Umrechnungs-Test, Tabellen
This commit is contained in:
163
ellipsoide.py
163
ellipsoide.py
@@ -5,6 +5,7 @@ import jacobian_Ligas
|
||||
import matplotlib.pyplot as plt
|
||||
from typing import Tuple
|
||||
from numpy.typing import NDArray
|
||||
import math
|
||||
|
||||
|
||||
class EllipsoidBiaxial:
|
||||
@@ -199,7 +200,10 @@ class EllipsoidTriaxial:
|
||||
c0 = (self.ax ** 2 * self.ay ** 2 + self.ax ** 2 * self.b ** 2 + self.ay ** 2 * self.b ** 2 -
|
||||
(self.ay ** 2 + self.b ** 2) * x ** 2 - (self.ax ** 2 + self.b ** 2) * y ** 2 - (
|
||||
self.ax ** 2 + self.ay ** 2) * z ** 2)
|
||||
t2 = (-c1 + sqrt(c1 ** 2 - 4 * c0)) / 2
|
||||
if c1 ** 2 - 4 * c0 < 0:
|
||||
t2 = np.nan
|
||||
else:
|
||||
t2 = (-c1 + sqrt(c1 ** 2 - 4 * c0)) / 2
|
||||
if t2 == 0:
|
||||
t2 = 1e-18
|
||||
t1 = c0 / t2
|
||||
@@ -316,12 +320,49 @@ class EllipsoidTriaxial:
|
||||
Z = self.b * sin(beta) * sqrt(k**2 + k_**2 * sin(lamb)**2)
|
||||
return np.array([X, Y, Z])
|
||||
|
||||
def cart2ell(self, point: NDArray, eps: float = 1e-12, maxI: int = 100) -> Tuple[float, float]:
|
||||
def cart2ell_yFake(self, point: NDArray, start_delta) -> Tuple[float, float]:
|
||||
"""
|
||||
|
||||
:param point:
|
||||
:return:
|
||||
"""
|
||||
x, y, z = point
|
||||
delta_y = 1e-4
|
||||
best_delta = np.inf
|
||||
while True:
|
||||
try:
|
||||
y1 = y - delta_y
|
||||
beta1, lamb1 = self.cart2ell(np.array([x, y1, z]), noFake=True)
|
||||
point1 = self.ell2cart(beta1, lamb1)
|
||||
|
||||
y2 = y + delta_y
|
||||
beta2, lamb2 = self.cart2ell(np.array([x, y2, z]), noFake=True)
|
||||
point2 = self.ell2cart(beta2, lamb2)
|
||||
|
||||
pointM = (point1 + point2) / 2
|
||||
|
||||
actual_delta = np.linalg.norm(point - pointM)
|
||||
except:
|
||||
actual_delta = np.inf
|
||||
|
||||
if actual_delta < best_delta:
|
||||
best_delta = actual_delta
|
||||
delta_y /= 10
|
||||
else:
|
||||
delta_y *= 10
|
||||
|
||||
y1 = y - delta_y
|
||||
beta1, lamb1 = self.cart2ell(np.array([x, y1, z]), noFake=True)
|
||||
|
||||
return beta1, lamb1
|
||||
|
||||
def cart2ell(self, point: NDArray, eps: float = 1e-12, maxI: int = 100, noFake: bool = False) -> Tuple[float, float]:
|
||||
"""
|
||||
Panou, Korakitis 2019 3f. (num)
|
||||
:param point: Punkt in kartesischen Koordinaten
|
||||
:param eps: zu erreichende Genauigkeit
|
||||
:param maxI: maximale Anzahl Iterationen
|
||||
:param noFake:
|
||||
:return: elliptische Breite und Länge [rad]
|
||||
"""
|
||||
x, y, z = point
|
||||
@@ -329,70 +370,48 @@ class EllipsoidTriaxial:
|
||||
delta_ell = np.array([np.inf, np.inf]).T
|
||||
