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process.py
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process.py
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#! /usr/bin/env python3
import numpy as np
import pandas as pd
import matplotlib
matplotlib.use('Agg')
import os
import scipy.optimize as opt
import matplotlib.pyplot as plt
import time
import sys
import scipy.special as spec
from scipy.special import wofz
from matplotlib.backends.backend_pdf import PdfPages
def model_gaussian(x, b):
"""Gaussian"""
return np.exp(-b*x**2)
def model_tanh(x, a, b):
return 1./2*(1 - np.tanh(b*x + a))
def model_gaussian_constant(x, a, b):
return (1 + a*x**2)*np.exp(-b*x**2)
def model_lorentzian(x, a):
return 1./(1 + (a*x)**2)
def model_voigt_norm(x, alpha, gamma):
"""
Return the Voigt line shape at x with Lorentzian component HWHM gamma
and Gaussian component HWHM alpha.
"""
sigma = 1/np.sqrt(2*alpha)
#sigma = alpha / np.sqrt(2 * np.log(2))
return np.real(wofz((x + 1j*gamma)/sigma/np.sqrt(2)))/np.real(wofz((1j*gamma)/sigma/np.sqrt(2)))
def model_fermi(x, a, b):
"""Fermi-like distribution"""
return 1./(1 + np.exp(b*x + a))
def model_gaussian_with_constant(x, a, b):
return 1. - a*(1. - np.exp(-a*x**2))
def model_quasigaussian(x, a, b):
"""Quasi gaussian model"""
return np.exp(-a*np.abs(x)**b)
def model_deltaz(x, a):
"""Quadratic"""
return a*x**2
def model_zmean_exp(x, a, b):
return a*np.exp(-x*b)
def model_zmean(x, a, b):
return a*np.exp(-b*x)
def model2d(x, a):
(k, deltaz) = x
return np.exp(-a * deltaz**2 * k**2)
def model3d(x, a, b):
(k, zmean, deltaz) = x
return np.ravel(np.exp(-a * k**2 * deltaz**2 * np.exp(-b * zmean)))
def model3d2(x, a):
(k, zmean, deltaz) = x
return np.ravel(np.exp(-a * k**2 *deltaz**2 / zmean**2))
def model3d3(x, a, b):
(k, zmean, deltaz) = x
return np.ravel(np.exp(-a * k**2 *deltaz**2 / (1 + zmean)**b))
def model3d4(x, a, b):
(k, zmean, deltaz) = x
return np.ravel(np.exp(-a * k**2 *deltaz**2 / (1 + b*zmean)))
def model3d5(x, a, b):
(k, zmean, deltaz) = x
return np.ravel(np.exp(-a * k**2 *deltaz**2 / (b + zmean)))
def model3d6(x, a, b):
(k, zmean, deltaz) = x
return np.ravel(np.exp(-a * k**2 *deltaz**2 / ((1 + zmean + deltaz/2.) * (1 + zmean - deltaz/2.))**b))
def process_data(prefix):
if not os.path.exists("%sprocess"%prefix):
os.mkdir("%sprocess"%prefix)
try:
corrcoeffmod = pd.read_pickle("%sprocess/saved_data.pkl" % prefix)
except FileNotFoundError:
print("Processed file not found, processing now...")
