def fit(self):
r"""actually run the fit"""
# we can ignore set_what, since I think there's a mechanism in
# lmfit to take care of that (it's for fixing parameters)
# but the rest of what it's doing is to pull apart the
# error, axis, etc, to be fed to minimize.
#
# It also automatically converts complex data to real data, and
# does other things for error handling -- let's not just throw this out
#
# I think that a lot of this could be copied with little modification
#
# But you should read through and see what the previous fit method is doing
# and then copy over what you can
x = self.getaxis(self.fit_axis)
if np.iscomplex(self.data.flatten()[0]):
logging.debug(strm("Warning, taking only real part of fitting data!"))
y = np.real(self.data)
sigma = self.get_error()
out = minimize(
self.residual,
self.pars,
args=(x, y, sigma),
)
# can you capture the following as a string? maybe return it?
report_fit(out, show_correl=True)
# {{{ capture the result for ouput, etc
self.fit_coeff = [out.params[j].value for j in self.symbol_list]
assert out.success
self.covariance = out.covar
# }}}
return
def normal_skewed(x, y, parameters=None, dfunc='pdf', check=False, *args, **kwargs):
# verbous.INFO('FITTING SKEWED-GAUSSIAN')
if parameters == None:
parameters = Parameters()
parameters = Parameters()
parameters.add('amp', value=max(y))
max_idx = np.argmin(abs(y - max(y)))
parameters.add('mu', value=x[max_idx])
parameters.add('sig', value=15.)
parameters.add('skew', value=-5.)
if y[0] > y[-1]:
reverse = True
else:
reverse = False
errfunc = lambda p, x, y: distributions.normal_skew(x, parameters, reverse=reverse, dfunc=dfunc) - y
fitout = minimize(errfunc, parameters, args=(x, y))
# verbous.INFO('FITTED PARAMETERS:')
if check:
printfuncs.report_fit(fitout.params)
x_fit = np.linspace(0, 600, 1000)
y_fit = distributions.normal_skew(x_fit, parameters, reverse=reverse, dfunc=dfunc)
plt.plot(x, y)
plt.plot(x_fit, y_fit)
plt.show()
return parameters
def test_constraints1():
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])
model = yg + yl + pars['line_off'] + x * pars['line_slope']
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) + lorentzian(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) + x * 0.5)
pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual,
pfit,
fcn_args=(x, ),
fcn_kws={
'sigma': sigma,
'data': data
},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
result = myfit.leastsq()
print(' Nfev = ', result.nfev)
print(result.chisqr, result.redchi, result.nfree)
report_fit(result.params)
pfit = result.params
fit = residual(result.params, x)
assert (pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
assert (pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
assert (pfit['wid_l'].value == 2 * pfit['wid_g'].value)
def test_constraints1():
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])
model = yg + yl + pars['line_off'] + x * pars['line_slope']
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data)/sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) +
lorentzian(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
result = myfit.leastsq()
print(' Nfev = ', result.nfev)
print( result.chisqr, result.redchi, result.nfree)
report_fit(result.params)
pfit= result.params
fit = residual(result.params, x)
assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
def fit_spready(self, ):
params = Parameters()
c1 = self.refx[np.argmax(self.refy)] - self.x[np.argmax(self.y)]
params.add('c1', value=c1, min=c1 - 50, max=c1 + 50)
params.add('c2', value=0.5e-2, min=1e-3, max=1e-2)
mini = Minimizer(self.lmfit_residuals, params, nan_policy='propagate')
self.lmfit_minimize_result = mini.minimize(
