def cauchy_pt(g, hess, delta): # General expression for the Cauchy point crv = np.dot(g, right_multiply_hessian(hess, g)) gnorm = np.linalg.norm(g) if crv <= 0.0: alpha = delta / gnorm else: alpha = min(delta / gnorm, gnorm**2 / crv) s = -alpha * g red = calculate_model_value(g, hess, s) crvmin = np.dot(s, right_multiply_hessian(hess, s)) / np.dot(s, s) if crvmin < 0.0: crvmin = -1.0 return s, red, crvmin
def runTest(self): n = 3 g = np.array([1.0, 0.0, 1.0]) H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) Delta = 2.0 hess = to_upper_triangular_vector(H) xopt = np.ones((n, )) # trying nonzero (since bounds inactive) sl = xopt + np.array([-0.5, -10.0, -10.0]) su = xopt + np.array([10.0, 10.0, 10.0]) d, gnew, crvmin = trsbox(xopt, g, hess, sl, su, Delta) true_d = np.array([-1.0, 0.0, -0.5]) est_min = calculate_model_value(g, hess, d) true_min = calculate_model_value(g, hess, true_d) # Hope to get actual correct answer for internal minimum? # self.assertTrue(np.all(d == true_d), 'Wrong answer') # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt_box( g, hess, Delta, sl - xopt, su - xopt) # print(s_cauchy) # print(d) self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') self.assertTrue(np.all(gnew == g + right_multiply_hessian(hess, d)), 'Wrong gnew') print(crvmin) self.assertAlmostEqual(crvmin, -1.0, 'Wrong crvmin')
def cauchy_pt_box(g, hess, delta, lower, upper): # General expression for the Cauchy point, lower <= s <= upper crv = np.dot(g, right_multiply_hessian(hess, g)) gnorm = np.linalg.norm(g) if crv <= 0.0: alpha = delta / gnorm else: alpha = min(delta / gnorm, gnorm**2 / crv) # print("alpha = %g" % alpha) # Then cap with bounds: for i in range(len(g)): if g[i] > 0: # s[i] negative, will hit lower alpha = min(alpha, -lower[i] / g[i]) elif g[i] < 0: # s[i] positive, will hit upper alpha = min(alpha, -upper[i] / g[i]) # print("alpha = %g after i=%g" % (alpha, i)) s = -alpha * g red = calculate_model_value(g, hess, s) crvmin = np.dot(s, right_multiply_hessian(hess, s)) / np.dot(s, s) if crvmin < 0.0: crvmin = -1.0 return s, red, crvmin
def runTest(self): n = 3 g = np.array([1.0, 0.0, 1.0]) H = np.array([[1.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]) Delta = 5.0 / 12.0 hess = to_upper_triangular_vector(H) xopt = np.zeros((n, )) sl = -1e20 * np.ones((n, )) su = 1e20 * np.ones((n, )) d, gnew, crvmin = trsbox(xopt, g, hess, sl, su, Delta) true_d = np.array([-1.0 / 3.0, 0.0, -0.25]) est_min = calculate_model_value(g, hess, d) true_min = calculate_model_value(g, hess, true_d) # Hope to get actual correct answer # self.assertTrue(np.all(d == true_d), 'Wrong answer') # self.assertAlmostEqual(est_min, true_min, 'Wrong min value') s_cauchy, red_cauchy, crvmin_cauchy = cauchy_pt(g, hess, Delta) self.assertTrue(est_min <= red_cauchy, 'Cauchy reduction not achieved') self.assertTrue(np.all(gnew == g + right_multiply_hessian(hess, d)), 'Wrong gnew') self.assertAlmostEqual(crvmin, 0.0, 'Wrong crvmin')