df_cross = dict()
df_pk = dict()
# reading all the data
for n1 in range(len(redshifts)):
for n2 in range(n1 + 1):
temp = pd.read_csv('%s/lcdm_pk%03d_phi_%03d.dat' % (prefix, n1, n2), sep = '\s+', header=None, names = ['k', 'Pk', 'sigma k', 'sigma Pk', 'count'], index_col=None, comment='#')
df_cross['%.1f, %.1f, pk' % (redshifts[n1], redshifts[n2])] = temp['Pk'].values
df_cross['%.1f, %.1f, sigmapk' % (redshifts[n1], redshifts[n2])] = temp['sigma Pk'].values
df_pk['%.1f, pk' % (redshifts[n1])] = temp['Pk'].values
df_pk['%.1f, k' % (redshifts[n1])] = temp['k'].values
df_pk['%.1f, sigmapk' % (redshifts[n1])] = temp['sigma Pk'].values
avg_cross = pd.DataFrame(index=range(bins))
avg_pk = pd.DataFrame(index=range(bins))
# averaging of the data (including the errors)
for n1 in range(len(redshifts)):
for n2 in range(n1 + 1):
avg_cross['%.1f, %.1f, pk' % (redshifts[n1], redshifts[n2])] = df_cross['%.1f, %.1f, pk' %(redshifts[n1], redshifts[n2])]
avg_cross['%.1f, %.1f, sigmapk' % (redshifts[n1], redshifts[n2])] = df_cross['%.1f, %.1f, sigmapk' %(redshifts[n1], redshifts[n2])]
avg_pk['%.1f, pk' % (redshifts[n1])] = df_pk['%.1f, pk' %(redshifts[n1])]
avg_pk['%.1f, sigmapk' % (redshifts[n1])] = df_pk['%.1f, sigmapk' %(redshifts[n1])]
# index for a single correlation coefficient must be the wavenumber k
corrcoeff = pd.DataFrame(index=df_pk['0.0, k'])
# setting the correlation coefficient
for i in range(len(redshifts)):
for j in range(i + 1):
corrcoeff['%.1f, %.1f, c' % (float(redshifts[i]), float(redshifts[j]))] = \
avg_cross['%.1f, %.1f, pk' % (redshifts[i], redshifts[j])].values\
/\
np.sqrt(\
avg_pk['%.1f, pk' % (redshifts[i])].values * avg_pk['%.1f, pk' % (redshifts[j])].values\
)
corrcoeff['%.1f, %.1f, sigmac' % (float(redshifts[i]), float(redshifts[j]))] = \
np.sqrt(\
(avg_cross['%.1f, %.1f, sigmapk' %(float(redshifts[i]), float(redshifts[j]))].values/avg_cross['%.1f, %.1f, pk'%(float(redshifts[i]), float(redshifts[j]))].values)**2 +\
(avg_pk['%.1f, sigmapk'%float(redshifts[i])].values/avg_pk['%.1f, pk'%float(redshifts[i])].values/2.)**2 +\
(avg_pk['%.1f, sigmapk'%float(redshifts[j])].values/avg_pk['%.1f, pk'%float(redshifts[j])].values/2.)**2)\
*\
np.abs(corrcoeff['%.1f, %.1f, c' % (float(redshifts[i]), float(redshifts[j]))])
corrcoeff['%.1f, %.1f, c' % (float(redshifts[j]), float(redshifts[i]))] = corrcoeff['%.1f, %.1f, c' % (float(redshifts[i]), float(redshifts[j]))]
corrcoeff['%.1f, %.1f, sigmac' % (float(redshifts[j]), float(redshifts[i]))] = corrcoeff['%.1f, %.1f, sigmac' % (float(redshifts[i]), float(redshifts[j]))]
ind = len(corrcoeff.index)*len(corrcoeff.columns)
corrcoeffmod = pd.DataFrame(index = range(ind))
ccc = 0
# putting everything in one giant dataframe
for k in range(len(corrcoeff.index)):
for i in range(len(redshifts)):
for j in range(len(redshifts)):
corrcoeffmod.at[ccc, 'k'] = corrcoeff.index[k]
corrcoeffmod.at[ccc, 'deltaz'] = np.abs(redshifts[i] - redshifts[j])
corrcoeffmod.at[ccc, 'z1'] = redshifts[i]
corrcoeffmod.at[ccc, 'z2'] = redshifts[j]
corrcoeffmod.at[ccc, 'zmean'] = (redshifts[i] + redshifts[j])/2
corrcoeffmod.at[ccc, 'c'] = corrcoeff['%.1f, %.1f, c' % (float(redshifts[i]), float(redshifts[j]))].iat[k]
corrcoeffmod.at[ccc, 'sigmac'] = corrcoeff['%.1f, %.1f, sigmac' % (float(redshifts[i]), float(redshifts[j]))].iat[k]
ccc += 1
corrcoeffmod.to_pickle('%sprocess/saved_data.pkl' % prefix)
print("Processing done")
return corrcoeffmod
# selects the redshift interval
def select_interval(corrcoeffmod, zmax=100, kmax=100, cmin = -1e10, dropna=False, deltaz_min = 0.0):
if dropna:
corrcoeffmod = corrcoeffmod.loc[corrcoeffmod['deltaz'] != 0].dropna()
corrcoeffmod = corrcoeffmod.loc[(corrcoeffmod['z1'] <= zmax) & (corrcoeffmod['zmean'] > 0) & (corrcoeffmod['k'].values <= kmax) & (corrcoeffmod['z2'] <= zmax) & (corrcoeffmod['c'] >= cmin) & (corrcoeffmod['deltaz'] >=deltaz_min)]
return corrcoeffmod
# plots the stuff from the UETC paper
def plot_uetc_paper(corrcoeffmod, prefix):
plt.ylim(ymin = 1e-6, ymax = 1e1)
plt.xlim(xmin = 1e-2, xmax = 1e1)
plt.xlabel('k [h/Mpc]')
plt.ylabel('1 - corr. coeff.')
