print "-" * 50
# Invert matrix
cov_pl = np.linalg.inv(Fpl)
# Calculate FOM
print "1D sigma(Mnu) = %3.4f" % np.sqrt(cov_pl[pMnu, pMnu])
print "1D sigma(n_s) = %3.4f" % np.sqrt(cov_pl[pNeff, pNeff])
x = 0.1 #rf.experiments.cosmo['w0'] # Mnu
y = rf.experiments.cosmo['ns'] #3.046 #rf.experiments.cosmo['wa'] # Neff
# Plot contours for w0, wa; omega_k free
transp = [1., 0.85]
w, h, ang, alpha = rf.ellipse_for_fisher_params(pMnu,
pNeff,
None,
Finv=cov_pl)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc=colours[k][kk],
ec=colours[k][0],
lw=1.5,
alpha=transp[kk]) for kk in [1, 0]
]
for e in ellipses:
ax.add_patch(e)
# Centroid
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
zvals.append(zc[i])
a, b, ang = rf.ellipse_for_fisher_params(p1[i], p2[i], F_b)
a /= rf.bias_HI(zc[i], cosmo)
b /= fc[i]
c = i * 0.97 / float(Nused - 1) # Colour (must be 0 <= c <= 1)
print c
# Get 1,2,3-sigma ellipses and plot
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[k] * b,
height=alpha[k] * a,
angle=ang,
fc='none',
ec=cmap(c),
lw=1.5) for k in [
0,
print names[k]
print "-" * 50
# Invert matrix
cov_pl = np.linalg.inv(F)
for jj in range(pf.size):
#if jj % 2 == 0: continue
print jj, lbls[pb[jj]], lbls[pf[jj]]
x = rf.bias_HI(zc[jj], cosmo) * cosmo['sigma_8']
y = fc[jj] * cosmo['sigma_8']
# Plot contours for w0, wa; omega_k free
w, h, ang, alpha = rf.ellipse_for_fisher_params(pb[jj],
pf[jj],
None,
Finv=cov_pl)
transp = [1., 0.85]
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc=colours[k][kk],
ec=colours[k][0],
lw=1.3,
alpha=0.85) for kk in [
1,
]
]
for e in ellipses:
print "-" * 50
print names[k]
print "-" * 50
# Invert matrix
cov_pl = np.linalg.inv(Fpl)
# Print 1D marginals
print "1D sigma(%s) = %3.4f" % (param1, np.sqrt(cov_pl[p1, p1]))
#print "1D sigma(%s) = %3.4f" % (param2, np.sqrt(cov_pl[p2,p2]))
# Plot contours for gamma, w0
#transp = [1., 0.85]
transp = [0.98, 0.8]
w, h, ang, alpha = rf.ellipse_for_fisher_params(p1, p2, None, Finv=cov_pl)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc=colours[k][kk],
ec=colours[k][0],
lw=1.5,
alpha=transp[kk]) for kk in [1, 0]
]
for e in ellipses:
ax.add_patch(e)
# Centroid
if k == 1: ax.plot(x, y, 'ko')
# Invert matrix
cov_pl = np.linalg.inv(Fpl)
# Print 1D marginals
print "1D sigma(w_0) = %3.4f" % np.sqrt(cov_pl[pw0,pw0])
print "1D sigma(gamma) = %3.4f" % np.sqrt(cov_pl[pgam,pgam])
print lbls
x = rf.experiments.cosmo['gamma']
y = rf.experiments.cosmo['w0']
# Plot contours for gamma, w0
transp = [1., 0.85]
if k == 1: transp = [1., 0.95]
w, h, ang, alpha = rf.ellipse_for_fisher_params(pgam, pw0, None, Finv=cov_pl)
ellipses = [matplotlib.patches.Ellipse(xy=(x, y), width=alpha[kk]*w,
height=alpha[kk]*h, angle=ang, fc=colours[k][kk],
ec=colours[k][0], lw=1.5, alpha=transp[kk]) for kk in [1,0]]
for e in ellipses: ax.add_patch(e)
# Centroid
if k == 0: ax.plot(x, y, 'ko')
# Report on what options were used
print "-"*50
s1 = "Marginalised over Omega_K" if MARGINALISE_CURVATURE else "Fixed Omega_K"
s2 = "Marginalised over ns, sigma8" if MARGINALISE_INITIAL_PK else "Fixed ns, sigma8"
s3 = "Marginalised over Omega_b" if MARGINALISE_OMEGAB else "Fixed Omega_b"
print "NOTE:", s1
print "NOTE:", s2
# Calculate FOM
fom = rf.figure_of_merit(pw0, pwa, None, cov=cov_pl)
print "%s: FOM = %3.2f" % (names[k], fom)
print "1D sigma(w_0) = %3.4f" % np.sqrt(cov_pl[pw0, pw0])
print "1D sigma(w_a) = %3.4f" % np.sqrt(cov_pl[pwa, pwa])
x = rf.experiments.cosmo['w0']
y1 = rf.experiments.cosmo['omega_lambda_0']
y2 = rf.experiments.cosmo['wa']
transp = [1., 0.85]
# Plot contours for w0, omega_DE
w, h, ang, alpha = rf.ellipse_for_fisher_params(pw0,
pode,
None,
Finv=cov_pl)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y1),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc=colours[k][kk],
ec=colours[k][0],
lw=1.5,
alpha=transp[kk]) for kk in [1, 0]
]
for e in ellipses:
ax1.add_patch(e)
ax1.plot(x, y1, 'kx', mew=1.2)
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']