method='differential_evolution')
printfuncs.report_fit(self.lmfit_minimize_result, min_correl=0.5)
def align_with_O2(spectra, O2_spectra, R=5000):
# Convert to ispec structures
spectra = ispec.create_spectrum_structure(spectra.T[0], spectra.T[1],
spectra.T[2])
O2_spectra = ispec.create_spectrum_structure(O2_spectra.T[0],
O2_spectra.T[1],
O2_spectra.T[2])
# Now normalise
normed_spectra, spectra_continuum_model = normalize_whole_spectrum(spectra)
#wfilter = ispec.create_wavelength_filter(normed_spectra, wave_base=np.min(O2_spectra['waveobs']) - 3, wave_top=np.max(O2_spectra['waveobs']) + 3)
wfilter = ispec.create_wavelength_filter(normed_spectra,
wave_base=684,
wave_top=690)
normed_spectra = normed_spectra[wfilter]
params = Parameters()
params.add('rv', value=0, min=-100, max=100)
params.add('strength', value=1, min=0.7, max=1.3)
params.add('zp', value=1., min=0.9, max=1.1, vary=False)
mini = Minimizer(lmfit_func,
params,
fcn_args=(np.copy(normed_spectra), np.copy(O2_spectra),
False))
lmfit_minimize_result = mini.minimize()
printfuncs.report_fit(lmfit_minimize_result, min_correl=0.5)
corrected_spectra, o2_model = lmfit_func(lmfit_minimize_result.params,
normed_spectra,
O2_spectra,
return_model=True)
f = plt.figure()
plt.plot(normed_spectra['waveobs'], normed_spectra['flux'], 'k', alpha=0.3)
plt.plot(corrected_spectra['waveobs'],
corrected_spectra['flux'],
'k',
label='Corrected solution')
plt.plot(O2_spectra['waveobs'], O2_spectra['flux'], 'r', alpha=0.3)
plt.plot(O2_spectra['waveobs'], o2_model, 'r', label='O2 model')
plt.gca().set(title='RV = {:.3f} +- {:.3f}'.format(
lmfit_minimize_result.params['rv'].value,
lmfit_minimize_result.params['rv'].stderr),
xlabel='Wavelength [nm]',
ylabel='Normalized flux')
plt.legend()
plt.xlim(685, 690)
corrected = ispec.correct_velocity(
np.copy(spectra), lmfit_minimize_result.params['rv'].value)
return f, np.array(
[corrected['waveobs'], corrected['flux'],
corrected['err']]).T, lmfit_minimize_result.params[
'rv'].value, lmfit_minimize_result.params['rv'].stderr
def do_fit(self, verbosity=False):
PeakFitter.ith_fit += 1
myfit = Minimizer(self.residual,
self.params,
fcn_args=(self.data_x, ),
fcn_kws={'data_y': self.data_y},
scale_covar=True)
self.result = myfit.leastsq()
self.init = self.residual(self.params, self.data_x)
self.fit = self.residual(self.result.params, self.data_x)
if verbosity:
# print fit details out
report_fit(self.result)
def main():
tmpname = 'data/templates/F0_+0.5_Dwarf.fits'
model = Model(tmpname)
# ftargetname = 'data/spec-4961-55719-0378.fits'
ftargetname = '/home/zzx/workspace/data/xiamen/P200-Hale_spec/blue/reduce_second/specdir/fawftbblue0073.fits'
# new_wo, new_fo, new_eo = specio.read_sdss(ftargetname, lw=3660, rw=10170)
new_wo, new_fo, new_eo = specio.read_iraf(ftargetname)
unit = func.get_unit(new_fo)
new_fo = new_fo / unit
new_eo = new_eo / unit
# new_wo, new_fo, new_eo = specio.read_iraf(targetname)
result = fit(model, new_wo, new_fo, new_eo, show=True, isprint=True)
residual = model.residual
out_parms = result.params
# spec_fit = model.get_spectrum(out_parms, new_wo)
scalepar = model.get_scale_par(out_parms)
parshift = model.get_shift_par(out_parms)
print(parshift[1])
velocity = str(parshift[1] * c.to('km/s'))
print('shift = ' + velocity)
myscale = model.get_scale(new_wo, scalepar)
plt.figure()
plt.plot(new_wo, myscale)
plt.show()
emcee_params = result.params.copy()
# emcee_params.add('__lnsigma', value=np.log(0.1), min=np.log(1.0e-20),
# max=np.log(1.0e20))
result_emcee = minimize(residual,
params=emcee_params,
args=(new_wo, new_fo, new_eo),
method='emcee',
nan_policy='omit',
steps=1000)
report_fit(result_emcee)
