def healpy_rejection_sampler_OLD(m, n):
"""
Special version of the generic rejection sampler. Here we sample map
indices uniformly across the map (range [0, pi]x[0, 2*pi]) and check if
the rejection criterium is fullfilled at that point.
We can sample indices uniformly because healpixel areas are are equal
across the sphere.
Rejection algorithm: For each point draw a uniform rand number and reject
the point if the value of the pdf is smaller. Else accept it and repeat
until the n points are sampled.
Returns n map indices drawn from the map transformed to a pdf.
The resolution is the same as the input map which is sampled from.
"""
if hp.maptype(m) != 0:
raise ValueError(
"Given map is no healpy map (-1) or a series of maps (>0) : " +
"{}.".format(hp.maptype(m)))
# Get map parameter
NPIX = hp.get_map_size(m)
# Make sure the map is in pdf form, which is all positive and area = 1
m = norm_healpy_map(m)
# Get the pdf maximium to set the sampling bounding box
fmax = np.amax(m)
def pdf(ind):
"""Simple wrapper to consistently use the name pdf.
Returns the mapvals at given indices"""
return m[ind]
# Create list to store the sampled events
sample = []
# Rejection sampling loop
nstart = n
efficiency = 0
while n > 0:
# Count trials for efficinecy, has nothing to do with the sampling
efficiency += n
# Only choose integer map indices randomly as we operate on discrete
# maps
r1 = np.random.randint(0, NPIX, size=n)
# Create n uniform distributed rand numbers between 0 and the maximum
# of the function
r2 = fmax * np.random.uniform(0, 1, n)
# Calculate the pdf value pdf(r1) and compare to r2
# --> If r2 is below or equal func(r1) accept the event, else reject it
accepted = (r2 <= pdf(r1))
# --> Where func(r2) is near the box boundary of fmax the efficiency is
# good, else it gets worse. Append only accepted random numbers
sample += r1[accepted].tolist()
# Redo with n = events that are missing until n = 0 and all n requested
# events are generated
n = np.sum(~accepted)
# eff first counts how many events where drawn from the pdf and is then the
# fraction of the actual desired events n by the generetaded events.
efficiency = nstart / float(efficiency)
return np.array(sample), efficiency
def _setup(self):
# Generate mapping from pix <-> angles
self.gsm.generate(100)
self._n_pix = hp.get_map_size(self.gsm.generated_map_data)
self._n_side = hp.npix2nside(self._n_pix)
self._theta, self._phi = hp.pix2ang(self._n_side,
np.arange(self._n_pix))
def supmaps(maps, supmapiso=None):
r"""Sum an ensemble of maps.
Parameters
----------
maps : float, array_like
A map or a list/array of maps.
supmapiso : float, ndarray, optional
A map limited in :math:`\theta`, used to account for the pixel weights
on map edges. Default: *None*.
Returns
-------
supmap : float, ndarray
A 1-D array resultant of the sum of the elements in `maps`. If `supmapiso`
is given, weights are assigned to the pixels on the edges of `supmap`.
"""
if maps[0].ndim == 0:
maps = np.reshape(maps, (1, len(maps)))
npix = hp.get_map_size(maps[0])
supmap = np.sum(maps, axis=0)
supmap *= npix / np.sum(supmap)
if np.any(supmapiso):
pixs = np.nonzero(supmapiso)
supmap[pixs] /= supmapiso[pixs]
supmap *= npix / np.sum(supmap)
return supmap
def _get_a_map(self,field=0):
print "Loading healpix map field="+str(field)+"."
h = hp.read_map(path.join(self.dir,self.fname),field)
if self.nside != []:
if (hp.get_map_size(h) > hp.nside2npix(self.nside)):
print "Downgrading."
h = hp.ud_grade(h,nside_out=self.nside)
print "Scaling from K_CMB to uK_CMB."
h = h * self.cal
return h
def kSZ_map(self, data_name):
self._map_ksz = hp.read_map(self.data_path + data_name,
field=0,
nest=self._nest,
verbose=self._feedback)
self.apply_mask(self._map_ksz)
#print np.min(np.abs(self._map_ksz))
#self._map_ksz[np.abs(self._map_ksz) < 1.00408215076e-2] = hp.UNSEEN
#self._map_ksz = hp.ma(self._map_ksz)
self._nside = hp.get_nside(self._map_ksz)
self._npix = hp.get_map_size(self._map_ksz)
def _setup(self):
self._freq = 100
self._time = Time(self.date.datetime())
# Generate mapping from pix <-> angles
self.gsm.generate(self._freq)
self._n_pix = hp.get_map_size(self.gsm.generated_map_data)
self._n_side = hp.npix2nside(self._n_pix)
self._theta, self._phi = hp.pix2ang(self._n_side,
np.arange(self._n_pix))
self._pix0 = None
self._mask = None
self._observed_ra = None
self._observed_dec = None
def __init__(self):
""" Initialize the Observer object.
