| """Enumerating the physical (lx,ly,lz) Cartesian components of a shell. | |
| Our integral tensors are shaped (degree+1, degree+1, degree+1, ...) for | |
| convenience, but only the (lx,ly,lz) triples with lx+ly+lz == degree | |
| are physical basis functions -- e.g. for a p shell (degree=1) that's | |
| (1,0,0), (0,1,0), (0,0,1), not e.g. (1,1,0) which the tensor shape | |
| happens to also have room for. | |
| """ | |
| import numpy as np | |
| def cartesian_powers(degree: int) -> np.ndarray: | |
| """Returns an (M, 3) array of (lx,ly,lz) triples with lx+ly+lz == degree, | |
| in a fixed canonical order (x-major, matching common conventions: | |
| for p, that's px, py, pz).""" | |
| return np.array( | |
| [(lx, degree - lx - lz, lz) for lx in range(degree, -1, -1) for lz in range(degree - lx, -1, -1)], | |
| dtype=np.int32, | |
| ) | |