def test_likelihoods():
""" The output should be samples of a chi squared distribution with lik_FT.nz_modes d.o.f. """
cls = [cl_pp, cl_noise, cl_unl]
labels = ["pp", "noise", "unl"]
sim_libs = [lib_pp, lib_noise, lib_cmb_unl]
ress = [HD_res, LD_res, HD_res]
histos = []
def is_ok(sig):
if abs(sig) < 0.01:
return "** deviation suspiciously small **"
if abs(sig) >= 0.01 and abs(sig) < 3.0:
return " Test OK"
if abs(sig) >= 3.0:
return "** deviation suspiciously large **"
for cl, label, sims, res in zip(cls, labels, sim_libs, ress):
histo = []
lik_FT = likelihoods.circulant_Gauss_pdf_fourierspace(cl, (res, res), lside)
for i, idx in enumerate_progress(np.arange(nsims), "+ test_likelihoods::collecting chi2 " + label + " sims"):
sim = sims.get_sim(idx)
Npix = lik_FT.dof
histo.append((lik_FT.eval_log(sim) + lik_FT.lnZ) / Npix)
histo = np.array(histo)
histos.append(histo)
# A chi sqd distribution with k d.o.f. has mean k and variance 2k
# The loglikelihood is - 1/2 chi sqd where d.o.f. is the number of modes with nonzero spectrum.
dev = (1.0 + 2 * np.mean(histo)) / np.sqrt(2.0 / lik_FT.dof / nsims)
print "+++++++++++++++++++++++++++++++++++++++++++++++++++"
print "+ Number of sims :", str(nsims)
print "+ d.o.f. / Npix :", np.round(float(lik_FT.dof) / (2 ** res) ** 2, 2)
print "+ Mean chi2, " + label + " sims, dev. from theory", np.round(dev, 3), " sig. "
print "+ ---->", is_ok((1.0 + 2 * np.mean(histo)) / np.sqrt(2.0 / lik_FT.dof / nsims))
print "+++++++++++++++++++++++++++++++++++++++++++++++++++"
return histos
def plot_gradients(number_of_sims=1):
"""
Plot the total curvature (F. info) for phi and Omega for different volumes.
"""
import pylab as pl
pl.ioff()
FT_lik = likelihoods.circulant_Gauss_pdf_fourierspace(cl_pp, (HD_res, HD_res), lside)
curvp, curvO, curvpO = Fisher_lib.get_curvature_matrix_PhiOmega_ell()
curvp = (1j + 1.0) * curvp
# curvp += FT_lik.eval_curv()
grad = curvp * 0
print "+++++++++++++++++++++++++++++++++++++++++++++++++++"
for i, idx in enumerate_progress(np.arange(number_of_sims), label="plot_gradients::collecting sims"):
dat = sim_lib_fixedphi.get_sim(idx)
umap = len_cov.apply_cg_inverse(dat)[0].reshape(LD_shape)
grad += len_cov.likelihood_gradient_phiOmega_ell(umap, nodisplacement=True)[0]
# Estimate of phi
nz = np.where(curvp != 0.0)
phik_est = grad * 0
phik_est[nz] = -grad[nz] / curvp[nz]
phi_est = np.fft.irfft2(phik_est, HD_shape) * np.prod(HD_shape) / np.sqrt(len_cov.HD_cub.vol())
counts, Cl_raw = rfft2_utils.rfft2cl(np.fft.rfft2(phi_est), lside)
ell = np.arange(len(counts))
nz = np.where(counts > 0.0)
N0 = np.zeros(len(counts))
ell_N0 = rfft2_utils.k2ell(Fisher_lib.kx_from_index(np.arange(1, Fisher_lib.N_2p1 - 1)))
N0[ell_N0] = 1.0 / (0.5 * curvp.real[0, 1 : Fisher_lib.N_2p1 - 1])
N0[10:] = np.exp(np.interp(np.log(ell[10:]), np.log(ell[ell_N0]), np.log(N0[ell_N0])))
pl.figure()
pl.title("Reconstruction")
pl.loglog(binner.bin_centers(), binner.bin_that(ell[nz], (Cl_raw * ell ** 4 / np.pi / 2.0)[nz]), label="Clraw")
pl.plot(
binner.bin_centers(),
binner.bin_that(ell[nz], ((Cl_raw - number_of_sims * N0) * ell ** 4 / np.pi / 2.0)[nz]),
label="Clraw - N0",
)
pl.plot(np.arange(len(cl_pp)), cl_pp * np.arange(len(cl_pp)) ** 4 / np.pi / 2.0)
nz0 = np.where(N0 > 0.0)
pl.plot(ell[nz0], number_of_sims * (N0 * ell ** 4 / 2.0 / np.pi)[nz0], label="N0")
pl.legend(frameon=False)
pl.xlabel("L")
pl.ylabel("$C_L L^2 (L+1)^2 /2 \pi$")
pl.ylim(1e-10, 2e-7)
pl.savefig(path_to_figs + "/reconstruction.pdf")
pl.close()
print "+++++++++++++++++++++++++++++++++++++++++++++++++++"
def plot_curvature():
"""
Plot the total curvature (F. info) for phi and Omega for different volumes.
"""
import pylab as pl
pl.ioff()
pl.figure()
d_ress = [0, 2]
print "+++++++++++++++++++++++++++++++++++++++++++++++++++"
for d_res in d_ress:
if d_res == d_ress[0]:
print "+plot_curvature:: doing res", HD_res + d_res
else:
print "+ doing res", HD_res + d_res
res = HD_res + d_res
lsides = lside * 2 ** d_res
Fisher = likelihoods.flatsky_Fisher_lib(cl_unl, (res, res), lsides, sN_uKamin, beam_FWHM_amin, verbose=False)
FT_p_lik = likelihoods.circulant_Gauss_pdf_fourierspace(cl_pp, (res, res), lsides)
idcs = np.arange(1, 2 ** (res - 1))
Fpp, FOO, FpO = Fisher.get_curvature_matrix_PhiOmega_ell()
Fpp = Fpp[0, idcs]
FOO = FOO[0, idcs]
Fpp += FT_p_lik.eval_curv().real[0, idcs]
kx = Fisher.kx_from_index(idcs)
Nlev_pp = 1.0 / Fpp * 2 # On complex modes
Nlev_OO = 1.0 / FOO * 2 # On complex modes
pl.loglog(kx, Nlev_pp * kx ** 2 * (kx + 1) ** 2 / 2.0 / np.pi * 1e7, label="$\phi$, res =" + str(res))
pl.loglog(kx, Nlev_OO * kx ** 2 * (kx + 1) ** 2 / 2.0 / np.pi * 1e7, label="$\Omega$, res =" + str(res))
pl.plot(
np.arange(len(cl_pp)),
cl_pp * np.arange(len(cl_pp)) ** 2 * (np.arange(len(cl_pp)) + 1) ** 2 / 2.0 / np.pi * 1e7,
label="$C^{\phi\phi}$",
)
pl.legend(frameon=False)
pl.title("Total inverse curvature")
pl.xlabel("$\ell$")
pl.ylabel("$C_\ell \ell^2 (\ell + 1)^2 /2\pi $")
print "+plot_curvature:: saving fig curvatures.pdf"
pl.savefig(path_to_figs + "/curvatures.pdf")
pl.close()
print "+++++++++++++++++++++++++++++++++++++++++++++++++++"
