def generate_weight(self, regen=False):
r"""Pregenerate the k weights array.
Parameters
----------
regen : boolean, optional
If True, force regeneration of the weights, to be used if
parameters have been changed,
"""
if self._weight_gen and not regen:
return
f1, f2 = np.meshgrid(self.nu_pixels, self.nu_pixels)
ch = self.frequency_covariance(f1, f2)
self._freq_weight, self._num_corr_freq = nputil.matrix_root_manynull(ch)
rf = gaussianfield.RandomFieldA2.like_map(self)
## Construct a lambda function to evalutate the array of
## k-vectors.
rf.powerspectrum = lambda karray: self.angular_ps((karray**2).sum(axis=2)**0.5)
self._ang_field = rf
self._weight_gen = True
def generate_weight(self, regen=False):
r"""Pregenerate the k weights array.
Parameters
----------
regen : boolean, optional
If True, force regeneration of the weights, to be used if
parameters have been changed,
"""
if self._weight_gen and not regen:
return
f1, f2 = np.meshgrid(self.nu_pixels, self.nu_pixels)
ch = self.frequency_covariance(f1, f2)
self._freq_weight, self._num_corr_freq = nputil.matrix_root_manynull(ch)
rf = gaussianfield.RandomFieldA2.like_map(self)
## Construct a lambda function to evalutate the array of
## k-vectors.
rf.powerspectrum = lambda karray: self.angular_ps(
(karray ** 2).sum(axis=2) ** 0.5
)
self._ang_field = rf
self._weight_gen = True
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 block_root(clzz):
"""Calculate the 'square root' of an angular powerspectrum matrix (with
nulls).
"""
trans = np.zeros_like(clzz)
for i in range(trans.shape[0]):
trans[i] = nputil.matrix_root_manynull(clzz[i], truncate=False)
return trans
def block_root(clzz):
"""Calculate the 'square root' of an angular powerspectrum matrix (with
nulls).
"""
trans = np.zeros_like(clzz)
for i in range(trans.shape[0]):
trans[i] = nputil.matrix_root_manynull(clzz[i], truncate=False)
return trans
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.")
alm_array = np.zeros((numz, 1, maxl + 1, maxl + 1), dtype=np.complex128)
# Generate gaussian deviates and transform to have correct correlation
# structure
for l in range(maxl + 1):
# Add in a small diagonal to try and ensure positive definiteness
cmax = corr[l].diagonal().max() * 1e-14
corrm = corr[l] + np.identity(numz) * cmax
trans = nputil.matrix_root_manynull(corrm, truncate=False)
gaussvars = nputil.complex_std_normal((numz, l + 1))
alm_array[:, 0, l, :(l + 1)] = np.dot(trans, gaussvars)
if alms:
return alm_array
# Perform the spherical harmonic transform for each z
sky = hputil.sphtrans_inv_sky(alm_array, nside)
sky = sky[:, 0]
return sky
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.")
alm_array = np.zeros((numz, 1, maxl + 1, maxl + 1), dtype=np.complex128)
# Generate gaussian deviates and transform to have correct correlation
# structure
for l in range(maxl + 1):
# Add in a small diagonal to try and ensure positive definiteness
cmax = corr[l].diagonal().max() * 1e-14
corrm = corr[l] + np.identity(numz) * cmax
trans = nputil.matrix_root_manynull(corrm, truncate=False)
gaussvars = nputil.complex_std_normal((numz, l + 1))
alm_array[:, 0, l, :(l + 1)] = np.dot(trans, gaussvars)
if alms:
return alm_array
# Perform the spherical harmonic transform for each z
sky = hputil.sphtrans_inv_sky(alm_array, nside)
sky = sky[:, 0]
return sky