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GHA1 num und ana richtig. Tests nach Beispielen aus Panou 2013

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Hendrik Möllersmann
2025-12-10 11:45:41 +01:00
parent 936b7c56f9
commit 946d028fae
6 changed files with 335 additions and 102 deletions
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111
GHA_triaxial/numeric_examples_panou.py Normal file
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@@ -0,0 +1,111 @@
import winkelumrechnungen as wu
table1 = [
(wu.deg2rad(0), wu.deg2rad(0), wu.deg2rad(0), wu.deg2rad(90), 1.00000000000,
wu.gms2rad([90,0,0.0000]), wu.gms2rad([90,0,0.0000]), 10018754.9569),
(wu.deg2rad(1), wu.deg2rad(0), wu.deg2rad(-80), wu.deg2rad(5), 0.05883743460,
wu.gms2rad([179,7,12.2719]), wu.gms2rad([174,40,13.8487]), 8947130.7221),
(wu.deg2rad(5), wu.deg2rad(0), wu.deg2rad(-60), wu.deg2rad(40), 0.34128138370,
wu.gms2rad([160,13,24.5001]), wu.gms2rad([137,26,47.0036]), 8004762.4330),
(wu.deg2rad(30), wu.deg2rad(0), wu.deg2rad(-30), wu.deg2rad(175), 0.86632464962,
wu.gms2rad([91,7,30.9337]), wu.gms2rad([91,7,30.8672]), 19547128.7971),
(wu.deg2rad(60), wu.deg2rad(0), wu.deg2rad(60), wu.deg2rad(175), 0.06207487624,
wu.gms2rad([2,52,26.2393]), wu.gms2rad([177,4,13.6373]), 6705715.1610),
(wu.deg2rad(75), wu.deg2rad(0), wu.deg2rad(80), wu.deg2rad(120), 0.11708984898,
wu.gms2rad([23,20,34.7823]), wu.gms2rad([140,55,32.6385]), 2482501.2608),
(wu.deg2rad(80), wu.deg2rad(0), wu.deg2rad(60), wu.deg2rad(90), 0.17478427424,
wu.gms2rad([72,26,50.4024]), wu.gms2rad([159,38,30.3547]), 3519745.1283)
]
table2 = [
(wu.deg2rad(0), wu.deg2rad(-90), wu.deg2rad(0), wu.deg2rad(89.5), 1.00000000000,
wu.gms2rad([90,0,0.0000]), wu.gms2rad([90,0,0.0000]), 19981849.8629),
(wu.deg2rad(1), wu.deg2rad(-90), wu.deg2rad(1), wu.deg2rad(89.5), 0.18979826428,
wu.gms2rad([10,56,33.6952]), wu.gms2rad([169,3,26.4359]), 19776667.0342),
(wu.deg2rad(5), wu.deg2rad(-90), wu.deg2rad(5), wu.deg2rad(89), 0.09398403161,
wu.gms2rad([5,24,48.3899]), wu.gms2rad([174,35,12.6880]), 18889165.0873),
(wu.deg2rad(30), wu.deg2rad(-90), wu.deg2rad(30), wu.deg2rad(86), 0.06004022935,
wu.gms2rad([3,58,23.8038]), wu.gms2rad([176,2,7.2825]), 13331814.6078),
(wu.deg2rad(60), wu.deg2rad(-90), wu.deg2rad(60), wu.deg2rad(78), 0.06076096484,
wu.gms2rad([6,56,46.4585]), wu.gms2rad([173,11,5.9592]), 6637321.6350),
(wu.deg2rad(75), wu.deg2rad(-90), wu.deg2rad(75), wu.deg2rad(66), 0.05805851008,
wu.gms2rad([12,40,34.9009]), wu.gms2rad([168,20,26.7339]), 3267941.2812),
(wu.deg2rad(80), wu.deg2rad(-90), wu.deg2rad(80), wu.deg2rad(55), 0.05817384452,
wu.gms2rad([18,35,40.7848]), wu.gms2rad([164,25,34.0017]), 2132316.9048)
]
table3 = [
(wu.deg2rad(0), wu.deg2rad(0.5), wu.deg2rad(80), wu.deg2rad(0.5), 0.05680316848,
wu.gms2rad([0,-0,16.0757]), wu.gms2rad([0,1,32.5762]), 8831874.3717),
(wu.deg2rad(-1), wu.deg2rad(5), wu.deg2rad(75), wu.deg2rad(5), 0.05659149555,
