class TMinuit: public TNamed

Minuit normal constructor*-*-*-*-
*-*                  ========================

Minuit normal constructor*-*-*-*-
*-*                  ========================

  maxpar is the maximum number of parameters used with this TMinuit object.

 Private TMinuit copy ctor. TMinuit can not be copied.

Minuit default destructor*-*-*-*-
*-*                  =========================

-*-*-*Create internal Minuit arrays for the maxpar parameters
*-*          =======================================================

 Make a clone of an object using the Streamer facility.
 Function pointer is copied to Clone

 execute a Minuit command
     Equivalent to MNEXCM except that the command is given as a
     character string.
 See TMinuit::mnhelp for the full list of available commands
 See also http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/node18.html for
  a complete documentation of all the available commands

 Returns the status of the execution:
   = 0: command executed normally
     1: command is blank, ignored
     2: command line unreadable, ignored
     3: unknown command, ignored
     4: abnormal termination (e.g., MIGRAD not converged)
     5: command is a request to read PARAMETER definitions
     6: 'SET INPUT' command
     7: 'SET TITLE' command
     8: 'SET COVAR' command
     9: reserved
    10: END command
    11: EXIT or STOP command
    12: RETURN command

*

 Creates a TGraph object describing the n-sigma contour of a
 TMinuit fit. The contour of the parameters pa1 and pa2 is calculated
 unsing npoints (>=4) points. The TMinuit status will be
  0   on success and
 -1   if errors in the calling sequence (pa1, pa2 not variable)
  1   if less than four points can be found
  2   if npoints<4
  n>3 if only n points can be found (n < npoints)
 The status can be obtained via TMinuit::GetStatus().

 To get the n-sigma contour the ERRDEF parameter in Minuit has to set
 to n^2. The fcn function has to be set before the routine is called.

 The TGraph object is created via the interpreter. The user must cast it
 to a TGraph*. Note that the TGraph is created with npoints+1 in order to
 close the contour (setting last point equal to first point).

 You can find an example in $ROOTSYS/tutorials/fit/fitcont.C

 Define a parameter

-*-*-*Delete internal Minuit arrays
*-*                    =============================

 Evaluate the minimisation function
  Input parameters:
    npar:    number of currently variable parameters
    par:     array of (constant and variable) parameters
    flag:    Indicates what is to be calculated (see example below)
    grad:    array of gradients
  Output parameters:
    fval:    The calculated function value.
    grad:    The (optional) vector of first derivatives).

 The meaning of the parameters par is of course defined by the user,
 who uses the values of those parameters to calculate his function value.
 The starting values must be specified by the user.
 Later values are determined by Minuit as it searches for the minimum
 or performs whatever analysis is requested by the user.

 Note that this virtual function may be redefined in a class derived from TMinuit.
 The default function calls the function specified in SetFCN

 Example of Minimisation function:

   if (flag == 1) {
      read input data,
      calculate any necessary constants, etc.
   }
   if (flag == 2) {
      calculate GRAD, the first derivatives of FVAL
     (this is optional)
   }
   Always calculate the value of the function, FVAL,
   which is usually a chisquare or log likelihood.
   if (iflag == 3) {
      will come here only after the fit is finished.
      Perform any final calculations, output fitted data, etc.
   }

  See concrete examples in TH1::H1FitChisquare, H1FitLikelihood

 fix a parameter

 return parameter value and error

 returns the number of currently fixed parameters

 returns the number of currently free parameters

 returns the total number of parameters that have been defined.
 (fixed and free)

 invokes the MIGRAD minimizer

 release a parameter

 To get the n-sigma contour the error def parameter "up" has to set to n^2.

To set the address of the minimization function*-
*-*          ===============================================
*

To set the address of the minimization function*-
*-*          ===============================================
     this function is called by CINT instead of the function above
*

set Minuit print level
 printlevel = -1  quiet (also suppresse all warnings)
            =  0  normal
            =  1  verbose

Initialize AMIN*-*-*-*-
*-*                      ===============
*-*C        Called  from many places.  Initializes the value of AMIN by
*-*C        calling the user function. Prints out the function value and
*-*C        parameter values if Print Flag value is high enough.
*

-*-*Compute reasonable histogram intervals
*-*                  ======================================
*-*        Function TO DETERMINE REASONABLE HISTOGRAM INTERVALS
*-*        GIVEN ABSOLUTE UPPER AND LOWER BOUNDS  A1 AND A2
*-*        AND DESIRED MAXIMUM NUMBER OF BINS NAA
*-*        PROGRAM MAKES REASONABLE BINNING FROM BL TO BH OF WIDTH BWID
*-*        F. JAMES,   AUGUST, 1974 , stolen for Minuit, 1988
*

