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mcmc_2d_planck.py
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mcmc_2d_planck.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
from schwimmbad import MPIPool
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)
#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.*.311*(1+x)**2+4*9.24*10**(-5)*(1+x)**3)/(2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))))*U[1] +6.*w*.311*np.exp(-2.*U[0])*((1.+x)/(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))-((np.power(10.,m))*10**(-3))**2*U[0]/(2.4*(x+1.)**2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))],float)
#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.*.311*(1+x)**2+4*9.24*10**(-5)*(1+x)**3)/(2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))))*U[1] +6.*w*.311*np.exp(-2.*U[0])*((1.+x)/(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))-((np.power(10.,m))*10**(-3))**2*U[0]/(2.4*(x+1.)**2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))],float)
#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.*.311*(1+x)**2+4*9.24*10**(-5)*(1+x)**3)/(2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))))*U[1] -6.*w*.311*np.exp(-2.*U[0])*((1.+x)/(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))-((np.power(10.,m))*10**(-3))**2*U[0]/(2.4*(x+1.)**2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))],float)
#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.*.311*(1+x)**2+4*9.24*10**(-5)*(1+x)**3)/(2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))))*U[1] -6.*w*.311*np.exp(-2.*U[0])*((1.+x)/(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))-(np.power(10.,m))**2*U[0]/((x+1.)**2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))],float)
def dU_dx(U, x,m,w):
return array([U[1], (2./(1.+x) - ((3.*.311*(1+x)**2+4*9.24*10**(-5)*(1+x)**3)/(2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))))*U[1] -6.*w*.311*np.exp(-2.*U[0])*((1.+x)/(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))-(np.power(10.,m))**2*U[0]/((x+1.)**2.*(.311*(1.+x)**3.+9.24*10**(-5)*(1+x)**4+.68))],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
#phi_0 = 0.002728293224780778
#phi_1 = 2.858399743936276e-07
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
rho_dat= [-.0035,.001,.081 ]
sigma = [.0069, .012, .049]
def log_likelihood(theta, rho_data, rhoerr):
zeta,m = theta
model = rho_cal(zeta,m)
sigma2 = [[1/rhoerr[0] ** 2,0,0], [0,1/rhoerr[1]**2,0], [0,0, 1/rhoerr[2]**2]]
rho_matrix= [(model[0]- rho_dat[0]),
(model[1]- rho_dat[1]),
(model[2]- rho_dat[2])]
chi= np.matmul(np.matmul(np.transpose(rho_matrix),sigma2),rho_matrix)
if np.isnan(model[0]):
return -1e12
#talk to dan about the normalization term
return -.5*chi
zeta_guess = -.0004
m_guess= 0
np.random.seed(42)
nll = lambda *args: -log_likelihood(*args)
initial = np.array([zeta_guess,m_guess]) + 1e-4 * np.random.randn(2)
#soln = minimize(nll, initial, args=(rho_dat, sigma))
#zeta_ml, m_ml = soln.x
#print(zeta_ml,m_ml)
soln = [1.9754204948260492e-07, 0]
def log_prior(theta):
zeta, m = theta
if -8 < m < 1 and -0.01 < zeta < .01:
return 0.0
return -np.inf
def log_probability(theta, rho_data, rho_err):
lp = log_prior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + log_likelihood(theta, rho_data, rho_err)
with MPIPool() as pool:
pos = soln + 1e-5 * np.random.randn(32, 2)
nwalkers, ndim = pos.shape
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_probability, args=(rho_dat, sigma), pool=pool)
sampler.run_mcmc(pos,7000, progress=True);
for i in range(0,32):
chain= []
chain= sampler.get_chain()[:,i,:]
chain= np.concatenate((np.zeros((len(sampler.get_chain()[:,0,0]),1), dtype=int), chain), axis=1)
chain= np.concatenate((np.ones((len(sampler.get_chain()[:,0,0]),1), dtype=int), chain), axis=1)
np.savetxt('test_'+str(i)+'.txt',chain)
fig, axes = plt.subplots(2, figsize=(10, 7), sharex=True)
samples = sampler.get_chain()
labels = ["zeta", "m"]
for i in range(ndim):
ax = axes[i]
ax.plot(samples[:, :, i], "k", alpha=0.3)
ax.set_xlim(0, len(samples))
ax.set_ylabel(labels[i])
ax.yaxis.set_label_coords(-0.1, 0.5)
axes[-1].set_xlabel("step number");
plt.savefig("plot.pdf")
tau = sampler.get_autocorr_time()
print(tau)
flat_samples = sampler.get_chain(discard=100, thin=15, flat=True)
print(flat_samples.shape)
import corner
labels = ["zeta", "m"]
fig = corner.corner(
flat_samples, labels=labels,levels=(0.68,0.95,0.99,)
);
fig.savefig("pcont_bsbm.pdf")