def fit_tex(eupper, nupperoverg, verbose=False, plot=False):
"""
Fit the Boltzmann diagram
"""
model = modeling.models.Linear1D()
#fitter = modeling.fitting.LevMarLSQFitter()
fitter = modeling.fitting.LinearLSQFitter()
result = fitter(model, eupper, np.log(nupperoverg))
tex = -1. / result.slope * u.K
partition_func = specmodel.calculate_partitionfunction(
hnco.data['States'], temperature=tex.value)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
Ntot = np.exp(result.intercept + np.log(Q_rot)) * u.cm**-2
if verbose:
print(("Tex={0}, Ntot={1}, Q_rot={2}".format(tex, Ntot, Q_rot)))
if plot:
import pylab as pl
L, = pl.plot(eupper, np.log10(nupperoverg), 'o')
xax = np.array([0, eupper.max().value])
line = (xax * result.slope.value + result.intercept.value)
pl.plot(xax,
np.log10(np.exp(line)),
'-',
color=L.get_color(),
label='$T={0:0.1f} \log(N)={1:0.1f}$'.format(
tex, np.log10(Ntot.value)))
return Ntot, tex, result.slope, result.intercept
def sio_model(xarr, vcen, width, tex, column, background=None, tbg=2.73):
if hasattr(tex, 'unit'):
tex = tex.value
if hasattr(tbg, 'unit'):
tbg = tbg.value
if hasattr(column, 'unit'):
column = column.value
if column < 25:
column = 10**column
if hasattr(vcen, 'unit'):
vcen = vcen.value
if hasattr(width, 'unit'):
width = width.value
if background is not None:
tbg = background
# assume equal-width channels
kwargs = dict(rest=ref_freq)
equiv = u.doppler_radio(**kwargs)
channelwidth = np.abs(xarr[1].to(u.Hz, equiv) -
xarr[0].to(u.Hz, equiv)).value
velo = xarr.to(u.km / u.s, equiv).value
mol_model = np.zeros_like(xarr).value
freqs_ = freqs.to(u.Hz).value
Q = m.calculate_partitionfunction(result.data['States'],
temperature=tex)[sio.Id]
jnu_bg = lte_molecule.Jnu_cgs(xarr.to(u.Hz).value, tbg)
bg_model = np.ones_like(xarr).value * jnu_bg
for voff, A, g, nu, eu in zip(vdiff, aij, deg, freqs_, EU):
tau_per_dnu = lte_molecule.line_tau_cgs(tex, column, Q, g, nu, eu,
10**A)
s = np.exp(-(velo - vcen - voff)**2 /
(2 * width**2)) * tau_per_dnu / channelwidth
jnu_mol = lte_molecule.Jnu_cgs(nu, tex)
# the "emission" model is generally zero everywhere, so we can just
# add to it as we move along
mol_model = mol_model + jnu_mol * (1 - np.exp(-s))
# background is assumed to start as a uniform value, then each
# absorption line multiplies to reduce it. s is zero for most velocities,
# so this is mostly bg_model *= 1
bg_model *= np.exp(-s)
if background:
# subtract jnu_bg because we *must* rezero for the case of
# having multiple components, otherwise the backgrounds add,
# which is nonsense
model = bg_model + mol_model - jnu_bg
else:
model = mol_model
return model
def pyspeckitfit(eupper, kkms, frequencies, degeneracies, einsteinAs, verbose=False, plot=False, guess=(150, 1e19)):
"""
Fit the Boltzmann diagram (but do it right, with no approximations, just
direct forward modeling)
This doesn't seem to work, though: it can't reproduce its own output
"""
bandwidth = (1 * u.km / u.s / constants.c) * (frequencies)
def model(tex, col, einsteinAs=einsteinAs, eupper=eupper):
tex = u.Quantity(tex, u.K)
col = u.Quantity(col, u.cm ** -2)
eupper = eupper.to(u.erg, u.temperature_energy())
einsteinAs = u.Quantity(einsteinAs, u.Hz)
partition_func = specmodel.calculate_partitionfunction(ch3oh.data["States"], temperature=tex.value)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
return lte_molecule.line_brightness(
tex,
bandwidth,
frequencies,
total_column=col,
partition_function=Q_rot,
degeneracy=degeneracies,
energy_upper=eupper,
einstein_A=einsteinAs,
)
def minmdl(args):
tex, col = args
return ((model(tex, col).value - kkms) ** 2).sum()
from scipy import optimize
result = optimize.minimize(minmdl, guess, method="Nelder-Mead")
tex, Ntot = result.x
if plot:
import pylab as pl
pl.subplot(2, 1, 1)
pl.plot(eupper, kkms, "o")
order = np.argsort(eupper)
pl.plot(eupper[order], model(tex, Ntot)[order])
pl.subplot(2, 1, 2)
xax = np.array([0, eupper.max().value])
pl.plot(eupper, np.log(nupper_of_kkms(kkms, frequencies, einsteinAs, degeneracies).value), "o")
partition_func = specmodel.calculate_partitionfunction(ch3oh.data["States"], temperature=tex)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
intercept = np.log(Ntot) - np.log(Q_rot)
pl.plot(
xax, np.log(xax * tex + intercept), "-", label="$T={0:0.1f} \log(N)={1:0.1f}$".format(tex, np.log10(Ntot))
)
return Ntot, tex, result
def ntot_of_nupper(nupper, eupper, tex, degen=1):
partition_func = specmodel.calculate_partitionfunction(
vamdc_result.data['States'], temperature=tex.value)[sio.Id]
Q_rot = partition_func
Ntot = nupper * (Q_rot / degen) * np.exp(eupper / (constants.k_B * tex))
return Ntot
def fit_tex(eupper, nupperoverg, errors=None, verbose=False, plot=False):
"""
Fit the Boltzmann diagram
"""
model = modeling.models.Linear1D()
#fitter = modeling.fitting.LevMarLSQFitter()
fitter = modeling.fitting.LinearLSQFitter()
# ignore negatives
good = nupperoverg > 0
if good.sum() < len(nupperoverg) / 2.:
return 0 * u.cm**-2, 0 * u.K, 0, 0
if errors is not None:
weights = 1 / errors**2
else:
weights = None
result = fitter(model,
eupper[good],
np.log(nupperoverg[good]),
weights=weights[good])
tex = -1. / result.slope * u.K
assert not np.isnan(tex)
partition_func = specmodel.calculate_partitionfunction(
