he2851/Masterprojekt
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

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

Browse Source
This commit is contained in:
Hendrik Möllersmann
2025-12-10 11:45:41 +01:00
parent 936b7c56f9
commit 946d028fae
6 changed files with 335 additions and 102 deletions
Download Patch File Download Diff File Expand all files Collapse all files

111
GHA_triaxial/numeric_examples_panou.py Normal file
View File

@@ -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
View File

@@ -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
View File

@@ -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)

44
Numerische_Integration/num_int_runge_kutta.py
View File

@@ -1,4 +1,4 @@
def verfahren(funktionen: list, startwerte: list, weite: float, schritte: int) -> list:
def verfahren(funktionen: list, startwerte: list, weite: float, schritte: int, fein: bool = True) -> list:
"""
Runge-Kutta-Verfahren für ein beliebiges DGLS
:param funktionen: Liste mit allen Funktionen
@@ -14,19 +14,21 @@ def verfahren(funktionen: list, startwerte: list, weite: float, schritte: int) -
zuschlaege_grob = zuschlaege(funktionen, werte[-1], h)
werte_grob = [werte[-1][j] if j == 0 else werte[-1][j] + zuschlaege_grob[j - 1]
for j in range(len(startwerte))]
if fein:
zuschlaege_fein_1 = zuschlaege(funktionen, werte[-1], h / 2)
werte_fein_1 = [werte[-1][j] + h/2 if j == 0 else werte[-1][j]+zuschlaege_fein_1[j-1]
for j in range(len(startwerte))]
zuschlaege_fein_1 = zuschlaege(funktionen, werte[-1], h / 2)
werte_fein_1 = [werte[-1][j] + h/2 if j == 0 else werte[-1][j]+zuschlaege_fein_1[j-1]
for j in range(len(startwerte))]
zuschlaege_fein_2 = zuschlaege(funktionen, werte_fein_1, h / 2)
werte_fein_2 = [werte_fein_1[j] + h/2 if j == 0 else werte_fein_1[j]+zuschlaege_fein_2[j-1]
for j in range(len(startwerte))]
zuschlaege_fein_2 = zuschlaege(funktionen, werte_fein_1, h / 2)
werte_fein_2 = [werte_fein_1[j] + h/2 if j == 0 else werte_fein_1[j]+zuschlaege_fein_2[j-1]
for j in range(len(startwerte))]
werte_korr = [werte_fein_2[j] if j == 0 else werte_fein_2[j] + 1/15 * (werte_fein_2[j] - werte_grob[j])
for j in range(len(startwerte))]
werte_korr = [werte_fein_2[j] if j == 0 else werte_fein_2[j] + 1/15 * (werte_fein_2[j] - werte_grob[j])
for j in range(len(startwerte))]
werte.append(werte_korr)
werte.append(werte_korr)
else:
werte.append(werte_grob)
return werte
@@ -60,3 +62,23 @@ def zuschlaege(funktionen: list, startwerte: list, h: float) -> list:
k_ = [(k1[i] + 2 * k2[i] + 2 * k3[i] + k4[i]) / 6 for i in range(len(k1))]
return k_
def rk_chat(F, v0: list, weite: float, schritte: int):
h = weite/schritte
v = v0
werte = [v]
for _ in range(schritte):
k1 = F(v)
k2 = F([v[i] + 0.5 * h * k1[i] for i in range(6)])
k3 = F([v[i] + 0.5 * h * k2[i] for i in range(6)])
k4 = F([v[i] + h * k3[i] for i in range(6)])
v = [
v[i] + (h / 6) * (k1[i] + 2 * k2[i] + 2 * k3[i] + k4[i])
for i in range(6)
]
werte.append(v)
return werte

