%perlcode %{
@EXPORT_OK = qw/
gsl_deriv_central
gsl_deriv_backward
gsl_deriv_forward
/;
%EXPORT_TAGS = ( all => [ @EXPORT_OK ] );
__END__
=head1 NAME
Math::GSL::Deriv - Numerical Derivatives
=head1 SYNOPSIS
use Math::GSL::Deriv qw/:all/;
use Math::GSL::Errno qw/:all/;
my ($x, $h) = (1.5, 0.01);
my ($status, $val,$err) = gsl_deriv_central ( sub { sin($_[0]) }, $x, $h);
my $res = abs($val - cos($x));
if ($status == $GSL_SUCCESS) {
printf "deriv(sin((%g)) = %.18g, max error=%.18g\n", $x, $val, $err;
printf " cos(%g)) = %.18g, residue= %.18g\n" , $x, cos($x), $res;
} else {
my $gsl_error = gsl_strerror($status);
print "Numerical Derivative FAILED, reason:\n $gsl_error\n\n";
}
=head1 DESCRIPTION
This module allows you to take the numerical derivative of a Perl subroutine. To find
a numerical derivative you must also specify a point to evaluate the derivative and a
"step size". The step size is a knob that you can turn to get a more finely or coarse
grained approximation. As the step size $h goes to zero, the formal definition of a
derivative is reached, but in practive you must choose a reasonable step size to get
a reasonable answer. Usually something in the range of 1/10 to 1/10000 is sufficient.
So long as your function returns a single scalar value, you can differentiate as
complicated a function as your heart desires.
=over
=item * C
use Math::GSL::Deriv qw/gsl_deriv_central/;
my ($x, $h) = (1.5, 0.01);
sub func { my $x=shift; $x**4 - 15 * $x + sqrt($x) };
my ($status, $val,$err) = gsl_deriv_central ( \&func , $x, $h);
This method approximates the central difference of the subroutine reference
$function, evaluated at $x, with "step size" $h. This means that the
function is evaluated at $x-$h and $x+h.
=item * C
use Math::GSL::Deriv qw/gsl_deriv_backward/;
my ($x, $h) = (1.5, 0.01);
sub func { my $x=shift; $x**4 - 15 * $x + sqrt($x) };
my ($status, $val,$err) = gsl_deriv_backward ( \&func , $x, $h);
This method approximates the backward difference of the subroutine
reference $function, evaluated at $x, with "step size" $h. This means that
the function is evaluated at $x-$h and $x.
=item * C
use Math::GSL::Deriv qw/gsl_deriv_forward/;
my ($x, $h) = (1.5, 0.01);
sub func { my $x=shift; $x**4 - 15 * $x + sqrt($x) };
my ($status, $val,$err) = gsl_deriv_forward ( \&func , $x, $h);
This method approximates the forward difference of the subroutine reference
$function, evaluated at $x, with "step size" $h. This means that the
function is evaluated at $x and $x+$h.
=back
For more informations on the functions, we refer you to the GSL offcial
documentation: L
=head1 AUTHORS
Jonathan Leto and Thierry Moisan
=head1 COPYRIGHT AND LICENSE
Copyright (C) 2008-2009 Jonathan Leto and Thierry Moisan
This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
=cut
%}