def check_Bessel_spectrum(l, k=None, r0=100):
# Initialise survey and spectra
cosmo = cosmicpy.cosmology()
surv = cosmicpy.survey(nzparams={
'type': 'gaussian',
'cosmology': cosmo,
'r0': r0
},
zmax=5,
fsky=1.0)
spectra = cosmicpy.spectra(cosmo, surv)
survey_volume = pi**(3.0 / 2.0) * r0**3
if k is None:
k = np.logspace(log(0.0001) / log(10),
log(0.25) / log(10),
512,
endpoint=False)
kw, w = spectra.W(l, k, evol=False)
kw = kw.squeeze()
w = w.squeeze()
w_exact = np.zeros_like(w)
for k1 in range(len(k)):
w_exact[k1, :] = gaussian_bessel_window(l, r0, k[k1],
kw[k1, :]) / survey_volume
pk = cosmo.pk_lin(kw)
integrand = np.square(kw * w_exact) * pk
res = (2.0 / pi)**2 * trapz(integrand, x=kw)
cl = spectra.cl_sfb(l, k)
return k, cl, res
def import_cosmology(filename, structure_name="fid"):
r""" Loads an icosmo cosmology from a fiducial structure stored in an
idl save file into a cosmicpy cosmology.
Parameters
----------
filename : str
Name of the idl save from which to load the cosmology.
structure_name : str, optional
Name of the icosmo fiducial structure stored in the save file.
Returns
-------
cosmo : cosmology
cosmicpy cosmology corresponding to the icosmo input.
"""
icosmo_file = readsav(filename)
icosmo = icosmo_file.get(structure_name)
h = icosmo['cosmo'][0]['h'][0]
Omega_m = icosmo['cosmo'][0]['omega_m'][0]
Omega_de = icosmo['cosmo'][0]['omega_l'][0]
Omega_b = icosmo['cosmo'][0]['omega_b'][0]
w0 = icosmo['cosmo'][0]['w0'][0]
wa = icosmo['cosmo'][0]['wa'][0]
tau = icosmo['cosmo'][0]['tau'][0]
n = icosmo['cosmo'][0]['n'][0]
sigma8 = icosmo['cosmo'][0]['sigma8'][0]
cosmo = cosmicpy.cosmology(h=h, Omega_m=Omega_m, Omega_de=Omega_de,
Omega_b=Omega_b, w0=w0, wa=wa, tau=tau,
n=n, sigma8=sigma8)
return cosmo
def check_Bessel_spectrum(l, k=None, r0=100):
# Initialise survey and spectra
cosmo = cosmicpy.cosmology()
surv = cosmicpy.survey(nzparams={'type': 'gaussian',
'cosmology': cosmo,
'r0': r0},
zmax=5,
fsky=1.0)
spectra = cosmicpy.spectra(cosmo, surv)
survey_volume = pi**(3.0 / 2.0) * r0**3
if k is None:
k = np.logspace(log(0.0001) / log(10), log(0.25) / log(10), 512,
endpoint=False)
kw, w = spectra.W(l, k, evol=False)
kw = kw.squeeze()
w = w.squeeze()
w_exact = np.zeros_like(w)
for k1 in range(len(k)):
w_exact[k1, :] = gaussian_bessel_window(l,r0, k[k1], kw[k1,:])/ survey_volume
pk = cosmo.pk_lin(kw)
integrand = np.square(kw * w_exact) * pk
res = (2.0 / pi)**2 * trapz(integrand, x=kw)
cl = spectra.cl_sfb(l, k)
return k, cl, res
def check_Bessel_window(l, k=None, r0=100):
r""" Checks the computation of the bessel window compared to the exact
solution
for Gaussian selection functions.
