More on fits

Fit the function  sin
4     APPLICATION SIGMA                                                                        
4        alpha=array(100,0#2*PI)                                                               
4        sina=sin(alpha)+rndm(alpha)*0.1                                                       
4        err=array(100,0.1#0.1)                                                                
4     EXIT                                                                                     
      zone 2 2
1     V/FIT ALPHA(1:50) SINA(1:50) ERR(1:50) G                                                 
1     V/FIT ALPHA SINA ERR P3                                                                  
1     V/FIT ALPHA SINA ERR P5                                                                  
      v/create par(1) r 10.
2     V/FIT ALPHA SINA ERR SINFIT.F ! 1 PAR                                                    
3     V/PRI PAR

In this macro two different types of predefined fits are used: Gaussian, Polynomial. As we will see later, the histograms fitting command HISTO/FIT has exactly the same syntax except that the 3 vectors are replaced by an unique parameter: the histogram identifier. On histograms some other minimization mechanisms are available via the commands SPLINE , SMOOTH , etc.. .

It is also possible to defined specific functions. Here the function SINFIT is defined as follow:

The function  SINFIT
      function sinfit(x)
      common /pawpar/ par(1)
      sinfit=par(1)*sin(x)
      end

This VECT/PRI shows that now PAR(1) is close to 1.
```
      PAR(1) = 0.994221
```
Vector initialization with SIGMA. We will see other SIGMA examples later.
Try to modify the macro and the COMIS program sinfit.f to have a fit with two parameters in order to improve the quality of the fit.

Output of the Gaussian fit
     **********************************************
     *                                            *
     * Function minimization by SUBROUTINE HFITV  *
     * Variable-metric method                     *
     * ID =          0  CHOPT =                   *
     *                                            *
     **********************************************
 Convergence when estimated distance to minimum (EDM) .LT.   .10E-03

 FCN=   2221.676     FROM MIGRAD    STATUS=CONVERGED    239 CALLS      240 TOTAL

                     EDM=   .85E-05    STRATEGY= 1      ERROR MATRIX ACCURATE

  EXT PARAMETER                                   STEP         FIRST
  NO.   NAME        VALUE          ERROR          SIZE      DERIVATIVE
   1      P1        1.1316        .24808E-01    .64412E-03    .15289
   2      P2        1.5419        .21417E-01    .62018E-03    .42301E-01
   3      P3       -.76813        .17032E-01    .43531E-03   -.25527

Output of the Polynomial fit (P3)
 CHISQUARE =  .2290E+02  NPFIT =  100
     **********************************************
     *                                            *
     * Function minimization by SUBROUTINE HFITV  *
     * Variable-metric method                     *
     * ID =          0  CHOPT =                   *
     *                                            *
     **********************************************
 Convergence when estimated distance to minimum (EDM) .LT.   .10E-03

 FCN=   49.31862     FROM MIGRAD    STATUS=FAILED        90 CALLS       91 TOTAL
                     EDM=   .79E-01  STRATEGY=1  ERROR MATRIX UNCERTAINTY= 70.2%

  EXT PARAMETER                APPROXIMATE        STEP         FIRST
  NO.   NAME        VALUE          ERROR          SIZE      DERIVATIVE
   1      P1       -.13523        .34965E-02    .00000E+00    5.6896
   2      P2        1.8729        .53793E-02    .00000E+00   -6.8643
   3      P3       -.86391        .32623E-03    .00000E+00    94.054
   4      P4        .91424E-01    .23105E-03    .00000E+00    6.6564

 CHISQUARE =  .5137E+00  NPFIT =  100

Output of the Polynomial fit (P5)
     **********************************************
     *                                            *
     * Function minimization by SUBROUTINE HFITV  *
     * Variable-metric method                     *
     * ID =          0  CHOPT =                   *
     *                                            *
     **********************************************
 Convergence when estimated distance to minimum (EDM) .LT.   .10E-03

 FCN=   7.164283     FROM MIGRAD    STATUS=FAILED       240 CALLS      241 TOTAL
                     EDM=   .19E+01    STRATEGY= 1      ERR MATRIX NOT POS-DEF

  EXT PARAMETER                APPROXIMATE        STEP         FIRST
  NO.   NAME        VALUE          ERROR          SIZE      DERIVATIVE
   1      P1        .46785E-01    .20704E-03    .68172E-07    32.993
   2      P2        .93224        .10038E-02    .74579E-06   -551.05
   3      P3        .20962        .33827E-03    .16770E-06   -3073.1
   4      P4       -.36899        .32674E-03    .29519E-06   -1084.4
   5      P5        .82836E-01    .19712E-04    .66269E-07    821.80
   6      P6       -.52834E-02    .12561E-05    .42267E-08   -5204.8

 CHISQUARE =  .7622E-01  NPFIT =  100

Output of the ``COMIS'' fit
     **********************************************
     *                                            *
     * Function minimization by SUBROUTINE HFITV  *
     * Variable-metric method                     *
     * ID =          0  CHOPT =                   *
     *                                            *
     **********************************************
 Convergence when estimated distance to minimum (EDM) .LT.   .10E-03

 FCN=   32.13273     FROM MIGRAD    STATUS=CONVERGED     21 CALLS       22 TOTAL
                     EDM=   .92E-05    STRATEGY= 1      ERROR MATRIX ACCURATE

  EXT PARAMETER                                   STEP         FIRST
  NO.   NAME        VALUE          ERROR          SIZE      DERIVATIVE
   1      P1        .99811        .13752E-01    .51510E-04   -.31172

 CHISQUARE =  .3246E+00  NPFIT =  100

			PAW Tutorial	Last update: 1999/04/01 14.57	Olivier.Couet@Cern.Ch