def lnprior(params, vsin_obs, sig_vsin_obs, dist_pc, sig_dist_pc, ranges,
model, stellar_prior, npy_star, pdf_mas, pdf_obl, pdf_age, pdf_dis,
pdf_ebv, grid_mas, grid_obl, grid_age, grid_dis, grid_ebv):
if model == 'befavor':
Mstar, oblat, Hfrac, cosi, dist, ebv = params[0], params[1],\
params[2], params[3], params[4], params[5]
if model == 'aara' or model == 'acol' or model == 'bcmi':
Mstar, oblat, Hfrac, cosi, dist, ebv = params[0], params[1],\
params[2], params[6], params[7], params[8]
if model == 'beatlas':
Mstar, oblat, Hfrac, cosi, dist, ebv = params[0], params[1],\
0.3, params[4], params[5], params[6]
# Reading Stellar Priors
if stellar_prior is True:
temp, idx_mas = find_nearest(grid_mas, value=Mstar)
temp, idx_obl = find_nearest(grid_obl, value=oblat)
temp, idx_age = find_nearest(grid_age, value=Hfrac)
temp, idx_dis = find_nearest(grid_dis, value=dist)
temp, idx_ebv = find_nearest(grid_ebv, value=ebv)
chi2_stellar_prior = Mstar * pdf_mas[idx_mas] +\
oblat * pdf_obl[idx_obl] + \
Hfrac * pdf_age[idx_age] + \
dist * pdf_dis[idx_dis] + \
ebv * pdf_ebv[idx_ebv]
else:
chi2_stellar_prior = 0.0
# Rpole, Lstar, Teff = vkg.geneve_par(Mstar, oblat, Hfrac, folder_tables)
t = np.max(np.array([hfrac2tms(Hfrac), 0.]))
Rpole, logL = geneva_interp_fast(Mstar,
oblat,
t,
neighbours_only=True,
isRpole=False)
wcrit = np.sqrt(8. / 27. * G * Mstar * Msun / (Rpole * Rsun)**3)
vsini = oblat2w(oblat) * wcrit * (Rpole * Rsun * oblat) *\
np.sin(np.arccos(cosi)) * 1e-5
chi2_vsi = (vsin_obs - vsini)**2 / sig_vsin_obs**2.
chi2_dis = (dist_pc - dist)**2 / sig_dist_pc**2.
chi2_prior = chi2_vsi + chi2_dis + chi2_stellar_prior
return -0.5 * chi2_prior
def plot_fit(par, lbd, logF, dlogF, minfo, listpar, lbdarr, logF_grid, isig,
dims, Nwalk, Nmcmc, par_list, ranges, include_rv, npy, log_scale):
'''
Plots best model fit over data
Usage:
plot_fit(par, lbd, logF, dlogF, minfo, logF_grid, isig, Nwalk, Nmcmc)
where
par = np.array([Mstar, oblat, Sig0, Rd, n, cosi, dist])
'''
# model parameters
if include_rv is True:
Mstar, oblat, Hfrac, cosi, dist, ebv, rv = par
lim = 3
lim2 = 2
else:
Mstar, oblat, Hfrac, cosi, dist, ebv = par
lim = 2
lim2 = 1
rv = 3.1
# Rpole, Lstar, Teff = vkg.geneve_par(Mstar, oblat, Hfrac, folder_tables)
# t = np.max(np.array([hfrac2tms(hfrac), 0.]))
t = np.max(np.array([hfrac2tms(Hfrac), 0.]))
