fit_seq

fit seq: fitting tscan data using the solution of sequtial decay equation covolved with gaussian/cauchy(lorenzian)/pseudo voigt irf function. It uses lmfit python module to fitting experimental time trace data to sequential decay module. To find contribution of each excited state species, it solves linear least square problem via scipy lstsq module.

It supports 4 types of sequential decay

  • Type 0: both raising and decay GS -> 1 -> 2 -> ... -> n -> GS

  • Type 1: no raising 1 -> 2 -> ... -> n -> GS

  • Type 2: no decay GS -> 1 -> 2 -> ... -> n

  • Type 3: Neither raising nor decay 1 -> 2 -> ... -> n

Note

  • The number of time zero parameter should be same as the number of scan to fit.

  • If you set shape of irf to pseudo voigt (pv), then you should provide two full width at half maximum value for gaussian and cauchy parts, respectively.

  • type 0 sequential decay needs n+1 lifetime

  • type 1, 2 sequential decay needs n lifetime

  • type 3 sequential decay needs n-1 lifetime

  • usage: fit_seq.py [-h] [-sdt SEQ_DECAY_TYPE] [–irf {g,c,pv}] [–fwhm_G FWHM_G] [–fwhm_L FWHM_L] [-t0 TIME_ZEROS [TIME_ZEROS …]] [-t0f TIME_ZEROS_FILE] [–tau [TAU [TAU …]]] [–fix_irf] [–slow] [-o OUT] prefix

  • positional arguments:

    • prefix prefix for tscan files It will read prefix_i.txt

  • optional arguments:

    • -h, –help show this help message and exit

    • -sdt SEQ_DECAY_TYPE, –seq_decay_type SEQ_DECAY_TYPE

      • type of sequential decay

      1. type 0: GS -> 1 -> 2 -> … -> n -> GS (both raising and decay)

      2. type 1: 1 -> 2 -> … -> n -> GS (No raising)

      3. type 2: GS -> 1 -> 2 -> … -> n (No decay)

      4. type 3: 1 -> 2 -> … -> n (Neither raising nor decay)

    • Default option is type 0 (both raising and decay)

    • –irf {g,c,pv} shape of instrument response function

      1. g: gaussian distribution

      2. c: cauchy distribution

      3. pv: pseudo voigt profile, linear combination of gaussian distribution and cauchy distribution pv = eta*c+(1-eta)*g the mixing parameter is fixed according to Journal of Applied Crystallography. 33 (6): 1311–1316.

    • –fwhm_G FWHM_G full width at half maximum for gaussian shape It should not used when you set cauchy irf function

    • –fwhm_L FWHM_L full width at half maximum for cauchy shape It should not used when you did not set irf or use gaussian irf function

    • -t0 TIME_ZEROS [TIME_ZEROS …], –time_zeros TIME_ZEROS [TIME_ZEROS …] time zeros for each tscan

    • -t0f TIME_ZEROS_FILE, –time_zeros_file TIME_ZEROS_FILE filename for time zeros of each tscan

    • –tau [TAU [TAU …]] lifetime of each decay

    • –fix_irf fix irf parameter (fwhm_G, fwhm_L) during fitting process

    • –slow use slower but robust global optimization algorithm

    • -o OUT, –out OUT prefix for output files

Parameter bound scheme

  • fwhm: temporal width of x-ray pulse

    • lower bound: 0.5*fwhm_init

    • upper bound: 2*fwhm_init

  • t_0: timezero for each scan

    • lower bound: t_0 - 2*fwhm_init

    • upper bound: t_0 + 2*fwhm_init

  • tau: life_time of each component

    • if tau < 0.1

      • lower bound: tau/2

      • upper bound: 1

    • if 0.1 < tau < 10

      • lower bound: 0.05

      • upper bound: 100

    • if 10 < tau < 100

      • lower bound: 5

      • upper bound: 500

    • if 100 < tau < 1000

      • lower bound: 50

      • upper bound: 2000

    • if 1000 < tau < 5000 then

      • lower bound: 500

      • upper bound: 10000

    • if 5000 < tau < 50000 then

      • lower bound: 2500

      • upper bound: 100000

    • if 50000 < tau < 500000 then

      • lower bound: 25000

      • upper bound: 1000000

    • if 500000 < tau < 1000000 then

      • lower bound: 250000

      • upper bound: 2000000

    • if 1000000 < tau then

      • lower bound: tau/4

      • upper bound: 4*tau

Mixing parameter eta

For pseudo voigt IRF function, mixing parameter eta is guessed to

\[\begin{equation*} \eta = 1.36603({fwhm}_L/f)-0.47719({fwhm}_L/f)^2+0.11116({fwhm}_L/f)^3 \end{equation*}\]

where

\[\begin{align*} f &= ({fwhm}_G^5+2.69269{fwhm}_G^4{fwhm}_L+2.42843{fwhm}_G^3{fwhm}_L^2 \\ &+ 4.47163{fwhm}_G^2{fwhm}_L^3+0.07842{fwhm}_G{fwhm}_L^4 \\ &+ {fwhm}_L^5)^{1/5} \end{align*}\]

This guess is according to J. Appl. Cryst. (2000). 33, 1311-1316