Function rgsl::numerical_differentiation::deriv_central

pub fn deriv_central<T>(
    f: function<T>,
    param: &mut T,
    x: f64,
    h: f64,
    result: &mut f64,
    abs_err: &mut f64
) -> Value

This function computes the numerical derivative of the function f at the point x using an adaptive central difference algorithm with a step-size of h. The derivative is returned in result and an estimate of its absolute error is returned in abserr.

The initial value of h is used to estimate an optimal step-size, based on the scaling of the truncation error and round-off error in the derivative calculation. The derivative is computed using a 5-point rule for equally spaced abscissae at x-h, x-h/2, x, x+h/2, x+h, with an error estimate taken from the difference between the 5-point rule and the corresponding 3-point rule x-h, x, x+h. Note that the value of the function at x does not contribute to the derivative calculation, so only 4-points are actually used.