Add slightly better n_body_matrix

physics.py

@@ -13,5 +13,24 @@ def rotations(a: np.ndarray):
 def n_body(pos: np.ndarray, vel: np.ndarray, mass: np.ndarray):
     for (o_pos, o_mass) in zip(rotations(pos), rotations(mass)):
         dist = o_pos - pos
-        vel += G * (dist / np.linalg.norm(dist, axis=1)[:, np.newaxis]) * o_mass / np.sum(dist ** 2, axis=1)[:, np.newaxis]
+        vel += G * dist * o_mass / (np.linalg.norm(dist, axis=1) ** 3)[:, np.newaxis]
+    pos += vel
+
+
+def n_body_matrix(pos: np.ndarray, vel: np.ndarray, mass: np.ndarray):
+    dist = np.zeros((len(pos) - 1, len(pos), 2))
+    rot_mass = np.zeros((len(mass) - 1, len(mass), 1))
+
+    pos2 = np.concatenate((pos, pos))
+    mass2 = np.concatenate((mass, mass))
+
+    for i in range(1, len(pos)):
+        dist[i - 1] = pos2[i: i + len(pos)] - pos
+        rot_mass[i - 1] = mass2[i: i + len(mass)]
+
+    vel += G * np.sum(
+        dist * rot_mass / (np.linalg.norm(dist, axis=2) ** 3)[:, :, np.newaxis],
+        axis=0
+    )
+
     pos += vel