Fehlerkorrektur
This commit is contained in:
Tammo.Weber
@@ -10,11 +10,17 @@ import ausgaben as aus
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from utils_angle import cot, arccot, wrap_to_pi
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def norm_a(a):
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if a < 0.0:
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a += np.pi
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def norm_a(a: float) -> float:
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a = float(a) % (2 * np.pi)
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return a
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def azimut(E: float, G: float, dbeta_du: float, dlamb_du: float) -> float:
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north = np.sqrt(E) * dbeta_du
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east = np.sqrt(G) * dlamb_du
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return norm_a(np.arctan2(east, north))
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def sph_azimuth(beta1, lam1, beta2, lam2):
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dlam = wrap_to_pi(lam2 - lam1)
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y = np.sin(dlam) * np.cos(beta2)
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@@ -24,6 +30,7 @@ def sph_azimuth(beta1, lam1, beta2, lam2):
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a += 2 * np.pi
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return a
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# Panou 2013
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def gha2_num(
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ell: EllipsoidTriaxial,
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@@ -51,62 +58,62 @@ def gha2_num(
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# Berechnung Koeffizienten, Gaußschen Fundamentalgrößen 1. Ordnung sowie deren Ableitungen
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def BETA_LAMBDA(beta, lamb):
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BETA = (ell.ay ** 2 * np.sin(beta) ** 2 + ell.b ** 2 * np.cos(beta) ** 2) / (
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ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2
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BETA = (ell.ay**2 * np.sin(beta) ** 2 + ell.b**2 * np.cos(beta) ** 2) / (
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ell.Ex**2 - ell.Ey**2 * np.sin(beta) ** 2
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)
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LAMBDA = (ell.ax ** 2 * np.sin(lamb) ** 2 + ell.ay ** 2 * np.cos(lamb) ** 2) / (
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ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2
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LAMBDA = (ell.ax**2 * np.sin(lamb) ** 2 + ell.ay**2 * np.cos(lamb) ** 2) / (
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ell.Ex**2 - ell.Ee**2 * np.cos(lamb) ** 2
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)
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BETA_ = (ell.ax ** 2 * ell.Ey ** 2 * np.sin(2 * beta)) / (
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ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2
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BETA_ = (ell.ax**2 * ell.Ey**2 * np.sin(2 * beta)) / (
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ell.Ex**2 - ell.Ey**2 * np.sin(beta) ** 2
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) ** 2
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LAMBDA_ = -(ell.b ** 2 * ell.Ee ** 2 * np.sin(2 * lamb)) / (
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ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2
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LAMBDA_ = -(ell.b**2 * ell.Ee**2 * np.sin(2 * lamb)) / (
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ell.Ex**2 - ell.Ee**2 * np.cos(lamb) ** 2
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) ** 2
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BETA__ = (
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(2 * ell.ax ** 2 * ell.Ey ** 4 * np.sin(2 * beta) ** 2)
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/ (ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2) ** 3
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+ (2 * ell.ax ** 2 * ell.Ey ** 2 * np.cos(2 * beta))
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/ (ell.Ex ** 2 - ell.Ey ** 2 * np.sin(beta) ** 2) ** 2
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(2 * ell.ax**2 * ell.Ey**4 * np.sin(2 * beta) ** 2)
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/ (ell.Ex**2 - ell.Ey**2 * np.sin(beta) ** 2) ** 3
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+ (2 * ell.ax**2 * ell.Ey**2 * np.cos(2 * beta))
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/ (ell.Ex**2 - ell.Ey**2 * np.sin(beta) ** 2) ** 2
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)
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LAMBDA__ = (
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(2 * ell.b ** 2 * ell.Ee ** 4 * np.sin(2 * lamb) ** 2)
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/ (ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2) ** 3
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- (2 * ell.b ** 2 * ell.Ee ** 2 * np.sin(2 * lamb))
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/ (ell.Ex ** 2 - ell.Ee ** 2 * np.cos(lamb) ** 2) ** 2
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(2 * ell.b**2 * ell.Ee**4 * np.sin(2 * lamb) ** 2)
