def test_full_sky():
"""do some tests with a full sky geo known results"""
#get dictionaries of parameters that various functions will need
#cosmo = defaults.cosmology_wmap.copy()
cosmo = { 'Omegabh2':0.02223,
'Omegach2':0.1153,
'Omegab' :0.04283392714316876,
'Omegac' :0.22216607285683124,
'Omegamh2':0.13752999999999999,
'OmegaL' :0.735,
'OmegaLh2':0.38145113207547166,
'Omegam' :0.265,
'H0' :72.04034509047493,
'sigma8' : 0.8269877678406697, #from the code
'h' :0.7204034509047493,
'Omegak' : 0.0,
'Omegakh2': 0.0,
'Omegar' : 0.0,
'Omegarh2': 0.0,
'ns' : 0.9608,
'tau' : 0.081,
'Yp' :0.299,
'As' : 2.464*10**-9,
'LogAs' :-19.821479791275138,
'w' :-1.0,
'de_model':'constant_w',#dark energy model
'mnu' :0.}
cosmo['de_model'] = 'constant_w'
cosmo['wa'] = 0.
cosmo['w0'] = -1.
cosmo['w'] = -1.
p_space = 'jdem'
camb_params = defaults.camb_params.copy()
camb_params['force_sigma8'] = False
camb_params['maxkh'] = 100.
camb_params['kmax'] = 30.
camb_params['npoints'] = 10000
camb_params['pivot_scalar'] = 0.002
power_params = defaults.power_params.copy()
power_params.camb = camb_params
power_params.camb['accuracy'] = 1
#prior_params = defaults.prior_fisher_params.copy()
zs = np.array([0.0001,3.])
z_fine = np.linspace(0.0001,zs[-1],10000)
basis_params = defaults.basis_params.copy()
basis_params['n_bessel_oversample'] = 400000*10
C = CosmoPie(cosmo,p_space=p_space)
l_max = 0
x_cut = 10*np.pi
z_max = z_fine[-1]+0.000001
r_max = C.D_comov(z_max)
k_cut = x_cut/r_max
P = MatterPower(C,power_params)
C.set_power(P)
geo1 = FullSkyGeo(zs,C,z_fine)
basis = SphBasisK(r_max,C,k_cut,basis_params,l_ceil=l_max,needs_m=True)
ddbar = basis.get_ddelta_bar_ddelta_alpha(geo1,tomography=True)
ns = np.arange(1,ddbar.size+1)
ddbar_pred = -3./(2.*np.pi**(5./2.))*(-1)**ns/ns**2
assert np.allclose(ddbar,ddbar_pred)
cov_pred = np.zeros((ns.size,ns.size))
xs = P.k*r_max
P_in = P.get_matter_power(np.array([0.]),pmodel='linear')[:,0]
for i1 in range(0,ns.size):
for i2 in range(i1,ns.size):
integrand1 = 8.*np.pi**3*(-1)**(ns[i1]+ns[i2])*ns[i1]**2*ns[i2]**2/r_max**3*np.sin(xs)**2/((ns[i1]**2*np.pi**2-xs**2)*(ns[i2]**2*np.pi**2-xs**2))
cov_pred[i1,i2] = np.trapz(integrand1*P_in,xs)
if i1!=i2:
cov_pred[i2,i1] = cov_pred[i1,i2]
cov_got = basis.get_covar_array()
var_pred = np.dot(ddbar_pred.T,np.dot(cov_pred,ddbar_pred))
var_got = basis.get_variance(geo1)
assert np.all(cov_got==cov_got.T)
assert np.allclose(basis.C_id[:,1],ns*np.pi/r_max)
assert np.allclose(cov_pred,cov_got,atol=1.e-15,rtol=1.e-3)
assert np.isclose(var_got[0,0],var_pred,atol=1.e-15,rtol=1.e-3)
ddbar_got2 = basis.get_dO_I_ddelta_alpha(geo1,geo1.r_fine**2)*3./r_max**3
assert np.allclose(ddbar,ddbar_got2,rtol=1.e-3)
def test_half_sky():
"""do some tests with a half sky geo known results"""
#get dictionaries of parameters that various functions will need
cosmo = { 'Omegabh2':0.0222,
'Omegach2':0.1153,
'Omegab' :0.04283392714316876,
'Omegac' :0.22216607285683124,
'Omegamh2':0.13752999999999999,
'OmegaL' :0.735,
'OmegaLh2':0.38145113207547166,
'Omegam' :0.265,
'H0' :72.04034509047493,
'sigma8' : 0.8269877678406697, #from the code
'h' :0.7204034509047493,
'Omegak' : 0.0,
'Omegakh2': 0.0,
'Omegar' : 0.0,
'Omegarh2': 0.0,
'ns' : 0.9608,
'tau' : 0.081,
'Yp' :0.299,
'As' : 2.464*10**-9,
'LogAs' :-19.821479791275138,
'w' :-1.0,
'de_model':'constant_w',#dark energy model
'mnu' :0.}
cosmo['de_model'] = 'constant_w'
cosmo['wa'] = 0.
