def simulation(imc):
# print(imc, "/", montecarlo)
fnumax = (np.array([random.gauss(0,1) for i in range(Ndata)]) * numax_perturb[inumax] + 1)
fdnu = (np.array([random.gauss(0,1) for i in range(Ndata)]) * dnu_perturb[idnu] + 1)
xdata, ydata = (numax*fnumax), (dnu*fdnu)
dist = distance_to_edge(xdata, ydata, xedge_pdv, yedge_pdv, tck_pdv, diagram=diagram, distance=distance)
obj = distfit(dist, hist_model, bins=obj_obs.bins)
obj.fit()
sharpness_pdv = hist_model.sharpness(obj.para_fit)
return xdata, ydata, obj, sharpness_pdv
def model(theta): #, obj_obs, xpdv, ypdv):
# tied to model6
weight = np.zeros(obj_obs.histx.shape, dtype=bool)
sigma, x0 = obj_obs.para_fit[0], obj_obs.para_fit[1]
idx = (obj_obs.histx <= x0 + sigma) & (obj_obs.histx >= x0 - 2 * sigma)
weight[idx] = True
# theta[0]: offset in distance
# theta[1]: perturb
Ndata = xpdv.shape[0]
if (e_xobs is None):
fx = np.zeros(Ndata)
else:
# fx1 = np.array([random.gauss(0,1) for i in range(Ndata)]) * 10.0**scipy.signal.resample(np.log10(e_xobs), Ndata) * scalar
fx2 = np.array([random.gauss(0, 1) for i in range(Ndata)]) * theta[1]
fx = fx2
if (e_yobs is None):
fy = np.zeros(Ndata)
else:
# fy1 = np.array([random.gauss(0,1) for i in range(Ndata)]) * 10.0**scipy.signal.resample(np.log10(e_yobs), Ndata) * scalar
fy2 = np.array([random.gauss(0, 1) for i in range(Ndata)]) * theta[1]
fy = fy2
# disturb with artificial scatter
xdata, ydata = (xpdv + xpdv * (fx)), (ypdv + ypdv * (fy))
hdist, xdata, ydata = distance_to_edge(xdata,
ydata,
xedge_pdv,
yedge_pdv,
tck_pdv,
tp_pdv,
diagram=diagram,
distance=distance)
hdist = hdist + theta[0]
obj = distfit(hdist, hist_model, bins=obj_obs.bins)
# normalize the number of points in the weighted region
histy = obj.histy / np.sum(obj.histy[weight]) * np.sum(
obj_obs.histy[weight])
return histy, weight, xdata, ydata
1], tnu_samples_obs[:,
2]
idx = (xobs**0.75 / yobs >= ycut) & (yobs >= np.min(yedge_obs)
) #& (yobs<=3.5)
idx = idx & (feh_obs >= feh_limits[ifeh]) & (feh_obs <
feh_limits[ifeh + 1])
xobs, yobs, feh_obs = xobs[idx], yobs[idx], feh_obs[idx]
hdist_obs = distance_to_edge(xobs,
yobs,
xedge_obs,
yedge_obs,
tck_obs,
diagram=diagram,
distance=distance)
obj_obs = distfit(hdist_obs, hist_model)
obj_obs = distfit(hdist_obs, hist_model, bins=obj_obs.bins)
obj_obs.fit()
sharpness_obs = hist_model.sharpness(obj_obs.para_fit)
Nobs = hdist_obs.shape[0]
# set up models
xedge_pdv, yedge_pdv = tnu_edges_pdv[:, 0], tnu_edges_pdv[:, 1]
idx = (xedge_pdv**0.75 / yedge_pdv >= ycut) #& (yedge<=3.5)
xedge_pdv, yedge_pdv = xedge_pdv[idx], yedge_pdv[idx]
numax, dnu, feh_pdv = tnu_samples_pdv[:,
0], tnu_samples_pdv[:,
1], tnu_samples_pdv[:,
2]
idx = (numax**0.75 / dnu >= ycut) & (dnu >= np.min(yedge_pdv)
# edge
xedge_obs, yedge_obs = mr_edges_obs[:, 0], mr_edges_obs[:, 1]
filepath = rootpath + "sample/obs/sharpness/"
if not os.path.exists(filepath): os.mkdir(filepath)
# calculate observational distance
dist = distance_to_edge(xobs,
yobs,
xedge_obs,
yedge_obs,
tck_obs,
diagram=diagram,
distance=distance)
# dist = dist[(dist>-0.2) ]#& (dist<4)]
obj_obs = distfit(dist, hist_model)
hist_model.set_priors(obj_obs.histx, obj_obs.histy, dist)
prior_guess = hist_model.prior_guess
para_guess = hist_model.para_guess
def lnprior(theta):
for ip in range(len(prior_guess)):
if not (prior_guess[ip][0] <= theta[ip] <= prior_guess[ip][1]):
return -np.inf
return 0.