Calls ephem.Observer.__init__ function and adds on gsm
"""
super(GSMObserver, self).__init__()
self.gsm = GlobalSkyModel()
self.observed_sky = None
# Generate mapping from pix <-> angles
self.gsm.generate(100)
self._n_pix = hp.get_map_size(self.gsm.generated_map_data)
self._n_side = hp.npix2nside(self._n_pix)
self._theta, self._phi = hp.pix2ang(self._n_side, np.arange(self._n_pix))
def __init__(self):
""" Initialize the Observer object.
Calls ephem.Observer.__init__ function and adds on gsm
"""
super(GSMObserver2016, self).__init__()
self.gsm = GlobalSkyModel2016(freq_unit='MHz')
self.observed_sky = None
# Generate mapping from pix <-> angles
self.gsm.generate(1000)
self._n_pix = hp.get_map_size(self.gsm.generated_map_data)
self._n_side = hp.npix2nside(self._n_pix)
self._theta, self._phi = hp.pix2ang(self._n_side, np.arange(self._n_pix))
def cartesian_proj(hp_map, projector):
"""Create an array containing the Cartesian projection of the map.
Parameters
----------
map : array-like
An array containing a healpix map, can be complex.
projector : cartesian projector
The Cartesian projector.
"""
nside = healpy.npix2nside(healpy.get_map_size(hp_map.real))
vec2pix_func = lambda x, y, z: healpy.vec2pix(nside, x, y, z)
cart_map = projector.projmap(hp_map.real, vec2pix_func)
if np.iscomplexobj(hp_map):
cart_map = cart_map + 1.0J * projector.projmap(hp_map.imag, vec2pix_func)
return cart_map
def cartesian_proj(hp_map, projector):
"""Create an array containing the Cartesian projection of the map.
Parameters
----------
map : array-like
An array containing a healpix map, can be complex.
projector : cartesian projector
The Cartesian projector.
"""
nside = healpy.npix2nside(healpy.get_map_size(hp_map.real))
vec2pix_func = lambda x, y, z: healpy.vec2pix(nside, x, y, z)
cart_map = projector.projmap(hp_map.real, vec2pix_func)
if np.iscomplexobj(hp_map):
cart_map = cart_map + 1.0J * projector.projmap(hp_map.imag,
vec2pix_func)
return cart_map
def __init__(self, gsm_instance):
"""Initialize the common Observer object with a GSM instance
Calls ephem.Observer.__init__ function and adds on gsm
"""
super(BaseObserver, self).__init__()
self.observed_sky = None
self.gsm = gsm_instance
# Inline replacement of self._setup() follows.
# Generate mapping from pix <-> angles
gen_freq_Hz = 100e6
fu = gsm_instance.freq_unit
gen_freq = 100
if fu == 'Hz':
gen_freq = 100e6
elif fu == 'GHz':
gen_freq = 0.1
self.gsm.generate(gen_freq)
self._n_pix = hp.get_map_size(self.gsm.generated_map_data)
self._n_side = hp.npix2nside(self._n_pix)
self._theta, self._phi = hp.pix2ang(self._n_side, np.arange(self._n_pix))
def add_sources_to_sky_map(
input_map,
frequencies,
sources,
fwhm_deg=("Auto", 1),
catalog_file="Auto",
reference_frequency="143",
):
"""
This function takes a PySM map array and adds point sources with a frequency behaviour
consistent with their SED as derived from the PCCS catalog. The point source is added in total intensity
and polarization (Q and U). Stokes parameters Q and U are derived using the polarization angle present in
the catalog
Input
input_map - NDARRAY - An array shaped (nfreq, npix, 3) containing sky maps in the
frequencies defined in the QUBIC dictionary (n_sub is the number
of frequencies, filter_nu is the center frequency,
filter_relative_bandwidth is the relative bandwidth
frequencies - LIST or NDARRAY - list of frequencies in Hz
sources - LIST or NDARRAY - list of sources ad defined in the QUBIC pccs
fwhm_deg - TUPLE - The fwhm in degrees of the gaussian used to smooth the source.