Rpole, logL = geneva_interp_fast(Mstar,
oblat,
t,
neighbours_only=True,
isRpole=False)
norma = (10. / dist)**2 # (Lstar*Lsun) / (4. * pi * (dist*pc)**2)
uplim = dlogF == 0
keep = np.logical_not(uplim)
# chain = np.load(npy)
# interpolate models
logF_mod = griddataBA(minfo, logF_grid, par[:-lim], listpar, dims)
logF_list = np.zeros([len(par_list), len(logF_mod)])
chi2 = np.zeros(len(logF_list))
for i in range(len(par_list)):
logF_list[i] = griddataBA(minfo, logF_grid, par_list[i, :-lim],
listpar, dims)
# convert to physical units
logF_mod += np.log10(norma)
logF_list += np.log10(norma)
for j in range(len(logF_list)):
chi2[j] = np.sum(
(logF[keep] - logF_list[j][keep])**2 / (dlogF[keep])**2)
# chib = chi2[np.argsort(chi2)[-30:]] / max(chi2)
flux = 10.**logF
dflux = dlogF * flux
flux_mod = 10.**logF_mod
flux_mod = pyasl.unred(lbd * 1e4, flux_mod, ebv=-1 * ebv, R_V=rv)
# Plot definitions
bottom, left = 0.75, 0.48
width, height = 0.96 - left, 0.97 - bottom
plt.axes([left, bottom, width, height])
# plot fit
if log_scale is True:
for i in range(len(par_list)):
if i % 80 == 0:
ebv_temp = np.copy(par_list[i][-lim2])
F_temp = pyasl.unred(lbd * 1e4,
10**logF_list[i],
ebv=-1 * ebv_temp,
R_V=rv)
plt.plot(lbd, lbd * F_temp, color='gray', alpha=0.1)
plt.errorbar(lbd,
lbd * flux,
yerr=lbd * dflux,
ls='',
marker='o',
alpha=0.5,
ms=10,
color='blue',
linewidth=2)
plt.plot(lbd,
lbd * flux_mod,
color='red',
ls='-',
lw=3.5,
alpha=0.4,
label='$\mathrm{Best\, fit}$')
plt.xlabel('$\lambda\,\mathrm{[\mu m]}$', fontsize=20)
plt.ylabel(r'$\lambda F_{\lambda}\,\mathrm{[erg\, s^{-1}\, cm^{-2}]}$',
fontsize=20)
plt.yscale('log')
else:
for i in range(len(par_list)):
if i % 80 == 0:
ebv_temp = np.copy(par_list[i][-lim2])
F_temp = pyasl.unred(lbd * 1e4,
10**logF_list[i],
ebv=-1 * ebv_temp,
R_V=rv)
plt.plot(lbd, F_temp, color='gray', alpha=0.1)
plt.errorbar(lbd,
flux,
yerr=lbd * dflux,
ls='',
marker='o',
alpha=0.5,
ms=10,
color='blue',
linewidth=2)
plt.plot(lbd,
flux_mod,
color='red',
ls='-',
lw=3.5,
alpha=0.4,
label='$\mathrm{Best\, fit}$')
plt.xlabel('$\lambda\,\mathrm{[\mu m]}$', fontsize=20)
plt.ylabel(r'$F_{\lambda}\,\mathrm{[erg\, s^{-1}\, cm^{-2} \mu m]}$',
fontsize=20)
plt.xlim(min(lbd), max(lbd))
plt.tick_params(direction='in',
length=6,
width=2,
colors='gray',
which='both')
plt.legend(loc='upper right')
return
def plot_residuals(par, lbd, logF, dlogF, minfo, listpar, lbdarr, logF_grid,
isig, dims, Nwalk, Nmcmc, ranges, include_rv, npy,
log_scale, model):
'''
Plots best model fit over data
Usage:
plot_fit(par, lbd, logF, dlogF, minfo, logF_grid, isig, Nwalk, Nmcmc)
where
par = np.array([Mstar, oblat, Sig0, Rd, n, cosi, dist])
'''
# model parameters
if include_rv is True:
Mstar, oblat, Hfrac, cosi, dist, ebv, rv = par
lim = 3
lim2 = 2
else:
if model == 'befavor':
Mstar, oblat, Hfrac, cosi, dist, ebv = par
if model == 'aara' or model == 'acol' or model == 'bcmi':
Mstar, oblat, Hfrac, Sig0, Rd, n, cosi, dist, ebv = par
if model == 'beatlas':
Mstar, oblat, Sig0, n, cosi, dist, ebv = par
Hfrac = 0.3
lim = 2
lim2 = 1
rv = 3.1
# Rpole, Lstar, Teff = vkg.geneve_par(Mstar, oblat, Hfrac, folder_tables)
# t = np.max(np.array([hfrac2tms(hfrac), 0.]))
t = np.max(np.array([hfrac2tms(Hfrac), 0.]))