plt.plot(new_wo, new_fo)
# plt.plot(new_wo, spec_fit)
spec_emcee = model.get_spectrum(result_emcee.params, new_wo)
plt.plot(new_wo, spec_emcee)
corner.corner(result_emcee.flatchain,
labels=result_emcee.var_names,
truths=list(result_emcee.params.valuesdict().values()))
plt.show()
def perform_fit(exp_volumes,
exp_pressures,
starting_params,
interval,
fix_vo=False,
bm2=False):
volumes = exp_volumes[:, 0]
sigV = exp_volumes[:, 1]
p = exp_pressures[:, 0]
sigP = exp_pressures[:, 1]
uncert = np.column_stack((sigV, sigP))
#initial starting parameters
fit_params = Parameters()
fit_params.add('vo', value=starting_params['vo'], min=0.0)
fit_params.add('ko', value=starting_params['ko'], min=0.0)
fit_params.add('kp', value=starting_params['kp'])
if fix_vo:
fit_params['vo'].vary = False
if bm2:
fit_params['kp'].vary = False
mini = Minimizer(bm3, fit_params, fcn_args=(volumes,), fcn_kws={'data': p,\
'uncert': uncert})
out1 = mini.minimize(method='Nedler')
out2 = mini.minimize(method='leastsq', params=out1.params)
results = out2.params.valuesdict()
plot_volumes = np.linspace((np.min(volumes) - 10), results['vo'], 1000)
fit = bm3(out2.params, plot_volumes)
report_fit(out2, show_correl=True, min_correl=0.001)
PVs = np.column_stack((fit, plot_volumes))
ci = conf_interval(mini, out2)
report_ci(ci)
return ci, mini, out2, PVs
def align_distorted_spectra(ref_spectra, traced_flux, verbose=False):
# First, sort out the two data sets
refx = np.arange(ref_spectra.shape[0])
refy = ref_spectra
datax = np.arange(traced_flux.shape[0])
datay = traced_flux
#plt.close()
#plt.plot(datax,datay, 'r')
#plt.plot(refx,refy, 'b')
#plt.show()
spreader = wavespreader(datax, datay, refx, refy)
dw = np.argmax(datay) - np.argmax(refy)
theta0 = np.array([dw, 3000, 0., 0.])
params = Parameters()
params.add('c0', value=theta0[0], min=theta0[0] - 50, max=theta0[0] + 50)
params.add('c1', value=theta0[1], min=theta0[1] - 10, max=theta0[1] + 10)
params.add('c2',
value=theta0[2],
min=theta0[2] - 1e-1,
max=theta0[2] + 1e-1)
params.add('c3',
value=theta0[3],
min=theta0[3] - 1e-5,
max=theta0[3] + 1e-5)
mini = Minimizer(spreader.residuals_lmfit, params, nan_policy='propagate')
lmfit_minimize_result = mini.minimize(method='differential_evolution')
if verbose:
print('Align distorted spectr fit report')
printfuncs.report_fit(lmfit_minimize_result, min_correl=0.5)
return spreader, lmfit_minimize_result
def test_constraints2():
"""add a user-defined function to symbol table"""
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value,
pars['cen_g'].value, pars['wid_g'].value)
yl = lorentzian(x, pars['amp_l'].value,
pars['cen_l'].value, pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data)/sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) +
lorentzian(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
def width_func(wpar):
""" """
return 2*wpar
myfit.params._asteval.symtable['wfun'] = width_func
try:
myfit.params.add(name='wid_l', expr='wfun(wid_g)')
except:
assert(False)
result = myfit.leastsq()
print(' Nfev = ', result.nfev)
print( result.chisqr, result.redchi, result.nfree)
report_fit(result.params)
pfit= result.params
fit = residual(result.params, x)
assert(pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
assert(pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
assert(pfit['wid_l'].value == 2 * pfit['wid_g'].value)
return model - data
n = 1500
xmin = 0.
xmax = 250.0
random.seed(0)
noise = random.normal(scale=2.80, size=n)
x = linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=13.0, max=20, min=0.0)
fit_params.add('period', value=2, max=10)
fit_params.add('shift', value=0.0, max=pi / 2., min=-pi / 2.)
