def emcee_delay_estimator(t, lc1, e1, lc2, e2, output_tag):
t0 = datetime.datetime.now()
print 'Process Started on', t0
crude_sig1, crude_tau1, crude_avg_lc1 = crude_lc_param_estimate(t, lc1)
crude_sig2, crude_tau2, crude_avg_lc2 = crude_lc_param_estimate(t, lc2)
print ''
print 'CRUDE LIGHT CURVE PARAMETERS'
print '----------------------------'
print 'parameter lc1 \tlc2'
print '----------------------------'
print 'sigma %+1.2f \t%+1.2f' % (crude_sig1, crude_sig2)
print 'tau %+1.2f \t%+1.2f' % (crude_tau1, crude_tau2)
print 'avg_mag %+1.2f \t%+1.2f' % (crude_avg_lc1, crude_avg_lc2)
print ''
print ''
print 'BEGINNING LIGHT CURVE PARAMETER OPTIMIZATION'
print ''
op_sig1, op_tau1, op_avg_lc1 = optimize_lc_param_estimate(t, lc1, e1)
op_sig2, op_tau2, op_avg_lc2 = optimize_lc_param_estimate(t, lc2, e2)
op_sig1 = abs(op_sig1)
op_sig2 = abs(op_sig2)
print ''
print 'OPTIMIZED LIGHT CURVE PARAMETERS'
print '--------------------------------'
print 'parameter lc1 \tlc2'
print '--------------------------------'
print 'sigma %+1.2f \t%+1.2f' % (op_sig1, op_sig2)
print 'tau %+1.2f \t%+1.2f' % (op_tau1, op_tau2)
print 'avg_mag %+1.2f \t%+1.2f' % (op_avg_lc1, op_avg_lc2)
print ''
print '\nProcess Started on', t0
print 'It is now ', datetime.datetime.now()
#ESTIMATE DELAY
print ''
print 'time series is %1.2f days long' % (t[len(t) - 1] - t[0])
print 'with %d data points' % (len(t))
nbins = int(len(t) / 50.)
fig = figure()
counts, bin_vals, somemore = hist(log10(diff(t)), nbins)
xlabel('Time Between Measurments, log10(days)')
fig.savefig("delta_t_histogram_%s.png" % (output_tag))
# ESTIMATE THE MODE OF THE DISTRIBUTION
n_max = argmax(counts)
mode = bin_vals[n_max]
print 'The most common sample time distance is %1.2f days within the range of [%1.2f,%1.2f] days' % (
10**mode, 10**(0.5 * (bin_vals[n_max - 1] + bin_vals[n_max])), 10
**(0.5 * (bin_vals[n_max] + bin_vals[n_max + 1])))
print ''
delta_delay = (10**mode / 50.)
print 'Scanning for initial delay estimate with delay step %1.2f' % (
delta_delay)
#del_array=arange(-1000.,1000.1,delta_delay)
del_array = arange(-1000., 1000.1, 10.)
count = -1
ll = []
max_val = -1.e10
c_sig = 0.5 * (op_sig1 + op_sig2)
c_tau = 0.5 * (op_tau1 + op_tau2)
c_avg_lc = (op_avg_lc1)
delta_mag = (op_avg_lc2 - op_avg_lc1)
for delta in del_array:
count += 1
ct, cx, ce = merge(t, lc1, e1, lc2, e2, delta, delta_mag)
val = kelly_ll([c_sig, c_tau, c_avg_lc], ct, cx, ce)
if (val > max_val):
max_val = val
if (count == int(0.01 * len(del_array))): print '1% done'
if (count == int(0.10 * len(del_array))): print '10% done'
if (count == int(0.25 * len(del_array))): print '25% done'
if (count == int(0.50 * len(del_array))): print '50% done'
if (count == int(0.75 * len(del_array))): print '75% done'
ll.append(val)
print 'DONE'
print '\nProcess Started on', t0
print 'It is now ', datetime.datetime.now()
print ''
#PLOT DELAY SEARCH
fig = figure()
subplot(311)
plot(del_array, ll, 'b-')
xlabel('delay, days')
ylabel('likelihood')
title('Delay Likelihood Scan\nsigma=%1.2f, tau=%1.2f, avg_mag=%1.2f' %
(c_sig, c_tau, c_avg_lc))
k_max = argmax(ll)
plot([del_array[k_max], del_array[k_max]], [min(ll), max(ll)], 'k--')
print 'BEST DELAY=%1.5e' % (del_array[k_max])
subplot(312)
delta_delay = del_array[1] - del_array[0]
k_lo = k_max - int(50 / (delta_delay) + 1)
k_up = k_max + int(50 / (delta_delay) + 1)
plot(del_array[k_lo:k_up], ll[k_lo:k_up], 'b-')
xlabel('delay, days')
ylabel('likelihood')
#title('Delay Likelihood Scan\nsigma=%1.2f, tau=%1.2f, avg_mag=%1.2f'%(c_sig, c_tau, c_avg_lc))
plot([del_array[k_max], del_array[k_max]], [min(ll), max(ll)], 'k--')
ylim(min(ll[k_lo:k_up]), ll[k_max] + 100.)
