def test_popov_SN1999em_emcee(self):
n = 100
start, end = 0.1, 200.
jd_shift = 20.
dm = -29.38 # D = 7.5e6 pc
# dm = -30.4 # D = 12.e6 pc
time = np.exp(np.linspace(np.log(start), np.log(end), n))
popov = Popov('test', R=450., M=15., Mni=0.04, E=0.7)
lc_m = popov.LCBol(time)
# ax = popov.plot_Lbol(time)
# sn1999em.plot_ubv(ax, path=sn1999em.sn_path, jd_shift=jd_shift, mshift=dm)
# plt.show()
curves_o = sn1999em.read_curves()
lc_o = curves_o.get('V')
lc_o.mshift = dm
print("Run: find tshift with bayesian: obs band %s with %s ..." %
(lc_o.Band.Name, popov))
fitter = FitMCMC()
fitter.is_debug = True
res = fitter.fit_lc(lc_o, lc_m)
tshift, tsigma = res.tshift, res.tsigma
print("Result: tshift= %s tsigma= %s ..." % (tshift, tsigma))
ax = popov.plot_Lbol(time)
lcp.lc_plot(lc_m, ax)
lcp.lc_plot(lc_o, ax, is_line=False)
# sn1999em.plot_ubv(ax, path=sn1999em.sn_path, jd_shift=-tshift, mshift=dm)
plt.show()
def test_fit_popov_SN1999em(self):
D = 11.5e6 # pc
dm = -5. * np.log10(D) + 5
# dm = -30.4 # D = 12.e6 pc
curves = sn1999em.read_curves()
lc = curves.get('R')
lc.mshift = dm
# lc.tshift = -lc.tmin
# fit
ppv, tshift = popov_fit(lc, R0=1200., M0=10., Mni0=0.01, E0=1., dt0=0.)
# print
txt = '{0:10} {1:.4e} R_sun\n'.format('R:', ppv.R0 / ps.phys.R_sun) + \
'{0:10} {1:.4e} M_sun\n'.format('Mtot:', ppv.Mtot / ps.phys.M_sun) + \
'{0:10} {1:.4e} M_sun\n'.format('Mni:', ppv.Mni / ps.phys.M_sun) + \
'{0:10} {1} ergs\n'.format('Etot:', ppv.Etot) + \
'{0:10} {1} d'.format('tshift:', tshift)
print(txt)
# plot model
# time = lc.Time - tshift
ax = ppv.plot_Lbol(lc.Time)
# plot obs
lc.tshift = lc.tshift + tshift
x = lc.Time
# x = lc.Time + jd_shift + res
y = lc.Mag
ax.plot(x,
y,
label='%s SN 1999em' % lc.Band.Name,
ls="",
color='red',
markersize=8,
marker="o")
plt.show()
def test_fit_time_popov_SN1999em(self):
jd_shift = 20.
