def fit_res(x, res):
fitter = fitting.LevMarLSQFitter()
p1_init = powerlaws.PowerLaw1D(res[:, 0].max(), 1, 0.5)
p2_init = powerlaws.PowerLaw1D(res[:, 1].max(), 1, 0.5)
p3_init = powerlaws.PowerLaw1D(res[:, 2].max(), 1, 0.5)
p1_init.alpha.fixed = True
p2_init.alpha.fixed = True
p3_init.alpha.fixed = True
p1_fit = fitter(p1_init, x, res[:, 0])
p2_fit = fitter(p2_init, x, res[:, 1])
p3_fit = fitter(p3_init, x, res[:, 2])
return p1_fit, p2_fit, p3_fit
def test_powerlaw(scale=5., alpha=2.):
x = np.linspace(10, 100)
y = scale * (x)**(-alpha)
plm = powerlaws.PowerLaw1D(1, 1, 1)
fitter = fitting.LevMarLSQFitter()
result = fitter(plm, x, y)
print("Result: ", result)
print("plm.params: ", plm)
return plm
def from_tree_transform(self, node):
return powerlaws.PowerLaw1D(amplitude=node['amplitude'],
x_0=node['x_0'],
alpha=node['alpha'])
def getAlpha(spec, wave_center, plot=False, plotname=None):
"""
spec = {'Wavelength(um)': wave,
'Flux_Density(Jy)': flux,
'Uncertainty(Jy)': unc}
"""
from astropy.modeling import models, fitting, powerlaws
from scipy.interpolate import interp1d
import astropy.constants as const
import numpy as np
c = const.c.cgs.value
# initial guess
x_ref = c / 1e5 / wave_center
f_flux = interp1d(c / 1e5 / spec['Wavelength(um)'],
spec['Flux_Density(Jy)'])
amp = f_flux(x_ref)
alpha = 0
# unit conversions
freq_dum = (c/1e5/spec['Wavelength(um)'])\
[(c/1e5/spec['Wavelength(um)']>= x_ref-100) & (c/1e5/spec['Wavelength(um)']<= x_ref+100)]
flux_dum = spec['Flux_Density(Jy)']\
[(c/1e5/spec['Wavelength(um)']>= x_ref-100) & (c/1e5/spec['Wavelength(um)']<= x_ref+100)]
pow_model = powerlaws.PowerLaw1D(amp, x_ref, alpha)
fitter = fitting.LevMarLSQFitter()
fit = fitter(pow_model, freq_dum, flux_dum)
alpha = -fit.alpha.value
if fitter.fit_info['param_cov'] is None:
alpha_err = np.nan
else:
alpha_err = fitter.fit_info['param_cov'][2, 2]**0.5
if plot:
# to avoid X server error
import matplotlib as mpl
mpl.use('Agg')
#
import matplotlib.pyplot as plt
fig = plt.figure(figsize=(10, 6))
ax = fig.add_subplot(111)
ax.plot(freq_dum, flux_dum, 'o')
ax.plot(freq_dum, fit(freq_dum), '-', color='k')
ax.text(0.6,
0.05,
r'$\alpha_{500} = %3.2f \pm %3.2f$' % (alpha, alpha_err),
transform=ax.transAxes,
fontsize=18)
[
ax.spines[axis].set_linewidth(1.5)
for axis in ['top', 'bottom', 'left', 'right']
]
ax.minorticks_on()
ax.tick_params('both',
labelsize=18,
width=1.5,
which='major',
pad=10,
length=5)
ax.tick_params('both',
labelsize=18,
width=1.5,
which='minor',
pad=10,
length=2.5)
ax.set_xlabel('Frequency [GHz]', fontsize=18)
ax.set_ylabel('Flux Density [Jy]', fontsize=18)
ax.set_xlim([400, 2000])
fig.savefig(plotname + 'Alpha500Hyperion.pdf',
format='pdf',
dpi=300,
bbox_inches='tight')
fig.clf()
return (alpha, alpha_err)
def spire_spectral_index(outdir, obsid, obj):
# to avoid X server error
import matplotlib as mpl
mpl.use('Agg')
#
# Note that the spectral index works in frequency
import matplotlib.pyplot as plt
from astropy.modeling import models, fitting, powerlaws
from scipy.interpolate import interp1d
import astropy.constants as const