subplot(313)
delta_delay = del_array[1] - del_array[0]
k_lo = k_max - int(5 / (delta_delay) + 1)
k_up = k_max + int(5 / (delta_delay) + 1)
plot(del_array[k_lo:k_up], ll[k_lo:k_up], 'b-')
xlabel('delay, days')
ylabel('likelihood')
#title('Delay Likelihood Scan\nsigma=%1.2f, tau=%1.2f, avg_mag=%1.2f'%(c_sig, c_tau, c_avg_lc))
plot([del_array[k_max], del_array[k_max]], [min(ll), max(ll)], 'k--')
ylim(max(ll) - 1000., max(ll))
fig.savefig("delay_search_%s.png" % (output_tag))
delay = del_array[k_max]
#ESTIMATES OF QSR LIGHT CURVE
delta_mag = (op_avg_lc2 - op_avg_lc1)
sigma = abs(c_sig)
tau = c_tau
avg_mag = op_avg_lc1
print ''
print 'INITIAL PARAMETERS (average of lc1 and lc2)'
print '-------------------------------------------'
print 'delay = %1.2f' % (delay)
print 'delta_mag = %1.2f' % (delta_mag)
print 'avg_mag = %1.2f' % (avg_mag)
print 'tau = %1.2f' % (tau)
print 'sigma = %1.2f' % (sigma)
print ''
ct, cx, ce = merge(t, lc1, e1, lc2, e2, delay, delta_mag)
c_sig, c_tau, c_avg_lc = optimize_lc_param_estimate(ct, cx, ce)
sigma = abs(c_sig)
tau = c_tau
avg_mag = c_avg_lc
print ''
print 'INITIAL PARAMETERS (optimization of merged light curve)'
print '-------------------------------------------------------'
print 'delay = %1.2f' % (delay)
print 'delta_mag = %1.2f' % (delta_mag)
print 'avg_mag = %1.2f' % (avg_mag)
print 'tau = %1.2f' % (tau)
print 'sigma = %1.2f' % (sigma)
print ''
#exit()
#PLOT LIGHT CURVES
fig = figure()
ax = subplot(311)
errorbar(t, lc1, e1, fmt='b.', ms=3, label='light curve 1')
errorbar(t, lc2, e2, fmt='r.', ms=3, label='light curve 2')
legend(loc=1)
xlabel('time, day')
ylabel('magnitude')
#plot(ct,cx,'k.', ms=3)
ax = subplot(312)
errorbar(t, lc1, e1, fmt='b.', ms=3, label='light curve 1')
errorbar(t - delay,
lc2 - delta_mag,
e2,
fmt='r.',
ms=3,
label='del. and mag. shift lc2')
xlabel('time, day')
ylabel('magnitude')
legend(loc=1)
#plot(ct,cx,'k.', ms=3)
ax = subplot(313)
ct, cx, ce = merge(t, lc1, e1, lc2, e2, delay, delta_mag)
errorbar(ct, cx, ce, fmt='b.', ms=3, label='merged light curve')
xlabel('time, day')
ylabel('magnitude')
legend(loc=1)
fig.savefig("op_light_curves_%s.png" % (output_tag))
#show()
def lnprior(_theta):
_delay, _delta_mag, _sigma, _tau, _avg_mag = _theta
if delay - 50. < _delay < delay + 50. and delta_mag - 1. < _delta_mag < delta_mag + 1. and sigma * 0.1 < _sigma < sigma * 10. and tau * 0.1 < _tau < tau * 10. and avg_mag - 1. < _avg_mag < avg_mag + 1.:
return 0.0
return -np.inf
def lnprob(theta, t, lc1, err1, lc2, err2):
lp = lnprior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + kelly_delay_ll(theta, t, lc1, err1, lc2, err2)
print ''
print '-------------'
print 'RUNNING EMCEE'
print '-------------'
print ''
#RUN EMCEE
ndim, nwalkers = 5, 100
n_burn_in_iterations = 100
n_iterations = 1000
print 'pos'
true_vals = [delay, delta_mag, sigma, tau, avg_mag]
#print 'np.random.randn(ndim)',np.random.randn(ndim)
pos = [true_vals + 1e-4 * np.random.randn(ndim) for i in range(nwalkers)]
#pos = [[uniform(delay-100,delay+100.),uniform(delta_mag-1.,delta_mag+1.), uniform(0.,sigma*10.), uniform(tau*0.1, tau*10.), uniform(avg_mag-0.2+avg_mag-0.2)] for i in range(nwalkers)]