Parameters
----------
l : int
Order of the multipole.
r0 : real, optional
Radius parameter for the survey Gaussian selection function in Mpc/h
Returns
-------
(k, W, Wexact) : tuple of ndarrays
Window compute the discrete spherical bessel transform and the exact
window computed from theory
"""
# Initialise survey and spectra
cosmo = cosmicpy.cosmology()
surv = cosmicpy.survey(nzparams={
'type': 'gaussian',
'cosmology': cosmo,
'r0': r0
},
zmax=0.5,
fsky=1.0)
spectra = cosmicpy.spectra(cosmo, surv)
survey_volume = pi**(3.0 / 2.0) * r0**3
if k is None:
k = np.logspace(log(0.001) / log(10),
log(0.20) / log(10),
512,
endpoint=False)
W = spectra.W(l, k, k, evol=False, kmax=0.5)
W = W.squeeze()
Wexact = np.zeros_like(W)
for k1 in range(len(k)):
Wexact[k1, :] = (gaussian_bessel_window(l, r0, k[k1], k) /
survey_volume)
print("Maximum absolute error vs maximum value: " +
str(abs(W - Wexact).max()) + " " + str(Wexact.max()))
return (k, W, Wexact)
def check_Bessel_window(l, k=None, r0=100):
r""" Checks the computation of the bessel window compared to the exact
solution
for Gaussian selection functions.
Parameters
----------
l : int
Order of the multipole.
r0 : real, optional
Radius parameter for the survey Gaussian selection function in Mpc/h
Returns
-------
(k, W, Wexact) : tuple of ndarrays
Window compute the discrete spherical bessel transform and the exact
window computed from theory
"""
# Initialise survey and spectra
cosmo = cosmicpy.cosmology()
surv = cosmicpy.survey(nzparams={'type': 'gaussian',
'cosmology': cosmo,
'r0': r0},
zmax=0.5,
fsky=1.0)
spectra = cosmicpy.spectra(cosmo, surv)
survey_volume = pi**(3.0 / 2.0) * r0**3
if k is None:
k = np.logspace(log(0.001) / log(10), log(0.20) / log(10), 512,
endpoint=False)
W = spectra.W(l, k, k, evol=False, kmax=0.5)
W = W.squeeze()
Wexact = np.zeros_like(W)
for k1 in range(len(k)):
Wexact[k1, :] = (gaussian_bessel_window(l, r0, k[k1], k) /
survey_volume)
print("Maximum absolute error vs maximum value: " +
str(abs(W - Wexact).max()) +
" " +
str(Wexact.max()))
return (k, W, Wexact)
def import_cosmology(filename, structure_name="fid"):
r""" Loads an icosmo cosmology from a fiducial structure stored in an
idl save file into a cosmicpy cosmology.
Parameters
----------
filename : str
Name of the idl save from which to load the cosmology.
structure_name : str, optional
Name of the icosmo fiducial structure stored in the save file.
Returns
-------
cosmo : cosmology
cosmicpy cosmology corresponding to the icosmo input.
"""
icosmo_file = readsav(filename)
icosmo = icosmo_file.get(structure_name)
h = icosmo['cosmo'][0]['h'][0]
Omega_m = icosmo['cosmo'][0]['omega_m'][0]
Omega_de = icosmo['cosmo'][0]['omega_l'][0]
Omega_b = icosmo['cosmo'][0]['omega_b'][0]
w0 = icosmo['cosmo'][0]['w0'][0]
wa = icosmo['cosmo'][0]['wa'][0]
tau = icosmo['cosmo'][0]['tau'][0]
n = icosmo['cosmo'][0]['n'][0]
sigma8 = icosmo['cosmo'][0]['sigma8'][0]
cosmo = cosmicpy.cosmology(h=h,
Omega_m=Omega_m,
Omega_de=Omega_de,
Omega_b=Omega_b,
w0=w0,
wa=wa,
tau=tau,
n=n,
sigma8=sigma8)
return cosmo
def check_cosmology(filename, structure_name="cosmo"):
r""" Loads an icosmo cosmology from an idl save file and compares the
content of the cosmology structure with results from cosmicpy.
Parameters
----------
filename : str
Name of the idl save from which to load the cosmology.
structure_name : str, optional
Name of the icosmo cosmology structure stored in the save file.
