def test_shell_pspec_dft():
"""
Take a gaussian shell and confirm its power spectrum using shell_project_pspec.
"""
select_radius = 10. #degrees
N_sections = 10
Nside = 256
Npix = 12 * Nside**2
Omega = 4 * np.pi / float(Npix)
Nfreq = 100
freqs = np.linspace(167.0, 177.0, Nfreq)
dnu = np.diff(freqs)[0]
Z = 1420 / freqs - 1.
sig = 2.0
mu = 0.0
shell = np.random.normal(mu, sig, (Npix, Nfreq))
dV0 = comoving_voxel_volume(Z[Nfreq / 2], dnu, Omega)
for fi in range(Nfreq):
dV = comoving_voxel_volume(Z[fi], dnu, Omega)
shell[:, fi] = np.random.normal(mu, sig * np.sqrt(dV0 / dV), Npix)
kbins, pk, errs = pspec_funcs.shell_project_pspec(shell,
Nside,
select_radius,
freqs=freqs,
Nkbins=100,
N_sections=N_sections,
cosmo=True,
method='dft',
error=True)
tol = np.sqrt(np.var(pk))
print 'Tolerance: ', tol
print 'Error: ', np.mean(pk / (sig**2 * dV0))
nt.assert_true(np.isclose(np.mean(pk), sig**2 * dV0, atol=tol))
def compare_averages_shell_pspec_dft():
"""
Take a gaussian shell and confirm its power spectrum using shell_project_pspec.
"""
import pylab as pl
select_radius = 5. #degrees
Nside = 256
Npix = 12 * Nside**2
Omega = 4 * np.pi / float(Npix)
Nfreq = 100
freqs = np.linspace(167.0, 177.0, Nfreq)
dnu = np.diff(freqs)[0]
Z = 1420 / freqs - 1.
sig = 2.0
mu = 0.0
shell = np.random.normal(mu, sig, (Npix, Nfreq))
dV = comoving_voxel_volume(Z[Nfreq / 2], dnu, Omega)
variances = []
pks = []
fig, (ax0, ax1, ax2) = pl.subplots(nrows=1, ncols=3)
steps = range(10, 110, 10)
for n in steps:
Nkbins = 100
kbins, pk = pspec_funcs.shell_project_pspec(shell,
Nside,
select_radius,
freqs=freqs,
Nkbins=Nkbins,
N_sections=n,
cosmo=True,
method='dft',
error=False)
variances.append(np.var(pk[0:Nkbins - 5]))
pks.append(pk)
ax0.plot(kbins, pk, label=str(n))
ax0.axhline(y=dV * sig**2)
ax0.legend()
ax1.plot(steps, variances)
ax2.imshow(np.log10(np.array(pks)[:, 0:Nkbins - 5]), aspect='auto')
pl.show()
def compare_selection_radii_shell_pspec_dft():
import pylab as pl
N_sections = 20
Nside = 256
Npix = 12 * Nside**2
Omega = 4 * np.pi / float(Npix)
Nfreq = 100
freqs = np.linspace(167.0, 177.0, Nfreq)
dnu = np.diff(freqs)[0]
Z = 1420 / freqs - 1.
sig = 2.0
mu = 0.0
shell = np.random.normal(mu, sig, (Npix, Nfreq))
dV = comoving_voxel_volume(Z[Nfreq / 2], dnu, Omega)
variances = []
pks = []
means = []
fig, (ax0, ax1, ax2) = pl.subplots(nrows=1, ncols=3)
steps = np.linspace(2, 20, 20)
for s in steps:
Nkbins = 100
kbins, pk = pspec_funcs.shell_project_pspec(shell,
Nside,
s,
freqs=freqs,
Nkbins=Nkbins,
N_sections=N_sections,
cosmo=True,
method='dft',
error=False)
variances.append(np.var(pk[0:Nkbins - 5]))
pks.append(pk)
means.append(np.mean(pk[0:Nkbins - 5]))
ax0.plot(kbins, pk, label=u'{:0.2f}°'.format(s))
ax0.axhline(y=dV * sig**2)
ax0.legend()
ax1.plot(steps, means)
im = ax2.imshow(np.log10(np.array(pks)[:, 0:Nkbins - 5]), aspect='auto')
fig.colorbar(im, ax=ax2)
pl.show()
def test_orthoslant_project():
Nside = 256
Npix = 12 * Nside**2
Omega = 4 * np.pi / float(Npix)
Nfreq = 100
freqs = np.linspace(167.0, 177.0, Nfreq)
dnu = np.diff(freqs)[0]
Z = 1420 / freqs - 1.