#pos = [true_vals + [uniform(-1.e3, 1.e3), uniform(-10.,10.), uniform(0.1,10.), uniform(0.1,800.), uniform(-50.,50.)] for i in range(nwalkers)]
#uniform([low, high, size])
r = np.random.randn(ndim)
#pos = [true_vals + [10**mode*r[0], 0.1*delta_mag*r[1], abs((sigma*r[2]+sigma)), ] for i in range(nwalkers)]
print 'sampler'
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
lnprob,
args=(t, lc1, e1, lc2, e2))
print 'Process Started on', t0
print 'It is currently ', datetime.datetime.now()
print 'burn-in sampler.run_mcmc'
#sampler.run_mcmc(pos, 500)
sampler.run_mcmc(pos, n_burn_in_iterations)
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))
print("\tMean acceptance fraction: {0:.3f}".format(
np.mean(sampler.acceptance_fraction)))
mc_delay, mc_delta_mag, mc_sigma, mc_tau, mc_avg_mag = map(
lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
print '\tErrors based on 16th, 50th, and 84th percentile'
print '\tParam \tMC_rec\terr_up\terr_low'
print '\tdelay \t%1.2e\t+%1.2e\t-%1.2e' % (mc_delay[0], mc_delay[1],
mc_delay[2])
print '\tdelta_mag \t%1.2e\t+%1.2e\t-%1.2e' % (
mc_delta_mag[0], mc_delta_mag[1], mc_delta_mag[2])
print '\tsigma \t%1.2e\t+%1.2e\t-%1.2e' % (mc_sigma[0], mc_sigma[1],
mc_sigma[2])
print '\ttau \t%1.2e\t+%1.2e\t-%1.2e' % (mc_tau[0], mc_tau[1],
mc_tau[2])
print '\tavg_mag \t%1.2e\t+%1.2e\t-%1.2e' % (
mc_avg_mag[0], mc_avg_mag[1], mc_avg_mag[2])
#fig = triangle.corner(samples, labels=["delay", "delta_mag", "$\sigma$", r"$\tau$", "avg_mag"],
#truths=[mc_delay[0], mc_delta_mag[0], mc_sigma[0], mc_tau[0], mc_avg_mag[0]])
fig = triangle.corner(
samples,
labels=["delay", "delta_mag", "$\sigma$", r"$\tau$", "avg_mag"])
fig.savefig("burn_in_triangle_%s.png" % (output_tag))
sampler.reset()
print 'Process Started on', t0
print 'It is currently ', datetime.datetime.now()
print 'sampler.run_mcmc'
#sampler.run_mcmc(pos, 100)
sampler.run_mcmc(pos, n_iterations)
print 'Process Started on', t0
print 'It is currently ', datetime.datetime.now()
print 'sampler.chain'
samples = sampler.chain[:, int(0.1 * n_iterations):, :].reshape((-1, ndim))
print len(samples)
print("Mean acceptance fraction: {0:.3f}".format(
np.mean(sampler.acceptance_fraction)))
mc_delay, mc_delta_mag, mc_sigma, mc_tau, mc_avg_mag = map(
lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
print 'Errors based on 16th, 50th, and 84th percentile'
print 'Param \tMC_rec\terr_up\terr_low'
print 'delay \t%1.2e\t+%1.2e\t-%1.2e' % (mc_delay[0], mc_delay[1],
mc_delay[2])
print 'delta_mag \t%1.2e\t+%1.2e\t-%1.2e' % (
mc_delta_mag[0], mc_delta_mag[1], mc_delta_mag[2])
print 'sigma \t%1.2e\t+%1.2e\t-%1.2e' % (mc_sigma[0], mc_sigma[1],
mc_sigma[2])
print 'tau \t%1.2e\t+%1.2e\t-%1.2e' % (mc_tau[0], mc_tau[1],
mc_tau[2])
print 'avg_mag \t%1.2e\t+%1.2e\t-%1.2e' % (mc_avg_mag[0], mc_avg_mag[1],
mc_avg_mag[2])
#figure(2)
#for i in range(ndim):
#figure()
#hist(sampler.flatchain[:,i], 100, color="k", histtype="step")
#title("Dimension {0:d}".format(i))
#fig = triangle.corner(samples, labels=["delay", "delta_mag", "$\sigma$", r"$\tau$", "avg_mag"],