"""
icosmo_file = readsav(filename)
icosmo = icosmo_file.get(structure_name)
# Reading cosmological parameters and creating corresponding
# cosmicpy object
h = icosmo['const'][0]['h'][0]
Omega_m = icosmo['const'][0]['omega_m'][0]
Omega_de = icosmo['const'][0]['omega_l'][0]
Omega_b = icosmo['const'][0]['omega_b'][0]
w0 = icosmo['const'][0]['w0'][0]
wa = icosmo['const'][0]['wa'][0]
tau = icosmo['const'][0]['tau'][0]
n = icosmo['const'][0]['n'][0]
sigma8 = icosmo['const'][0]['sigma8'][0]
cosmo = cosmicpy.cosmology(h=h, Omega_m=Omega_m, Omega_de=Omega_de,
Omega_b=Omega_b, w0=w0, wa=wa, tau=tau,
n=n, sigma8=sigma8)
print(cosmo)
# Comparing derived quantities
Omega_k = icosmo['const'][0]['omega_k'][0]
r0 = icosmo['const'][0]['r0'][0] * h
gamma = icosmo['const'][0]['gamma'][0]
sh = icosmo['const'][0]['sh'][0] * h
print("\nComparing derived constants :")
print("parameter: [icosmo] | [cosmicpy] |"
" diff | relative error in percents ")
_print_diff("Omega_k ", Omega_k, cosmo.Omega_k)
_print_diff("gamma ", gamma, cosmo.gamma)
_print_diff("sh ", sh, cosmo.sh_r)
# Comparing evolved quantities
rh = icosmo['const'][0]['rh'][0] * h
z = icosmo['evol'][0]['z'][0]
a = icosmo['evol'][0]['a'][0]
chi = icosmo['evol'][0]['chi'][0] * rh
hc = icosmo['evol'][0]['hc'][0] / h
Omega_m = icosmo['evol'][0]['omega_m_a'][0]
Omega_de_a = icosmo['evol'][0]['omega_l_a'][0]
dzdr = icosmo['evol'][0]['dzdr'][0] / h
da = icosmo['evol'][0]['da'][0] * h
print("\nComparing evolved quantities, maximum relative error:")
print("Radial Comoving Distance : " +
str(abs((chi[1:] - cosmo.a2chi(a[1:])) / chi[1:]).max()))
print("Angular Diameter Distance : " +
str(abs((da[1:] - a[1:] * cosmo.f_k(a[1:])) / da[1:]).max()))
print("Hubble constant : " +
str(abs((hc - cosmo.H(a)) / hc).max()))
print("Omega_m(a) : " +
str(abs((Omega_m - cosmo.Omega_m_a(a)) / Omega_m).max()))
print("Omega_de(a) : " +
str(abs((Omega_de_a - cosmo.Omega_de_a(a)) / Omega_de_a).max()))
print("dzdr : " +
str(abs((dzdr - cosmo.dzoverda(a) /
cosmo.dchioverda(a)) / dzdr).max()))
# Comparing Power spectrum
k = icosmo['pk'][0]['k'][0]
zpk = icosmo['pk'][0]['z'][0]
pk = icosmo['pk'][0]['pk'][0]
pk_l = icosmo['pk'][0]['pk_l'][0]
print("\nComparing linear power spectra")
pk2 = cosmo.pk_lin(k, cosmicpy.z2a(zpk))
plt.figure()
plt.contourf(k, zpk, abs(pk2.T - pk_l) / pk_l, 250)
plt.xlabel(r"Scale in Mpc/h")
plt.ylabel(r"Redshift")
plt.xscale('log')
plt.colorbar()
plt.title('Relative Error in linear power specrum computation')
plt.show()
print("Maximum relative error on linear power specrum : " +
str((abs(pk2.T - pk_l) / pk_l).max()))
def check_cosmology(filename, structure_name="cosmo"):
r""" Loads an icosmo cosmology from an idl save file and compares the
content of the cosmology structure with results from cosmicpy.