vamdc_result.data['States'], temperature=tex.value)[ch3cn.Id]
Q_rot = partition_func
Ntot = np.exp(result.intercept + np.log(Q_rot)) * u.cm**-2
if verbose:
print(("Tex={0}, Ntot={1}, Q_rot={2}".format(tex, Ntot, Q_rot)))
if plot:
import pylab as pl
if errors is not None:
L, _, _ = pl.errorbar(
x=eupper.value,
y=np.log10(nupperoverg),
marker='o',
linestyle='none',
yerr=np.array([
np.log10(nupperoverg) - np.log10(nupperoverg - errors),
np.log10(nupperoverg + errors) - np.log10(nupperoverg)
]))
else:
L, = pl.plot(eupper, np.log10(nupperoverg), 'o')
xax = np.array([0, eupper.max().value])
line = (xax * result.slope.value + result.intercept.value)
pl.plot(xax,
np.log10(np.exp(line)),
'-',
color=L.get_color(),
label='$T={0:0.1f} \log(N)={1:0.1f}$'.format(
tex, np.log10(Ntot.value)))
return Ntot, tex, result.slope, result.intercept
def pyspeckitfit(eupper, kkms, frequencies, degeneracies, einsteinAs,
verbose=False, plot=False, guess=(150,1e19)):
"""
Fit the Boltzmann diagram (but do it right, with no approximations, just
direct forward modeling)
This doesn't seem to work, though: it can't reproduce its own output
"""
bandwidth = (1*u.km/u.s/constants.c)*(frequencies)
def model(tex, col, einsteinAs=einsteinAs, eupper=eupper):
tex = u.Quantity(tex, u.K)
col = u.Quantity(col, u.cm**-2)
eupper = eupper.to(u.erg, u.temperature_energy())
einsteinAs = u.Quantity(einsteinAs, u.Hz)
partition_func = specmodel.calculate_partitionfunction(ch3oh.data['States'],
temperature=tex.value)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
return lte_molecule.line_brightness(tex, bandwidth, frequencies,
total_column=col,
partition_function=Q_rot,
degeneracy=degeneracies,
energy_upper=eupper,
einstein_A=einsteinAs)
def minmdl(args):
tex, col = args
return ((model(tex, col).value - kkms)**2).sum()
from scipy import optimize
result = optimize.minimize(minmdl, guess, method='Nelder-Mead')
tex, Ntot = result.x
if plot:
import pylab as pl
pl.subplot(2,1,1)
pl.plot(eupper, kkms, 'o')
order = np.argsort(eupper)
pl.plot(eupper[order], model(tex, Ntot)[order])
pl.subplot(2,1,2)
xax = np.array([0, eupper.max().value])
pl.plot(eupper, np.log(nupper_of_kkms(kkms, frequencies, einsteinAs, degeneracies).value), 'o')
partition_func = specmodel.calculate_partitionfunction(ch3oh.data['States'],
temperature=tex)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
intercept = np.log(Ntot) - np.log(Q_rot)
pl.plot(xax, np.log(xax*tex + intercept), '-',
label='$T={0:0.1f} \log(N)={1:0.1f}$'.format(tex, np.log10(Ntot)))
return Ntot, tex, result
def ch3oh_model(xarr, vcen, width, tex, column, background=None, tbg=2.73):
if hasattr(tex,'unit'):
tex = tex.value
if hasattr(tbg,'unit'):
tbg = tbg.value
if hasattr(column, 'unit'):
column = column.value
if column < 25:
column = 10**column
if hasattr(vcen, 'unit'):
vcen = vcen.value
if hasattr(width, 'unit'):
width = width.value
ckms = constants.c.to(u.km/u.s).value
# assume equal-width channels
#kwargs = dict(rest=ref_freq)
#equiv = u.doppler_radio(**kwargs)
#channelwidth = np.abs(xarr[1].to(u.Hz, ) - xarr[0].to(u.Hz, )).value
#channelwidth = xarr.as_unit(u.Hz).dxarr
#velo = xarr.to(u.km/u.s, equiv).value
freq = xarr.to(u.Hz).value # same unit as nu below
model = np.zeros_like(xarr).value
freqs_ = freqs.to(u.Hz).value
Q = specmodel.calculate_partitionfunction(result.data['States'],
temperature=tex)[ch3oh.Id]
for A, g, nu, eu in zip(aij, deg, freqs_, EU):
taudnu = lte_molecule.line_tau_cgs(tex,
column,
Q,
g,
nu,
eu,
10**A)
width_dnu = width / ckms * nu
effective_linewidth_dnu = (2 * np.pi)**0.5 * width_dnu
fcen = (1 - vcen/ckms) * nu
tauspec = (np.exp(-(freq - fcen)**2 / (2 * width_dnu**2)) *
taudnu/effective_linewidth_dnu)
jnu = (lte_molecule.Jnu_cgs(nu, tex)-lte_molecule.Jnu_cgs(nu, tbg))
model = model + jnu*(1-np.exp(-tauspec))
if background is not None:
return background-model
return model
def model(tex, col, einsteinAs=einsteinAs, eupper=eupper):
tex = u.Quantity(tex, u.K)
col = u.Quantity(col, u.cm**-2)
eupper = eupper.to(u.erg, u.temperature_energy())
einsteinAs = u.Quantity(einsteinAs, u.Hz)
partition_func = specmodel.calculate_partitionfunction(ch3oh.data['States'],
temperature=tex.value)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
return lte_molecule.line_brightness(tex, bandwidth, frequencies,
total_column=col,
partition_function=Q_rot,
degeneracy=degeneracies,
energy_upper=eupper,
einstein_A=einsteinAs)
def model(tex, col, einsteinAs=einsteinAs, eupper=eupper):
tex = u.Quantity(tex, u.K)
col = u.Quantity(col, u.cm**-2)
eupper = eupper.to(u.erg, u.temperature_energy())
einsteinAs = u.Quantity(einsteinAs, u.Hz)
partition_func = specmodel.calculate_partitionfunction(hnco.data['States'],
temperature=tex.value)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
return lte_molecule.line_brightness(tex, bandwidth, frequencies,
total_column=col,
partition_function=Q_rot,
degeneracy=degeneracies,
energy_upper=eupper,
einstein_A=einsteinAs)
def hnco_model(xarr, vcen, width, tex, column, background=None, tbg=2.73):
if hasattr(tex,'unit'):
tex = tex.value
if hasattr(tbg,'unit'):
tbg = tbg.value
if hasattr(column, 'unit'):
column = column.value
if column < 25:
column = 10**column
if hasattr(vcen, 'unit'):
vcen = vcen.value
if hasattr(width, 'unit'):
width = width.value
