def lnlike4(theta, x, y, z, xerr, yerr, zerr):
alpha, beta, h0, Om, w0, w1 = theta
if (0.0 <= beta <= 10.0 and 20.0 <= alpha <= 40.0 and 0.5 <= h0 <= 1.0
and 0.0 <= Om <= 1.0 and -2.0 <= w0 <= 0.0 and -1.0 <= w1 <= 1.0):
c = const.c.to('km/s').value
Or = 4.153e-5 * h0**(-2)
Ok = 0.0
Mum = z*0.0
MumErr = z*0.0
for k in range(0, len(z)):
if z[k] > 10:
Mum[k] = z[k]
MumErr[k] = zerr[k]
else:
Mum[k] = 5*np.log10(distL(z[k], h0, Or, Om, Ok, w0, w1)) + 25
MumErr[k] = (5.0/np.log(10)) * (zerr[k]/z[k])
Mu = 2.5*(beta*x + alpha) - 2.5*y - 100.195
MuErr = 2.5*np.sqrt(yerr**2 + beta**2*xerr**2)
inv_sigma2 = 1.0/(MuErr**2 + MumErr**2)
xsq = np.sum((Mu-Mum)**2*inv_sigma2)
print theta, xsq
return -0.5*(xsq)
else:
return -np.inf
def lnlike4(theta, x, y, z, xerr, yerr, zerr):
alpha, beta, h0, Om, w0, w1 = theta
if (0.0 <= beta <= 10.0 and 20.0 <= alpha <= 40.0 and 0.5 <= h0 <= 1.0
and 0.0 <= Om <= 1.0 and -2.0 <= w0 <= 0.0 and -1.0 <= w1 <= 1.0):
c = const.c.to('km/s').value
Or = 4.153e-5 * h0**(-2)
Ok = 0.0
Mum = z * 0.0
MumErr = z * 0.0
for k in range(0, len(z)):
if z[k] > 10:
Mum[k] = z[k]
MumErr[k] = zerr[k]
else:
Mum[k] = 5 * np.log10(distL(z[k], h0, Or, Om, Ok, w0, w1)) + 25
MumErr[k] = (5.0 / np.log(10)) * (zerr[k] / z[k])
Mu = 2.5 * (beta * x + alpha) - 2.5 * y - 100.195
MuErr = 2.5 * np.sqrt(yerr**2 + beta**2 * xerr**2)
inv_sigma2 = 1.0 / (MuErr**2 + MumErr**2)
xsq = np.sum((Mu - Mum)**2 * inv_sigma2)
print theta, xsq
return -0.5 * (xsq)
else:
return -np.inf
def hubblediagram(path, ve, vZ, vMu, vMuErr, index):
import numpy as np
import math as m
import matplotlib.pyplot as plt
from cosmoc import distL
print '+++++++++++++++++++++++++++++++++++++++++++'
print 'HUBBLEDIAGRAM: '
print '+++++++++++++++++++++++++++++++++++++++++++'
#====================================================================================
#============= Parameters ===========================================================
#====================================================================================
c = 2.9979e+5
#====================================================================================
#============= Main Body ============================================================
#====================================================================================
# ;;;;;Calculating Theoretical Mu (LCDM)
vZfit = np.arange(0.0001, 3.5, 0.0001, dtype=np.float)
Hp = 70.0
Om = 0.286
Ok = 0.0
h0 = Hp / 100.0
Or = 4.153e-5 * h0**(-2)
w0 = -1.0
vDLConc = vZfit * 0.0
for i in range(0, len(vZfit)):
vDLConc[i] = distL(vZfit[i], h0, Or, Om, Ok, w0, 0.0)
vMufit = 5.0 * np.log10(vDLConc) + 25.0
plt.rc('font', family='serif')
plt.plot(vZfit, vMufit)
plt.errorbar(vZ,
vMu,
yerr=vMuErr,
linestyle="None",
capsize=0,
ecolor="red")
plt.scatter(vZ, vMu, s=8, c='r', marker=".")