dm = -29.38 # D = 7.5e6 pc
# dm = -30.4 # D = 12.e6 pc
curves = sn1999em.read_curves()
lc = curves.get('V')
lc.mshift = dm
time = lc.Time - lc.Tmin
# time = np.exp(np.linspace(np.log(start), np.log(end), n))
popov = Popov('test', R=450., M=15., Mni=0.04, E=0.7)
mags = popov.MagBol(time)
# fit
tshift = myfit(mags, lc)
# plot
ax = popov.plot_Lbol(time)
x = lc.Time + tshift
# x = lc.Time + jd_shift + res
y = lc.Mag
ax.plot(x,
y,
label='%s SN 1999em' % lc.Band.Name,
ls=":",
color='red',
markersize=8,
marker="o")
plt.show()
def test_lc_gp_Ntime(self):
from plugin import sn1999em
from pystella.fit.fit_gp import FitGP
Ntime = 50
colors = band.colors()
fig, ax = plt.subplots(figsize=(12, 10))
ax.invert_yaxis()
curves_o = sn1999em.read_curves()
for bname in curves_o.BandNames:
lc_o = curves_o.get(bname)
lc_o_gp, gp = FitGP.fit_lc(lc_o, Ntime=Ntime)
# plot
ax.errorbar(lc_o.Time, lc_o.Mag, label='{0} {1}'.format(bname, 'obs'), yerr=lc_o.MagErr,
fmt='s', color=colors[bname], ls='', markersize=2.5)
x = lc_o_gp.Time
y_pred = lc_o_gp.Mag
sigma = lc_o_gp.MagErr
ax.fill(np.concatenate([x, x[::-1]]),
np.concatenate([y_pred - sigma,
(y_pred + sigma)[::-1]]),
# np.concatenate([y_pred - 1.9600 * sigma,
# (y_pred + 1.9600 * sigma)[::-1]]),
alpha=.7, fc='grey', ec='None', label='95% confidence interval')
ax.plot(x, y_pred, ls='', marker='o', markersize=2, color=colors[bname])
plt.show()
def test_fit_GP_SN1999em(self):
# add data
dm = -29.38 # D = 7.5e6 pc
# dm = -30.4 # D = 12.e6 pc
curves = sn1999em.read_curves()
lc = curves.get('V')
lc.mshift = dm
t = lc.Time
y = lc.Mag
yerr = lc.MagErr
# k = gptools.SquaredExponentialKernel()
# gp = gptools.GaussianProcess(k)
# k = gptools.SquaredExponentialKernel(param_bounds=[(0, 1e3), (0, 100)])
k = gptools.SquaredExponentialKernel(param_bounds=[(0., max(np.abs(y))),
(0, np.std(t))])
gp = gptools.GaussianProcess(k, mu=gptools.LinearMeanFunction())
gp.add_data(t, y, err_y=yerr)
is_mcmc = True
is_mcmc = False
if is_mcmc:
out = gp.predict(t, use_MCMC=True, full_MCMC=True,
return_std=False,
num_proc=0,
nsamp=200,
plot_posterior=True,
plot_chains=False,
burn=100,
thin=1)
else:
gp.optimize_hyperparameters(verbose=True)
out = gp.predict(t, use_MCMC=False)
y_star, err_y_star = out
# gp.optimize_hyperparameters()
# y_star, err_y_star = gp.predict(t)
fig = plt.figure()
ax = fig.add_axes((0.1, 0.3, 0.8, 0.65))
ax.invert_yaxis()
ax.plot(t, y, color='blue', label='L bol', lw=2.5)
ax.errorbar(t, y, yerr=yerr, fmt='o', color='blue', label='%s obs.')
#
# ax.plot(t, y_star, color='red', ls='--', lw=1.5, label='GP')
# third: plot a constrained function with errors
ax.plot(t, y_star, '-', color='gray')
ax.fill_between(t, y_star - 2 * err_y_star, y_star + 2 * err_y_star, color='gray', alpha=0.3)
# ax.errorbar(t, y_star, err_y_star, fmt='.k', ms=6)
plt.legend()
plt.show()
def test_fit_GP_SN1999em(self):
# add data
dm = -29.38 # D = 7.5e6 pc
# dm = -30.4 # D = 12.e6 pc
curves = sn1999em.read_curves()
lc = curves.get('V')
lc.mshift = dm
t = lc.Time
y = lc.Mag
yerr = lc.Err
# k = gptools.SquaredExponentialKernel()
# gp = gptools.GaussianProcess(k)
# k = gptools.SquaredExponentialKernel(param_bounds=[(0, 1e3), (0, 100)])
k = gptools.SquaredExponentialKernel(param_bounds=[(0., max(np.abs(y))),
(0, np.std(t))])
gp = gptools.GaussianProcess(k, mu=gptools.LinearMeanFunction())
gp.add_data(t, y, err_y=yerr)
is_mcmc = True
is_mcmc = False
if is_mcmc:
out = gp.predict(t, use_MCMC=True, full_MCMC=True,
return_std=False,
num_proc=0,
nsamp=200,
plot_posterior=True,
plot_chains=False,
burn=100,
thin=1)
else:
gp.optimize_hyperparameters(verbose=True)
out = gp.predict(t, use_MCMC=False)
y_star, err_y_star = out
# gp.optimize_hyperparameters()
# y_star, err_y_star = gp.predict(t)
fig = plt.figure()
ax = fig.add_axes((0.1, 0.3, 0.8, 0.65))
ax.invert_yaxis()
ax.plot(t, y, color='blue', label='L bol', lw=2.5)
ax.errorbar(t, y, yerr=yerr, fmt='o', color='blue', label='%s obs.')
