from typing import Tuple import numpy as np from numpy.typing import NDArray import ausgaben as aus import numeric_examples_karney as ne_karney import numeric_examples_panou as ne_panou import winkelumrechnungen as wu from ellipsoid_triaxial import EllipsoidTriaxial from runge_kutta import rk4, rk4_end, rk4_integral from utils_angle import cot, wrap_0_2pi, wrap_mpi_pi def norm_a(a: float) -> float: a = float(a) % (2 * np.pi) return a def azimut(E: float, G: float, dbeta_du: float, dlamb_du: float) -> float: north = np.sqrt(E) * dbeta_du east = np.sqrt(G) * dlamb_du return norm_a(np.arctan2(east, north)) def sph_azimuth(beta1, lam1, beta2, lam2): dlam = wrap_mpi_pi(lam2 - lam1) y = np.sin(dlam) * np.cos(beta2) x = np.cos(beta1) * np.sin(beta2) - np.sin(beta1) * np.cos(beta2) * np.cos(dlam) a = np.arctan2(y, x) if a < 0: a += 2 * np.pi return a # Panou 2013 def gha2_num( ell: EllipsoidTriaxial, beta_0: float, lamb_0: float, beta_1: float, lamb_1: float, n: int = 16000, epsilon: float = 10**-12, iter_max: int = 30, all_points: bool = False, ) -> Tuple[float, float, float] | Tuple[float, float, float, NDArray, NDArray]: """ :param ell: Ellipsoid :param beta_0: Beta Punkt 0 :param lamb_0: Lambda Punkt 0 :param beta_1: Beta Punkt 1 :param lamb_1: Lambda Punkt 1 :param n: Anzahl Schritte :param epsilon: Genauigkeit :param iter_max: Maximale Iterationen :param all_points: Ausgabe aller Punkte :return: Azimut Startpunkt, Azumit Zielpunkt, Strecke """ ax2 = float(ell.ax) * float(ell.ax) ay2 = float(ell.ay) * float(ell.ay) b2 = float(ell.b) * float(ell.b) Ex2 = float(ell.Ex) * float(ell.Ex) Ey2 = float(ell.Ey) * float(ell.Ey) Ee2 = float(ell.Ee) * float(ell.Ee) Ey4 = Ey2 * Ey2 Ee4 = Ee2 * Ee2 two_pi = 2.0 * np.pi # Berechnung Koeffizienten, Gaußschen Fundamentalgrößen 1. Ordnung sowie deren Ableitungen def BETA_LAMBDA(beta, lamb): sb = np.sin(beta) cb = np.cos(beta) sl = np.sin(lamb) cl = np.cos(lamb) sb2 = sb * sb cb2 = cb * cb sl2 = sl * sl cl2 = cl * cl s2b = 2.0 * sb * cb c2b = cb2 - sb2 s2l = 2.0 * sl * cl c2l = cl2 - sl2 denB = Ex2 - Ey2 * sb2 denL = Ex2 - Ee2 * cl2 BETA = (ay2 * sb2 + b2 * cb2) / denB LAMBDA = (ax2 * sl2 + ay2 * cl2) / denL BETA_ = (ax2 * Ey2 * s2b) / (denB * denB) LAMBDA_ = -(b2 * Ee2 * s2l) / (denL * denL) BETA__ = (2.0 * ax2 * Ey4 * (s2b * s2b)) / (denB * denB * denB) + (2.0 * ax2 * Ey2 * c2b) / ( denB * denB ) LAMBDA__ = (2.0 * b2 * Ee4 * (s2l * s2l)) / (denL * denL * denL) - (2.0 * b2 * Ee2 * s2l) / ( denL * denL ) Q = Ey2 * cb2 + Ee2 * sl2 E = BETA * Q G = LAMBDA * Q E_beta = BETA_ * Q - BETA * Ey2 * s2b E_lamb = BETA * Ee2 * s2l G_beta = -LAMBDA * Ey2 * s2b G_lamb = LAMBDA_ * Q + LAMBDA * Ee2 * s2l E_beta_beta = BETA__ * Q - 2.0 * BETA_ * Ey2 * s2b - 2.0 * BETA * Ey2 * c2b E_beta_lamb = BETA_ * Ee2 * s2l E_lamb_lamb = 2.0 * BETA * Ee2 * c2l G_beta_beta = -2.0 * LAMBDA * Ey2 * c2b G_beta_lamb = -LAMBDA_ * Ey2 * s2b