def test_legendre_table_wrapper_logic():
# tests the SSE 2 logic in the high-level wrapper by using an odd number of thetas
theta = np.asarray([np.pi/2, np.pi/4, 3 * np.pi / 4])
m = 3
lmax = 10
Plm = normalized_associated_legendre_table(lmax, m, theta)
assert np.allclose(Plm[1, :], normalized_associated_legendre_table(lmax, m, np.pi/4)[0, :])
assert np.allclose(Plm[2, :], normalized_associated_legendre_table(lmax, m, 3 * np.pi/4)[0, :])
def test_legendre_table_wrapper_logic():
# tests the SSE 2 logic in the high-level wrapper by using an odd number of thetas
theta = np.asarray([np.pi / 2, np.pi / 4, 3 * np.pi / 4])
m = 3
lmax = 10
Plm = normalized_associated_legendre_table(lmax, m, theta)
assert np.allclose(
Plm[1, :],
normalized_associated_legendre_table(lmax, m, np.pi / 4)[0, :])
assert np.allclose(
Plm[2, :],
normalized_associated_legendre_table(lmax, m, 3 * np.pi / 4)[0, :])
def arbitrary_beam_by_l(beam_function, params, lmax):
"""
Find the Legendre coefficients :math:`b_\ell` for an arbitrary (symmetric)
real-space beam function, such that
:math:`B(\theta) = \sum_\ell (2\ell + 1) b_\ell P_\ell(\cos \theta)`.
Arguments:
beam_function -- Python function which takes arguments fn(theta, params)
params -- Tuple containing parameters for the beam function (e.g. FWHM)
lmax -- Max. l to calculate :math:`b_\ell` up to
Returns:
b_l -- 1D array of coefficients, for the l-range [0, lmax].
"""
order = lmax
l = np.arange(lmax + 1)
# Get zeros and weights of the Legendre polynomials
# (Zeros are symmetric about x=0, so only keep the nonzero ones)
xi, wi = libsharp.legendre_roots(2 * order)
xi = xi[order:]
wi = 2. * wi[order:]
# Get Legendre polynomials and normalise them
leg = libsharp.normalized_associated_legendre_table(lmax, 0, np.arccos(xi))
leg *= np.sqrt(4 * np.pi) / np.sqrt(2 * l + 1)
# Perform Gauss-Legendre sum
f = np.atleast_2d(wi * beam_function(np.arccos(xi), *params)).T * leg
return 0.25 * np.sum(f, axis=0)
def test(theta, m, lmax):
Plm = normalized_associated_legendre_table(lmax, m, theta)
Plm_p = sph_harm(m, np.arange(m, lmax + 1), 0, theta)[None, :]
if not np.allclose(Plm_p, Plm):
print(Plm_p)
print(Plm)
return ok_, np.allclose(Plm_p, Plm)
def test(theta, m, lmax):
Plm = normalized_associated_legendre_table(lmax, m, theta)
Plm_p = sph_harm(m, np.arange(m, lmax + 1), 0, theta)[None, :]
if not np.allclose(Plm_p, Plm):
print(Plm_p)
print(Plm)
return ok_, np.allclose(Plm_p, Plm)