#truths=[mc_delay[0], mc_delta_mag[0], mc_sigma[0], mc_tau[0], mc_avg_mag[0]])
fig = triangle.corner(
samples,
labels=["delay", "delta_mag", "$\sigma$", r"$\tau$", "avg_mag"])
fig.savefig("triangle_%s.png" % (output_tag))
fig = figure()
ax = subplot(311)
errorbar(t, lc1, e1, fmt='b.', ms=3, label='light curve 1')
errorbar(t, lc2, e2, fmt='r.', ms=3, label='light curve 2')
legend(loc=1)
xlabel('time, day')
ylabel('magnitude')
#plot(ct,cx,'k.', ms=3)
ax = subplot(312)
errorbar(t, lc1, e1, fmt='b.', ms=3, label='light curve 1')
errorbar(t - mc_delay[0],
lc2 - mc_delta_mag[0],
e2,
fmt='r.',
ms=3,
label='del. and mag. shift lc2')
xlabel('time, day')
ylabel('magnitude')
legend(loc=1)
#plot(ct,cx,'k.', ms=3)
ax = subplot(313)
ct, cx, ce = merge(t, lc1, e1, lc2, e2, mc_delay[0], mc_delta_mag[0])
errorbar(ct, cx, ce, fmt='b.', ms=3, label='merged light curve')
xlabel('time, day')
ylabel('magnitude')
legend(loc=1)
fig.savefig("mc_light_curves_%s.png" % (output_tag))
print 'Process Started on', t0
print 'It is currently ', datetime.datetime.now()
def kelly_delay_ll(theta, time_array, flux_array1, ph_err_array1, flux_array2,
ph_err_array2):
delay, delta_mag, sig, tau, avg_mag = theta
t, x, e = merge(time_array, flux_array1, ph_err_array1, flux_array2,
ph_err_array2, delay, delta_mag)
return kelly_ll([sig, tau, avg_mag], t, x, e)
def optimize_lc_param_estimate(_t, _x, _e):
nll = lambda *args: -kelly_ll(*args)
result = op.fmin(nll, crude_lc_param_estimate(_t, _x), args=(_t, _x, _e))
return result
def optimize_lc_param_estimate(_t, _x, _e): nll = lambda *args: -kelly_ll(*args) result = op.fmin(nll, crude_lc_param_estimate(_t, _x), args=(_t, _x, _e)) return result
def emcee_delay_estimator(t, lc1, e1, lc2, e2, output_tag):
t0 = datetime.datetime.now()
print 'Process Started on', t0
crude_sig1, crude_tau1, crude_avg_lc1 = crude_lc_param_estimate(t,lc1)
crude_sig2, crude_tau2, crude_avg_lc2 = crude_lc_param_estimate(t,lc2)
print ''
print 'CRUDE LIGHT CURVE PARAMETERS'
print '----------------------------'
print 'parameter lc1 \tlc2'
print '----------------------------'
print 'sigma %+1.2f \t%+1.2f'%(crude_sig1, crude_sig2)
print 'tau %+1.2f \t%+1.2f'%(crude_tau1, crude_tau2)
print 'avg_mag %+1.2f \t%+1.2f'%(crude_avg_lc1, crude_avg_lc2)
print ''
print ''
print 'BEGINNING LIGHT CURVE PARAMETER OPTIMIZATION'
print ''
op_sig1, op_tau1, op_avg_lc1 = optimize_lc_param_estimate(t,lc1,e1)
op_sig2, op_tau2, op_avg_lc2 = optimize_lc_param_estimate(t,lc2,e2)
op_sig1=abs(op_sig1)
op_sig2=abs(op_sig2)
print ''
print 'OPTIMIZED LIGHT CURVE PARAMETERS'
print '--------------------------------'
print 'parameter lc1 \tlc2'
print '--------------------------------'
print 'sigma %+1.2f \t%+1.2f'%(op_sig1, op_sig2)
print 'tau %+1.2f \t%+1.2f'%(op_tau1, op_tau2)
print 'avg_mag %+1.2f \t%+1.2f'%(op_avg_lc1, op_avg_lc2)
print ''
print '\nProcess Started on', t0
print 'It is now ', datetime.datetime.now()
#ESTIMATE DELAY
print ''
print 'time series is %1.2f days long'%(t[len(t)-1]-t[0])
print 'with %d data points'%(len(t))
nbins=int(len(t)/50.)
