def lnlike(theta, x, y, yerr, singcomp=False):
vs_n, am_n, fw_n, vs_b, am_b, fw_b, h1_col, h1_b, h1_vel, d2h = theta
y_model = lyapy.damped_lya_profile(x,vs_n,10**am_n,fw_n,vs_b,10**am_b,fw_b,h1_col,
h1_b,h1_vel,d2h=d2h,resolution=resolution,
single_component_flux=singcomp)/1e14
return -0.5 * np.sum(np.log(2 * np.pi * yerr**2) + (y - y_model) ** 2 / yerr**2)
def lnlike_single(theta, x, y, yerr):
vs_n, am_n, fw_n, h1_col, h1_b, h1_vel = theta
y_model = lyapy.damped_lya_profile(x,vs_n,10**am_n,fw_n,h1_col, 0., 0., 0.,
h1_b,h1_vel,d2h=d2h_true,resolution=resolution,
single_component_flux=True)/1e14
return -0.5 * np.sum(np.log(2 * np.pi * yerr**2) + (y - y_model) ** 2 / yerr**2)
h1_b_mcmc, h1_vel_mcmc))
print("Mean acceptance fraction: {0:.3f}"
.format(np.mean(sampler.acceptance_fraction)))
print("should be between 0.25 and 0.5")
print ""
## best fit intrinsic profile
lya_intrinsic_profile_mcmc,lya_intrinsic_flux_mcmc = lyapy.lya_intrinsic_profile_func(wave_to_fit,
vs_n_mcmc[0],10**am_n_mcmc[0],fw_n_mcmc[0],vs_b_mcmc[0],10**am_b_mcmc[0],fw_b_mcmc[0],
return_flux=True)
## best fit attenuated profile
model_best_fit = lyapy.damped_lya_profile(wave_to_fit,vs_n_mcmc[0],10.**am_n_mcmc[0],fw_n_mcmc[0],
vs_b_mcmc[0],10.**am_b_mcmc[0],fw_b_mcmc[0],h1_col_mcmc[0],
h1_b_mcmc[0],h1_vel_mcmc[0],d2h_true,resolution,
single_component_flux=single_component_flux)/1.e14
'Here I will calculate 1-sigma errors on the total integrated flux'
print "Calculating Total Flux Errors..."
print ""
flux_errors = []
vs_n_errors = samples[:,0]
am_n_errors = samples[:,1]
fw_n_errors = samples[:,2]
vs_b_errors = samples[:,3]
am_b_errors = samples[:,4]
fw_b_errors = samples[:,5]
for i in range(len(vs_n_errors)):
10**variables['am_n']['best'][0],
variables['fw_n']['best'][0],
variables['vs_b']['best'][0],
10**variables['am_b']['best'][0],
variables['fw_b']['best'][0],
return_flux=True,
single_component_flux=variables['am_b']['single_comp'])
