# Fixed bias evol.
zfns = [6, 7, 8]
excl = [2, 4, 5, 9, 10, 11, 12, 13, 14, 15] #6,7,8 ]
excl += [i for i in range(len(pnames)) if "pk" in pnames[i]]
F2, lbls2 = rf.combined_fisher_matrix(F_list,
expand=zfns,
names=pnames,
exclude=excl)
# Invert matrices
cov = np.linalg.inv(F)
cov2 = np.linalg.inv(F2)
# Indices of fns. of z
zfns = [1, 3, 4, 5] # Update after other params subtracted
pf = rf.indexes_for_sampled_fns(3, zc.size, zfns)
pDA = rf.indexes_for_sampled_fns(4, zc.size, zfns)
pH = rf.indexes_for_sampled_fns(5, zc.size, zfns)
# Indices of fns. of z (bias fixed in z)
zfns = [3, 4, 5] # Update after other params subtracted
pf2 = rf.indexes_for_sampled_fns(3, zc.size, zfns)
pDA2 = rf.indexes_for_sampled_fns(4, zc.size, zfns)
pH2 = rf.indexes_for_sampled_fns(5, zc.size, zfns)
# SKA marginal errorbars
err_f = np.sqrt(np.diag(cov)[pf])
err_f2 = np.sqrt(np.diag(cov2)[pf2])
err_H = np.sqrt(cov[pH, pH]) * 100.
err_H2 = np.sqrt(cov2[pH2, pH2]) * 100.
err_DA = np.sqrt(cov[pDA, pDA]) * 1e3
# Trim params we don't care about here
# A(z), bHI(z), f(z), sig2, dA(z), H(z), [fNL], [omega_k_ng], [omega_DE_ng], pk
_F = rf.fisher_with_excluded_params(F_list[i], [6, 7, 8, 9])
# Expand fns. of z one-by-one for the current z bin. (Indices of fns. of z
# are given in reverse order, to make figuring out where they are in the
# updated matrix from the prev. step easier.)
# b_HI(z), f(z), dA(z), H(z)
zfns_b = [5, 4, 2, 1]
FF = _F
for idx in zfns_b:
FF = rf.expand_matrix_for_sampled_fn(FF, idx, Nbins, i)
F_b += FF
# Overlay error ellipses as a fn. of z
p1 = rf.indexes_for_sampled_fns(1, zc.size, zfns_b) # y
p2 = rf.indexes_for_sampled_fns(2, zc.size, zfns_b) # x
x = 1.
y = 1.
alpha = [1.52, 2.48, 3.44]
cmap = matplotlib.cm.get_cmap("spectral")
ZMAX = 1.39
print "Max:", np.max(zc)
ax = P.subplot(111)
Nused = np.where(zc <= ZMAX)[0].size # No. of z bins that are actually used
zvals = []
for i in range(len(p1)):
#if i % 2 == 0: continue
if zc[i] > ZMAX: continue
] #, 'fNL']
pnames += ["pk%d" % i for i in range(kc.size)]
zfns = [0, 1, 6, 7, 8]
excl = [2, 4, 5, 9, 10, 11, 12, 13, 14,
15] #,16] # Exclude all cosmo params
excl += [i for i in range(len(pnames)) if "pk" in pnames[i]]
F, lbls = rf.combined_fisher_matrix(F_list,
expand=zfns,
names=pnames,
exclude=excl)
cov = np.linalg.inv(F)
# Get functions of z
zfns = [0, 1, 3, 4, 5]
pA = rf.indexes_for_sampled_fns(0, zc.size, zfns)
print "A:", [lbls[j] for j in pA], "\n"
# Plot errorbars
errs = np.sqrt(np.diag(cov))
err = errs[pA]
P.plot(zc,
err,
color=colours[k],
lw=1.8,
marker='.',
label=labels[k],
ls=linestyle[k])
P.xlim((0.31, 2.52))
excl = [2, 4, 5, 6, 7, 8, 12, 14, 15] # wa fixed
excl += [i for i in range(len(pnames)) if "pk" in pnames[i]]
F, lbls = rf.combined_fisher_matrix(F_list,
expand=zfns,
names=pnames,
exclude=excl)
# Add Planck prior
Fpl = euclid.add_planck_prior(F, lbls, info=False)
print "-" * 50
print names[k]
print "-" * 50
# Invert matrices
pw0 = rf.indexes_for_sampled_fns(5, zc.size, zfns) #4, for omegak=fixed
pok = rf.indexes_for_sampled_fns(3, zc.size, zfns) #5
cov_pl = np.linalg.inv(Fpl)
print lbls[pw0], lbls[pok]
fom = rf.figure_of_merit(pw0, pok, None, cov=cov_pl)
print "%s: FOM = %3.2f" % (names[k], fom)
y = rf.experiments.cosmo['w0']
x = 0.
