def test_auto_diff_square(self):
"""Test automatic differentiation using
dual numbers for the square function.
f(x) = x^2
f'(x) = d/dx f(x) = 2x
"""
ga = GeometricAlgebra(metric=dual_metric)
one = ga.from_scalar(1.0)
five = ga.from_scalar(5.0)
eps = ga.from_tensor_with_kind(tf.ones(1), kind="pseudoscalar")
x = one + eps
# f(1) = 1^2 = 1, f'(1) = 2
x_squared = ga.geom_prod(x, x)
self.assertTensorsEqual(ga.select_blades(x_squared, ""), 1.0)
self.assertTensorsEqual(ga.select_blades(x_squared, "0"), 2.0)
y = five + eps
# f(5) = 5^2 = 25, f'(5) = 10
y_squared = ga.geom_prod(y, y)
self.assertTensorsEqual(ga.select_blades(y_squared, ""), 25.0)
self.assertTensorsEqual(ga.select_blades(y_squared, "0"), 10.0)
def test_mul_tf_mv(self):
ga = GeometricAlgebra(metric=dual_metric)
zero = ga.from_scalar(0.0)
one = ga.from_scalar(1.0)
eps = ga.from_tensor_with_kind(tf.ones(1), kind="pseudoscalar")
ten = ga.from_scalar(10.0)
zero_tf = tf.convert_to_tensor([0, 0], dtype=tf.float32)
one_tf = tf.convert_to_tensor([1, 0], dtype=tf.float32)
eps_tf = tf.convert_to_tensor([0, 1], dtype=tf.float32)
ten_tf = tf.convert_to_tensor([10, 0], dtype=tf.float32)
self.assertTensorsEqual(ga.geom_prod(one, one_tf), one)
self.assertTensorsEqual(ga.geom_prod(one_tf, one), one)
self.assertTensorsEqual(ga.geom_prod(zero, one_tf), zero)
self.assertTensorsEqual(ga.geom_prod(one_tf, zero), zero)
self.assertTensorsEqual(ga.geom_prod(zero_tf, one), zero)
self.assertTensorsEqual(ga.geom_prod(one, zero_tf), zero)
self.assertTensorsEqual(ga.geom_prod(one_tf, eps), eps)
self.assertTensorsEqual(ga.geom_prod(eps, one_tf), eps)
self.assertTensorsEqual(ga.geom_prod(zero_tf, zero), zero)
self.assertTensorsEqual(ga.geom_prod(zero, zero_tf), zero)
self.assertTensorsEqual(ga.geom_prod(ten_tf, zero), zero)
self.assertTensorsEqual(ga.geom_prod(zero, ten_tf), zero)
self.assertTensorsEqual(ga.geom_prod(ten, zero_tf), zero)
self.assertTensorsEqual(ga.geom_prod(zero_tf, ten), zero)
self.assertTensorsEqual(ga.geom_prod(ga.geom_prod(ten_tf, eps), eps),
zero)
self.assertTensorsEqual(ga.geom_prod(ten_tf, one), ten)
self.assertTensorsEqual(ga.geom_prod(one, ten_tf), ten)
self.assertTensorsEqual(ga.geom_prod(ten, one_tf), ten)
self.assertTensorsEqual(ga.geom_prod(one_tf, ten), ten)
def test_mul_inverse(self):
ga = GeometricAlgebra(metric=dual_metric)
# a = 2
a = ga.from_tensor_with_kind(tf.fill([1], 2.0), kind="scalar")
# b = 3 + 3e0
b = ga.from_tensor_with_kind(tf.fill([2], 3.0), kind="mv")
# a * b = 2 * (3 + 3e0) = 6 + 6e0
c = ga.geom_prod(a, b)
self.assertTensorsEqual(c, ga.from_scalar(6.0) + 6.0 * ga.e("0"))
# a^-1 = 1 / 2
a_inv = ga.inverse(a)
self.assertTensorsEqual(ga.select_blades(a_inv, ""), 0.5)
# c = a * b
# => a_inv * c = b
self.assertTensorsEqual(ga.geom_prod(a_inv, c), b)
# Since a is scalar, should commute too.
# => c * a_inv = b
self.assertTensorsEqual(ga.geom_prod(c, a_inv), b)
# b is not invertible and will throw an exception
self.assertRaises(Exception, ga.inverse, b)
def test_mul_mv_mv(self):
ga = GeometricAlgebra(metric=dual_metric)
zero = ga.from_scalar(0.0)
one = ga.from_scalar(1.0)
eps = ga.from_tensor_with_kind(tf.ones(1), kind="pseudoscalar")
ten = ga.from_scalar(10.0)
self.assertTensorsEqual(ga.geom_prod(eps, eps), zero)
self.assertTensorsEqual(ga.geom_prod(one, one), one)
self.assertTensorsEqual(ga.geom_prod(zero, one), zero)
self.assertTensorsEqual(ga.geom_prod(one, zero), zero)
self.assertTensorsEqual(ga.geom_prod(one, eps), eps)
self.assertTensorsEqual(ga.geom_prod(eps, one), eps)
self.assertTensorsEqual(ga.geom_prod(zero, zero), zero)
self.assertTensorsEqual(ga.geom_prod(ten, zero), zero)
self.assertTensorsEqual(ga.geom_prod(zero, ten), zero)
self.assertTensorsEqual(ga.geom_prod(ga.geom_prod(ten, eps), eps),
zero)
self.assertTensorsEqual(ga.geom_prod(ten, one), ten)
self.assertTensorsEqual(ga.geom_prod(one, ten), ten)