Compute the gradient of the SVM loss function

The method to calculate gradient in this case is Calculus (analytically, NOT numerically!). So we differentiate loss function with respect to W(yi) like this:

and with respect to W(j) when j!=yi is:

The 1 is just indicator function so we can ignore the middle form when condition is true. And when you write in code, the example you provided is the answer.

Since you are using cs231n example, you should definitely check note and videos if needed.

Hope this helps!