def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
# min sum_entries(t) + kq
# s.t. x <= t + q
# 0 <= t
x = arg_objs[0]
k = lu.create_const(data[0], (1, 1))
q = lu.create_var((1, 1))
t = lu.create_var(x.size)
sum_t, constr = sum_entries.graph_implementation([t], (1, 1))
obj = lu.sum_expr([sum_t, lu.mul_expr(k, q, (1, 1))])
prom_q = lu.promote(q, x.size)
constr.append(lu.create_leq(x, lu.sum_expr([t, prom_q])))
constr.append(lu.create_geq(t))
return (obj, constr)
def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
# min sum_entries(t) + kq
# s.t. x <= t + q
# 0 <= t
x = arg_objs[0]
k = lu.create_const(data[0], (1, 1))
q = lu.create_var((1, 1))
t = lu.create_var(x.size)
sum_t, constr = sum_entries.graph_implementation([t], (1, 1))
obj = lu.sum_expr([sum_t, lu.mul_expr(k, q, (1, 1))])
prom_q = lu.promote(q, x.size)
constr.append( lu.create_leq(x, lu.sum_expr([t, prom_q])) )
constr.append( lu.create_geq(t) )
return (obj, constr)
def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
x = arg_objs[0]
t = lu.create_var((1, 1))
# sum(exp(x - t))
prom_t = lu.promote(t, x.size)
expr = lu.sub_expr(x, prom_t)
obj, constraints = exp.graph_implementation([expr], x.size)
obj, constr = sum_entries.graph_implementation([obj], (1, 1))
# obj <= 1
one = lu.create_const(1, (1, 1))
constraints += constr + [lu.create_leq(obj, one)]
return (t, constraints)
def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
x = arg_objs[0]
t = lu.create_var((1, 1))
# sum(exp(x - t))
prom_t = lu.promote(t, x.size)
expr = lu.sub_expr(x, prom_t)
obj, constraints = exp.graph_implementation([expr], x.size)
obj, constr = sum_entries.graph_implementation([obj], (1, 1))
# obj <= 1
one = lu.create_const(1, (1, 1))
constraints += constr + [lu.create_leq(obj, one)]
return (t, constraints)
def graph_implementation(arg_objs, size, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
size : tuple
The size of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
x = arg_objs[0]
obj, abs_constr = abs.graph_implementation([x], x.size)
obj, sum_constr = sum_entries.graph_implementation([obj], (1, 1))
return (obj, abs_constr + sum_constr)