ckms = constants.c.to(u.km/u.s).value
# assume equal-width channels
#kwargs = dict(rest=ref_freq)
#equiv = u.doppler_radio(**kwargs)
channelwidth = np.abs(xarr[1].to(u.Hz, ) - xarr[0].to(u.Hz, )).value
#velo = xarr.to(u.km/u.s, equiv).value
freq = xarr.to(u.Hz).value # same unit as nu below
model = np.zeros_like(xarr).value
freqs_ = freqs.to(u.Hz).value
Q = specmodel.calculate_partitionfunction(result.data['States'],
temperature=tex)[hnco.Id]
for A, g, nu, eu in zip(aij, deg, freqs_, EU):
tau_per_dnu = lte_molecule.line_tau_cgs(tex,
column,
Q,
g,
nu,
eu,
10**A)
width_dnu = width / ckms * nu
s = np.exp(-(freq-(1-vcen/ckms)*nu)**2/(2*width_dnu**2))*tau_per_dnu/channelwidth
jnu = (lte_molecule.Jnu_cgs(nu, tex)-lte_molecule.Jnu_cgs(nu, tbg))
model = model + jnu*(1-np.exp(-s))
if background is not None:
return background-model
return model
def fit_tex(eupper, nupperoverg, errors=None, verbose=False, plot=False):
"""
Fit the Boltzmann diagram
"""
model = modeling.models.Linear1D()
#fitter = modeling.fitting.LevMarLSQFitter()
fitter = modeling.fitting.LinearLSQFitter()
# ignore negatives
good = nupperoverg > 0
if good.sum() < len(nupperoverg)/2.:
return 0*u.cm**-2, 0*u.K, 0, 0
if errors is not None:
weights = 1/errors**2
else:
weights=None
result = fitter(model, eupper[good], np.log(nupperoverg[good]),
weights=weights[good])
tex = -1./result.slope*u.K
assert not np.isnan(tex)
partition_func = specmodel.calculate_partitionfunction(vamdc_result.data['States'],
temperature=tex.value)[ch3cn.Id]
Q_rot = partition_func
Ntot = np.exp(result.intercept + np.log(Q_rot)) * u.cm**-2
if verbose:
print(("Tex={0}, Ntot={1}, Q_rot={2}".format(tex, Ntot, Q_rot)))
if plot:
import pylab as pl
if errors is not None:
L,_,_ = pl.errorbar(x=eupper.value, y=np.log10(nupperoverg),
marker='o', linestyle='none',
yerr=np.array([np.log10(nupperoverg)-np.log10(nupperoverg-errors),
np.log10(nupperoverg+errors)-np.log10(nupperoverg)]))
else:
L, = pl.plot(eupper, np.log10(nupperoverg), 'o')
xax = np.array([0, eupper.max().value])
line = (xax*result.slope.value +
result.intercept.value)
pl.plot(xax, np.log10(np.exp(line)), '-', color=L.get_color(),
label='$T={0:0.1f} \log(N)={1:0.1f}$'.format(tex, np.log10(Ntot.value)))
return Ntot, tex, result.slope, result.intercept
def ch3cn_model(xarr, vcen, width, tex, column, background=None, tbg=2.73):
if hasattr(tex,'unit'):
tex = tex.value
if hasattr(tbg,'unit'):
tbg = tbg.value
if hasattr(column, 'unit'):
column = column.value
if column < 25:
column = 10**column
if hasattr(vcen, 'unit'):
vcen = vcen.value
if hasattr(width, 'unit'):
width = width.value
# assume equal-width channels
kwargs = dict(rest=ref_freq)
equiv = u.doppler_radio(**kwargs)
channelwidth = np.abs(xarr[1].to(u.Hz, equiv) - xarr[0].to(u.Hz, equiv)).value
velo = xarr.to(u.km/u.s, equiv).value
model = np.zeros_like(xarr).value
freqs_ = freqs.to(u.Hz).value
Q = m.calculate_partitionfunction(result.data['States'],
temperature=tex)[ch3cn.Id]
for voff, A, g, nu, eu in zip(vdiff, aij, deg, freqs_, EU):
tau_per_dnu = lte_molecule.line_tau_cgs(tex,
column,
Q,
g,
nu,
eu,
10**A)
s = np.exp(-(velo-vcen-voff)**2/(2*width**2))*tau_per_dnu/channelwidth
jnu = (lte_molecule.Jnu_cgs(nu, tex)-lte_molecule.Jnu_cgs(nu, tbg))
model = model + jnu*(1-np.exp(-s))
if background is not None:
return background-model
return model
def hnco_model(xarr, vcen, width, tex, column, background=None, tbg=2.73):
if hasattr(tex, "unit"):
tex = tex.value
if hasattr(tbg, "unit"):
tbg = tbg.value
if hasattr(column, "unit"):
column = column.value
if column < 25:
column = 10 ** column
if hasattr(vcen, "unit"):
vcen = vcen.value
if hasattr(width, "unit"):
width = width.value
ckms = constants.c.to(u.km / u.s).value
# assume equal-width channels
# kwargs = dict(rest=ref_freq)
# equiv = u.doppler_radio(**kwargs)
channelwidth = np.abs(xarr[1].to(u.Hz) - xarr[0].to(u.Hz)).value
# velo = xarr.to(u.km/u.s, equiv).value
freq = xarr.to(u.Hz).value # same unit as nu below
model = np.zeros_like(xarr).value
freqs_ = freqs.to(u.Hz).value
Q = specmodel.calculate_partitionfunction(result.data["States"], temperature=tex)[hnco.Id]
for A, g, nu, eu in zip(aij, deg, freqs_, EU):
tau_per_dnu = lte_molecule.line_tau_cgs(tex, column, Q, g, nu, eu, 10 ** A)
width_dnu = width / ckms * nu
s = np.exp(-(freq - (1 - vcen / ckms) * nu) ** 2 / (2 * width_dnu ** 2)) * tau_per_dnu / channelwidth
jnu = lte_molecule.Jnu_cgs(nu, tex) - lte_molecule.Jnu_cgs(nu, tbg)
model = model + jnu * (1 - np.exp(-s))
if background is not None:
return background - model
return model
def fit_tex(eupper, nupperoverg, verbose=False, plot=False, uplims=None,
errors=None, min_nupper=1,
replace_errors_with_uplims=False,
max_uplims='half'):
"""
Fit the Boltzmann diagram
Parameters
----------
max_uplims: str or number
The maximum number of upper limits before the fit is ignored completely
and instead zeros are returned
"""
model = modeling.models.Linear1D()
#fitter = modeling.fitting.LevMarLSQFitter()
fitter = modeling.fitting.LinearLSQFitter()
nupperoverg_tofit = nupperoverg.copy()
if uplims is not None:
upperlim_mask = nupperoverg < uplims
# allow this magical keyword 'half'
max_uplims = len(nupperoverg)/2. if max_uplims == 'half' else max_uplims
if upperlim_mask.sum() > max_uplims:
