Torch/Lua, how to compute Area Under the Curve (AUC)?

I'm new to Torch, and I am working on a problem where I have to depict the Receiver Operating Characteristic (ROC) curves and their Areas Under the Curve (AUC).

I have to arrays: TPrate on the y axis and FPrate on the x axis, having both size n

How could I compute the Area Under the Curve of this function in Torch7 or Lua?

I also found this code from JayClascoe.com but I don't know how to use its functions.

Solution

You won't be able to use the code from JayClascoe as it works with functions and yours is a set of points. Assuming FPrate has x values for x coordinate sorted and TPrate has corresponding values, you can use Trapezoidal rule. Something like this may work:

local area = 0
for i = 2, n do
  area = area + (FPrate[i] - FPrate[i-1]) * (TPrate[i-1] + TPrate[i])/2
end