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# PDL::GSL::MROOT

# NAME

PDL::GSL::MROOT - PDL interface to multidimensional root-finding routines in GSL

=head1 DESCRIPTION

This is an interface to the multidimensional root-finding package present in the GNU Scientific Library.

At the moment there is a single function **gslmroot_fsolver** which provides an interface
to the algorithms in the GSL library that do not use derivatives.

# SYNOPSIS

use PDL; use PDL::GSL::MROOT;

my $init = pdl (-10.00, -5.0); my $epsabs = 1e-7;

$res = gslmroot_fsolver($init, \&rosenbrock, {Method => 0, EpsAbs => $epsabs});

sub rosenbrock{ my ($x) = @_; my $a = 1; my $b = 10; my $y = zeroes($x);

my $y0 = $y->slice(0); $y0 .= $a * (1 - $x->slice(0));

my $y1 = $y->slice(1); $y1 .= $b * ($x->slice(1) - $x->slice(0)**2);

return $y; }

=head1 FUNCTIONS

## gslmroot_fsolver -- Multidimensional root finder without using derivatives

This function provides an interface to the multidimensional root finding algorithms in the GSL library. It takes a minimum of two argumennts: a piddle $init with an initial guess for the roots of the system and a reference to a function. The latter function must return a piddle whose i-th element is the i-th equation evaluated at the vector x (a piddle which is the sole input to this function). See the example in the Synopsis above for an illustration. The function returns a piddle with the roots for the system of equations.

Two optional arguments can be specified as shown below. One is **Method**, 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 **Epsabs**, 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.

Usage:

$res = gslmroot_fsolver($init, $function_ref, [{Method => $method, Epsabs => $epsabs}]);

# SEE ALSO

The GSL documentation is online at

http://www.gnu.org/software/gsl/manual/

# 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.

# FUNCTIONS

## fsolver_meat

Signature: (double xfree(n); double epsabs(); int method(); SV* funcion1)

info not available

fsolver_meat 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.