - num_obj_terms]
for i in term_ids_per_subproblem[index] if i >= num_obj_terms
]
problem_list.append(Problem(problem.objective.copy([obj]), constrs))
# Append constant terms to the first separable problem.
if constant_terms:
# Avoid adding an extra 0 in the objective
sum_constant_terms = sum(constant_terms[1:], constant_terms[0])
if problem_list:
problem_list[0].objective.args[0] += sum_constant_terms
else:
problem_list.append(
Problem(problem.objective.copy([sum_constant_terms])))
return problem_list
