sasfit4 - fitting peaks in sequences of SANS data

sasfit4 - fitting up to four peaks for sequences of SANS data

version 1.3 R. Ghosh, ILL, April 2000

Summary

This program uses the fitfun package to refine the starting parameters for fitting a sequence of diffraction patterns. A sequence of single runs with the same extension can then be analysed or runs which have been sectored with several resulting file extensionnumbers. Simple graphics are incorporated to enable the variation of derived peak parameters to be viewed and printed.

The program fits up to four peaks, Gaussian, Lorentzian or Voigt profiles, which allow an interesting peak to be analysed when it is merging with other unchanging peaks.

Fitting Sequences

There are two methods for fitting data (T or U). In the first case the trial fit parameters are re-used again and again. In the second, the previous fit serves as a starting point for the next in sequence. The first works well when the peak does not move. The second will follow a peak moving as the sequence evolves

Example of sasfit4

is1 109% sasfit4

 sasfit4   v1.3  April 2000 (Ron Ghosh, ILL)


 Options: 
        F          Fit one spectrum (manual fitfun)
                    + other options - plots/cursor etc
        U  i j k l Treat a set of runs i to j
                     and extensions k to l
                   Updating parameters
        T  i j k l Treat a set of runs i to j
                     and extensions k to l
                   (re-use initial fitfun parameters)
        D  j k     Display sequence results
        C          Cursor for next plot (toggle)
        P  j k     PostScript file of seq. plot
        H          for help
        E          Exit

Typically the user must use option F to choose some regrouped data to examine and trial fit an initial pattern: At this stage the program enters the fitfuns routines and a secondary choice of options is offered.



 SEQfit option F,C,D,P,T,U, Help or Exit : f            


 Manual peak fitting and parameter initialisation

 Peak type :
           1 Single Gaussian
           2 Single Lorenztian
           3 Voigt - Lorenztian width shown
 Width values are half width at half height
 Background is value at centre of first peak


 Command J for component  plots

 fit4               version  1.1
 TYPE HELP OR OPTION: H,R,D,X,Y,V,F,O,P,L,W,C,E,J,S,T,Z
 fit4>h
 fit4 Version  1.1 (using FITFUN-6.4)    6-Apr-2000 17:34:18

 sasfit4  fitting peaks to diffraction data

 PEAK TYPE 1 Single Gaussian
           2 Single Lorentzian
           3 Voigt - Lorentzian width shown
 Width values are half width at half height

 Command J for component  plots


 Basic fitting and control commands
 H              type this list
 R              read in fresh data
 D              display data
 X min max      change current x-scale to min<x<max
                if min and max are 0, show current limits
 Y min max      change current y-scale to min<y<max  etc.
 V n v s        change parameter number n to v
                with associated step s (about 1.0) if
                this is to be fitted.
                if s is negative parameter n is tied
                to preceding parameter #-s
 V              (no parameters) list current values
 F n (N)        fit n iterations (0 to show current curve)
                N (optional) for no plot while fitting
 O a b c d e f  only fit spectrum between range of a<x<b
                and c<x<d etc. (ignored if both are zero)
 P              plot fit and data on hardcopy
 W flnme        write fit and data onto output file flname.fpl
 L (F)          list last fit (F for full listing)
 S              save current parameters
 C              enable/disable cursor(in next plot)
 Z              clear screen
 T extra text   set manual title for graphs
 J              jump to special routine
 E              EXIT from program.
 TYPE HELP OR OPTION: H,R,D,X,Y,V,F,O,P,L,W,C,E,J,S,T,Z
 fit4>r
        GIVE  RUN NUMBER ... EXT : 54498
 C12E4 B10 60% ch 90 
            62 values of I(Q) have been read in.
 THERE ARE   21 DATA POINTS IN CURRENT FITTING RANGE
 TYPE HELP OR OPTION: H,R,D,X,Y,V,F,O,P,L,W,C,E,J,S,T,Z
 fit4>d

 TYPE HELP OR OPTION: H,R,D,X,Y,V,F,O,P,L,W,C,E,J,S,T,Z
 TYPE HELP OR OPTION: H,R,D,X,Y,V,F,O,P,L,W,C,E,J,S,T,Z
 fit4>v
 FITFUN 6.4  TITLE:Run 54498  ext.  0  C12E4 B10 60% ch 90           
 FITTING Y : Intensity              VERSUS X : Q A-1               
 NUMBER  PARAMETER   VALUE    (  OLD VALUE )     STEP     % DEVIATION 
    1   FLAT BGD     60.21    (   60.21    )   1.000          0.00
    2   slope BG    -460.6    (  -460.6    )   5.000          0.00
    3   Vgauwdth    0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
    4   FACTOR F    0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
    5   P1 type      1.000    (   1.000    )  0.0000E+00      0.00
    6   P1 area      14.39    (   14.39    )   1.000          0.00
    7   P1 width    0.6912E-02(  0.6912E-02)   1.000          0.00
    8   P1 posn     0.1078    (  0.1078    )   1.000          0.00
    9   P2 type     0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   10   P2 area     0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   11   P2 width    0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   12   P2 posn     0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   13   P3 type     0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   14   P3 area     0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   15   P3 width    0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   16   P3 posn     0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   17   P4 type     0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   18   P4 area     0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   19   P4 width    0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
   20   P4 posn     0.0000E+00(  0.0000E+00)  0.0000E+00      0.00
  100     MAXIMUM STEP    100.0       300  SUBSTEP   0.01000
  200     ACCURACY      0.1000E-01
 THERE ARE  21 POINTS IN THE CURRENT RANGE SET BY "ONLY" COMMAND.
 CURRENT LIMITS (IF RANGE IS NON-ZERO) ARE : 
  0.650E-01 TO 0.150      0.000E+00 TO 0.000E+00  0.000E+00 TO 0.000E+00
 TYPE HELP OR OPTION: H,R,D,X,Y,V,F,O,P,L,W,C,E,J,S,T,Z
 fit4>v 6 10 1
 fit4>s
 fit4>f 100

 FITTING.....

