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ell2

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ni3019
2026-02-05 15:56:09 +01:00
parent 39641b5293
commit 09ae06e9b2
1 changed files with 140 additions and 127 deletions
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GHA_triaxial/gha2_num.py
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@@ -17,39 +17,72 @@ def sph_azimuth(beta1, lam1, beta2, lam2):
a += 2 * np.pi a += 2 * np.pi
return a return a
def BETA_LAMBDA(ell, 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) # Panou 2013
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) def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float, lamb_2: 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: triaxiales Ellipsoid
:param beta_1: reduzierte ellipsoidische Breite Punkt 1
:param lamb_1: elllipsoidische Länge Punkt 1
:param beta_2: reduzierte ellipsoidische Breite Punkt 2
:param lamb_2: elllipsoidische Länge Punkt 2
:param n: Anzahl Schritte
:param epsilon:
:param iter_max: Maximale Anzhal Iterationen
:param all_points:
:return:
"""
# h_x, h_y, h_e entsprechen E_x, E_y, E_e
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)
# Erste Ableitungen von ΒETA und LAMBDA # Erste Ableitungen von ΒETA und LAMBDA
BETA_ = (ell.ax ** 2 * ell.Ey ** 2 * np.sin(2 * beta)) / (ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2) ** 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 LAMBDA_ = - (ell.b ** 2 * ell.Ee ** 2 * np.sin(2 * lamb)) / (ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2) ** 2
# Zweite Ableitungen von ΒETA und LAMBDA # Zweite Ableitungen von ΒETA und LAMBDA
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) BETA__ = ((2 * ell.ax ** 2 * ell.Ey ** 4 * np.sin(2 * beta) ** 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) - ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2) ** 3) + (
((2 * ell.b**2 * ell.Ee**2 * np.sin(2*lamb)) / (ell.Ex**2 - ell.Ee**2 * np.cos(lamb)**2)**2)) (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) E = BETA * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
F = 0 F = 0
G = LAMBDA * (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)
# Erste Ableitungen von E und G # Erste Ableitungen von E und G
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_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) E_lamb = BETA * ell.Ee ** 2 * np.sin(2 * lamb)
G_beta = - LAMBDA * ell.Ey ** 2 * np.sin(2 * beta) 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) 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)
# Zweite Ableitungen von E und G # Zweite Ableitungen von E und G
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_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_beta_lamb = BETA_ * ell.Ee ** 2 * np.sin(2 * lamb)
E_lamb_lamb = 2 * BETA * ell.Ee ** 2 * np.cos(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_beta = - 2 * LAMBDA * ell.Ey ** 2 * np.cos(2 * beta)
G_beta_lamb = - LAMBDA_ * ell.Ey ** 2 * np.sin(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) 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, return (BETA, LAMBDA, E, G,
BETA_, LAMBDA_, BETA__, LAMBDA__, BETA_, LAMBDA_, BETA__, LAMBDA__,
@@ -63,7 +96,7 @@ def p_coef(beta, lamb):
BETA_, LAMBDA_, BETA__, LAMBDA__, BETA_, LAMBDA_, BETA__, LAMBDA__,
E_beta, E_lamb, G_beta, G_lamb, E_beta, E_lamb, G_beta, G_lamb,
E_beta_beta, E_beta_lamb, E_lamb_lamb, E_beta_beta, E_beta_lamb, E_lamb_lamb,
G_beta_beta, G_beta_lamb, G_lamb_lamb) = BETA_LAMBDA(ell, beta, lamb) G_beta_beta, G_beta_lamb, G_lamb_lamb) = BETA_LAMBDA(beta, lamb)
p_3 = - 0.5 * (E_lamb / G) p_3 = - 0.5 * (E_lamb / G)
p_2 = (G_beta / G) - 0.5 * (E_beta / E) p_2 = (G_beta / G) - 0.5 * (E_beta / E)
@@ -102,7 +135,7 @@ def q_coef(beta, lamb):
BETA_, LAMBDA_, BETA__, LAMBDA__, BETA_, LAMBDA_, BETA__, LAMBDA__,
E_beta, E_lamb, G_beta, G_lamb, E_beta, E_lamb, G_beta, G_lamb,
E_beta_beta, E_beta_lamb, E_lamb_lamb, E_beta_beta, E_beta_lamb, E_lamb_lamb,
G_beta_beta, G_beta_lamb, G_lamb_lamb) = BETA_LAMBDA(ell, beta, lamb) G_beta_beta, G_beta_lamb, G_lamb_lamb) = BETA_LAMBDA(beta, lamb)
q_3 = - 0.5 * (G_beta / E) q_3 = - 0.5 * (G_beta / E)
q_2 = (E_lamb / E) - 0.5 * (G_lamb / G) q_2 = (E_lamb / E) - 0.5 * (G_lamb / G)
