04: Try to reduce the copy overhead

I failed.

Exercise sheet 4/exercise_sheet_04.ipynb

@@ -916,11 +916,35 @@
     "def remains_valid_after_move(x,i,next_position,L):\n",
     "    '''Returns True if replacing x[i] by next_position would yield a valid configuration,\n",
     "    otherwise False.'''\n",
-    "    # We need to create a copy as not to alter the original x\n",
-    "    # outside this function.\n",
-    "    copy_x = np.copy(x)\n",
-    "    copy_x[i] = next_position\n",
-    "    return disk_config_valid(copy_x, L)"
+    "    # We need to ensure that x is not changed after this function,\n",
+    "    # as alterations done on x will affect x outside the function.\n",
+    "    \n",
+    "    #current_position = np.copy(x[i])\n",
+    "    current_position = x[i].copy()\n",
+    "    #print(type(current_position))\n",
+    "    x[i] = next_position\n",
+    "    ret = disk_config_valid(x, L)\n",
+    "    x[i] = current_position\n",
+    "    return ret\n",
+    "    \n",
+    "    # An alternative approach was to fully copy x, but that turned\n",
+    "    # out to be a lot slower:\n",
+    "    #copy_x = np.copy(x)\n",
+    "    #copy_x[i] = next_position\n",
+    "    #return disk_config_valid(copy_x, L)\n",
+    "    \n",
+    "    # This was tested using the following code.\n",
+    "    #\n",
+    "    #    L = 11.3\n",
+    "    #    N = 20\n",
+    "    #    delta = .3\n",
+    "    #    x = generate_initial_positions(N, L)\n",
+    "    #    %timeit [MH_disk_move(x, L, delta) for _ in range(1000)]\n",
+    "    #\n",
+    "    # For the full copy method:\n",
+    "    #    2.05 s ± 46.5 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
+    "    # For the current method, changing x[i] back:\n",
+    "    #    138 ms ± 12.3 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)"
    ]
   },
   {