Chris Marshall > PDL > PDL::GSL::MROOT

# NAME

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

# 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;
}```

# 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}]);```

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