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delta_cl.py
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delta_cl.py
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import numpy as np
import random
import tqdm
from scipy.integrate import odeint
import matplotlib
import matplotlib.pyplot as plt
matplotlib.use('pdf')
#import corner
from scipy.interpolate import interp1d
from numpy import array, arange
from scipy.optimize import minimize
#import emcee
from numpy import genfromtxt
import sys
# %matplotlib inline
z = np.loadtxt("EM_1.dat")[:, 0]
alpha = np.loadtxt("EM_1.dat")[:, 1]
z2 = np.loadtxt("EM_2.dat")[:, 0]
alpha2 = np.loadtxt("EM_2.dat")[:, 1]
z3 = np.loadtxt("EM_3.dat")[:, 0]
alpha3 = np.loadtxt("EM_3.dat")[:, 1]
interpolation= interp1d(z,alpha, fill_value='extrapolate' )
interpolation2= interp1d(z2,alpha2, fill_value='extrapolate' )
interpolation3= interp1d(z3,alpha3, fill_value='extrapolate' )
def simpson(a,b,f,N):
h=(b-a)/(N)
integral = f(a)+f(b)
#initializing sum for even and odd
even =0
odd =0
#initializing step sizes using 5.10 in book odd and even case
n= a+h
for i in range(1,int(N/2)+1):
even = even+f(n)
n= n+ 2*h
n= a+2*h
for i in range(1,int(N/2)):
odd= odd+ float(f(n))
n = n+2*h
#returning the integral
return (h/3)*(integral+2*even+4*odd)
def dU_dx(U, x,m,w):
# Here U is a vector such that y=U[0] and z=U[1]. This function should return [y', z']
return array( [U[1], -(2./(1.+x)+(3.*.3/(2.*(1.+x)**2.*(.3*(1.+x)**3.+.7))))*U[1] +2.*w*.3*np.exp(-2.*U[0])*((1.+x)/(.3*(1.+x)**3.+.7))-(np.power(10.,m))*U[0]/((x+1.)**2.*((1.+x)**3.+.7))],float)
c1 = 1.0 / 2.0
c2 = (7.0 + np.sqrt(21) ) / 14.0
c3= (7.0 - np.sqrt(21))/14.0
a21 = 1.0 / 2.0;
a31 = 1.0 / 4.0;
a32 = 1.0 / 4.0
a41 = 1.0 / 7.0
a42 = -(7.0 + 3.0 * np.sqrt(21) ) / 98.0
a43 = (21.0 + 5.0 * np.sqrt(21) ) / 49.0
a51 = (11.0 + np.sqrt(21) ) / 84.0
a53 = (18.0 + 4.0 * np.sqrt(21) ) / 63.0
a54 = (21.0 - np.sqrt(21) ) / 252.0
a61 = (5.0 + np.sqrt(21) ) / 48.0
a63 = (9.0 + np.sqrt(21) ) / 36.0
a64 = (-231.0 + 14.0 * np.sqrt(21) ) / 360.0
a65 = (63.0 - 7.0 * np.sqrt(21) ) / 80.0
a71 = (10.0 - np.sqrt(21) ) / 42.0
a73 = (-432.0 + 92.0 * np.sqrt(21) ) / 315.0
a74 = (633.0 - 145.0 * np.sqrt(21) ) / 90.0
a75 = (-504.0 + 115.0 * np.sqrt(21) ) / 70.0
a76 = (63.0 - 13.0 * np.sqrt(21) ) / 35.0
a81 = 1.0 / 14.0
a85 = (14.0 - 3.0 * np.sqrt(21) ) / 126.0
a86 = (13.0 - 3.0 * np.sqrt(21) ) / 63.0
a87 = 1.0 / 9.0
a91 = 1.0 / 32.0
a95 = (91.0 - 21.0 * np.sqrt(21) ) / 576.0
a96 = 11.0 / 72.0
a97 = -(385.0 + 75.0 * np.sqrt(21) ) / 1152.0
a98 = (63.0 + 13.0 * np.sqrt(21) ) / 128.0
a10_1 = 1.0 / 14.0
a10_5 = 1.0 / 9.0
a10_6 = -(733.0 + 147.0 * np.sqrt(21) ) / 2205.0
