def test_mul_other():
model = Graph()
p1 = GP(EQ(), TensorProductMean(lambda x: x ** 2), graph=model)
p2 = 5. * p1
p3 = p1 * 5.
x = np.random.randn(5, 1)
yield assert_allclose, 5. * p1.mean(x), p2.mean(x)
yield assert_allclose, 5. * p1.mean(x), p3.mean(x)
yield assert_allclose, 25. * p1.kernel(x), p2.kernel(x)
yield assert_allclose, 25. * p1.kernel(x), p3.kernel(x)
yield assert_allclose, model.kernels[p2, p3](x, x), 25. * p1.kernel(x)
# Check that a `GP` cannot be multiplied with a `Normal`.
yield raises, NotImplementedError, lambda: p1 * Normal(np.eye(3))
yield raises, NotImplementedError, lambda: Normal(np.eye(3)) * p1
def test_mul_other():
model = Graph()
p1 = GP(EQ(), TensorProductMean(lambda x: x ** 2), graph=model)
p2 = 5. * p1
p3 = p1 * 5.
x = np.random.randn(5, 1)
allclose(5. * p1.mean(x), p2.mean(x))
allclose(5. * p1.mean(x), p3.mean(x))
allclose(25. * p1.kernel(x), p2.kernel(x))
allclose(25. * p1.kernel(x), p3.kernel(x))
allclose(model.kernels[p2, p3](x, x), 25. * p1.kernel(x))
# Check that a `GP` cannot be multiplied with a `Normal`.
with pytest.raises(NotImplementedError):
p1 * Normal(np.eye(3))
with pytest.raises(NotImplementedError):
Normal(np.eye(3)) * p1
def test_sum_other():
model = Graph()
p1 = GP(EQ(), TensorProductMean(lambda x: x ** 2), graph=model)
p2 = p1 + 5.
p3 = 5. + p1
p4 = model.sum(5., p1)
x = np.random.randn(5, 1)
allclose(p1.mean(x) + 5., p2.mean(x))
allclose(p1.mean(x) + 5., p3.mean(x))
allclose(p1.mean(x) + 5., p4.mean(x))
allclose(p1.kernel(x), p2.kernel(x))
allclose(p1.kernel(x), p3.kernel(x))
allclose(p1.kernel(x), p4.kernel(x))
allclose(p1.kernel(p2(x), p3(x)), p1.kernel(x))
allclose(p1.kernel(p2(x), p4(x)), p1.kernel(x))
# Check that a `GP` cannot be summed with a `Normal`.
with pytest.raises(NotImplementedError):
p1 + Normal(np.eye(3))
with pytest.raises(NotImplementedError):
Normal(np.eye(3)) + p1
def test_construction():
model = Graph()
p = GP(EQ(), graph=model)
x = np.random.randn(10, 1)
p.mean(x)
p.mean(p(x))
p.kernel(x)
p.kernel(p(x))
p.kernel(x, x)
p.kernel(p(x), x)
p.kernel(x, p(x))
p.kernel(p(x), p(x))
p.kernel.elwise(x)
p.kernel.elwise(p(x))
p.kernel.elwise(x, x)
p.kernel.elwise(p(x), x)
p.kernel.elwise(x, p(x))
p.kernel.elwise(p(x), p(x))
# Test resolution of kernel and mean.
k = EQ()
m = TensorProductMean(lambda x: x ** 2)
assert isinstance(GP(k, graph=model).mean, ZeroMean)
assert isinstance(GP(k, 5, graph=model).mean, ScaledMean)
assert isinstance(GP(k, 1, graph=model).mean, OneMean)
assert isinstance(GP(k, 0, graph=model).mean, ZeroMean)
assert isinstance(GP(k, m, graph=model).mean, TensorProductMean)
assert isinstance(GP(k, graph=model).kernel, EQ)
assert isinstance(GP(5, graph=model).kernel, ScaledKernel)
assert isinstance(GP(1, graph=model).kernel, OneKernel)
assert isinstance(GP(0, graph=model).kernel, ZeroKernel)
# Test construction of finite-dimensional distribution.
d = GP(k, m, graph=model)(x)
allclose(d.var, k(x))
allclose(d.mean, m(x))
def test_marginals():
model = Graph()
p = GP(EQ(), TensorProductMean(lambda x: x ** 2), graph=model)
x = np.linspace(0, 5, 10)
# Check that `marginals` outputs the right thing.
mean, lower, upper = p(x).marginals()
var = B.diag(p.kernel(x))
yield assert_allclose, mean, p.mean(x)[:, 0]
yield assert_allclose, lower, p.mean(x)[:, 0] - 2 * var ** .5
yield assert_allclose, upper, p.mean(x)[:, 0] + 2 * var ** .5
# Test correctness.
y = p(x).sample()
mean, lower, upper = (p | (x, y))(x).marginals()
yield assert_allclose, mean, y[:, 0]
yield le, B.mean(B.abs(upper - lower)), 1e-5
mean, lower, upper = (p | (x, y))(x + 100).marginals()
yield assert_allclose, mean, p.mean(x + 100)[:, 0]
yield assert_allclose, upper - lower, 4 * np.ones(10)