G_lamb_lamb = LAMBDA__ * Q + 2.0 * LAMBDA_ * Ee2 * s2l + 2.0 * LAMBDA * Ee2 * c2l return ( BETA, LAMBDA, E, G, BETA_, LAMBDA_, BETA__, LAMBDA__, E_beta, E_lamb, G_beta, G_lamb, E_beta_beta, E_beta_lamb, E_lamb_lamb, G_beta_beta, G_beta_lamb, G_lamb_lamb, ) # Berechnung der ODE Koeffizienten für Fall 1 (lambda_0 != lambda_1) def p_coef(beta, lamb): ( BETA, LAMBDA, E, G, BETA_, LAMBDA_, BETA__, LAMBDA__, E_beta, E_lamb, G_beta, G_lamb, E_beta_beta, E_beta_lamb, E_lamb_lamb, G_beta_beta, G_beta_lamb, G_lamb_lamb, ) = BETA_LAMBDA(beta, lamb) p_3 = -0.5 * (E_lamb / G) p_2 = (G_beta / G) - 0.5 * (E_beta / E) p_1 = 0.5 * (G_lamb / G) - (E_lamb / E) p_0 = 0.5 * (G_beta / E) p_33 = -0.5 * ((E_beta_lamb * G - E_lamb * G_beta) / (G**2)) p_22 = ((G * G_beta_beta - G_beta * G_beta) / (G**2)) - 0.5 * ( (E * E_beta_beta - E_beta * E_beta) / (E**2) ) p_11 = 0.5 * ((G * G_beta_lamb - G_beta * G_lamb) / (G**2)) - ( (E * E_beta_lamb - E_beta * E_lamb) / (E**2) ) p_00 = 0.5 * ((E * G_beta_beta - E_beta * G_beta) / (E**2)) return BETA, LAMBDA, E, G, p_3, p_2, p_1, p_0, p_33, p_22, p_11, p_00 # Berechnung der ODE Koeffizienten für Fall 2 (lambda_0 == lambda_1) def q_coef(beta, lamb): ( BETA, LAMBDA, E, G, BETA_, LAMBDA_, BETA__, LAMBDA__, E_beta, E_lamb, G_beta, G_lamb, E_beta_beta, E_beta_lamb, E_lamb_lamb, G_beta_beta, G_beta_lamb, G_lamb_lamb, ) = BETA_LAMBDA(beta, lamb) q_3 = -0.5 * (G_beta / E) q_2 = (E_lamb / E) - 0.5 * (G_lamb / G) q_1 = 0.5 * (E_beta / E) - (G_beta / G) q_0 = 0.5 * (E_lamb / G) q_33 = -0.5 * ((E * G_beta_lamb - E_lamb * G_lamb) / (E**2)) q_22 = ((E * E_lamb_lamb - E_lamb * E_lamb) / (E**2)) - 0.5 * ( (G * G_lamb_lamb - G_lamb * G_lamb) / (G**2) ) q_11 = 0.5 * ((E * E_beta_lamb - E_beta * E_lamb) / (E**2)) - ( (G * G_beta_lamb - G_beta * G_lamb) / (G**2) ) q_00 = 0.5 * ((E_lamb_lamb * G - E_lamb * G_lamb) / (G**2)) return BETA, LAMBDA, E, G, q_3, q_2, q_1, q_0, q_33, q_22, q_11, q_00 def integrand_lambda(lamb, y): beta = y[0] beta_p = y[1] (_, _, E, G, *_) = BETA_LAMBDA(beta, lamb) return np.sqrt(E * beta_p**2 + G) def integrand_beta(beta, y): lamb = y[0] lamb_p = y[1] (_, _, E, G, *_) = BETA_LAMBDA(beta, lamb) return np.sqrt(E + G * lamb_p**2) def solve_lambda_branch(beta0, lamb0, beta1, lamb1_target, N_run, N_newt, it_max): dlamb = float(lamb1_target - lamb0) if abs(dlamb) < 1e-15: return None sgn = 1.0 if dlamb >= 0.0 else -1.0 def ode_lamb(lamb, v): beta, beta_p, X3, X4 = v (_, _, _, _, p_3, p_2, p_1, p_0, p_33, p_22, p_11, p_00) = p_coef(beta, lamb) dbeta = beta_p dbeta_p = p_3 * beta_p**3 + p_2 * beta_p**2 + p_1 * beta_p + p_0 dX3 = X4 dX4 = (p_33 * beta_p**3 + p_22 * beta_p**2 + p_11 * beta_p + p_00) * X3 + ( 3 * p_3 * beta_p**2 + 2 * p_2 * beta_p + p_1 ) * X4 return np.array([dbeta, dbeta_p, dX3, dX4], dtype=float) alpha0_sph = sph_azimuth(beta0, lamb0, beta1, lamb1_target) (_, _, E0, G0, *_) = BETA_LAMBDA(beta0, lamb0) beta_p0_sph = np.sqrt(G0 / E0) * cot(alpha0_sph) def solve_newton(beta_p0_init: float): beta_p0 = float(beta_p0_init) for _ in range(it_max): v0 = np.array([beta0, beta_p0, 0.0, 1.0], dtype=float) _, y_end = rk4_end(ode_lamb, lamb0, v0, dlamb, N_newt) beta_end, _, X3_end, _ = y_end delta = beta_end - beta1 if abs(delta) < epsilon: return True, beta_p0 if abs(X3_end) < 1e-20: return False, None step = delta / X3_end step = float(np.clip(step, -0.5, 0.5)) beta_p0 -= step return False, None seeds = [beta_p0_sph, -beta_p0_sph, 0.5 * beta_p0_sph, 2.0 * beta_p0_sph] best = None for seed in seeds: ok, sol = solve_newton(seed) if not ok: continue v0_sol = np.array([beta0, sol, 0.0, 1.0], dtype=float) _, _, s_val = rk4_integral(ode_lamb, lamb0, v0_sol, dlamb, N_run, integrand_lambda) if (best is None) or (s_val < best[0]): best = (float(s_val), float(sol)) if best is None: return None return best[0], best[1], sgn, dlamb, ode_lamb def solve_beta_branch(beta0, lamb0, beta1, lamb1, N_run, N_newt, it_max): dbeta = float(beta1 - beta0) if abs(dbeta) < 1e-15: return None sgn = 1.0 if dbeta >= 0.0 else -1.0 def ode_beta(beta, v): lamb, lamb_p, Y3, Y4 = v (_, _, _, _, q_3, q_2, q_1, q_0, q_33, q_22, q_11, q_00) = q_coef(beta, lamb) dlamb = lamb_p dlamb_p = q_3 * lamb_p**3 + q_2 * lamb_p**2 + q_1 * lamb_p + q_0 dY3 = Y4 dY4 = (q_33 * lamb_p**3 + q_22 * lamb_p**2 + q_11 * lamb_p + q_00) * Y3 + ( 3 * q_3 * lamb_p**2 + 2 * q_2 * lamb_p + q_1 ) * Y4 return np.array([dlamb, dlamb_p, dY3, dY4], dtype=float) def solve_newton(lamb_p0_init: float): lamb_p0 = float(lamb_p0_init) for _ in range(it_max): v0 = np.array([lamb0, lamb_p0, 0.0, 1.0], dtype=float) _, y_end = rk4_end(ode_beta, beta0, v0, dbeta, N_newt) lamb_end, _, Y3_end, _ = y_end delta = lamb_end - lamb1 if abs(delta) < epsilon: return True, lamb_p0 if abs(Y3_end) < 1e-20: return False, None step = delta / Y3_end step = float(np.clip(step, -1.0, 1.0)) lamb_p0 -= step return False, None seeds = [0.0, 0.25, -0.25, 1.0, -1.0] best = None for seed in seeds: ok, sol = solve_newton(seed) if not ok: continue v0_sol = np.array([lamb0, sol, 0.0, 1.0], dtype=float) _, _, s_val = rk4_integral(ode_beta, beta0, v0_sol, dbeta, N_run, integrand_beta) if (best is None) or (s_val < best[0]): best = (float(s_val), float(sol)) if best is None: return None return best[0], best[1], sgn, dbeta, ode_beta lamb0 = float(wrap_mpi_pi(lamb_0)) lamb1 = float(wrap_mpi_pi(lamb_1)) beta0 = float(beta_0) beta1 = float(beta_1) N_full = int(n) if N_full < 2: N_full = 2 if all_points: N_fast = min(2000, max(400, N_full // 10)) else: N_fast = min(1500, max(300, N_full // 12)) k0 = int(np.round((lamb0 - lamb1) / two_pi)) lamb_targets = [] for dk in (-1, 0, 1): lt = lamb1 + two_pi * float(k0 + dk) dl = lt - lamb0 if abs(dl) <= np.pi + 1e-12: lamb_targets.append(float(lt)) if not lamb_targets: lamb_targets = [float(lamb1 + two_pi * float(k0))] best_fast = None for lt in lamb_targets: if abs(lt - lamb0) >= 1e-15: res = solve_lambda_branch(beta0, lamb0, beta1, lt, N_fast, min(N_fast, 800), min(iter_max, 12)) if res is None: continue s_fast, beta_p0_fast, sgn_fast, dlamb_fast, _ = res cand = ("lambda", s_fast, lt, beta_p0_fast, sgn_fast, dlamb_fast) else: res = solve_beta_branch(beta0, lamb0, beta1, lamb1, N_fast, min(N_fast, 800), min(iter_max, 12)) if res is None: continue s_fast, lamb_p0_fast, sgn_fast, dbeta_fast, _ = res cand = ("beta", s_fast, lt, lamb_p0_fast, sgn_fast, dbeta_fast) if (best_fast is None) or (cand[1] < best_fast[1]): best_fast = cand if best_fast is None: if abs(lamb1 - lamb0) >= 1e-15: best_fast = ("lambda", 0.0, lamb1, None, 1.0, float(lamb1 - lamb0)) else: best_fast = ("beta", 0.0, lamb1, None, 1.0, float(beta1 - beta0)) if best_fast[0] == "lambda": lt = float(best_fast[2]) dlamb = float(lt - lamb0) sgn = 1.0 if dlamb >= 0.0 else -1.0 def ode_lamb(lamb, v): beta, beta_p, X3, X4 = v (_, _, _, _, p_3, p_2, p_1, p_0, p_33, p_22, p_11, p_00) = p_coef(beta, lamb) dbeta = beta_p dbeta_p = p_3 * beta_p**3 + p_2 * beta_p**2 + p_1 * beta_p + p_0 dX3 = X4 dX4 = (p_33 * beta_p**3 + p_22 * beta_p**2 + p_11 * beta_p + p_00) * X3 + ( 3 * p_3 * beta_p**2 + 2 * p_2 * beta_p + p_1 ) * X4 return np.array([dbeta, dbeta_p, dX3, dX4], dtype=float) alpha0_sph = sph_azimuth(beta0, lamb0, beta1, lt) (_, _, E0, G0, *_) = BETA_LAMBDA(beta0, lamb0) beta_p0_sph = np.sqrt(G0 / E0) * cot(alpha0_sph) beta_p0_init = best_fast[3] if beta_p0_init is None: beta_p0_init = beta_p0_sph beta_p0_init = float(beta_p0_init) N_newton = min(N_full, 4000) def solve_newton_refine(beta_p0_init: float): beta_p0 = float(beta_p0_init) for _ in range(iter_max): v0 = np.array([beta0, beta_p0, 0.0, 1.0], dtype=float) _, y_end = rk4_end(ode_lamb, lamb0, v0, dlamb, N_newton) beta_end, _, X3_end, _ = y_end delta = beta_end - beta1 if abs(delta) < epsilon: return True, beta_p0 if abs(X3_end) < 1e-20: return False, None step = delta / X3_end step = float(np.clip(step, -0.5, 0.5)) beta_p0 -= step return False, None ok, beta_p0_sol = solve_newton_refine(beta_p0_init) if not ok: seeds = [beta_p0_sph, -beta_p0_sph, 0.5 * beta_p0_sph, 2.0 * beta_p0_sph] best = None for seed in seeds: ok_s, sol_s = solve_newton_refine(seed) if not ok_s: continue v0_s = np.array([beta0, sol_s, 0.0, 1.0], dtype=float) _, _, s_s = rk4_integral(ode_lamb, lamb0, v0_s, dlamb, min(N_full, 2000), integrand_lambda) if (best is None) or (s_s < best[0]): best = (float(s_s), float(sol_s)) if best is None: raise RuntimeError("GHA2_num: Keine Startwert-Variante konvergiert (lambda-Fall)") beta_p0_sol = best[1] beta_p0 = float(beta_p0_sol) v0_final = np.array([beta0, beta_p0, 0.0, 1.0], dtype=float) if all_points: lamb_list, states = rk4(ode_lamb, lamb0, v0_final, dlamb, N_full, False) lamb_arr = np.array(lamb_list, dtype=float) beta_arr = np.array([st[0] for