wu.gms2rad([0,-1,47.2105]), wu.gms2rad([0,6,54.0958]), 8405370.4947),
(wu.deg2rad(-5), wu.deg2rad(30), wu.deg2rad(60), wu.deg2rad(30), 0.04921108945,
wu.gms2rad([0,-4,22.3516]), wu.gms2rad([0,8,42.0756]), 7204083.8568),
(wu.deg2rad(-30), wu.deg2rad(45), wu.deg2rad(30), wu.deg2rad(45), 0.04017812574,
wu.gms2rad([0,-3,41.2461]), wu.gms2rad([0,3,41.2461]), 6652788.1287),
(wu.deg2rad(-60), wu.deg2rad(60), wu.deg2rad(5), wu.deg2rad(60), 0.02843082609,
wu.gms2rad([0,-8,40.4575]), wu.gms2rad([0,4,22.1675]), 7213412.4477),
(wu.deg2rad(-75), wu.deg2rad(85), wu.deg2rad(1), wu.deg2rad(85), 0.00497802414,
wu.gms2rad([0,-6,44.6115]), wu.gms2rad([0,1,47.0474]), 8442938.5899),
(wu.deg2rad(-80), wu.deg2rad(89.5), wu.deg2rad(0), wu.deg2rad(89.5), 0.00050178253,
wu.gms2rad([0,-1,27.9705]), wu.gms2rad([0,0,16.0490]), 8888783.7815)
]
table4 = [
(wu.deg2rad(0), wu.deg2rad(0), wu.deg2rad(0), wu.deg2rad(90), 1.00000000000,
wu.gms2rad([90,0,0.0000]), wu.gms2rad([90,0,0.0000]), 10018754.1714),
(wu.deg2rad(1), wu.deg2rad(0), wu.deg2rad(0), wu.deg2rad(179.5), 0.30320665822,
wu.gms2rad([17,39,11.0942]), wu.gms2rad([162,20,58.9032]), 19884417.8083),
(wu.deg2rad(5), wu.deg2rad(0), wu.deg2rad(-80), wu.deg2rad(170), 0.03104258442,
wu.gms2rad([178,12,51.5083]), wu.gms2rad([10,17,52.6423]), 11652530.7514),
(wu.deg2rad(30), wu.deg2rad(0), wu.deg2rad(-75), wu.deg2rad(120), 0.24135347134,
wu.gms2rad([163,49,4.4615]), wu.gms2rad([68,49,50.9617]), 14057886.8752),
(wu.deg2rad(60), wu.deg2rad(0), wu.deg2rad(-60), wu.deg2rad(40), 0.19408499032,
wu.gms2rad([157,9,33.5589]), wu.gms2rad([157,9,33.5589]), 13767414.8267),
(wu.deg2rad(75), wu.deg2rad(0), wu.deg2rad(-30), wu.deg2rad(0.5), 0.00202789418,
wu.gms2rad([179,33,3.8613]), wu.gms2rad([179,51,57.0077]), 11661713.4496),
(wu.deg2rad(80), wu.deg2rad(0), wu.deg2rad(-5), wu.deg2rad(120), 0.15201222384,
wu.gms2rad([61,5,33.9600]), wu.gms2rad([171,13,22.0148]), 11105138.2902),
(wu.deg2rad(0), wu.deg2rad(0), wu.deg2rad(60), wu.deg2rad(0), 0.00000000000,
wu.gms2rad([0,0,0.0000]), wu.gms2rad([0,0,0.0000]), 6663348.2060)
]
tables = [table1, table2, table3, table4]
def get_example(table, example):
table -= 1
example -= 1
return tables[table][example]
def get_tables():
return tables
if __name__ == "__main__":
test = get_example(1, 4)
pass

123
GHA_triaxial/panou.py
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@@ -1,4 +1,5 @@
import numpy as np
from numpy import sin, cos, sqrt, arctan2
import ellipsoide
import Numerische_Integration.num_int_runge_kutta as rk
import winkelumrechnungen as wu
@@ -6,33 +7,66 @@ import ausgaben as aus
import GHA.rk as ghark
from scipy.special import factorial as fact
from math import comb
import GHA_triaxial.numeric_examples_panou as nep
# Panou, Korakitits 2019
def gha1_num(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, num):
def gha1_num_old(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, num):
phi, lamb, h = ell.cart2geod("ligas3", point)