54
ellipsoide.py
View File

@@ -1,4 +1,5 @@
import numpy as np
from numpy import sin, cos, arctan, arctan2, sqrt
import winkelumrechnungen as wu
import ausgaben as aus
import jacobian_Ligas
@@ -246,7 +247,10 @@ class EllipsoidTriaxial:
# print(s1, s2, s3)
beta = np.arctan(np.sqrt((-self.b**2 - s2) / (self.ay**2 + s2)))
lamb = np.arctan(np.sqrt((-self.ay**2 - s3) / (self.ax**2 + s3)))
if abs((-self.ay**2 - s3) / (self.ax**2 + s3)) > 1e-7:
lamb = np.arctan(np.sqrt((-self.ay**2 - s3) / (self.ax**2 + s3)))
else:
lamb = 0
u = np.sqrt(self.b**2 + s1)
return beta, lamb, u
@@ -328,39 +332,21 @@ class EllipsoidTriaxial:
if abs(xG) < eps and abs(yG) < eps: # Punkt in der z-Achse
phi = np.pi / 2 if zG > 0 else -np.pi / 2
lamb = 0.0
h = abs(zG) - ell.b
h = abs(zG) - self.b
return phi, lamb, h
elif abs(xG) < eps and abs(zG) < eps: # Punkt in der y-Achse
phi = 0.0
lamb = np.pi / 2 if yG > 0 else -np.pi / 2
h = abs(yG) - ell.ay
h = abs(yG) - self.ay
return phi, lamb, h
elif abs(yG) < eps and abs(zG) < eps: # Punkt in der x-Achse
phi = 0.0
lamb = 0.0 if xG > 0 else np.pi
h = abs(xG) - ell.ax
h = abs(xG) - self.ax
return phi, lamb, h
# elif abs(zG) < eps: # Punkt in der xy-Ebene
# phi = 0
# lamb = np.arctan2(yG / ell.ay**2, xG / ell.ax**2)
# rG = np.sqrt(xG ** 2 + yG ** 2)
# pE = np.array([self.ax * xG / rG, self.ax * yG / rG, self.ax * zG / rG], dtype=np.float64)
# rE = np.sqrt(pE[0] ** 2 + pE[1] ** 2)
# h = rG - rE
# return phi, lamb, h
#
# elif abs(yG) < eps: # Punkt in der xz-Ebene
# phi = np.arctan2(zG / ell.b**2, xG / ell.ax**2)
# lamb = 0 if xG > 0 else np.pi
# rG = np.sqrt(xG ** 2 + zG ** 2)
# pE = np.array([self.ax * xG / rG, self.ax * yG / rG, self.ax * zG / rG], dtype=np.float64)
# rE = np.sqrt(pE[0] ** 2 + pE[2] ** 2)
# h = rG - rE
# return phi, lamb, h
rG = np.sqrt(xG ** 2 + yG ** 2 + zG ** 2)
pE = np.array([self.ax * xG / rG, self.ax * yG / rG, self.ax * zG / rG], dtype=np.float64)
@@ -471,7 +457,17 @@ class EllipsoidTriaxial:
return u, v
def p_q(self, x, y, z) -> dict:
def func_H(self, x, y, z):
return x ** 2 + y ** 2 / (1 - self.ee ** 2) ** 2 + z ** 2 / (1 - self.ex ** 2) ** 2
def func_n(self, x, y, z, H=None):
if H is None:
H = self.func_H(x, y, z)
return np.array([x / sqrt(H),
y / ((1 - self.ee ** 2) * sqrt(H)),
z / ((1 - self.ex ** 2) * sqrt(H))])
def p_q(self, x, y, z) -> tuple[np.ndarray, np.ndarray]:
"""
Berechnung sämtlicher Größen
:param x: x
@@ -479,11 +475,9 @@ class EllipsoidTriaxial:
:param z: z
:return: Dictionary sämtlicher Größen
"""
H = x ** 2 + y ** 2 / (1 - self.ee ** 2) ** 2 + z ** 2 / (1 - self.ex ** 2) ** 2
n = self.func_n(x, y, z)
n = np.array([x / np.sqrt(H), y / ((1 - self.ee ** 2) * np.sqrt(H)), z / ((1 - self.ex ** 2) * np.sqrt(H))])
beta, lamb, u = self.cart2ellu(np.array([x, y, z]))
beta, lamb = self.cart2ell(np.array([x, y, z]))
B = self.Ex ** 2 * np.cos(beta) ** 2 + self.Ee ** 2 * np.sin(beta) ** 2
L = self.Ex ** 2 - self.Ee ** 2 * np.cos(lamb) ** 2
@@ -507,11 +501,9 @@ class EllipsoidTriaxial:
p = np.array([p1, p2, p3])
q = np.array([n[1] * p[2] - n[2] * p[1],
n[2] * p[0] - n[0] * p[2],
n[1] * p[1] - n[1] * p[0]])
n[0] * p[1] - n[1] * p[0]])
return {"H": H, "n": n, "beta": beta, "lamb": lamb, "u": u, "B": B, "L": L, "c1": c1, "c0": c0, "t1": t1,
"t2": t2,
"F": F, "p": p, "q": q}
return p, q
if __name__ == "__main__":

