I am trying to remove the for loop i.e. to vectorize the following code that computes the numerical Jacobian using finite difference. I think the vectorized version of the code will be faster than the current version especially for computing the Jacobian of a large-scale problem.
In addition, I will like to multiply J^T with v, where v is any vector with dimension equal to the rows of J, how can I include this in my code? Please, can anybody help me out?