Parameters
----------
filename : str
Name of the idl save from which to load the cosmology.
structure_name : str, optional
Name of the icosmo cosmology structure stored in the save file.
"""
icosmo_file = readsav(filename)
icosmo = icosmo_file.get(structure_name)
# Reading cosmological parameters and creating corresponding
# cosmicpy object
h = icosmo['const'][0]['h'][0]
Omega_m = icosmo['const'][0]['omega_m'][0]
Omega_de = icosmo['const'][0]['omega_l'][0]
Omega_b = icosmo['const'][0]['omega_b'][0]
w0 = icosmo['const'][0]['w0'][0]
wa = icosmo['const'][0]['wa'][0]
tau = icosmo['const'][0]['tau'][0]
n = icosmo['const'][0]['n'][0]
sigma8 = icosmo['const'][0]['sigma8'][0]
cosmo = cosmicpy.cosmology(h=h,
Omega_m=Omega_m,
Omega_de=Omega_de,
Omega_b=Omega_b,
w0=w0,
wa=wa,
tau=tau,
n=n,
sigma8=sigma8)
print(cosmo)
# Comparing derived quantities
Omega_k = icosmo['const'][0]['omega_k'][0]
r0 = icosmo['const'][0]['r0'][0] * h
gamma = icosmo['const'][0]['gamma'][0]
sh = icosmo['const'][0]['sh'][0] * h
print("\nComparing derived constants :")
print("parameter: [icosmo] | [cosmicpy] |"
" diff | relative error in percents ")
_print_diff("Omega_k ", Omega_k, cosmo.Omega_k)
_print_diff("gamma ", gamma, cosmo.gamma)
_print_diff("sh ", sh, cosmo.sh_r)
# Comparing evolved quantities
rh = icosmo['const'][0]['rh'][0] * h
z = icosmo['evol'][0]['z'][0]
a = icosmo['evol'][0]['a'][0]
chi = icosmo['evol'][0]['chi'][0] * rh
hc = icosmo['evol'][0]['hc'][0] / h
Omega_m = icosmo['evol'][0]['omega_m_a'][0]
Omega_de_a = icosmo['evol'][0]['omega_l_a'][0]
dzdr = icosmo['evol'][0]['dzdr'][0] / h
da = icosmo['evol'][0]['da'][0] * h
print("\nComparing evolved quantities, maximum relative error:")
print("Radial Comoving Distance : " +
str(abs((chi[1:] - cosmo.a2chi(a[1:])) / chi[1:]).max()))
print("Angular Diameter Distance : " +
str(abs((da[1:] - a[1:] * cosmo.f_k(a[1:])) / da[1:]).max()))
print("Hubble constant : " +
str(abs((hc - cosmo.H(a)) / hc).max()))
print("Omega_m(a) : " +
str(abs((Omega_m - cosmo.Omega_m_a(a)) / Omega_m).max()))
print("Omega_de(a) : " +
str(abs((Omega_de_a - cosmo.Omega_de_a(a)) / Omega_de_a).max()))
print("dzdr : " + str(
abs((dzdr - cosmo.dzoverda(a) / cosmo.dchioverda(a)) / dzdr).max()))
# Comparing Power spectrum
k = icosmo['pk'][0]['k'][0]
zpk = icosmo['pk'][0]['z'][0]
pk = icosmo['pk'][0]['pk'][0]
pk_l = icosmo['pk'][0]['pk_l'][0]
print("\nComparing linear power spectra")
pk2 = cosmo.pk_lin(k, cosmicpy.z2a(zpk))
plt.figure()
plt.contourf(k, zpk, abs(pk2.T - pk_l) / pk_l, 250)
plt.xlabel(r"Scale in Mpc/h")
plt.ylabel(r"Redshift")
plt.xscale('log')
plt.colorbar()
plt.title('Relative Error in linear power specrum computation')
plt.show()
print("Maximum relative error on linear power specrum : " +
str((abs(pk2.T - pk_l) / pk_l).max()))