# Plot contours for w0, omega_k; wa fixed
w, h, ang, alpha = rf.ellipse_for_fisher_params(pok,
pw0,
None,
names=pnames,
exclude=excl)
# Just do the simplest thing for P(k) and get 1/sqrt(F)
cov = [
np.sqrt(1. / np.diag(F)[lbls.index(lbl)]) for lbl in lbls
if "pk" in lbl
]
cov = np.array(cov)
pk = cosmo['pk_nobao'](kc) * (1. + fbao(kc))
# Replace nan/inf values
cov[np.where(np.isnan(cov))] = 1e10
cov[np.where(np.isinf(cov))] = 1e10
pw0 = rf.indexes_for_sampled_fns(11, zc.size, zfns)
pwa = rf.indexes_for_sampled_fns(12, zc.size, zfns)
print "-" * 50
print names[k]
#print cov
print lbls[pw0], 1. / np.sqrt(F[pw0, pw0])
print lbls[pwa], 1. / np.sqrt(F[pwa, pwa])
"""
if k == 0:
# Plot shaded region
P.fill_between(kc, np.ones(kc.size)*1e-10, cov, facecolor='#e1e1e1', edgecolor='none')
else:
# Plot errorbars
P.plot(kc, cov, color=colours[k], label=labels[k], lw=2.2, ls=linestyle[k])
"""
expand=zfns,
names=pnames,
exclude=excl)
# Add Planck prior
Fpl = F.copy()
for i in range(0, 4):
for j in range(0, 4):
Fpl[3 + i, 3 + j] += euclid.planck_prior[i, j]
print lbls[3 + i], lbls[3 + j]
# Invert matrices
cov = np.linalg.inv(F)
cov_pl = np.linalg.inv(Fpl)
# Indices of fns. of z
pok = rf.indexes_for_sampled_fns(3, zc.size, zfns)
pw0 = rf.indexes_for_sampled_fns(5, zc.size, zfns)
# Fiducial point
x = rf.experiments.cosmo['omega_k_0']
y = rf.experiments.cosmo['w0']
if k == 0: ax.plot(x, y, 'kx', ms=10)
# w0, omega_K
w, h, ang, alpha = rf.ellipse_for_fisher_params(pok, pw0, cov, Finv=cov)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc='none',
Nbins = zc.size
# EOS FISHER MATRIX
pnames = [
'A', 'b_HI', 'Tb', 'sigma_NL', 'sigma8', 'n_s', 'f', 'aperp', 'apar',
'omegak', 'omegaDE', 'w0', 'wa', 'h', 'gamma'
]
zfns = [
1,
]
F_eos, lbls = rf.combined_fisher_matrix(F_eos_list,
exclude=[2, 4, 5, 6, 7, 8, 9, 12],
expand=zfns,
names=pnames)
# Overlay error ellipses as a fn. of z
p1 = rf.indexes_for_sampled_fns(4, zc.size, zfns) # w0 # y
#p2 = rf.indexes_for_sampled_fns(5, zc.size, zfns) # # x
p3 = rf.indexes_for_sampled_fns(5, zc.size, zfns) # h
p4 = rf.indexes_for_sampled_fns(6, zc.size, zfns) # gamma
Finv = np.linalg.inv(F_eos) # Pre-invert, for efficiency
i = 0
##################################
# w0 - h
##################################
x = rf.experiments.cosmo['w0']
y = rf.experiments.cosmo['h']
w, h, ang, alpha = rf.ellipse_for_fisher_params(p1[i],
p3[i],
F_eos,
1,
]
# Marginalise over omega_k
F_eos, lbls = rf.combined_fisher_matrix(
F_eos_list,
#exclude=[2,4,5,6,7,8,9,12],
exclude=[2, 4, 5, 6, 7, 8, 9, 14],
expand=zfns,
names=pnames)
Finv = np.linalg.inv(F_eos) # Pre-invert, for efficiency
print "Cond. No.:", np.linalg.cond(F_eos)
print "sig(h):", np.sqrt(Finv[6, 6])
px = rf.indexes_for_sampled_fns(4, zc.size, zfns) # x 4
py = rf.indexes_for_sampled_fns(5, zc.size, zfns) # y 5
#rf.plot_corrmat(Finv, lbls)
"""
# Fix omega_k
F_eos2, lbls2 = rf.combined_fisher_matrix( F_eos_list,
exclude=[2,4,5,6,7,8, 9,12],
expand=zfns, names=pnames)
Finv2 = np.linalg.inv(F_eos2) # Pre-invert, for efficiency
px2 = rf.indexes_for_sampled_fns(6, zc.size, zfns) # x
