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Umrechnung alpha, Näherungslösung GHA 1

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Hendrik Möllersmann
2026-01-11 13:14:43 +01:00
parent 797afdfd6f
commit 4d5b6fcc3e
6 changed files with 205 additions and 71 deletions
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125
GHA_triaxial/panou.py
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@@ -68,7 +68,7 @@ def buildODE(ell: EllipsoidTriaxial) -> Callable:
return np.array([dxds, ddx, dyds, ddy, dzds, ddz])
return ODE
def gha1_num(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float, num: int) -> tuple[np.ndarray, float]:
def gha1_num(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float, num: int) -> tuple[np.ndarray, float, list]:
"""
Panou, Korakitits 2019
:param ell:
@@ -95,15 +95,15 @@ def gha1_num(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float,
p1, q1 = pq_ell(ell, x1, y1, z1)
sigma = np.array([dx1ds, dy1ds, dz1ds])
P = p1 @ sigma
Q = q1 @ sigma
P = float(p1 @ sigma)
Q = float(q1 @ sigma)
alpha1 = arctan2(P, Q)
if alpha1 < 0:
alpha1 += 2 * np.pi
return np.array([x1, y1, z1]), alpha1
return np.array([x1, y1, z1]), alpha1, werte
# ---------------------------------------------------------------------------------------------------------------------
@@ -225,8 +225,8 @@ def gha1_ana_step(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
# 52-53
sigma = np.array([dx_s, dy_s, dz_s])
P = p_s @ sigma
Q = q_s @ sigma
P = float(p_s @ sigma)
Q = float(q_s @ sigma)
# 51
alpha1 = arctan2(P, Q)
@@ -237,7 +237,7 @@ def gha1_ana_step(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
return np.array([x_s, y_s, z_s]), alpha1
def gha1_ana(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float, maxM: int, maxPartCircum: int = 4):
def gha1_ana(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float, maxM: int, maxPartCircum: int = 4) -> tuple[np.ndarray, float]:
if s > np.pi / maxPartCircum * ell.ax:
s /= 2
point_step, alpha_step = gha1_ana(ell, point, alpha0, s, maxM, maxPartCircum)
@@ -251,39 +251,103 @@ def gha1_ana(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float,
return point_end, alpha_end
def alpha_para2ell(ell: EllipsoidTriaxial, u: float, v: float, alpha_para: float) -> tuple[float, float, float]:
x, y, z = ell.para2cart(u, v)
beta, lamb = ell.para2ell(u, v)
p_para, q_para = pq_para(ell, x, y, z)
sigma_para = p_para * sin(alpha_para) + q_para * cos(alpha_para)
p_ell, q_ell = pq_ell(ell, x, y, z)
alpha_ell = arctan2(p_ell @ sigma_para, q_ell @ sigma_para)
sigma_ell = p_ell * sin(alpha_ell) + q_ell * cos(alpha_ell)
if np.linalg.norm(sigma_para - sigma_ell) > 1e-12:
raise Exception("Alpha Umrechnung fehlgeschlagen")
return beta, lamb, alpha_ell
def alpha_ell2para(ell: EllipsoidTriaxial, beta: float, lamb: float, alpha_ell: float) -> tuple[float, float, float]:
x, y, z = ell.ell2cart(beta, lamb)
u, v = ell.ell2para(beta, lamb)
p_ell, q_ell = pq_ell(ell, x, y, z)
sigma_ell = p_ell * sin(alpha_ell) + q_ell * cos(alpha_ell)
p_para, q_para = pq_para(ell, x, y, z)
alpha_para = arctan2(p_para @ sigma_ell, q_para @ sigma_ell)
sigma_para = p_para * sin(alpha_para) + q_para * cos(alpha_para)
if np.linalg.norm(sigma_para - sigma_ell) > 1e-12:
raise Exception("Alpha Umrechnung fehlgeschlagen")
print("Alpha Umrechnung fehlgeschlagen:", np.linalg.norm(sigma_para - sigma_ell))
return u, v, alpha_para
def func_sigma_ell(ell, x, y, z, alpha):
p, q = pq_ell(ell, x, y, z)
sigma = p * sin(alpha) + q * cos(alpha)
