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# 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(\$_) }, \$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 informations on the functions, we refer you to the GSL offcial documentation: <http://www.gnu.org/software/gsl/manual/html_node/>

# AUTHORS

Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com> Visit the GSP FreeBSD Man Page Interface.