 .....ENDED
 TYPE HELP OR OPTION: H,R,D,X,Y,V,F,O,P,L,W,C,E,J,S,T,Z

Having now obtained a good set of starting parameters for fitting the sequence this is now performed:

 fit4>e

 SEQfit option F,C,D,P,T,U, Help or Exit : t 54498 54505
   run    ext  Backgr   %         Area   %    Width  %  Position  %     B-Slope    B-Con.  fit 
  54498    0  60.07500  18.7      14.4  2.83 0.0069  2.62 0.10779  0.16 -464.385   60.075  0
  54499    0 108.42580  35.5      36.3  8.18 0.0072  2.09 0.10738  0.20 -613.967  108.426  0
  54500    0 120.86198  47.2      40.8  9.69 0.0072  3.05 0.10787  0.20 -797.150  120.862  0
  54501    0 119.89059  39.1      42.0  9.38 0.0072  2.62 0.10821  0.19 -660.759  119.891  0
  54502    0 113.64807  37.5      41.8  9.09 0.0071  6.88 0.10842  0.23 -613.890  113.648  0
  54503    0 113.38006  35.1      41.4  8.96 0.0071  3.31 0.10854  0.21 -580.074  113.380  0
  54504    0 117.37156  39.6      41.2  9.20 0.0071  3.64 0.10850  0.19 -672.662  117.372  0
  54505    0 118.80327  50.6      40.9 10.22 0.0071  2.68 0.10833  0.25 -788.728  118.803  0
 SEQfit option F,C,D,P,T,U, Help or Exit : d 1 8

 SEQfit option F,C,D,P,T,U, Help or Exit : p 1 8
 SEQfit option F,C,D,P,T,U, Help or Exit : e
 Closing listing file d164709.lis
 Closing listing file d164708.res
 %PGPLOT,  Closing file fit4707.ps

Summary of using fitfun to set up initial parameters

The pattern is read-in using the R command.

The fitfun package offers a D (display option) to view the input data and cursors/scale settings etc. as well as the ability to trial fit the data manually, and with a number of automatic iterations.

The current parameters are listed with the V command. The starting parameters can be modified with the V command setting an initial non-zero step if the parameter is to be refined. Normally the step is about unity. This is used as a local multiplier for the standard step defined in parameter 300 (typically 2%). When the fit appears very sensitive to the step size then reduce the individual parameter step, say to 0.05. If the fit appears very insensitive to the step increase the individual parameter step by a factor of say 20. Do not attempt to set steps for the parameters which control the type of model fit!

The current variables can be saved with the S command manually. These will be reread should the program be interrupted and restarted.

The fit is then started limiting the number of iterations to a maximum of 100.

When the fit terminates these parameters can be transferred to the sequence treatment by exiting E from this manual phase. The results are stored temporarily.

Fitting a sequence of SANS regrouped data files

The principal program options now reappear and a sequence of runs and subpatterns may then be treated with the T or U command depending on whether the starting parameters are to be reinitialised or not. The program will treat ascending or descending series, to allow the best, but disappearing, peaks to be used to set the initial search state. When fitting becomes progressively more difficult certain parameters, notably the position, should be held fixed (step 0.0) which will limit the program from diverging when the peak is really difficult to resolve distinctly.

The D command allows any of the fitted parameters to be plotted as a function of run number (D 1 n or extension number D 2 n. A hardcopy PostScript plot is generated using the P command similarly.

The program produces a listing file of the summary, and the plot file is a PostScript plot. For spread-sheet use a summary file of twenty columns is produced including data on backgrounds. The flat background value is set at the center of the first peak (parameter 8).

The final column contains a fit result. Usually this is 0, indicating that a minimum has been found without any problems. When set to 1 the final fit may not be the absolute minimum because the step sizes are typically too small for peak areas, or too large for positions. The manual fitfun option F can be used to modify this, or to examine the fit for any individual component, by opening that data file O, going back into fitfun F, and selecting the subspectrum in doubt, and reperforming the fit.

Environment Variables used by the program

sasfit4 uses environment variables to avoid repitition of questions concerning which type of graphics to use etc. Typical commands to set up this environment are:

setenv PGPLOT_DIR /usr/ill/lib
setenv PGPLOT_ILL_DEV_1 /xserv
setenv PGPLOT_ILL_DEV_2 /VCPS
setenv PGPLOT_ILL_PPAGE 2

These control the graphical output.

Feedback on these programs will be welcomed by the author,
Ron Ghosh, reghosh (at) gmail.com