fig=figure()
counts, bin_vals, somemore =hist(log10(diff(t)), nbins)
xlabel('Time Between Measurments, log10(days)')
fig.savefig("delta_t_histogram_%s.png"%(output_tag))
# ESTIMATE THE MODE OF THE DISTRIBUTION
n_max=argmax(counts)
mode=bin_vals[n_max]
print 'The most common sample time distance is %1.2f days within the range of [%1.2f,%1.2f] days'%(10**mode, 10**(0.5*(bin_vals[n_max-1]+bin_vals[n_max])), 10**(0.5*(bin_vals[n_max]+bin_vals[n_max+1])))
print ''
delta_delay=(10**mode/50.)
print 'Scanning for initial delay estimate with delay step %1.2f'%(delta_delay)
#del_array=arange(-1000.,1000.1,delta_delay)
del_array=arange(-1000.,1000.1,10.)
count=-1
ll=[]
max_val = -1.e10
c_sig = 0.5*(op_sig1+op_sig2)
c_tau = 0.5*(op_tau1+op_tau2)
c_avg_lc = (op_avg_lc1)
delta_mag=(op_avg_lc2-op_avg_lc1)
for delta in del_array:
count+=1
ct, cx, ce = merge(t, lc1, e1, lc2, e2, delta, delta_mag)
val = kelly_ll([c_sig, c_tau, c_avg_lc] , ct, cx, ce)
if(val>max_val):
max_val=val
if(count==int(0.01*len(del_array))): print '1% done'
if(count==int(0.10*len(del_array))): print '10% done'
if(count==int(0.25*len(del_array))): print '25% done'
if(count==int(0.50*len(del_array))): print '50% done'
if(count==int(0.75*len(del_array))): print '75% done'
ll.append(val)
print 'DONE'
print '\nProcess Started on', t0
print 'It is now ', datetime.datetime.now()
print ''
#PLOT DELAY SEARCH
fig=figure()
subplot(311)
plot(del_array,ll,'b-')
xlabel('delay, days')
ylabel('likelihood')
title('Delay Likelihood Scan\nsigma=%1.2f, tau=%1.2f, avg_mag=%1.2f'%(c_sig, c_tau, c_avg_lc))
k_max=argmax(ll)
plot([del_array[k_max],del_array[k_max]],[min(ll),max(ll)],'k--')
print 'BEST DELAY=%1.5e'%(del_array[k_max])
subplot(312)
delta_delay=del_array[1]-del_array[0]
k_lo = k_max - int(50/(delta_delay)+1)
k_up = k_max + int(50/(delta_delay)+1)
plot(del_array[k_lo:k_up],ll[k_lo:k_up],'b-')
xlabel('delay, days')
ylabel('likelihood')
#title('Delay Likelihood Scan\nsigma=%1.2f, tau=%1.2f, avg_mag=%1.2f'%(c_sig, c_tau, c_avg_lc))
plot([del_array[k_max],del_array[k_max]],[min(ll),max(ll)],'k--')
ylim(min(ll[k_lo:k_up]),ll[k_max]+100.)