x, y, z = ell.geod2cart(phi, lamb, 0)
values = ell.p_q(x, y, z)
H = values["H"]
p = values["p"]
q = values["q"]
p, q = ell.p_q(x, y, z)
dxds0 = p[0] * np.sin(alpha0) + q[0] * np.cos(alpha0)
dyds0 = p[1] * np.sin(alpha0) + q[1] * np.cos(alpha0)
dzds0 = p[2] * np.sin(alpha0) + q[2] * np.cos(alpha0)
dxds0 = p[0] * sin(alpha0) + q[0] * cos(alpha0)
dyds0 = p[1] * sin(alpha0) + q[1] * cos(alpha0)
dzds0 = p[2] * sin(alpha0) + q[2] * cos(alpha0)
h = lambda dxds, dyds, dzds: dxds**2 + 1/(1-ell.ee**2)*dyds**2 + 1/(1-ell.ex**2)*dzds**2
f1 = lambda s, x, dxds, y, dyds, z, dzds: dxds
f2 = lambda s, x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / H * x
f3 = lambda s, x, dxds, y, dyds, z, dzds: dyds
f4 = lambda s, x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / H * y/(1-ell.ee**2)
f5 = lambda s, x, dxds, y, dyds, z, dzds: dzds
f6 = lambda s, x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / H * z/(1-ell.ex**2)
f1 = lambda x, dxds, y, dyds, z, dzds: dxds
f2 = lambda x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / ell.func_H(x, y, z) * x
f3 = lambda x, dxds, y, dyds, z, dzds: dyds
f4 = lambda x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / ell.func_H(x, y, z) * y/(1-ell.ee**2)
f5 = lambda x, dxds, y, dyds, z, dzds: dzds
f6 = lambda x, dxds, y, dyds, z, dzds: -h(dxds, dyds, dzds) / ell.func_H(x, y, z) * z/(1-ell.ex**2)
funktionswerte = rk.verfahren([f1, f2, f3, f4, f5, f6], [x, dxds0, y, dyds0, z, dzds0], s, num, fein=False)
P2 = funktionswerte[-1]
P2 = (P2[0], P2[2], P2[4])
return P2
def buildODE(ell):
def ODE(v):
x, dxds, y, dyds, z, dzds = v
H = ell.func_H(x, y, z)
h = dxds**2 + 1/(1-ell.ee**2)*dyds**2 + 1/(1-ell.ex**2)*dzds**2
ddx = -(h/H)*x
ddy = -(h/H)*y/(1-ell.ee**2)
ddz = -(h/H)*z/(1-ell.ex**2)
return [dxds, ddx, dyds, ddy, dzds, ddz]
return ODE
def gha1_num(ell, point, alpha0, s, num):
phi, lam, _ = ell.cart2geod("ligas3", point)
x0, y0, z0 = ell.geod2cart(phi, lam, 0)
p, q = ell.p_q(x0, y0, z0)
dxds0 = p[0] * sin(alpha0) + q[0] * cos(alpha0)
dyds0 = p[1] * sin(alpha0) + q[1] * cos(alpha0)
dzds0 = p[2] * sin(alpha0) + q[2] * cos(alpha0)
v_init = [x0, dxds0, y0, dyds0, z0, dzds0]
F = buildODE(ell)
werte = rk.rk_chat(F, v_init, s, num)
x1, _, y1, _, z1, _ = werte[-1]
return x1, y1, z1
funktionswerte = rk.verfahren([f1, f2, f3, f4, f5, f6], [0, x, dxds0, y, dyds0, z, dzds0], s, num)
return funktionswerte
def checkLiouville(ell: ellipsoide.EllipsoidTriaxial, points):
constantValues = []
@@ -52,9 +86,9 @@ def checkLiouville(ell: ellipsoide.EllipsoidTriaxial, points):
P = p[0]*dxds + p[1]*dyds + p[2]*dzds
Q = q[0]*dxds + q[1]*dyds + q[2]*dzds
alpha = np.arctan(P/Q)
alpha = arctan2(P, Q)
c = ell.ay**2 - (t1 * np.sin(alpha)**2 + t2 * np.cos(alpha)**2)
c = ell.ay**2 - (t1 * sin(alpha)**2 + t2 * cos(alpha)**2)
constantValues.append(c)
pass
@@ -63,9 +97,7 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
"""
Panou, Korakitits 2020, 5ff.
