def sigma(k,Pk,R):
yinit = np.array([0.0], dtype=np.float64)
eps = 1e-9 #change this for higher/lower accuracy
h1 = 1e-12
hmin = 0.0
W = 3.0*(np.sin(k*R) - k*R*np.cos(k*R))/(k*R)**3
Pk1 = Pk*W**2*k**2/(2.0*pi**2)
return np.sqrt(IL.odeint(yinit, k[0], k[-1], eps,
h1, hmin, np.log10(k), np.log10(Pk1),
'sigma', verbose=False)[0])
def sigma(k,Pk,R):
yinit = np.array([0.0], dtype=np.float64)
eps = 1e-13 #change this for higher/lower accuracy
h1 = 1e-12
hmin = 0.0
W = 3.0*(np.sin(k*R) - k*R*np.cos(k*R))/(k*R)**3
Pk1 = Pk*W**2*k**2/(2.0*pi**2)
return np.sqrt(IL.odeint(yinit, k[0], k[-1], eps,
h1, hmin, np.log10(k), Pk1,
'sigma', verbose=False)[0])
def analytic_Fisher(parameter, z, V, kmax, root_derv):
num_params = len(parameter)
# define the Fisher matrix
Fisher = np.zeros((num_params, num_params), dtype=np.float64)
# compute the value of kmin
kmin = 2.0 * np.pi / V**(1.0 / 3.0)
# check that all ks are equally spaced in log
for i in xrange(num_params):
k, deriv = np.loadtxt('%s/derivative_%s_z=%.1f.txt' %
(root_derv, parameter[i], z),
unpack=True)
dk = np.log10(k[1:]) - np.log10(k[:-1])
if not (np.allclose(dk, dk[0])):
raise Exception('k-values not log distributed')
# compute sub-Fisher matrix
for i in xrange(num_params):
for j in xrange(i, num_params):
#if i==5:
# k1, deriv1 = np.loadtxt('%s/log_derivative_%s_cb_z=%.1f.txt'%(root_derv,parameter[i],z), unpack=True)
#else:
k1, deriv1 = np.loadtxt('%s/log_derivative_%s_z=%.1f.txt' %
(root_derv, parameter[i], z),
unpack=True)
#if j==5:
# k2, deriv2 = np.loadtxt('%s/log_derivative_%s_cb_z=%.1f.txt'%(root_derv,parameter[j],z), unpack=True)
#else:
k2, deriv2 = np.loadtxt('%s/log_derivative_%s_z=%.1f.txt' %
(root_derv, parameter[j], z),
unpack=True)
if np.any(k1 != k2): raise Exception('k-values are different!')
yinit = np.zeros(1, dtype=np.float64)
eps = 1e-16
h1 = 1e-18
hmin = 0.0
function = 'log'
I = IL.odeint(yinit,
kmin,
kmax,
eps,
h1,
hmin,
np.log10(k1),
k**2 * deriv1 * deriv2,
function,
verbose=False)[0]
Fisher[i, j] = I
if i != j: Fisher[j, i] = Fisher[i, j]
# add prefactors to subFisher matrix
Fisher = Fisher * V / (2.0 * np.pi)**2
return Fisher
np.savetxt(f_out, np.transpose([M, MF]))
M = np.ascontiguousarray(M)
MF = np.ascontiguousarray(MF)
M_HI = M0 * (M / Mmin)**alpha * np.exp(-Mmin / M)
A = MF * M_HI**2
B = MF * M_HI
yinit = np.array([0.0], dtype=np.float64)
numerator = IL.odeint(yinit,
1e8,
M_max,
eps,
h1,
hmin,
np.log10(M),
np.log10(A),
'sigma',
verbose=True)[0]
yinit = np.array([0.0], dtype=np.float64)
denominator = IL.odeint(yinit,
1e8,
M_max,
eps,
h1,
hmin,
np.log10(M),
np.log10(B),
'sigma',
#sigma_DLAs = np.zeros(bins+1, dtype=np.float64)
#if z==2: M0 = 10.22955643 #value of 10^20
#if z==3: M0 = 9.89018152 #value of 10^20
#for i in xrange(bins+1):
# sigma_DLAs[i] = sigma_DLAs_func(M[i], M0, N_HI=10**20.0)
# integral value, its limits and precision parameters
eps = 1e-14
h1 = 1e-15
hmin = 0.0
# integral method and integrand function
function = 'log'
yinit = np.zeros(1, dtype=np.float64)
I1 = IL.odeint(yinit, Mmin, Mmax, eps, h1, hmin, np.log10(M),
np.log10(MF*sigma_DLAs*b), function, verbose=True)[0]
yinit = np.zeros(1, dtype=np.float64)
I2 = IL.odeint(yinit, Mmin, Mmax, eps, h1, hmin, np.log10(M),
np.log10(MF*sigma_DLAs), function, verbose=True)[0]
print I1
print I2
print 'b_DLAs(z=%d) = %.3f'%(z,I1/I2)