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#! /usr/bin/env python
"""
Sample points from a gaussian likelihood
"""
from __future__ import absolute_import, division
import sys
import argparse
import multiprocessing
import numpy as np
from scipy.stats import multivariate_normal
import emcee
import tqdm
MEASURED_FR = [1, 1, 1]
SIGMA = 0.001
def solve_ratio(fr):
denominator = reduce(gcd, fr)
return [int(x/denominator) for x in fr]
def angles_to_fr(angles):
sphi4, c2psi = angles
psi = (0.5)*np.arccos(c2psi)
sphi2 = np.sqrt(sphi4)
cphi2 = 1. - sphi2
spsi2 = np.sin(psi)**2
cspi2 = 1. - spsi2
x = sphi2*cspi2
y = sphi2*spsi2
z = cphi2
return x, y, z
def triangle_llh(theta):
"""-Log likelihood function for a given theta."""
fr = angles_to_fr(theta)
fr_bf = MEASURED_FR
cov_fr = np.identity(3) * SIGMA
return np.log(multivariate_normal.pdf(fr, mean=fr_bf, cov=cov_fr))
def lnprior(theta):
"""Priors on theta."""
sphi4, c2psi = theta
# Flavour ratio bounds
if 0. <= sphi4 <= 1.0 and -1.0 <= c2psi <= 1.0:
pass
else: return -np.inf
return 0.
def lnprob(theta):
"""Prob function for mcmc."""
lp = lnprior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + triangle_llh(theta)
def parse_args():
"""Parse command line arguments"""
parser = argparse.ArgumentParser(description=__doc__)
parser.add_argument(
'--measured-ratio', type=int, nargs=3, default=[1, 1, 1],
help='Set the central value for the measured flavour ratio at IceCube'
)
parser.add_argument(
'--sigma-ratio', type=float, default=0.01,
help='Set the 1 sigma for the measured flavour ratio'
)
parser.add_argument(
'--burnin', type=int, default=100,
help='Amount to burnin'
)
parser.add_argument(
'--nwalkers', type=int, default=100,
help='Number of walkers'
)
parser.add_argument(
'--nsteps', type=int, default=2000,
help='Number of steps to run'
)
parser.add_argument(
'--seed', type=int, default=99,
help='Set the random seed value'
)
parser.add_argument(
'--outfile', type=str, default='./untitled',
help='Path to output chains'
)
args = parser.parse_args()
return args
def main():
args = parse_args()
np.random.seed(args.seed)
global MEASURED_FR
global SIGMA
MEASURED_FR = np.array(args.measured_ratio) / float(np.sum(args.measured_ratio))
SIGMA = args.sigma_ratio
print 'MEASURED_FR = {0}'.format(MEASURED_FR)
print 'SIGMA = {0}'.format(SIGMA)
ndim = 2
nwalkers = args.nwalkers
ntemps = 1
burnin = args.burnin
betas = np.array([1e0, 1e-1, 1e-2, 1e-3, 1e-4])
p0_base = [0.5, 0.5]
p0_std = [.2, 0.2]
print 'p0_base', p0_base
print 'p0_std', p0_std
p0 = np.random.normal(p0_base, p0_std, size=[ntemps, nwalkers, ndim])
print map(lnprior, p0[0])
# threads = multiprocessing.cpu_count()
threads = 1
sampler = emcee.PTSampler(
ntemps, nwalkers, ndim, triangle_llh, lnprior, threads=threads
)
print "Running burn-in"
for result in tqdm.tqdm(sampler.sample(p0, iterations=burnin), total=burnin):
pos, prob, state = result
sampler.reset()
print "Finished burn-in"
nsteps = args.nsteps
print "Running"
for _ in tqdm.tqdm(sampler.sample(pos, iterations=nsteps), total=nsteps):
pass
print "Finished"
mr = solve_ratio(MEASURED_FR)
outfile = args.outfile+'_{0}_{1}_{2}_{3:.1E}'.format(
mr[0], mr[1], mr[2], SIGMA
)
samples = sampler.chain[0, :, :, :].reshape((-1, ndim))
print 'acceptance fraction', sampler.acceptance_fraction
print 'sum of acceptance fraction', np.sum(sampler.acceptance_fraction)
print 'np.unique(samples[:,0]).shape', np.unique(samples[:,0]).shape
try:
print 'autocorrelation', sampler.acor
except:
print 'WARNING : NEED TO RUN MORE SAMPLES FOR FILE ' + outfile
print 'outfile = ', outfile
fr_samples = np.array(map(angles_to_fr, samples))
np.save(outfile+'.npy', fr_samples)
print "DONE!"
main.__doc__ = __doc__
if __name__ == '__main__':
main()
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