How to make functions from datasets

Question

I have a csv that encodes the results of plugging certain parameters (say, A and B) into certain functions (say, f and g). Think matrix with (say, 4) columns and a million rows with the columns corresponding to A, B, C = f(A, B), and D = g(A, B) respectively. I'd like to be able to use the dynamic visualization features of mathematica, but this requires turning this data into discreet functions, and the columns into their own lists to use as domains in the Manipulate environment.

I want to be able to do something like Manipulate[Plot[function[A, B], {A, (list of values)}], {B, (list of values)}, {function, {f, g}}]

I have been poring over the Help guide for hours and this seems to be such a basic thing to do that I feel crazy for not being able to find it.

kglr · Answer

Perhaps you can use DiscretePlot3D

{alist, blist} =  RandomReal[{-2 Pi, 2 Pi}, {2, 20}];

Manipulate[DiscretePlot3D[f[a + b], {a, alist}, {b, blist},
                          PlotStyle -> Hue[RandomReal[]], ExtentSize -> Scaled[.5]],
           {f, {Sin, Cos}}]

hieron · Answer

C, D, E, I, K, N, O are symbols already in use by Mathematica (ONCE KID)
you do not follow the recommended convention that user variables are written lowercase.

You can see that when typing the letter it is colored black, and not blue.

most probably the Evaluate statement solves your other problem in your given metacode

Manipulate[Plot[function[A, B]//Evaluate, {A, (list of values)}], {B, (list of values)}, {function, {f, g}}]

How to make functions from datasets

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