def post(dt,a0,te,ib,DT,A0,TE,IB,v1,v2,v3,tdet,Nt,a,b):
import numpy as np
from juliantime import juliandate
from posterior import MT
from fileread import readFile
from convert import magConvert
#-------------------------------------------------------------------------
# - Prior distributions -
#-------------------------------------------------------------------------
pi_dt = np.exp(-((np.log(dt/0.0202)-DT[0])**2)/(2*DT[1]**2))
pi_a0 = A0[0]*np.exp(-A0[1]*np.log(np.log(a0)))+A0[2]
pi_te = TE[0]*np.exp(-((np.log(te/0.04)-TE[1])**2)/(2*TE[2]**2)) + \
TE[3]*np.exp(-((np.log(te/0.04)-TE[4])**2)/(2*TE[5]**2))
pi_ib = IB[0]*np.exp(-((ib-IB[1])**2)/(2*IB[2]**2)) + \
IB[3]*np.exp(-((ib-IB[4])**2)/(2*IB[5]**2)) + \
IB[6]*np.exp(-((ib-IB[7])**2)/(2*IB[8]**2))
#-------------------------------------------------------------------------
# - likelihood distribution -
#-------------------------------------------------------------------------
t = v1[0:Nt]
f = v2[0:Nt]
fsig = v3[0:Nt]
#Calibration for BLG-004 (Converting to mag units)
m = magConvert(f,a,b)
msig = magConvert(fsig,a,b)
#print('index of peak - '+str((m.tolist()).index(max(m))))
M = np.zeros(len(m))
M = MT(t,a0,te,dt,tdet)
Li = np.exp(-sum(((m-M)**2)/(2*msig**2)))
#-------------------------------------------------------------------------
# - Posterior distribution -
#-------------------------------------------------------------------------
p = Li*pi_dt*pi_te*pi_ib*pi_a0
return p
#Plotting example of light curve
import numpy as np
import matplotlib.pyplot as plt
from fileread import readFile
from posterior import MT
from magfit import magfit
from convert import magConvert
(v1,v2,v3,tdet,s3,Ca0,Cte,t0_actual) = readFile('2015BLG285.txt')
Cdt = t0_actual - tdet
mcal = MT(v1,Ca0,Cte,Cdt,tdet)
(a,b) = magfit(v2,mcal)
plt.figure()
plt.plot(v1-tdet,magConvert(v2,a,b),'k.',label='Actual Light Curve')
plt.title('Light Curve for MOA '+s3)
plt.xlabel('$t$ (days)')
plt.ylabel('$Magnification$')
plt.show()
def MCMC(v1,v2,v3,tdet,s3,Ca0,Cte,t0_actual,Nt):
import numpy as np
from posterior import post
import time
from juliantime import juliandate
from progressbar import ProgressBar
import warnings
from scipy import stats
from fileread import readFile
import matplotlib.pyplot as plt
from posterior import MT
from convert import magConvert
from magfit import magfit
from scipy.optimize import minimize
from scipy.optimize import leastsq
from numpy import linalg as LA
def fxn():
warnings.warn("deprecated", DeprecationWarning)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
fxn()
#initial parameters with arbitrary starting point theta:
#---------------------------------------------------
a0 = np.exp(2)
te = 0.04*np.exp(6)
ib = 18
dt = 0.0202*np.exp(6)
start = time.time()
#Prior distribution parameters:
#---------------------------------------------------
DT = [5.558,1.8226]
A0 = [0.4023,0.591,0.0124]
TE = [0.8284,6.0709,1.4283,0.1716,13.7152,1.3578]
IB = [0.1782,7.4511,3.1355,0.6704,18.89,2.0186,0.1514,28.0466,1.5002]
#Calibrating Magnification:
#---------------------------------------------------
Cdt = t0_actual - tdet
mcal = MT(v1,Ca0,Cte,Cdt,tdet)
(a,b) = magfit(v2,mcal)
#initialising MCMC:
#---------------------------------------------------
theta = [dt,a0,te,ib]
thetaN = np.zeros(4)
alpha = 0.9
N = 50000
p = post(theta[0],theta[1],theta[2],theta[3],DT,A0,TE,IB,v1,v2,v3,tdet,Nt,a,b)
samples = []
pdens = []
count = 0.0
pbar = ProgressBar()
print('\n\n')
print('==============================================================================')
print(' Light Curve for MOA '+s3+' Nt = '+str(Nt)+ ' Data Points')
print('==============================================================================\n')
print('Progress bar:')
#------------------------------------------------------------------------------
# -Metropolis-Hastings-
#------------------------------------------------------------------------------
for i in pbar(range(N)):
thetaN = theta + alpha*np.random.normal(size=4)
if all(thetaN) > 0:
pn = post(thetaN[0],thetaN[1],thetaN[2],thetaN[3],DT,A0,TE,IB,v1,v2,v3,tdet,Nt,a,b)
if pn >= p:
p = pn
theta = thetaN
pdens.append(p)
#print(thetaN,p,end='\r')
count = count + 1
else:
u = np.random.rand()
#Modified acceptance ratio to allow for truncation.
