def test_mul_py_mv(self):
ga = GeometricAlgebra(metric=dual_metric)
zero = ga.zeros([], kind="scalar")
zero_py = 0.0
one = ga.ones([], kind="scalar")
one_py = 1.0
eps = ga.ones([], kind="pseudoscalar")
ten = ga.fill([], fill_value=10.0, kind="scalar")
ten_py = 10.0
self.assertEqual(one * one_py, one)
self.assertEqual(one_py * one, one)
self.assertEqual(zero * one_py, zero)
self.assertEqual(one_py * zero, zero)
self.assertEqual(zero_py * one, zero)
self.assertEqual(one * zero_py, zero)
self.assertEqual(one_py * eps, eps)
self.assertEqual(eps * one_py, eps)
self.assertEqual(zero_py * zero, zero)
self.assertEqual(zero * zero_py, zero)
self.assertEqual(ten_py * zero, zero)
self.assertEqual(zero * ten_py, zero)
self.assertEqual(ten * zero_py, zero)
self.assertEqual(zero_py * ten, zero)
self.assertEqual((ten_py * eps) * eps, zero)
self.assertEqual(ten_py * one, ten)
self.assertEqual(one * ten_py, ten)
self.assertEqual(ten * one_py, ten)
self.assertEqual(one_py * ten, ten)
def test_mul_tf_mv(self):
ga = GeometricAlgebra(metric=dual_metric)
zero = ga.zeros([], kind="scalar")
zero_tf = ga.as_mv(tf.convert_to_tensor(0.0, dtype=tf.float32))
one = ga.ones([], kind="scalar")
one_tf = ga.as_mv(tf.convert_to_tensor(1.0, dtype=tf.float32))
eps = ga.ones([], kind="pseudoscalar")
ten = ga.fill([], fill_value=10.0, kind="scalar")
ten_tf = ga.as_mv(tf.convert_to_tensor([10.0], dtype=tf.float32))
self.assertEqual(one * one_tf, one)
self.assertEqual(one_tf * one, one)
self.assertEqual(zero * one_tf, zero)
self.assertEqual(one_tf * zero, zero)
self.assertEqual(zero_tf * one, zero)
self.assertEqual(one * zero_tf, zero)
self.assertEqual(one_tf * eps, eps)
self.assertEqual(eps * one_tf, eps)
self.assertEqual(zero_tf * zero, zero)
self.assertEqual(zero * zero_tf, zero)
self.assertEqual(ten_tf * zero, zero)
self.assertEqual(zero * ten_tf, zero)
self.assertEqual(ten * zero_tf, zero)
self.assertEqual(zero_tf * ten, zero)
self.assertEqual((ten_tf * eps) * eps, zero)
self.assertEqual(ten_tf * one, ten)
self.assertEqual(one * ten_tf, ten)
self.assertEqual(ten * one_tf, ten)
self.assertEqual(one_tf * ten, ten)
def test_batched_auto_diff_square(self):
"""Test automatic differentiation using
dual numbers for the square function.
Use batch with identical elements.
f(x) = x^2
f'(x) = d/dx f(x) = 2x
"""
ga = GeometricAlgebra(metric=dual_metric)
batch_shape = [3, 4]
one = ga.ones(batch_shape, kind="scalar")
five = 5.0 * ga.ones(batch_shape, kind="scalar")
eps = ga.ones(batch_shape, kind="pseudoscalar")
x = one + eps
self.assertEqual(x[""], one)
self.assertEqual(x["0"], eps)
self.assertAllElementsEqualTo(x.scalar, 1.0)
self.assertEqual(x.mv_of_kind("pseudoscalar"), eps)
self.assertAllElementsEqualTo(x.tensor_of_kind("scalar"), 1.0)
self.assertAllElementsEqualTo(x.tensor_of_kind("pseudoscalar"), 1.0)
# f(1) = 1^2 = 1, f'(1) = 2
x_squared = x * x
self.assertAllElementsEqualTo(x_squared.scalar, 1.0)
self.assertEqual(x_squared["0"], 2.0 * eps)
y = five + eps
self.assertEqual(y[""], five)
self.assertEqual(y["0"], eps)
self.assertAllElementsEqualTo(y.scalar, 5.0)
self.assertEqual(y.mv_of_kind("pseudoscalar"), eps)
self.assertAllElementsEqualTo(y.tensor_of_kind("scalar"), 5.0)
self.assertAllElementsEqualTo(y.tensor_of_kind("pseudoscalar"), 1.0)
# f(5) = 5^2 = 25, f'(5) = 10
y_squared = y * y
self.assertAllElementsEqualTo(y_squared.scalar, 25.0)
self.assertEqual(y_squared["0"], eps * 10.0)