Transform FCN to find further minima
*-*                ====================================
*-*        Called only from MNIMPR.  Transforms the function FCN
*-*        by dividing out the quadratic part in order to find further
*-*        minima.    Calculates  ycalf = (f-fmin)/(x-xmin)*v*(x-xmin)
*

-*-*-*Resets the parameter list to UNDEFINED
*-*                  ======================================
*-*        Called from MINUIT and by option from MNEXCM
*

Print function contours in two variables, on line printer
*-*      =========================================================
-
*-*                input arguments: parx, pary, devs, ngrid
*

-*Reads a command string and executes
*-*                  ===================================
*-*        Called by user.  'Reads' a command string and executes.
*-*     Equivalent to MNEXCM except that the command is given as a
*-*          character string.
-
*-*     ICONDN = 0: command executed normally
*-*              1: command is blank, ignored
*-*              2: command line unreadable, ignored
*-*              3: unknown command, ignored
*-*              4: abnormal termination (e.g., MIGRAD not converged)
*-*              5: command is a request to read PARAMETER definitions
*-*              6: 'SET INPUT' command
*-*              7: 'SET TITLE' command
*-*              8: 'SET COVAR' command
*-*              9: reserved
*-*             10: END command
*-*             11: EXIT or STOP command
*-*             12: RETURN command
-
*

Find points along a contour where FCN is minimum
*-*          ================================================
*-*       Find NPTU points along a contour where the function
*-*             FMIN (X(KE1),X(KE2)) =  AMIN+UP
*-*       where FMIN is the minimum of FCN with respect to all
*-*       the other NPAR-2 variable parameters (if any).
*-*   IERRF on return will be equal to the number of points found:
*-*     NPTU if normal termination with NPTU points found
*-*     -1   if errors in the calling sequence (KE1, KE2 not variable)
*-*      0   if less than four points can be found (using MNMNOT)
*-*     n>3  if only n points can be found (n < NPTU)
-
*-*                 input arguments: parx, pary, devs, ngrid
*
System generated locals

Cracks the free-format input*-
*-*                    ============================
*-*       Cracks the free-format input, expecting zero or more
*-*         alphanumeric fields (which it joins into COMAND(1:LNC))
*-*         followed by one or more numeric fields separated by
*-*         blanks and/or one comma.  The numeric fields are put into
*-*         the LLIST (but at most MXP) elements of PLIST.
*-*      IERR = 0 if no errors,
*-*           = 1 if error(s).
-
*
Initialized data

Find point where MNEVAL=AMIN+UP*-
*-*                  ===============================
*-*       Find point where MNEVAL=AMIN+UP, along the line through
*-*       XMIDCR,YMIDCR with direction XDIRCR,YDIRCR,   where X and Y
*-*       are parameters KE1CR and KE2CR.  If KE2CR=0 (from MINOS),
*-*       only KE1CR is varied.  From MNCONT, both are varied.
*-*       Crossing point is at
*-*        (U(KE1),U(KE2)) = (XMID,YMID) + AOPT*(XDIR,YDIR)
-
*

-*-*-*Makes sure that the current point is a local minimum
*-*            ====================================================
*-*        Makes sure that the current point is a local
*-*        minimum and that the error matrix exists,
*-*        or at least something good enough for MINOS and MNCONT
*

Calculates the first derivatives of FCN (GRD)
*-*            =============================================
*-*        Calculates the first derivatives of FCN (GRD),
*-*        either by finite differences or by transforming the user-
*-*        supplied derivatives to internal coordinates,
*-*        according to whether fISW[2] is zero or one.
*

-*-*Calculates the transformation factor between ext/internal values
*-*    =====================================================================
*-*        calculates the transformation factor between external and
*-*        internal parameter values.     this factor is one for
*-*        parameters which are not limited.     called from MNEMAT.
*

Compute matrix eigen values*-
*-*                    ===========================
System generated locals

 Calculates the external error matrix from the internal matrix

 Note that if the matrix is declared like Double_t matrix[5][5]
 in the calling program, one has to call mnemat with, eg
     gMinuit->mnemat(&matrix[0][0],5);

Utility routine to get MINOS errors*-
*-*                ===================================
*-*    Called by user.
*-*    NUMBER is the parameter number
*-*    values returned by MNERRS:
*-*       EPLUS, EMINUS are MINOS errors of parameter NUMBER,
*-*       EPARAB is 'parabolic' error (from error matrix).
*-*                 (Errors not calculated are set = 0)
*-*       GCC is global correlation coefficient from error matrix
*

