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logITAM.py
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logITAM.py
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import numpy as N
from scipy.stats import norm,lognorm
import hankel3d as hank
import itertools
import warnings
import matplotlib.pyplot as plt
class logITAM:
"""
Same as ITAM, but assuming lognormal PDF
Input::
boxsize: of the simulation
ng: grid resolution (per side)
Rth: smoothing scale
nmax: for the Wiener-Khinchin transform
stepzise: for the Wiener-Khinchin transform
beta: for the update of the pre-translation power spectrum
eps: convergence paraeter
pathto_pk: lookup table with target simulation
plotty: boolean to show the convergence to target power spectrum
Output::
the class stores the pre-translation power spectrum pk_g and the translated one pk_ng,
to be compared to the target, also stored as pk.
"""
def __init__( self , boxsize=256., ng=256 , Rth = 2. , nmax=10000 , stepsize=1e-04 , beta=1.0 , eps = 0.001, Deps=0.001, plotty=0,
pathto_linpk=None, pathto_pk=None):
self.nmax = nmax # for hankel transform
self.stepsize = stepsize # for hankel transform
self.beta = beta # update pk
self.eps = eps
self.Deps = Deps
self.boxsize = boxsize
self.ng = ng
self.Rth = Rth
self.plotty = plotty
try:
kbins,pk = N.loadtxt(pathto_pk)
except:
raise ValueError("Select correctly the path to lookup table of target power spectrum")
if not pathto_linpk==None:
self.flag_lin = True
print('you specified the linear power spectrum for the initilization')
if not os.path.exists(pathto_linpk):
raise ValueError("The path to the linear power spectrum does not exist")
else:
kbins,pk_l = N.loadtxt(pathto_pk)
else:
self.flag_lin = False
pass
cellsize = boxsize/float(ng)
lmin = boxsize/float(ng)/10.
lmax = boxsize
self.kmin = 2.*N.pi/lmax
self.kmax = 2.*N.pi/lmin
self.k = N.logspace( N.log10(self.kmin) , N.log10(self.kmax) , 200 )
self.r = N.logspace( N.log10(lmin) , N.log10(lmax) , 200 )
self.pk = 10.**N.interp(N.log10(self.k),N.log10(kbins),N.log10(pk),left=0.,right=0.)
Wk2 = N.exp(-self.k*self.k*Rth*Rth)
self.pk *= Wk2
if self.flag_lin == True:
pk_l *= correction
self.pk_l = 10.**N.interp(N.log10(self.k),N.log10(kbins),N.log10(pk_l),left=0.,right=0.)
Wk2 = N.exp(-self.k*self.k*Rth*Rth)
self.pk_l *= Wk2
self.pk_g , self.pk_ng = self.itam()
# Coles and Jones case
xi_ng = hank.pk_to_xi( self.pk , self.r , self.k , self.nmax , self.stepsize )
xi_g = N.log1p(xi_ng)
self.pk_g_CJ = hank.xi_to_pk( xi_g , self.r , self.k , self.nmax , self.stepsize*10 )
#self.test_realization(seed=31415)
if plotty==1:
plt.figure(figsize=(1.62*5.5,5.5))
with warnings.catch_warnings():
warnings.simplefilter( "ignore" , category = RuntimeWarning )
plt.semilogx(self.k,(self.pk_g_CJ-self.pk_g)/self.pk_g_CJ,'-',lw=2.,label='pre-translation')
plt.semilogx(self.k,(self.pk-self.pk_ng_exact)/self.pk,'--',lw=2.,label='itam')
plt.grid()
plt.legend
plt.ylim([-0.05,0.05])
plt.xlim([0.02,1.5])
plt.xlabel('$k \ [h/Mpc]$',fontsize='xx-large')
plt.ylabel('$\Delta P(k) \ [Mpc/h]^3$',fontsize='xx-large')
plt.show()
def itam(self):
''' the main algorithm '''
target_s = self.pk
if self.flag_lin == True:
s_g_iterate = self.pk_l
else:
s_g_iterate = self.pk
eps0 = 1.
eps1 = 1.
ii = 0
Deps = 1.
while Deps > self.Deps and eps1>self.eps:
ii += 1
print('iteration =', ii)
eps0 = eps1
r_g_iterate = hank.pk_to_xi( s_g_iterate , self.r , self.k, self.nmax, self.stepsize )
if N.any( N.isnan(r_g_iterate) ):
raise ValueError("r_g_iterate contains NaN")
sigma2 = r_g_iterate[0]
r_ng_iterate = N.asarray([ self.solve_integral(r_g/sigma2,sigma2) for r_g in r_g_iterate ])
if N.any( N.isnan(r_ng_iterate) ):
raise ValueError("r_ng_iterate contains NaN")
s_ng_iterate = hank.xi_to_pk( r_ng_iterate , self.r , self.k, self.nmax, self.stepsize*10 )
eps1 = N.sqrt( N.sum((target_s - s_ng_iterate) ** 2. )/N.sum(target_s**2) )
Deps = abs(eps1-eps0)
Deps/= eps1
print('eps = %.5f' % eps1,'Deps =%.5f' % Deps)
if Deps > self.Deps and eps1>self.eps:
with warnings.catch_warnings():
warnings.simplefilter( "ignore" , category = RuntimeWarning )
s_g_iterate = N.power( target_s / s_ng_iterate, self.beta ) * s_g_iterate
s_g_iterate[N.isnan(s_g_iterate)] = 0.
if N.any( N.isnan(s_g_iterate) ):
raise ValueError("s_g_iterate contains NaN")
else:
print('converged at', ii, 'iteration')
return s_g_iterate,s_ng_iterate
def solve_integral(self,rho,sigma2):
if rho >= 1.0:
rho = 1-1e-08
nhg = 30
x, w = N.polynomial.hermite.hermgauss(nhg)
Sigma = sigma2*N.array([[1., rho], [rho, 1.]])
