def initModelFit(sci_data, lsf, modelset='btsettl08'):
"""
Conduct simple chisquare fit to obtain the initial parameters
for the forward modeling MCMC.
The function would calculate the chisquare for teff, logg, vini, rv, and alpha.
Parameters
----------
data : spectrum object
input science data
lsf : float
line spread function for the NIRSPEC
Returns
-------
best_params_dic : dic
a dictionary that stores the best parameters for
teff, logg, vsini, rv, and alpha
chisquare : int
minimum chisquare
"""
data = copy.deepcopy(sci_data)
## set up the parameter grid for chisquare computation
teff_array = np.arange(1200,3001,100)
logg_array = np.arange(3.5,5.51,0.5)
vsini_array = np.arange(10,101,10)
rv_array = np.arange(-200,201,50)
alpha_array = np.arange(0.5,2.01,0.5)
chisquare_array = np.empty(len(teff_array)*len(logg_array)*len(vsini_array)*len(rv_array)*len(alpha_array))\
.reshape(len(teff_array),len(logg_array),len(vsini_array),len(rv_array),len(alpha_array))
time1 = time.time()
for i, teff in enumerate(teff_array):
for j, logg in enumerate(logg_array):
for k, vsini in enumerate(vsini_array):
for l, rv in enumerate(rv_array):
for m, alpha in enumerate(alpha_array):
model = nsp.makeModel(teff, logg, 0.0, vsini, rv, alpha, 0, 0,
lsf=lsf, order=data.order, data=data, modelset=modelset)
chisquare_array[i,j,k,l,m] = nsp.chisquare(data, model)
time2 = time.time()
print("total time:",time2-time1)
ind = np.unravel_index(np.argmin(chisquare_array, axis=None), chisquare_array.shape)
print("ind ",ind)
chisquare = chisquare_array[ind]
best_params_dic = {'teff':teff_array[ind[0]], 'logg':logg_array[ind[1]],
'vsini':vsini_array[ind[2]], 'rv':rv_array[ind[3]], 'alpha':alpha_array[ind[4]]}
print(best_params_dic, chisquare)
return best_params_dic , chisquare
def lnlike(theta, data=data): """ Log-likelihood, computed from chi-squared. Parameters ---------- theta data Returns ------- -0.5 * chi-square + sum of the log of the noise """ ## Parameters MCMC lsf, alpha, A, B = theta model = makeTelluricModel(lsf, alpha, A, B, data=data) chisquare = nsp.chisquare(data, model) return -0.5 * (chisquare + np.sum(np.log(2*np.pi*data.noise**2)))
def lnlike(theta, data, lsf):
"""
Log-likelihood, computed from chi-squared.
Parameters
----------
theta
lsf
data
Returns
-------
-0.5 * chi-square + sum of the log of the noise
"""
## Parameters MCMC
teff, logg, vsini, rv, alpha, A, N = theta #A: flux offset; N: noise prefactor
## wavelength offset is set to 0
model = makeModel(teff,
logg,
0.0,
vsini,
rv,
alpha,
0.0,
A,
lsf=lsf,
data=data,
modelset=modelset,
instrument=instrument)
print(len(data.wave), len(model.wave), len(data.noise), teff, logg,
modelset, instrument)
chisquare = nsp.chisquare(data, model) / N**2
print(chisquare)
return -0.5 * (chisquare + np.sum(np.log(2 * np.pi * (data.noise * N)**2)))
def lnlike(theta, data, lsf):
"""
Log-likelihood, computed from chi-squared.
Parameters
----------
theta
lsf
data
Returns
-------
-0.5 * chi-square + sum of the log of the noise
"""
## Parameters MCMC
teff, logg, vsini, rv, alpha, A, B, N = theta #N noise prefactor
#teff, logg, vsini, rv, alpha, A, B, freq, amp, phase = theta
model = nsp.makeModel(teff,
logg,
0.0,
vsini,
rv,
alpha,
B,
A,
lsf=lsf,
order=data.order,
data=data,
modelset=modelset)
chisquare = nsp.chisquare(data, model) / N**2
return -0.5 * (chisquare + np.sum(np.log(2 * np.pi * (data.noise * N)**2)))
round(teff_mcmc[2]),
round(logg_mcmc[0],1),
round(logg_mcmc[1],3),
round(logg_mcmc[2],3),
round(vsini_mcmc[0],2),
round(vsini_mcmc[1],2),
round(vsini_mcmc[2],2),
round(rv_mcmc[0]+barycorr,2),
round(rv_mcmc[1],2),
round(rv_mcmc[2],2)),
color='C0',
horizontalalignment='right',
verticalalignment='center',
fontsize=12)
plt.figtext(0.89,0.79,r"$\chi^2$ = {}, DOF = {}".format(\
round(nsp.chisquare(data,model)), round(len(data.wave-ndim)/3)),
color='k',
horizontalalignment='right',
verticalalignment='center',
fontsize=12)
plt.minorticks_on()
ax2 = ax1.twiny()
ax2.plot(pixel, data.flux, color='w', alpha=0)
ax2.set_xlabel('Pixel', fontsize=15)
ax2.tick_params(labelsize=15)
ax2.set_xlim(pixel[0], pixel[-1])
ax2.minorticks_on()
#plt.legend()
plt.savefig(save_to_path + '/spectrum.png', dpi=300, bbox_inches='tight')
def getAlpha(telluric_data,lsf,continuum=True,test=False,save_path=None):
"""
Return a best alpha value from a telluric data.
