Function diff2
Calculate the derivative of a function using a two-point formula, i.e. a forward- or backward-difference formula.
real diff2(Func)
(
scope Func f,
real x,
real fx,
real scale = 1.00000
);
This method only evaluates the function once (in addition
to the function value provided by the user), and is therefore
the fastest way to compute a derivative. However, it is also
the least accurate method, and should only be used if the
function is very expensive to compute and you have
already calculated f(x).
Parameters
| Name | Description |
|---|---|
| f | The function to differentiate. |
| x | The point at which to take the derivative. |
| fx | The function value at x, i.e. f(x) |
| scale | A characteristic scale for f. When this
is positive, the forward-difference formula
is used, and when it is negative, the
backward-difference formula is used. |
Returns
An approximation to the derivative of f at the point
x. The relative error in the result is at best
on the order of sqrt(real.
Usually it is much higher.