Minuit(3pm)						User Contributed Perl Documentation					       Minuit(3pm)

NAME

       PDL::Minuit -- a PDL interface to the Minuit library

DESCRIPTION

       This package implements an interface to the Minuit minimization routines (part of the CERN Library)

SYNOPSIS

       A basic fit with Minuit will call three functions in this package. First, a basic initialization is done with mn_init(). Then, the
       parameters are defined via the function mn_def_pars(), which allows to set upper and lower bounds. Then the function mn_excm() can be used
       to issue many Minuit commands, including simplex and migrad minimization algorithms (see Minuit manual for more details).

       See the test file minuit.t in the test (t/) directory for a basic example.

FUNCTIONS

   mn_init()
       The function mn_init() does the basic initialization of the fit. The first argument has to be a reference to the function to be minimized.
       The function to be minimized has to receive five arguments ($npar,$grad,$fval,$xval,$iflag). The first is the number of parameters
       currently variable. The second is the gradient of the function (which is not necessarily used, see the Minuit documentation). The third is
       the current value of the function. The fourth is a piddle with the values of the parameters.  The fifth is an integer flag, which indicates
       what the function is supposed to calculate. The function has to return the  values ($fval,$grad), the function value and the function
       gradient.

       There are three optional arguments to mn_init(). By default, the output of Minuit will come through STDOUT unless a filename $logfile is
       given in the Log option. Note that this will mercilessly erase $logfile if it already exists. Aditionally, a title can be given to the fit
       by the Title option, the default is 'Minuit Fit'. If the output is written to a logfile, this is assigned Fortran unit number 88. If for
       whatever reason you want to have control over the unit number that Fortran associates to the logfile, you can pass the number through the
       Unit option.

       Usage:

	mn_init($function_ref,{Log=>$logfile,Title=>$title,Unit=>$unit})

       Example:

	mn_init(&my_function);

	#same as above but outputting to a file 'log.out'.
	#title for fit is 'My fit'
	mn_init(&my_function,
		{Log => 'log.out', Title => 'My fit'});

	sub my_function{
	   # the five variables input to the function to be minimized
	   # xval is a piddle containing the current values of the parameters
	   my ($npar,$grad,$fval,$xval,$iflag) = @_;

	   # Here is code computing the value of the function
	   # and potentially also its gradient
	   # ......

	   # return the two variables. If no gradient is being computed
	   # just return the $grad that came as input
	   return ($fval, $grad);
	}

   mn_def_pars()
       The function mn_def_pars() defines the initial values of the parameters of the function to be minimized and the value of the initial steps
       around these values that the minimizer will use for the first variations of the parameters in the search for the minimum.  There are
       several optional arguments. One allows to assign names to these parameters which otherwise get names (Par_0, Par_1,....,Par_n) by default.
       Another two arguments can give lower and upper bounds for the parameters via two piddles. If the lower and upper bound for a given
       parameter are both equal to 0 then the parameter is unbound. By default these lower and upper bound piddles are set to  zeroes(n), where n
       is the number of parameters, i.e. the parameters are unbound by default.

       The function needs two input variables: a piddle giving the initial values of the parameters and another piddle giving the initial steps.
       An optional reference to a perl array with the  variable names can be passed, as well as piddles with upper and lower bounds for the
       parameters (see example below).

       It returns an integer variable which is 0 upon success.

       Usage:

	$iflag = mn_def_pars($pars, $steps,{Names => @names,
			       Lower_bounds => $lbounds,
			       Upper_bounds => $ubounds})

       Example:

	#initial parameter values
	my $pars = pdl(2.5,3.0);

	#steps
	my $steps = pdl(0.3,0.5);

	#parameter names
	my @names = ('intercept','slope');

	#use mn_def_pars with default parameter names (Par_0,Par_1,...)
	my $iflag = mn_def_pars($pars,$steps);

	#use of mn_def_pars explictly specify parameter names
	$iflag = mn_def_pars($pars,$steps,{Names => @names});

	# specify lower and upper bounds for the parameters.
	# The example below leaves parameter 1 (intercept) unconstrained
	# and constrains parameter 2 (slope) to be betwen 0 and 100
	my $lbounds = pdl(0, 0);
	my $ubounds = pdl(0, 100);

	$iflag = mn_def_pars($pars,$steps,{Names => @names,
			       Lower_bounds => $lbounds,
			       Upper_bounds => $ubounds}});

	#same as above because $lbounds is by default zeroes(n)
	$iflag = mn_def_pars($pars,$steps,{Names => @names,
			       Upper_bounds => $ubounds}});

   mn_excm()
       The function mn_excm() executes a Minuit command passed as a string. The first argument is the command string and an optional second
       argument is a piddle with arguments to the command.  The available commands are listed in Chapter 4 of the Minuit manual (see url below).

       It returns an integer variable which is 0 upon success.