a10_7 = (515.0 + 111.0 * np.sqrt(21) ) / 504.0
a10_8 = -(51.0 + 11.0 * np.sqrt(21) ) / 56.0
a10_9 = (132.0 + 28.0 * np.sqrt(21) ) / 245.0
a11_5 = (-42.0 + 7.0 * np.sqrt(21) ) / 18.0
a11_6 = (-18.0 + 28.0 * np.sqrt(21) ) / 45.0
a11_7 = -(273.0 + 53.0 * np.sqrt(21) ) / 72.0
a11_8 = (301.0 + 53.0 * np.sqrt(21) ) / 72.0
a11_9 = (28.0 - 28.0 * np.sqrt(21) ) / 45.0
a11_10 = (49.0 - 7.0 * np.sqrt(21) ) / 18.0
b1 = 9.0 / 180.0
b8 = 49.0 / 180.0
b9 = 64.0 / 180.0
def rk8(m,zeta):
phi_0 = 0
phi_1 = 0
z0 = 0
zf = 4000
N = 75000
h = (zf - z0)/N
delta_alpha= []
zpoints = np.arange(z0, zf, h)
xpoints = []
vpoints = []
p = array([phi_0, phi_1], float)
c1h = c1 * h
c2h = c2 * h
c3h = c3 * h
for z in zpoints:
xpoints.append(2*p[0])
vpoints.append(p[1])
k_1 = h* dU_dx(p, z , m, zeta)
k_2 = h* dU_dx(p+ a21*k_1, z+ c1h, m, zeta)
k_3 = h* dU_dx(p+ ( a31 * k_1 + a32 * k_2 ) , z+ c1h, m, zeta)
k_4 = h* dU_dx(p+ ( a41 * k_1 + a42 * k_2 + a43 * k_3 ) , z+ c2h, m, zeta)
k_5 = h* dU_dx(p+ ( a51 * k_1 + a53 * k_3 + a54 * k_4 ) , z+ c2h, m, zeta)
k_6 = h* dU_dx(p+ ( a61 * k_1 + a63 * k_3 + a64 * k_4 + a65 * k_5 ) , z+ c1h, m, zeta)
k_7 = h* dU_dx(p+ ( a71 * k_1 + a73 * k_3 + a74 * k_4 + a75 * k_5 + a76 * k_6 ), z+ c3h, m, zeta)
k_8 = h* dU_dx(p+ ( a81 * k_1 + a85 * k_5 + a86 * k_6 + a87 * k_7 ), z+ c3h , m, zeta)
k_9 = h* dU_dx(p+ ( a91 * k_1 + a95 * k_5 + a96 * k_6+ a97 * k_7 + a98 * k_8 ), z+ c1h, m, zeta)
k_10 = h* dU_dx(p+ ( a10_1 * k_1 + a10_5 * k_5 + a10_6 * k_6 + a10_7 * k_7 + a10_8 * k_8 + a10_9 * k_9 ), z+ c2h, m, zeta)
k_11 = h* dU_dx(p + ( a11_5 * k_5 + a11_6 * k_6 + a11_7 * k_7+ a11_8 * k_8 + a11_9 * k_9 + a11_10 * k_10 ), z+ h, m, zeta)
p = p + (b1 * k_1 + b8 * k_8 + b9 * k_9 + b8 * k_10 + b1 * k_11)
return [xpoints, vpoints, zpoints]
def rho_cal( zeta,m):
phi,phi_prime,z =rk8(m ,zeta )
ys = phi
interpolated_alpha= interp1d(z,ys, fill_value='extrapolate' )
def rhoi1(redshift):
return interpolated_alpha(redshift)*interpolation(redshift)
def rhoi2(redshift):
return interpolated_alpha(redshift)*interpolation2(redshift)
def rhoi3(redshift):
return interpolated_alpha(redshift)*interpolation3(redshift)
rho_1= simpson(0,4000,rhoi1,5000)
rho_2= simpson(0,4000,rhoi2,5000)
rho_3= simpson(0,4000,rhoi3,5000)
rho_val= np.transpose([rho_1,rho_2,rho_3])
return rho_val
l = np.loadtxt("alpha_cl1.dat")[:, 0]
cl_tt = np.loadtxt("alpha_cl1.dat")[:, 1]
cl2_tt = np.loadtxt("alpha_cl2.dat")[:, 1]
cl3_tt = np.loadtxt("alpha_cl3.dat")[:, 1]
fid_tt= np.loadtxt("fid_cl.dat")[:, 1]
l = np.loadtxt("alpha_cl1.dat")[:, 0]
cl_ee = np.loadtxt("alpha_cl1.dat")[:, 2]
cl2_ee = np.loadtxt("alpha_cl2.dat")[:, 2]
cl3_ee = np.loadtxt("alpha_cl3.dat")[:, 2]