#
# ax.plot(t, y_star, color='red', ls='--', lw=1.5, label='GP')
# third: plot a constrained function with errors
ax.plot(t, y_star, '-', color='gray')
ax.fill_between(t, y_star - 2 * err_y_star, y_star + 2 * err_y_star, color='gray', alpha=0.3)
# ax.errorbar(t, y_star, err_y_star, fmt='.k', ms=6)
plt.legend()
plt.show()
def test_FitMCMC_best_curves_dt_SN1999em(self):
from pystella.rf import light_curve_func as lcf
from pystella.rf import light_curve_plot as lcp
# Get observations
D = 11.5e6 # pc
dm = -5. * np.log10(D) + 5
# dm = -30.4 # D = 12.e6 pc
curves_obs = sn1999em.read_curves()
curves_obs.set_mshift(dm)
# Get model
name = 'cat_R500_M15_Ni006_E12'
path = join(dirname(dirname(abspath(__file__))), 'data', 'stella')
curves_mdl = lcf.curves_compute(name,
path,
distance=10,
bands=curves_obs.BandNames)
# fit
is_debug = True # True
# fitter = FitLcMcmc()
fitter = ps.FitMCMC()
fitter.is_info = True
if is_debug:
fitter.is_debug = is_debug
fitter.nwalkers = 100 # number of MCMC walkers
fitter.nburn = 20 # "burn-in" period to let chains stabilize
fitter.nsteps = 200 # number of MCMC steps to take
threads = 1
# fitter.is_debug = False
fit_result, res, (th, e1,
e2), samples = fitter.best_curves(curves_mdl,
curves_obs,
dt0=0.,
threads=threads,
is_sampler=True)
fig = fitter.plot_corner(samples,
labels=('dt', ),
bnames=curves_obs.BandNames)
# print
# '{:10s} {:.4f} ^{:.4f}_{:.4f}\n'.format('lnf:', res['lnf'], res['lnfsig2'], res['lnfsig1']) + \
txt = '{:10s} {:.4f} ^{:.4f}_{:.4f} \n'.format('tshift:', th.dt, e1.dt, e2.dt) + \
'{:10s} chi2= {:.1f} BIC= {:.1f} AIC= {:.1f} dof= {} accept= {:.3f}\n'. \
format('stat:', res['chi2'], res['bic'], res['aic'], res['dof'], res['acceptance_fraction'])
print(txt)
# plot model
curves_obs.set_tshift(-th.dt)
ax = lcp.curves_plot(curves_mdl)
lt = {lc.Band.Name: 'o' for lc in curves_obs}
lcp.curves_plot(curves_obs, ax, lt=lt, xlim=(-10, 300), is_line=False)
ax.text(0.1, 0.1, txt, transform=ax.transAxes)
plt.show()
def test_fit_mpfit_curves_Stella_SN1999em(self):
from pystella.rf import light_curve_func as lcf
from pystella.rf import light_curve_plot as lcp
# matplotlib.rcParams['backend'] = "TkAgg"
# matplotlib.rcParams['backend'] = "Qt4Agg"
# from matplotlib import pyplot as plt
# Get observations
D = 11.5e6 # pc
dm = -5. * np.log10(D) + 5
# dm = -30.4 # D = 12.e6 pc
curves_obs = sn1999em.read_curves()
curves_obs.set_mshift(dm)
# Get model
name = 'cat_R500_M15_Ni006_E12'
path = join(dirname(dirname(abspath(__file__))), 'data', 'stella')
curves_mdl = lcf.curves_compute(name, path, curves_obs.BandNames)
# fit
# fitter = FitLcMcmc()
fitter = ps.FitMPFit()
fitter.is_debug = True
res = fitter.fit_curves(curves_obs, curves_mdl)
# print
# txt = '{0:10} {1:.4e} \n'.format('tshift:', res.tshift) + \
# '{0:10} {1:.4e} \n'.format('tsigma:', res.tsigma) + \
# '{0}\n'.format(res.comm)
txt = '{:10s} {:.4f}+-{:.4f} \n'.format('tshift:', res.tshift, res.tsigma) + \
'{:10s} {:.4f}+-{:.4f}\n'.format('msigma:', res.mshift, res.msigma) + \
'{0}\n'.format(res.comm)
print(txt)
# plot model
curves_obs.set_tshift(res.tshift)