sig = 2.0
mu = 0.0
shell = np.random.normal(mu, sig, (Npix, Nfreq))
center = [np.sqrt(2) / 2., np.sqrt(2) / 2., 0]
## For orientation tests, replace with a single point at center
# import healpy
# cind = healpy.vec2pix(Nside, *center)
# shell *= 0.0
# shell[cind] += 10
orthogrid = pspec_funcs.orthoslant_project(shell, center, 10, degrees=True)
Nx, Ny, Nz = orthogrid.shape
Lx = comoving_transverse_length(Z[Nfreq / 2], Omega) * Nx
Ly = Lx
Lz = comoving_radial_length(Z[Nfreq / 2], dnu) * Nz
dV = comoving_voxel_volume(Z[Nfreq / 2], dnu, Omega)
r_mpc = WMAP9.comoving_distance(Z).to("Mpc").value
kbins, pk = pspec_funcs.box_dft_pspec(orthogrid, [Lx, Ly, Lz],
r_mpc=r_mpc,
cosmo=True)
tol = np.sqrt(np.var(pk))
nt.assert_true(np.allclose(np.mean(pk), sig**2 * dV, atol=tol))
# Frequency
freqs = np.linspace(1e8, 1.3e8, Nfreqs) #30 MHz
Nfreqs = freqs.size
# Shells
Nside = args.Nside
Npix = 12*Nside**2
sig = args.sigma
Nskies = args.Nskies
#shell0 = np.zeros((Nskies,Npix,Nfreqs), dtype=float)
shell0 = utils.mparray((Nskies, Npix, Nfreqs), dtype=float)
#shell0 = np.random.normal(0.0, sig, (Nskies, Npix, Nfreqs))
dnu = np.diff(freqs)[0]/1e6
om = 4*np.pi/float(Npix)
Zs = 1420e6/freqs - 1
dV0 = comoving_voxel_volume(Zs[Nfreqs/2], dnu, om)
print("Making skies")
for fi in range(Nfreqs):
dV = comoving_voxel_volume(Zs[fi], dnu, om)
s = sig * np.sqrt(dV0/dV)
shell0[:,:,fi] = np.random.normal(0.0, s, (Nskies, Npix))
#Make observatories
visibs = []
#fwhms = [2.5, 5.0, 10.0, 20.0, 25.0, 30.0]
#fwhms = [35, 40, 45.0, 50.0, 55.0, 60.0]
fwhm = args.fwhm
sigma = fwhm/2.355
obs = visibility.observatory(latitude, longitude, array=[bl], freqs=freqs)
obs.set_fov(fov)
obs.set_pointings(time_arr)
def compare_selection_radii_shell_pspec_dft():
N_sections=10
Nside=256
Npix = 12 * Nside**2
Omega = 4*np.pi/float(Npix)
Nfreq = 100
freqs = np.linspace(167.0, 177.0, Nfreq)
dnu = np.diff(freqs)[0]
Z = 1420/freqs - 1.
sig = 2.0
mu = 0.0
shell = np.random.normal(mu, sig, (Npix, Nfreq))
dV = comoving_voxel_volume(Z[Nfreq/2], dnu, Omega)
variances = []
pks = []
means = []
gs = gridspec.GridSpec(2, 3)
fig = pl.figure()
ax0 = pl.subplot(gs[0, 0:2])
ax1 = pl.subplot(gs[1, 0])
ax3 = pl.subplot(gs[1, 1])
ax2 = pl.subplot(gs[:, 2])
steps = np.linspace(2,20,20)
vmin,vmax = min(steps),max(steps)
normalize = mcolors.Normalize(vmin=vmin, vmax=vmax)
colormap = cm.viridis
for s in steps:
Nkbins = 100
kbins, pk = pspec_funcs.shell_project_pspec(shell, Nside, s, freqs=freqs, Nkbins=Nkbins, N_sections=N_sections, cosmo=True, method='dft', error=False)
variances.append(np.var(pk[0:Nkbins-5]))
pks.append(pk)
means.append(np.mean(pk[0:Nkbins-5]))
ax0.plot(kbins, pk, label=u'{:0.2f}°'.format(s), color=colormap(normalize(s)))
ax0.axhline(y=dV*sig**2)
# ax0.legend(ncol=2,loc=3)
scalarmappable = cm.ScalarMappable(norm=normalize, cmap=colormap)
scalarmappable.set_array(steps)
fig.colorbar(scalarmappable,label=r'Selection radius', ax=ax0)
ax0.set_ylabel(r"P(k) [mK$^2$ Mpc$^{3}]$")
ax0.set_xlabel(r"k [Mpc$^{-1}]$")
ax1.plot(steps, np.array(variances), label="Variance")
ax1.set_ylabel(r"Variance(P(k)) [mK$^4$ Mpc$^{6}]$")
ax1.set_xlabel(u"Selection radius (degrees)")
ax3.plot(steps, means, label="Mean")
ax3.set_ylabel(r"Mean(P(k)) [mK$^2$ Mpc$^{3}]$")
ax3.set_xlabel(u"Selection radius (degrees)")
ax1.legend()
ax3.legend()
ax1.xaxis.set_major_formatter(FormatStrFormatter(u'%0.2f°'))
ax3.xaxis.set_major_formatter(FormatStrFormatter(u'%0.2f°'))
im = ax2.imshow(np.array(pks)[:,0:Nkbins-5], aspect='auto', norm=mcolors.LogNorm())
fig.colorbar(im, ax=ax2)
pl.show()
def compare_averages_shell_pspec_dft():
"""
Take a gaussian shell and confirm its power spectrum using shell_project_pspec.