Nd = 2
const = N.pi**(-0.5*Nd)
# gaussian variable
xn = N.array(list(itertools.product(*(x,)*Nd)))
# gauss hermite weights
wn = N.prod(N.array(list(itertools.product(*(w,)*Nd))), 1)
# normalized diagonal variables
yn = 2.0**0.5*N.dot(N.linalg.cholesky(Sigma), xn.T).T
yn = norm.cdf( yn ,loc=0., scale= N.sqrt(sigma2) )
gn = lognorm.ppf( yn , s = N.sqrt(sigma2) ,loc=0.0, scale=1.0)
# Eq. 16
gn *= N.exp(-sigma2/2.)
gn -= 1.
gn = N.prod( gn, 1 )
if not N.all( N.isfinite( gn ) ):
gn[N.where(N.isinf(gn))] = 0.
z = N.sum( (wn * const ) * gn , axis=0 )
return z
def getkgrid(self):
''' It returns a grid of k in fft format '''
kmin = 2*N.pi/N.float(self.boxsize)
sh = (self.ng,self.ng,self.ng//2+1)
kx,ky,kz = N.mgrid[0:sh[0],0:sh[1],0:sh[2]].astype(N.float64)
kx[N.where(kx > self.ng//2)] -= self.ng
ky[N.where(ky > self.ng//2)] -= self.ng
kz[N.where(kz > self.ng//2)] -= self.ng
kx *= kmin
ky *= kmin
kz *= kmin
k = N.sqrt(kx**2+ky**2+kz**2)
return k
def test_realization(self,seed=1):
'''
To make a realization with the newly found power spectrum.
Inputs::
seed: seed of random number generator
amp: whether to vary the amplitudes of the power spectrum. If 0 (default) they are fixed.
Outputs::
the fourier space random field simulation
'''
r = N.random.RandomState(seed)
kgrid = self.getkgrid()
shc = N.shape(kgrid)
sh = N.prod(shc)
dk = N.empty(sh,dtype=N.complex64)
dk.real = r.normal(size=sh).astype(N.float32)
dk.imag = r.normal(size=sh).astype(N.float32)
dk /= N.sqrt(2.)
with warnings.catch_warnings():
warnings.simplefilter( "ignore" , category = RuntimeWarning )
pk = N.power(10.,N.interp(N.log10(kgrid.flatten()),N.log10(self.k),N.log10(self.pk_g),right=0)).astype(N.complex64)
pk[ pk < 0. ] = 0.
pk[ N.isnan(pk) ] = 0.
dk *= N.sqrt(pk)/self.boxsize**1.5 * self.ng**3.
dk[0] = 0.
dk = N.reshape(dk,shc)
# Hermitian symmetric: dk(-k) = conjugate(dk(k))
dk[self.ng // 2 + 1:, 1:,
0] = N.conj(N.fliplr(N.flipud(dk[1:self.ng // 2, 1:, 0])))
dk[self.ng // 2 + 1:, 0, 0] = N.conj(dk[self.ng // 2 - 1:0:-1, 0, 0])
dk[0, self.ng // 2 + 1:, 0] = N.conj(dk[0, self.ng // 2 - 1:0:-1, 0])
dk[self.ng // 2, self.ng // 2 + 1:,
0] = N.conj(dk[self.ng // 2, self.ng // 2 - 1:0:-1, 0])
dk[self.ng // 2 + 1:, 1:, self.ng //
2] = N.conj(N.fliplr(N.flipud(dk[1:self.ng // 2, 1:, self.ng // 2])))
dk[self.ng // 2 + 1:, 0, self.ng //
2] = N.conj(dk[self.ng // 2 - 1:0:-1, 0, self.ng // 2])
dk[0, self.ng // 2 + 1:, self.ng //
2] = N.conj(dk[0, self.ng // 2 - 1:0:-1, self.ng // 2])
dk[self.ng // 2, self.ng // 2 + 1:, self.ng //
2] = N.conj(dk[self.ng // 2, self.ng // 2 - 1:0:-1, self.ng // 2])
d_g = N.fft.irfftn(dk)
cdf = norm.cdf( d_g ,loc= N.mean(d_g), scale= N.std(d_g) )
d_ng = lognorm.ppf( cdf , s = N.std(d_g) ,loc=0.0, scale=1.0)
# Eq. 16
d_ng *= N.exp(-N.var(d_g)/2.)
d_ng -= 1.
return d_ng