# curves_mdl.set_tshift(0.)
ax = lcp.curves_plot(curves_mdl)
lt = {lc.Band.Name: 'o' for lc in curves_obs}
lcp.curves_plot(curves_obs, ax, lt=lt, xlim=(-10, 300), is_line=False)
ax.text(0.1, 0.1, txt, transform=ax.transAxes)
plt.show()
def test_fit_popov_SN1999em(self):
D = 11.5e6 # pc
dm = -5. * np.log10(D) + 5
# dm = -30.4 # D = 12.e6 pc
curves = sn1999em.read_curves()
lc = curves.get('R')
lc.mshift = dm
# lc.tshift = -lc.tmin
# fit
ppv, tshift = popov_fit(lc, R0=1000., M0=10., Mni0=0.01, E0=1., dt0=0.)
# plot model
# time = lc.Time - tshift
ax = ppv.plot_Lbol(lc.Time)
# plot obs
lc.tshift = lc.tshift + tshift
x = lc.Time
# x = lc.Time + jd_shift + res
y = lc.Mag
ax.plot(x, y, label='%s SN 1999em' % lc.Band.Name,
ls=".", color='red', markersize=8, marker="o")
plt.show()
def test_FitMPFit_best_curves_gp_SN1999em(self):
from pystella.rf import light_curve_func as lcf
from pystella.rf import light_curve_plot as lcp
# matplotlib.rcParams['backend'] = "TkAgg"
# matplotlib.rcParams['backend'] = "Qt4Agg"
# from matplotlib import pyplot as plt
# Get observations
D = 11.5e6 # pc
ebv_sn = 0.1
dm = -5. * np.log10(D) + 5
# dm = -30.4 # D = 12.e6 pc
curves_obs = sn1999em.read_curves()
curves_obs.set_mshift(dm)
# Get model
name = 'cat_R500_M15_Ni006_E12'
path = join(dirname(dirname(abspath(__file__))), 'data', 'stella')
curves_mdl = lcf.curves_compute(name, path, curves_obs.BandNames)
# fit
# fitter = FitLcMcmc()
fitter = ps.FitMPFit()
fitter.is_info = True
fitter.is_debug = True
res = fitter.best_curves_gp(curves_mdl, curves_obs, dt0=0., dm0=0.)