cosmo['w0'] = -1.
cosmo['w'] = -1.
p_space = 'jdem'
camb_params = defaults.camb_params.copy()
camb_params['force_sigma8'] = False
camb_params['maxkh'] = 100.
camb_params['kmax'] = 30.
camb_params['npoints'] = 10000
camb_params['pivot_scalar'] = 0.002
power_params = defaults.power_params.copy()
power_params.camb = camb_params
power_params.camb['accuracy'] = 1
#prior_params = defaults.prior_fisher_params.copy()
zs = np.array([0.0001,3.])
z_fine = np.linspace(0.0001,zs[-1],10000)
basis_params = defaults.basis_params.copy()
basis_params['n_bessel_oversample'] = 400000*10
#test with half sky using results calculated in mathematica
basis_params = defaults.basis_params.copy()
basis_params['n_bessel_oversample'] = 400000*10
C = CosmoPie(cosmo,p_space=p_space)
l_max = 4
x_cut = 10
z_max = z_fine[-1]+0.000001
r_max = C.D_comov(z_max)
k_cut = x_cut/r_max
geo1 = HalfSkyGeo(zs,C,z_fine)
P = MatterPower(C,power_params)
P.P_lin = 1./(P.k*r_max)
C.set_power(P)
basis = SphBasisK(r_max,C,k_cut,basis_params,l_ceil=l_max,needs_m=False)
basis2 = SphBasisK(r_max,C,k_cut,basis_params,l_ceil=l_max,needs_m=True)
ddbar = basis.get_ddelta_bar_ddelta_alpha(geo1,tomography=True)
ddbar2 = basis2.get_ddelta_bar_ddelta_alpha(geo1,tomography=True)
ddbar_got2 = basis.get_dO_I_ddelta_alpha(geo1,geo1.r_fine**2)*3./r_max**3
#ns = np.arange(1,ddbar.size+1)
cov_got = basis.get_covar_array()
cov_got2 = basis2.get_covar_array()
var_got = basis.get_variance(geo1)
var_got2 = basis2.get_variance(geo1)
cov_pred0 = np.array([[3.220393570704632e-11,-9.51309537893619e-12,9.955267964241254e-12],[-9.51309537893619e-12,5.937410951604845e-11,-1.2342996089442917e-11],[9.955267964241254e-12,-1.2342996089442917e-11,8.524795995567036e-11]])
cov_pred1 = np.array([[4.306831299006748e-11,-7.977015797357624e-12],[-7.977015797357624e-12,6.907871421795387e-11]])
cov_pred2 = np.array([[5.467066924435653e-11,-7.056047462103054e-12],[-7.056047462103054e-12,7.984696153964485e-11]])
cov_pred3 = np.array([[6.70079506270691e-11]])
cov_pred4 = np.array([[7.985214180284307e-11]])
cov_pred = np.zeros((ddbar.size,ddbar.size))
cov_pred[0:3,0:3] = cov_pred0
cov_pred[3:5,3:5] = cov_pred1
cov_pred[5:7,5:7] = cov_pred2
cov_pred[7,7] = cov_pred3
cov_pred[8,8] = cov_pred4
var_pred = np.dot(ddbar,np.dot(cov_pred,ddbar.T))
var_pred2 = np.dot(ddbar2,np.dot(cov_got2,ddbar2.T))
assert np.all(cov_got==cov_got.T)
assert np.all(cov_got2==cov_got2.T)
assert np.isclose(var_got[0,0],var_pred,atol=1.e-15,rtol=1.e-3)
assert np.isclose(var_got2[0,0],var_pred2,atol=1.e-15,rtol=1.e-3)
assert np.isclose(var_got2[0,0],var_pred,atol=1.e-15,rtol=1.e-3)
assert np.allclose(cov_pred,cov_got,atol=1.e-15,rtol=1.e-3)
assert np.allclose(ddbar,ddbar_got2,rtol=1.e-3,atol=1.e-15)
for itr in range(0,basis.C_id.shape[0]):
if basis.C_id[itr,0]>0 and np.mod(basis.C_id[itr,0],2)==0.:
assert ddbar[0,itr] == 0.
for itr in range(0,basis2.C_id.shape[0]):
if basis2.C_id[itr,0]>0 and np.mod(basis2.C_id[itr,0],2)==0.:
assert ddbar2[0,itr] == 0.
elif basis2.C_id[itr,2]!=0:
assert ddbar2[0,itr] == 0.