---
name: "Math::GSL::Deriv"
section: "3pm"
platform: "linux"
package: "libmath-gsl-perl"
version: "0.45-2+b1"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/Math::GSL::Deriv"
---

# Math::GSL::Deriv(3pm)

Numerical Derivatives

## NAME

Math::GSL::Deriv - Numerical Derivatives

## 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";
    }
```

## 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.

- •

  `"gsl_deriv_central($function, $x, $h)"`

  ```
      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.

- •

  `"gsl_deriv_backward($function, $x, $h)"`

  ```
      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`.

- •

  `"gsl_deriv_forward($function, $x, $h)"`

  ```
      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.

For more information on the functions, we refer you to the GSL official documentation: \<http://www.gnu.org/software/gsl/manual/html\_node/\>

## AUTHORS

Jonathan "Duke" Leto \<jonathan@leto.net\> and Thierry Moisan \<thierry.moisan@gmail.com\>

## COPYRIGHT AND LICENSE

Copyright (C) 2008-2024 Jonathan "Duke" Leto and Thierry Moisan

This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.