for z in [0.2, 0.5, 1.5, 2.0]:
temp = corrcoeffmod.loc[(round(corrcoeffmod['z1'], 2) == 1.0) & (round(corrcoeffmod['z2'], 2) == z)]
plt.loglog(temp['k'].values, 1 - temp['c'].values, label="z2 = %.2f"%z)
plt.title("z1 = 1.0")
plt.legend()
plt.grid()
plt.savefig("%sprocess/uetc_comp_x_k_y_c.jpg" % (prefix), dpi = 300)
plt.close()
plt.xlim(xmin = 0, xmax = 3)
plt.ylim(ymin = 1e-5, ymax = 1e2)
plt.xlabel('z2')
plt.ylabel('1 - corr. coeff.')
for k in [0.5, 1.0, 5.0, 10]:
temp = corrcoeffmod.loc[(round(corrcoeffmod['k'], 2) == k) & (round(corrcoeffmod['z1'], 2) == 1.0)]
plt.semilogy(temp['z2'].values, 1 - temp['c'].values, label="k = %.2f" % k)
plt.title("z1 = 1.0")
plt.legend()
plt.grid()
plt.savefig("%sprocess/uetc_comp_x_z_y_c.jpg" % (prefix), dpi = 300)
plt.close()
# fitting the data
def fit_data(corrcoeffmod, models):
df = pd.DataFrame(index=range(len(models)), columns = ["par", "cov", "sigma", "model", "chi2"])
for i in range(len(models)):
params, cov = opt.curve_fit(\
models[i],\
(corrcoeffmod['k'].values, corrcoeffmod['zmean'].values, corrcoeffmod['deltaz'].values),\
corrcoeffmod['c'].values,\
sigma = corrcoeffmod['sigmac'].values,\
maxfev = 100000\
)
df.at[i, "par"] = params
df.at[i, "cov"] = cov
df.at[i, "sigma"] = np.sqrt(np.diag(cov))
df.at[i, "model"] = models[i].__name__
df.at[i, "chi2"] = sum(\
((corrcoeffmod['c'].values - models[i]((corrcoeffmod['k'].values, corrcoeffmod['zmean'].values, corrcoeffmod['deltaz'].values), *params)) / corrcoeffmod['sigmac'].values) ** 2\
)/(len(corrcoeffmod.index) - len(params))
return df
# making plots for fixed zmean and deltaz as well as the model
def plot_zmean_deltaz(corrcoeffmod, models, params):
for deltaz in np.unique(corrcoeffmod['deltaz'].values):
temp_outer = corrcoeffmod.loc[corrcoeffmod['deltaz'] == deltaz]
for zmean in np.unique(temp_outer['zmean'].values):
temp_inner = temp_outer.loc[temp_outer['zmean'] == zmean]
plt.ylim(ymin = 0.0, ymax = 1.2)
plt.xlabel('k [h/Mpc]')
plt.ylabel('corr. coeff.')