fwhm_deg is specified as a tuple. If fwhm_deg[0] == 'Auto' then
the fwhm is derived automatically by the pixel size multiplying it
by the factor specified in fwhm_deg[1]. If fwhm_deg[0] == 'Man' then
the fwhm is specified directly, in degrees, in fwhm_deg[1]. Default
is fwhm_deg = ('Auto', 1)
catalog_file - STRING - the catalog filename (in pickle format) If catalog_file = 'Auto'
(Default) then catalog_file = qubic.data.PATH + 'qubic_pccs2.pickle'
reference_frequency - STRING - the reference frequency in GHz in the catalog to derive the source
coordinates. It defaults to 143 GHz. Can be left to this value also
for 220 GHz, as the source location is weakly dependent on the
frequency
Output
output_map - NDARRAY - An array shaped (nfreq, npix, 3) containing sky + point
sources maps
"""
import qubic
import pickle
import numpy as np
import healpy as h
catalog_frequencies = ['030', '044', '070', '100', '143', '217', '353']
complement_frequencies = [
f for f in catalog_frequencies if f != reference_frequency
]
output_map = input_map.copy()
# Check that the number of frequencies is consistent with the input map
if len(input_map) != len(frequencies):
print("The number of maps and frequencies are inconsistent.")
print("There are %i maps and %i frequencies" %
(len(input_map), len(frequencies)))
return -1
nside = h.get_nside(input_map[0, :, 0])
# Define catalog file if not provided manually
if catalog_file == "Auto":
catalog_file = qubic.data.PATH + "qubic_pccs2.pickle"
# Define fwhm in degrees
if type(fwhm_deg) is not tuple:
print(
"The variable fwhm_deg must be a tuple. Call help(add_sources_to_sky_map) for more info"
)
return -1
if fwhm_deg[0] != "Auto" and fwhm_deg[0] != "Man":
print("fwhm_deg[0] must be either 'Auto' or 'Man'")
return -1
if fwhm_deg[0] == "Auto": # Then fwhm is the map pixel size
npix = h.get_map_size(input_map[0, :, 0])
pix_size_deg = (2 * np.sqrt(np.pi / npix) * 180 / np.pi
) # It's sqrt(4pi/npix) converted to deg
fwhm = fwhm_deg[1] * pix_size_deg
else:
fwhm = fwhm_deg[1]
# Open point source catalog
with open(catalog_file, "rb") as handle:
catalog = pickle.load(handle)
for source in sources:
# Check if source is in catalog with the reference frequency otherwise shift to the previous
# frequency
if source not in catalog[reference_frequency].keys():
isincatalog = [
source in catalog[f].keys() for f in complement_frequencies
]
if True not in isincatalog:
print('Source %s is not in catalog' % source)
return -1
print('Source %s is not in catalog at frequency %s GHz' %
(source, reference_frequency))
goodfreq = [i for i, x in enumerate(isincatalog) if x]
diff_freq = np.abs(
np.array(
list(
map(float,
[complement_frequencies[i] for i in goodfreq]))) -
float(reference_frequency))
index = np.where(diff_freq == np.min(diff_freq))[0]
reference_frequency = complement_frequencies[index[0]]
print('Switched to new reference frequency %s GHz' %
reference_frequency)
print("Processing source %s (%i/%i)" %
(source, list(sources).index(source) + 1, len(sources)))
source_center_deg = (
catalog[reference_frequency][source]["GLON"],
catalog[reference_frequency][source]["GLAT"],
)
# Calculate SED of source in T and P and fitting polynomial
sed = qubic.compact_sources_sed.build_sed(source, catalog, plot=False)
fi = np.poly1d(sed[source]["i_fit"])
fp = np.poly1d(sed[source]["p_fit"])
# Loop over frequencies, for each frequency get the corresponding flux in I and P
for fq in frequencies:
fq_index = list(frequencies).index(fq)
print("Processing frequency # %i of %i" %
(fq_index + 1, len(frequencies)))
i_flux = fi(fq / 1e9) / 1e3 # Conversion from mJy -> Jy
p_flux = fp(fq / 1e9) / 1e3 # Conversion from mJy -> Jy
polarization_angle = (
catalog[reference_frequency][source]["ANGLE_P"] * np.pi /
180.0)
if p_flux > 0.0:
q_flux = p_flux * np.cos(2.0 * polarization_angle)
u_flux = p_flux * np.sin(2.0 * polarization_angle)