# print
txt = '{0:10} {1:.4e} \n'.format('tshift:', res['dt']) + \
'{0:10} {1:.4e} \n'.format('tsigma:', res['dtsig'])
print(txt)
# plot model
curves_obs.set_tshift(res['dt'])
# curves_mdl.set_tshift(0.)
ax = lcp.curves_plot(curves_mdl)
lt = {lc.Band.Name: 'o' for lc in curves_obs}
lcp.curves_plot(curves_obs, ax, lt=lt, xlim=(-10, 300), is_line=False)
plt.show()
def test_fit_time_popov_SN1999em(self):
jd_shift = 20.
dm = -29.38 # D = 7.5e6 pc
# dm = -30.4 # D = 12.e6 pc
curves = sn1999em.read_curves()
lc = curves.get('V')
lc.mshift = dm
time = lc.Time - lc.tmin
# time = np.exp(np.linspace(np.log(start), np.log(end), n))
popov = Popov('test', R=450., M=15., Mni=0.04, E=0.7)
mags = popov.MagBol(time)
# fit
tshift = myfit(mags, lc)
# plot
ax = popov.plot_Lbol(time)
x = lc.Time + tshift
# x = lc.Time + jd_shift + res
y = lc.Mag
ax.plot(x, y, label='%s SN 1999em' % lc.Band.Name,
ls=".", color='red', markersize=8, marker="o")
plt.show()
def test_FitMCMC_fake_curves(self):
# Get observations
# D = 11.5e6 # pc
D = 10.5e6 # pc
dm = -5. * np.log10(D) + 5
curves_o = sn1999em.read_curves()
curves_o.set_mshift(dm)
# Model
fname = 'cat_R500_M15_Ni006_E12.tt.ubv'
path = join(dirname(dirname(abspath(__file__))), 'data', 'stella')
# curves_m = pd.read_csv(join(path, fname), header=0, delim_whitespace=True)
curves_m = ps.curves_read(join(path, fname))
# Filter
bnames = curves_m.BandNames
for bname in bnames:
if bname not in curves_o.BandNames:
curves_m.pop(bname)
# curves_m = curves_m[curves_m.TimeCommon > 0]
# fit
is_debug = True
fitter = ps.FitMCMC()
fitter.is_info = True # True False
fitter.is_debug = is_debug
if is_debug:
fitter.nwalkers = 100 # number of MCMC walkers
fitter.nburn = 20 # "burn-in" period to let chains stabilize
fitter.nsteps = 200 # number of MCMC steps to take
else:
fitter.nwalkers = 200 # number of MCMC walkers
fitter.nburn = 100 # "burn-in" period to let chains stabilize
fitter.nsteps = 500 # number of MCMC steps to take
print('is_debug ', is_debug)
res, samples = fitter.best_curves(curves_m,
curves_o,
dt0=0.,
dm0=0.,
is_sampler=True)
curves_o.set_tshift(0.)
curves_o.set_mshift(dm)
curves_m.set_tshift(-res['dt'])
curves_m.set_mshift(-res['dm'])
# Plot
fig, (ax, axhist) = plt.subplots(2, 1, figsize=(9, 9))
fig = fitter.plot_corner(samples, axhist=axhist)
ps.curves_plot(curves_m, ax=ax)
ps.curves_plot(curves_o, ax=ax, is_line=False, markersize=2)
# print
txt = '{:10s} {:.4f} ^{:.4f}_{:.4f} \n'.format('tshift:', res['dt'], res['dtsig2'], res['dtsig1']) + \
'{:10s} {:.4f} ^{:.4f}_{:.4f}\n'.format('msigma:', res['dm'], res['dmsig2'], res['dmsig1']) + \
'{:10s} {:.4f} ^{:.4f}_{:.4f}\n'.format('lnf:', res['lnf'], res['lnfsig2'], res['lnfsig1']) + \
