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
Last update: 96/05/24 17.18 Olivier.Couet@Cern.Ch