subplot(313)
delta_delay=del_array[1]-del_array[0]
k_lo = k_max - int(5/(delta_delay)+1)
k_up = k_max + int(5/(delta_delay)+1)
plot(del_array[k_lo:k_up],ll[k_lo:k_up],'b-')
xlabel('delay, days')
ylabel('likelihood')
#title('Delay Likelihood Scan\nsigma=%1.2f, tau=%1.2f, avg_mag=%1.2f'%(c_sig, c_tau, c_avg_lc))
plot([del_array[k_max],del_array[k_max]],[min(ll),max(ll)],'k--')
ylim(max(ll)-1000.,max(ll))
fig.savefig("delay_search_%s.png"%(output_tag))
delay = del_array[k_max]
#ESTIMATES OF QSR LIGHT CURVE
delta_mag = (op_avg_lc2-op_avg_lc1)
sigma = abs(c_sig)
tau = c_tau
avg_mag=op_avg_lc1
print ''
print 'INITIAL PARAMETERS (average of lc1 and lc2)'
print '-------------------------------------------'
print 'delay = %1.2f'%(delay)
print 'delta_mag = %1.2f'%(delta_mag)
print 'avg_mag = %1.2f'%(avg_mag)
print 'tau = %1.2f'%(tau)
print 'sigma = %1.2f'%(sigma)
print ''
ct, cx, ce = merge(t, lc1, e1, lc2, e2, delay, delta_mag)
c_sig, c_tau, c_avg_lc = optimize_lc_param_estimate(ct,cx,ce)
sigma = abs(c_sig)
tau = c_tau
avg_mag = c_avg_lc
print ''
print 'INITIAL PARAMETERS (optimization of merged light curve)'
print '-------------------------------------------------------'
print 'delay = %1.2f'%(delay)
print 'delta_mag = %1.2f'%(delta_mag)
print 'avg_mag = %1.2f'%(avg_mag)
print 'tau = %1.2f'%(tau)
print 'sigma = %1.2f'%(sigma)
print ''
#exit()
#PLOT LIGHT CURVES
fig = figure()
ax=subplot(311)
errorbar(t,lc1,e1, fmt='b.', ms=3, label='light curve 1')
errorbar(t,lc2,e2, fmt='r.', ms=3, label='light curve 2')
legend(loc=1)
xlabel('time, day')
ylabel('magnitude')
#plot(ct,cx,'k.', ms=3)
ax=subplot(312)
errorbar(t,lc1,e1, fmt='b.', ms=3, label='light curve 1')
errorbar(t-delay, lc2-delta_mag, e2, fmt='r.', ms=3, label='del. and mag. shift lc2')
xlabel('time, day')
ylabel('magnitude')
legend(loc=1)
#plot(ct,cx,'k.', ms=3)
ax=subplot(313)
ct, cx, ce = merge(t, lc1, e1, lc2, e2, delay, delta_mag)
errorbar(ct,cx, ce,fmt='b.', ms=3, label = 'merged light curve')
xlabel('time, day')
ylabel('magnitude')
legend(loc=1)
fig.savefig("op_light_curves_%s.png"%(output_tag))
#show()
def lnprior(_theta):
_delay, _delta_mag, _sigma, _tau, _avg_mag = _theta
if delay-50.<_delay<delay+50. and delta_mag-1.<_delta_mag<delta_mag+1. and sigma*0.1<_sigma<sigma*10. and tau*0.1<_tau<tau*10. and avg_mag-1.<_avg_mag<avg_mag+1.:
return 0.0
return -np.inf
def lnprob(theta, t, lc1, err1, lc2, err2):
lp = lnprior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + kelly_delay_ll(theta, t, lc1, err1, lc2, err2)
print ''
print '-------------'
print 'RUNNING EMCEE'
print '-------------'
print ''
#RUN EMCEE
ndim, nwalkers = 5, 100
n_burn_in_iterations = 100
n_iterations = 1000
print 'pos'
true_vals=[delay, delta_mag, sigma, tau, avg_mag]
#print 'np.random.randn(ndim)',np.random.randn(ndim)
pos = [true_vals + 1e-4*np.random.randn(ndim) for i in range(nwalkers)]
#pos = [[uniform(delay-100,delay+100.),uniform(delta_mag-1.,delta_mag+1.), uniform(0.,sigma*10.), uniform(tau*0.1, tau*10.), uniform(avg_mag-0.2+avg_mag-0.2)] for i in range(nwalkers)]
#pos = [true_vals + [uniform(-1.e3, 1.e3), uniform(-10.,10.), uniform(0.1,10.), uniform(0.1,800.), uniform(-50.,50.)] for i in range(nwalkers)]