from astropy.io import ascii
import numpy as np
c = const.c.cgs.value
# Read in spectra
spire_sect = ascii.read(outdir + obsid + '_spire_sect.txt', data_start=4)
fig = plt.figure(figsize=(10, 6))
ax = fig.add_subplot(111)
spire, = ax.plot(c / 1e5 / spire_sect['wave_segm1_0'],
spire_sect['flux_segm1_0'],
linewidth=1,
color='b')
ax.plot(c / 1e5 / spire_sect['wave_segm2_0'],
spire_sect['flux_segm2_0'],
linewidth=1,
color='r')
f_ssw = interp1d(c / 1e5 / spire_sect['wave_segm2_0'],
spire_sect['flux_segm2_0'])
f_slw = interp1d(c / 1e5 / spire_sect['wave_segm1_0'],
spire_sect['flux_segm1_0'])
fitted_alpha = []
fitted_alpha_err = []
for band in [250, 350, 500]:
x_ref = c / 1e5 / band
if band != 250:
amp = f_slw(x_ref)
freq_dum = (c/1e5/spire_sect['wave_segm1_0'])\
[(c/1e5/spire_sect['wave_segm1_0'] >= x_ref-100) & (c/1e5/spire_sect['wave_segm1_0'] <= x_ref+100)]
flux_dum = spire_sect['flux_segm1_0']\
[(c/1e5/spire_sect['wave_segm1_0'] >= x_ref-100) & (c/1e5/spire_sect['wave_segm1_0'] <= x_ref+100)]
else:
amp = f_ssw(x_ref)
freq_dum = (c/1e5/spire_sect['wave_segm2_0'])\
[(c/1e5/spire_sect['wave_segm2_0'] >= x_ref-100) & (c/1e5/spire_sect['wave_segm2_0'] <= x_ref+100)]
flux_dum = spire_sect['flux_segm2_0']\
[(c/1e5/spire_sect['wave_segm2_0'] >= x_ref-100) & (c/1e5/spire_sect['wave_segm2_0'] <= x_ref+100)]
alpha = 0
pow_model = powerlaws.PowerLaw1D(amp, x_ref, alpha)
fitter = fitting.LevMarLSQFitter()
fit = fitter(pow_model, freq_dum, flux_dum)
ax.plot(freq_dum, fit(freq_dum), '-', color='k')
# take negative sign because the frequency array is reversed
fitted_alpha.append(-fit.alpha.value)
# the uncertainty part somehow does work on bettyjo.
# probably something wrong with the python config
if 'bettyjo' not in archive_dir:
fitted_alpha_err.append(fitter.fit_info['param_cov'][2, 2]**0.5)
print - fit.alpha.value, '+/-', fitter.fit_info['param_cov'][
2, 2]**0.5
else:
fitted_alpha_err.append(0)
print - fit.alpha.value
ax.text(0.35,
0.15,
r'$\alpha_{250,350,500} = %3.2f, %3.2f, %3.2f$' %
(fitted_alpha[0], fitted_alpha[1], fitted_alpha[2]),
transform=ax.transAxes,
fontsize=18)
ax.text(0.35,
0.05,
r'$\sigma_{\alpha}\,(250,350,500) = %5.3f, %5.3f, %5.3f$' %
(fitted_alpha_err[0], fitted_alpha_err[1], fitted_alpha_err[2]),
transform=ax.transAxes,
fontsize=18)
[
ax.spines[axis].set_linewidth(1.5)
for axis in ['top', 'bottom', 'left', 'right']
]
ax.minorticks_on()
ax.tick_params('both',
labelsize=18,
width=1.5,
which='major',
pad=10,
length=5)
ax.tick_params('both',
labelsize=18,
width=1.5,
which='minor',
pad=10,
length=2.5)
ax.set_xlabel('Frequency [GHz]', fontsize=18)
ax.set_ylabel('Flux Density [Jy]', fontsize=18)
ax.set_xlim([400, 2000])
fig.savefig(outdir + obj + '_spire_alpha.pdf',
format='pdf',
dpi=300,
bbox_inches='tight')
fig.clf()
# write out the alpha index
foo = open(outdir + obj + '_alpha.txt', 'w')
foo.write('250um \t 350um \t 500um \n')
foo.write('%8.6f \t %8.6f \t %8.6f \n' %
(fitted_alpha[0], fitted_alpha[1], fitted_alpha[2]))
foo.write('%8.6f \t %8.6f \t %8.6f \n' %
(fitted_alpha_err[0], fitted_alpha_err[1], fitted_alpha_err[2]))
foo.close()