def test_evaluate_quadratic(self): s = np.array([1.0, -1.0]) value = evaluate_quadratic(self.J, self.g, s) assert_equal(value, 4.85) value = evaluate_quadratic(self.J, self.g, s, diag=self.diag) assert_equal(value, 6.35) s = np.array([[1.0, -1.0], [1.0, 1.0], [0.0, 0.0]]) values = evaluate_quadratic(self.J, self.g, s) assert_allclose(values, [4.85, -0.91, 0.0]) values = evaluate_quadratic(self.J, self.g, s, diag=self.diag) assert_allclose(values, [6.35, 0.59, 0.0])
def test_evaluate_quadratic(self): s = np.array([1.0, -1.0]) value = evaluate_quadratic(self.J, self.g, s) assert_equal(value, 4.85) value = evaluate_quadratic(self.J, self.g, s, diag=self.diag) assert_equal(value, 6.35) s = np.array([[1.0, -1.0], [1.0, 1.0], [0.0, 0.0]]) values = evaluate_quadratic(self.J, self.g, s) assert_allclose(values, [4.85, -0.91, 0.0]) values = evaluate_quadratic(self.J, self.g, s, diag=self.diag) assert_allclose(values, [6.35, 0.59, 0.0])
def trf_no_bounds( fun, jac, x0, f0, J0, ftol, xtol, gtol, max_nfev, x_scale, loss_function, tr_solver, tr_options, verbose, ): x = x0.copy() f = f0 f_true = f.copy() nfev = 1 J = J0 njev = 1 m, n = J.shape if loss_function is not None: rho = loss_function(f, x) cost = 0.5 * np.sum(rho[0]) J, f = scale_for_robust_loss_function(J, f, rho) else: cost = 0.5 * np.dot(f, f) g = compute_grad(J, f) jac_scale = isinstance(x_scale, str) and x_scale == "jac" if jac_scale: scale, scale_inv = compute_jac_scale(J) else: scale, scale_inv = x_scale, 1 / x_scale Delta = norm(x0 * scale_inv) if Delta == 0: Delta = 1.0 if tr_solver == "lsmr": reg_term = 0 damp = tr_options.pop("damp", 0.0) regularize = tr_options.pop("regularize", True) if max_nfev is None: max_nfev = x0.size * 100 alpha = 0.0 # "Levenberg-Marquardt" parameter termination_status = None iteration = 0 step_norm = None actual_reduction = None if verbose == 2: print_header_nonlinear() while True: g_norm = norm(g, ord=np.inf) if g_norm < gtol: termination_status = 1 if verbose == 2: print_iteration_nonlinear(iteration, nfev, cost, actual_reduction, step_norm, g_norm) if termination_status is not None or nfev == max_nfev: break d = scale g_h = d * g if tr_solver == "exact": J_h = J * d U, s, V = svd(J_h, full_matrices=False) V = V.T uf = U.T.dot(f) elif tr_solver == "lsmr": J_h = right_multiplied_operator(J, d) if regularize: a, b = build_quadratic_1d(J_h, g_h, -g_h) to_tr = Delta / norm(g_h) ag_value = minimize_quadratic_1d(a, b, 0, to_tr)[1] reg_term = -ag_value / Delta**2 damp_full = (damp**2 + reg_term)**0.5 gn_h = lsmr(J_h, f, damp=damp_full, **tr_options)[0] S = np.vstack((g_h, gn_h)).T S, _ = qr(S, mode="economic") JS = J_h.dot(S) B_S = np.dot(JS.T, JS) g_S = S.T.dot(g_h) actual_reduction = -1 while actual_reduction <= 0 and nfev < max_nfev: if tr_solver == "exact": step_h, alpha, n_iter = solve_lsq_trust_region( n, m, uf, s, V, Delta, initial_alpha=alpha) elif tr_solver == "lsmr": p_S, _ = solve_trust_region_2d(B_S, g_S, Delta) step_h = S.dot(p_S) predicted_reduction = -evaluate_quadratic(J_h, g_h, step_h) step = d * step_h x_new = x + step f_new = fun(x_new) nfev += 1 step_h_norm = norm(step_h) if not np.all(np.isfinite(f_new)): Delta = 0.25 * step_h_norm continue # Usual trust-region step quality estimation. if loss_function is not None: cost_new = loss_function(f_new, x_new, cost_only=True) else: cost_new = 0.5 * np.dot(f_new, f_new) actual_reduction = cost - cost_new Delta_new, ratio = update_tr_radius( Delta, actual_reduction, predicted_reduction, step_h_norm, step_h_norm > 0.95 * Delta, ) step_norm = norm(step) termination_status = check_termination(actual_reduction, cost, step_norm, norm(x), ratio, ftol, xtol) if termination_status is not None: break alpha *= Delta / Delta_new Delta = Delta_new if actual_reduction > 0: x = x_new f = f_new f_true = f.copy() cost = cost_new J = jac(x, f) njev += 1 if loss_function is not None: rho = loss_function(f, x) J, f = scale_for_robust_loss_function(J, f, rho) g = compute_grad(J, f) if jac_scale: scale, scale_inv = compute_jac_scale(J, scale_inv) else: step_norm = 0 actual_reduction = 0 iteration += 1 if termination_status is None: termination_status = 0 active_mask = np.zeros_like(x) return OptimizeResult( x=x, cost=cost, fun=f_true, jac=J, grad=g, optimality=g_norm, active_mask=active_mask, nfev=nfev, njev=njev, status=termination_status, )