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2a87ede | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | """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,
)
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