image-match/python/py/Lib/site-packages/scipy/optimize/tests/test_lbfgsb_hessinv.py

import numpy as np
from numpy.testing import assert_allclose
import scipy.linalg
from scipy.optimize import minimize


def test_1():
    def f(x):
        return x**4, 4*x**3

    for gtol in [1e-8, 1e-12, 1e-20]:
        for maxcor in range(20, 35):
            result = minimize(fun=f, jac=True, method='L-BFGS-B', x0=20,
                options={'gtol': gtol, 'maxcor': maxcor})

            H1 = result.hess_inv(np.array([1])).reshape(1,1)
            H2 = result.hess_inv.todense()

            assert_allclose(H1, H2)


def test_2():
    H0 = [[3, 0], [1, 2]]

    def f(x):
        return np.dot(x, np.dot(scipy.linalg.inv(H0), x))

    result1 = minimize(fun=f, method='L-BFGS-B', x0=[10, 20])
    result2 = minimize(fun=f, method='BFGS', x0=[10, 20])

    H1 = result1.hess_inv.todense()

    H2 = np.vstack((
        result1.hess_inv(np.array([1, 0])),
        result1.hess_inv(np.array([0, 1]))))

    assert_allclose(
        result1.hess_inv(np.array([1, 0]).reshape(2,1)).reshape(-1),
        result1.hess_inv(np.array([1, 0])))
    assert_allclose(H1, H2)
    assert_allclose(H1, result2.hess_inv, rtol=1e-2, atol=0.03)


def test_3():

    def todense_old_impl(self):
        s, y, n_corrs, rho = self.sk, self.yk, self.n_corrs, self.rho
        I_arr = np.eye(*self.shape, dtype=self.dtype)
        Hk = I_arr

        for i in range(n_corrs):
            A1 = I_arr - s[i][:, np.newaxis] * y[i][np.newaxis, :] * rho[i]
            A2 = I_arr - y[i][:, np.newaxis] * s[i][np.newaxis, :] * rho[i]

            Hk = np.dot(A1, np.dot(Hk, A2)) + (rho[i] * s[i][:, np.newaxis] *
                                                        s[i][np.newaxis, :])
        return Hk

    H0 = [[3, 0], [1, 2]]

    def f(x):
        return np.dot(x, np.dot(scipy.linalg.inv(H0), x))

    result1 = minimize(fun=f, method='L-BFGS-B', x0=[10, 20])
    assert_allclose(result1.hess_inv.todense(), todense_old_impl(result1.hess_inv))