       Usage:

	$iflag = mn_excm($command_string, {$arglis})

       Example:

	 #start a simplex minimization
	 my $iflag = mn_excm('simplex');

	 #same as above but specify the maximum allowed numbers of
	 #function calls in the minimization
	 my $arglist = pdl(1000);
	 $iflag = mn_excm('simplex',$arglist);

	 #start a migrad minimization
	 $iflag = mn_excm('migrad')

	 #set Minuit strategy in order to get the most reliable results
	 $arglist = pdl(2)
	 $iflag = mn_excm('set strategy',$arglist);

	 # each command can be specified by a minimal string that uniquely
	 # identifies it (see Chapter 4 of Minuit manual). The comannd above
	 # is equivalent to:
	 $iflag = mn_excm('set stra',$arglis);

   mn_pout()
       The function mn_pout() gets the current value of a parameter. It takes as input the parameter number and returns an array with the
       parameter value, the current estimate of its uncertainty (0 if parameter is constant), lower bound on the parameter, if any (otherwise 0),
       upper bound on the parameter, if any (otherwise 0), integer flag (which is equal to the parameter number if variable, zero if the parameter
       is constant and negative if parameter is not defined) and the parameter name.

       Usage:

	    ($val,$err,$bnd1,$bnd2,$ivarbl,$par_name) = mn_pout($par_number);

   mn_stat()
       The function mn_stat() gets the current status of the minimization.  It returns an array with the best function value found so far, the
       estimated vertical distance remaining to minimum, the value of UP defining parameter uncertainties (default is 1), the number of currently
       variable parameters, the highest parameter defined and an integer flag indicating how good the covariance matrix is (0=not calculated at
       all; 1=diagonal approximation, not accurate; 2=full matrix, but forced positive definite; 3=full accurate matrix)

       Usage:

	   ($fmin,$fedm,$errdef,$npari,$nparx,$istat) = mn_stat();

   mn_emat()
       The function mn_emat returns the covariance matrix as a piddle.

       Usage:

	 $emat = mn_emat();

   mn_err()
       The function mn_err() returns the current existing values for the error in the fitted parameters. It returns an array with the positive
       error, the negative error, the "parabolic" parameter error from the error matrix and the global correlation coefficient, which is a number
       between 0 and 1 which gives the correlation between the requested parameter and that linear combination of all other parameters which is
       most strongly correlated with it. Unless the command 'MINOS' has been issued via the function mn_excm(), the first three values will be
       equal.

       Usage:

	 ($eplus,$eminus,$eparab,$globcc) = mn_err($par_number);

   mn_contour()
       The function mn_contour() finds contours of the function being minimized with respect to two chosen parameters. The contour level is given
       by F_min + UP, where F_min is the minimum of the function and UP is the ERRordef specfied by the user, or 1.0 by default (see Minuit
       manual). The contour calculated by this function is dynamic, in the sense that it represents the minimum of the funcion being minimized
       with respect to all the other NPAR-2 parameters (if any).

       The function takes as input the parameter numbers with respect to which the contour is to be determined (two) and the number of points $npt
       required on the contour (>4).  It returns an array with piddles $xpt,$ypt containing the coordinates of the contour and a variable $nfound
       indicating the number of points actually found in the contour.  If all goes well $nfound will be equal to $npt, but it can be negative if
       the input arguments are not valid, zero if less than four points have been found or <$npt if the program could not find $npt points.

       Usage:

	 ($xpt,$ypt,$nfound) = mn_contour($par_number_1,$par_number_2,$npt)

SEE ALSO

       PDL

       The Minuit documentation is online at

	 http://wwwasdoc.web.cern.ch/wwwasdoc/minuit/minmain.html

AUTHOR

       This file copyright (C) 2007 Andres Jordan <ajordan@eso.org>.  All rights reserved. There is no warranty. You are allowed to redistribute
       this software/documentation under certain conditions. For details, see the file COPYING in the PDL distribution. If this file is separated
       from the PDL distribution, the copyright notice should be included in the file.

FUNCTIONS

   mninit
	 Signature: (int a();int b(); int c())

       info not available

       mninit does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mn_abre
	 Signature: (int l(); char* nombre; char* mode)

       info not available

       mn_abre does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mn_cierra
	 Signature: (int l())

       info not available

       mn_cierra does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input
       piddles.

   mnparm
	 Signature: (int a(); double b(); double c(); double d(); double e(); int [o] ia(); char* str)

       info not available

       mnparm does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mnexcm
	 Signature: (double a(n); int ia(); int [o] ib(); char* str; SV* funcion; int numelem)

       info not available

       mnexcm does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mnpout
	 Signature: (int ia(); double [o] a(); double [o] b(); double [o] c(); double [o] d();int [o] ib(); SV* str)

       info not available

       mnpout does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mnstat
	 Signature: (double [o] a(); double [o] b(); double [o] c(); int [o] ia(); int [o] ib(); int [o] ic())

       info not available

       mnstat does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mnemat
	 Signature: (double [o] mat(n,n))

       info not available

       mnemat does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mnerrs
	 Signature: (int ia(); double [o] a(); double [o] b(); double [o] c(); double [o] d())

       info not available

       mnerrs does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

   mncont
	 Signature: (int ia(); int ib(); int ic(); double [o] a(n); double [o] b(n); int [o] id(); SV* funcion; int numelem)

       info not available

       mncont does not process bad values.  It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.

perl v5.14.2							    2012-05-30							       Minuit(3pm)