#uniform([low, high, size])
r=np.random.randn(ndim)
#pos = [true_vals + [10**mode*r[0], 0.1*delta_mag*r[1], abs((sigma*r[2]+sigma)), ] for i in range(nwalkers)]
print 'sampler'
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(t, lc1, e1, lc2, e2))
print 'Process Started on', t0
print 'It is currently ', datetime.datetime.now()
print 'burn-in sampler.run_mcmc'
#sampler.run_mcmc(pos, 500)
sampler.run_mcmc(pos, n_burn_in_iterations)
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))
print("\tMean acceptance fraction: {0:.3f}".format(np.mean(sampler.acceptance_fraction)))
mc_delay, mc_delta_mag, mc_sigma, mc_tau, mc_avg_mag = map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]), zip(*np.percentile(samples, [16, 50, 84],axis=0)))
print '\tErrors based on 16th, 50th, and 84th percentile'
print '\tParam \tMC_rec\terr_up\terr_low'
print '\tdelay \t%1.2e\t+%1.2e\t-%1.2e'%(mc_delay[0], mc_delay[1], mc_delay[2])
print '\tdelta_mag \t%1.2e\t+%1.2e\t-%1.2e'%(mc_delta_mag[0], mc_delta_mag[1], mc_delta_mag[2])
print '\tsigma \t%1.2e\t+%1.2e\t-%1.2e'%(mc_sigma[0], mc_sigma[1], mc_sigma[2])
print '\ttau \t%1.2e\t+%1.2e\t-%1.2e'%(mc_tau[0], mc_tau[1], mc_tau[2])
print '\tavg_mag \t%1.2e\t+%1.2e\t-%1.2e'%(mc_avg_mag[0], mc_avg_mag[1], mc_avg_mag[2])
#fig = triangle.corner(samples, labels=["delay", "delta_mag", "$\sigma$", r"$\tau$", "avg_mag"],
#truths=[mc_delay[0], mc_delta_mag[0], mc_sigma[0], mc_tau[0], mc_avg_mag[0]])
fig = triangle.corner(samples, labels=["delay", "delta_mag", "$\sigma$", r"$\tau$", "avg_mag"])
fig.savefig("burn_in_triangle_%s.png"%(output_tag))
sampler.reset()
print 'Process Started on', t0
print 'It is currently ', datetime.datetime.now()
print 'sampler.run_mcmc'
#sampler.run_mcmc(pos, 100)
sampler.run_mcmc(pos, n_iterations)
print 'Process Started on', t0
print 'It is currently ', datetime.datetime.now()
print 'sampler.chain'
samples = sampler.chain[:, int(0.1*n_iterations):, :].reshape((-1, ndim))
print len(samples)
print("Mean acceptance fraction: {0:.3f}".format(np.mean(sampler.acceptance_fraction)))
mc_delay, mc_delta_mag, mc_sigma, mc_tau, mc_avg_mag = map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]), zip(*np.percentile(samples, [16, 50, 84],axis=0)))
print 'Errors based on 16th, 50th, and 84th percentile'
print 'Param \tMC_rec\terr_up\terr_low'
print 'delay \t%1.2e\t+%1.2e\t-%1.2e'%(mc_delay[0], mc_delay[1], mc_delay[2])
print 'delta_mag \t%1.2e\t+%1.2e\t-%1.2e'%(mc_delta_mag[0], mc_delta_mag[1], mc_delta_mag[2])
print 'sigma \t%1.2e\t+%1.2e\t-%1.2e'%(mc_sigma[0], mc_sigma[1], mc_sigma[2])
print 'tau \t%1.2e\t+%1.2e\t-%1.2e'%(mc_tau[0], mc_tau[1], mc_tau[2])
print 'avg_mag \t%1.2e\t+%1.2e\t-%1.2e'%(mc_avg_mag[0], mc_avg_mag[1], mc_avg_mag[2])
#figure(2)
#for i in range(ndim):
#figure()
#hist(sampler.flatchain[:,i], 100, color="k", histtype="step")
#title("Dimension {0:d}".format(i))
#fig = triangle.corner(samples, labels=["delay", "delta_mag", "$\sigma$", r"$\tau$", "avg_mag"],
#truths=[mc_delay[0], mc_delta_mag[0], mc_sigma[0], mc_tau[0], mc_avg_mag[0]])
fig = triangle.corner(samples, labels=["delay", "delta_mag", "$\sigma$", r"$\tau$", "avg_mag"])