# too many upper limits = bad idea to fit.
return 0*u.cm**-2, 0*u.K, 0, 0
if errors is None:
# if errors are not specified, we set the upper limits as actual values
# (which gives a somewhat useful upper limit on the temperature)
nupperoverg_tofit[upperlim_mask] = uplims[upperlim_mask]
else:
# otherwise, we set the values to zero-column and set the errors to
# be whatever the upper limits are (hopefully a 1-sigma upper
# limit)
# 1.0 here becomes 0.0 in log and makes the relative errors meaningful
nupperoverg_tofit[upperlim_mask] = 1.0
if replace_errors_with_uplims:
errors[upperlim_mask] = uplims[upperlim_mask]
# always ignore negatives & really low values
good = nupperoverg_tofit > min_nupper
# skip any fits that have fewer than 50% good values
if good.sum() < len(nupperoverg_tofit)/2.:
return 0*u.cm**-2, 0*u.K, 0, 0
if errors is not None:
rel_errors = errors / nupperoverg_tofit
weights = 1. / rel_errors**2
log.debug("Fitting with data = {0}, weights = {1}, errors = {2},"
"relative_errors = {3}"
.format(np.log(nupperoverg_tofit[good]),
np.log(weights[good]),
errors[good],
rel_errors[good],
))
else:
# want log(weight) = 1
weights = np.exp(np.ones_like(nupperoverg_tofit))
result = fitter(model, eupper[good], np.log(nupperoverg_tofit[good]),
weights=np.log(weights[good]))
tex = -1./result.slope*u.K
partition_func = specmodel.calculate_partitionfunction(hnco.data['States'],
temperature=tex.value)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
Ntot = np.exp(result.intercept + np.log(Q_rot)) * u.cm**-2
if verbose:
print(("Tex={0}, Ntot={1}, Q_rot={2}, nuplim={3}".format(tex, Ntot, Q_rot, upperlim_mask.sum())))
if plot:
import pylab as pl
L, = pl.plot(eupper, np.log10(nupperoverg_tofit), 'ro',
markeredgecolor='none', alpha=0.5)
L, = pl.plot(eupper, np.log10(nupperoverg), 'bo', alpha=0.2)
if errors is not None:
yerr = np.array([np.log10(nupperoverg_tofit)-np.log10(nupperoverg_tofit-errors),
np.log10(nupperoverg_tofit+errors)-np.log10(nupperoverg_tofit)])
# if lower limit is nan, set to zero
yerr[0,:] = np.nan_to_num(yerr[0,:])
if np.any(np.isnan(yerr[1,:])):
print("*** Some upper limits are NAN")
pl.errorbar(eupper.value,
np.log10(nupperoverg_tofit),
yerr=yerr,
linestyle='none',
linewidth=0.5,
marker='.', zorder=-5)
xax = np.array([0, eupper.max().value])
line = (xax*result.slope.value +
result.intercept.value)
pl.plot(xax, np.log10(np.exp(line)), '-', color=L.get_color(),
alpha=0.3,
label='$T={0:0.1f}$ $\log(N)={1:0.1f}$'.format(tex, np.log10(Ntot.value)))
pl.ylabel("log N$_u$ (cm$^{-2}$)")
pl.xlabel("E$_u$ (K)")
if (uplims is not None) and ((errors is None) or replace_errors_with_uplims):
# if errors are specified, their errorbars will be better
# representations of what's actually being fit
pl.plot(eupper, np.log10(uplims), marker='_', alpha=0.5,
linestyle='none', color='k')
return Ntot, tex, result.slope, result.intercept
def fit_tex(eupper, nupperoverg, verbose=False, plot=False, uplims=None,
errors=None, min_nupper=1,
replace_errors_with_uplims=False,
max_uplims='half'):
"""
Fit the Boltzmann diagram
Parameters
----------
max_uplims: str or number
The maximum number of upper limits before the fit is ignored completely
and instead zeros are returned
"""
model = modeling.models.Linear1D()
#fitter = modeling.fitting.LevMarLSQFitter()
fitter = modeling.fitting.LinearLSQFitter()
nupperoverg_tofit = nupperoverg.copy()
if uplims is not None:
upperlim_mask = nupperoverg < uplims
# allow this magical keyword 'half'
max_uplims = len(nupperoverg)/2. if max_uplims == 'half' else max_uplims
if upperlim_mask.sum() > max_uplims:
# too many upper limits = bad idea to fit.
return 0*u.cm**-2, 0*u.K, 0, 0
if errors is None:
# if errors are not specified, we set the upper limits as actual values
# (which gives a somewhat useful upper limit on the temperature)
nupperoverg_tofit[upperlim_mask] = uplims[upperlim_mask]
else:
# otherwise, we set the values to zero-column and set the errors to
# be whatever the upper limits are (hopefully a 1-sigma upper
# limit)
# 1.0 here becomes 0.0 in log and makes the relative errors meaningful
nupperoverg_tofit[upperlim_mask] = 1.0
if replace_errors_with_uplims:
errors[upperlim_mask] = uplims[upperlim_mask]
# always ignore negatives & really low values
good = nupperoverg_tofit > min_nupper
# skip any fits that have fewer than 50% good values
if good.sum() < len(nupperoverg_tofit)/2.:
return 0*u.cm**-2, 0*u.K, 0, 0
if errors is not None:
rel_errors = errors / nupperoverg_tofit
weights = 1. / rel_errors**2
log.debug("Fitting with data = {0}, weights = {1}, errors = {2},"
"relative_errors = {3}"
.format(np.log(nupperoverg_tofit[good]),
np.log(weights[good]),
errors[good],
rel_errors[good],
))
else:
# want log(weight) = 1
weights = np.exp(np.ones_like(nupperoverg_tofit))
result = fitter(model, eupper[good], np.log(nupperoverg_tofit[good]),
weights=np.log(weights[good]))
tex = -1./result.slope*u.K
partition_func = specmodel.calculate_partitionfunction(ch3oh.data['States'],
temperature=tex.value)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
Ntot = np.exp(result.intercept + np.log(Q_rot)) * u.cm**-2
if verbose:
print(("Tex={0}, Ntot={1}, Q_rot={2}, nuplim={3}".format(tex, Ntot, Q_rot, upperlim_mask.sum())))
if plot:
import pylab as pl
L, = pl.plot(eupper, np.log10(nupperoverg_tofit), 'ro',
markeredgecolor='none', alpha=0.5)
L, = pl.plot(eupper, np.log10(nupperoverg), 'bo', alpha=0.2)
if errors is not None:
yerr = np.array([np.log10(nupperoverg_tofit)-np.log10(nupperoverg_tofit-errors),
np.log10(nupperoverg_tofit+errors)-np.log10(nupperoverg_tofit)])
# if lower limit is nan, set to zero
yerr[0,:] = np.nan_to_num(yerr[0,:])
if np.any(np.isnan(yerr[1,:])):
print("*** Some upper limits are NAN")
pl.errorbar(eupper.value,
np.log10(nupperoverg_tofit),
yerr=yerr,
linestyle='none',
linewidth=0.5,
marker='.', zorder=-5)
xax = np.array([0, eupper.max().value])
line = (xax*result.slope.value +
result.intercept.value)
pl.plot(xax, np.log10(np.exp(line)), '-', color=L.get_color(),
alpha=0.3,
label='$T={0:0.1f}$ $\log(N)={1:0.1f}$'.format(tex, np.log10(Ntot.value)))
pl.ylabel("log N$_u$ (cm$^{-2}$)")
pl.xlabel("E$_u$ (K)")
if (uplims is not None) and ((errors is None) or replace_errors_with_uplims):
# if errors are specified, their errorbars will be better
# representations of what's actually being fit
pl.plot(eupper, np.log10(uplims), marker='_', alpha=0.5,
linestyle='none', color='k')
return Ntot, tex, result.slope, result.intercept
def partfunc(tem):
Q = list(
specmodel.calculate_partitionfunction(result.data['States'],
temperature=tem).values())[0]
return Q
def get_molecular_parameters(molecule_name,
molecule_name_vamdc=None,
tex=50,
fmin=1 * u.GHz,
fmax=1 * u.THz,
line_lists=['SLAIM'],
chem_re_flags=0,
**kwargs):
"""
Get the molecular parameters for a molecule from the CDMS database using
vamdclib
Parameters
----------
molecule_name : string
The string name of the molecule (normal name, like CH3OH or CH3CH2OH)
molecule_name_vamdc : string or None
If specified, gives this name to vamdc instead of the normal name.
Needed for some molecules, like CH3CH2OH -> C2H5OH.
tex : float
Optional excitation temperature (basically checks if the partition
function calculator works)
fmin : quantity with frequency units
fmax : quantity with frequency units
The minimum and maximum frequency to search over
line_lists : list
A list of Splatalogue line list catalogs to search. Valid options
include SLAIM, CDMS, JPL. Only a single catalog should be used to
avoid repetition of transitions and species
chem_re_flags : int
An integer flag to be passed to splatalogue's chemical name matching
tool
Examples
--------
>>> freqs, aij, deg, EU, partfunc = get_molecular_parameters(molecule_name='CH2CHCN',
... fmin=220*u.GHz,
... fmax=222*u.GHz,
... molecule_name_vamdc='C2H3CN')
>>> freqs, aij, deg, EU, partfunc = get_molecular_parameters('CH3OH',
... fmin=90*u.GHz,
... fmax=100*u.GHz)
"""
from astroquery.vamdc import load_species_table
from astroquery.splatalogue import Splatalogue
from vamdclib import nodes
from vamdclib import request
from vamdclib import specmodel
lut = load_species_table.species_lookuptable()
species_id_dict = lut.find(molecule_name_vamdc or molecule_name,
flags=chem_re_flags)
if len(species_id_dict) == 1:
species_id = list(species_id_dict.values())[0]
elif len(species_id_dict) == 0:
raise ValueError("No matches for {0}".format(molecule_name))
else:
raise ValueError(
"Too many species matched: {0}".format(species_id_dict))
# do this here, before trying to compute the partition function, because
# this query could fail
tbl = Splatalogue.query_lines(fmin,
fmax,
chemical_name=molecule_name,
line_lists=line_lists,
show_upper_degeneracy=True,
**kwargs)
nl = nodes.Nodelist()
nl.findnode('cdms')
cdms = nl.findnode('cdms')
request = request.Request(node=cdms)
query_string = "SELECT ALL WHERE VAMDCSpeciesID='%s'" % species_id
request.setquery(query_string)
result = request.dorequest()
Q = list(
specmodel.calculate_partitionfunction(result.data['States'],
temperature=tex).values())[0]
def partfunc(tem):
Q = list(
specmodel.calculate_partitionfunction(result.data['States'],
temperature=tem).values())[0]
return Q
freqs = np.array(tbl['Freq-GHz']) * u.GHz
aij = tbl['Log<sub>10</sub> (A<sub>ij</sub>)']
deg = tbl['Upper State Degeneracy']
EU = (np.array(tbl['E_U (K)']) * u.K * constants.k_B).to(u.erg).value
return freqs, aij, deg, EU, partfunc
import numpy as np
import paths
import pylab as pl
from astroquery.vamdc import Vamdc
from vamdclib import specmodel
ch3oh = Vamdc.query_molecule('CH3OH')
temperatures = np.linspace(10, 300)
partition_func = [
specmodel.calculate_partitionfunction(ch3oh.data['States'],
temperature=tex)['XCDMS-149']
for tex in temperatures
]
pl.matplotlib.rc_file('pubfiguresrc')
pl.figure(1).clf()
pl.plot(temperatures, partition_func)
pl.xlabel("T (K)")
pl.ylabel("$Q_{rot}$")
pl.savefig(paths.fpath("chemistry/ch3oh_partition_function.png"))
def fit_tex(
eupper,
nupperoverg,
verbose=False,
plot=False,
uplims=None,
errors=None,
min_nupper=1,
replace_errors_with_uplims=False,
molecule=None,
color='r',
marker='o',
max_uplims='half',
label='',
):
"""
Fit the Boltzmann diagram
Parameters
----------
max_uplims: str or number
The maximum number of upper limits before the fit is ignored completely
and instead zeros are returned
"""
nupperoverg_tofit = nupperoverg.copy().to(u.cm**-2).value
if errors is not None:
errors = errors.to(u.cm**-2).value
if uplims is not None:
upperlim_mask = nupperoverg < uplims
# allow this magical keyword 'half'
max_uplims = len(
nupperoverg) / 2. if max_uplims == 'half' else max_uplims
if upperlim_mask.sum() > max_uplims:
# too many upper limits = bad idea to fit.
return 0 * u.cm**-2, 0 * u.K, 0, 0
if errors is None:
# if errors are not specified, we set the upper limits as values to
# be fitted
# (which gives a somewhat useful upper limit on the temperature)
nupperoverg_tofit[upperlim_mask] = uplims[upperlim_mask]
else:
# otherwise, we set the values to zero-column and set the errors to
# be whatever the upper limits are (hopefully a 1-sigma upper
# limit)
# 1.0 here becomes 0.0 in log and makes the relative errors meaningful
nupperoverg_tofit[upperlim_mask] = 1.0
if replace_errors_with_uplims:
errors[upperlim_mask] = uplims[upperlim_mask]
else:
upperlim_mask = np.ones_like(nupperoverg_tofit, dtype='bool')
# always ignore negatives & really low values
good = nupperoverg_tofit > min_nupper
# skip any fits that have fewer than 50% good values
if good.sum() < len(nupperoverg_tofit) / 2.:
return 0 * u.cm**-2, 0 * u.K, 0, 0
if errors is not None:
rel_errors = errors / nupperoverg_tofit
weights = 1. / rel_errors**2
log.debug("Fitting with data = {0}, weights = {1}, errors = {2},"
"relative_errors = {3}".format(
np.log(nupperoverg_tofit[good]),
np.log(weights[good]),
errors[good],
rel_errors[good],
))
else:
# want log(weight) = 1
weights = np.exp(np.ones_like(nupperoverg_tofit))
#model = modeling.models.Linear1D()
model = simple_lte_model_generator()
fitter = modeling.fitting.LevMarLSQFitter()
#fitter = modeling.fitting.LinearLSQFitter()
#model.slope.bounds = [0, -1000]
if good.sum() >= 2:
result = fitter(model,
eupper[good].to(u.K).value,
np.log(nupperoverg_tofit[good]),
weights=np.log(weights[good]))
#tex = u.Quantity(-1./result.slope, u.K)
tex = u.Quantity(result.tem, u.K)
if tex < 0 * u.K:
tex = 100 * u.K
partition_func = specmodel.calculate_partitionfunction(
molecule.data['States'], temperature=tex.value)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
#Ntot = np.exp(result.intercept + np.log(Q_rot)) * u.cm**-2
Ntot = np.exp(result.logcolumn) * Q_rot * u.cm**-2
else:
Ntot = 1e10 * u.cm**-2
tex = 100 * u.K
Q_rot = 1
result = model
if verbose:
print(("Tex={0}, Ntot={1}, log(Ntot)={4}, Q_rot={2}, "
"nuplim={3}".format(
tex,
Ntot,
Q_rot,
upperlim_mask.sum(),
np.log10(Ntot.value),
)))
if plot:
import pylab as pl
L, = pl.plot(
eupper,
np.log10(nupperoverg_tofit),
marker=marker,
color=color,
markeredgecolor='none',
alpha=0.5,
linestyle='none',
#markersize=2,
)
if uplims is not None:
L, = pl.plot(eupper[upperlim_mask],
np.log10(uplims)[upperlim_mask],
'bv',
alpha=0.2,
markersize=2)
#L, = pl.plot(eupper[upperlim_mask],
# np.log10(nupperoverg)[upperlim_mask], 'bv', alpha=0.2)
if errors is not None:
yerr = np.array([
np.log10(nupperoverg_tofit) -
np.log10(nupperoverg_tofit - errors),
np.log10(nupperoverg_tofit + errors) -
np.log10(nupperoverg_tofit)
])
# if lower limit is nan, set to zero
yerr[0, :] = np.nan_to_num(yerr[0, :])
if np.any(np.isnan(yerr[1, :])):
#raise ValueError("*** Some upper limits are NAN")
print(ValueError("*** Some upper limits are NAN"))
# use 'good' to exclude plotting errorbars for upper limits
pl.errorbar(eupper.value[good],
np.log10(nupperoverg_tofit)[good],
yerr=yerr[:, good],
linestyle='none',
linewidth=0.5,
color='k',
marker='.',
zorder=-5,
markersize=2)
xax = np.array([0, eupper.max().value + 500])
line = (xax * (-1 / result.tem.value) + result.logcolumn.value)
pl.plot(xax,
np.log10(np.exp(line)),
'--',
color=color,
alpha=0.6,
linewidth=1.0,
label='{2}$T={0:0.1f}$ $\log(N)={1:0.1f}$'.format(
tex, np.log10(Ntot.value), label))
pl.ylabel("log N$_u$/g (cm$^{-2}$)")
pl.xlabel("E$_u$ (K)")
if (uplims is not None) and ((errors is None)
or replace_errors_with_uplims):
# if errors are specified, their errorbars will be better
# representations of what's actually being fit
pl.plot(eupper,
np.log10(uplims),
marker='_',
alpha=0.5,
linestyle='none',
color='k')
return Ntot, tex, result.tem, result.logcolumn
def Qrot(temperature):
Q = m.calculate_partitionfunction(result.data['States'],
temperature=temperature)[h2co.Id]
return Q
def get_molecular_parameters(molecule_name,
molecule_name_vamdc=None,
tex=50, fmin=1*u.GHz, fmax=1*u.THz,
line_lists=['SLAIM'],
chem_re_flags=0, **kwargs):
"""
Get the molecular parameters for a molecule from the CDMS database using
vamdclib
Parameters
----------
molecule_name : string
The string name of the molecule (normal name, like CH3OH or CH3CH2OH)
molecule_name_vamdc : string or None
If specified, gives this name to vamdc instead of the normal name.