Rpole, logL = geneva_interp_fast(Mstar,
oblat,
t,
neighbours_only=True,
isRpole=False)
norma = (10. / dist)**2 # (Lstar*Lsun) / (4. * pi * (dist*pc)**2)
uplim = dlogF == 0
keep = np.logical_not(uplim)
# ***
chain = np.load(npy)
par_list = chain[:, -1, :]
# interpolate models
if model == 'beatlas':
logF_mod = griddataBAtlas(minfo, logF_grid, par[:-lim], listpar, dims,
isig)
else:
logF_mod = griddataBA(minfo, logF_grid, par[:-lim], listpar, dims)
logF_list = np.zeros([len(par_list), len(logF_mod)])
chi2 = np.zeros(len(logF_list))
for i in range(len(par_list)):
if model == 'beatlas':
logF_list[i] = griddataBAtlas(minfo, logF_grid, par_list[i, :-lim],
listpar, dims, isig)
else:
logF_list[i] = griddataBA(minfo, logF_grid, par_list[i, :-lim],
listpar, dims)
# convert to physical units
logF_mod += np.log10(norma)
logF_list += np.log10(norma)
for j in range(len(logF_list)):
chi2[j] = np.sum(
(logF[keep] - logF_list[j][keep])**2 / (dlogF[keep])**2)
# chib = chi2[np.argsort(chi2)[-30:]] / max(chi2)
flux = 10.**logF
dflux = dlogF * flux
flux_mod = 10.**logF_mod
flux_mod = pyasl.unred(lbd * 1e4, flux_mod, ebv=-1 * ebv, R_V=rv)
# alphas = (1. - chi2 / max(chi2)) / 50.
# Plot definitions
bottom, left = 0.71, 0.48
width, height = 0.96 - left, 0.785 - bottom
plt.axes([left, bottom, width, height])
# plot fit
for i in range(len(par_list)):
ebv_temp = np.copy(par_list[i][-lim2])
F_temp = pyasl.unred(lbd * 1e4,
10**logF_list[i],
ebv=-1 * ebv_temp,
R_V=rv)
plt.plot(lbd, (flux - F_temp) / dflux, 'bs', alpha=0.2)
# plt.plot(lbd, (flux - flux_mod) / dflux, 'bs', markersize=5, alpha=0.1)
# plt.ylabel('$(\mathrm{F}-F_\mathrm{model})/\sigma$', fontsize=20)
plt.ylabel('$(F-F_\mathrm{m})/\sigma$', fontsize=20)
plt.xlabel('$\lambda\,\mathrm{[\mu m]}$', fontsize=20)
# plt.ylim(-100, 100)
plt.hlines(y=0,
xmin=min(lbd),
xmax=max(lbd),
linestyles='--',
color='black')
plt.xlim(min(lbd), max(lbd))
if model == 'aara' or model == 'beatlas' or\
model == 'acol' or model == 'bcmi':
plt.xscale('log')
plt.tick_params(direction='in',
length=6,
width=2,
colors='gray',
which='both')
plt.legend(loc='upper right')
return
def emcee_inference(star, Ndim, ranges, lbdarr, wave, logF, dlogF, minfo,
listpar, logF_grid, vsin_obs, sig_vsin_obs, dist_pc,
sig_dist_pc, isig, dims, include_rv, a_parameter,
af_filter, tag, plot_fits, long_process, log_scale, model,
acrux, pool, Nproc, stellar_prior, npy_star, pdf_mas,
pdf_obl, pdf_age, pdf_dis, pdf_ebv, grid_mas, grid_obl,
grid_age, grid_dis, grid_ebv):
if long_process is True:
Nwalk = 500 # 200 # 500
nint_burnin = 100 # 50
nint_mcmc = 1000 # 500 # 1000
else:
Nwalk = 20
nint_burnin = 5
nint_mcmc = 10
p0 = [
np.random.rand(Ndim) * (ranges[:, 1] - ranges[:, 0]) + ranges[:, 0]
for i in range(Nwalk)
]
start_time = time.time()
if acrux is True:
sampler = emcee.EnsembleSampler(
Nwalk,
Ndim,
lnprob,
args=[
wave, logF, dlogF, minfo, listpar, logF_grid, vsin_obs,
