Question

I want to interpolate a function in mathematica.

The function depends on a parameter a, in fact it is the inverse of a function F which also depends on a, so I build my approximation as follows,

approx = Interpolation[Table[{F[0.1 n, a], 0.1 n}, {n, -100, 100}]]

now I can simply call approx[x] to evaluate the inverse function at a point.

Instead I would like to do something like this: Define a function which takes a parameter,

G[x_,a_] = "construct the interpolating function,
            and return the value of the function at x"

Then write G[x,a] to evaluate the function. Otherwise I would have to repeat the interpolation for all the parameters I am interested in and have lots of variables lying around. I have tried putting the Interpolation[] call inside a module but that just constructs the interpolation every time I call G[x,a]! How would I avoid this?

Thanks for reading.

Answer 1

Try something along these lines:

G[a_]:=G[a]=Interpolation[Table[{F[0.1 n, a], 0.1 n}, {n, -100, 100}]]

G[0.2]  (* particular value of G[a] *)

G[0.2][0.3] (* the value you want *)

You will only evaluate G the first time you call it for each particular value of a.