fid_ee= np.loadtxt("fid_cl.dat")[:, 2]
cl_te = np.loadtxt("alpha_cl1.dat")[:, 3]
cl2_te = np.loadtxt("alpha_cl2.dat")[:, 3]
cl3_te = np.loadtxt("alpha_cl3.dat")[:, 3]
fid_te= np.loadtxt("fid_cl.dat")[:, 3]
sigma = [.006, .012, .036]
cl_tt_pc1= (1/np.sqrt(sigma[0])**2)*(fid_tt-cl_tt)
cl_tt_pc2= (1/np.sqrt(sigma[1])**2)*(fid_tt-cl2_tt)
cl_tt_pc3= (1/np.sqrt(sigma[2])**2)*(fid_tt-cl3_tt)
cl_te_pc1= (1/np.sqrt(sigma[0])**2)*(fid_te-cl_te)
cl_te_pc2= (1/np.sqrt(sigma[1])**2)*(fid_te-cl2_te)
cl_te_pc3= (1/np.sqrt(sigma[2])**2)*(fid_te-cl3_te)
cl_ee_pc1= (1/np.sqrt(sigma[0])**2)*(fid_ee-cl_ee)
cl_ee_pc2= (1/np.sqrt(sigma[1])**2)*(fid_ee-cl2_ee)
cl_ee_pc3= (1/np.sqrt(sigma[2])**2)*(fid_ee-cl3_ee)
rho =rho_cal(3.5e-05, 1)
rho_1sig =rho_cal(5e-5,1)
rho_2sig =rho_cal(9e-5, 1)
dcl_tt_1nsig=[]
dcl_te_1nsig=[]
dcl_ee_1nsig=[]
l_list= []
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_1sig[0]*cl_tt_pc1[j]
delta_cl2 = rho_1sig[1]*cl_tt_pc2[j]
delta_cl3 = rho_1sig[2]*cl_tt_pc3[j]
dcl_tt_1nsig.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_1sig[0]*cl_te_pc1[j]*100000
delta_cl2 = rho_1sig[1]*cl_te_pc2[j]*100000
delta_cl3 = rho_1sig[2]*cl_te_pc3[j]*100000
dcl_te_1nsig.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_1sig[0]*cl_ee_pc1[j]
delta_cl2 = rho_1sig[1]*cl_ee_pc2[j]
delta_cl3 = rho_1sig[2]*cl_ee_pc3[j]
dcl_ee_1nsig.append((delta_cl+delta_cl2+delta_cl3))
dcl_tt_2nsig=[]
dcl_te_2nsig=[]
dcl_ee_2nsig=[]
l_list= []
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_2sig[0]*cl_tt_pc1[j]
delta_cl2 = rho_2sig[1]*cl_tt_pc2[j]
delta_cl3 = rho_2sig[2]*cl_tt_pc3[j]
dcl_tt_2nsig.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_2sig[0]*cl_te_pc1[j]
delta_cl2 = rho_2sig[1]*cl_te_pc2[j]
delta_cl3 = rho_2sig[2]*cl_te_pc3[j]
dcl_te_2nsig.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_2sig[0]*cl_ee_pc1[j]
delta_cl2 = rho_2sig[1]*cl_ee_pc2[j]
delta_cl3 = rho_2sig[2]*cl_ee_pc3[j]
dcl_ee_2nsig.append((delta_cl+delta_cl2+delta_cl3))
dcl_tt_best=[]
dcl_te_best=[]
dcl_ee_best=[]
l_list= []
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho[0]*cl_tt_pc1[j]
delta_cl2 = rho[1]*cl_tt_pc2[j]
delta_cl3 = rho[2]*cl_tt_pc3[j]
dcl_tt_best.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho[0]*cl_te_pc1[j]
delta_cl2 = rho[1]*cl_te_pc2[j]
delta_cl3 = rho[2]*cl_te_pc3[j]
dcl_te_best.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho[0]*cl_ee_pc1[j]
delta_cl2 = rho[1]*cl_ee_pc2[j]
delta_cl3 = rho[2]*cl_ee_pc3[j]
dcl_ee_best.append((delta_cl+delta_cl2+delta_cl3))
dcl_tt_1sig=[]
dcl_te_1sig=[]
dcl_ee_1sig=[]
l_list= []
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_1sig[0]*cl_tt_pc1[j]
delta_cl2 = rho_1sig[1]*cl_tt_pc2[j]
