def test_logistic_grad_hess():
    rng = np.random.RandomState(0)
    n_samples, n_features = 50, 5
    X_ref = rng.randn(n_samples, n_features)
    y = np.sign(X_ref.dot(5 * rng.randn(n_features)))
    X_ref -= X_ref.mean()
    X_ref /= X_ref.std()
    X_sp = X_ref.copy()
    X_sp[X_sp < .1] = 0
    X_sp = sp.csr_matrix(X_sp)
    for X in (X_ref, X_sp):
        w = .1 * np.ones(n_features)

        # First check that _logistic_grad_hess is consistent
        # with _logistic_loss_and_grad
        loss, grad = _logistic_loss_and_grad(w, X, y, alpha=1.)
        grad_2, hess = _logistic_grad_hess(w, X, y, alpha=1.)
        assert_array_almost_equal(grad, grad_2)

        # Now check our hessian along the second direction of the grad
        vector = np.zeros_like(grad)
        vector[1] = 1
        hess_col = hess(vector)

        # Computation of the Hessian is particularly fragile to numerical
        # errors when doing simple finite differences. Here we compute the
        # grad along a path in the direction of the vector and then use a
        # least-square regression to estimate the slope
        e = 1e-3
        d_x = np.linspace(-e, e, 30)
        d_grad = np.array([
            _logistic_loss_and_grad(w + t * vector, X, y, alpha=1.)[1]
            for t in d_x
            ])

        d_grad -= d_grad.mean(axis=0)
        approx_hess_col = linalg.lstsq(d_x[:, np.newaxis], d_grad)[0].ravel()

        assert_array_almost_equal(approx_hess_col, hess_col, decimal=3)

        # Second check that our intercept implementation is good
        w = np.zeros(n_features + 1)
        loss_interp, grad_interp = _logistic_loss_and_grad(w, X, y, alpha=1.)
        loss_interp_2 = _logistic_loss(w, X, y, alpha=1.)
        grad_interp_2, hess = _logistic_grad_hess(w, X, y, alpha=1.)
        assert_array_almost_equal(loss_interp, loss_interp_2)
        assert_array_almost_equal(grad_interp, grad_interp_2)
dataset/ETHPy150Open scikit-learn/scikit-learn/sklearn/linear_model/tests/test_logistic.py/test_logistic_grad_hess/original