Draw N = 100 random points uniformly distributed over D. For each point, run a local minimization of f using scipy. optimize. minimize with the following methods: CG, BFGS, Newton-CG, L-BFGS-B. For this task, you will have to write two other functions, one that returns the Jacobian matrix of f and one that returns the Hessian matrix of f . Store the answers in an array with shape N x 6, each row of which has the following data:

(x1, y1,x2, y2,v, c),

where (x1, y1) and (x2, y2) are respectively the starting and the final point of the optimization, while v is the final value of f . The final element of the row c is code of the used method, according to this correspondence: CG:1, BFGS:2, Newton-CG:3, L-BFGSB:4

must be submitted as a Jupyter notebook