FIT.KUMAC Documentation

The PAW macro FIT.KUMAC is an easy interface to fit several functions to a histogram. The general syntax for calling FIT is as follows:

PAW> exec fit  HID[(low:up)]  FCT_EXPR  BG_FST  [PAR1]...[PARn]

• HID

number of an histogram to be fitted. Optionally, a fit range may be specified analogously to HISTO/PLOT. Note that INTEGER values correspond to channel numbers, while REAL values correspond to the abscissa.

• FCT_EXPR

is a function expression, analogously to HISTO/FIT. Valid functions presently are:

• G    for Gauss distribution
• BW   for Breit-Wigner distribution
• Pn   for polynomial of order n
• LBG  for a polynomial background model of leading order
These functions may be summed up in arbitrary order. Functions preceded by an ampersand '&', are marked as background functions and drawn separately in the histogram after the fit.
• BG_FST

activates (1) or deactivates (0) a fit of the specified background functions before fitting the whole function.

• PAR1 ... PARn

is the optional list of the start values for the fit parameters. A valid expression is one of the following:

 

1	<value>	an integer or real value as explicit initialization for a single parameter
2	<value>F	as (1), but the parameter is fixed during the fit
3	<value>(low:up)	as (1), but the parameter is bounded to the interval [low;up]
4	!	a parameter's value of the last iteration is taken as the start value for the next iteration (default). NB : This is only the case, if the function expression was not changed since last fit.
5	F	as (4), but the parameter is fixed during the fit
6	(low:up)	as(4), but the parameter is bounded to the interval [low;up]

 

As mentioned in (1), background functions may be specified by precedence of an '&'. This is advantageous in some cases:

• in addition to the total function, the background function is drawn in the histogram after the fit. This can be helpful in deciding, whether the model of the background is adequate.
• the histogram 999999 is filled with the background function and is available for further operations.
• histogram 999998 contains the difference of original and background histograms and is in the case of 'good' fit the signal. Thus, the intensity of a signal can be derived without integrating any explicit distribution (this is helpful in case of asymmetric signals)

The package consists of two files:

FIT.KUMAC is a KUIP-macro which contains the directives to PAW. FUNCTION_FIT_HISTOGRAM.FOR   is a FORTRAN file, in which the functions are implemented. Both communicate via the COMIS interface, using common blocks and vectors. The FORTRAN routine uses several vectors declared in FIT.KUMAC:

• VECTOR PARAMETER_VEC(100)  is the vector containing the fitted parameters, visible to the user. Internally, the vector PARAM_VEC(100) is used and passed to the routine via the COMMON-block /PAWPAR/.
• VECTOR PARAM_FUNCTION_VEC(20) passes integer values as function codes. Those are defined as global macros in PAW (CONST_BREITWIGNER etc.) as well as constants in the FORTRAN Routine (MY_CONST_BREITWIGNER etc.)
• VECTOR PARAM_FUNCTION_DIMENSION_VEC(20) passes the dimension of the functions, which are defined only in  FIT.KUMAC.
• VECTOR PARAM_USE_FCT(20) passes 0 or 1 for every function.
• For each Function. Correspondingly its value is or is not added to the return value of FUNCTION_FIT_HISTOGRAM.FOR. Thus, the function value of the background function can be fitted or plotted separately.

PAW> FUNCTION/PLOT FUNCTION_FIT_HISTOGRAM.FOR <low> <up>