fit_params.add('decay', value=0.02, max=0.10, min=0.00)
out = minimize(residual, fit_params, args=(x, ), kws={'data': data})
fit = residual(out.params, x)
report_fit(out, show_correl=True, modelpars=p_true)
print('\n\nRaw (unordered, unscaled) Covariance Matrix:')
print(out.covar)
if HASPYLAB:
plt.plot(x, data, 'ro')
plt.plot(x, fit, 'b')
plt.show()
def test_constraints(with_plot=True):
with_plot = with_plot and WITHPLOT
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])
model = yg + yl + pars['line_off'] + x * pars['line_slope']
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 201
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) +
lorentzian(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) +
x*0.5)
if with_plot:
pylab.plot(x, data, 'r+')
pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
result = myfit.leastsq()
print(' Nfev = ', result.nfev)
print( result.chisqr, result.redchi, result.nfree)
report_fit(result.params, min_correl=0.3)
fit = residual(result.params, x)
if with_plot:
pylab.plot(x, fit, 'b-')
assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
assert(result.params['wid_l'].value == 2 * result.params['wid_g'].value)
# now, change fit slightly and re-run
myfit.params['wid_l'].expr = '1.25*wid_g'
result = myfit.leastsq()
report_fit(result.params, min_correl=0.4)
fit2 = residual(result.params, x)
if with_plot:
pylab.plot(x, fit2, 'k')
pylab.show()
assert(result.params['cen_l'].value == 1.5 + result.params['cen_g'].value)
assert(result.params['amp_l'].value == result.params['amp_tot'].value - result.params['amp_g'].value)
assert(result.params['wid_l'].value == 1.25 * result.params['wid_g'].value)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma': sigma, 'data': data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
if HASPYLAB:
pylab.plot(x, init, 'b--')
result = myfit.leastsq()
report_fit(result)
fit = residual(result.params, x)
if HASPYLAB:
pylab.plot(x, fit, 'k-')
pylab.show()
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual,
pfit,
fcn_args=(x, ),
fcn_kws={
'sigma': sigma,
'data': data
},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
if HASPYLAB:
pylab.plot(x, init, 'b--')
result = myfit.leastsq()
report_fit(result)
fit = residual(result.params, x)
if HASPYLAB:
pylab.plot(x, fit, 'k-')
pylab.show()
xmin = 0.
xmax = 250.0
random.seed(0)
noise = random.normal(scale=2.80, size=n)
x = linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=13.0, max=20, min=0.0)
fit_params.add('period', value=2, max=10)
fit_params.add('shift', value=0.0, max=pi/2., min=-pi/2.)
fit_params.add('decay', value=0.02, max=0.10, min=0.00)
out = minimize(residual, fit_params, args=(x,), kws={'data':data})
fit = residual(fit_params, x)
print '# N_func_evals, N_free = ', out.nfev, out.nfree
print '# chi-square, reduced chi-square = % .7g, % .7g' % (out.chisqr, out.redchi)
report_fit(fit_params, show_correl=True, modelpars=p_true)
print 'Raw (unordered, unscaled) Covariance Matrix:'
print out.covar
if HASPYLAB:
pylab.plot(x, data, 'ro')
pylab.plot(x, fit, 'b')
pylab.show()
def slit_fit(nu,
spec,
init_params=None,
lineshape='sGaussian',
power_factor=1.,
eval_only=False,
save_fit=False,
dir_save=None,
file_name=None,
**kwargs):
r"""fitting the experimental slit function with a chosen lineshape
.. attention::
It is recommended to always look for initial parameters by using the
`eval_only` option to roughly match the shape of the experimental slit
function. The built-in initial parameters may not work for all the
cases.
Parameters
----------
nu : 1d array of floats
Spectral positions in [:math:`\mathrm{cm}^{-1}`].
spec : 1d array of floats
Experimentally obtained slit function, usually an isolated atomic line
from a calibration lamp.
init_params : dict, optional
Initial fitting parameters for the lineshape. Refer to
:mod:`carspy.convol_fcn.asym_Voigt` and
:mod:`carspy.convol_fcn.asym_Gaussian` for the required arguments.
lineshape : str, optional
Type of the lineshape, by default 'sGaussian'. Choose between
'sGaussian' and 'sVoigt'.
eval_only : bool, optional
If true, returns the evaluation with given initial parameters.
save_fit : bool, optional
If true, fit results will be saved in a pickle file.
dir_save : str, optional
If `save_fit` is true, a string to the desired directory for saving.
file_name : str, optional
If `save_fit` is true, specify the file name without file extension.
Other Parameters
----------------
**kwargs:
Keyword arguments of the `Model.fit()` method from the module `lmfit`.
Returns
-------
1d array
If `eval_only` is true, the evaluation result is returned.
