Can MATLAB find a function that generated a random set of points?

Hi I'm new with MATLAB. I have a random function that generates 1000 points (x,y). If I only have those points, how can I get the function that generated those random points (x,y)?

[Azzi Abdelmalek]

The question is not clear, especially when you say:If I only have those points

[Stephen23]

"how can I get the function..."

There are infinite functions that will fit your one thousand points. Which of those infinite functions do you want to "get" ?

Answer 1

[John D'Errico]

In general, no, you cannot find the underlying function. In fact, there are infinitely many functions that will pass through a given set of points. How should MATLAB know which of those functions apply to this set of points?

For example, suppose I choose 3 points.

x = [0 1 2];
y1 = exp(x) + x.^3 - 3*x.^2 + 2*x;
y2 = exp(x);

As it turns out, the polynomial part there is zero on the point set [0,1,2]. So if you have only function values at those three points, then MATLAB could not possibly know which expression was used to generate either y1 or y2.

Again, there are infinitely many "functions" that will pass through any set of points. In order to estimate a model, the analyst needs to pose some model family that will apply. If you are unwilling to provide any input on the question, then a spline interpolant is generally your best choice.