# -*- coding: utf-8 -*-
# Copyright (c) 2015-2022, Exa Analytics Development Team
# Distributed under the terms of the Apache License 2.0
r"""
Cartesian to spherical transforms, obtained symbolically, numbafied.
Generated using the following code.
.. code-block:: Python
from exatomic.algorithms.basis import enum_cartesian, car2sph
def _car2sph_raw(L):
fmt = '{: 20.16f},'
c2s = car2sph(sh, enum_cartesian)
for L in range(11):
if not L:
f += ' if not L: return np.array([1.])\n'
continue
tmt = (fmt * 4 + '\n') * (c2s[L].size // 4) + fmt * (c2s[L].size % 4)
cdim, sdim = c2s[L].shape
scaled = c2s[L] / (2 * np.pi ** 0.5)
vals = tmt.format(*scaled.flatten())
f += ' if L == {}:\n return np.array([\n{}])\n'.format(L, vals)
return f
"""
import numpy as np
from numba import jit
[docs]@jit(nopython=True, cache=True)
def car2sph_scaled(L):
"""Coefficients of symbolic solid harmonics / (2 * pi ** 0.5)."""
return _car2sph_2d(L)
@jit(nopython=True, cache=True)
def _car2sph_2d(L):
"""Reshape the arrays to avoid nested memory-managed objects."""
cdim = (L + 1) * (L + 2) // 2
sdim = 2 * L + 1
flat = _car2sph_raw(L)
sq = np.empty((cdim, sdim))
for c in range(cdim):
for s in range(sdim):
sq[c, s] = flat[c * sdim + s]
return sq
@jit(nopython=True, cache=True)
def _car2sph_raw(L):
"""Dump of numerical coefficients from symbolic solid harmonics
scaled by (4pi)**-0.5 to match the real spherical harmonics."""
if not L:
return np.array([1.])
if L == 1:
return np.array([
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if L == 2:
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