def mkfullsky(corr, nside, alms=False):
"""Construct a set of correlated Healpix maps.
Make a set of full sky gaussian random fields, given the correlation
structure. Useful for constructing a set of different redshift slices.
Parameters
----------
corr : np.ndarray (lmax+1, numz, numz)
The correlation matrix :math:`C_l(z, z')`.
nside : integer
The resolution of the Healpix maps.
alms : boolean, optional
If True return the alms instead of the sky maps.
Returns
-------
hpmaps : np.ndarray (numz, npix)
The Healpix maps. hpmaps[i] is the i'th map.
"""
numz = corr.shape[1]
maxl = corr.shape[0]-1
if corr.shape[2] != numz:
raise Exception("Correlation matrix is incorrect shape.")
trans = np.zeros_like(corr)
for i in range(maxl+1):
trans[i] = nputil.matrix_root_manynull(corr[i], truncate=False)
la, ma = healpy.Alm.getlm(maxl)
matshape = la.shape + (numz,)
# Construct complex gaussian random variables of unit variance
gaussvars = (np.random.standard_normal(matshape)
+ 1.0J * np.random.standard_normal(matshape)) / 2.0**0.5
# Transform variables to have correct correlation structure
for i, l in enumerate(la):
gaussvars[i] = np.dot(trans[l], gaussvars[i])
if alms:
alm_freq = np.zeros((numz, maxl+1, maxl+1), dtype=np.complex128)
for i in range(numz):
alm_freq[i] = hputil.unpack_alm(gaussvars[:, i], maxl)
return alm_freq
hpmaps = np.empty((numz, healpy.nside2npix(nside)))
# Perform the spherical harmonic transform for each z
for i in range(numz):
hpmaps[i] = healpy.alm2map(gaussvars[:,i].copy(), nside)
return hpmaps
def test_pack_unpack_half():
pck1 = np.arange(10.0, dtype=np.complex128)
pck2 = hputil.pack_alm(hputil.unpack_alm(pck1, 3))
assert np.allclose(pck1, pck2).all()