st in states], dtype=float) beta_p_arr = np.array([st[1] for st in states], dtype=float) (_, _, E_start, G_start, *_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0]) (_, _, E_end, G_end, *_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1]) alpha_0 = azimut(E_start, G_start, dbeta_du=beta_p_arr[0] * sgn, dlamb_du=1.0 * sgn) alpha_1 = azimut(E_end, G_end, dbeta_du=beta_p_arr[-1] * sgn, dlamb_du=1.0 * sgn) integrand = np.zeros(N_full + 1, dtype=float) for i in range(N_full + 1): (_, _, Ei, Gi, *_) = BETA_LAMBDA(beta_arr[i], lamb_arr[i]) integrand[i] = np.sqrt(Ei * beta_p_arr[i] ** 2 + Gi) h = abs(dlamb) / N_full if N_full % 2 == 0: S = integrand[0] + integrand[-1] + 4.0 * np.sum(integrand[1:-1:2]) + 2.0 * np.sum( integrand[2:-1:2] ) s = h / 3.0 * S else: s = np.trapz(integrand, dx=h) return float(wrap_0_2pi(alpha_0)), float(wrap_0_2pi(alpha_1)), float(s), beta_arr, lamb_arr _, y_end, s = rk4_integral(ode_lamb, lamb0, v0_final, dlamb, N_full, integrand_lambda) beta_end, beta_p_end, _, _ = y_end (_, _, E_start, G_start, *_) = BETA_LAMBDA(beta0, lamb0) alpha_0 = azimut(E_start, G_start, dbeta_du=beta_p0 * sgn, dlamb_du=1.0 * sgn) (_, _, E_end, G_end, *_) = BETA_LAMBDA(float(beta_end), float(lamb0 + dlamb)) alpha_1 = azimut(E_end, G_end, dbeta_du=float(beta_p_end) * sgn, dlamb_du=1.0 * sgn) return float(wrap_0_2pi(alpha_0)), float(wrap_0_2pi(alpha_1)), float(s) # Fall 2 (lambda_0 == lambda_1) N = int(n) dbeta = float(beta_1 - beta_0) if abs(dbeta) < 1e-15: if all_points: return 0.0, 0.0, 0.0, np.array([]), np.array([]) return 0.0, 0.0, 0.0 sgn = 1.0 if dbeta >= 0.0 else -1.0 def ode_beta(beta, v): lamb, lamb_p, Y3, Y4 = v (_, _, _, _, q_3, q_2, q_1, q_0, q_33, q_22, q_11, q_00) = q_coef(beta, lamb) dlamb = lamb_p dlamb_p = q_3 * lamb_p**3 + q_2 * lamb_p**2 + q_1 * lamb_p + q_0 dY3 = Y4 dY4 = (q_33 * lamb_p**3 + q_22 * lamb_p**2 + q_11 * lamb_p + q_00) * Y3 + ( 3 * q_3 * lamb_p**2 + 2 * q_2 * lamb_p + q_1 ) * Y4 return np.array([dlamb, dlamb_p, dY3, dY4], dtype=float) lamb_p0 = float(best_fast[3]) if (best_fast[0] == "beta" and best_fast[3] is not None) else 0.0 for _ in range(iter_max): v0 = np.array([lamb0, lamb_p0, 0.0, 1.0], dtype=float) _, y_end = rk4_end(ode_beta, beta0, v0, dbeta, N) lamb_end, _, Y3_end, _ = y_end delta = lamb_end - lamb1 if abs(delta) < epsilon: break if abs(Y3_end) < 1e-20: raise RuntimeError("GHA2_num: Ableitung ~ 0 im beta-Fall") step = delta / Y3_end step = float(np.clip(step, -1.0, 1.0)) lamb_p0 -= step v0_final = np.array([lamb0, lamb_p0, 0.0, 1.0], dtype=float) if all_points: beta_list, states = rk4(ode_beta, beta0, v0_final, dbeta, N, False) beta_arr = np.array(beta_list, dtype=float) lamb_arr = np.array([st[0] for st in states], dtype=float) lamb_p_arr = np.array([st[1] for st in states], dtype=float) (_, _, E_start, G_start, *_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0]) (_, _, E_end, G_end, *_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1]) alpha_0 = azimut(E_start, G_start, dbeta_du=1.0 * sgn, dlamb_du=lamb_p_arr[0] * sgn) alpha_1 = azimut(E_end, G_end, dbeta_du=1.0 * sgn, dlamb_du=lamb_p_arr[-1] * sgn) integrand = np.zeros(N + 1, dtype=float) for i in range(N + 1): (_, _, Ei, Gi, *_) = BETA_LAMBDA(beta_arr[i], lamb_arr[i]) integrand[i] = np.sqrt(Ei + Gi * lamb_p_arr[i] ** 2) h = abs(dbeta) / N if N % 2 == 0: S = integrand[0] + integrand[-1] + 4.0 * np.sum(integrand[1:-1:2]) + 2.0 * np.sum( integrand[2:-1:2] ) s = h / 3.0 * S else: s = np.trapz(integrand, dx=h) return float(wrap_0_2pi(alpha_0)), float(wrap_0_2pi(alpha_1)), float(s), beta_arr, lamb_arr _, y_end, s = rk4_integral(ode_beta, beta0, v0_final, dbeta, N, integrand_beta) lamb_end, lamb_p_end, _, _ = y_end (_, _, E_start, G_start, *_) = BETA_LAMBDA(beta0, lamb0) alpha_0 = azimut(E_start, G_start, dbeta_du=1.0 * sgn, dlamb_du=lamb_p0 * sgn) (_, _, E_end, G_end, *_) = BETA_LAMBDA(beta1, float(lamb_end)) alpha_1 = azimut(E_end, G_end, dbeta_du=1.0 * sgn, dlamb_du=float(lamb_p_end) * sgn) return float(wrap_0_2pi(alpha_0)), float(wrap_0_2pi(alpha_1)), float(s) if __name__ == "__main__": ell = EllipsoidTriaxial.init_name("BursaSima1980round") beta1 = np.deg2rad(75) lamb1 = np.deg2rad(-90) beta2 = np.deg2rad(75) lamb2 = np.deg2rad(66) a0, a1, s = gha2_num(ell, beta1, lamb1, beta2, lamb2, n=100) print(aus.gms("a0", a0, 4)) print(aus.gms("a1", a1, 4)) print("s: ", s) # print(aus.gms("a2", a2, 4)) # print(s) cart1 = ell.para2cart(0, 0) cart2 = ell.para2cart(0.4, 1.4) beta1, lamb1 = ell.cart2ell(cart1) beta2, lamb2 = ell.cart2ell(cart2) a1, a2, s = gha2_num(ell, beta1, lamb1, beta2, lamb2, n=5000) print(s) ell = EllipsoidTriaxial.init_name("BursaSima1980round") diffs_panou = [] examples_panou = ne_panou.get_random_examples(4) for example in examples_panou: beta0, lamb0, beta1, lamb1, _, alpha0, alpha1, s = example P0 = ell.ell2cart(beta0, lamb0) try: alpha0_num, alpha1_num, s_num = gha2_num(ell, beta0, lamb0, beta1, lamb1, n=4000, iter_max=10) diffs_panou.append( (wu.rad2deg(abs(alpha0 - alpha0_num)), wu.rad2deg(abs(alpha1 - alpha1_num)), abs(s - s_num))) except: print(f"Fehler für {beta0}, {lamb0}, {beta1}, {lamb1}") diffs_panou = np.array(diffs_panou) print(diffs_panou) ell = EllipsoidTriaxial.init_name("KarneyTest2024") diffs_karney = [] # examples_karney = ne_karney.get_examples((30500, 40500)) examples_karney = ne_karney.get_random_examples(2) for example in examples_karney: beta0, lamb0, alpha0, beta1, lamb1, alpha1, s = example try: alpha0_num, alpha1_num, s_num = gha2_num(ell, beta0, lamb0, beta1, lamb1, n=4000, iter_max=10) diffs_karney.append((wu.rad2deg(abs(alpha0-alpha0_num)), wu.rad2deg(abs(alpha1-alpha1_num)), abs(s-s_num))) except: print(f"Fehler für {beta0}, {lamb0}, {beta1}, {lamb1}") diffs_karney = np.array(diffs_karney) print(diffs_karney) pass