def test_derivative_eq():
# Test derivative of kernel `EQ()`.
k = EQ()
x1 = B.randn(tf.float64, 10, 1)
x2 = B.randn(tf.float64, 5, 1)
# Test derivative with respect to first input.
allclose(k.diff(0, None)(x1, x2), -k(x1, x2) * (x1 - B.transpose(x2)))
allclose(k.diff(0, None)(x1), -k(x1) * (x1 - B.transpose(x1)))
# Test derivative with respect to second input.
allclose(k.diff(None, 0)(x1, x2), -k(x1, x2) * (B.transpose(x2) - x1))
allclose(k.diff(None, 0)(x1), -k(x1) * (B.transpose(x1) - x1))
# Test derivative with respect to both inputs.
ref = k(x1, x2) * (1 - (x1 - B.transpose(x2)) ** 2)
allclose(k.diff(0, 0)(x1, x2), ref)
allclose(k.diff(0)(x1, x2), ref)
ref = k(x1) * (1 - (x1 - B.transpose(x1)) ** 2)
allclose(k.diff(0, 0)(x1), ref)
allclose(k.diff(0)(x1), ref)
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()