## best fit attenuated profile
model_best_fit = lyapy.damped_lya_profile(
wave_to_fit,
variables['vs_n']['best'][0],
10**variables['am_n']['best'][0],
variables['fw_n']['best'][0],
variables['vs_b']['best'][0],
10**variables['am_b']['best'][0],
variables['fw_b']['best'][0],
variables['h1_col']['best'][0],
variables['h1_b']['best'][0],
variables['h1_vel']['best'][0],
variables['d2h']['best'][0],
resolution,
single_component_flux=variables['am_b']['single_comp']) / 1.e14
## Here's the big messy part where I determine the 1-sigma error bars on the
## reconstructed, intrinsic LyA flux. From my paper: "For each of the 9 parameters,
## the best-fit values are taken as the 50th percentile (the median) of the marginalized
## distributions, and 1-σ error bars as the 16th and 84th percentiles (shown as dashed
## vertical lines in Figures 3 and 4). The best-fit reconstructed Lyα fluxes are determined
## from the best-fit amplitude, FWHM, and velocity centroid parameters, and the 1-σ error bars
## of the reconstructed Lyα flux are taken by varying these parameters individually between
## their 1-σ error bars and keeping all others fixed at their best-fit value.
def profile(wave_to_fit, flux_to_fit, error_to_fit, resolution,
model_best_fit, lya_intrinsic_profile_mcmc, variables, param_order, samples = None):
f = plt.figure()
plt.rc('text', usetex=True)
plt.rc('font', family='serif', size=14)
ax = f.add_subplot(1,1,1)
## plots 1 sigma contours of the Lya profile - Will draws samples from the walkers and plots them
## e.g., from the emcee website example of fitting a straight line -
## for m, b, lnf in samples[np.random.randint(len(samples), size=100)]:
## plt.plot(xl, m*xl+b, color="k", alpha=0.1)
## Should we implement this? Will, share your code on this?
if samples is not None:
ndim = len(samples[0])
#print ndim
model_fits = np.zeros((len(samples),len(wave_to_fit)))
#for i, sample in enumerate(samples[np.random.randint(len(samples), size=10)]):
for i, sample in enumerate(samples):
theta_all = []
j = 0
for p in param_order:
if variables[p]['vary']:
theta_all.append(sample[j])
j = j+1
else:
theta_all.append(variables[p]['value'])
vs_n_i, am_n_i, fw_n_i, vs_b_i, am_b_i, fw_b_i, h1_col_i, h1_b_i, \
h1_vel_i, d2h_i = theta_all
singcomp = variables['am_b']['single_comp']
model_fit = lyapy.damped_lya_profile(wave_to_fit,vs_n_i,10**am_n_i,fw_n_i,
vs_b_i,10**am_b_i,fw_b_i,h1_col_i,
h1_b_i,h1_vel_i,d2h_i,resolution,
single_component_flux=singcomp)/1e14
model_fits[i,:] = model_fit
#plt.plot(wave_to_fit,model_fit,'deeppink',linewidth=1., alpha=0.1)
low = np.zeros_like(wave_to_fit)
mid = np.zeros_like(wave_to_fit)
high = np.zeros_like(wave_to_fit)
for i in np.arange(len(wave_to_fit)):
low[i], mid[i], high[i] = np.percentile(model_fits[:,i], [16,50,84])
plt.fill_between(wave_to_fit, low, high)
# end 1 sigma contours plotting
ax.step(wave_to_fit,flux_to_fit,'k')
short_wave = np.linspace(wave_to_fit[0],wave_to_fit[-1],25)
error_bars_short = np.interp(short_wave,wave_to_fit,error_to_fit)
short_flux = np.interp(short_wave,wave_to_fit,flux_to_fit)
ax.errorbar(short_wave,short_flux,yerr=error_bars_short,
fmt="none",ecolor='limegreen',elinewidth=3,capthick=3)
ax.plot(wave_to_fit,model_best_fit,'deeppink',linewidth=1.5)
ax.plot(wave_to_fit,lya_intrinsic_profile_mcmc,'b--',linewidth=1.3)
# chi2_mcmc = np.sum( ( (flux_to_fit[~mask] - model_best_fit[~mask]) / error_to_fit[~mask] )**2 )
# dof_mcmc = len(flux_to_fit[~mask]) - ndim - 1 #####
#
# ax.step(wave_to_fit[mask],flux_to_fit[mask],'lightblue',linewidth=0.8) ## plotting "masked" region
ax.set_ylabel(r'Flux ' r'(erg s$^{-1}$ cm$^{-2}$ \AA$^{-1}$)',fontsize=14)
ax.set_xlabel(r'Wavelength (\AA)',fontsize=14)
# defining max of y axis
y_max = np.max( np.array( [np.max(flux_to_fit),np.max(model_best_fit)] ) )
y_min = 0.0
ax.set_ylim([y_min,y_max+0.5e-13])
ax.set_xlim( [np.min(wave_to_fit),np.max(wave_to_fit)] )
plt.ticklabel_format(useOffset=False)