461 lines
16 KiB
Python
461 lines
16 KiB
Python
import numpy as np
|
|
from ellipsoide import EllipsoidTriaxial
|
|
from runge_kutta import rk4, rk4_step, rk4_end, rk4_integral
|
|
import GHA_triaxial.numeric_examples_karney as ne_karney
|
|
import GHA_triaxial.numeric_examples_panou as ne_panou
|
|
import winkelumrechnungen as wu
|
|
from typing import Tuple
|
|
from numpy.typing import NDArray
|
|
import ausgaben as aus
|
|
from utils_angle import cot, arccot, wrap_to_pi
|
|
|
|
|
|
def norm_a(a):
|
|
if a < 0.0:
|
|
a += np.pi
|
|
return a
|
|
|
|
def sph_azimuth(beta1, lam1, beta2, lam2):
|
|
dlam = wrap_to_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
|
|
"""
|
|
|
|
# Berechnung Koeffizienten, Gaußschen Fundamentalgrößen 1. Ordnung sowie deren Ableitungen
|
|
def BETA_LAMBDA(beta, lamb):
|
|
BETA = (ell.ay ** 2 * np.sin(beta) ** 2 + ell.b ** 2 * np.cos(beta) ** 2) / (
|
|
ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2
|
|
)
|
|
LAMBDA = (ell.ax ** 2 * np.sin(lamb) ** 2 + ell.ay ** 2 * np.cos(lamb) ** 2) / (
|
|
ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2
|
|
)
|
|
|
|
BETA_ = (ell.ax ** 2 * ell.Ey ** 2 * np.sin(2 * beta)) / (
|
|
ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2
|
|
) ** 2
|
|
LAMBDA_ = -(ell.b ** 2 * ell.Ee ** 2 * np.sin(2 * lamb)) / (
|
|
ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2
|
|
) ** 2
|
|
|
|
BETA__ = (
|
|
(2 * ell.ax ** 2 * ell.Ey ** 4 * np.sin(2 * beta) ** 2)
|
|
/ (ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2) ** 3
|
|
+ (2 * ell.ax ** 2 * ell.Ey ** 2 * np.cos(2 * beta))
|
|
/ (ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2) ** 2
|
|
)
|
|
LAMBDA__ = (
|
|
(2 * ell.b ** 2 * ell.Ee ** 4 * np.sin(2 * lamb) ** 2)
|
|
/ (ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2) ** 3
|
|
- (2 * ell.b ** 2 * ell.Ee ** 2 * np.sin(2 * lamb))
|
|
/ (ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2) ** 2
|
|
)
|
|
|
|
E = BETA * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
|
|
G = LAMBDA * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
|
|
|
|
E_beta = (
|
|
BETA_ * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
|
|
- BETA * ell.Ey ** 2 * np.sin(2 * beta)
|
|
)
|
|
E_lamb = BETA * ell.Ee ** 2 * np.sin(2 * lamb)
|
|
|
|
G_beta = -LAMBDA * ell.Ey ** 2 * np.sin(2 * beta)
|
|
G_lamb = (
|
|
LAMBDA_ * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
|
|
+ LAMBDA * ell.Ee ** 2 * np.sin(2 * lamb)
|
|
)
|
|
|
|
E_beta_beta = (
|
|
BETA__ * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
|
|
- 2 * BETA_ * ell.Ey ** 2 * np.sin(2 * beta)
|
|
- 2 * BETA * ell.Ey ** 2 * np.cos(2 * beta)
|
|
)
|
|
E_beta_lamb = BETA_ * ell.Ee ** 2 * np.sin(2 * lamb)
|
|
E_lamb_lamb = 2 * BETA * ell.Ee ** 2 * np.cos(2 * lamb)
|
|
|
|
G_beta_beta = -2 * LAMBDA * ell.Ey ** 2 * np.cos(2 * beta)
|
|
G_beta_lamb = -LAMBDA_ * ell.Ey ** 2 * np.sin(2 * beta)
|
|
G_lamb_lamb = (
|
|
LAMBDA__ * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
|
|
+ 2 * LAMBDA_ * ell.Ee ** 2 * np.sin(2 * lamb)
|
|
+ 2 * LAMBDA * ell.Ee ** 2 * np.cos(2 * lamb)
|
|
)
|
|
|
|
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)
|
|
|
|
# Fall 1 (lambda_0 != lambda_1)
|
|
if abs(lamb_1 - lamb_0) >= 1e-15:
|
|
N = int(n)
|
|
dlamb = float(lamb_1 - lamb_0)
|
|
|
|
