def simulate_MultinomialLognormalSky(self, NSIDE, Npts_per_sqdeg):
if self.verbose:
t0 = time.time()
utils.PrtMsg("Generating Lognormal field :", self.verbose)
rho = self.simulate_LognormalSky(NSIDE)
if self.verbose:
t0 = utils.PrtAndRstTime(self.verbose, t0)
utils.PrtMsg("Multinomial sampling and returning: ", self.verbose)
Ntot = hp.nside2pixarea(NSIDE, degrees=True) * Npts_per_sqdeg * hp.nside2npix(NSIDE)
return np.random.multinomial(Ntot, rho / np.sum(rho))
def simulate_PoissonLognormalSky(self, NSIDE, NGal_per_sqdeg):
if self.verbose:
t0 = time.time()
utils.PrtMsg("Generating Lognormal field :", self.verbose)
rho = self.simulate_LognormalSky(NSIDE)
rate = hp.nside2pixarea(NSIDE, degrees=True) * NGal_per_sqdeg
if self.verbose:
t0 = utils.PrtAndRstTime(self.verbose, t0)
utils.PrtMsg("Poisson sampling and returning : ", self.verbose)
return np.random.poisson(rho * rate, size=rho.size)
def simulate_GaussianSky(self, NSIDE, seed=None):
"""
Returns a healpy sky map from the Cl with synfast
"""
if self.lmin > 0:
if self.verbose: utils.PrtMsg("Filling ell (0 : " + str(self.lmin) + ") with zeros.", self.verbose)
Cl = Cl_lmax(self.ell(), self.Cl).Cl # In order to fill in the missing ells
else:
Cl = self.Cl
if seed is not None: np.random.set_state(seed)
return hp.synfast(Cl, NSIDE, new=True)
def to_realspace(self, cos_t):
"""
Performs the Legendre transform to get the real space 2pcf.
"""
cos_t = np.array(cos_t)
if self.lmin > 0:
if self.verbose: utils.PrtMsg("Filling ell (0 : " + str(self.lmin) + ") with zeros.", self.verbose)
Cl_temp = Cl_lmax(self.ell(), self.Cl) # In order to fill in the missing ells
Cl = Cl_temp.Cl
ell = Cl_temp.ell()
else:
Cl = self.Cl
ell = self.ell()
Clell2_4pi = Cl * (2. * ell + 1.) / (4. * np.pi)
return np.polynomial.legendre.legval(cos_t, Clell2_4pi)
def Cl_log(self, NSIDE=2048, lmax=None):
"""
Returns the spectrum of the log field assuming lognormal statistics :
This produces a fake map with map(n) = xi(cost), take the log and get the new alm.
Input parameter NSIDE is the healpix res of the fake map. (lmax \sim 3*NSIDE -1)
"""
if self.verbose and self.lmin > 0:
utils.PrtMsg("Filling ell (0 : " + str(self.lmin) + ") with lowest l entry.", self.verbose)
Clc = Cl_lmax(self.ell(), self.Cl)
Clc.Cl[0:self.lmin] = self.Cl[0]
alm = 1j * np.zeros(self.lmax + 1) + Clc.Cl
w = np.sqrt((2. * Clc.ell() + 1.) / 4. / np.pi) # weights -> sum_l Cl/w_l Y_l0(cost) = xi(n)
# This creates a map xi with xi(hat n) = xi(cos t)
print "Generating NSIDE " + str(NSIDE) + " xi map"
xi = hp.alm2map(w * alm, NSIDE, lmax=self.lmax, mmax=0, verbose=False)
assert (np.all(xi > -1.)), "Procedure ill-defined"
alm_log = hp.map2alm(np.log(1. + xi), lmax=lmax, mmax=0)
alm_log /= np.sqrt((2. * np.arange(len(alm_log)) + 1.) / 4. / np.pi)
if not (np.all(alm_log.real >= 0.)):
"Warning , negative values in Plog"
return Cl_lminlmax(np.arange(len(alm_log)), alm_log.real, verbose=self.verbose)