else:
q_flux = 0
u_flux = 0
flux = [i_flux, q_flux, u_flux]
for index in [0, 1, 2]:
outmap = insert_source(
source_center_deg,
fwhm,
flux[index],
nside,
units="uK_CMB",
input_map=input_map[fq_index, :, index],
frequency=fq,
)
output_map[fq_index, :, index] = outmap
input_map = output_map.copy()
print("")
return output_map
def similar_range(params, map_struct):
if params['doObservability']:
observability_struct = map_struct['observability']
telescope = observability_struct.keys()[0]
prob = observability_struct[telescope]['prob']
else:
prob = map_struct['prob']
nested_map = hp.pixelfunc.reorder(prob, r2n=True)
regions = params['Nregions']
region_nsides = int((regions / 12)**.5)
res = hp.get_map_size(prob)
region_size = res / regions
sliced_array = np.zeros([regions, region_size])
start = 0
end = start + region_size
for region in range(regions):
sliced_array[region] = nested_map[start:end]
start += region_size
end += region_size
# Theres def a way to do this with numpy but i'm on a train, can't see docs
sum_hp = lambda arr: np.array([np.sum(row) for row in arr])
sums = sum_hp(sliced_array)
sum_neighbours = lambda n: np.sum(
[sums[p] for p in hp.get_all_neighbours(region_nsides, n, nest=True)])
nb_sums = np.array([sums[i] + sum_neighbours(i) for i in range(len(sums))])
region_order = np.argsort(nb_sums)[::-1]
significant_regions = np.array([])
for idx in region_order:
if sums[idx] > max(sums) * 0.0001:
significant_regions = np.append(significant_regions, idx)
significant_regions = significant_regions.astype(int)
groups = []
def group_neighbours(group):
neighbours = np.array([])
for i in group:
neighbours = np.append(
neighbours,
hp.get_all_neighbours(region_nsides, int(i), nest=True))
return neighbours
for idx in significant_regions:
if len(groups) == 0:
groups.append([idx])
continue
for group in groups:
if idx in group_neighbours(group):
group.append(idx)
break
else:
groups.append([idx])
group_maps = []
for group in groups:
combined_map = np.array([])
for i in range(len(sliced_array)):
if i in group:
combined_map = np.append(combined_map, sliced_array[i])
else:
combined_map = np.append(combined_map,
np.zeros(len(sliced_array[0])))
group_maps.append(combined_map)
group_maps = [hp.reorder(hp_map, n2r=True) for hp_map in group_maps]
return group_maps
sys.stdout = open(os.devnull, "w")
mask = hp.read_map('galacticMask.fits')
sys.stdout = sys.__stdout__
map_mask = []
for i in range(6):
map_mask.append(map_smooth[i] * mask)
print 'ILC on full sky'
f_nu = ilc.dist_SZ(freq)
a = np.ones(n_obs)
a_t = np.transpose(a)
b = np.ones(n_obs)
b = f_nu
b_t = np.transpose(b)
CMB = np.zeros(hp.get_map_size(map_smooth[0]))
TSZ = np.zeros(hp.get_map_size(map_smooth[0]))
J = np.cov((map_smooth[0], map_smooth[1], map_smooth[2], map_smooth[3],
map_smooth[4], map_smooth[5]))
K = np.linalg.inv(J)
WK, WT = ilc.weight(K, a, a_t, b, b_t)
# test with mask
if args.mask:
print 'ILC on full sky with mask'
L = np.cov((map_mask[0], map_mask[1], map_mask[2], map_mask[3],
map_mask[4], map_mask[5]))
P = np.linalg.inv(L)
WK_mask, WT_mask = ilc.weight(P, a, a_t, b, b_t)
for i in range(n_obs):
fact = 1.42144524614e-05
filename = 'data/HFI_CompMap_ThermalDustModel_2048_R1.20.fits'
filename = 'data/HFI_SkyMap_353_2048_R2.02_full.fits'
test_map = hp.read_map(filename)
#hp.mollview(test_map, title=filename, coord='G', unit='K', norm='hist', min=1e-7,max=1e-3, xsize=800)
hp.mollview(test_map, title=filename, coord='G', unit='K', norm='hist', xsize=800)
#hp.mollview(test_map)
#hp.cartview(test_map, title=filename, coord='G', rot=[0,0], unit='K', norm='hist', min=-1375,max=2687, xsize=800, lonra=[-1,1], latra=[-1,1])
#hp.orthview(test_map)
#hp.gnomview(test_map)
print hp.get_nside(test_map)
print hp.maptype(test_map)
print hp.get_map_size(test_map)
print len(test_map)
print test_map[0:10]*np.float(fact)
equateur_lon = [10.,0.]