plt.axis([-0.08, 3.5, 18, 49])
plt.xlabel(r'\textbf{$z$}', fontsize=16)
plt.ylabel(r'\textbf{$\mu$}', fontsize=16)
plt.savefig(path)
return
def hubblediagram(path, ve, vZ, vMu, vMuErr, index):
import numpy as np
import math as m
import matplotlib.pyplot as plt
from cosmoc import distL
print '+++++++++++++++++++++++++++++++++++++++++++'
print 'HUBBLEDIAGRAM: '
print '+++++++++++++++++++++++++++++++++++++++++++'
#====================================================================================
#============= Parameters ===========================================================
#====================================================================================
c = 2.9979e+5
#====================================================================================
#============= Main Body ============================================================
#====================================================================================
# ;;;;;Calculating Theoretical Mu (LCDM)
vZfit = np.arange(0.0001, 3.5, 0.0001, dtype=np.float)
Hp = 70.0
Om = 0.286
Ok = 0.0
h0 = Hp/100.0
Or = 4.153e-5 * h0**(-2)
w0 = -1.0
vDLConc = vZfit * 0.0
for i in range(0, len(vZfit)):
vDLConc[i] = distL(vZfit[i], h0, Or, Om, Ok, w0, 0.0)
vMufit = 5.0*np.log10(vDLConc) + 25.0
plt.rc('font', family='serif')
plt.plot(vZfit, vMufit)
plt.errorbar(vZ,vMu,yerr=vMuErr, linestyle="None", capsize = 0, ecolor = "red")
plt.scatter(vZ, vMu, s=8, c='r', marker=".")
plt.axis([-0.08, 3.5, 18, 49])
plt.xlabel(r'\textbf{$z$}', fontsize=16)
plt.ylabel(r'\textbf{$\mu$}', fontsize=16)
plt.savefig(path)
return
def lnlike1(theta, x, y, w, m, z, xerr, yerr, werr, merr, zerr):
alpha, beta, MB1, DM, Om = theta
if (0.0 <= alpha <= 1.0 and 0.0 <= beta <= 6.0 and -25.0 <= MB1 <= -15.0
and -1.0 <= DM <= 0.0 and 0.0 <= Om <= 1.0):
c = const.c.to('km/s').value
h0 = 0.7
Or = 4.153e-5 * h0**(-2)
Ok = 0.0
w0 = -1.0
w1 = 0.0
Mum = z*0.0
MB = z*0.0
for k in range(0, len(z)):
Mum[k] = 5*np.log10(distL(z[k], h0, Or, Om, Ok, w0, w1)) + 25
if m[k] < 10:
MB[k] = MB1
else:
MB[k] = MB1 + DM
Mu = x - (MB - alpha*y + beta*w)
inv_sigma2 = 1.0/(xerr**2 + alpha**2*yerr**2 + beta**2*werr**2)
res = (Mu - Mum)
xsq = np.sum((Mu-Mum)**2*inv_sigma2)
llq = -0.5*(xsq)
print theta, xsq
llq2 = -0.5*(np.sum((Mu-Mum)**2*inv_sigma2 - np.log(inv_sigma2)))
return llq2, xsq, res
else:
return -np.inf, np.inf, np.inf
def lnlike1(theta, x, y, w, m, z, xerr, yerr, werr, merr, zerr):
alpha, beta, MB1, DM, Om = theta
if (0.0 <= alpha <= 1.0 and 0.0 <= beta <= 6.0 and -25.0 <= MB1 <= -15.0
and -1.0 <= DM <= 0.0 and 0.0 <= Om <= 1.0):
c = const.c.to('km/s').value
h0 = 0.7
Or = 4.153e-5 * h0**(-2)
Ok = 0.0
w0 = -1.0
w1 = 0.0
Mum = z * 0.0
MB = z * 0.0
for k in range(0, len(z)):
Mum[k] = 5 * np.log10(distL(z[k], h0, Or, Om, Ok, w0, w1)) + 25
if m[k] < 10:
MB[k] = MB1
else:
MB[k] = MB1 + DM
Mu = x - (MB - alpha * y + beta * w)
inv_sigma2 = 1.0 / (xerr**2 + alpha**2 * yerr**2 + beta**2 * werr**2)
res = (Mu - Mum)
xsq = np.sum((Mu - Mum)**2 * inv_sigma2)
llq = -0.5 * (xsq)
print theta, xsq
llq2 = -0.5 * (np.sum((Mu - Mum)**2 * inv_sigma2 - np.log(inv_sigma2)))
return llq2, xsq, res
else:
return -np.inf, np.inf, np.inf