Simultaneous vs sequential fit¶

pymultipleis offers a fit_sequential() method for fitting individual spectra with or without a dependence. It is based on the regular complex nonlinear least squares and uses the least-squares minimization algorithm from the jaxopt API .

1: Preserving correlation between parameters¶

For simpler models, it is possible to observe tendencies of parameter changes using both fit_sequential() and the simultaneous fit methods.

a. Nyquist plot¶

_images/seq_all_impedance.png — A sequential fit on all spectra¶

_images/simul_impedance.png — A simultaneous fit¶

b. Parameter plot¶

_images/seq_all_params.png — A sequential fit on all spectra¶

However as the model becomes more complicated or the spectra noisier, fit_sequential() becomes more susceptible to jumps in the values of the parameters and therefore loses the ability to preserve the dependence between spectra. This is where the fit_simultaneous() method becomes essential. This method preserves the correlation between parameters, is slightly less sensitive to initial values and can be used to obtain a reasonable initial guesses. Basically, the idea is to initially fit the data with fit_simultaneous() and then run fit_sequential() or fit_simultaneous_zero(). A detailed example can be found in the Examples page.

eis_her_sequential = pym.Multieis(p0, F_her, Y_her, bounds, smf_modulus, her, weight= Yerr, immittance='admittance')
eis_her_sequential.fit_sequential()
eis_her_sequential.plot_params()

_images/seq_only_params.png — Sequential fit only¶

eis_her_simultaneous = pym.Multieis(p0, F_her, Y_her, bounds, smf_modulus, her, weight= 'modulus', immittance='admittance')
popt, perr, chisqr, chitot, AIC = eis_her_simultaneous.fit_simultaneous()
popt, perr, chisqr, chitot, AIC = eis_her_simultaneous.fit_sequential()
eis_her_simultaneous.plot_params()

_images/simul_plus_seq_params.png — Simultaneous fit followed by sequential fit¶

2. Fitting a subset of the sequence of data¶

The fit_sequential() offers a possibility to fit only a subset of the total spectra based on the index of the spectra.

popt, perr, chisqr, chitot, AIC = eis_redox_sequential.fit_sequential(indices=[1, 2, 15, 25, 45])
eis_redox_sequential.plot_nyquist()
eis_redox_sequential.plot_params(show_errorbar = False, labels = labels)

_images/seq_select_impedance.png — A sequential fit on selected spectra¶

_images/seq_select_params.png — Parameter trend obtained from sequential fit of selected spectra¶

More examples on using fit_sequential() can be found in the Examples page.