def qol_elemwise(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]
y = arg_objs[1]
t = lu.create_var(x.size)
two = lu.create_const(2, (1, 1))
constraints = [
SOC_Elemwise(
lu.sum_expr([y, t]),
[lu.sub_expr(y, t), lu.mul_expr(two, x, x.size)]),
lu.create_geq(y)
]
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)
"""
# Promote scalars.
for idx, arg in enumerate(arg_objs):
if arg.size != size:
arg_objs[idx] = lu.promote(arg, size)
x = arg_objs[0]
y = arg_objs[1]
v = lu.create_var(x.size)
two = lu.create_const(2, (1, 1))
# SOC(x + y, [y - x, 2*v])
constraints = [
SOC_Elemwise(lu.sum_expr([x, y]),
[lu.sub_expr(y, x),
lu.mul_expr(two, v, v.size)])
]
# 0 <= x, 0 <= y
constraints += [lu.create_geq(x), lu.create_geq(y)]
return (v, 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)
"""
t = lu.create_var(size)
for i, obj in enumerate(arg_objs):
# Promote obj.
if obj.size != size:
arg_objs[i] = lu.promote(obj, size)
return (t, [SOC_Elemwise(t, arg_objs)])
def gm(t, x, y):
return SOC_Elemwise(lu.sum_expr([x, y]),
[lu.sub_expr(x, y),
lu.mul_expr(two, t, t.size)])