delta_cl3 = rho_1sig[2]*cl_tt_pc3[j]
dcl_tt_1sig.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_1sig[0]*cl_te_pc1[j]
delta_cl2 = rho_1sig[1]*cl_te_pc2[j]
delta_cl3 = rho_1sig[2]*cl_te_pc3[j]
dcl_te_1sig.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_1sig[0]*cl_ee_pc1[j]
delta_cl2 = rho_1sig[1]*cl_ee_pc2[j]
delta_cl3 = rho_1sig[2]*cl_ee_pc3[j]
dcl_ee_1sig.append((delta_cl+delta_cl2+delta_cl3))
dcl_tt_2sig=[]
dcl_te_2sig=[]
dcl_ee_2sig=[]
l_list= []
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_2sig[0]*cl_tt_pc1[j]
delta_cl2 = rho_2sig[1]*cl_tt_pc2[j]
delta_cl3 = rho_2sig[2]*cl_tt_pc3[j]
dcl_tt_2sig.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_2sig[0]*cl_te_pc1[j]
delta_cl2 = rho_2sig[1]*cl_te_pc2[j]
delta_cl3 = rho_2sig[2]*cl_te_pc3[j]
dcl_te_2sig.append((delta_cl+delta_cl2+delta_cl3))
for j in range(0, len(cl_tt_pc1)):
delta_cl = rho_2sig[0]*cl_ee_pc1[j]
delta_cl2 = rho_2sig[1]*cl_ee_pc2[j]
delta_cl3 = rho_2sig[2]*cl_ee_pc3[j]
dcl_ee_2sig.append((delta_cl+delta_cl2+delta_cl3))
matplotlib.rcParams['font.family'] = 'Times New Roman'
plt.rcParams["figure.figsize"] = [8.0,6.0]
axislabelfontsize= 54
matplotlib.mathtext.rcParams['legend.fontsize']=20
matplotlib.rcParams['mathtext.fontset'] = 'stix'
matplotlib.rcParams['font.family'] = 'STIXGeneral'
plt.rc("axes", linewidth=2.0)
plt.rc("lines", markeredgewidth=3)
plt.rc('axes', labelsize=32)
plt.rc('xtick', labelsize = 32)
plt.rc('ytick', labelsize = 32)
fig_width_pt = 703.27 #513.17 # Get this from LaTeX using \showthe\columnwidth
inches_per_pt = 1.0/72.27 # Convert pt to inches
golden_mean=0.9
fig_width = fig_width_pt*inches_per_pt # width in inches
fig_height =fig_width*golden_mean # height in inches
fig_size = [fig_width,fig_height]
#
params = {'backend': 'pdf',
'axes.labelsize': 54,
'lines.markersize': 4,
'font.size': 100,
'xtick.major.size':6,
'xtick.minor.size':3,
'ytick.major.size':6,
'ytick.minor.size':3,
'xtick.major.width':0.5,
'ytick.major.width':0.5,
'xtick.minor.width':0.5,
'ytick.minor.width':0.5,
'lines.markeredgewidth':1,
'axes.linewidth':1.2,
'xtick.labelsize': 32,
'ytick.labelsize': 32,
'savefig.dpi':2000,
# 'path.simplify':True,
'font.family': 'serif',
'font.serif':'Times',
'text.usetex':True,
'text.latex.preamble': [r'\usepackage{amsmath}'],
'figure.figsize': fig_size}
plt.plot(l, dcl_tt_1sig, linewidth = 4)
plt.plot(l, dcl_tt_2sig, linewidth = 4)
plt.plot(l, dcl_tt_best, linewidth = 4)
plt.xlabel(r' $\ell$')
plt.ylabel(r'$\frac{\ell(\ell+1)C_{\ell}}{2\pi}$ $\mu$ K$^2$')
plt.xscale('log')
plt.title(r'$\Delta$ TT', fontsize= 24)
plt.tight_layout()
plt.savefig('tt.pdf')
plt.close()
plt.plot(l, dcl_te_1sig , linewidth = 4)
