How do I compute the second derivative of an one dimensional array in C#

Question

How do I compute the second derivative of an one dimensional array in C#? has anyone done this before ?

Try to be more specific. Do you mean you have a single array of values, for example y = [1, 7, 17, 31, 49, 71, 97], and you want to assume a constant dx value, and therefore compute the approximate (i.e. mean) derivative and 2nd derivative? — Joshua Huber, May 18 '22 at 22:19
First differences approximate the first derivative; second differences the second. https://en.wikipedia.org/wiki/Finite_difference — duffymo, May 18 '22 at 23:23
lol see I was specific , because you knew what I was talking about — TerriB4545, May 19 '22 at 03:35
[like so?](https://stackoverflow.com/questions/28902728/c-sharp-method-for-element-by-element-difference-of-an-array-derivative-approxi) — TaW, May 19 '22 at 05:26

score 0 · Accepted Answer · answered May 19 '22 at 06:59

You can declare an extension method that returns pairs of sequential numbers:

public static IEnumerable<(T Previous, T Next)> PreviousAndNext<T>(this IEnumerable<T> self)
{
    using (var iter = self.GetEnumerator())
    {
        if (!iter.MoveNext())
            yield break;
        var previous = iter.Current;
        while (iter.MoveNext())
        {
            var next = iter.Current;
            yield return (previous, next);
            previous = next;
        }
    }
}

If you want the discrete derivative, i.e. difference between sequential numbers you would do: myArray.PreviousAndNext().Select((p, n) => n-p). If you want the second discrete derivative you would just repeat the function, i.e.

myArray.PreviousAndNext().Select((p, n) => n-p)
       .PreviousAndNext().Select((p, n) => n-p);

You could repeat this pattern however many times you want.

How do I compute the second derivative of an one dimensional array in C#

1 Answers1