return sigma
def func_sigma_para(ell, x, y, z, alpha):
p, q = pq_para(ell, x, y, z)
sigma = p * sin(alpha) + q * cos(alpha)
return sigma
def louville_constant(ell: EllipsoidTriaxial, p0: np.ndarray, alpha: float) -> float:
beta, lamb = ell.cart2ell(p0)
l = ell.Ey**2 * cos(beta)**2 * sin(alpha)**2 - ell.Ee**2 * sin(lamb)**2 * cos(alpha)**2
# x, y, z = p0
# t1, t2 = ell.func_t12(x, y, z)
# l_cart = ell.ay**2 - (t1 * sin(alpha)**2 + t2 * cos(alpha)**2)
# if abs(l - l_cart) > 1e-12:
# # raise Exception("Louville constant fehlgeschlagen")
# print("Diff zwischen constant:", abs(l - l_cart))
return l
def louville_l2c(ell, l):
return sqrt((l + ell.Ee**2) / ell.Ex**2)
def louville_c2l(ell, c):
return ell.Ex**2 * c**2 - ell.Ee**2
if __name__ == "__main__":
ell = ellipsoide.EllipsoidTriaxial.init_name("BursaSima1980round")
diffs_panou = []
examples_panou = ne_panou.get_random_examples(5)
for example in examples_panou:
beta0, lamb0, beta1, lamb1, _, alpha0, alpha1, s = example
P0 = ell.ell2cart(beta0, lamb0)
P1_num, alpha1_num = gha1_num(ell, P0, alpha0, s, 100)
beta1_num, lamb1_num = ell.cart2ell(P1_num)
P1_ana, alpha1_ana = gha1_ana(ell, P0, alpha0, s, 60)
beta1_ana, lamb1_ana = ell.cart2ell(P1_ana)
diffs_panou.append((abs(beta1-beta1_num), abs(lamb1-lamb1_num), abs(beta1-beta1_ana), abs(lamb1-lamb1_ana)))
diffs_panou = np.array(diffs_panou)
mask_360 = (diffs_panou > 359) & (diffs_panou < 361)
diffs_panou[mask_360] = np.abs(diffs_panou[mask_360] - 360)
print(diffs_panou)
# ell = ellipsoide.EllipsoidTriaxial.init_name("BursaSima1980round")
# diffs_panou = []
# examples_panou = ne_panou.get_random_examples(5)
# for example in examples_panou:
# beta0, lamb0, beta1, lamb1, _, alpha0_ell, alpha1_ell, s = example
# P0 = ell.ell2cart(beta0, lamb0)
#
# P1_num, alpha1_num, _ = gha1_num(ell, P0, alpha0_ell, s, 100)
# beta1_num, lamb1_num = ell.cart2ell(P1_num)
#
# _, _, alpha0_para = alpha_ell2para(ell, beta0, lamb0, alpha0_ell)
# P1_ana, alpha1_ana = gha1_ana(ell, P0, alpha0_para, s, 60)
# beta1_ana, lamb1_ana = ell.cart2ell(P1_ana)
# diffs_panou.append((abs(beta1-beta1_num), abs(lamb1-lamb1_num), abs(beta1-beta1_ana), abs(lamb1-lamb1_ana)))
# diffs_panou = np.array(diffs_panou)
# mask_360 = (diffs_panou > 359) & (diffs_panou < 361)
# diffs_panou[mask_360] = np.abs(diffs_panou[mask_360] - 360)
# print(diffs_panou)
ell = ellipsoide.EllipsoidTriaxial.init_name("KarneyTest2024")
diffs_karney = []
examples_karney = ne_karney.get_examples((30499, 30500, 40500))
# examples_karney = ne_karney.get_random_examples(5)
# examples_karney = ne_karney.get_examples((30499, 30500, 40500))
examples_karney = ne_karney.get_random_examples(20)
for example in examples_karney:
beta0, lamb0, alpha0, beta1, lamb1, alpha1, s = example
beta0, lamb0, alpha0_ell, beta1, lamb1, alpha1_ell, s = example
P0 = ell.ell2cart(beta0, lamb0)
P1_num, alpha1_num = gha1_num(ell, P0, alpha0, s, 100)
P1_num, alpha1_num, _ = gha1_num(ell, P0, alpha0_ell, s, 5000)
beta1_num, lamb1_num = ell.cart2ell(P1_num)
try:
P1_ana, alpha1_ana = gha1_ana(ell, P0, alpha0, s, 40)
_, _, alpha0_para = alpha_ell2para(ell, beta0, lamb0, alpha0_ell)
P1_ana, alpha1_ana = gha1_ana(ell, P0, alpha0_para, s, 30, maxPartCircum=16)
beta1_ana, lamb1_ana = ell.cart2ell(P1_ana)
except:
beta1_ana, lamb1_ana = np.inf, np.inf
@@ -293,4 +357,5 @@ if __name__ == "__main__":
mask_360 = (diffs_karney > 359) & (diffs_karney < 361)
diffs_karney[mask_360] = np.abs(diffs_karney[mask_360] - 360)
print(diffs_karney)
pass
pass