"""
if lineshape == 'sGaussian':
slit_func = partial(asym_Gaussian, power_factor=power_factor)
elif lineshape == 'sVoigt':
slit_func = partial(asym_Voigt, power_factor=power_factor)
else:
raise ValueError("Please choose between 'sGaussian' and 'sVoigt'")
slit_func.__name__ = 'slit_func'
fit_model = Model(
slit_func,
independent_vars='w',
)
if init_params is None:
init_params = (('w0', 0, True), ('sigma', 2, True, 0.01, 10),
('k', 2, True, 0, 10), ('a_sigma', -0.8, True, -5, 5),
('a_k', 1, True, -5, 5), ('sigma_L_l', 0.1, True, 0.01,
5), ('sigma_L_h', 0.1, True,
0.01, 5), ('offset', 0,
True, 0, 1))
params = fit_model.make_params()
params.add_many(*init_params)
if eval_only:
return fit_model.eval(params, w=nu)
else:
fit_result = fit_model.fit((spec / spec.max())**power_factor,
params,
w=nu,
**kwargs)
report_fit(fit_result, show_correl=True, modelpars=params)
fit_result.plot()
if save_fit and dir_save and file_name:
path_write = Path(dir_save) / (file_name + '.pkl')
pkl_dump(path_write, fit_result)
params_kinetic_seasonal.add("mu_partition",
value=0.5,
min=math.pow(10.0, -6.0),
max=1.0,
vary=True)
params_kinetic_seasonal.add("tau_mu",
value=100.0,
min=1.0,
max=365.0,
vary=True)
kinetic_seasonal_model = Model(SIRD_kinetic_seasonal,
independent_vars=['t', 'x0'])
optimization_method = "differential_evolution" # change to another method if desired
out_kinetic_seasonal = minimize(loss_function,
params_kinetic_seasonal,
args=(
T,
X0,
),
kws={
"model": kinetic_seasonal_model,
"data": data_array
},
method=optimization_method)
report_fit(out_kinetic_seasonal, show_correl=False)
params_json = out_kinetic_seasonal.params.dumps()
with open(optimization_method + "_params.json", mode='w') as fname:
json.dump(params_json, fname)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual,
pfit,
fcn_args=(x, ),
fcn_kws={
'sigma': sigma,
'data': data
},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
if HASPYLAB:
pylab.plot(x, init, 'b--')
myfit.leastsq()
print(' Nfev = ', myfit.nfev)
print(myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(myfit.params)
fit = residual(myfit.params, x)
if HASPYLAB:
pylab.plot(x, fit, 'k-')
pylab.show()
def test_constraints2():
"""add a user-defined function to symbol table"""
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value, pars['cen_g'].value,
pars['wid_g'].value)
yl = loren(x, pars['amp_l'].value, pars['cen_l'].value,
pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) + loren(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) + x * 0.5)
pfit = [
Parameter(name='amp_g', value=10),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='amp_tot', value=20),
Parameter(name='amp_l', expr='amp_tot - amp_g'),
Parameter(name='cen_l', expr='1.5+cen_g'),
Parameter(name='line_slope', value=0.0),
Parameter(name='line_off', value=0.0)
]
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual,
pfit,
fcn_args=(x, ),
fcn_kws={
'sigma': sigma,
'data': data
},
scale_covar=True)
def width_func(wpar):
""" """
return 2 * wpar
myfit.asteval.symtable['wfun'] = width_func
myfit.params.add(name='wid_l', expr='wfun(wid_g)')
myfit.leastsq()
print(' Nfev = ', myfit.nfev)
print(myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(myfit.params)
pfit = myfit.params
fit = residual(myfit.params, x)
assert (pfit['cen_l'].value == 1.5 + pfit['cen_g'].value)
assert (pfit['amp_l'].value == pfit['amp_tot'].value - pfit['amp_g'].value)
assert (pfit['wid_l'].value == 2 * pfit['wid_g'].value)
xmin = 0.
xmax = 250.0
random.seed(0)
noise = random.normal(scale=2.80, size=n)
x = linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=13.0, max=20, min=0.0)
fit_params.add('period', value=2, max=10)
fit_params.add('shift', value=0.0, max=pi/2., min=-pi/2.)
