README.md

clifford_algebra_pytorch

Simple pytorch implement to compute basic Clifford algebra (Geometric algebra) operation.

Usage

Use ga.GA

import torch
from ga import GA

ga = GA(3)
x = 3 + ga[1] + 2 * ga[2] - 2 * ga[3] + ga[1, 2] - ga[2, 3] + 2.5 * ga[1, 3] - ga[1, 2, 3]
print(x)
r = x * (~x) * ga.I
print(r)
q = ga.tensor_to_mv(torch.tensor([1, 1, 1, 1]))
print(q)

# output
# 3.0 + 1.0*[e1] + 2.0*[e2] + 1.0*[e1,e2] + -2.0*[e3] + 2.5*[e1,e3] + -1.0*[e2,e3] + -1.0*[e1,e2,e3]
# -15.0*[e1,e2] + -19.0*[e1,e3] + 2.0*[e2,e3] + 27.25*[e1,e2,e3]
# 1 + 1*[e1] + 1*[e2] + 1*[e1,e2]

Use mv.MultiVector

from mv import MultiVector
a = MultiVector(4, device='cpu')
a.set_values(torch.tensor([1., 1, 2, 3, 4]), torch.tensor([0, 1, 2, 3, 4]))
b = MultiVector(4, device='cpu')
b.set_values(torch.tensor([1., -1]), torch.tensor([1, 2]))
c = MultiVector(4, device='cpu')
c.set_values(torch.ones(16, dtype=torch.float32), torch.arange(16))
print(a + b)
print(a - b)
print(a * b)
print(a / 2)

# output
# 1.0 + 2.0*[e1] + 1.0*[e2] + 3.0*[e1,e2] + 4.0*[e3]
# 1.0 + 3.0*[e2] + 3.0*[e1,e2] + 4.0*[e3]
# -1.0 + -2.0*[e1] + -4.0*[e2] + -3.0*[e1,e2] + -4.0*[e1,e3] + 4.0*[e2,e3]
# 0.5 + 0.5*[e1] + 1.0*[e2] + 1.5*[e1,e2] + 2.0*[e3]

Other

Reference

Original vanilla python implement: https://github.com/tdvance/GeometricAlgebra