def __init__(self, lh_expr, rh_expr):
lh_expr = DivExpression.cast_to_const(lh_expr)
rh_expr = DivExpression.cast_to_const(rh_expr)
if lh_expr.is_scalar() and not rh_expr.is_scalar():
lh_expr = promote(lh_expr, rh_expr.shape)
elif rh_expr.is_scalar() and not lh_expr.is_scalar():
rh_expr = promote(rh_expr, lh_expr.shape)
super(DivExpression, self).__init__(lh_expr, rh_expr)
def __init__(self, lh_expr, rh_expr):
lh_expr = multiply.cast_to_const(lh_expr)
rh_expr = multiply.cast_to_const(rh_expr)
if lh_expr.is_scalar() and not rh_expr.is_scalar():
lh_expr = promote(lh_expr, rh_expr.shape)
elif rh_expr.is_scalar() and not lh_expr.is_scalar():
rh_expr = promote(rh_expr, lh_expr.shape)
super(multiply, self).__init__(lh_expr, rh_expr)
def kl_div_canon(expr, args):
shape = expr.shape
x = promote(args[0], shape)
y = promote(args[1], shape)
t = Variable(shape)
constraints = [ExpCone(t, x, y)]
obj = y - x - t
return obj, constraints
def norm_inf_canon(expr, args):
x = args[0]
shape = expr.shape
t = Variable(shape)
promoted_t = promote(t, x.shape)
return t, [x <= promoted_t, x + promoted_t >= 0]
def lambda_max_canon(expr, args):
A = args[0]
n = A.shape[0]
t = Variable()
prom_t = promote(t, (n, ))
# Constrain I*t - A to be PSD; note that this expression must be symmetric.
tmp_expr = diag_vec(prom_t) - A
constr = [tmp_expr == tmp_expr.T, PSD(tmp_expr)]
return t, constr
def lambda_max_canon(expr, args):
A = args[0]
n = A.shape[0]
t = Variable()
prom_t = promote(t, (n, ))
# Constrain I*t - A to be PSD; note that this expression must be symmetric.
tmp_expr = diag_vec(prom_t) - A
constr = [PSD(tmp_expr)]
if not A.is_symmetric():
ut = upper_tri(A)
lt = upper_tri(A.T)
constr.append(ut == lt)
return t, constr
def add_canon(expr, args):
if expr.is_scalar():
return log_sum_exp(hstack(args)), []
rows = []
summands = [promote(s, expr.shape) if s.is_scalar() else s for s in args]
if len(expr.shape) == 1:
for i in range(expr.shape[0]):
row = []
row.append(
log_sum_exp(hstack([summand[i] for summand in summands])))
rows.append(row)
return reshape(bmat(rows), expr.shape), []
else:
for i in range(expr.shape[0]):
row = []
for j in range(expr.shape[1]):
row.append(
log_sum_exp(hstack([summand[i, j]
for summand in summands])))
rows.append(row)
return reshape(bmat(rows), expr.shape), []
