def test_variable_tracking(self):
x = Variable((5,), name='x')
y = Variable((3, 4), name='y')
# Should have a single integer.
val1 = np.unique([id(v.parent) for v in x.scalar_variables()])
assert val1.size == 1
# Should have a single integer (distinct from above).
val2 = np.unique([id(v.parent) for v in y.scalar_variables()])
assert val2.size == 1 and val2[0] != val1[0]
# Should have single integer (same as immediately above).
val3 = np.unique([id(v.parent) for v in y[:5].scalar_variables()])
assert val3.size == 1 and val3[0] == val2[0]
assert x.is_proper()
assert y.is_proper()
assert not y[:3].is_proper()
# This variable does nothing for the first test.
z = Variable((2, 2, 2), name='z')
# First statement should be "True", second should be ['x','y']
constrs1 = [affine.sum(x) == 1, affine.sum(x) - affine.sum(y) <= 0]
vars1 = find_variables_from_constraints(constrs1)
assert all(v.is_proper() for v in vars1)
assert [v.name for v in vars1] == ['x', 'y']
# First statement should be "False", second should be "True", third should be ['y', 'z']
zz = z[:, :, 1]
assert not zz.is_proper()
constrs2 = [y == 0, affine.trace(zz) >= 10]
vars2 = find_variables_from_constraints(constrs2)
assert all(v.is_proper() for v in vars2)
assert [v.name for v in vars2] == ['y', 'z']
def test_triu(self):
A = np.random.randn(5, 5).round(decimals=3)
A_cl = Variable(shape=A.shape)
A_cl.value = A
temp = aff.triu(A)
expr0 = aff.sum(temp)
expr1 = aff.sum(np.triu(A_cl))
assert Expression.are_equivalent(expr0, expr1.value)
def test_tile(self):
x = np.array([0, 1, 2])
x_cl = Variable(shape=x.shape)
x_cl.value = x
A = aff.tile(x_cl, 2)
assert np.allclose(np.tile(x, 2), A.value)
expr0 = aff.sum(A)
expr1 = aff.sum(x) * 2
assert Expression.are_equivalent(expr0.value, expr1)
def test_trace_and_diag(self):
x = Variable(shape=(5, ))
A = np.random.randn(5, 5).round(decimals=3)
for i in range(5):
A[i, i] = 0
temp = A + aff.diag(x)
expr0 = aff.trace(temp)
expr1 = aff.sum(x)
assert Expression.are_equivalent(expr0, expr1)
def test_repeat(self):
x = np.array([3])
x_cl = Variable(shape=x.shape)
x_cl.value = x
A = aff.repeat(x_cl, 4)
assert np.allclose(np.repeat(x, 4), A.value)
expr0 = aff.sum(A.value)
expr1 = aff.sum(x_cl) * 4
assert Expression.are_equivalent(expr0, expr1.value)
# x_cl.value = x + 1
# assert not np.allclose(np.repeat(x, 4), A)
x1 = np.array([[1, 2], [3, 4]])
x1_cl = Variable(shape=x1.shape)
x1_cl.value = x1
A1 = aff.repeat(x1_cl, 2)
assert np.allclose(np.repeat(x1, 2), A1.value)
expr2 = aff.sum(A1.value)
expr3 = aff.sum(x1_cl) * 2
assert Expression.are_equivalent(expr2, expr3.value)
def age_witnesses(self):
if self._age_witnesses is None:
self._age_witnesses = dict()
if self._m > 1:
for i in self.ech.U_I:
wi_expr = Expression(np.zeros(self._m,))
num_cover = self.ech.expcover_counts[i]
if num_cover > 0:
x_i = self._nus[i]
wi_expr[self.ech.expcovers[i]] = pos_operator(x_i, eval_only=True)
wi_expr[i] = -aff.sum(wi_expr[self.ech.expcovers[i]])
self._age_witnesses[i] = wi_expr
else:
self.age_vectors[0] = self.c
self._age_witnesses[0] = Expression([0])
return self._age_witnesses
def test_pos_1(self):
x = Variable(shape=(3, ), name='x')
con = [cl_pos(affine.sum(x) - 7) <= 5]
A_expect = np.array([[0, 0, 0, -1], [0, 0, 0, 1], [-1, -1, -1, 1]])
A, b, K, _1, _2, _3 = compile_constrained_system(con)
A = np.round(A.toarray(), decimals=1)
assert np.all(A == A_expect)
assert np.all(b == np.array([5, 0, 7]))
assert K == [Cone('+', 1), Cone('+', 2)]
# value propagation
x.value = np.array([4, 4, 4])
viol = con[0].violation()
assert viol == 0
x.value = np.array([4.2, 3.9, 4.0])
viol = con[0].violation()
assert abs(viol - 0.1) < 1e-7
def test_abs_1(self):
x = Variable(shape=(2, ), name='x')
one_norm = affine.sum(cl_abs(x))
con = [one_norm <= 5]
A_expect = np.array([[0, 0, -1, -1], [1, 0, 1, 0], [-1, 0, 1, 0],
[0, 1, 0, 1], [0, -1, 0, 1]])
A, b, K, _1, _2, _3 = compile_constrained_system(con)
A = np.round(A.toarray(), decimals=1)
assert np.all(A == A_expect)
assert np.all(b == np.array([5, 0, 0, 0, 0]))
assert K == [Cone('+', 1), Cone('+', 2), Cone('+', 2)]
# value propagation
x.value = np.array([1, -2])
viol = con[0].violation()
assert viol == 0
x.value = np.array([-3, 3])
viol = con[0].violation()
assert viol == 1
def test_relent_2(self):
# compilation with the elementwise option
x = Variable(shape=(2, ), name='x')
y = Variable(shape=(2, ), name='y')
re = affine.sum(relent(2 * x, np.exp(1) * y, elementwise=True))
con = [re <= 1]
A, b, K, _, _, _ = compile_constrained_system(con)
A_expect = np.array([
[0., 0., 0., 0., -1.,
-1.], # linear inequality on epigraph for relent constr
[0., 0., 0., 0., -1., 0.], # first exponential cone
[0., 0., 2.72, 0., 0., 0.], #
[2., 0., 0., 0., 0., 0.], #
[0., 0., 0., 0., 0., -1.], # second exponential cone
[0., 0., 0., 2.72, 0., 0.], #
[0., 2., 0., 0., 0., 0.]
]) #
A = np.round(A.toarray(), decimals=2)
assert np.all(A == A_expect)
assert np.all(b == np.array([1., 0., 0., 0., 0., 0., 0.]))
assert K == [Cone('+', 1), Cone('e', 3), Cone('e', 3)]