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: (longlong a();longlong b(); longlong 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: (longlong 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: (longlong 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: (longlong a(); double b(); double c(); double d(); double e(); longlong [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); longlong ia(); longlong [o] ib(); char* str; SV* funcion; IV 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: (longlong ia(); double [o] a(); double [o] b(); double [o] c(); double [o] d();longlong [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(); longlong [o] ia(); longlong [o] ib(); longlong [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: (longlong 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: (longlong ia(); longlong ib(); longlong ic(); double [o] a(n); double [o] b(n); longlong [o] id(); SV* funcion; IV 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.