py2 = rf.indexes_for_sampled_fns(4, zc.size, zfns) # y
"""
# Fiducial point
x = rf.experiments.cosmo['w0']
'omegak', 'omegaDE', 'w0', 'wa', 'h', 'gamma'
]
#0:A, 1:b_HI, 2:sigma_NL, [3:omegak,] 4:omegaDE, 5:w0, 6:wa, 7:h, 8:gamma
zfns = [
1,
]
# Fix w0,wa
F_eos, lbls = rf.combined_fisher_matrix(
F_eos_list,
#exclude=[2,4,5,6,7,8,9,12],
exclude=[2, 4, 5, 6, 7, 8, 11, 12],
expand=zfns,
names=pnames)
Finv = np.linalg.inv(F_eos) # Pre-invert, for efficiency
px = rf.indexes_for_sampled_fns(3, zc.size, zfns) # x
py = rf.indexes_for_sampled_fns(4, zc.size, zfns) # y
#rf.plot_corrmat(F_eos, lbls)
# Fix wa
F_eos2, lbls2 = rf.combined_fisher_matrix(F_eos_list,
exclude=[2, 4, 5, 6, 7, 8, 12],
expand=zfns,
names=pnames)
Finv2 = np.linalg.inv(F_eos2) # Pre-invert, for efficiency
px2 = rf.indexes_for_sampled_fns(3, zc.size, zfns) # x
py2 = rf.indexes_for_sampled_fns(4, zc.size, zfns) # y
print "sigma(h) =", np.sqrt(
Finv2[rf.indexes_for_sampled_fns(6, zc.size, zfns),
]
F, lbls = rf.combined_fisher_matrix(F_list,
expand=zfns,
names=pnames,
exclude=[2, 4, 5, 6, 7, 8])
# Remove elements with zero diagonal (completely unconstrained)
zero_idxs = np.where(np.diag(F) == 0.)[0]
print "Zero idxs:", zero_idxs
F = rf.fisher_with_excluded_params(F, excl=zero_idxs)
lbls = lbls[:-zero_idxs.size]
#rf.plot_corrmat(F, lbls)
# Overlay error ellipses as a fn. of z
p1 = rf.indexes_for_sampled_fns(4, zc.size, zfns)
#p2 = rf.indexes_for_sampled_fns(5, zc.size, zfns)
# Full covmat
cov = np.linalg.inv(F)
diags = np.sqrt(np.diag(cov))
# Reduced covmat
#F2 = rf.fisher_with_excluded_params(F, excl=[l for l in range(19, 55)])
#cov2 = np.linalg.inv(F2)
#diags2 = np.sqrt(np.diag(cov2))
# Print diags.
for i in range(diags.size):
#if i < diags2.size:
# print "%2d %10s %3.4f %3.4f" % (i, lbls[i], diags[i], diags2[i])
'omegak', 'omegaDE', 'w0', 'wa', 'h', 'gamma', 'Mnu'
]
#0:A, 1:b_HI, 2:sigma_NL, 3:omegak, 4:omegaDE, 5:w0, [6:wa,] 7:h, 8:gamma, 9:Mnu
zfns = [
1,
]
# Marginalise over omega_k
F_eos, lbls = rf.combined_fisher_matrix(
F_eos_list,
#exclude=[2,4,5,6,7,8,9,12],
exclude=[2, 4, 5, 6, 7, 8, 12],
expand=zfns,
names=pnames)
Finv = np.linalg.inv(F_eos) # Pre-invert, for efficiency
px = rf.indexes_for_sampled_fns(7, zc.size, zfns) # x
py = rf.indexes_for_sampled_fns(5, zc.size, zfns) # y
"""
print "sigma(Mnu) =", np.sqrt( Finv[rf.indexes_for_sampled_fns(8, zc.size, [1,8]),rf.indexes_for_sampled_fns(8, zc.size, [1,8])] )
sigma_mnu = np.sqrt( Finv[rf.indexes_for_sampled_fns(8, zc.size, [1,8]),rf.indexes_for_sampled_fns(8, zc.size, [1,8])] )
P.subplot(111)
P.plot(zc, sigma_mnu, 'r-', lw=1.5)
P.plot(zc, sigma_mnu, 'r.', lw=1.5)
P.axhline(0.04, color='b', ls='dotted', lw=1.5)
P.ylabel(r"$\sigma(\Sigma m_\nu)$")
P.xlabel("z")
P.title(r"$\Sigma m_\nu|_\mathrm{fid.} = 0.1 \mathrm{eV}$")
P.show()
exit()
print "-" * 50
print names[k]
print "-" * 50
cov = np.linalg.inv(F)
cov_pl = np.linalg.inv(Fpl)
for j in range(len(lbls)):
print "%10s %3.4f %3.4f %3.4f" % (lbls[j], np.sqrt(
cov[j, j]), np.sqrt(cov_pl[j, j]), 1. / np.sqrt(np.diag(F))[j])
# Invert matrices
cov = np.linalg.inv(F)