84
test_algorithms.py Normal file
View File

@@ -0,0 +1,84 @@
import GHA_triaxial.numeric_examples_panou as nep
import ellipsoide
from GHA_triaxial.panou_2013_2GHA_num import gha2_num
from GHA_triaxial.panou import gha1_ana, gha1_num
import numpy as np
import time
def test():
ell = ellipsoide.EllipsoidTriaxial.init_name("BursaSima1980round")
tables = nep.get_tables()
diffs_gha1_num = []
diffs_gha1_ana = []
diffs_gha2_num = []
times_gha1_num = []
times_gha1_ana = []
times_gha2_num = []
for table in tables:
diffs_gha1_num.append([])
diffs_gha1_ana.append([])
diffs_gha2_num.append([])
times_gha1_num.append([])
times_gha1_ana.append([])
times_gha2_num.append([])
for example in table:
beta0, lamb0, beta1, lamb1, c, alpha0, alpha1, s = example
P0 = ell.ell2cart(beta0, lamb0)
P1 = ell.ell2cart(beta1, lamb1)
start = time.perf_counter()
try:
P1_num = gha1_num(ell, P0, alpha0, s, 10000)
end = time.perf_counter()
diff_P1_num = np.linalg.norm(P1 - P1_num)
except:
end = time.perf_counter()
diff_P1_num = None
time_gha1_num = end - start
start = time.perf_counter()
try:
P1_ana = gha1_ana(ell, P0, alpha0, s, 50)
end = time.perf_counter()
diff_P1_ana = np.linalg.norm(P1 - P1_ana)
except:
end = time.perf_counter()
diff_P1_ana = None
time_gha1_ana = end - start
start = time.perf_counter()
try:
alpha0_num, alpha1_num, s_num = gha2_num(ell, beta0, lamb0, beta1, lamb1, n=1000)
end = time.perf_counter()
diff_s_num = abs(s - s_num)
except:
end = time.perf_counter()
diff_s_num = None
time_gha2_num = None
time_gha2_num = end - start
diffs_gha1_num[-1].append(diff_P1_num)
diffs_gha1_ana[-1].append(diff_P1_ana)
diffs_gha2_num[-1].append(diff_s_num)
times_gha1_num[-1].append(time_gha1_num)
times_gha1_ana[-1].append(time_gha1_ana)
times_gha2_num[-1].append(time_gha2_num)
print(diffs_gha1_num, diffs_gha1_ana, diffs_gha2_num)
print(times_gha1_num, times_gha1_ana, times_gha2_num)
def display():
diffs = [[{'gha1_num': np.float64(3.410763124264611e-05), 'gha1_ana': np.float64(3.393273802112796e-05), 'gha2_num': np.float64(3.3931806683540344e-05)}, {'gha1_num': np.float64(0.0008736425000530604), 'gha1_ana': np.float64(0.0008736458415010259), 'gha2_num': None}, {'gha1_num': np.float64(0.0007739730058338136), 'gha1_ana': np.float64(0.0007739621469802854), 'gha2_num': np.float64(1.5832483768463135e-07)}, {'gha1_num': np.float64(0.00010554956741100295), 'gha1_ana': np.float64(8.814246009944831), 'gha2_num': np.float64(4.864111542701721e-05)}, {'gha1_num': np.float64(0.0002135908394614854), 'gha1_ana': np.float64(0.0002138610897967267), 'gha2_num': np.float64(5.0179407158866525)}, {'gha1_num': np.float64(0.00032727226891456654), 'gha1_ana': np.float64(0.00032734569198545905), 'gha2_num': np.float64(9.735533967614174e-05)}, {'gha1_num': np.float64(0.0005195973303787956), 'gha1_ana': np.float64(0.0005197766935509641), 'gha2_num': None}], [{'gha1_num': np.float64(1.780250537652368e-05), 'gha1_ana': np.float64(1.996805145339501e-05), 