'{:10s} chi2= {:.4f} dof= {} accept= {:.3f}\n'. \
format('stat:', res['chi2'], res['dof'], res['acceptance_fraction'])
print(txt)
ax.text(0.1, 0.02, txt, transform=ax.transAxes)
xlim = ax.get_xlim()
xlim = -30, xlim[1]
ax.set_xlim(xlim)
fig.tight_layout()
plt.show()
def test_FitMCMC_best_curves_dtdm_SN1999em(self):
from pystella.rf import light_curve_func as lcf
from pystella.rf import light_curve_plot as lcp
# Get observations
D = 11.5e6 # pc
# MD0 = -5. * np.log10(D) + 5
ebv_sn = 0.1
# dm = -30.4 # D = 12.e6 pc
curves_obs = sn1999em.read_curves()
# curves_obs.set_mshift(MD0)
# Get model
name = 'cat_R500_M15_Ni006_E12'
path = join(dirname(dirname(abspath(__file__))), 'data', 'stella')
curves_mdl = ps.Stella(name, path=path).curves(curves_obs.BandNames,
distance=D,
ebv=ebv_sn)
# fit
is_debug = True # True
# fitter = FitLcMcmc()
fitter = ps.FitMCMC()
fitter.is_info = True
if is_debug:
fitter.is_debug = is_debug
fitter.nwalkers = 100 # number of MCMC walkers
fitter.nburn = 20 # "burn-in" period to let chains stabilize
fitter.nsteps = 200 # number of MCMC steps to take
threads = 3
# fitter.is_debug = False
# fit_result, res, samples \
fit_result, res, (th, ep,
em), sampler = fitter.best_curves(curves_mdl,
curves_obs,
dt0=0.,
dm0=0.,
threads=threads,
is_sampler=True)
nb = curves_obs.Length
dt, dm, sigs = fitter.theta2arr(th, nb)
ep_dt, ep_dm, ep_sigs = fitter.theta2arr(ep, nb)
em_dt, em_dm, em_sigs = fitter.theta2arr(em, nb)
samples = sampler.flatchain[fitter.nburn:, :]
fig = fitter.plot_corner(samples,
bnames=curves_obs.BandNames,
bins=55,
alpha=0.5,
verbose=fitter.is_info)
# print
txt = 'chi2= {:.1f} BIC= {:.1f} AIC= {:.1f} measure= {:.3f}\n'.\
format(res['chi2'], res['bic'], res['aic'], res['measure'])
txt += '\n dt= {:.1f} ^{{{:.1f}}}_{{{:.1f}}} '.format(dt, ep_dt, em_dt)
txt += '\n dm= {:.2f} ^{{{:.2f}}}_{{{:.2f}}} '.format(dm, ep_dm, em_dm)
for i, bname in enumerate(curves_obs.BandNames):
txt += '\n sigma_{{{:s}}} = {:.2f}^{{{:.2f}}}_{{{:.2f}}} '. \
format(bname, sigs[i], ep_sigs[i], em_sigs[i])
print(txt)
curves_mdl.set_tshift(dt)
curves_mdl.set_mshift(dm)
ax = None
errs = {}
for i, bn in enumerate(curves_mdl.BandNames):
errs[bn] = [
sigs[i]
] * curves_mdl[bn].Length # The error are the same for all points
curves_clone = curves_mdl.clone(err=errs)
ax = ps.curves_plot(curves_clone,
ax=ax,
is_legend=False,
is_fill=True,
alpha=0.2)
# Obs
lt = {lc.Band.Name: 'o' for lc in curves_obs}
lcp.curves_plot(curves_obs, ax, lt=lt, xlim=(-10, 300), is_line=False)
ax.text(0.05, 0.05, txt, transform=ax.transAxes)
plt.show()
def test_FitMPF_best_curves_SN1999em(self):
from pystella.rf import light_curve_func as lcf
from pystella.rf import light_curve_plot as lcp
# Get observations
D = 11.5e6 # pc
ebv_sn = 0.