plt.errorbar(temp_inner['k'].values, temp_inner['c'].values, yerr = temp_inner['sigmac'].values, fmt = 'ko', markersize = 2)
for i in range(len(models)):
plt.plot(temp_inner['k'].values, models[i]((temp_inner['k'].values, zmean, deltaz), *(params.loc[params["model"] == models[i].__name__]["par"].values[0])), label = '%s' % models[i].__name__)
plt.legend()
plt.grid()
plt.xscale('log')
plt.savefig("%sprocess/plot_deltaz_%.1f_zmean_%.2f.pdf" % (prefix, deltaz, zmean), dpi = 300)
plt.close()
plt.xlabel('k [h/Mpc]')
plt.ylabel('residual')
for i in range(len(models)):
plt.plot(temp_inner['k'].values, temp_inner['c'].values - models[i]((temp_inner['k'].values, zmean, deltaz), *(params.loc[params["model"] == models[i].__name__]["par"].values[0])), 'o', markersize = 2, label = '%s' % (models[i].__name__))
plt.legend()
plt.grid()
plt.xscale('log')
plt.savefig("%sprocess/plot_deltaz_%.1f_zmean_%.2f_res.pdf" % (prefix, deltaz, zmean), dpi = 300)
plt.close()
def find_nearest(array, value):
array = np.asarray(array)
idx = (np.abs(array - value)).argmin()
return array[idx]
# fit correlation coefficient as a function of wavenumber k for FIXED zmean and deltaz
def plot_zmean_deltaz_fit(prefix, df, model, name="gaussian"):
total_chi2 = 0
all_par = list()
all_zmean = list()
all_deltaz = list()
if (model.__name__ == "model_voigt_norm"):
bounds = ([0, 0],[100, 100])
else:
bounds = (-np.inf, np.inf)
for zmean in np.unique(df.zmean.values):
# has fixed zmean
temp = df.loc[df.zmean == zmean]
for deltaz in np.unique(temp.deltaz.values):
# has fixed zmean AND deltaz
temp_inner = temp.loc[temp.deltaz == deltaz]
par, cov = opt.curve_fit(\
model,\
(temp_inner.k.values),\
temp_inner.c.values,\
sigma = temp_inner.sigmac.values,\
maxfev = 100000,\
bounds = bounds\
)
all_par.append(par)
all_zmean.append(zmean)
all_deltaz.append(deltaz)
chi2_dof = sum(((temp_inner.c.values - model((temp_inner.k.values), *par)) / temp_inner.sigmac.values) ** 2)/(len(temp_inner.index) - len(par))
total_chi2 += sum(((temp_inner.c.values - model((temp_inner.k.values), *par)) / temp_inner.sigmac.values) ** 2)
print(zmean, deltaz, np.sqrt(chi2_dof), *par)
with PdfPages("%sprocess/%s_plot_deltaz_%.1f_zmean_%.2f.pdf" % (prefix, name, deltaz, zmean)) as pdf:
# plain
plt.ylim(ymin = 0.0, ymax = 1.2)
plt.xlabel('k [h/Mpc]')
plt.ylabel('corr. coeff.')
plt.plot(temp_inner['k'].values, temp_inner['c'].values, 'ko', markersize = 2)
plt.plot(temp_inner['k'].values, model((temp_inner['k'].values), *par), label = name)
plt.title("sqrt(chi2/dof) = %e" % np.sqrt(chi2_dof))
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
# semilogy
plt.ylim(ymin = 1e-6, ymax = 1.2)
plt.xlabel('k [h/Mpc]')
plt.ylabel('corr. coeff.')
plt.semilogy(temp_inner['k'].values, temp_inner['c'].values, 'ko', markersize = 2)
plt.semilogy(temp_inner['k'].values, model((temp_inner['k'].values), *par), label = name)
plt.title("sqrt(chi2/dof) = %e" % np.sqrt(chi2_dof))
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
# semilogx
plt.ylim(ymax = 1.2)
plt.xlabel('k [h/Mpc]')
plt.ylabel('corr. coeff.')