accMod = (stats.norm.cdf(theta[0])*stats.norm.cdf(theta[1])*stats.norm.cdf(theta[2])*stats.norm.cdf(theta[3]))\
/(stats.norm.cdf(thetaN[0])*stats.norm.cdf(thetaN[1])*stats.norm.cdf(thetaN[2])*stats.norm.cdf(thetaN[3]))
if u < accMod*pn/p:
p = pn
theta = thetaN
pdens.append(p)
#print(thetaN,p,end='\r')
count = count + 1
samples.append(theta)
#Maximum likelihood:
#---------------------------------------------------
xinit = [a0,te,dt]
xinit = np.array(xinit)
tl = v1[0:Nt]-tdet
fl = v2[0:Nt]
ml = magConvert(fl,a,b)
objective = lambda x: (ml - (-2 + 2*x[0]*np.sqrt(1/(x[0]**2 - 1))+((tl-x[2])/x[1])**2 + 2)\
/(np.sqrt((-2 + 2*x[0]*np.sqrt(1/(x[0]**2 - 1))+((tl-x[2])/x[1])**2)**2 \
+4*((-2 + 2*x[0]*np.sqrt(1/(x[0]**2 - 1))+((tl-x[2])/x[1])**2)))))
#res = minimize(objective,xinit)
plsq = leastsq(objective, xinit)
#print(plsq)
#Results:
#---------------------------------------------------
tt = np.linspace(0,v1[-1]-tdet,1000)
mdt = samples[pdens.index(max(pdens))][0]
ma0 = samples[pdens.index(max(pdens))][1]
mte = samples[pdens.index(max(pdens))][2]
mib = samples[pdens.index(max(pdens))][3]
mcon = magConvert(v2,a,b)
mcon = mcon.tolist()
acc_ratio = count/N
samples = np.array(samples)
elapsedtime = time.time()-start
final_time = tl[-1]
#Printing Results:
#----------------------------------------------------
if(0):
print('==============================================')
print('Report:')
print('==============================================')
print('Bayesian Estimate:')
print('Elapsed time = ' + str(elapsedtime))
print('t0 = '+str(mdt))
print('a0 = '+str(ma0))
print('te = '+str(mte))
print('ib = '+str(mib))
print('MAP - '+str(max(pdens)))
print('Acceptance ratio = '+ str(acc_ratio))
print('Actual t0 = '+ str(t0_actual - tdet))
print('==============================================')
print('Least-squares estimate:')
print('a0 = '+str(plsq[0][0]))
print('te = '+str(plsq[0][1]))
print('t0 = '+str(plsq[0][2]))
print('==============================================')
#Plotting Results:
#----------------------------------------------------
if(0):
plt.figure()
plt.plot(tt,MT(tt+tdet,ma0,mte,mdt,tdet),label='Bayesian prediction')
plt.plot(v1-tdet,magConvert(v2,a,b),'k.',label='Actual Light Curve')
plt.plot(tt,MT(tt+tdet,plsq[0][0],plsq[0][1],plsq[0][2],tdet),'grey',label='Least squares')
plt.plot(final_time*np.ones(100),np.linspace(0,Ca0+1,100),'r',label='Data inclusion point')
plt.title('Light Curve for MOA '+s3+' with N = '+str(Nt)+' data points')
plt.legend()
plt.xlabel('$t$ (days)')
plt.ylabel('$Magnification$')
plt.ylim(0,18)
plt.xlim(0,60)
plt.show()
print('Ca0 = '+str(Ca0))
print('Ba0 = '+str(ma0))
print('MLa0 = '+str(plsq[0][0]))
return tdet,ma0,mte,mdt,plsq[0][0],plsq[0][1],plsq[0][2]