# ebv_sn = 0.1
# dm = -5. * np.log10(D) + 5
# dm = -30.4 # D = 12.e6 pc
curves_obs = sn1999em.read_curves()
# Get model
name = 'cat_R500_M15_Ni006_E12'
path = join(dirname(dirname(abspath(__file__))), 'data', 'stella')
curves_mdl = ps.Stella(name, path=path).curves(curves_obs.BandNames,
distance=D,
ebv=ebv_sn)
# fit
fitter = ps.FitMPFit()
fitter.is_info = True
fitter.is_debug = True
fitter.is_quiet = True
fit_result, res, dum = fitter.best_curves(
curves_mdl,
curves_obs,
dt0=0.,
)
# fit_result, res, dum = fitter.best_curves(curves_mdl, curves_obs, dt0=0., dm0=0.)
dt, dtsig = res['dt'], res['dtsig']
dm, dmsig = res['dm'], res['dmsig']
# plot model
curves_mdl.set_tshift(dt)
ax = lcp.curves_plot(curves_mdl)
lt = {lc.Band.Name: 'o' for lc in curves_obs}
lcp.curves_plot(curves_obs, ax, lt=lt, xlim=(-10, 300), is_line=False)
# print
txt = '{:10} {:.2f} +- {:.4f}'.format('dt:', res['dt'], res['dtsig'])
txt += '\n{:10} {:.2f} +- {:.4f}'.format('dm:', res['dm'],
res['dmsig'])
print(txt)
title_font = {
'size': '12',
'color': 'black',
'weight': 'normal',
'verticalalignment': 'bottom'
}
ax.text(0.03,
0.95,
txt,
transform=ax.transAxes,
bbox={
'facecolor': 'none',
'alpha': 0.2,
'edgecolor': 'none'
},
**title_font)
plt.show()
def test_fit_stella_model(self):
"""Example: Fitting a Stella model to Sn1999em"""
# obs data
dm = -29.38
curves = sn1999em.read_curves()
lc_obs = curves.get('V')
lc_obs.mshift = -dm
lc_obs.tshift = -lc_obs.Tmin
# model light curves
name = 'cat_R1000_M15_Ni007_E15'
path = join(dirname(abspath(__file__)), 'data', 'stella')
curves_model = lcf.curves_compute(name, path, bands='V')
lc_mdl = curves_model.get('V')
todo
# Choose the "true" parameters.
dt_init = 0. # initial time shift
dm_init = 0. # initial time shift
f_true = 0.534
# Generate some synthetic data from the model.
# N = 50
t = lc_obs.Time
merr = lc_obs.Err
m = lc_obs.Mag
def lnlike(theta, t, m, yerr):
dt, dm, lnf = theta
model = lc_mdl.Mag
inv_sigma2 = 1.0 / (yerr**2 + model**2 * np.exp(2 * lnf))
return -0.5 * (np.sum((lc_obs - model)**2 * inv_sigma2 -
np.log(inv_sigma2)))
nll = lambda *args: -lnlike(*args)
result = op.minimize(
nll, [dt_init, dm_init, np.log(f_true)], args=(t, m, merr))
m_ml, b_ml, lnf_ml = result["x"]
def lnprior(theta):
m, b, lnf = theta
if -5.0 < m < 0.5 and 0.0 < b < 10.0 and -10.0 < lnf < 1.0:
return 0.0
return -np.inf
def lnprob(theta, x, y, yerr):
lp = lnprior(theta)
if not np.isfinite(lp):
return -np.inf
return lp + lnlike(theta, x, y, yerr)
ndim, nwalkers = 3, 100
pos = [
result["x"] + 1e-4 * np.random.randn(ndim) for i in range(nwalkers)
]
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
lnprob,
args=(t, m, merr))
sampler.run_mcmc(pos, 500)
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))
xl = np.array([0, 10])
for m, b, lnf in samples[np.random.randint(len(samples), size=100)]:
plt.plot(xl, m * xl + b, color="k", alpha=0.1)
plt.plot(xl, dt_init * xl + dm_init, color="r", lw=2, alpha=0.8)
plt.errorbar(t, m, yerr=merr, fmt=".k")
plt.show()
samples[:, 2] = np.exp(samples[:, 2])
m_mcmc, b_mcmc, f_mcmc = map(
lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
def print_v3(v3):
print("v = %f + %f - %f" % v3)
map(print_v3, (m_mcmc, b_mcmc, f_mcmc))
