You are creating a function handle, fun, that takes an x and y input. Then in
value = s*(trapz(trapz(data_file*fun)))*0.00021
you are trying to multiple data_file by fun. But fun is the function handle, not the result of executing the function at any particular location.
"E(x,y) is the input matrix"
Not in that equation it is not. The dx and dy tell you that E_I(x,y) in the equation has to be considered over the entire range -infinity to +infinity. That is not meaningful for a matrix, so it follows that E_I(x,y) must be a function rather than a matrix.
If your passed in data_file represents the previous evaluation of some E_I over a fixed set of coordinates, then you should be evaluating your fun at the same coordinates (whatever they are.) You should also be passing the coordinates in to trapz()
