def sph_tree_cartesian(x):
azimuthal, polar = cartesian_to_spherical(x.T).T
return numpy.concatenate(
orthopy.sphere.tree_sph(polar,
azimuthal,
scheme.degree + 1,
standardization="quantum mechanic"))
def f(x):
degree = 19
data = [
(x[0], _f((math.sqrt(1.0 / 3.0), 3))),
(x[1], _f2(x[6])),
(x[2], _f2(x[7])),
(x[3], _f2(x[8])),
(x[4], _f2(x[9])),
(x[5], _f11(x[10], x[11])),
]
points, weights = untangle(data)
azimuthal, polar = cartesian_to_spherical(points).T
out = orthopy.sphere.tree_sph(
polar, azimuthal, degree, standardization="quantum mechanic"
)
A = numpy.array([row for level in out for row in level])
out = numpy.dot(A, weights)
out[0] -= 1.0 / (2 * numpy.sqrt(numpy.pi))
v = numpy.sqrt(out.real ** 2 + out.imag ** 2)
norm_v = numpy.sqrt(numpy.vdot(v, v))
print(norm_v)
return norm_v
def test_scheme_cartesian(scheme, tol):
def sph_tree_cartesian(x):
azimuthal, polar = cartesian_to_spherical(x.T).T
return numpy.concatenate(
orthopy.sphere.tree_sph(polar,
azimuthal,
scheme.degree + 1,
standardization="quantum mechanic"))
assert scheme.points.dtype == numpy.float64, scheme.name
assert scheme.weights.dtype == numpy.float64, scheme.name
# We're using the spherical harmonic iterator here; it's much less memory-intensive
# than computing the full tree at once. Unfortunately, we cannot use
# scheme.integrate with it, but that's okay.
azimuthal, polar = cartesian_to_spherical(scheme.points).T
sph_iterator = orthopy.sphere.Iterator(polar,
azimuthal,
standardization="quantum mechanic")
degree = None
for k in range(scheme.degree + 2):
vals = next(sph_iterator)
approximate = 4 * numpy.pi * numpy.dot(vals, scheme.weights)
# construct exact value
if k == 0:
exact = [numpy.sqrt(4 * numpy.pi)]
else:
exact = numpy.zeros_like(approximate)
if numpy.any(numpy.abs(approximate - exact) > tol):
degree = k - 1
break
assert degree == scheme.degree, "{} -- Observed: {}, expected: {}".format(
scheme.name, degree, scheme.degree)
return