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/ (ell.Ex**2 - ell.Ee**2 * np.cos(lamb) ** 2) ** 3
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- (2 * ell.b**2 * ell.Ee**2 * np.sin(2 * lamb))
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/ (ell.Ex**2 - ell.Ee**2 * np.cos(lamb) ** 2) ** 2
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)
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E = BETA * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
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G = LAMBDA * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
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E = BETA * (ell.Ey**2 * np.cos(beta) ** 2 + ell.Ee**2 * np.sin(lamb) ** 2)
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G = LAMBDA * (ell.Ey**2 * np.cos(beta) ** 2 + ell.Ee**2 * np.sin(lamb) ** 2)
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E_beta = (
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BETA_ * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
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- BETA * ell.Ey ** 2 * np.sin(2 * beta)
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BETA_ * (ell.Ey**2 * np.cos(beta) ** 2 + ell.Ee**2 * np.sin(lamb) ** 2)
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- BETA * ell.Ey**2 * np.sin(2 * beta)
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)
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E_lamb = BETA * ell.Ee ** 2 * np.sin(2 * lamb)
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E_lamb = BETA * ell.Ee**2 * np.sin(2 * lamb)
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G_beta = -LAMBDA * ell.Ey ** 2 * np.sin(2 * beta)
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G_beta = -LAMBDA * ell.Ey**2 * np.sin(2 * beta)
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G_lamb = (
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LAMBDA_ * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
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+ LAMBDA * ell.Ee ** 2 * np.sin(2 * lamb)
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LAMBDA_ * (ell.Ey**2 * np.cos(beta) ** 2 + ell.Ee**2 * np.sin(lamb) ** 2)
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+ LAMBDA * ell.Ee**2 * np.sin(2 * lamb)
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)
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E_beta_beta = (
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BETA__ * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
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- 2 * BETA_ * ell.Ey ** 2 * np.sin(2 * beta)
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- 2 * BETA * ell.Ey ** 2 * np.cos(2 * beta)
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BETA__ * (ell.Ey**2 * np.cos(beta) ** 2 + ell.Ee**2 * np.sin(lamb) ** 2)
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- 2 * BETA_ * ell.Ey**2 * np.sin(2 * beta)
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- 2 * BETA * ell.Ey**2 * np.cos(2 * beta)
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)
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E_beta_lamb = BETA_ * ell.Ee ** 2 * np.sin(2 * lamb)
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E_lamb_lamb = 2 * BETA * ell.Ee ** 2 * np.cos(2 * lamb)
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E_beta_lamb = BETA_ * ell.Ee**2 * np.sin(2 * lamb)
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E_lamb_lamb = 2 * BETA * ell.Ee**2 * np.cos(2 * lamb)
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G_beta_beta = -2 * LAMBDA * ell.Ey ** 2 * np.cos(2 * beta)
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G_beta_lamb = -LAMBDA_ * ell.Ey ** 2 * np.sin(2 * beta)
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G_beta_beta = -2 * LAMBDA * ell.Ey**2 * np.cos(2 * beta)
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G_beta_lamb = -LAMBDA_ * ell.Ey**2 * np.sin(2 * beta)
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G_lamb_lamb = (
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LAMBDA__ * (ell.Ey ** 2 * np.cos(beta) ** 2 + ell.Ee ** 2 * np.sin(lamb) ** 2)
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+ 2 * LAMBDA_ * ell.Ee ** 2 * np.sin(2 * lamb)
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+ 2 * LAMBDA * ell.Ee ** 2 * np.cos(2 * lamb)
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LAMBDA__ * (ell.Ey**2 * np.cos(beta) ** 2 + ell.Ee**2 * np.sin(lamb) ** 2)
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+ 2 * LAMBDA_ * ell.Ee**2 * np.sin(2 * lamb)
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+ 2 * LAMBDA * ell.Ee**2 * np.cos(2 * lamb)
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)
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return (
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@@ -220,10 +227,14 @@ def gha2_num(
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(_, _, E, G, *_) = BETA_LAMBDA(beta, lamb)
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return np.sqrt(E + G * lamb_p**2)
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lamb_0 = wrap_to_pi(lamb_0)
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lamb_1 = wrap_to_pi(lamb_1)
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# Fall 1 (lambda_0 != lambda_1)
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if abs(lamb_1 - lamb_0) >= 1e-15:
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N = int(n)
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dlamb = float(lamb_1 - lamb_0)
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dlamb = wrap_to_pi(lamb_1 - lamb_0)
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sgn = 1.0 if dlamb >= 0.0 else -1.0