fit_params.add('decay', value=0.02, max=0.10, min=0.00)
out = minimize(residual, fit_params, args=(x,), kws={'data':data})
fit = residual(out.params, x)
print '# N_func_evals, N_free = ', out.nfev, out.nfree
print '# chi-square, reduced chi-square = % .7g, % .7g' % (out.chisqr, out.redchi)
report_fit(out.params, show_correl=True, modelpars=p_true)
print 'Raw (unordered, unscaled) Covariance Matrix:'
print out.covar
if HASPYLAB:
pylab.plot(x, data, 'ro')
pylab.plot(x, fit, 'b')
pylab.show()
def fit(template,
wave,
flux,
err,
params=None,
show=False,
isprint=False,
mask=None):
print('run fit')
if params is None:
params = Parameters()
# set_pars(params, 'shift', [0, 1], valuelst=[1.16, -0.00076])
shiftparname = set_pars(params, 'shift', [1], valuelst=[0.0])
# sigmaparname = set_pars(params, 'sigma', [1], valuelst=[0.00001],
# minlst=[1.0e-8], maxlst=[5.0e-4])
scalevalst = [1.0, -1.0, -1.0, 0.22, -0.1, -0.13]
scaleparname = set_pars(params, 'scale', 5, valuelst=scalevalst)
# template.set_lmpar_name(scaleparname, sigmaparname, shiftparname)
template.set_lmpar_name(scaleparname, None, shiftparname)
# start = time.process_time()
# print(start)
if mask is not None:
argsel = func.mask(wave, mask)
# print('len wave, flux, err')
# print(len(wave))
# print(len(flux))
# print(len(err))
def residual(pars, x, data, eps):
# print('flag')
# print(pars)
# print(x)
# print('length of template is ')
# print(len(template.wave))
flux_fit1 = template.get_spectrum(pars, x)
# print(len(flux_fit1))
# arrpar = read_lmpar(pars, sigmaparname)
# flux_fit2 = np.array(convol.gauss_filter(x, data, arrpar))
if mask is not None:
return ((flux_fit1 - data) / eps)[argsel]
return (flux_fit1 - flux_fit2) / eps
# out = minimize(template.residual, params, args=(wave, flux, err),
# method='leastsq')
# end = time.process_time()
# print("Time used:", end-start)
out = minimize(residual, params, args=(wave, flux, err), method='leastsq')
if isprint:
report_fit(out)
# shift = out.params['shift1'].value * c
# shifterr = out.params['shift1'].stderr * c
# print('-'*20+' velocity '+'-'*20)
# print(shift.to('km/s'))
# print(shifterr.to('km/s'))
if show:
plt.figure()
# arrpar = read_lmpar(out.params, sigmaparname)
# print('gaussian filter par = ')
# print(arrpar)
plt.plot(wave, flux)
spec_fit = template.get_spectrum(out.params, wave)
# lower = spec_fit - err
# upper = spec_fit + err
#
# plt.fill_between(wave, lower, upper, alpha=0.3, color='grey')
plt.plot(wave, spec_fit)
plt.show()
return out
if data is None:
return model
return model - data
###############################################################################
# Generate synthetic data and initialize fitting Parameters:
random.seed(0)
x = linspace(0, 250, 1500)
noise = random.normal(scale=2.8, size=x.size)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=13, max=20, min=0)
fit_params.add('period', value=2, max=10)
fit_params.add('shift', value=0, max=pi/2., min=-pi/2.)
fit_params.add('decay', value=0.02, max=0.1, min=0)
###############################################################################
# Perform the fit and show the results:
out = minimize(residual, fit_params, args=(x,), kws={'data': data})
fit = residual(out.params, x)
###############################################################################
report_fit(out, modelpars=p_true)
###############################################################################
plt.plot(x, data, 'o', label='data')
plt.plot(x, fit, label='best fit')
plt.legend()
Parameter(name='line_off', value=0.0)]
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
if HASPYLAB:
pylab.plot(x, init, 'b--')
myfit.leastsq()
print(' Nfev = ', myfit.nfev)
print( myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(myfit.params)
fit = residual(myfit.params, x)
if HASPYLAB:
pylab.plot(x, fit, 'k-')
pylab.show()
def test_constraints(with_plot=True):
with_plot = with_plot and WITHPLOT