:param ell:
:param x:
:param y:
:param z:
:param point:
:param alpha0:
:param s:
:param maxM:
@@ -77,21 +109,22 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
z_m = [z]
# erste Ableitungen (7-8)
sqrtH = np.sqrt(ell.p_q(x, y, z)["H"])
H = x ** 2 + y ** 2 / (1 - ell.ee ** 2) ** 2 + z ** 2 / (1 - ell.ex ** 2) ** 2
sqrtH = sqrt(H)
n = np.array([x / sqrtH,
y / ((1-ell.ee**2) * sqrtH),
z / ((1-ell.ex**2) * sqrtH)])
u, v = ell.cart2para(np.array([x, y, z]))
G = np.sqrt(1 - ell.ex**2 * np.cos(u)**2 - ell.ee**2 * np.sin(u)**2 * np.sin(v)**2)
q = np.array([-1/G * np.sin(u) * np.cos(v),
-1/G * np.sqrt(1-ell.ee**2) * np.sin(u) * np.sin(v),
1/G * np.sqrt(1-ell.ex**2) * np.cos(u)])
G = sqrt(1 - ell.ex**2 * cos(u)**2 - ell.ee**2 * sin(u)**2 * sin(v)**2)
q = np.array([-1/G * sin(u) * cos(v),
-1/G * sqrt(1-ell.ee**2) * sin(u) * sin(v),
1/G * sqrt(1-ell.ex**2) * cos(u)])
p = np.array([q[1]*n[2] - q[2]*n[1],
q[2]*n[0] - q[0]*n[2],
q[0]*n[1] - q[1]*n[0]])
x_m.append(p[0] * np.sin(alpha0) + q[0] * np.cos(alpha0))
y_m.append(p[1] * np.sin(alpha0) + q[1] * np.cos(alpha0))
z_m.append(p[2] * np.sin(alpha0) + q[2] * np.cos(alpha0))
x_m.append(p[0] * sin(alpha0) + q[0] * cos(alpha0))
y_m.append(p[1] * sin(alpha0) + q[1] * cos(alpha0))
z_m.append(p[2] * sin(alpha0) + q[2] * cos(alpha0))
# H Ableitungen (7)
H_ = lambda p: np.sum([comb(p, i) * (x_m[p - i] * x_m[i] +
@@ -143,32 +176,16 @@ def gha1_ana(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
if __name__ == "__main__":
# ell = ellipsoide.EllipsoidTriaxial.init_name("Eitschberger1978")
ell = ellipsoide.EllipsoidTriaxial.init_name("BursaSima1980")
ellbi = ellipsoide.EllipsoidTriaxial.init_name("Bessel-biaxial")
ell = ellipsoide.EllipsoidTriaxial.init_name("BursaSima1980round")
# ellbi = ellipsoide.EllipsoidTriaxial.init_name("Bessel-biaxial")
re = ellipsoide.EllipsoidBiaxial.init_name("Bessel")
# Panou 2013, 7, Table 1, beta0=60°
beta1 = wu.deg2rad(60)
lamb1 = wu.deg2rad(0)
beta2 = wu.deg2rad(60)
lamb2 = wu.deg2rad(175)
P1 = ell.ell2cart(wu.deg2rad(60), wu.deg2rad(0))
P2 = ell.ell2cart(wu.deg2rad(60), wu.deg2rad(175))
para1 = ell.cart2para(P1)
para2 = ell.cart2para(P2)
cart1 = ell.para2cart(para1[0], para1[1])
cart2 = ell.para2cart(para2[0], para2[1])
ell11 = ell.cart2ell(P1)
ell21 = ell.cart2ell(P2)
ell1 = ell.cart2ell(cart1)
ell2 = ell.cart2ell(cart2)
beta0, lamb0, beta1, lamb1, c, alpha0, alpha1, s = nep.get_example(table=1, example=5)
P0 = ell.ell2cart(beta0, lamb0)
P1 = ell.ell2cart(beta1, lamb1)
c = 0.06207487624
alpha0 = wu.gms2rad([2, 52, 26.2393])
alpha1 = wu.gms2rad([177, 4, 13.6373])
s = 6705715.1610
pass
P2_num = gha1_num(ell, P1, alpha0, s, 1000)
P2_ana = gha1_ana(ell, P1, alpha0, s, 70)
# P1_num = gha1_num(ell, P0, alpha0, s, 1000)
P1_num = gha1_num(ell, P0, alpha0, s, 10000)
P1_ana = gha1_ana(ell, P0, alpha0, s, 30)
pass

21
GHA_triaxial/panou_2013_2GHA_num.py
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@@ -319,13 +319,20 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1, lamb_1, beta_2, lamb_2, n=16000, ep
if __name__ == "__main__":
ell = EllipsoidTriaxial.init_name("BursaSima1980round")
beta1 = np.deg2rad(75)
lamb1 = np.deg2rad(-90)
beta2 = np.deg2rad(75)
lamb2 = np.deg2rad(66)
a1, a2, s = gha2_num(ell, beta1, lamb1, beta2, lamb2)
print(aus.gms("a1", a1, 4))
print(aus.gms("a2", a2, 4))
# beta1 = np.deg2rad(75)
# lamb1 = np.deg2rad(-90)
# beta2 = np.deg2rad(75)
# lamb2 = np.deg2rad(66)
# a1, a2, s = gha2_num(ell, beta1, lamb1, beta2, lamb2)
# print(aus.gms("a1", a1, 4))
# print(aus.gms("a2", a2, 4))
# print(s)
cart1 = ell.para2cart(0, 0)
cart2 = ell.para2cart(0.4, 0.4)
beta1, lamb1 = ell.cart2ell(cart1)
beta2, lamb2 = ell.cart2ell(cart2)
a1, a2, s = gha2_num(ell, beta1, lamb1, beta2, lamb2, n=2500)
print(s)