cov_pl = np.linalg.inv(Fpl)
# Indices of fns. of z
pw0 = rf.indexes_for_sampled_fns(4, zc.size, zfns)
pwa = rf.indexes_for_sampled_fns(5, zc.size, zfns)
# Fiducial point
x = rf.experiments.cosmo['w0']
y = rf.experiments.cosmo['wa']
if k == 0: ax.plot(x, y, 'kx', ms=10)
"""
# omega_k, gamma fixed
w, h, ang, alpha = rf.ellipse_for_fisher_params(pw0, pwa, cov, Finv=cov)
ellipses = [matplotlib.patches.Ellipse(xy=(x, y), width=alpha[kk]*w,
height=alpha[kk]*h, angle=ang, fc='none', ec=colours[k],
lw=2.5, alpha=1.) for kk in range(0, 2)]
for e in ellipses: ax.add_patch(e)
"""
# b_HI(z), f(z), fix w_0, w_a
_F = F_eos_list[i]
_F = rf.fisher_with_excluded_params(_F, [6, 7])
zfns_fix_w0wa = [
2,
]
FF = _F
for idx in zfns_fix_w0wa:
FF = rf.expand_matrix_for_sampled_fn(FF, idx, Nbins, i)
F_w0wa += FF
ax = P.subplot(111)
# Overlay error ellipses as a fn. of z
p1 = rf.indexes_for_sampled_fns(4, zc.size, zfns_base) # omega_k # y
p2 = rf.indexes_for_sampled_fns(5, zc.size, zfns_base) # omega_de # x
# 1D marginals
cov = np.linalg.inv(F_wa)
print "sigma(ok) =", np.sqrt(cov[p1, p1])
print "sigma(oDE) =", np.sqrt(cov[p2, p2])
y = rf.experiments.cosmo['omega_k_0']
x = rf.experiments.cosmo['omega_lambda_0']
Fs = [F_base, F_wa, F_w0wa]
for i in range(len(Fs)):
FF = Fs[i]
a, b, ang = rf.ellipse_for_fisher_params(p1, p2, FF)
ellipses = [
F, lbls = rf.combined_fisher_matrix(F_list,
expand=zfns,
names=pnames,
exclude=excl)
# Add Planck prior
Fpl = F.copy()
# Indices of Planck prior Fisher matrix in our Fisher matrix
# w0:6, wa:7, omega_DE:5, omega_k:4, w_m, w_b, n_s:3
_names = ['w0', 'wa', 'omegaDE', 'omegak', 'w_m', 'w_b', 'n_s']
idxs_in_f = [6, 7, 5, 4, -1, -1, 3]
for i in range(len(idxs_in_f)):
if idxs_in_f[i] == -1: continue
for j in range(len(idxs_in_f)):
if idxs_in_f[j] == -1: continue
ii = rf.indexes_for_sampled_fns(idxs_in_f[i], zc.size, zfns)
jj = rf.indexes_for_sampled_fns(idxs_in_f[j], zc.size, zfns)
Fpl[ii, jj] += euclid.planck_prior_full[i, j]
#print ">>>", _names[i], _names[j], lbls[idxs_in_f[i]], lbls[idxs_in_f[j]]
cov = np.linalg.inv(F)
cov_pl = np.linalg.inv(Fpl)
print names[k]
for i in range(len(lbls)):
print "%2d %10s %3.4f %3.4f" % (i, lbls[i], np.sqrt(
cov[i, i]), np.sqrt(cov_pl[i, i]))
print "-" * 50
# Indices of fns. of z
pmnu = rf.indexes_for_sampled_fns(10, zc.size, zfns)
excl = [2, 4, 6, 7, 8, 9, 11, 12, 14] # Want to see n_s and M_nu
excl += [i for i in range(len(pnames)) if "pk" in pnames[i]]
F, lbls = rf.combined_fisher_matrix(F_list,
expand=zfns,
names=pnames,
exclude=excl)
# Add Planck prior
Fpl = euclid.add_planck_prior(F, lbls, info=False)
print "-" * 50
print names[k]
print "-" * 50
# Invert matrices
pns = rf.indexes_for_sampled_fns(3, zc.size, zfns)
pmnu = rf.indexes_for_sampled_fns(6, zc.size, zfns)
cov_pl = np.linalg.inv(Fpl)
print lbls[pns], lbls[pmnu]
fom = rf.figure_of_merit(pns, pmnu, None, cov=cov_pl)
print "%s: FOM = %3.2f" % (names[k], fom)
x = rf.experiments.cosmo['n']
y = 0.1 #rf.experiments.cosmo['wa']
# Plot contours for n_s, Mnu
w, h, ang, alpha = rf.ellipse_for_fisher_params(pns,
pmnu,
None,