@@ -136,26 +169,6 @@ def buildODEbeta():
return ODE return ODE
# Panou 2013
def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float, lamb_2: 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: triaxiales Ellipsoid
:param beta_1: reduzierte ellipsoidische Breite Punkt 1
:param lamb_1: elllipsoidische Länge Punkt 1
:param beta_2: reduzierte ellipsoidische Breite Punkt 2
:param lamb_2: elllipsoidische Länge Punkt 2
:param n: Anzahl Schritte
:param epsilon:
:param iter_max: Maximale Anzhal Iterationen
:param all_points:
:return:
"""
# h_x, h_y, h_e entsprechen E_x, E_y, E_e
if lamb_1 != lamb_2: if lamb_1 != lamb_2:
N = n N = n
dlamb = lamb_2 - lamb_1 dlamb = lamb_2 - lamb_1
@@ -164,7 +177,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
if abs(dlamb) < 1e-15: if abs(dlamb) < 1e-15:
beta_0 = 0.0 beta_0 = 0.0
else: else:
(_, _, E1, G1, *_) = BETA_LAMBDA(ell, beta_1, lamb_1) (_, _, E1, G1, *_) = BETA_LAMBDA(beta_1, lamb_1)
beta_0 = np.sqrt(G1 / E1) * cot(alpha0_sph) beta_0 = np.sqrt(G1 / E1) * cot(alpha0_sph)
ode_lamb = buildODElamb() ode_lamb = buildODElamb()
@@ -196,7 +209,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
return False, None, None, None return False, None, None, None
alpha0_sph = sph_azimuth(beta_1, lamb_1, beta_2, lamb_2) alpha0_sph = sph_azimuth(beta_1, lamb_1, beta_2, lamb_2)
(_, _, E1, G1, *_) = BETA_LAMBDA(ell, beta_1, lamb_1) (_, _, E1, G1, *_) = BETA_LAMBDA(beta_1, lamb_1)
beta_p0_sph = np.sqrt(G1 / E1) * cot(alpha0_sph) beta_p0_sph = np.sqrt(G1 / E1) * cot(alpha0_sph)
guesses = [ guesses = [
@@ -220,7 +233,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
integrand = np.zeros(N + 1) integrand = np.zeros(N + 1)
for i in range(N + 1): for i in range(N + 1):
(_, _, Ei, Gi, *_) = BETA_LAMBDA(ell, beta_arr_c[i], lamb_arr_c[i]) (_, _, Ei, Gi, *_) = BETA_LAMBDA(beta_arr_c[i], lamb_arr_c[i])
integrand[i] = np.sqrt(Ei * beta_p_arr_c[i] ** 2 + Gi) integrand[i] = np.sqrt(Ei * beta_p_arr_c[i] ** 2 + Gi)
h = abs(dlamb) / N h = abs(dlamb) / N
@@ -253,9 +266,9 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
beta_p_arr[i] = state[1] beta_p_arr[i] = state[1]
(_, _, E1, G1, (_, _, E1, G1,
*_) = BETA_LAMBDA(ell, beta_arr[0], lamb_arr[0]) *_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0])
(_, _, E2, G2, (_, _, E2, G2,
*_) = BETA_LAMBDA(ell, beta_arr[-1], lamb_arr[-1]) *_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1])
alpha_1 = arccot(np.sqrt(E1 / G1) * beta_p_arr[0]) alpha_1 = arccot(np.sqrt(E1 / G1) * beta_p_arr[0])
alpha_2 = arccot(np.sqrt(E2 / G2) * beta_p_arr[-1]) alpha_2 = arccot(np.sqrt(E2 / G2) * beta_p_arr[-1])
@@ -263,7 +276,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
integrand = np.zeros(N + 1) integrand = np.zeros(N + 1)
for i in range(N + 1): for i in range(N + 1):
(_, _, Ei, Gi, (_, _, Ei, Gi,
*_) = BETA_LAMBDA(ell, beta_arr[i], lamb_arr[i]) *_) = BETA_LAMBDA(beta_arr[i], lamb_arr[i])
integrand[i] = np.sqrt(Ei * beta_p_arr[i] ** 2 + Gi) integrand[i] = np.sqrt(Ei * beta_p_arr[i] ** 2 + Gi)
h = abs(dlamb) / N h = abs(dlamb) / N
@@ -341,9 +354,9 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
# Azimute # Azimute
(BETA1, LAMBDA1, E1, G1, (BETA1, LAMBDA1, E1, G1,
*_) = BETA_LAMBDA(ell, beta_arr[0], lamb_arr[0]) *_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0])
(BETA2, LAMBDA2, E2, G2, (BETA2, LAMBDA2, E2, G2,
*_) = BETA_LAMBDA(ell, beta_arr[-1], lamb_arr[-1]) *_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1])
alpha_1 = (np.pi / 2.0) - arccot(np.sqrt(LAMBDA1 / BETA1) * lambda_p_arr[0]) alpha_1 = (np.pi / 2.0) - arccot(np.sqrt(LAMBDA1 / BETA1) * lambda_p_arr[0])
alpha_2 = (np.pi / 2.0) - arccot(np.sqrt(LAMBDA2 / BETA2) * lambda_p_arr[-1]) alpha_2 = (np.pi / 2.0) - arccot(np.sqrt(LAMBDA2 / BETA2) * lambda_p_arr[-1])
@@ -351,7 +364,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float
integrand = np.zeros(N + 1) integrand = np.zeros(N + 1)
for i in range(N + 1): for i in range(N + 1):
(_, _, Ei, Gi, (_, _, Ei, Gi,
*_) = BETA_LAMBDA(ell, beta_arr[i], lamb_arr[i]) *_) = BETA_LAMBDA(beta_arr[i], lamb_arr[i])
integrand[i] = np.sqrt(Ei + Gi * lambda_p_arr[i] ** 2) integrand[i] = np.sqrt(Ei + Gi * lambda_p_arr[i] ** 2)
h = abs(dbeta) / N h = abs(dbeta) / N