Glen Cowan
                                                             1 December, 1999

              Sample MINUIT session with the program FITTER

This file contains the output from a session with the interactive version 
of MINUIT, implemented in a sample program called fitter.  The commands 
that are entered by the user are indicated by arrows <---------- like this.
More information on all of the MINUIT commands can be found in the
minuit manual; both PS and HTML versions are available from 

http://consult.cern.ch/writeup/minuit/

In addition, you can type help at the MINUIT prompt when running
the program.

In order to use the interactive version, you should have a file
that describes your parameters and assigns initial values.  A
sample file is given in ls_fit.min.  The file must have the
suffix .min, and IT MUST END WITH A BLANK LINE. 

The program is set up to fit a polynomial, and the parameter file
is set up to define 10 parameters, i.e. a 9th order polynomial.
In order to fit a different function, you need to change the subroutine
FCN.  In particular, you change the double precision function f, which
is called from FCN, and is in the same file (fcn.f) at the end.

In the example below, several of the parameters are fixed
with the "fix" command.  They can later be made adjustable again
with the "rel" command.   They can also be set to specific values
with the "set par" command.  Notice that in these commands, the
parameters are referred to by their numbers, not their names.

The session below generated a ps file fitter_plot.ps as output showing the 
fit result.  This is done by entering "call 3".  This forces the program
to call the subroutine FCN with iflag=3, which in turn calls routines 
to make the plot (see fcn.f).

In addition, plots of chi2 vs parameter values can be made with the
scan and contour commands, but these are only made with text characters 
(see below).

./fitter.lnk  <-------------------------- link the program
./fitter      <-------------------------- run the program
 Version 1.23/09 of HIGZ started
 ***************************************************************************
  MINUIT RELEASE 96.03  INITIALIZED.   DIMENSIONS 100/ 50  EPSMAC=  0.89E-15
 ***************************************************************************
                          MINUIT DATA BLOCK NO.   1
 ***************************************************************************
 ENTER MINUIT TITLE, or "SET INPUT n" :
set input 1 ls_fit.min         <------------ read in the parameter file
 **********
 **    1 **set input 1 ls_fit.min
 **********
 UNIT NO. :1
 FILE NAME IS:ls_fit.min
 UNIT  1 IS NOT OPENED.
 FILE OPENED SUCCESSFULLY.
 SHOULD UNIT  1 BE REWOUND?
                                <----------- accept with a carriage return
 polynomial fit
 ******************************************************************************

 PARAMETER DEFINITIONS:
    NO.   NAME         VALUE      STEP SIZE      LIMITS
     1 'c0        '   0.00000E+00   1.0000         no limits
     2 'c1        '   0.00000E+00   1.0000         no limits
     3 'c2        '   0.00000E+00   1.0000         no limits
     4 'c3        '   0.00000E+00   1.0000         no limits
     5 'c4        '   0.00000E+00   1.0000         no limits
     6 'c5        '   0.00000E+00   1.0000         no limits
     7 'c6        '   0.00000E+00   1.0000         no limits
     8 'c7        '   0.00000E+00   1.0000         no limits
     9 'c8        '   0.00000E+00   1.0000         no limits
    10 'c9        '   0.00000E+00   1.0000         no limits
    ***************************************************************************

 MINUIT: FIRST CALL TO USER FUNCTION, WITH IFLAG=1
enter file name for input data (<CR>=ls_data.dat) ls_data.dat  <--- data file

FCN=   3215.025     FROM PARAMETR  STATUS=RESET          2 CALLS        2 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX

  EXT PARAMETER               CURRENT GUESS      PHYSICAL LIMITS
  NO.   NAME        VALUE          ERROR       NEGATIVE      POSITIVE
   1      c0       0.00000E+00    1.0000
   2      c1       0.00000E+00    1.0000
   3      c2       0.00000E+00    1.0000
   4      c3       0.00000E+00    1.0000
   5      c4       0.00000E+00    1.0000
   6      c5       0.00000E+00    1.0000
   7      c6       0.00000E+00    1.0000
   8      c7       0.00000E+00    1.0000
   9      c8       0.00000E+00    1.0000
  10      c9       0.00000E+00    1.0000
 END OF DATA ON UNIT NO.  1
 INPUT WILL NOW BE READ IN INTERACTIVE MODE FROM UNIT NO.  5
 FILENAME: /dev/ttyq2
 ENTER MINUIT COMMAND:
fix 10                     <------------- fix parameter number 10 (i.e. c9)
 **********
 **    2 **FIX    10.00
 **********
 ENTER MINUIT COMMAND:
fix 9                      <------------- fix parameter number 9
 **********
 **    3 **FIX    9.000
 **********
 ENTER MINUIT COMMAND:
fix 8                      <------------- fix parameter number 8
 **********
 **    4 **FIX    8.000
 **********
 ENTER MINUIT COMMAND:
fix 7                      <------------- fix parameter number 7
 **********
 **    5 **FIX    7.000
 **********
 ENTER MINUIT COMMAND:
fix 6                      <------------- fix parameter number 6
 **********
 **    6 **FIX    6.000
 **********
 ENTER MINUIT COMMAND:
sim                        <------------- minimize with the simplex algorithm
 **********
 **    7 **SIM
 **********
 START SIMPLEX MINIMIZATION.    CONVERGENCE WHEN EDM .LT.  0.10E+00

FCN=   555.9934     FROM SIMPLEX   STATUS=PROGRESS      15 CALLS       17 TOTAL
                     EDM=  0.21E+10    STRATEGY= 1      NO ERROR MATRIX

  EXT PARAMETER               CURRENT GUESS      PHYSICAL LIMITS
  NO.   NAME        VALUE          ERROR       NEGATIVE      POSITIVE
   1      c0        13.000        1.0000
   2      c1       0.00000E+00    1.0000
   3      c2       0.00000E+00    1.0000
   4      c3       0.00000E+00    1.0000
   5      c4       0.00000E+00    1.0000
   6      c5       0.00000E+00     fixed
   7      c6       0.00000E+00     fixed
   8      c7       0.00000E+00     fixed
   9      c8       0.00000E+00     fixed
  10      c9       0.00000E+00     fixed
 SIMPLEX MINIMIZATION HAS CONVERGED.

FCN=   64.49479     FROM SIMPLEX   STATUS=PROGRESS     203 CALLS      205 TOTAL
                     EDM=  0.60E-01    STRATEGY= 1      NO ERROR MATRIX

  EXT PARAMETER               CURRENT GUESS      PHYSICAL LIMITS
  NO.   NAME        VALUE          ERROR       NEGATIVE      POSITIVE
   1      c0       0.31974        1.0000
   2      c1        3.5602        1.0000
   3      c2       0.29110E-01    1.0000
   4      c3      -0.27472E-01    1.0000
   5      c4       0.92691E-03    1.0000
   6      c5       0.00000E+00     fixed
   7      c6       0.00000E+00     fixed
   8      c7       0.00000E+00     fixed
   9      c8       0.00000E+00     fixed
  10      c9       0.00000E+00     fixed
 ENTER MINUIT COMMAND:
mig                          <---------- minimize with MIGRAD
 **********
 **    8 **MIG
 **********
 START MIGRAD MINIMIZATION.  STRATEGY 1.  CONVERGENCE WHEN EDM .LT. 0.10E-03

FCN=   64.49479     FROM MIGRAD    STATUS=INITIATE      20 CALLS      225 TOTAL
                     EDM= unknown      STRATEGY= 1      NO ERROR MATRIX

  EXT PARAMETER               CURRENT GUESS       STEP         FIRST
  NO.   NAME        VALUE          ERROR          SIZE      DERIVATIVE
   1      c0       0.31974        1.0000       0.16589       0.46727
   2      c1        3.5602        1.0000       0.47838E-01    5.0985
   3      c2       0.29110E-01    1.0000       0.53033E-03   -7.7307
   4      c3      -0.27472E-01    1.0000       0.47078E-03    113.83
   5      c4       0.92691E-03    1.0000       0.19185E-04   -7138.8
   6      c5       0.00000E+00     fixed
   7      c6       0.00000E+00     fixed
   8      c7       0.00000E+00     fixed
   9      c8       0.00000E+00     fixed
  10      c9       0.00000E+00     fixed

 MIGRAD MINIMIZATION HAS CONVERGED.

