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.\" ========================================================================
.\"
.IX Title "MROOT 3pm"
.TH MROOT 3pm "2016-10-10" "perl v5.24.1" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
.\" way too many mistakes in technical documents.
.if n .ad l
.nh
.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 
\&\s-1GNU\s0 Scientific Library.
.PP
At the moment there is a single function \fBgslmroot_fsolver\fR which provides an interface
to the algorithms in the \s-1GSL\s0 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 $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 $y;
\&  }
.Ve
.SH "FUNCTIONS"
.IX Header "FUNCTIONS"
.SS "fsolver_meat"
.IX Subsection "fsolver_meat"
.Vb 1
\&  Signature: (double  xfree(n);   double epsabs(); int method(); SV* function1)
.Ve
.PP
info not available
.PP
fsolver_meat does not process bad values.
It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
.SS "gslmroot_fsolver"
.IX Subsection "gslmroot_fsolver"
Multidimensional root finder without using derivatives
.PP
This function provides an interface to the multidimensional root finding algorithms
in the \s-1GSL\s0 library. It takes a minimum of two argumennts: a piddle \f(CW$init\fR with an 
initial guess for the roots of the system and a reference to a function. The latter
function must return 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.
.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 \s-1GSL\s0 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
Usage:
.PP
.Vb 2
\&   $res = gslmroot_fsolver($init, $function_ref,
\&                           [{Method => $method, Epsabs => $epsabs}]);
.Ve
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\s-1PDL\s0
.PP
The \s-1GSL\s0 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
\&\s-1COPYING\s0 in the \s-1PDL\s0 distribution. If this file is separated from the
\&\s-1PDL\s0 distribution, the copyright notice should be included in the file.