def norm_inf_canon(expr, args):
x = args[0]
axis = expr.axis
shape = expr.shape
t = Variable(shape)
if axis is None: # shape = (1, 1)
promoted_t = promote(t, x.shape)
elif axis == 0: # shape = (1, n)
promoted_t = Constant(np.ones(
(x.shape[0], 1))) * reshape(t, (1, x.shape[1]))
else: # shape = (m, 1)
promoted_t = reshape(t, (x.shape[0], 1)) * Constant(
np.ones((1, x.shape[1])))
return t, [x <= promoted_t, x + promoted_t >= 0]
def max_canon(expr, args):
x = args[0]
shape = expr.shape
axis = expr.axis
t = Variable(shape)
if axis is None: # shape = (1, 1)
promoted_t = promote(t, x.shape)
elif axis == 0: # shape = (1, n)
promoted_t = Constant(np.ones((x.shape[0], 1))) * reshape(
t, (1, x.shape[1]))
else: # shape = (m, 1)
promoted_t = reshape(t, (x.shape[0], 1)) * Constant(
np.ones((1, x.shape[1])))
constraints = [x <= promoted_t]
return t, constraints
def log_sum_exp_canon(expr, args):
x = args[0]
shape = expr.shape
axis = expr.axis
t = Variable(shape)
# log(sum(exp(x))) <= t <=> sum(exp(x-t)) <= 1
if axis is None: # shape = (1, 1)
promoted_t = promote(t, x.shape)
elif axis == 0: # shape = (1, n)
promoted_t = Constant(np.ones(
(x.shape[0], 1))) * reshape(t, (1, ) + x.shape[1:])
else: # shape = (m, 1)
promoted_t = reshape(t, x.shape[:-1] +
(1, )) * Constant(np.ones((1, x.shape[1])))
exp_expr = exp(x - promoted_t)
obj, constraints = exp_canon(exp_expr, exp_expr.args)
obj = sum(obj, axis=axis)
ones = Constant(np.ones(shape))
constraints.append(obj <= ones)
return t, constraints
def exp_canon(expr, args):
x = promote(args[0], expr.shape)
t = Variable(expr.shape)
ones = Constant(np.ones(expr.shape))
constraints = [ExpCone(x, ones, t)]
return t, constraints