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beta0 = float(beta_0)
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lamb0 = float(lamb_0)
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@@ -237,7 +248,9 @@ def gha2_num(
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dbeta = beta_p
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dbeta_p = p_3 * beta_p**3 + p_2 * beta_p**2 + p_1 * beta_p + p_0
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dX3 = X4
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dX4 = (p_33 * beta_p**3 + p_22 * beta_p**2 + p_11 * beta_p + p_00) * X3 + (3*p_3*beta_p**2 + 2*p_2*beta_p + p_1) * X4
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dX4 = (p_33 * beta_p**3 + p_22 * beta_p**2 + p_11 * beta_p + p_00) * X3 + (
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3 * p_3 * beta_p**2 + 2 * p_2 * beta_p + p_1
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) * X4
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return np.array([dbeta, dbeta_p, dX3, dX4], dtype=float)
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alpha0_sph = sph_azimuth(beta0, lamb0, beta1, lamb1)
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@@ -297,34 +310,36 @@ def gha2_num(
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(_, _, E_start, G_start, *_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0])
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(_, _, E_end, G_end, *_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1])
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alpha_1 = norm_a(arccot(np.sqrt(E_start / G_start) * beta_p_arr[0]))
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alpha_2 = norm_a(arccot(np.sqrt(E_end / G_end) * beta_p_arr[-1]))
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alpha_0 = azimut(E_start, G_start, dbeta_du=beta_p_arr[0] * sgn, dlamb_du=1.0 * sgn)
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alpha_1 = azimut(E_end, G_end, dbeta_du=beta_p_arr[-1] * sgn, dlamb_du=1.0 * sgn)
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# Distanz aus Arrays
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integrand = np.zeros(N + 1, dtype=float)
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for i in range(N + 1):
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(_, _, Ei, Gi, *_) = BETA_LAMBDA(beta_arr[i], lamb_arr[i])
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integrand[i] = np.sqrt(Ei * beta_p_arr[i]**2 + Gi)
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integrand[i] = np.sqrt(Ei * beta_p_arr[i] ** 2 + Gi)
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h = abs(dlamb) / N
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if N % 2 == 0:
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S = integrand[0] + integrand[-1] + 4.0*np.sum(integrand[1:-1:2]) + 2.0*np.sum(integrand[2:-1:2])
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s = h/3.0 * S
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S = integrand[0] + integrand[-1] + 4.0 * np.sum(integrand[1:-1:2]) + 2.0 * np.sum(
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integrand[2:-1:2]
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)
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s = h / 3.0 * S
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else:
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s = np.trapz(integrand, dx=h)
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return float(alpha_1), float(alpha_2), float(s), beta_arr, lamb_arr
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return float(alpha_0), float(alpha_1), float(s), beta_arr, lamb_arr
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_, y_end, s = rk4_integral(ode_lamb, lamb0, v0_final, dlamb, N, integrand_lambda)
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beta_end, beta_p_end, _, _ = y_end
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(_, _, E_start, G_start, *_) = BETA_LAMBDA(beta0, lamb0)
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(_, _, E_end, G_end, *_) = BETA_LAMBDA(beta1, lamb1)
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alpha_0 = azimut(E_start, G_start, dbeta_du=beta_p0 * sgn, dlamb_du=1.0 * sgn)
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alpha_1 = norm_a(arccot(np.sqrt(E_start / G_start) * beta_p0))
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alpha_2 = norm_a(arccot(np.sqrt(E_end / G_end) * beta_p_end))
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(_, _, E_end, G_end, *_) = BETA_LAMBDA(float(beta_end), lamb1)
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alpha_1 = azimut(E_end, G_end, dbeta_du=float(beta_p_end) * sgn, dlamb_du=1.0 * sgn)
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return float(alpha_1), float(alpha_2), float(s)
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return float(alpha_0), float(alpha_1), float(s)
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# Fall 2 (lambda_0 == lambda_1)
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N = int(n)
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@@ -339,15 +354,18 @@ def gha2_num(
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lamb0 = float(lamb_0)
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beta1 = float(beta_1)
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lamb1 = float(lamb_1)
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sgn = 1.0 if dbeta >= 0.0 else -1.0
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def ode_beta(beta, v):
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lamb, lamb_p, Y3, Y4 = v