tiny = 1e-30
|
||||
|
||||
i = 0
|
||||
while np.linalg.norm(delta_ell) > eps and i < maxI:
|
||||
if abs(y) < eps:
|
||||
delta_y = 1e-4
|
||||
best_delta = np.inf
|
||||
while True:
|
||||
try:
|
||||
y1 = y - delta_y
|
||||
beta1, lamb1 = self.cart2ell(np.array([x, y1, z]))
|
||||
point1 = self.ell2cart(beta1, lamb1)
|
||||
try:
|
||||
i = 0
|
||||
while np.linalg.norm(delta_ell) > eps and i < maxI:
|
||||
x0, y0, z0 = self.ell2cart(beta, lamb)
|
||||
delta_l = np.array([x-x0, y-y0, z-z0]).T
|
||||
|
||||
y2 = y + delta_y
|
||||
beta2, lamb2 = self.cart2ell(np.array([x, y2, z]))
|
||||
point2 = self.ell2cart(beta2, lamb2)
|
||||
B = max(self.Ex ** 2 * cos(beta) ** 2 + self.Ee ** 2 * sin(beta) ** 2, tiny)
|
||||
L = max(self.Ex ** 2 - self.Ee ** 2 * cos(lamb) ** 2, tiny)
|
||||
|
||||
pointM = (point1 + point2) / 2
|
||||
J = np.array([[(-self.ax * self.Ey ** 2) / (2 * self.Ex) * sin(2 * beta) / sqrt(B) * cos(lamb),
|
||||
-self.ax / self.Ex * sqrt(B) * sin(lamb)],
|
||||
[-self.ay * sin(beta) * sin(lamb),
|
||||
self.ay * cos(beta) * cos(lamb)],
|
||||
[self.b / self.Ex * cos(beta) * sqrt(L),
|
||||
(self.b * self.Ee ** 2) / (2 * self.Ex) * sin(beta) * sin(2 * lamb) / sqrt(L)]])
|
||||
|
||||
actual_delta = np.linalg.norm(point-pointM)
|
||||
except:
|
||||
actual_delta = np.inf
|
||||
N = J.T @ J
|
||||
det = N[0, 0] * N[1, 1] - N[0, 1] * N[1, 0]
|
||||
N_inv = 1 / det * np.array([[N[1, 1], -N[0, 1]], [-N[1, 0], N[0, 0]]])
|
||||
delta_ell = N_inv @ J.T @ delta_l
|
||||
# delta_ell, *_ = np.linalg.lstsq(J, delta_l, rcond=None)
|
||||
|
||||
if actual_delta < best_delta:
|
||||
best_delta = actual_delta
|
||||
delta_y /= 10
|
||||
else:
|
||||
delta_y *= 10
|
||||
beta += delta_ell[0]
|
||||
lamb += delta_ell[1]
|
||||
i += 1
|
||||
|
||||
y1 = y - delta_y
|
||||
beta1, lamb1 = self.cart2ell(np.array([x, y1, z]))
|
||||
if i == maxI:
|
||||
raise Exception("Umrechnung ist nicht konvergiert")
|
||||
|
||||
return beta1, lamb1
|
||||
point_n = self.ell2cart(beta, lamb)
|
||||
delta_r = np.linalg.norm(point - point_n, axis=-1)
|
||||
if delta_r > 1e-6:
|
||||
raise Exception("Fehler in der Umrechnung cart2ell")
|
||||
|
||||
x0, y0, z0 = self.ell2cart(beta, lamb)
|
||||
delta_l = np.array([x-x0, y-y0, z-z0]).T
|
||||
return beta, lamb
|
||||
|
||||
B = max(self.Ex ** 2 * cos(beta) ** 2 + self.Ee ** 2 * sin(beta) ** 2, tiny)
|
||||
L = max(self.Ex ** 2 - self.Ee ** 2 * cos(lamb) ** 2, tiny)
|
||||
|
||||
J = np.array([[(-self.ax * self.Ey ** 2) / (2 * self.Ex) * sin(2 * beta) / sqrt(B) * cos(lamb),
|
||||
-self.ax / self.Ex * sqrt(B) * sin(lamb)],