plt.plot(l, dcl_te_2sig, linewidth = 4)
plt.plot(l, dcl_te_best, linewidth = 4)
plt.ylabel(r'$\frac{\ell(\ell+1)C_{\ell}}{2\pi}$ $\mu$ K$^2$ ($\times 10^{5}$)')
plt.xscale('log')
plt.xlabel(r'$\ell$')
plt.title(r'$\Delta$ TE', fontsize= 24)
plt.tight_layout()
plt.savefig('te.pdf')
plt.close()
plt.plot(l, dcl_ee_1sig, label= r'$ \Delta C_{\ell} $ for $ 1 \sigma $ value of $ \zeta/ \omega $', linewidth = 4)
plt.plot(l, dcl_ee_2sig, label= r'$ \Delta C_{\ell} $ for $ 2 \sigma $ value of $ \zeta/ \omega $', linewidth = 4)
plt.plot(l, dcl_ee_best, label= r'$ \Delta C_{\ell} $ for Bestfit value of $ \zeta/ \omega $', linewidth = 4)
plt.ylabel(r'$\frac{\ell(\ell+1)C_{\ell}}{2\pi}$ $\mu$ K$^2$')
plt.xlabel(r'$\ell$', fontsize= 24)
plt.xscale('log')
plt.title(r'$\Delta$ EE', fontsize= 24)
plt.legend()
plt.tight_layout()
plt.savefig('ee.pdf')
plt.close()
plt.plot(l, (dcl_tt_1sig/(fid_tt+dcl_tt_1sig)), linewidth = 4)
plt.plot(l, (dcl_tt_2sig/(fid_tt+dcl_tt_2sig)), linewidth = 4)
plt.plot(l, (dcl_tt_best/(fid_tt+dcl_tt_best)), linewidth = 4)
plt.xscale('log')
plt.xlabel(r'$\ell$')
plt.title('Fractional change in TT (Planck)', fontsize= 24)
plt.tight_layout()
plt.savefig('tt_frac.pdf')
plt.close()
#plt.plot(l, (dcl_te_1nsig/((fid_te+dcl_te_1nsig)**2+(fid_tt+dcl_tt_1nsig)*np.abs(fid_te+dcl_te_1nsig))**(1/2)) , linewidth = 3 )
#plt.plot(l, (dcl_te_2nsig/((fid_te+dcl_te_2nsig)**2+(fid_tt+dcl_tt_2nsig)*np.abs(fid_te+dcl_te_2nsig))**(1/2)) , linewidth = 3 )
#plt.plot(l, (dcl_te_best/((fid_te+dcl_te_best)**2+(fid_tt+dcl_tt_best)*np.abs(fid_te+dcl_te_best))**(1/2)) , linewidth = 3 )
#plt.plot(l, (dcl_te_best/(fid_te+dcl_te_best)))
#plt.xscale('log')
#plt.xlabel(r'$\ell$')
#plt.title(r'$\Delta C_l^{TE} / {\sqrt{C_l^{TT} C_l^{TE}+\left(C_l^{TE}\right)^2}}$ (Planck)', fontsize= 24)
plt.plot(l, (dcl_te_1sig/(fid_te+dcl_te_1sig)), linewidth = 4)
plt.plot(l, (dcl_te_2sig/(fid_te+dcl_te_2sig)), linewidth =4)
plt.plot(l, (dcl_te_best/(fid_te+dcl_te_best)), linewidth = 4)
plt.xscale('log')
plt.xlabel(r'$\ell$')
plt.title('Fractional change in TE (Planck)', fontsize= 24)
plt.tight_layout()
plt.savefig('te_frac.pdf')
plt.close()
plt.plot(l, (dcl_ee_1sig/(fid_ee+dcl_ee_1sig)), linewidth = 4, label= r'$ \Delta C_{\ell} $ for $ 1 \sigma $ constraint')
plt.plot(l, (dcl_ee_2sig/(fid_ee+dcl_ee_2sig)), linewidth = 4 , label= r'$ \Delta C_{\ell} $ for $ 2 \sigma $ constraint')
plt.plot(l, (dcl_ee_best/(fid_ee+dcl_ee_best)), linewidth = 4 , label= r'$ \Delta C_{\ell} $ for bestfit value ')
plt.xscale('log')
plt.xlabel(r'$\ell$')
plt.title('Fractional change in EE (Planck)', fontsize= 24)
plt.legend()
plt.tight_layout()
plt.savefig('ee_frac.pdf')
plt.close()