I have an equation f(x,y,z) where for every experimental pair of x, y, and z, the value of f(x,y,z) is the same. So f(x1,y1,z1) = f(x2,y2,z2) = f(x3,y3,z3)..... etc. at these specific sets of points. They are related by some parameters which are unknown, lets say a, b, c, and d. How would I go about solving for these parameters, given that I have around 1000 sets of x, y, z pairs. f(x,y,z) is between 0 and 1. Another way to word this would be solving for the parameters which make f(x1,y1,z1) = f(x2,y2,z2)...etc
I do not know where to begin with this, and any guidance on packages / methods to look at would be greatly appreciated. I suspect I will need to use some sort of minimization methods, as there are so quite a few parameters. I have not listed the equation as it is too complex, and would only complicate the problem, but can do so if requested.