|
||||
[-self.ay * sin(beta) * sin(lamb),
|
||||
self.ay * cos(beta) * cos(lamb)],
|
||||
[self.b / self.Ex * cos(beta) * sqrt(L),
|
||||
(self.b * self.Ee ** 2) / (2 * self.Ex) * sin(beta) * sin(2 * lamb) / sqrt(L)]])
|
||||
|
||||
N = J.T @ J
|
||||
det = N[0, 0] * N[1, 1] - N[0, 1] * N[1, 0]
|
||||
N_inv = 1 / det * np.array([[N[1, 1], -N[0, 1]], [-N[1, 0], N[0, 0]]])
|
||||
delta_ell = N_inv @ J.T @ delta_l
|
||||
|
||||
beta += delta_ell[0]
|
||||
lamb += delta_ell[1]
|
||||
i += 1
|
||||
|
||||
if i == maxI:
|
||||
raise Exception("Umrechnung ist nicht konvergiert")
|
||||
|
||||
point_n = self.ell2cart(beta, lamb)
|
||||
delta_r = np.linalg.norm(point - point_n, axis=-1)
|
||||
|
||||
if delta_r > 1e-3:
|
||||
raise Exception("Fehler in der Umrechnung cart2ell")
|
||||
|
||||
return beta, lamb
|
||||
except Exception as e:
|
||||
delta_y = 10 ** math.floor(math.log10(abs(self.ay/1000)))
|
||||
if abs(y) < delta_y and not noFake:
|
||||
return self.cart2ell_yFake(point, delta_y)
|
||||
else:
|
||||
raise e
|
||||
|
||||
def cart2ell_panou(self, point: NDArray) -> Tuple[float, float]:
|
||||
"""
|
||||
@@ -548,18 +567,28 @@ class EllipsoidTriaxial:
|
||||
pE = pEi
|
||||
i += 1
|
||||
|
||||
phi = arctan((1-self.ee**2) / (1-self.ex**2) * pE[2] / sqrt((1-self.ee**2)**2 * pE[0]**2 + pE[1]**2))
|
||||
lamb = arctan(1/(1-self.ee**2) * pE[1]/pE[0])
|
||||
h = np.sign(zG - pE[2]) * np.sign(pE[2]) * sqrt((pE[0] - xG) ** 2 + (pE[1] - yG) ** 2 + (pE[2] - zG) ** 2)
|
||||
if i == maxIter and loa > maxLoa:
|
||||
act_mode = int(mode[-1])
|
||||
new_mode = 3 if act_mode == 1 else act_mode - 1
|
||||
phi, lamb, h = self.cart2geod(point, f"ligas{new_mode}", maxIter, maxLoa)
|
||||
|
||||
if xG < 0 and yG < 0:
|
||||
lamb = -pi + lamb
|
||||
else:
|
||||
phi = arctan((1-self.ee**2) / (1-self.ex**2) * pE[2] / sqrt((1-self.ee**2)**2 * pE[0]**2 + pE[1]**2))
|
||||
lamb = arctan(1/(1-self.ee**2) * pE[1]/pE[0])
|
||||
h = np.sign(zG - pE[2]) * np.sign(pE[2]) * sqrt((pE[0] - xG) ** 2 + (pE[1] - yG) ** 2 + (pE[2] - zG) ** 2)
|
||||
if h < -self.ax:
|
||||
act_mode = int(mode[-1])
|
||||
new_mode = 3 if act_mode == 1 else act_mode - 1
|
||||
phi, lamb, h = self.cart2geod(point, f"ligas{new_mode}", maxIter, maxLoa)
|
||||
else:
|
||||
if xG < 0 and yG < 0:
|
||||
lamb = -pi + lamb
|
||||
|
||||
elif xG < 0:
|
||||
lamb = pi + lamb
|
||||
elif xG < 0:
|
||||
lamb = pi + lamb
|
||||
|
||||
if abs(zG) < eps:
|
||||
phi = 0
|
||||
if abs(zG) < eps:
|
||||
phi = 0
|
||||
|
||||
return phi, lamb, h
|
||||
|
||||
|
||||
Reference in New Issue
Block a user