Evaluates the function being analyzed by MNCROS*-
*-*          ===============================================
*-*      Evaluates the function being analyzed by MNCROS, which is
*-*      generally the minimum of FCN with respect to all remaining
*-*      variable parameters.  The class data members contains the
*-*      data necessary to know the values of U(KE1CR) and U(KE2CR)
*-*      to be used, namely     U(KE1CR) = XMIDCR + ANEXT*XDIRCR
*-*      and (if KE2CR .NE. 0)  U(KE2CR) = YMIDCR + ANEXT*YDIRCR
*

Interprets a command and takes appropriate action*-*-
*-*        =================================================
*-*        either directly by skipping to the corresponding code in
*-*        MNEXCM, or by setting up a call to a function
-
*-*  recognized MINUIT commands:
*-*  obsolete commands:
*-*      IERFLG is now (94.5) defined the same as ICONDN in MNCOMD
*-*            = 0: command executed normally
*-*              1: command is blank, ignored
*-*              2: command line unreadable, ignored
*-*              3: unknown command, ignored
*-*              4: abnormal termination (e.g., MIGRAD not converged)
*-*              9: reserved
*-*             10: END command
*-*             11: EXIT or STOP command
*-*             12: RETURN command
-
*-*     see also http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/node18.html for the possible list
*-*     of all Minuit commands
-
*

-*-*Transforms the external parameter values U to internal values
*-*      =============================================================
*-*        Transforms the external parameter values U to internal
*-*        values in the dense array PINT.
*

-*-*-*-*Removes parameter IINT from the internal parameter list
*-*          =======================================================
*-*        and arranges the rest of the list to fill the hole.
*

Restores one or more fixed parameter(s) to variable status*-*-
*-*    ==========================================================
*-*        Restores one or more fixed parameter(s) to variable status
*-*        by inserting it into the internal parameter list at the
*-*        appropriate place.
-
*-*        K = 0 means restore all parameters
*-*        K = 1 means restore the last parameter fixed
*-*        K = -I means restore external parameter I (if possible)
*-*        IQ = fix-location where internal parameters were stored
*-*        IR = external number of parameter being restored
*-*        IS = internal number of parameter being restored
*

Interprets the SET GRAD command*-*-*-
*-*                ===============================
*-*       Called from MNSET
*-*       Interprets the SET GRAD command, which informs MINUIT whether
*-*       the first derivatives of FCN will be calculated by the user
*-*       inside FCN.  It can check the user derivative calculation
*-*       by comparing it with a finite difference approximation.
*

interface to Minuit help

HELP routine for MINUIT interactive commands*-
*-*            ============================================
-
*-*      COMD ='*' or "" prints a global help for all commands
*-*      COMD =Command_name: print detailed help for one command.
*-*         Note that at least 3 characters must be given for the command
*-*         name.
-
*-*     Author: Rene Brun
*-*             comments extracted from the MINUIT documentation file.
-
*

Calculates the full second-derivative matrix of FCN*-*-
*-*        ===================================================
*-*        by taking finite differences. When calculating diagonal
*-*        elements, it may iterate so that step size is nearly that
*-*        which gives function change= UP/10. The first derivatives
*-*        of course come as a free side effect, but with a smaller
*-*        step size in order to obtain a known accuracy.
*

Calculate first derivatives (GRD) and uncertainties (DGRD)*-*-
*-*    ==========================================================
*-*         and appropriate step sizes GSTEP
*-*      Called from MNHESS and MNGRAD
*

Attempts to improve on a good local minimum*-*-*-
*-*          ===========================================
*-*        Attempts to improve on a good local minimum by finding a
*-*        better one.   The quadratic part of FCN is removed by MNCALF
*-*        and this transformed function is minimized using the simplex
*-*        method from several random starting points.
*-*        ref. -- Goldstein and Price, Math.Comp. 25, 569 (1971)
*

-*Transforms from internal coordinates (PINT) to external (U)
*-*      ===========================================================
*-*        The minimizing routines which work in
*-*        internal coordinates call this routine before calling FCN.
*

Main initialization member function for MINUIT*-*-*-
*-*        ==============================================
*-*     It initializes some constants
*-*                (including the logical I/O unit nos.),
*

Interprets the SET LIM command, to reset the parameter limits
*-*    =============================================================
*-*       Called from MNSET
*

-*-*Perform a line search from position START
*-*                =========================================
*-*        along direction STEP, where the length of vector STEP
*-*                   gives the expected position of minimum.
*-*        FSTART is value of function at START
*-*        SLOPE (if non-zero) is df/dx along STEP at START
*-*        TOLER is initial tolerance of minimum in direction STEP
-
*-* SLAMBG and ALPHA control the maximum individual steps allowed.
*-* The first step is always =1. The max length of second step is SLAMBG.
*-* The max size of subsequent steps is the maximum previous successful
*-*   step multiplied by ALPHA + the size of most recent successful step,
*-*   but cannot be smaller than SLAMBG.
*

