def test_derivative():
# Test construction:
p = GP(EQ(), TensorProductMean(lambda x: x ** 2), graph=Graph())
yield eq, str(p.diff(1)), 'GP(d(1) EQ(), d(1) <lambda>)'
# Test case:
B.backend_to_tf()
s = B.Session()
model = Graph()
x = np.linspace(0, 1, 100)[:, None]
y = 2 * x
p = GP(EQ(), graph=model)
dp = p.diff()
# Test conditioning on function.
yield le, abs_err(s.run(dp.condition(p(x), y)(x).mean - 2)), 1e-3
# Test conditioning on derivative.
post = p.condition((B.cast(0., np.float64), B.cast(0., np.float64)),
(dp(x), y))
yield le, abs_err(s.run(post(x).mean - x ** 2)), 1e-3
s.close()
B.backend_to_np()
def test_derivative():
B.backend_to_tf()
s = B.Session()
m = TensorProductMean(lambda x: x**2)
m2 = TensorProductMean(lambda x: x**3)
x = B.array(np.random.randn(10, 1))
yield assert_allclose, s.run(m.diff(0)(x)), s.run(2 * x)
yield assert_allclose, s.run(m2.diff(0)(x)), s.run(3 * x**2)
s.close()
B.backend_to_np()
def test_derivative():
# First, check properties.
k = EQ().diff(0)
yield eq, k.stationary, False
yield raises, RuntimeError, lambda: k.length_scale
yield raises, RuntimeError, lambda: k.var
yield raises, RuntimeError, lambda: k.period
# Test equality.
yield eq, EQ().diff(0), EQ().diff(0)
yield neq, EQ().diff(0), EQ().diff(1)
yield neq, Matern12().diff(0), EQ().diff(0)
yield raises, RuntimeError, lambda: EQ().diff(None, None)(1)
# Third, check computation.
B.backend_to_tf()
s = B.Session()
# Test derivative of kernel EQ.
k = EQ()
x1 = B.array(np.random.randn(10, 1))
x2 = B.array(np.random.randn(5, 1))
# Test derivative with respect to first input.
ref = s.run(-dense(k(x1, x2)) * (x1 - B.transpose(x2)))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1, x2))), ref
ref = s.run(-dense(k(x1)) * (x1 - B.transpose(x1)))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1))), ref
# Test derivative with respect to second input.
ref = s.run(-dense(k(x1, x2)) * (B.transpose(x2) - x1))
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1, x2))), ref
ref = s.run(-dense(k(x1)) * (B.transpose(x1) - x1))
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1))), ref
# Test derivative with respect to both inputs.
ref = s.run(dense(k(x1, x2)) * (1 - (x1 - B.transpose(x2))**2))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1, x2))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1, x2))), ref
ref = s.run(dense(k(x1)) * (1 - (x1 - B.transpose(x1))**2))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1))), ref
# Test derivative of kernel Linear.
k = Linear()
x1 = B.array(np.random.randn(10, 1))
x2 = B.array(np.random.randn(5, 1))
# Test derivative with respect to first input.
ref = s.run(B.ones((10, 5), dtype=np.float64) * B.transpose(x2))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1, x2))), ref
ref = s.run(B.ones((10, 10), dtype=np.float64) * B.transpose(x1))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1))), ref
# Test derivative with respect to second input.
ref = s.run(B.ones((10, 5), dtype=np.float64) * x1)
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1, x2))), ref
ref = s.run(B.ones((10, 10), dtype=np.float64) * x1)
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1))), ref
# Test derivative with respect to both inputs.
ref = s.run(B.ones((10, 5), dtype=np.float64))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1, x2))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1, x2))), ref
ref = s.run(B.ones((10, 10), dtype=np.float64))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1))), ref
s.close()
B.backend_to_np()
