From d76f89459183dc9ebb00484da46df8d00f203d83 Mon Sep 17 00:00:00 2001 From: Kees van Kempen Date: Mon, 3 Oct 2022 15:59:12 +0200 Subject: [PATCH] 04: Solve the last one: looks finished! --- Exercise sheet 4/exercise_sheet_04.ipynb | 106 +++++++++++++++++++---- 1 file changed, 90 insertions(+), 16 deletions(-) diff --git a/Exercise sheet 4/exercise_sheet_04.ipynb b/Exercise sheet 4/exercise_sheet_04.ipynb index 7b6c391..326aab0 100644 --- a/Exercise sheet 4/exercise_sheet_04.ipynb +++ b/Exercise sheet 4/exercise_sheet_04.ipynb @@ -802,7 +802,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, "id": "f86a04ed", "metadata": { "deletable": false, @@ -817,19 +817,39 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "def generate_initial_positions(N,L):\n", " '''Return array of positions of N disks in non-overlapping positions.'''\n", - " # YOUR CODE HERE\n", - " raise NotImplementedError()\n", + " assert N <= np.ceil( (.5*L**2 - 1)**2 )\n", + " \n", + " disks = np.zeros((N, 2))\n", + " i = 0\n", + " # To have the disks non-touchting, we have them 2.0001 apart instead of 2.\n", + " for x in np.arange(1, L - 1, 2.0001):\n", + " for y in np.arange(1, L - 1, 2.0001):\n", + " if i + 1 > N: return disks\n", + " disks[i] = x, y\n", + " i += 1\n", + " return disks\n", " \n", "plot_disk_configuration(generate_initial_positions(33,14.5),14.5)" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, "id": "3d3dc3db", "metadata": { "deletable": false, @@ -876,7 +896,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, "id": "56252046", "metadata": { "deletable": false, @@ -896,13 +916,15 @@ "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", - " # YOUR CODE HERE\n", - " raise NotImplementedError()" + " # TODO: Do I need to operate on a copy?\n", + " copy_x = np.copy(x)\n", + " copy_x[i] = next_position\n", + " return disk_config_valid(copy_x, L)" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, "id": "167bdc3e", "metadata": { "deletable": false, @@ -950,7 +972,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "id": "ccaa8f9f", "metadata": { "deletable": false, @@ -966,17 +988,69 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Of 10000 proposed moves, 5019 were taken (50.2%).\n" + ] + } + ], "source": [ "def MH_disk_move(x,L,delta):\n", " '''Perform random MH move on configuration x, thus changing the array x (if accepted). \n", " Return True if move was accepted, False otherwise.'''\n", - " # YOUR CODE HERE\n", - " raise NotImplementedError()\n", - "\n", + " \n", + " # Although it is tempting to use the wacky method of pulling two independent\n", + " # normal RVs using the method developed two weeks ago, let's just use Numpy.\n", + " N1, N2 = rng.normal(), rng.normal()\n", + " n = len(x)\n", + " i = np.floor(rng.random()*n).astype(int)\n", + " new_position = x[i] + delta*np.array([N1, N2])\n", + " new_position %= L\n", + " \n", + " if remains_valid_after_move(x, i, new_position, L):\n", + " x[i] = new_position\n", + " return True\n", + " return False\n", + " \n", "# Test run and plot resulting configuration\n", - "# YOUR CODE HERE\n", - "raise NotImplementedError()" + "steps = 10000\n", + "num_moves = 0\n", + "\n", + "L = 11.3\n", + "N = 20\n", + "delta = .3\n", + "\n", + "x = generate_initial_positions(N, L)\n", + "plot_disk_configuration(x, L)\n", + "\n", + "for _ in range(steps):\n", + " num_moves += MH_disk_move(x, L, delta)\n", + "\n", + "plot_disk_configuration(x, L)\n", + "print(\"Of {} proposed moves, {} were taken ({:.1f}%).\".format(steps, num_moves, num_moves/steps*100))" ] } ],