def lnlikelihood(theta):
# return np.sum(np.log(hist_model.ymodel(theta, dist)))
# sig = obj_obs.histy
sig = 1
def fit(filepath, distance, diagram, hist_model, edges, tck, xobs, yobs):
if not os.path.exists(filepath): os.mkdir(filepath)
# edges
xedge, yedge = edges[:,0], edges[:,1]
# calculate observational distance
dist = distance_to_edge(xobs, yobs, xedge, yedge, tck, diagram=diagram, distance=distance)
# dist = dist[dist>0.]
# dist = dist[(dist>-0.2) ]#& (dist<4)]
obj_obs = distfit(dist, hist_model, density=True)
hist_model.set_priors(obj_obs.histx, obj_obs.histy, dist)
prior_guess = hist_model.prior_guess
para_guess = hist_model.para_guess
def lnprior(theta):
for ip in range(len(prior_guess)):
if not (prior_guess[ip][0] <= theta[ip] <= prior_guess[ip][1]):
return -np.inf
return 0.
def lnlikelihood(theta):
return np.sum(np.log(hist_model.ymodel(theta, dist)))
# chi2 = (hist_model.ymodel(theta, obj_obs.histx) - obj_obs.histy)**2.0/2.0
# return -np.sum((chi2))
def lnpost(theta):
lp = lnprior(theta)
if not np.isfinite(lp):
return -np.inf
else:
return lnlikelihood(theta)
def minus_lnpost(theta):
lp = lnprior(theta)
if not np.isfinite(lp):
return np.inf
else:
return -lnlikelihood(theta)
ndim, nwalkers, nburn, nsteps = 3, 500, 1000, 1000
ifmle = True
if ifmle:
# mle
res = minimize(minus_lnpost, para_guess)
para_fit = res.x
xfit = np.linspace(obj_obs.histx.min(), obj_obs.histx.max(), 500)
yfit = hist_model.ymodel(para_fit, xfit)
else:
# run mcmc with ensemble sampler
print("enabling Ensemble sampler.")
pos0 = [para_guess + 1.0e-6*np.random.randn(ndim) for j in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnpost)
# # burn-in
print("start burning in. nburn:", nburn)
for j, result in enumerate(sampler.sample(pos0, iterations=nburn, thin=10)):
display_bar(j, nburn)
sys.stdout.write("\n")
pos, lnpost, rstate = result
sampler.reset()
# actual iteration
print("start iterating. nsteps:", nsteps)
for j, result in enumerate(sampler.sample(pos, iterations=nsteps)):
display_bar(j, nsteps)
sys.stdout.write("\n")
# modify samples
samples = sampler.chain[:,:,:].reshape((-1,ndim))
# save estimation result
# 16, 50, 84 quantiles
result = np.array(list(map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]),
zip(*np.percentile(samples, [16, 50, 84],axis=0)))))
para_fit = result[:,0]
result = np.concatenate([result, para_fit.reshape(ndim,1)], axis=1)
# save acceptance fraction
# acceptance_fraction = np.array([np.mean(sampler.acceptance_fraction)])
# np.savetxt(filepath+"acceptance_fraction.txt", acceptance_fraction, delimiter=",", fmt=("%0.8f"), header="acceptance_fraction")
# save samples if the switch is toggled on
if False: np.save(filepath+"samples.npy", samples)
# save guessed parameters
# np.savetxt(filepath+"guess.txt", para_guess, delimiter=",", fmt=("%0.8f"), header="para_guess")
# plot triangle and save
para_names = hist_model.para_name
fig = corner.corner(samples, labels=para_names, quantiles=(0.16, 0.5, 0.84))
fig.savefig(filepath+"triangle.png")
plt.close()
# plot traces and save
fig = plot_mcmc_traces(ndim, samples, para_names)
plt.savefig(filepath+'traces.png')
plt.close()
# save estimation result
np.savetxt(filepath+"summary.txt", result, delimiter=",", fmt=("%0.8f", "%0.8f", "%0.8f", "%0.8f"), header="50th quantile, 16th quantile sigma, 84th quantile sigma, maximum")
xfit = np.linspace(obj_obs.histx.min(), obj_obs.histx.max(), 500)
yfit = hist_model.ymodel(para_fit, xfit)
# plot fitting results and save
fig = plt.figure(figsize=(12,6))
axes = fig.subplots(nrows=1, ncols=1)
axes.hist(dist,density=True,bins=250)
obj_obs.plot_hist(ax=axes, histkwargs={"color":"red", "label":"Kepler"})
axes.plot(xfit, yfit, "k--", label="Kepler fit")
# obj_obs.plot_fit(ax=axes, theta=para_fit, fitkwargs={"color":"black", "label":"Kepler fit"})
axes.grid(True)
axes.set_xlim(obj_obs.histx.min(), obj_obs.histx.max())
axes.set_ylim(0., obj_obs.histy.max()*1.5)
axes.legend()
plt.savefig(filepath+"fitmedian.png")
plt.close()
