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.IX Title "MROOT 3pm"
.TH MROOT 3pm 2024-05-12 "perl v5.38.2" "User Contributed Perl Documentation"
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.SH NAME
PDL::GSL::MROOT \- PDL interface to multidimensional root\-finding routines in GSL
.SH DESCRIPTION
.IX Header "DESCRIPTION"
This is an interface to the multidimensional root-finding package present in the
GNU Scientific Library.
.PP
At the moment there is a single function \fBgslmroot_fsolver\fR which provides an interface
to the algorithms in the GSL library that do not use derivatives.
.SH SYNOPSIS
.IX Header "SYNOPSIS"
.Vb 2
\&   use PDL;
\&   use PDL::GSL::MROOT;
\&
\&   my $init = pdl (\-10.00, \-5.0);
\&   my $epsabs = 1e\-7;
\&
\&  $res = gslmroot_fsolver($init, \e&rosenbrock,
\&                          {Method => 0, EpsAbs => $epsabs});
\&
\&  sub rosenbrock{
\&     my ($x) = @_;
\&     my $c = 1;
\&     my $d = 10;
\&     my $y = zeroes($x);
\&
\&     my $y0 = $y\->slice(0);
\&     $y0 .=  $c * (1 \- $x\->slice(0));
\&
\&     my $y1 = $y\->slice(1);
\&     $y1 .=  $d * ($x\->slice(1) \- $x\->slice(0)**2);
\&
\&     return $y;
\&  }
\&#line 68 "MROOT.pm"
.Ve
.SH FUNCTIONS
.IX Header "FUNCTIONS"
.SS gslmroot_fsolver
.IX Subsection "gslmroot_fsolver"
.Vb 1
\&  Signature: (double [io]xfree(n);   double epsabs(); int method(); SV* function1)
.Ve
.PP
Multidimensional root finder without using derivatives
.PP
This function provides an interface to the multidimensional root finding algorithms
in the GSL library. It takes a minimum of two arguments: an ndarray \f(CW$init\fR with an
initial guess for the roots of the system and a reference to a function. The latter
function must return an ndarray whose i\-th element is the i\-th equation evaluated at
the vector x (an ndarray which is the sole input to this function). See the example in
the Synopsis above for an illustration. The function returns an ndarray with the roots
for the system of equations.
.PP
Two optional arguments can be specified as shown below. One is \fBMethod\fR, which can
take the values 0,1,2,3. They correspond to the 'hybrids', 'hybrid', 'dnewton' and
\&'broyden' algorithms respectively (see GSL documentation for details). The other
optional argument is \fBEpsabs\fR, which sets the absolute accuracy to which the roots
of the system of equations are required. The default value for Method is 0 ('hybrids'
algorithm) and the default for Epsabs is 1e\-3.
.PP
.Vb 2
\&   $res = gslmroot_fsolver($init, $function_ref,
\&                           [{Method => $method, Epsabs => $epsabs}]);
.Ve
.PP
gslmroot_fsolver does not process bad values.
It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
PDL
.PP
The GSL documentation is online at
.PP
.Vb 1
\&  http://www.gnu.org/software/gsl/manual/
.Ve
.SH AUTHOR
.IX Header "AUTHOR"
This file copyright (C) 2006 Andres Jordan <ajordan@eso.org>
and Simon Casassus <simon@das.uchile.cl>
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.