Needed for some molecules, like CH3CH2OH -> C2H5OH.
tex : float
Optional excitation temperature (basically checks if the partition
function calculator works)
fmin : quantity with frequency units
fmax : quantity with frequency units
The minimum and maximum frequency to search over
line_lists : list
A list of Splatalogue line list catalogs to search. Valid options
include SLAIM, CDMS, JPL. Only a single catalog should be used to
avoid repetition of transitions and species
chem_re_flags : int
An integer flag to be passed to splatalogue's chemical name matching
tool
Examples
--------
>>> freqs, aij, deg, EU, partfunc = get_molecular_parameters(molecule_name='CH2CHCN',
... fmin=220*u.GHz,
... fmax=222*u.GHz,
... molecule_name_vamdc='C2H3CN')
>>> freqs, aij, deg, EU, partfunc = get_molecular_parameters('CH3OH',
... fmin=90*u.GHz,
... fmax=100*u.GHz)
"""
from astroquery.vamdc import load_species_table
from astroquery.splatalogue import Splatalogue
from vamdclib import nodes
from vamdclib import request
from vamdclib import specmodel
lut = load_species_table.species_lookuptable()
species_id_dict = lut.find(molecule_name_vamdc or molecule_name,
flags=chem_re_flags)
if len(species_id_dict) == 1:
species_id = list(species_id_dict.values())[0]
elif len(species_id_dict) == 0:
raise ValueError("No matches for {0}".format(molecule_name))
else:
raise ValueError("Too many species matched: {0}"
.format(species_id_dict))
# do this here, before trying to compute the partition function, because
# this query could fail
tbl = Splatalogue.query_lines(fmin, fmax, chemical_name=molecule_name,
line_lists=line_lists,
show_upper_degeneracy=True, **kwargs)
nl = nodes.Nodelist()
nl.findnode('cdms')
cdms = nl.findnode('cdms')
request = request.Request(node=cdms)
query_string = "SELECT ALL WHERE VAMDCSpeciesID='%s'" % species_id
request.setquery(query_string)
result = request.dorequest()
# run it once to test that it works
Q = list(specmodel.calculate_partitionfunction(result.data['States'],
temperature=tex).values())[0]
def partfunc(tem):
Q = list(specmodel.calculate_partitionfunction(result.data['States'],
temperature=tem).values())[0]
return Q
freqs = (np.array(tbl['Freq-GHz'])*u.GHz if 'Freq-GHz' in tbl else
np.array(tbl['Freq-GHz(rest frame,redshifted)'])*u.GHz)
aij = tbl['Log<sub>10</sub> (A<sub>ij</sub>)']
deg = tbl['Upper State Degeneracy']
EU = (np.array(tbl['E_U (K)'])*u.K*constants.k_B).to(u.erg).value
return freqs, aij, deg, EU, partfunc
import numpy as np
import paths
import pylab as pl
from astroquery.vamdc import Vamdc
from vamdclib import specmodel
ch3oh = Vamdc.query_molecule("CH3OH")
temperatures = np.linspace(10, 300)
partition_func = [
specmodel.calculate_partitionfunction(ch3oh.data["States"], temperature=tex)["XCDMS-149"] for tex in temperatures
]
pl.matplotlib.rc_file("pubfiguresrc")
pl.figure(1).clf()
pl.plot(temperatures, partition_func)
pl.xlabel("T (K)")
pl.ylabel("$Q_{rot}$")
pl.savefig(paths.fpath("chemistry/ch3oh_partition_function.png"))
def partfunc(tem):
Q = list(specmodel.calculate_partitionfunction(result.data['States'],
temperature=tem).values())[0]
return Q
def fit_multi_tex(eupper,
nupperoverg,
vstate,
jstate,
vibenergies,
rotenergies,
verbose=False,
plot=False,
uplims=None,
errors=None,
min_nupper=1,
replace_errors_with_uplims=False,
molecule=None,
colors='rgbcmyk',
molname=None,
collims=(np.log(1e9), np.log(1e17)),
rottemlims=(10, 300),
vibtemlims=(500, 16000),
marker='o',
max_uplims='half'):
"""
Fit the Boltzmann diagram with a vibrational and a rotational temperature
Parameters
----------
max_uplims: str or number
The maximum number of upper limits before the fit is ignored completely
and instead zeros are returned
"""
nupperoverg_tofit = nupperoverg.copy().to(u.cm**-2).value
if errors is not None:
errors = errors.to(u.cm**-2).value
if uplims is not None:
upperlim_mask = nupperoverg < uplims
# allow this magical keyword 'half'
max_uplims = len(
nupperoverg) / 2. if max_uplims == 'half' else max_uplims
if upperlim_mask.sum() > max_uplims:
# too many upper limits = bad idea to fit.
return 0 * u.cm**-2, 0 * u.K, 0, 0
if errors is None:
# if errors are not specified, we set the upper limits as values to
# be fitted
# (which gives a somewhat useful upper limit on the temperature)
nupperoverg_tofit[upperlim_mask] = uplims[upperlim_mask]
else:
# otherwise, we set the values to zero-column and set the errors to
# be whatever the upper limits are (hopefully a 1-sigma upper
# limit)
# 1.0 here becomes 0.0 in log and makes the relative errors meaningful
nupperoverg_tofit[upperlim_mask] = 1.0
if replace_errors_with_uplims:
errors[upperlim_mask] = uplims[upperlim_mask]
else:
upperlim_mask = np.ones_like(nupperoverg_tofit, dtype='bool')
# always ignore negatives & really low values
good = nupperoverg_tofit > min_nupper
# skip any fits that have fewer than 50% good values
if good.sum() < len(nupperoverg_tofit) / 2.:
return 0 * u.cm**-2, 0 * u.K, 0, 0
if errors is not None:
rel_errors = errors / nupperoverg_tofit
weights = 1. / rel_errors**2
log.debug("Fitting with data = {0}, weights = {1}, errors = {2},"
"relative_errors = {3}".format(
np.log(nupperoverg_tofit[good]),
np.log(weights[good]),
errors[good],
rel_errors[good],
))
else:
# want log(weight) = 1
weights = np.exp(np.ones_like(nupperoverg_tofit))
model = rovib_lte_model_generator(vibenergies, rotenergies)
#print('vibenergies:',vibenergies, '\nrotenergies:', rotenergies)
fitter = modeling.fitting.LevMarLSQFitter()
#fitter = modeling.fitting.LinearLSQFitter()
model_to_fit = model
model_to_fit.logcolumn.bounds = collims
model_to_fit.rottem.bounds = rottemlims
model_to_fit.vibtem.bounds = vibtemlims
#model_to_fit.rottem.fixed = True
# check that the model works
#first_check = model_to_fit(eupper[good].to(u.K).value)
#print("Result of first check: ",first_check)
result = fitter(model_to_fit,
jstate[good].astype('int'),
vstate[good].astype('int'),
np.log(nupperoverg_tofit[good]),
weights=np.log(weights[good]))
print(result)
tex = result.rottem #u.Quantity(-1./result.slope, u.K)
tvib = result.vibtem
partition_func = specmodel.calculate_partitionfunction(
molecule.data['States'], temperature=tex.value)
assert len(partition_func) == 1
Q_rot = tuple(partition_func.values())[0]
print("Q_rot:", Q_rot)
Ntot = np.exp(result.logcolumn + np.log(Q_rot)) * u.cm**-2
if verbose:
print(("Tex={0}, Ntot={1}, log(Ntot)={4}, Q_rot={2}, "
"nuplim={3}".format(
tex,
Ntot,
Q_rot,
upperlim_mask.sum(),
np.log10(Ntot.value),
)))
if plot:
import pylab as pl
for vib, color in zip(np.arange(vstate.max() + 1), colors):
mask = vstate == vib
if mask.sum() == 0:
continue
L, = pl.plot(
eupper[mask],
np.log10(nupperoverg_tofit[mask]),
marker=marker,
color=color,
markeredgecolor='none',
alpha=0.5,
linestyle='none',
#markersize=2,
)
if uplims is not None:
L, = pl.plot(eupper[upperlim_mask & mask],
np.log10(uplims)[upperlim_mask & mask],
'bv',
alpha=0.2,
markersize=2)
#L, = pl.plot(eupper[upperlim_mask],
# np.log10(nupperoverg)[upperlim_mask], 'bv', alpha=0.2)
if errors is not None:
yerr = np.array([
np.log10(nupperoverg_tofit) -
np.log10(nupperoverg_tofit - errors),
np.log10(nupperoverg_tofit + errors) -
np.log10(nupperoverg_tofit)
])
# if lower limit is nan, set to zero
yerr[0, :] = np.nan_to_num(yerr[0, :])
if np.any(np.isnan(yerr[1, :])):
print(ValueError("*** Some upper limits are NAN"))
# use 'good' to exclude plotting errorbars for upper limits
pl.errorbar(eupper.value[good & mask],
np.log10(nupperoverg_tofit)[good & mask],
yerr=yerr[:, good & mask],
linestyle='none',
linewidth=0.5,
color=L.get_color(),
marker='.',
zorder=-5,
markersize=2)
#xax = np.array([0, eupper.max().value+500])
jstates = np.arange(1, np.max(list(rotenergies.keys())) + 1)
vstates = np.ones(np.max(list(rotenergies.keys()))) * vib
line = result(jstates, vstates)
xax = np.array(
[rotenergies[ju] + vibenergies[vib] for ju in jstates])
for marker, mask in (('.', (jstates > -1) & (jstates <= 10)),
('s', (jstates > 10) & (jstates <= 20)),
('o', (jstates > 20) & (jstates <= 30)),
('D', (jstates > 30) & (jstates <= 40)),
('p', (jstates > 40) & (jstates <= 50))):
pl.plot(
xax[mask],
np.log10(np.exp(line))[mask],
marker=marker,
linestyle='none',
color=color,
alpha=0.3,
linewidth=1.0,
markersize=4,
)
#label='v={0}'.format(vib),
#label=('v={2}$T_R={0:0.1f}$ $T_v={3:0.1f}$ $\log(N)={1:0.1f}$'
# .format(tex.value, np.log10(Ntot.value), vib,
# tvib.value
# ))
for jj in np.unique(jstate):
#jstates = np.arange(1,np.max(list(rotenergies.keys()))+1)
#vstates = np.ones(np.max(list(rotenergies.keys())))*vib
vstates = np.arange(9)
jstates = np.ones(9) * jj
line = result(jstates, vstates)
xax = np.array(
[rotenergies[jj] + vibenergies[vv] for vv in vstates])
pl.plot(
xax,
np.log10(np.exp(line)),
'--',
color='k',
alpha=0.1,
linewidth=1.0,
)
#label="Ju={0}".format(jj),
#label=('v={2}$T_R={0:0.1f}$ $T_v={3:0.1f}$ $\log(N)={1:0.1f}$'
# .format(tex.value, np.log10(Ntot.value), vib,
# tvib.value
# ))
for eu, nu, jj, vv in zip(eupper, nupperoverg_tofit, jstate, vstate):
model_nu = result(jj, vv)
#print("POINT MATCHING: ",eu, model_nu, np.log(nu), jj, vv)
pl.plot(u.Quantity([eu, eu]),
np.log10(np.exp([np.log(nu), model_nu])),
linestyle='-',
alpha=0.3,
color='k',
linewidth=0.5)
pl.ylabel("log N$_u$/g (cm$^{-2}$)")
pl.xlabel("E$_u$ (K)")
pl.plot(
[], [],
linestyle='-',
color='k',
label=('$T_R={0:0.1f}$ $T_v={2:0.1f}$ $\log(N)={1:0.1f}$'.format(
tex.value, np.log10(Ntot.value), tvib.value)))
if (uplims is not None) and ((errors is None)
or replace_errors_with_uplims):
# if errors are specified, their errorbars will be better
# representations of what's actually being fit
pl.plot(eupper,
np.log10(uplims),
marker='_',
alpha=0.5,
linestyle='none',
color='k')
return Ntot, tex, result.rottem, result.vibtem, result.logcolumn
