res_hess_decay

TRXASprefitpack.res.res_hess_decay()[source]

Hessian for fitting multiple set of time delay scan with the sum of convolution of exponential decay and instrumental response function

Parameters:

  • x0 –

    initial parameter, if irf == ‘g’,’c’:

    • 1st: fwhm_(G/L)

    • 2nd to \(2+N_{scan}\): time zero of each scan

    • \(2+N_{scan}\) to \(2+N_{scan}+N_{\tau}\): time constant of each decay component

    if irf == ‘pv’:

    • 1st and 2nd: fwhm_G, fwhm_L

    • 3rd to \(3+N_{scan}\): time zero of each scan

    • \(3+N_{scan}\) to \(3+N_{scan}+N_{\tau}\): time constant of each decay component

  • num_comp – number of exponential decay component (except base)

  • base – whether or not include baseline (i.e. very long lifetime component)

  • irf –

    shape of instrumental response function

    • ’g’: normalized gaussian distribution,

    • ’c’: normalized cauchy distribution,

    • ’pv’: pseudo voigt profile \((1-\eta)g(f) + \eta c(f)\)

    For pseudo voigt profile, the mixing parameter \(\eta(f_G, f_L)\) and uniform fwhm paramter \(f(f_G, f_L)\) are calculated by calc_eta and calc_fwhm routine

  • tau_mask (sequence of boolean np.ndarray) – whether or not include jth time constant in ith dataset fitting (tau_mask[i][j]) If base is True, size of tau_mask[i] should be num_tau+1.

  • t – time points for each data set

  • intensity – sequence of intensity of datasets

  • eps – sequence of estimated error of datasets

Returns:

Hessian of scalar residual function \((\frac{1}{2}\sum_i {res}^2_i)\) based on the seperation scheme