sig_vsin_obs, dist_pc, sig_dist_pc, isig, ranges, dims,
include_rv, model, stellar_prior, npy_star, pdf_mas, pdf_obl,
pdf_age, pdf_dis, pdf_ebv, grid_mas, grid_obl, grid_age,
grid_dis, grid_ebv
],
a=a_parameter,
threads=Nproc,
pool=pool)
else:
sampler = emcee.EnsembleSampler(
Nwalk,
Ndim,
lnprob,
args=[
wave, logF, dlogF, minfo, listpar, logF_grid, vsin_obs,
sig_vsin_obs, dist_pc, sig_dist_pc, isig, ranges, dims,
include_rv, model, stellar_prior, npy_star, pdf_mas, pdf_obl,
pdf_age, pdf_dis, pdf_ebv, grid_mas, grid_obl, grid_age,
grid_dis, grid_ebv
],
a=a_parameter,
threads=1)
sampler_tmp = run_emcee(p0,
sampler,
nint_burnin,
nint_mcmc,
Ndim,
file_name=star)
print("--- %s minutes ---" % ((time.time() - start_time) / 60))
sampler, params_fit, errors_fit, maxprob_index,\
minprob_index, af = sampler_tmp
if include_rv is True:
mass_true, obt_true, xc_true,\
cos_true, ebv_true, dist_true, rv_true = params_fit
else:
if model == 'befavor':
mass_true, obt_true, xc_true,\
cos_true, ebv_true, dist_true = params_fit
if model == 'aara' or model == 'acol' or model == 'bcmi':
mass_true, obt_true, xc_true, n0, Rd, n_true,\
cos_true, ebv_true, dist_true = params_fit
if model == 'beatlas':
mass_true, obt_true, rh0_true, nix_true,\
inc_true, dis_true, ebv_true = params_fit
# if model is False:
# angle_in_rad = np.arccos(params_fit[6])
# params_fit[6] = (np.arccos(params_fit[6])) * (180. / np.pi)
# errors_fit[6] = (errors_fit[6] / (np.sqrt(1. -
# (np.cos(angle_in_rad)**2.)))) * (180. / np.pi)
chain = sampler.chain
if af_filter is True:
acceptance_fractions = sampler.acceptance_fraction
chain = chain[(acceptance_fractions >= 0.20)
& (acceptance_fractions <= 0.50)]
af = acceptance_fractions[(acceptance_fractions >= 0.20)
& (acceptance_fractions <= 0.50)]
af = np.mean(af)
af = str('{0:.2f}'.format(af))
# Saving first sample
file_npy = 'figures/' + str(star) + '/' + 'Walkers_' +\
str(Nwalk) + '_Nmcmc_' + str(nint_mcmc) +\
'_af_' + str(af) + '_a_' + str(a_parameter) +\
tag + ".npy"
np.save(file_npy, chain)
# plot results
mpl.rcParams['mathtext.fontset'] = 'stix'
mpl.rcParams['font.family'] = 'STIXGeneral'
mpl.rcParams['font.size'] = 16
# Loading first dataframe
chain_1 = np.load(file_npy)
Ndim_1 = np.shape(chain_1)[-1]
flatchain_1 = chain_1.reshape((-1, Ndim_1))
if model == 'befavor':
mas_1 = flatchain_1[:, 0]
obl_1 = flatchain_1[:, 1]
age_1 = flatchain_1[:, 2]
inc_1 = flatchain_1[:, 3]
dis_1 = flatchain_1[:, 4]
ebv_1 = flatchain_1[:, 5]
if model == 'aara' or model == 'acol' or model == 'bcmi':
mas_1 = flatchain_1[:, 0]
obl_1 = flatchain_1[:, 1]
age_1 = flatchain_1[:, 2]
rh0_1 = flatchain_1[:, 3]
rdk_1 = flatchain_1[:, 4]
nix_1 = flatchain_1[:, 5]
inc_1 = flatchain_1[:, 6]
dis_1 = flatchain_1[:, 7]
ebv_1 = flatchain_1[:, 8]
if model == 'beatlas':
mas_1 = flatchain_1[:, 0]
obl_1 = flatchain_1[:, 1]
rh0_1 = flatchain_1[:, 2]
