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lib/Math/Brent.pm  view on Meta::CPAN

Provides a simple interface to the L</BracketMinimum()> and L</Brent()>
routines.

Given a function, an initial guess for the function's
minimum, and its scaling, this routine converges
to the function's minimum using Brent's method.

    ($x, $y) = Minimise1D($guess, $scale, \&func);

The minimum is reached within a certain tolerance (defaulting 1e-7), and
attempts to do so within a maximum number of iterations (defaulting to 100).
You may override them by providing alternate values:

    ($x, $y) = Minimise1D($guess, $scale, \&func, 1.5e-8, 120);

=cut

sub Minimise1D
{
    my ($guess, $scale, $func, $tol, $itmax) = @_;
    my ($a, $b, $c) = BracketMinimum($guess - $scale, $guess + $scale, $func);

lib/Math/Brent.pm  view on Meta::CPAN

=item 1. B<$bx> is between B<$ax> and B<$cx>, and

=item 2. B<func($bx)> is less than both B<func($ax)> and B<func($cx)>),

=back

Brent() isolates the minimum to a fractional precision of about B<$tol>
using Brent's method.

A maximum number of iterations B<$itmax> may be specified for this search - it
defaults to 100. Returned is a list consisting of the abcissa of the minum
and the function value there.

=cut

sub Brent
{
    my ($ax, $bx, $cx, $func, $tol, $ITMAX) = @_;
    my ($d, $u, $x, $w, $v); # ordinates
    my ($fu, $fx, $fw, $fv); # function evaluations