Iteratively Modifying a Function in C

Question

I'm trying to create a numerical root finder in C, to find the zeros of Bessel Functions. Mathematical functions, F(x), can be deflated, by dividing the function by (x-x0), where x0 is a known root. The resulting function G(x) = F(x)/(x-x0), has all roots that F(x) had except at x0. This is useful as it prevents the same root being found twice by the solver.

When I find a root using my solver it is written to the array Roots[]. The Bessel Function is defined in math.h as double j0(double x).

I want to iteratively modify double j0(double x) so that I can have:

double my_j0(double x) = j0(x)/(x-Roots[n]);

I can then call this new, deflated function in my solver.

The above syntax doesn't make sense, but I don't know how to represent it.

I attempted to use a function pointer and defined

double (*my_j0)(double); my_j0 = &j0;

But now I don't know how to iteratively modify the function, each time dividing by the root I found with my solving algorithm.

Thanks for the help!

The function `F(x)/(x - x0)` has a removable singularity at `x0`. What you really want to solve is the analytic continuation of that function across the singularity. — Kerrek SB, Oct 21 '14 at 23:37
In essence I think what I was trying ask was this: http://stackoverflow.com/questions/1839965/dynamically-creating-functions-in-c And I think the result is what I'm trying to do is effectively impossible/very difficult in C. — Rohan, Oct 22 '14 at 15:35

score 0 · Answer 1 · answered Oct 21 '14 at 23:45

you could pass it as an argument in a recursive function with a starting case. Something like this might work if your trying to solve iterativley.

double my_j0(double x, double my_root){
    if(//some base case){
        //final calculation
        return calculation
    }
    if(my_root == some_initialization){
    //do initial calculation work
        my_root = calculated_root;
    }
    else{
    //do calculations using your root
        my_root = calculated_root;
    }
    return my_j0(x, my_root)

score 0 · Answer 2 · edited May 23 '17 at 12:12

After more experience, I've realized what I was really looking for was an Anonymous Function or lambda function. A great introduction as to what a lambda function is can be found on this SO question.

Unfortunately, C does not support lambda functions, however, there are language extensions supported by both GCC (using macros) and Clang compilers for implementing lambda functions which can be found on Wikipedia.

Iteratively Modifying a Function in C

2 Answers2