"""
alpha_list = []
test_alpha = np.arange(0.1,7,0.1)
data = copy.deepcopy(telluric_data)
if continuum is True:
data = nsp.continuumTelluric(data=data, order=data.order)
for i in test_alpha:
telluric_model = nsp.convolveTelluric(lsf,data,
alpha=i)
#telluric_model.flux **= i
if data.order == 59:
# mask hydrogen absorption feature
data2 = copy.deepcopy(data)
tell_mdl = copy.deepcopy(telluric_model)
mask_pixel = 450
data2.wave = data2.wave[mask_pixel:]
data2.flux = data2.flux[mask_pixel:]
data2.noise = data2.noise[mask_pixel:]
tell_mdl.wave = tell_mdl.wave[mask_pixel:]
tell_mdl.flux = tell_mdl.flux[mask_pixel:]
chisquare = nsp.chisquare(data2,tell_mdl)
else:
chisquare = nsp.chisquare(data,telluric_model)
alpha_list.append([chisquare,i])
if test is True:
plt.plot(telluric_model.wave,telluric_model.flux+i*10,
'k-',alpha=0.5)
if test is True:
plt.plot(telluric_data.wave,telluric_data.flux,
'r-',alpha=0.5)
plt.rc('font', family='sans-serif')
plt.title("Test Alpha",fontsize=15)
plt.xlabel("Wavelength ($\AA$)",fontsize=12)
plt.ylabel("Transmission + Offset",fontsize=12)
plt.minorticks_on()
if save_path is not None:
plt.savefig(save_path+\
"/{}_O{}_alpha_data_mdl.png"\
.format(telluric_data.name,
telluric_data.order))
plt.show()
plt.close()
fig, ax = plt.subplots()
plt.rc('font', family='sans-serif')
for i in range(len(alpha_list)):
ax.plot(alpha_list[i][1],alpha_list[i][0],'k.',alpha=0.5)
ax.plot(min(alpha_list)[1],min(alpha_list)[0],'r.',
label="best alpha {}".format(min(alpha_list)[1]))
ax.set_xlabel(r"$\alpha$",fontsize=12)
ax.set_ylabel("$\chi^2$",fontsize=12)
plt.minorticks_on()
plt.legend(fontsize=10)
if save_path is not None:
plt.savefig(save_path+\
"/{}_O{}_alpha_chi2.png"\
.format(telluric_data.name,
telluric_data.order))
plt.show()
plt.close()
alpha = min(alpha_list)[1]
return alpha
def getLSF(telluric_data, alpha=1.0, continuum=True,test=False,save_path=None):
"""
Return a best LSF value from a telluric data.
"""
lsf_list = []
test_lsf = np.arange(3.0,13.0,0.1)
data = copy.deepcopy(telluric_data)
if continuum is True:
data = nsp.continuumTelluric(data=data)
data.flux **= alpha
for i in test_lsf:
telluric_model = nsp.convolveTelluric(i,data)
if telluric_data.order == 59:
telluric_model.flux **= 3
# mask hydrogen absorption feature
data2 = copy.deepcopy(data)
tell_mdl = copy.deepcopy(telluric_model)
mask_pixel = 450
data2.wave = data2.wave[mask_pixel:]
data2.flux = data2.flux[mask_pixel:]
data2.noise = data2.noise[mask_pixel:]
tell_mdl.wave = tell_mdl.wave[mask_pixel:]
tell_mdl.flux = tell_mdl.flux[mask_pixel:]
chisquare = nsp.chisquare(data2,tell_mdl)
else:
chisquare = nsp.chisquare(data,telluric_model)
lsf_list.append([chisquare,i])
if test is True:
plt.plot(telluric_model.wave,telluric_model.flux+(i-3)*10+1,
'r-',alpha=0.5)
if test is True:
plt.plot(data.wave,data.flux,
'k-',label='telluric data',alpha=0.5)
plt.title("Test LSF",fontsize=15)
plt.xlabel("Wavelength ($\AA$)",fontsize=12)
plt.ylabel("Transmission + Offset",fontsize=12)
plt.minorticks_on()
if save_path is not None:
plt.savefig(save_path+\
"/{}_O{}_lsf_data_mdl.png"\
.format(data.name, data.order))
#plt.show()
plt.close()
fig, ax = plt.subplots()
for i in range(len(lsf_list)):
ax.plot(lsf_list[i][1],lsf_list[i][0],'k.',alpha=0.5)
ax.plot(min(lsf_list)[1],min(lsf_list)[0],'r.',
label="best LSF {} km/s".format(min(lsf_list)[1]))
ax.set_xlabel("LSF (km/s)",fontsize=12)
ax.set_ylabel("$\chi^2$",fontsize=11)
plt.minorticks_on()
plt.legend(fontsize=10)
if save_path is not None:
plt.savefig(save_path+\
"/{}_O{}_lsf_chi2.png"\
.format(data.name, data.order))
#plt.show()
plt.close()
lsf = min(lsf_list)[1]
if telluric_data.order == 61 or telluric_data.order == 62 \
or telluric_data.order == 63: #or telluric_data.order == 64:
lsf = 5.5
print("The LSF is obtained from orders 60 and 65 (5.5 km/s).")
return lsf