fig.savefig("triangle_%s.png"%(output_tag))
fig = figure()
ax=subplot(311)
errorbar(t,lc1,e1, fmt='b.', ms=3, label='light curve 1')
errorbar(t,lc2,e2, fmt='r.', ms=3, label='light curve 2')
legend(loc=1)
xlabel('time, day')
ylabel('magnitude')
#plot(ct,cx,'k.', ms=3)
ax=subplot(312)
errorbar(t,lc1,e1, fmt='b.', ms=3, label='light curve 1')
errorbar(t-mc_delay[0], lc2-mc_delta_mag[0], e2, fmt='r.', ms=3, label='del. and mag. shift lc2')
xlabel('time, day')
ylabel('magnitude')
legend(loc=1)
#plot(ct,cx,'k.', ms=3)
ax=subplot(313)
ct, cx, ce = merge(t, lc1, e1, lc2, e2, mc_delay[0], mc_delta_mag[0])
errorbar(ct,cx, ce,fmt='b.', ms=3, label = 'merged light curve')
xlabel('time, day')
ylabel('magnitude')
legend(loc=1)
fig.savefig("mc_light_curves_%s.png"%(output_tag))
print 'Process Started on', t0
print 'It is currently ', datetime.datetime.now()
figure()
subplot(111)
errorbar(t, X_data, yerr=error, fmt='k.', label='2% error')
plot(t, X, 'rs', ms=4, mec='r', label='Light Curve')
legend(loc=2)
xlabel('time, days')
ylabel('Rel. Mag.')
#show()
figure()
subplot(311)
avg_array = arange(avg_mag - 50., avg_mag + 50., 1.)
ll_avg_array = []
for m in avg_array:
ll_avg_array.append(
kelly_ll([sigma, tau, m], t, X_data, error * ones(len(t))))
print len(avg_array), len(ll_avg_array)
plot(avg_array, ll_avg_array, 'k-')
plot([avg_mag, avg_mag],
[max(ll_avg_array) - 10., max(ll_avg_array) + 1.], 'k--')
ylim(max(ll_avg_array) - 5., max(ll_avg_array) + 1.)
xlabel('avg magnitude, mag')
ylabel('log likelihood')
subplot(312)
tau_array = 10**arange(-1., 5., 0.01)
#tau_array=arange(tau-50.,tau+50.,0.1)
ll_tau_array = []
for m in tau_array:
ll_tau_array.append(
kelly_ll([sigma, m, avg_mag], t, X_data, error * ones(len(t))))
def lnprob(theta, t, lc, err):
lp = lnprior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + kelly_ll(theta, t, lc, err)
def lnprob(theta, t, lc, err):
lp = lnprior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + kelly_ll(theta, t, lc, err)
def kelly_delay_ll(theta, time_array, flux_array1, ph_err_array1, flux_array2, ph_err_array2): delay, delta_mag, sig, tau, avg_mag = theta t, x, e = merge(time_array, flux_array1, ph_err_array1, flux_array2, ph_err_array2, delay, delta_mag) return kelly_ll([sig,tau,avg_mag], t, x, e)
figure()
subplot(111)
errorbar(t,X_data,yerr=error, fmt='k.', label='2% error')
plot(t,X, 'rs', ms=4, mec='r', label='Light Curve')
legend(loc=2)
xlabel('time, days')
ylabel('Rel. Mag.')
#show()
figure()
subplot(311)
avg_array=arange(avg_mag-50.,avg_mag+50.,1.)
ll_avg_array=[]
for m in avg_array:
ll_avg_array.append(kelly_ll([sigma, tau, m], t, X_data, error*ones(len(t))))
print len(avg_array), len(ll_avg_array)
plot(avg_array,ll_avg_array, 'k-')
plot([avg_mag,avg_mag],[max(ll_avg_array)-10.,max(ll_avg_array)+1.],'k--')
ylim(max(ll_avg_array)-5.,max(ll_avg_array)+1.)
xlabel('avg magnitude, mag')
ylabel('log likelihood')
subplot(312)
tau_array=10**arange(-1.,5.,0.01)
#tau_array=arange(tau-50.,tau+50.,0.1)
ll_tau_array=[]
for m in tau_array:
ll_tau_array.append(kelly_ll([sigma, m, avg_mag], t, X_data, error*ones(len(t))))
semilogx(tau_array,ll_tau_array, 'k-')
plot([tau,tau],[max(ll_tau_array)-10.,max(ll_tau_array)+1.],'k--')