nix_1 = flatchain_1[:, 3]
inc_1 = flatchain_1[:, 4]
dis_1 = flatchain_1[:, 5]
ebv_1 = flatchain_1[:, 6]
if include_rv is True:
rv_1 = flatchain_1[:, 6]
par_list = np.zeros([len(mas_1), 7])
else:
if model == 'befavor':
par_list = np.zeros([len(mas_1), 6])
if model == 'aara' or model == 'acol' or model == 'bcmi':
par_list = np.zeros([len(mas_1), 9])
if model == 'beatlas':
par_list = np.zeros([len(mas_1), 7])
for i in range(len(mas_1)):
if include_rv is True:
par_list[i] = [
mas_1[i], obl_1[i], age_1[i], inc_1[i], dis_1[i], ebv_1[i],
rv_1[i]
]
else:
if model == 'befavor':
par_list[i] = [
mas_1[i], obl_1[i], age_1[i], inc_1[i], dis_1[i], ebv_1[i]
]
if model == 'aara' or model == 'acol' or model == 'bcmi':
par_list[i] = [
mas_1[i], obl_1[i], age_1[i], rh0_1[i], rdk_1[i], nix_1[i],
inc_1[i], dis_1[i], ebv_1[i]
]
if model == 'beatlas':
par_list[i] = [
mas_1[i], obl_1[i], rh0_1[i], nix_1[i], inc_1[i], dis_1[i],
ebv_1[i]
]
# plot corner
if include_rv is True:
samples = np.vstack((mas_1, obl_1, age_1, inc_1, dis_1, ebv_1, rv_1)).T
else:
if model == 'befavor':
samples = np.vstack((mas_1, obl_1, age_1, inc_1, dis_1, ebv_1)).T
if model == 'aara' or model == 'acol' or model == 'bcmi':
samples = np.vstack((mas_1, obl_1, age_1, rh0_1, rdk_1, nix_1,
inc_1, dis_1, ebv_1)).T
if model == 'beatlas':
samples = np.vstack(
(mas_1, obl_1, rh0_1, nix_1, inc_1, dis_1, ebv_1)).T
k, arr_t_tc, arr_Xc = t_tms_from_Xc(mass_true,
savefig=False,
plot_fig=False)
ttms_ip = np.arange(0.001, 1., 0.001)
Xc_ip = np.interp(ttms_ip, arr_t_tc[k], arr_Xc[k])
for i in range(len(samples)):
if model == 'befavor' or model == 'aara' or\
model == 'acol' or model == 'bcmi':
# Calculating logg for the non_rotating case
Mstar, oblat, Hfrac = samples[i][0], samples[i][1],\
samples[i][2]
else:
Mstar, oblat, Hfrac = samples[i][0], samples[i][1], 0.3
t = np.max(np.array([hfrac2tms(Hfrac), 0.]))
Rpole, logL = geneva_interp_fast(Mstar,
oblat,
t,
neighbours_only=True,
isRpole=False)
# Converting oblat to W
samples[i][1] = obl2W(samples[i][1])
if model == 'befavor':
# Converting angles to degrees
samples[i][3] = (np.arccos(samples[i][3])) * (180. / np.pi)
# Converting Xc to t(tms)
samples[i][2] = ttms_ip[find_nearest(Xc_ip, samples[i][2])[1]]
if model == 'aara':
# Converting Xc to t(tms)
samples[i][2] = ttms_ip[find_nearest(Xc_ip, samples[i][2])[1]]
samples[i][5] = samples[i][5] + 1.5
samples[i][6] = (np.arccos(samples[i][6])) * (180. / np.pi)
if model == 'acol' or model == 'bcmi':
# Converting Xc to t(tms)
samples[i][2] = ttms_ip[find_nearest(Xc_ip, samples[i][2])[1]]
samples[i][6] = (np.arccos(samples[i][6])) * (180. / np.pi)
if model == 'beatlas':
samples[i][4] = (np.arccos(samples[i][4])) * (180. / np.pi)
# plot corner
quantiles = [0.16, 0.5, 0.84]
if include_rv is True:
labels = [
r'$M\,[M_\odot]$', r'$W$', r"$t/t_\mathrm{ms}$",
r'$i[\mathrm{^o}]$', r'$d\,[pc]$', r'E(B-V)', r'$R_\mathrm{V}$'