plt.semilogx(temp_inner['k'].values, temp_inner['c'].values, 'ko', markersize = 2)
plt.semilogx(temp_inner['k'].values, model((temp_inner['k'].values), *par), label = name)
plt.title("sqrt(chi2/dof) = %e" % np.sqrt(chi2_dof))
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
# loglog
plt.ylim(ymin = 1e-6, ymax = 1.2)
plt.xlabel('k [h/Mpc]')
plt.ylabel('corr. coeff.')
plt.loglog(temp_inner['k'].values, temp_inner['c'].values, 'ko', markersize = 2)
plt.loglog(temp_inner['k'].values, model((temp_inner['k'].values), *par), label = name)
plt.title("sqrt(chi2/dof) = %e" % np.sqrt(chi2_dof))
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
df_par = pd.DataFrame({'zmean':all_zmean, 'deltaz':all_deltaz})
for i in df_par.index:
for j in range(len(all_par[i])):
df_par.at[i, 'par%d' % (j + 1)] = all_par[i][j]
# fix zmean, plot parameters as function of deltaz
for zmean in np.unique(df_par.zmean):
temp = df_par.loc[df_par.zmean == zmean]
name_par = [col for col in df_par.columns if 'par' in col]
# only plot data if there is more than 4 points
if (len(temp.index) > 4):
with PdfPages("%sprocess/%s_plot_params_zmean_%.2f.pdf" % (prefix, name, zmean)) as pdf:
# regular
for parname in name_par:
plt.plot(temp.deltaz, temp[parname].values, 'o', label=parname)
plt.xlabel('deltaz')
plt.ylabel('par_value')
plt.ylim(ymin=0.0)
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
# semilogy
for parname in name_par:
plt.semilogy(temp.deltaz, temp[parname].values, 'o', label=parname)
plt.xlabel('deltaz')
plt.ylabel('par_value')
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
# loglog
for parname in name_par:
plt.loglog(temp.deltaz, temp[parname].values, 'o', label=parname)
plt.xlabel('deltaz')
plt.ylabel('par_value')
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
# fix deltaz, plot parameters as function of zmean
for deltaz in np.unique(df_par.deltaz):
temp = df_par.loc[df_par.deltaz == deltaz]
name_par = [col for col in df_par.columns if 'par' in col]
if (len(temp.index) > 4):
with PdfPages("%sprocess/%s_plot_params_deltaz_%.2f.pdf" % (prefix, name, deltaz)) as pdf:
# regular
for parname in name_par:
plt.plot(temp.zmean, temp[parname].values, 'o', label=parname)
plt.xlabel('zmean')
plt.ylabel('par_value')
plt.ylim(ymin=0.0)
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
# semilogy
for parname in name_par:
plt.semilogy(temp.zmean, temp[parname].values, 'o', label=parname)
plt.xlabel('zmean')
plt.ylabel('par_value')
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
# loglog
for parname in name_par:
plt.loglog(temp.zmean, temp[parname].values, 'o', label=parname)
plt.xlabel('zmean')
plt.ylabel('par_value')
plt.legend()
plt.grid()
pdf.savefig()
plt.close()
total_chi2 = np.sqrt(total_chi2/len(df.index))
print("total sqrt(chi2/N) = %e" % total_chi2)
# parameters
prefix = "daint_2048_smallbox"
redshifts = np.array([60, 30, 10, 5,3, 2.9, 2.8, 2.7, 2.6, 2.5, 2.4, 2.3, 2.2, 2.1, 2, 1.9, 1.8, 1.7, 1.6, 1.5, 1.4, 1.3, 1.2, 1.1, 1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0])
ngrid = 2048
Lbox = 256
knyq = np.pi * ngrid/Lbox
bins = 1024
df = process_data(prefix).dropna()
df = select_interval(df, zmax=3.0, dropna=True, kmax = 7.)
# power spectrum errors influence the fit significantly!
for i in df.index:
df.at[i, "sigmac"] = 1
# plots the data and fit for it
plot_zmean_deltaz_fit(prefix, df, model_gaussian, "gaussian")