equateur_lat = [10.,0.]
hp.projplot(equateur_lon, equateur_lat, lonlat=True, coord='G')
# plt.loglog(hp.anafast(test_map))
# plt.grid()
# plt.xlabel("$\ell$")
# plt.ylabel("$C_\ell$")
plt.grid()
plt.show()
def make_normmaps(maps, supmap, etacut=0.9):
r"""Divide an ensemble of maps by a single map, preferably the sum of
said ensemble.
Parameters
----------
maps : float, array_like
A single map or an ensemble of maps. They should be limited in
pseudorapidity by the value in `etacut`.
supmap : float, ndarray
A 1-D array usually representing the sum of all elements in `maps`.
etacut : float, scalar, optional
The value of the pseudorapidity limit, :math:`|\eta|` < `etacut`.
If there is no limit, set it to *None*. Default: 0.9.
Returns
-------
norm_maps : float, array_like
The result of dividing `maps` by `supmap`. Its shape will be the same
as `maps`.
Notes
-----
In the power spectral analysis at hand [1]_ [2]_, `supmap` is the sum
of all event maps and it is represented by :math:`F^{all}(\mathbf{n_p})`,
where :math:`\mathbf{n_p}` is a pixel number. A normalized map is thus defined
by the following expression:
.. math:: \bar{f}(\mathbf{n_p}) = \frac{f(\mathbf{n_p})}{F^{all}(\mathbf{n_p})},
where :math:`f(\mathbf{n_p})` is a map from the original event ensemble, the latter
denoted by the `maps` parameter.
References
----------
.. [1] M. Machado, P.H. Damgaard, J.J. Gaardhoeje, and C. Bourjau, "Angular power spectrum of heavy ion collisions", Phys. Rev. C **99**, 054910 (2019).
.. [2] M. Machado, "Heavy ion anisotropies: a closer look at the angular power spectrum", arXiv:1907.00413 [hep-ph] (2019).
"""
if maps[0].ndim == 0:
maps = np.reshape(maps, (1, len(maps)))
npix = hp.get_map_size(maps[0])
nside = hp.npix2nside(npix)
if etacut:
qi, qf = 2. * np.arctan(np.exp(-np.array([etacut, -etacut])))
mask = np.ones(npix)
mask[hp.query_strip(nside, qi, qf)] = 0.
else:
qi, qf = 0., 2 * np.pi
mask = 0.
finmap = supmap / npix * (1. - mask) + mask
pixs = np.where(finmap == 0.)
finmap[pixs] = 1.
norm_maps = maps / (npix * finmap)
norm_maps *= npix / np.sum(norm_maps, axis=1)[:, None]
return norm_maps
Nside = 4 # = 1, 2, 4, 8, 16, 64, ...
Resolution = hp.nside2resol(Nside)
print('(1)', Nside, '-->', Resolution, 'radians')
Resolution = hp.nside2resol(Nside, arcmin=True)
print('(2)', Nside, '-->', Resolution, 'arcmin =', Resolution / 60., 'deg')
Area = hp.nside2pixarea(Nside, degrees=True)
print('(3)', Nside, '-->', Area, 'square deg')
# get_map_size / get_nside
mapa = hp.read_map('COM_CMB_IQU-smica_1024_R2.02_full.fits')
Npix_mapa = hp.get_map_size(mapa)
Nside_mapa = hp.get_nside(mapa)
print('Nside =', Nside_mapa)
print('Npix =', Npix_mapa)
#%%
"""
STEP 6: Nside / Npix / Resolution
"""
mapa = hp.read_map('COM_CMB_IQU-smica_1024_R2.02_full.fits')
hp.mollview(mapa, title='CMB map - Nside=1024', unit='K')
mapa_deg = hp.ud_grade(mapa, 64, order_in='RING', order_out='NEST')
def __init__(self, noise_cov, mask):
self.tau = np.min(noise_cov[mask == 1])
self.t_cov = self.tau * np.ones(hp.get_map_size(noise_cov))
self.noise_cov = noise_cov
