def test_power(self):
x = Variable(3)
y = Variable(3)
self.assertFalse(x.is_constant())
self.assertTrue(x.is_affine())
self.assertTrue(x.is_quadratic())
with warnings.catch_warnings():
warnings.simplefilter("ignore")
s = power(x.T*y, 0)
self.assertTrue(s.is_constant())
self.assertTrue(s.is_affine())
self.assertTrue(s.is_quadratic())
t = power(x-y, 1)
self.assertFalse(t.is_constant())
self.assertTrue(t.is_affine())
self.assertTrue(t.is_quadratic())
u = power(x+2*y, 2)
self.assertFalse(u.is_constant())
self.assertFalse(u.is_affine())
self.assertTrue(u.is_quadratic())
self.assertTrue(u.is_dcp())
w = (x+2*y)**2
self.assertFalse(w.is_constant())
self.assertFalse(w.is_affine())
self.assertTrue(w.is_quadratic())
self.assertTrue(w.is_dcp())
def test_power(self):
x = Variable(3)
y = Variable(3)
self.assertFalse(x.is_constant())
self.assertTrue(x.is_affine())
self.assertTrue(x.is_quadratic())
s = power(x.T*y, 0)
self.assertTrue(s.is_constant())
self.assertTrue(s.is_affine())
self.assertTrue(s.is_quadratic())
t = power(x-y, 1)
self.assertFalse(t.is_constant())
self.assertTrue(t.is_affine())
self.assertTrue(t.is_quadratic())
u = power(x+2*y, 2)
self.assertFalse(u.is_constant())
self.assertFalse(u.is_affine())
self.assertTrue(u.is_quadratic())
self.assertTrue(u.is_dcp())
w = (x+2*y)**2
self.assertFalse(w.is_constant())
self.assertFalse(w.is_affine())
self.assertTrue(w.is_quadratic())
self.assertTrue(w.is_dcp())
def test_power(self):
x = Variable(3)
y = Variable(3)
self.assertFalse(x.is_constant())
self.assertTrue(x.is_affine())
self.assertTrue(x.is_quadratic())
with warnings.catch_warnings():
warnings.simplefilter("ignore")
s = power(x.T*y, 0)
self.assertTrue(s.is_constant())
self.assertTrue(s.is_affine())
self.assertTrue(s.is_quadratic())
t = power(x-y, 1)
self.assertFalse(t.is_constant())
self.assertTrue(t.is_affine())
self.assertTrue(t.is_quadratic())
u = power(x+2*y, 2)
self.assertFalse(u.is_constant())
self.assertFalse(u.is_affine())
self.assertTrue(u.is_quadratic())
self.assertTrue(u.is_dcp())
w = (x+2*y)**2
self.assertFalse(w.is_constant())
self.assertFalse(w.is_affine())
self.assertTrue(w.is_quadratic())
self.assertTrue(w.is_dcp())
def xexp_canon(expr, args):
x = args[0]
u = Variable(expr.shape, nonneg=True)
t = Variable(expr.shape, nonneg=True)
power_expr = power(x, 2)
power_obj, constraints = power_canon(power_expr, power_expr.args)
constraints += [ExpCone(u, x, t), u >= power_obj, x >= 0]
return t, constraints
def test_non_quadratic(self):
x = Variable()
y = Variable()
z = Variable()
s = max(vstack([x, y, z]))**2
self.assertFalse(s.is_quadratic())
t = max(vstack([x**2, power(y, 2), z]))
self.assertFalse(t.is_quadratic())
def test_non_quadratic(self):
x = Variable()
y = Variable()
z = Variable()
with self.assertRaises(Exception) as cm:
(x*y*z).is_quadratic()
self.assertEqual(str(cm.exception), "Cannot multiply UNKNOWN and AFFINE.")
s = max_entries(vstack(x, y, z))**2
self.assertFalse(s.is_quadratic())
t = max_entries(vstack(x**2, power(y, 2), z))
self.assertFalse(t.is_quadratic())
def inv_prod(value):
"""The reciprocal of a product of the entries of a vector ``x``.
Parameters
----------
x : Expression or numeric
The expression whose reciprocal product is to be computed. Must have
positive entries.
Returns
-------
Expression
.. math::
\\left(\\prod_{i=1}^n x_i\\right)^{-1},
where :math:`n` is the length of :math:`x`.
"""
return power(inv_pos(geo_mean(value)), sum(value.shape))
def huber_canon(expr, args):
M = expr.M
x = args[0]
shape = expr.shape
n = Variable(shape)
s = Variable(shape)
# n**2 + 2*M*|s|
# TODO(akshayka): Make use of recursion inherent to canonicalization
# process and just return a power / abs expressions for readability sake
power_expr = power(n, 2)
n2, constr_sq = power_canon(power_expr, power_expr.args)
abs_expr = abs(s)
abs_s, constr_abs = abs_canon(abs_expr, abs_expr.args)
obj = n2 + 2 * M * abs_s
constraints = constr_sq + constr_abs
constraints.append(x == s + n)
return obj, constraints
def square(x):
return power(x, 2)
def square(x):
"""The square of an expression."""
return power(x, 2)
def inv_pos(x):
return power(x, -1)
def square(x):
return power(x, 2)
def inv_pos(x):
""":math:`x^{-1}` for :math:`x > 0`.
"""
return power(x, -1)
def sqrt(x):
"""The square root of an expression."""
return power(x, Fraction(1, 2))
def sqrt(x):
return power(x, Fraction(1, 2))