Minuit(3) User Contributed Perl Documentation Minuit(3)NAMEPDL::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.
FUNCTIONSmn_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 v5.14.1 2011-07-26 Minuit(3)
