def qe_m4(px,mlmax,Talm=None,fTalm=None):
"""
px is a pixelization object, initialized like this:
px = pixelization(shape=shape,wcs=wcs) # for CAR
px = pixelization(nside=nside) # for healpix
output: curved sky multipole=4 estimator
"""
ells = np.arange(mlmax)
#prepare temperature map
rmapT=px.alm2map(np.stack((Talm,Talm)),spin=0,ncomp=1,mlmax=mlmax)[0]
#find tbarf
t_alm=cs.almxfl(fTalm,np.sqrt((ells-3.)*(ells-2.)*(ells-1.)*ells*(ells+1.)*(ells+2.)*(ells+3.)*(ells+4.)))
alms=np.stack((t_alm,t_alm))
rmap=px.alm2map_spin(alms,0,4,ncomp=2,mlmax=mlmax)
#multiply the two fields together
rmap=np.nan_to_num(rmap)
prodmap=rmap*rmapT
prodmap=np.nan_to_num(prodmap)
if not(px.hpix): prodmap=enmap.enmap(prodmap,px.wcs)
realsp2=prodmap[0] #spin +4 real space real space field
if not(px.hpix): realsp2 = enmap.enmap(realsp2,px.wcs)
#convert the above spin4 fields to spin pm 4 alms
res1 = px.map2alm_spin(realsp2,mlmax,4,4) #will return pm4
#spin 4 ylm
ttalmsp2=rot2dalm(res1,4)[0] #pick up the spin 4 alm of the first one
ttalmsm2=rot2dalm(res1,4)[1] #pick up the spin -4 alm of the second one
m4_alm=ttalmsp2+ttalmsm2
return m4_alm
def qe_shear(px,mlmax,Talm=None,fTalm=None):
"""
px is a pixelization object, initialized like this:
px = pixelization(shape=shape,wcs=wcs) # for CAR
px = pixelization(nside=nside) # for healpix
output: curved sky shear estimator
"""
ells = np.arange(mlmax)
#prepare temperature map
rmapT=px.alm2map(np.stack((Talm,Talm)),spin=0,ncomp=1,mlmax=mlmax)[0]
#find tbarf
t_alm=cs.almxfl(fTalm,np.sqrt((ells-1.)*ells*(ells+1.)*(ells+2.)))
alms=np.stack((t_alm,t_alm))
rmap=px.alm2map_spin(alms,0,2,ncomp=2,mlmax=mlmax) #same as 2 2
#multiply the two fields together
prodmap=rmap*rmapT
if not(px.hpix): prodmap=enmap.enmap(prodmap,px.wcs)
realsp2=prodmap[0] #spin +2 real space real space field
realsm2=prodmap[1] #spin -2 real space real space field
if not(px.hpix):
realsp2 = enmap.enmap(realsp2,px.wcs)
realsm2=enmap.enmap(realsm2,px.wcs)
#convert the above spin2 fields to spin pm 2 alms
res1 = px.map2alm_spin(realsp2,mlmax,2,2) #will return pm2
res2= px.map2alm_spin(realsm2,mlmax,-2,2) #will return pm2
#spin 2 ylm
ttalmsp2=rot2dalm(res1,2)[0] #pick up the spin 2 alm of the first one
ttalmsm2=rot2dalm(res1,2)[1] #pick up the spin -2 alm of the second one
shear_alm=ttalmsp2+ttalmsm2
return shear_alm
def filter_alms(alms,filt,lmin=None,lmax=None):
"""
Filter the alms with transfer function specified
by filt (indexed starting at ell=0).
"""
mlmax = get_mlmax(alms)
ls = np.arange(filt.size)
if lmax is not None:
assert lmax<=ls.max()
assert lmax<=mlmax
if lmin is not None: filt[ls<lmin] = 0
if lmax is not None: filt[ls>lmax] = 0
return cs.almxfl(alms.copy(),filt)
def qe_source(px,mlmax,fTalm,profile=None,xfTalm=None):
"""generalised source estimator
Args:
px (object): pixelization object
mlmax (int): maximum ell to perform alm2map transforms
profile (narray): profile of reconstructed source in ell space.
If none is provided, defaults to point source hardening
fTalm (narray): inverse filtered temperature map
xfTalm (narray, optional): inverse filtered temperature map. Defaults to None
Returns:
narray: profile reconstruction
"""
if profile is not None:
#filter the first map with the source profile
fTalm = cs.almxfl(fTalm, profile)
#If we don't provide a second map,
#copy the first (which is already filtered)
if xfTalm is None:
xfTalm = fTalm.copy()
else:
#otherwise, we still need to filter
#the second map
if profile is not None:
xfTalm = cs.almxfl(xfTalm, profile)
rmap1 = px.alm2map(fTalm,spin=0,ncomp=1,mlmax=mlmax)[0]
rmap2 = px.alm2map(xfTalm,spin=0,ncomp=1,mlmax=mlmax)[0]
#multiply the two fields together
prodmap=rmap1*rmap2
if not(px.hpix): prodmap=enmap.enmap(prodmap,px.wcs) #spin +0 real space field
res=px.map2alm_spin(prodmap,mlmax,0,0)
#spin 0 salm
salm=0.5*res[0]
if profile is not None:
salm=cs.almxfl(salm,1./profile)
return salm
def test_almxfl(self):
import healpy as hp
for lmax in [100, 400, 500, 1000]:
ainfo = sharp.alm_info(lmax)
alms = hp.synalm(np.ones(lmax + 1), lmax=lmax)
filtering = np.ones(lmax + 1)
alms0 = ainfo.lmul(alms.copy(), filtering)
assert np.all(np.isclose(alms0, alms))
for lmax in [100, 400, 500, 1000]:
ainfo = sharp.alm_info(lmax)
alms = hp.synalm(np.ones(lmax + 1), lmax=lmax)
alms0 = curvedsky.almxfl(alms.copy(), lambda x: np.ones(x.shape))
assert np.all(np.isclose(alms0, alms))
for ar_id, ar in enumerate(arrays):
win_T = so_map.read_map(d["window_T_%s_%s" % (sv, ar)])
win_pol = so_map.read_map(d["window_pol_%s_%s" % (sv, ar)])
window_tuple = (win_T, win_pol)
del win_T, win_pol
# we add fg alms to cmb alms in temperature
alms_beamed = alms.copy()
alms_beamed[0] += fglms[id_freq[d["nu_eff_%s_%s" % (sv, ar)]]]
# we convolve signal + foreground with the beam of the array
l, bl = pspy_utils.read_beam_file(d["beam_%s_%s" % (sv, ar)])
alms_beamed = curvedsky.almxfl(alms_beamed, bl)
if scenario == "noE": alms_beamed[1] *= 0
if scenario == "noB": alms_beamed[2] *= 0
# generate our signal only sim
split = sph_tools.alm2map(alms_beamed, template[sv])
# compute the alms of the sim
master_alms[sv, ar, "nofilter"] = sph_tools.get_alms(
split, window_tuple, niter, lmax, dtype=sim_alm_dtype)
# apply the k-space filter
binary = so_map.read_map("%s/binary_%s_%s.fits" %
def almxfl(alm,fl):
alm = np.asarray(alm)
ncomp = alm.shape[0]
assert ncomp in [1,2,3]
res = cs.almxfl(alm,fl)
return res