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value, pars['cen_g'].value,
pars['wid_g'].value)
yl = lorentzian(x, pars['amp_l'].value, pars['cen_l'].value,
pars['wid_l'].value)
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = yg + yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data) / sigma
n = 201
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
data = (gaussian(x, 21, 8.1, 1.2) + lorentzian(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=n) + x * 0.5)
if with_plot:
pylab.plot(x, data, 'r+')
pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual,
pfit,
fcn_args=(x, ),
fcn_kws={
'sigma': sigma,
'data': data
},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
myfit.leastsq()
print(' Nfev = ', myfit.nfev)
print(myfit.chisqr, myfit.redchi, myfit.nfree)
report_fit(myfit.params, min_correl=0.3)
fit = residual(myfit.params, x)
if with_plot:
pylab.plot(x, fit, 'b-')
assert (myfit.params['cen_l'].value == 1.5 + myfit.params['cen_g'].value)
assert (myfit.params['amp_l'].value == myfit.params['amp_tot'].value -
myfit.params['amp_g'].value)
assert (myfit.params['wid_l'].value == 2 * myfit.params['wid_g'].value)
# now, change fit slightly and re-run
myfit.params['wid_l'].expr = '1.25*wid_g'
myfit.leastsq()
report_fit(myfit.params, min_correl=0.4)
fit2 = residual(myfit.params, x)
if with_plot:
pylab.plot(x, fit2, 'k')
pylab.show()
assert (myfit.params['cen_l'].value == 1.5 + myfit.params['cen_g'].value)
assert (myfit.params['amp_l'].value == myfit.params['amp_tot'].value -
myfit.params['amp_g'].value)
assert (myfit.params['wid_l'].value == 1.25 * myfit.params['wid_g'].value)
def ls_fit(self, add_params=None, path_fit=None, show_fit=False,
eval_only=False, **kwargs):
"""
Fitting the experimental CARS spectrum.
.. attention::
The least-quare fit module ``lmfit`` is necessary for this method.
Please be aware that certain Python versions may not be supported
by ``lmfit``. For displaying the fit results ``matplotlib`` will be
needed as well.
Parameters
----------
add_params : nested tuple, optional
List of parameters controlling the fitting process. This option can
be used to modify these initial parameters:
.. code-block:: python
(('temperature', 2000, True, 250, 3000),
('del_Tv', 0, False),
('x_mol', 0.6, x_mol_var, 0.2, 1.5),
('nu_shift', fit_params['nu_shift'], False),
('nu_stretch', fit_params['nu_stretch'], False),
('pump_lw', fit_params['pump_lw'], False),
('param1', fit_params['param1'], False),
('param2', fit_params['param2'], False),
('param3', fit_params['param3'], False),
('param4', fit_params['param4'], False),
('param5', fit_params['param5'], False),
('param6', fit_params['param6'], False))
Each element of the nested tuple has the following element in
order:
variable_name : str
All the arguments of
:mod:`carspy.cars_fit.CarsFit.cars_expt_synth`
are admissible variables except for the independent
variable `nu_expt`.
initial_guess : float
Initial guess or fixed value set for this variable.
variable : bool
Determine if the variable is fixed (False) or not (True)
during the fit.
lower_bound : float
Lower boundary for the fitting variable. If not provided,
negative infinity will be assumed.
upper_bound : float
Upper boundary for the fitting variable. If not provide,
positive infinity will be assumed.
For more details refer to the documentation of ``lmfit.Model``.
path_fit : str
Path to the `.pkl` file of fitting result created by
:mod:`carspy.cars_fit.CarsFit.save_fit`. This allows importing
the fitting result of an existing spectrum, such that the inferred
values of certain parameters (such as those related to the
spectrometer) could be re-used in the next fit. A standard use case
for this would be the fitting result of a room-temperature
spectrum. This is needed if the `fit` in `fit_mode` of
:mod:`carspy.cars_fit.CarsFit` is set to `T_x`.
show_fit : bool, optional
If True, the fitting results will be reported and plotted. This is
done via built-in functions in ``lmfit``.