 MIGRAD WILL VERIFY CONVERGENCE AND ERROR MATRIX.
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY

FCN=   45.50617     FROM MIGRAD    STATUS=CONVERGED    144 CALLS      349 TOTAL
                     EDM=  0.13E-13    STRATEGY= 1      ERROR MATRIX ACCURATE

  EXT PARAMETER                                   STEP         FIRST
  NO.   NAME        VALUE          ERROR          SIZE      DERIVATIVE
   1      c0        4.5047        1.1388       0.74996E-03   0.27499E-07
   2      c1      -0.54278E-01   0.85422       0.65221E-04   0.27154E-06
   3      c2       0.78713       0.17407       0.39124E-05   0.47265E-05
   4      c3      -0.82833E-01   0.12866E-01   0.22219E-06   0.64359E-04
   5      c4       0.22356E-02   0.31143E-03   0.12292E-07   0.11735E-02
   6      c5       0.00000E+00     fixed
   7      c6       0.00000E+00     fixed
   8      c7       0.00000E+00     fixed
   9      c8       0.00000E+00     fixed
  10      c9       0.00000E+00     fixed

 EXTERNAL ERROR MATRIX.    NDIM=  50    NPAR=  5    ERR DEF=  1.00
  0.130E+01-0.902E+00 0.167E+00-0.113E-01 0.253E-03
 -0.902E+00 0.730E+00-0.144E+00 0.101E-01-0.233E-03
  0.167E+00-0.144E+00 0.303E-01-0.221E-02 0.522E-04
 -0.113E-01 0.101E-01-0.221E-02 0.166E-03-0.398E-05
  0.253E-03-0.233E-03 0.522E-04-0.398E-05 0.970E-07

 PARAMETER  CORRELATION COEFFICIENTS
       NO.  GLOBAL     1     2     3     4     5
        1  0.98025  1.000-0.927 0.840-0.769 0.713
        2  0.99974 -0.927 1.000-0.970 0.921-0.875
        3  0.99998  0.840-0.970 1.000-0.987 0.962
        4  0.99999 -0.769 0.921-0.987 1.000-0.993
        5  0.99993  0.713-0.875 0.962-0.993 1.000
 ENTER MINUIT COMMAND:
hesse               <------------- compute covariance matrix with HESSE
 **********
 **    9 **HESSE
 **********
 COVARIANCE MATRIX CALCULATED SUCCESSFULLY

FCN=   45.50617     FROM HESSE     STATUS=OK            31 CALLS      380 TOTAL
                     EDM=  0.23E-13    STRATEGY= 1      ERROR MATRIX ACCURATE

  EXT PARAMETER                                INTERNAL      INTERNAL
  NO.   NAME        VALUE          ERROR       STEP SIZE       VALUE
   1      c0        4.5047        1.1409       0.14999E-03    4.5047
   2      c1      -0.54278E-01   0.85653       0.13044E-04  -0.54278E-01
   3      c2       0.78713       0.17462       0.78248E-06   0.78713
   4      c3      -0.82833E-01   0.12909E-01   0.44438E-07  -0.82833E-01
   5      c4       0.22356E-02   0.31245E-03   0.24583E-08   0.22356E-02
   6      c5       0.00000E+00     fixed
   7      c6       0.00000E+00     fixed
   8      c7       0.00000E+00     fixed
   9      c8       0.00000E+00     fixed
  10      c9       0.00000E+00     fixed

 EXTERNAL ERROR MATRIX.    NDIM=  50    NPAR=  5    ERR DEF=  1.00
  0.130E+01-0.907E+00 0.168E+00-0.113E-01 0.254E-03
 -0.907E+00 0.734E+00-0.145E+00 0.102E-01-0.234E-03
  0.168E+00-0.145E+00 0.305E-01-0.223E-02 0.525E-04
 -0.113E-01 0.102E-01-0.223E-02 0.167E-03-0.401E-05
  0.254E-03-0.234E-03 0.525E-04-0.401E-05 0.976E-07