"""
select_radius = 5. #degrees
Nside=256
Npix = 12 * Nside**2
Omega = 4*np.pi/float(Npix)
Nfreq = 100
freqs = np.linspace(167.0, 177.0, Nfreq)
dnu = np.diff(freqs)[0]
Z = 1420/freqs - 1.
sig = 2.0
mu = 0.0
shell = np.random.normal(mu, sig, (Npix, Nfreq))
dV = comoving_voxel_volume(Z[Nfreq/2], dnu, Omega)
variances = []
means = []
pks = []
gs = gridspec.GridSpec(2, 3)
fig = pl.figure()
ax0 = pl.subplot(gs[0, 0:2])
ax1 = pl.subplot(gs[1, 0])
ax3 = pl.subplot(gs[1, 1])
ax2 = pl.subplot(gs[:, 2])
steps = range(10,110,10)
vmin,vmax = min(steps),max(steps)
normalize = mcolors.Normalize(vmin=vmin, vmax=vmax)
colormap = cm.viridis
for n in steps:
Nkbins = 100
kbins, pk = pspec_funcs.shell_project_pspec(shell, Nside, select_radius, freqs=freqs, Nkbins=Nkbins, N_sections=n, cosmo=True, method='dft', error=False)
variances.append(np.var(pk[0:Nkbins-5]))
means.append(np.mean(pk[0:Nkbins-5]))
pks.append(pk)
ax0.plot(kbins, pk, label=str(n), color=colormap(normalize(n)))
ax0.axhline(y=dV*sig**2, color='k', lw=2.0)
# ax0.legend()
scalarmappable = cm.ScalarMappable(norm=normalize, cmap=colormap)
scalarmappable.set_array(steps)
fig.colorbar(scalarmappable,label=r'Number of snapshots', ax=ax0)
ax0.set_ylabel(r"P(k) [mK$^2$ Mpc$^{3}]$")
ax0.set_xlabel(r"k [Mpc$^{-1}]$")
ax1.plot(steps, np.array(variances), label="Variance")
ax1.set_ylabel(r"Variance(P(k)) [mK$^4$ Mpc$^{6}]$")
ax1.set_xlabel(u"Number of 5° snapshots")
ax3.plot(steps, means, label="Mean")
ax3.set_ylabel(r"Mean(P(k)) [mK$^2$ Mpc$^{3}]$")
ax3.set_xlabel(u"Number of 5° snapshots")
ax1.legend()
ax3.legend()
im = ax2.imshow(np.array(pks)[:,0:Nkbins-5], aspect='auto')#, norm=mcolors.LogNorm())
fig.colorbar(im, ax=ax2)
print('Fractional deviation: ', np.mean(np.abs(pk - dV*sig**2)))
pl.show()
# bins = np.average(bins, axis=0)
# cs = np.average(cs, axis=0)
save_dict['covar_data'] = cs
time_arr = np.average(bins, axis=0)
version = data_cfg['root'].split('/')[-1]
save_dict['times'] = time_arr
save_results(save_dict, data_cfg, out_cfg)
# Get a reference line, if available
if 'Nside' in catalog_cfg:
if 'sigma' in catalog_cfg:
nside = catalog_cfg['Nside']
sigma = catalog_cfg['sigma']
om = 4 * np.pi / (12. * nside**2)
dnu = np.diff(freq_obs)[0] / 1e6 #MHz
ref_line = comoving_voxel_volume(Zmean, dnu, om) * (sigma)**2
if 'furlanetto_flat' in catalog_cfg:
f = readsav('/users/alanman/FHD/catalog_data/eor_power_1d.idlsave')
maxpow = max(f['power'])
ref_line = maxpow / 0.7**3 #Furlanetto's curve includes little-h
if 'npz' in catalog_cfg:
# Setting reference level to the most averaged spectrum in an npz file.
f = np.load(catalog_cfg['npz'])
try:
ref_avg_mode = f['avg_mode']
except KeyError:
ref_avg_mode = 'over_k'
ref_avgs = f['avgs']
if ref_avg_mode == 'over_k':
print ref_avgs.shape