beta0 = float(beta_0)
|
|
lamb0 = float(lamb_0)
|
|
beta1 = float(beta_1)
|
|
lamb1 = float(lamb_1)
|
|
|
|
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)
|
|
(_, _, E0, G0, *_) = BETA_LAMBDA(beta0, lamb0)
|
|
beta_p0_sph = np.sqrt(G0 / E0) * cot(alpha0_sph)
|
|
|
|
N_newton = min(N, 4000)
|
|
|
|
def solve_newton(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 = np.clip(step, -0.5, 0.5)
|
|
beta_p0 -= step
|
|
|
|
return False, None
|
|
|
|
ok, beta_p0_sol = solve_newton(beta_p0_sph)
|
|
|
|
if not ok:
|
|
candidates = [-beta_p0_sph, 0.5 * beta_p0_sph, 2.0 * beta_p0_sph]
|
|
N_quick = min(N, 2000)
|
|
best = None
|
|
for g in candidates:
|
|
ok_g, sol = solve_newton(g)
|
|
if not ok_g:
|
|
continue
|
|
v0_g = np.array([beta0, sol, 0.0, 1.0], dtype=float)
|
|
_, _, s_quick = rk4_integral(ode_lamb, lamb0, v0_g, dlamb, N_quick, integrand_lambda)
|
|
if (best is None) or (s_quick < best[0]):
|
|
best = (s_quick, sol)
|
|
if best is None:
|
|
raise RuntimeError("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, 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_1 = norm_a(arccot(np.sqrt(E_start / G_start) * beta_p_arr[0]))
|
|
alpha_2 = norm_a(arccot(np.sqrt(E_end / G_end) * beta_p_arr[-1]))
|
|
|
|
# Distanz aus Arrays
|
|
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 * beta_p_arr[i]**2 + Gi)
|
|
|
|
h = abs(dlamb) / 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(alpha_1), float(alpha_2), float(s), beta_arr, lamb_arr
|
|
|
|
_, y_end, s = rk4_integral(ode_lamb, lamb0, v0_final, dlamb, N, integrand_lambda)
|
|
beta_end, beta_p_end, _, _ = y_end
|
|
|
|
(_, _, E_start, G_start, *_) = BETA_LAMBDA(beta0, lamb0)
|
|
(_, _, E_end, G_end, *_) = BETA_LAMBDA(beta1, lamb1)
|
|
|
|
alpha_1 = norm_a(arccot(np.sqrt(E_start / G_start) * beta_p0))
|
|
alpha_2 = norm_a(arccot(np.sqrt(E_end / G_end) * beta_p_end))
|
|
|
|
return float(alpha_1), float(alpha_2), 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
|
|
|
|
beta0 = float(beta_0)
|
|
lamb0 = float(lamb_0)
|
|
beta1 = float(beta_1)
|
|
lamb1 = float(lamb_1)
|
|
|
|
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 = 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("Abbruch (Ableitung ~ 0) im beta-Fall.")
|
|
|
|
step = delta / Y3_end
|
|
step = 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)
|
|
|
|
(BETA_s, LAMBDA_s, _, _, *_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0])
|
|
(BETA_e, LAMBDA_e, _, _, *_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1])
|
|
|
|
alpha_1 = norm_a((np.pi/2.0) - arccot(np.sqrt(LAMBDA_s / BETA_s) * lamb_p_arr[0]))
|
|
alpha_2 = norm_a((np.pi/2.0) - arccot(np.sqrt(LAMBDA_e / BETA_e) * lamb_p_arr[-1]))
|
|
|
|
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(alpha_1), float(alpha_2), 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
|
|
|
|
(BETA_s, LAMBDA_s, _, _, *_) = BETA_LAMBDA(beta0, lamb0)
|
|
(BETA_e, LAMBDA_e, _, _, *_) = BETA_LAMBDA(beta1, lamb1)
|
|
|
|
alpha_1 = norm_a((np.pi/2.0) - arccot(np.sqrt(LAMBDA_s / BETA_s) * lamb_p0))
|
|
alpha_2 = norm_a((np.pi/2.0) - arccot(np.sqrt(LAMBDA_e / BETA_e) * lamb_p_end))
|
|
|
|
return float(alpha_1), float(alpha_2), 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=5000)
|
|
# 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
|