 PARAMETER  CORRELATION COEFFICIENTS
       NO.  GLOBAL     1     2     3     4     5
        1  0.98032  1.000-0.928 0.841-0.770 0.714
        2  0.99974 -0.928 1.000-0.970 0.922-0.875
        3  0.99998  0.841-0.970 1.000-0.987 0.962
        4  0.99999 -0.770 0.922-0.987 1.000-0.993
        5  0.99993  0.714-0.875 0.962-0.993 1.000
 ENTER MINUIT COMMAND:
call 3                 <---------- make plot by calling FCN with iflag=3
 **********
 **   10 **CALL    3.000
 **********
store plot in ps file (0=no,1=yes) (<CR>=0) 1
PostScript file (<CR>=minuit_fit.ps) fitter_plot.ps
enter x_min (<CR>=0) 0
enter x_max (<CR>=0) 22
enter y_min (<CR>=0) 0
enter y_max (<CR>=0) 35
enter x axis title x
 ENTER MINUIT COMMAND:
scan 1                <---------- make plot of chi2 vs parameter number 1
 **********
 **   11 **SCAN    1.000
 **********
0SCAN OF PARAMETER NO.  1,  c0
   75.00000     ......................................................
                  . *                       .                        .
   73.00000     ...                         .                       *.
                  .                         .                        .
   71.00000     ...                         .                        .
                  .                         .                        .
   69.00000     ...   *                     .                     *  .
                  .                         .                        .
   67.00000     ...                         .                        .
                  .                         .                        .
   65.00000     ...     *                   .                   *    .
                  .                         .                        .
   63.00000     ...                         .                        .
                  .                         .                        .
   61.00000     ...       *                 .                 *      .
                  .                         .                        .
   59.00000     ...                         .                        .
                  .         *               .                        .
   57.00000     ...                         .               *        .
                  .                         .                        .
   55.00000     ...           *             .             *          .
                  .                         .                        .
   53.00000     ...                         .                        .
                  .             *           .           *            .
   51.00000     ...                         .                        .
                  .               *         .         *              .
   49.00000     ...                         .                        .
                  .                 *       .       *                .
   47.00000     ...                   *     .     *                  .
                  .                     *   .   *                    .
   45.00000     ..........................*.&.*.......................
   44.00000     ......................................................
                  /         /         /         /         /         /
             3.250     3.750     4.250     4.750     5.250     5.750
                         ONE COLUMN=0.5000000E-01   Overprint character is &

FCN=   45.50617     FROM SCAn      STATUS=NO CHANGE     25 CALLS      406 TOTAL
                     EDM=  0.23E-13    STRATEGY= 1      ERROR MATRIX ACCURATE

  EXT PARAMETER                                   STEP         FIRST
  NO.   NAME        VALUE          ERROR          SIZE      DERIVATIVE
   1      c0        4.5047        1.1409       0.14999E-03   0.27713E-07
   2      c1      -0.54278E-01   0.85653       0.13044E-04   0.25329E-06
   3      c2       0.78713       0.17462       0.78248E-06   0.45434E-05
   4      c3      -0.82833E-01   0.12909E-01   0.44438E-07   0.60984E-04
   5      c4       0.22356E-02   0.31245E-03   0.24583E-08   0.12731E-02
   6      c5       0.00000E+00     fixed
   7      c6       0.00000E+00     fixed
   8      c7       0.00000E+00     fixed
   9      c8       0.00000E+00     fixed
  10      c9       0.00000E+00     fixed
 ENTER MINUIT COMMAND:
con 1 2           <-------- make contour plot of chi2 for params 1 and 2
 **********
 **   12 **CON    1.000       2.000
 **********
 Y-AXIS: PARAMETER   2: c1
    1.584                 *
    1.435                 *
    1.286                 *
    1.137                 *
   0.9885                 *
   0.8395                 *
   0.6905                 *
   0.5416                 *
   0.3926     DDEEFFGGHHIJJ
   0.2436     777888899AABCCDEEFGGHIJJ
   0.9468E-01 76654433333345567889ABBCD
  -0.5428E-01 7665443333334333333445667
  -0.2032     DCBBA98876554333333445667
  -0.3522      JJIHGGFEEDCCBAA998888777
  -0.5012                 JJIHHGGFFEEDD
  -0.6501                 *
  -0.7991                 *
  -0.9480                 *
   -1.097                 *
   -1.246                 *
   -1.395                 *
   -1.544                 *
   -1.693                 *
              I           I           I
           2.223                    6.786
                       4.505
       X-AXIS: PARAMETER  1: c0          ONE COLUMN=  0.1825
 FUNCTION VALUES: F(I)=   45.51     +   1.000     *I**2
 ENTER MINUIT COMMAND:
exit                        <-------------- quit program
 **********
 **   13 **EXIT
 **********
 ..........MINUIT TERMINATED BY MINUIT COMMAND: EXIT