Understanding Jacobian exit scipy.optimize.minimize

Question

I work with scipy.optimize.minimize to find the minimum RSS for a custom nonlinear function. I will give a simple linear example to illustrate what I am doing:

import numpy as np
from scipy import optimize

def response(X, b0, b1, b2):
    return b2 * X[1]**2 + b1 * X[0] + b0

def obj_rss(model_params, y_true, X):
    return np.sum((y_true - response(X, *model_params))**2)  

x = np.array([np.arange(0, 10), np.arange(10, 20)])
r = 15. * x[1]**2 - 32. * x[0] + 10.

init_guess = np.array([0., 50., 10.])
res = optimize.minimize(obj_rss, init_guess, args=(r, x))

print res

This gives the results:

      fun: 3.0218799331864133e-08
 hess_inv: array([[  7.50606278e+00,   2.38939463e+00,  -8.33333575e-02],
       [  2.38939463e+00,   8.02462363e-01,  -2.74621294e-02],
       [ -8.33333575e-02,  -2.74621294e-02,   9.46969972e-04]])
      jac: array([ -3.31359843e-07,  -5.42022462e-08,   2.34304025e-08])
  message: 'Optimization terminated successfully.'
     nfev: 45
      nit: 6
     njev: 9
   status: 0
  success: True
        x: array([ 10.00066577, -31.99978062,  14.99999243])

And we see that the set parameters 10, -32 and 15 are equivalent to those used to generate the actual data. It's great. Now my question is:

I understand that the Jacobian should be the matrix mxn, where m is the number of entries from input X, and n is the number of parameters. Clearly, I do not have this in the results object. The result object gives an array that is referred to as the Jacobian in the documentation ( 1 and 2 ), but is only one-dimensional, the number of elements of which is equal to the number of parameters.

, = 'SLSQP', , , .

.,

- , , t- p- , , , , , .

EDIT:

, SLSQP , , BFGS, L-BFGS-B SLSQP, , ( ). SLSQP .

import numpy as np
from scipy import optimize


def response(X, b0, b1, b2):
    return b2 * X[1]**2 + b1 * X[0] + b0

def obj_rss(model_params, y_true, X):
    return np.sum((y_true - response(X, *model_params))**2)


x = np.array([np.arange(0, 10), np.arange(10, 20)])
r = 15. * x[1]**2 - 32. * x[0] + 10.

init_guess = np.array([0., 50., 10.])
res = optimize.minimize(obj_rss, init_guess, method='SLSQP', args=(r, x))

print res

r_pred = response(x, *res.x)

:

     fun: 7.5269461938291697e-10
     jac: array([  2.94677643e-05,   5.52844499e-04,   2.59870917e-02,
         0.00000000e+00])
 message: 'Optimization terminated successfully.'
    nfev: 58
     nit: 10
    njev: 10
  status: 0
 success: True
       x: array([ 10.00004495, -31.9999794 ,  14.99999938])

, , SLSQP, . , .