How to test if equation in .p file is linear.

I have a .p file that has an equation in it that I can’t ever know. How would you call it in a script and test for linearity (additivity, scalability).

[V_Izepatchy]

If it helps, I’m using a unit step function

Answer 1

[Walter Roberson]

In some cases you might get lucky, in that if you pass purely symbolic variables to the function, you might get back a formula. That would fail if the function has conditional tests based on the inputs.

The existence of conditional tests based on the input would tend to hint that likely the function is not linear. It is, however, not proof, as the conditional tests might effectively be irrelevant. For example,

if x >= 0
    y = x.^2;
else
    y = (-x).^2;
end

In this example although there is a conditional test, algebraically it turns out not to matter for the outcome -- so the presence of conditional elements is not proof that the function is not linear.

Answer 2

[Matt J]

Well, there's no test that will verify linearity globally (for all inputs), but you can select random inputs and test the applicable properties, e.g.,

x=rand; y=rand;

norm(  func(x)+func(y)-func(x+y)  )  %should be close to zero