]
else:
if model == 'befavor':
labels = [
r'$M\,[M_\odot]$', r'$W$', r"$t/t_\mathrm{ms}$",
r'$i[\mathrm{^o}]$', r'$d\,[pc]$', r'E(B-V)'
]
if model == 'aara' or model == 'acol' or model == 'bcmi':
labels = [
r'$M\,[M_\odot]$', r'$W$', r"$t/t_\mathrm{ms}$",
r'$\log \, n_0 \, [cm^{-3}]$', r'$R_\mathrm{D}\, [R_\star]$',
r'$n$', r'$i[\mathrm{^o}]$', r'$d\,[pc]$', r'E(B-V)'
]
if model == 'beatlas':
labels = [
r'$M\,[M_\odot]$', r'$W$', r'$\Sigma_0$', r'$n$',
r'$i[\mathrm{^o}]$', r'$d\,[pc]$', r'E(B-V)'
]
if model == 'befavor':
ranges[1] = obl2W(ranges[1])
ranges[2][0] = ttms_ip[find_nearest(Xc_ip, ranges[2][1])[1]]
ranges[2][1] = ttms_ip[find_nearest(Xc_ip, ranges[2][0])[1]]
ranges[3] = (np.arccos(ranges[3])) * (180. / np.pi)
ranges[3] = np.array([ranges[3][1], ranges[3][0]])
if model == 'aara':
ranges[1] = obl2W(ranges[1])
ranges[2][0] = ttms_ip[find_nearest(Xc_ip, ranges[2][1])[1]]
ranges[2][1] = ttms_ip[find_nearest(Xc_ip, ranges[2][0])[1]]
ranges[3] = np.array([ranges[3][1], ranges[3][0]])
ranges[5] = ranges[5] + 1.5
ranges[6] = (np.arccos(ranges[6])) * (180. / np.pi)
ranges[6] = np.array([ranges[6][1], ranges[6][0]])
if model == 'acol' or model == 'bcmi':
ranges[1] = obl2W(ranges[1])
ranges[2][0] = ttms_ip[find_nearest(Xc_ip, ranges[2][1])[1]]
ranges[2][1] = ttms_ip[find_nearest(Xc_ip, ranges[2][0])[1]]
ranges[3] = np.array([ranges[3][1], ranges[3][0]])
ranges[6] = (np.arccos(ranges[6])) * (180. / np.pi)
ranges[6] = np.array([ranges[6][1], ranges[6][0]])
if model == 'beatlas':
ranges[1] = obl2W(ranges[1])
ranges[3] = np.array([ranges[3][-1], ranges[3][0]])
ranges[4] = (np.arccos(ranges[4])) * (180. / np.pi)
ranges[4] = np.array([ranges[4][1], ranges[4][0]])
corner(samples,
labels=labels,
range=ranges,
quantiles=quantiles,
plot_contours=True,
smooth=2.,
smooth1d=False,
plot_datapoints=True,
label_kwargs={'fontsize': 22},
truths=None,
show_titles=True,
color_hist='black',
plot_density=True,
fill_contours=False,
no_fill_contours=False,
normed=True)
if plot_fits is True:
# plot_fit(params_fit, wave, logF, dlogF, minfo,
# listpar, lbdarr, logF_grid, isig, dims,
# Nwalk, nint_mcmc, par_list, ranges, include_rv,
# log_scale)
plot_fit_last(params_fit, wave, logF, dlogF, minfo, listpar, lbdarr,
logF_grid, isig, dims, Nwalk, nint_mcmc, ranges,
include_rv, file_npy, log_scale, model)
current_folder = 'figures/' + str(star) + '/'
fig_name = 'Walkers_' + np.str(Nwalk) + '_Nmcmc_' +\
np.str(nint_mcmc) + '_af_' + str(af) + '_a_' +\
str(a_parameter) + tag
plt.savefig(current_folder + fig_name + '.png', dpi=100)
# plt.close()
# plt.clf()
plot_residuals(params_fit, wave, logF, dlogF, minfo, listpar, lbdarr,
logF_grid, isig, dims, Nwalk, nint_mcmc, ranges, include_rv,
file_npy, log_scale, model)
plt.savefig(current_folder + fig_name + '_residuals' + '.png', dpi=100)
plot_convergence(file_npy, file_npy[:-4] + '_convergence', model)
return