"""
# general setup
fit_model = Model(self.cars_expt_synth, independent_vars=['nu_expt'])
initi_params = []
# different fitting modes
if self.fit_mode['fit'] == 'T_x':
if path_fit is None:
raise ValueError("Please provide path to a .pkl file "
"containing the fitting result of a spectrum")
if self.fit_mode['chem_eq']:
x_mol_var = False
else:
x_mol_var = True
fit_params = pkl_load(path_fit).params
initi_params = (('temperature', 2000, True, 250, 3000),
('del_Tv', 0, False),
('x_mol', 0.6, x_mol_var, 0.2, 1.5),
('nu_shift', fit_params['nu_shift'], False),
('nu_stretch', fit_params['nu_stretch'], False),
('pump_lw', fit_params['pump_lw'], False),
('param1', fit_params['param1'], False),
('param2', fit_params['param2'], False),
('param3', fit_params['param3'], False),
('param4', fit_params['param4'], False),
('param5', fit_params['param5'], False),
('param6', fit_params['param6'], False))
if self.fit_mode['fit'] == 'custom':
if add_params is None:
raise ValueError("Please specify fitting parameters first "
"using add_params")
params = fit_model.make_params()
params.add_many(*initi_params)
if add_params is not None:
params.add_many(*add_params)
if eval_only:
return fit_model.eval(params, nu_expt=self.nu)
else:
self.fit_result = fit_model.fit(np.nan_to_num(self.spec_cars),
params,
nu_expt=self.nu, **kwargs)
if show_fit:
report_fit(self.fit_result, show_correl=True, modelpars=params)
self.fit_result.plot()
def fit_lamost():
bluelst, redlst = [], []
namelst = glob.glob('/home/zzx/workspace/data/stellar_X/*.fits')
namelst = [
'/home/zzx/workspace/data/stellar_X/med-58409-TD045606N223435B01_sp16-102.fits'
]
for name in namelst:
# fig1 = plt.figure()
# fig2 = plt.figure()
# ax1 = fig1.add_subplot(111)
# ax2 = fig2.add_subplot(111)
print(name)
size = len(fits.open(name))
for ind in range(3, size):
spec = specio.Spectrum(name, ind)
spec.clean_cosmic_ray()
if 'B' in spec.header['EXTNAME']:
bluelst.append(spec)
else:
redlst.append(spec)
name = namelst[0]
model_blue = Model(name, 3)
model_blue.clean_cosmic_ray()
model_red = Model(name, 11)
model_red.clean_cosmic_ray()
params = Parameters()
shiftparname = set_pars(params, 'shift', [1], valuelst=[0.0])
scalevalst = [
0.99608100, -0.00931768, 0.00319284, 5.5658e-04, -4.4060e-04, 0.0
]
bscaleparname = set_pars(params, 'b_scale', 5, valuelst=scalevalst)
rscaleparname = set_pars(params, 'r_scale', 5, valuelst=scalevalst)
bsimgapar = set_pars(params, 'b_sigma', [1], valuelst=[0.0004])
rsigmapar = set_pars(params, 'r_sigma', [1], valuelst=[0.0004])
model_blue.set_lmpar_name(bscaleparname, bsimgapar, shiftparname)
model_red.set_lmpar_name(rscaleparname, rsigmapar, shiftparname)
shiftlst, shifterrlst = [], []
def residual(pars, x1, data1, eps1, x2, data2, eps2):
res1 = model_blue.residual(pars, x1, data1, eps1)
res2 = model_red.residual(pars, x2, data2, eps2)
return np.append(res2, res1)
return res2
for ind in range(len(redlst)):
bspec = bluelst[ind]
# bspec = redlst[ind]
rspec = redlst[ind]
arg1 = func.select(bspec.wave, [[4920, 5300]])
bnw = bspec.wave[arg1]
bnf = bspec.flux[arg1]
bne = bspec.err[arg1]
arg2 = func.select(rspec.wave, [[6320, 6860]])
rnw = rspec.wave[arg2]
rnf = rspec.flux[arg2]
rne = rspec.err[arg2]
bfakeerr = np.ones(len(bnw), dtype=np.float64) * 0.01
rfakeerr = np.ones(len(rnw), dtype=np.float64) * 0.01
bne = bfakeerr
rne = rfakeerr
# out = minimize(model_blue.residual, params, args=(nw, nf))
# out = minimize(model_red.residual, params, args=(nw, nf))
out = minimize(residual, params, args=(bnw, bnf, bne, rnw, rnf, rne))
report_fit(out)
shiftlst.append(out.params['shift1'].value * c)
shifterrlst.append(out.params['shift1'].stderr * c)
plt.figure()
spec_fit_blue = model_blue.get_spectrum(out.params, model_blue.wave)
spec_fit_red = model_red.get_spectrum(out.params, model_red.wave)
plt.plot(bnw, bnf)
plt.plot(model_blue.wave, spec_fit_blue)
plt.figure()
plt.plot(rnw, rnf)
plt.plot(model_red.wave, spec_fit_red)
plt.show()
for ind, value in enumerate(shiftlst):
# print(value.to('km/s'))
print(value.to('km/s'), shifterrlst[ind].to('km/s'))