y = rf.experiments.cosmo['wa']
if k == 0: ax.plot(x, y, 'kx', ms=10)
# Marginalise over omega_k
w, h, ang, alpha = rf.ellipse_for_fisher_params(px[0],
py[0],
F_eos,
Finv=Finv)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc='none',
ec=colours[k],
lw=2.,
alpha=0.9) for kk in range(0, 2)
]
for e in ellipses:
ax.add_patch(e)
"""
# Fix omega_k
# 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',
ec=colours[k],
lw=2.5,
alpha=1.) for kk in range(0, 2)
]
for e in ellipses:
ax.add_patch(e)
# w0, omega_K, plus Planck prior
w, h, ang, alpha = rf.ellipse_for_fisher_params(pok, pw0, cov, Finv=cov_pl)
print "-" * 50
# Invert matrix
cov_pl = np.linalg.inv(Fpl)
# Calculate FOM
print "2*sigma(M_nu) = %3.4f" % (2. * np.sqrt(cov_pl[pmnu, pmnu]))
x = 0.06 #rf.experiments.cosmo['Mnu']
y = rf.experiments.cosmo['sigma_8']
transp = [1., 0.85]
# Plot contours for w0, omega_DE
w, h, ang, alpha = rf.ellipse_for_fisher_params(pmnu,
psig8,
None,
Finv=cov_pl)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc=colours[k][kk],
ec=colours[k][0],
lw=1.5,
alpha=transp[kk]) for kk in [1, 0]
]
for e in ellipses:
ax1.add_patch(e)
ax1.plot(x, y, 'kx', mew=1.2)
# 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,
Finv=Finv)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc='none',
ec=colours[k],
lw=2.,
alpha=0.85) for kk in range(0, 2)
]
for e in ellipses:
ax1.add_patch(e)
if k == 0: ax1.plot(x, y, 'kx')
#exclude=[2,4,5,6,7,8,9,12],
exclude=[2, 4, 5, 6, 7, 8, 11, 12, 14],
expand=zfns,
names=pnames)
Finv3 = np.linalg.inv(F_eos3) # Pre-invert, for efficiency
px3 = rf.indexes_for_sampled_fns(3, zc.size, zfns) # x
py3 = rf.indexes_for_sampled_fns(4, zc.size, zfns) # y
# Fiducial point
x = rf.experiments.cosmo['omega_k_0']
y = rf.experiments.cosmo['omega_lambda_0']
if k == 0: ax.plot(x, y, 'kx', ms=10)
# omega_k, omega_DE (wa fixed)
w, h, ang, alpha = rf.ellipse_for_fisher_params(px2[0],
py2[0],
F_eos2,
Finv=Finv2)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc='y',
ec='y',
lw=2.,
alpha=0.25) for kk in range(0, 2)
]
for e in ellipses:
ax.add_patch(e)
# omega_k, omega_DE (w0,wa fixed)
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
print "sigma(Mnu) =", np.sqrt(
Finv[rf.indexes_for_sampled_fns(7, zc.size, zfns),
rf.indexes_for_sampled_fns(7, zc.size, zfns)])
# Fiducial point
x = rf.experiments.cosmo['gamma']
y = rf.experiments.cosmo['w0']
if k == 0: ax.plot(x, y, 'kx', ms=10)
# Marginalise over omega_k
w, h, ang, alpha = rf.ellipse_for_fisher_params(px[0],
py[0],
F_eos,
Finv=Finv)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc='none',
ec=colours[k],
lw=2.,
alpha=0.9) for kk in range(0, 2)
]
for e in ellipses:
ax.add_patch(e)
# Fix omega_k
# 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)
"""
# omega_k, gamma fixed, plus Planck prior
w, h, ang, alpha = rf.ellipse_for_fisher_params(pw0, pwa, cov, Finv=cov_pl)
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)
"""
# Fix omega_k
w, h, ang, alpha = rf.ellipse_for_fisher_params(px2[0], py2[0], F_eos2, Finv=Finv2)
# 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 = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * b,
height=alpha[kk] * a,
angle=ang,
fc='none',
ec=colours[i],
lw=2.,
alpha=0.85) for kk in range(0, 2)
]
for e in ellipses:
ax.add_patch(e)
ax.plot(x, y, 'kx')
ax.set_ylabel(r"$\Omega_K$", fontdict={'fontsize': '20'})
pns = rf.indexes_for_sampled_fns(3, zc.size, zfns)
x = 0.15 #rf.experiments.cosmo['mnu']
y = rf.experiments.cosmo['n']
"""
# Mnu, n_s
w, h, ang, alpha = rf.ellipse_for_fisher_params(pmnu, pns, 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)
"""
# Mnu, n_s + Planck
w, h, ang, alpha = rf.ellipse_for_fisher_params(pmnu,
pns,
None,
Finv=cov_pl)
ellipses = [
matplotlib.patches.Ellipse(xy=(x, y),
width=alpha[kk] * w,
height=alpha[kk] * h,
angle=ang,
fc='none',
ec=colours[k + 1],
lw=2.5,
alpha=1.,
ls='solid') for kk in range(0, 2)
]
for e in ellipses:
ax.add_patch(e)
"""
