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.\"
.IX Title "Math::GSL::Deriv 3pm"
.TH Math::GSL::Deriv 3pm 2024-03-07 "perl v5.38.2" "User Contributed Perl Documentation"
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.SH NAME
Math::GSL::Deriv \- Numerical Derivatives
.SH SYNOPSIS
.IX Header "SYNOPSIS"
.Vb 2
\&    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\en", $x, $val, $err;
\&        printf "       cos(%g)) = %.18g, residue=  %.18g\en"  , $x, cos($x), $res;
\&    } else {
\&        my $gsl_error = gsl_strerror($status);
\&        print "Numerical Derivative FAILED, reason:\en $gsl_error\en\en";
\&    }
.Ve
.SH DESCRIPTION
.IX Header "DESCRIPTION"
This module allows you to take the numerical derivative of a Perl subroutine. To find
a numerical derivative you must also specify a point to evaluate the derivative and a
"step size". The step size is a knob that you can turn to get a more finely or coarse
grained approximation. As the step size \f(CW$h\fR 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.
.PP
So long as your function returns a single scalar value, you can differentiate as
complicated a function as your heart desires.
.IP \(bu 4
\&\f(CW\*(C`gsl_deriv_central($function, $x, $h)\*(C'\fR
.Sp
.Vb 3
\&    use Math::GSL::Deriv qw/gsl_deriv_central/;
\&    my ($x, $h) = (1.5, 0.01);
\&    sub func { my $x=shift; $x**4 \- 15 * $x + sqrt($x) };
\&
\&    my ($status, $val,$err) = gsl_deriv_central ( \e&func , $x, $h);
.Ve
.Sp
This method approximates the central difference of the subroutine reference
\&\f(CW$function\fR, evaluated at \f(CW$x\fR, with "step size" \f(CW$h\fR. This means that the
function is evaluated at \f(CW$x\fR\-$h and \f(CW$x\fR+h.
.IP \(bu 4
\&\f(CW\*(C`gsl_deriv_backward($function, $x, $h)\*(C'\fR
.Sp
.Vb 3
\&    use Math::GSL::Deriv qw/gsl_deriv_backward/;
\&    my ($x, $h) = (1.5, 0.01);
\&    sub func { my $x=shift; $x**4 \- 15 * $x + sqrt($x) };
\&
\&    my ($status, $val,$err) = gsl_deriv_backward ( \e&func , $x, $h);
.Ve
.Sp
This method approximates the backward difference of the subroutine
reference \f(CW$function\fR, evaluated at \f(CW$x\fR, with "step size" \f(CW$h\fR. This means that
the function is evaluated at \f(CW$x\fR\-$h and \f(CW$x\fR.
.IP \(bu 4
\&\f(CW\*(C`gsl_deriv_forward($function, $x, $h)\*(C'\fR
.Sp
.Vb 3
\&    use Math::GSL::Deriv qw/gsl_deriv_forward/;
\&    my ($x, $h) = (1.5, 0.01);
\&    sub func { my $x=shift; $x**4 \- 15 * $x + sqrt($x) };
\&
\&    my ($status, $val,$err) = gsl_deriv_forward ( \e&func , $x, $h);
.Ve
.Sp
This method approximates the forward difference of the subroutine reference
\&\f(CW$function\fR, evaluated at \f(CW$x\fR, with "step size" \f(CW$h\fR. This means that the
function is evaluated at \f(CW$x\fR and \f(CW$x\fR+$h.
.PP
For more information on the functions, we refer you to the GSL official
documentation: <http://www.gnu.org/software/gsl/manual/html_node/>
.SH AUTHORS
.IX Header "AUTHORS"
Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
.SH "COPYRIGHT AND LICENSE"
.IX Header "COPYRIGHT AND LICENSE"
Copyright (C) 2008\-2023 Jonathan "Duke" Leto and Thierry Moisan
.PP
This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.