Prints the covariance matrix v when KODE=1*-
*-*            ==========================================
*-*        always prints the global correlations, and
*-*        calculates and prints the individual correlation coefficients
*

Performs a local function minimization*-
*-*              ======================================
*-*        Performs a local function minimization using basically the
*-*        method of Davidon-Fletcher-Powell as modified by Fletcher
*-*        ref. -- Fletcher, Comp.J. 13,317 (1970)   "switching method"
*

Performs a MINOS error analysis*-
*-*                  ===============================
*-*        Performs a MINOS error analysis on those parameters for
*-*        which it is requested on the MINOS command by calling
*-*        MNMNOT for each parameter requested.
*

Performs a MINOS error analysis on one parameter*-*-*-
*-*        ================================================
*-*        The parameter ILAX is varied, and the minimum of the
*-*        function with respect to the other parameters is followed
*-*        until it crosses the value FMIN+UP.
*

Implements one parameter definition*-*-*-
*-*              ===================================
*-*        Called from MNPARS and user-callable
*-*    Implements one parameter definition, that is:
*-*          K     (external) parameter number
*-*          CNAMK parameter name
*-*          UK    starting value
*-*          WK    starting step size or uncertainty
*-*          A, B  lower and upper physical parameter limits
*-*    and sets up (updates) the parameter lists.
*-*    Output: IERFLG=0 if no problems
*-*                  >0 if MNPARM unable to implement definition
*

Implements one parameter definition*-*-*-*-*-
*-*            =========== =======================
*-*        Called from MNREAD and user-callable
*-*    Implements one parameter definition, that is:
*-*       parses the string CRDBUF and calls MNPARM
-
*-* output conditions:
*-*        ICONDN = 0    all OK
*-*        ICONDN = 1    error, attempt to define parameter is ignored
*-*        ICONDN = 2    end of parameter definitions
*

To fit a parabola to npar2p points*-
*-*                ==================================
*-*   npar2p   no. of points
*-*   parx2p(i)   x value of point i
*-*   pary2p(i)   y value of point i
-
*-*   coef2p(1...3)  coefficients of the fitted parabola
*-*   y=coef2p(1) + coef2p(2)*x + coef2p(3)*x**2
*-*   sdev2p= variance
*-*   method : chi**2 = min equation solved explicitly
*

Calculates the internal parameter value PINTI*-
*-*          =============================================
*-*        corresponding  to the external value PEXTI for parameter I.
*

Plots points in array xypt onto one page with labelled axes*-
*-*    ===========================================================
*-*        NXYPT is the number of points to be plotted
*-*        XPT(I) = x-coord. of ith point
*-*        YPT(I) = y-coord. of ith point
*-*        CHPT(I) = character to be plotted at this position
*-*        the input point arrays XPT, YPT, CHPT are destroyed.
-
-
*-*   If fGraphicsmode is true (default), a TGraph object is produced
*-*   via the Plug-in handler. To get the plot, you can do:
*-*       TGraph *gr = (TGraph*)gMinuit->GetPlot();
*-*       gr->Draw("al");
-
*

-*Provides the user with information concerning the current status
*-*    ================================================================
*-*          of parameter number IUEXT. Namely, it returns:
*-*        CHNAM: the name of the parameter
*-*        VAL: the current (external) value of the parameter
*-*        ERR: the current estimate of the parameter uncertainty
*-*        XLOLIM: the lower bound (or zero if no limits)
*-*        XUPLIM: the upper bound (or zero if no limits)
*-*        IUINT: the internal parameter number (or zero if not variable,
*-*           or negative if undefined).
*-*  Note also:  If IUEXT is negative, then it is -internal parameter
*-*           number, and IUINT is returned as the EXTERNAL number.
*-*     Except for IUINT, this is exactly the inverse of MNPARM
*-*     User-called
*

Prints the values of the parameters at the time of the call*-
*-*    ===========================================================
*-*        also prints other relevant information such as function value,
*-*        estimated distance to minimum, parameter errors, step sizes.
-
*-*         According to the value of IKODE, the printout is:
*-*    IKODE=INKODE= 0    only info about function value
*-*                  1    parameter values, errors, limits
*-*                  2    values, errors, step sizes, internal values
*-*                  3    values, errors, step sizes, first derivs.
*-*                  4    values, parabolic errors, MINOS errors
*-*    when INKODE=5, MNPRIN chooses IKODE=1,2, or 3, according to fISW[1]
*