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(_, _, _, _, q_3, q_2, q_1, q_0, q_33, q_22, q_11, q_00) = q_coef(beta, lamb)
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dlamb = lamb_p
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dlamb_p = q_3*lamb_p**3 + q_2*lamb_p**2 + q_1*lamb_p + q_0
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dlamb_p = q_3 * lamb_p**3 + q_2 * lamb_p**2 + q_1 * lamb_p + q_0
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dY3 = Y4
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dY4 = (q_33*lamb_p**3 + q_22*lamb_p**2 + q_11*lamb_p + q_00)*Y3 + (3*q_3*lamb_p**2 + 2*q_2*lamb_p + q_1)*Y4
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dY4 = (q_33 * lamb_p**3 + q_22 * lamb_p**2 + q_11 * lamb_p + q_00) * Y3 + (
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3 * q_3 * lamb_p**2 + 2 * q_2 * lamb_p + q_1
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) * Y4
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return np.array([dlamb, dlamb_p, dY3, dY4], dtype=float)
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lamb_p0 = 0.0
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@@ -376,36 +394,39 @@ def gha2_num(
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lamb_arr = np.array([st[0] for st in states], dtype=float)
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lamb_p_arr = np.array([st[1] for st in states], dtype=float)
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(BETA_s, LAMBDA_s, _, _, *_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0])
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(BETA_e, LAMBDA_e, _, _, *_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1])
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(_, _, E_start, G_start, *_) = BETA_LAMBDA(beta_arr[0], lamb_arr[0])
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(_, _, E_end, G_end, *_) = BETA_LAMBDA(beta_arr[-1], lamb_arr[-1])
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alpha_1 = norm_a((np.pi/2.0) - arccot(np.sqrt(LAMBDA_s / BETA_s) * lamb_p_arr[0]))
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alpha_2 = norm_a((np.pi/2.0) - arccot(np.sqrt(LAMBDA_e / BETA_e) * lamb_p_arr[-1]))
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alpha_0 = azimut(E_start, G_start, dbeta_du=1.0 * sgn, dlamb_du=lamb_p_arr[0] * sgn)
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alpha_1 = azimut(E_end, G_end, dbeta_du=1.0 * sgn, dlamb_du=lamb_p_arr[-1] * sgn)
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integrand = np.zeros(N + 1, dtype=float)
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for i in range(N + 1):
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(_, _, Ei, Gi, *_) = BETA_LAMBDA(beta_arr[i], lamb_arr[i])
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integrand[i] = np.sqrt(Ei + Gi * lamb_p_arr[i]**2)
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integrand[i] = np.sqrt(Ei + Gi * lamb_p_arr[i] ** 2)
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h = abs(dbeta) / N
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if N % 2 == 0:
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S = integrand[0] + integrand[-1] + 4.0*np.sum(integrand[1:-1:2]) + 2.0*np.sum(integrand[2:-1:2])
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s = h/3.0 * S
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S = integrand[0] + integrand[-1] + 4.0 * np.sum(integrand[1:-1:2]) + 2.0 * np.sum(
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integrand[2:-1:2]
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)
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s = h / 3.0 * S
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else:
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s = np.trapz(integrand, dx=h)
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return float(alpha_1), float(alpha_2), float(s), beta_arr, lamb_arr
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return float(alpha_0), float(alpha_1), float(s), beta_arr, lamb_arr
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_, y_end, s = rk4_integral(ode_beta, beta0, v0_final, dbeta, N, integrand_beta)
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lamb_end, lamb_p_end, _, _ = y_end
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(BETA_s, LAMBDA_s, _, _, *_) = BETA_LAMBDA(beta0, lamb0)
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(BETA_e, LAMBDA_e, _, _, *_) = BETA_LAMBDA(beta1, lamb1)
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(_, _, E_start, G_start, *_) = BETA_LAMBDA(beta0, lamb0)
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alpha_0 = azimut(E_start, G_start, dbeta_du=1.0 * sgn, dlamb_du=lamb_p0 * sgn)
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alpha_1 = norm_a((np.pi/2.0) - arccot(np.sqrt(LAMBDA_s / BETA_s) * lamb_p0))
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alpha_2 = norm_a((np.pi/2.0) - arccot(np.sqrt(LAMBDA_e / BETA_e) * lamb_p_end))
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(_, _, E_end, G_end, *_) = BETA_LAMBDA(beta1, float(lamb_end))
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alpha_1 = azimut(E_end, G_end, dbeta_du=1.0 * sgn, dlamb_du=float(lamb_p_end) * sgn)
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return float(alpha_0), float(alpha_1), float(s)
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return float(alpha_1), float(alpha_2), float(s)
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if __name__ == "__main__":
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# ell = EllipsoidTriaxial.init_name("BursaSima1980round")
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