diverse Änderungen, Versuch der Lösung der zweiten GHA mit Louville

GHA_triaxial/approx_louville.py

@@ -0,0 +1,108 @@
+import numpy as np
+from numpy import sin, cos, arcsin, arccos, arctan2
+from ellipsoide import EllipsoidTriaxial
+import matplotlib.pyplot as plt
+
+dbeta_dc = lambda ell, beta, lamb, alpha: -2 * ell.Ey**2 * sin(alpha)**2 * cos(beta) * sin(beta)
+dlamb_dc = lambda ell, beta, lamb, alpha: -2 * ell.Ee**2 * cos(alpha)**2 * sin(lamb) * cos(lamb)
+dalpha_dc = lambda ell, beta, lamb, alpha:  (2 * sin(alpha) * cos(alpha) *
+                                             (ell.Ey**2 * cos(beta)**2 + ell.Ee**2 * sin(lamb)**2))
+
+lamb2_sphere = lambda r, phi1, lamb1, a12, s: lamb1 + arctan2(sin(s/r) * sin(a12),
+                                                              cos(phi1) * cos(s/r) - sin(s/r) * cos(a12))
+phi2_sphere = lambda r, phi1, lamb1, a12, s: arcsin(sin(phi1) * cos(s/r) + cos(phi1) * sin(s/r) * cos(a12))
+
+a12_sphere = lambda phi1, lamb1, phi2, lamb2: arctan2(cos(phi2) * sin(lamb2 - lamb1),
+                                                      cos(phi1) * cos(phi2) -
+                                                      sin(phi1) * cos(phi2) * cos(lamb2 - lamb1))
+s_sphere = lambda r, phi1, lamb1, phi2, lamb2: r * arccos(sin(phi1) * sin(phi2) +
+                                                          cos(phi1) * cos(phi2) * cos(lamb2 - lamb1))
+
+louville = lambda beta, lamb, alpha: (ell.Ey**2 * cos(beta)**2 * sin(alpha)**2 -
+                                          ell.Ee**2 * sin(lamb)**2 * cos(alpha)**2)
+
+def points_approx_gha2(r: float, phi1: np.ndarray, lamb1: np.ndarray, phi2: np.ndarray, lamb2: np.ndarray, num: int = None, step_size: float = 10000):
+    s_approx = s_sphere(r, phi1, lamb1, phi2, lamb2)
+    if num is not None:
+        step_size = s_approx / (num+1)
+    a_approx = a12_sphere(phi1, lamb1, phi2, lamb2)
+
+    points = [np.array([phi1, lamb1, a_approx])]
+    current_s = step_size
+    while current_s < s_approx:
+        phi_n = phi2_sphere(r, phi1, lamb1, a_approx, current_s)
+        lamb_n = lamb2_sphere(r, phi1, lamb1, a_approx, current_s)
+        points.append(np.array([phi_n, lamb_n, a_approx]))
+        current_s += step_size
+    points.append(np.array([phi2, lamb2, a_approx]))
+    return points
+
+
+def num_update(ell: EllipsoidTriaxial, points, diffs):
+    for i, (beta, lamb, alpha) in enumerate(points):
+        dalpha = dalpha_dc(ell, beta, lamb, alpha)
+        if i == 0 or i == len(points) - 1:
+            grad = np.array([0, 0, dalpha])
+        else:
+            dbeta = dbeta_dc(ell, beta, lamb, alpha)
+            dlamb = dlamb_dc(ell, beta, lamb, alpha)
+            grad = np.array([dbeta, dlamb, dalpha])
+
+        delta = -diffs[i] * grad / np.dot(grad, grad)
+        points[i] += delta
+    return points
+
+
+def gha2(ell: EllipsoidTriaxial, p1: np.ndarray, p2: np.ndarray, maxI: int):
+    beta1, lamb1 = ell.cart2ell2(p1)
+    beta2, lamb2 = ell.cart2ell2(p2)
+    points = points_approx_gha2(ell.ax, beta1, lamb1, beta2, lamb2, 5)
+
+    for j in range(maxI):
+        constants = [louville(point[0], point[1], point[2]) for point in points]
+        mean_constant = np.mean(constants)
+        diffs = constants - mean_constant
+        if np.mean(np.abs(diffs)) > 10:
+            points = num_update(ell, points, diffs)
+        else:
+            break
+        for k in range(maxI):
+
+
+            last_diff_alpha = points[-2][-1] - points[-3][-1]
+            alpha_extrap = points[-2][-1] + last_diff_alpha
+            if abs(alpha_extrap - points[-1][-1]) > 0.0005:
+                pass
+            else:
+                break
+            pass
+    pass
+    return points
+
+def show_points(ell: EllipsoidTriaxial, points):
+    points_cart = []
+    for point in points:
+        points_cart.append(ell.ell2cart2(point[0], point[1]))
+    points_cart = np.array(points_cart)
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111, projection='3d')
+
+    ax.plot(points_cart[:, 0], points_cart[:, 1], points_cart[:, 2])
+    ax.scatter(points_cart[:, 0], points_cart[:, 1], points_cart[:, 2])
+
+    ax.set_xlabel('X')
+    ax.set_ylabel('Y')
+    ax.set_zlabel('Z')
+
+    plt.show()
+
+
+if __name__ == "__main__":
+    ell = EllipsoidTriaxial.init_name("Eitschberger1978")
+    p1 = np.array([4189000, 812000, 4735000])
+    p2 = np.array([4090000, 868000, 4808000])
+    p1, phi1, lamb1, h1 = ell.cartonell(p1)
+    p2, phi2, lamb2, h2 = ell.cartonell(p2)
+    points = gha2(ell, p1, p2, 10)
+    show_points(ell, points)