def graph_implementation(arg_objs, shape, data=None):
"""Reduces the atom to an affine expression and list of constraints.
Parameters
----------
arg_objs : list
LinExpr for each argument.
shape : tuple
The shape 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] # Known to be a scalar.
v = lu.create_var((1, 1))
two = lu.create_const(2, (1, 1))
t = lu.sum_expr([y, v])
X_shape = (y.shape[0] + x.shape[0], 1)
X = lu.vstack([lu.sub_expr(y, v), lu.mul_expr(two, x, x.shape)], X_shape)
constraints = [SOC(t, X), lu.create_geq(y)]
return (v, constraints)
def gm(t, x, y):
length = t.size[0] * t.size[1]
return SOC_Axis(
lu.reshape(lu.sum_expr([x, y]), (length, 1)),
lu.vstack([
lu.reshape(lu.sub_expr(x, y), (1, length)),
lu.reshape(lu.mul_expr(two, t, t.size), (1, length))
], (2, length)), 0)
def gm(t, x, y):
length = t.size[0]*t.size[1]
return SOC_Axis(lu.reshape(lu.sum_expr([x, y]), (length, 1)),
lu.vstack([
lu.reshape(lu.sub_expr(x, y), (1, length)),
lu.reshape(lu.mul_expr(two, t, t.size), (1, length))
], (2, length)),
0)
def graph_implementation(arg_objs, size, data=None):
"""Stack the expressions vertically.
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)
"""
return (lu.vstack(arg_objs, size), [])
def graph_implementation(arg_objs, size, data=None):
"""Stack the expressions vertically.
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)
"""
return (lu.vstack(arg_objs, size), [])
def graph_implementation(self,
arg_objs,
shape: Tuple[int, ...],
data=None) -> Tuple[lo.LinOp, List[Constraint]]:
"""Stack the expressions vertically.
Parameters
----------
arg_objs : list
LinExpr for each argument.
shape : tuple
The shape of the resulting expression.
data :
Additional data required by the atom.
Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
return (lu.vstack(arg_objs, shape), [])
def combine_lin_ops(operators):
"""Combines the LinOps by stacking their output into a vector.
Parameters
----------
operators : list
A list of LinOps.
Returns
-------
LinOp
The combined LinOp.
"""
# First vectorize all the LinOp outputs.
vect_lin_ops = []
total_length = 0
for lin_op in operators:
if lin_op.size[1] != 1:
new_size = (lin_op.size[0] * lin_op.size[1], 1)
lin_op = lu.reshape(lin_op, new_size)
vect_lin_ops.append(lin_op)
total_length += lin_op.size[0]
# Stack all the outputs into a single vector.
return lu.vstack(vect_lin_ops, (total_length, 1))