'gha2_num': np.float64(1.8164515495300293e-05)}, {'gha1_num': np.float64(4.8607540473363564e-05), 'gha1_ana': np.float64(2205539.954949392), 'gha2_num': None}, {'gha1_num': np.float64(0.00017376854985685854), 'gha1_ana': np.float64(328124.1513636429), 'gha2_num': np.float64(0.17443156614899635)}, {'gha1_num': np.float64(5.83429352558999e-05), 'gha1_ana': np.float64(0.01891628037258558), 'gha2_num': np.float64(1.4207654744386673)}, {'gha1_num': np.float64(0.0006421087024666934), 'gha1_ana': np.float64(0.0006420400127297228), 'gha2_num': np.float64(0.12751091085374355)}, {'gha1_num': np.float64(0.0004456207867164434), 'gha1_ana': np.float64(0.0004455649707698245), 'gha2_num': np.float64(0.00922046648338437)}, {'gha1_num': np.float64(0.0002340879908275419), 'gha1_ana': np.float64(0.00023422217242111216), 'gha2_num': np.float64(0.001307751052081585)}], [{'gha1_num': np.float64(976.6580096633622), 'gha1_ana': np.float64(976.6580096562798), 'gha2_num': np.float64(6.96033239364624e-05)}, {'gha1_num': np.float64(2825.2936643258527), 'gha1_ana': np.float64(2794.954866417055), 'gha2_num': np.float64(1.3615936040878296e-05)}, {'gha1_num': np.float64(1248.8942058074501), 'gha1_ana': np.float64(538.5550561841195), 'gha2_num': np.float64(3.722589462995529e-05)}, {'gha1_num': np.float64(2201.1793359793814), 'gha1_ana': np.float64(3735.376499414938), 'gha2_num': np.float64(1.4525838196277618e-05)}, {'gha1_num': np.float64(2262.134819997246), 'gha1_ana': np.float64(25549.567793410763), 'gha2_num': np.float64(9.328126907348633e-06)}, {'gha1_num': np.float64(2673.219788119847), 'gha1_ana': np.float64(21760.866677295206), 'gha2_num': np.float64(8.635222911834717e-06)}, {'gha1_num': np.float64(1708.758419275875), 'gha1_ana': np.float64(3792.1128807063437), 'gha2_num': np.float64(2.4085864424705505e-05)}], [{'gha1_num': np.float64(0.7854659044152204), 'gha1_ana': np.float64(0.785466068424286), 'gha2_num': np.float64(0.785466069355607)}, {'gha1_num': np.float64(237.79878717216718), 'gha1_ana': np.float64(1905080.064324282), 'gha2_num': None}, {'gha1_num': np.float64(55204.601699830164), 'gha1_ana': np.float64(55204.60175211949), 'gha2_num': None}, {'gha1_num': np.float64(12766.348063015519), 'gha1_ana': np.float64(12766.376619517901), 'gha2_num': np.float64(12582.786206113175)}, {'gha1_num': np.float64(29703.049988324146), 'gha1_ana': np.float64(29703.056427749252), 'gha2_num': np.float64(28933.668131249025)}, {'gha1_num': np.float64(43912.03007182513), 'gha1_ana': np.float64(43912.03007528712), 'gha2_num': None}, {'gha1_num': np.float64(28522.29828970693), 'gha1_ana': np.float64(28522.29830145182), 'gha2_num': None}, {'gha1_num': np.float64(17769.115549537233), 'gha1_ana': np.float64(17769.115549483362), 'gha2_num': np.float64(17769.121286311187)}]]
arr = []
for table in diffs:
for example in table:
arr.append([example['gha1_num'], example['gha1_ana'], example['gha2_num']])
arr = np.array(arr)
pass
if __name__ == "__main__":
# test()
display()