-*Calculates the eigenvalues of v to see if positive-def
*-*        ======================================================
*-*        if not, adds constant along diagonal to make positive.
*

Called only by MNSIMP (and MNIMPR) to add a new point*-*-
*-*      =====================================================
*-*        and remove an old one from the current simplex, and get the
*-*        estimated distance to minimum.
*

This is a super-portable random number generator
*-*          ================================================
*-*         It should not overflow on any 32-bit machine.
*-*         The cycle is only ~10**9, so use with care!
*-*         Note especially that VAL must not be undefined on input.
*-*                    Set Default Starting Seed
*

Resets function value and errors to UNDEFINED
*-*            =============================================
*-*    If IOPT=1,
*-*    If IOPT=0, sets only MINOS errors to undefined
*-*        Called from MNCLER and whenever problem changes, for example
*-*        after SET LIMITS, SET PARAM, CALL FCN 6
*

-*Writes current parameter values and step sizes onto file ISYSSA
*-*    ===============================================================
*-*          in format which can be reread by Minuit for restarting.
*-*       The covariance matrix is also output if it exists.
*

Scans the values of FCN as a function of one parameter*-
*-*      ======================================================
*-*        and plots the resulting values as a curve using MNPLOT.
*-*        It may be called to scan one parameter or all parameters.
*-*        retains the best function and parameter values found.
*

-*-*Performs a rough (but global) minimization by monte carlo search
*-*    ================================================================
*-*        Each time a new minimum is found, the search area is shifted
*-*        to be centered at the best value.  Random points are chosen
*-*        uniformly over a hypercube determined by current step sizes.
*-*   The Metropolis algorithm accepts a worse point with probability
*-*      exp(-d/UP), where d is the degradation.  Improved points
*-*      are of course always accepted.  Actual steps are random
*-*      multiples of the nominal steps (DIRIN).
*

Interprets the commands that start with SET and SHOW*-*-
*-*      ====================================================
*-*        Called from MNEXCM
*-*        file characteristics for SET INPUT
*-*       'SET ' or 'SHOW',  'ON ' or 'OFF', 'SUPPRESSED' or 'REPORTED  '
*-*        explanation of print level numbers -1:3  and strategies 0:2
*-*        identification of debug options
*-*        things that can be set or shown
*-*        options not intended for normal users
*

Minimization using the simplex method of Nelder and Mead
*-*      ========================================================
*-*        Performs a minimization using the simplex method of Nelder
*-*        and Mead (ref. -- Comp. J. 7,308 (1965)).
*

Returns concerning the current status of the minimization
*-*      =========================================================
*-*       User-called
*-*          Namely, it returns:
*-*        FMIN: the best function value found so far
*-*        FEDM: the estimated vertical distance remaining to minimum
*-*        ERRDEF: the value of UP defining parameter uncertainties
*-*        NPARI: the number of currently variable parameters
*-*        NPARX: the highest (external) parameter number defined by user
*-*        ISTAT: a status integer indicating how good is the covariance
*-*           matrix:  0= not calculated at all
*-*                    1= approximation only, not accurate
*-*                    2= full matrix, but forced positive-definite
*-*                    3= full accurate covariance matrix
*

To find the machine precision*-*-*-*-*-*-*-
*-*            =============================
*-*        Compares its argument with the value 1.0, and returns
*-*        the value .TRUE. if they are equal.  To find EPSMAC
*-*        safely by foiling the Fortran optimizer
*

-*-*Returns .TRUE. if CFNAME contains unprintable characters
*-*        ========================================================
*

Inverts a symmetric matrix*-
*-*                    ==========================
*-*        inverts a symmetric matrix.   matrix is first scaled to
*-*        have all ones on the diagonal (equivalent to change of units)
*-*        but no pivoting is done since matrix is positive-definite.
*

Prints Warning messages*-*-
*-*                    =======================
*-*     If COPT='W', CMES is a WARning message from CORG.
*-*     If COPT='D', CMES is a DEBug message from CORG.
*-*         If SET WARnings is in effect (the default), this routine
*-*             prints the warning message CMES coming from CORG.
*-*         If SET NOWarnings is in effect, the warning message is
*-*             stored in a circular buffer of length kMAXMES.
*-*         If called with CORG=CMES='SHO', it prints the messages in
*-*             the circular buffer, FIFO, and empties the buffer.
*

-*Calculates the WERR, external parameter errors
*-*            ==============================================
*-*      and the global correlation coefficients, to be called
*-*      whenever a new covariance matrix is available.
*