From 9ffbf26dc7e2679fcf64765c7a0c91fd6d8ce3b3 Mon Sep 17 00:00:00 2001 From: Kees van Kempen Date: Tue, 13 Sep 2022 11:56:59 +0200 Subject: [PATCH] 01: Finish up and submit --- Exercise sheet 1/exercise_sheet_01.ipynb | 149 +++++++++++++++++------ 1 file changed, 112 insertions(+), 37 deletions(-) diff --git a/Exercise sheet 1/exercise_sheet_01.ipynb b/Exercise sheet 1/exercise_sheet_01.ipynb index f3f0c9d..ff5e87d 100644 --- a/Exercise sheet 1/exercise_sheet_01.ipynb +++ b/Exercise sheet 1/exercise_sheet_01.ipynb @@ -199,14 +199,14 @@ { "data": { "text/plain": [ - "array([[1.60000000e+01, 3.96949304e-01],\n", - " [3.20000000e+01, 2.84220425e-01],\n", - " [6.40000000e+01, 2.15515371e-01],\n", - " [1.28000000e+02, 1.59275704e-01],\n", - " [2.56000000e+02, 1.00798933e-01],\n", - " [5.12000000e+02, 6.87799562e-02],\n", - " [1.02400000e+03, 4.87684636e-02],\n", - " [2.04800000e+03, 3.85210905e-02]])" + "array([[1.60000000e+01, 4.08380950e-01],\n", + " [3.20000000e+01, 2.90718399e-01],\n", + " [6.40000000e+01, 2.12682826e-01],\n", + " [1.28000000e+02, 1.51102637e-01],\n", + " [2.56000000e+02, 1.12557602e-01],\n", + " [5.12000000e+02, 6.94441168e-02],\n", + " [1.02400000e+03, 5.69283874e-02],\n", + " [2.04800000e+03, 3.67265915e-02]])" ] }, "execution_count": 3, @@ -368,7 +368,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -516,17 +516,16 @@ }, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "N = 10000 \td = 1 \tV_d = 2.000 \tdirect-sampled V_d = 2.000\n", - "N = 10000 \td = 2 \tV_d = 3.142 \tdirect-sampled V_d = 3.144\n", - "N = 10000 \td = 3 \tV_d = 4.189 \tdirect-sampled V_d = 4.161\n", - "N = 10000 \td = 4 \tV_d = 4.935 \tdirect-sampled V_d = 4.898\n", - "N = 10000 \td = 5 \tV_d = 5.264 \tdirect-sampled V_d = 5.357\n", - "N = 10000 \td = 6 \tV_d = 5.168 \tdirect-sampled V_d = 5.146\n", - "N = 10000 \td = 7 \tV_d = 4.725 \tdirect-sampled V_d = 4.659\n" - ] + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ @@ -598,15 +597,15 @@ "text": [ "N delta 4*hits/trials E[(4*hits/trials - pi)^2]\n", "2000 0.0000 4.0000 0.737\n", - "2000 0.3333 3.1409 0.014\n", - "2000 0.6667 3.1351 0.005\n", - "2000 1.0000 3.1381 0.006\n", - "2000 1.3333 3.1406 0.004\n", - "2000 1.6667 3.1316 0.007\n", - "2000 2.0000 3.1377 0.007\n", - "2000 2.3333 3.1311 0.011\n", - "2000 2.6667 3.1547 0.011\n", - "2000 3.0000 3.1417 0.015\n" + "2000 0.3333 3.1625 0.015\n", + "2000 0.6667 3.1381 0.006\n", + "2000 1.0000 3.1450 0.006\n", + "2000 1.3333 3.1471 0.004\n", + "2000 1.6667 3.1429 0.006\n", + "2000 2.0000 3.1508 0.008\n", + "2000 2.3333 3.1429 0.011\n", + "2000 2.6667 3.1362 0.015\n", + "2000 3.0000 3.1297 0.016\n" ] } ], @@ -622,6 +621,7 @@ " for i in range(m):\n", " hits[index_delta][i] = markov_pebble(p0, delta, N)\n", "\n", + "## Print the results\n", "print(\"{:4} {:6} {:8} {:<10}\".format('N','delta','4*hits/trials','E[(4*hits/trials - pi)^2]'))\n", "for index_delta, delta in enumerate(delta_range):\n", " pi_estimates = hits[index_delta]/N*4\n", @@ -651,7 +651,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "deletable": false, "nbgrader": { @@ -666,10 +666,55 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "N delta 4*hits/trials E[(4*hits/trials - pi)^2] rejection rate\n", + "2000 0.0000 4.0000 0.737 0.999\n", + "2000 0.3333 3.1449 0.014 0.138\n", + "2000 0.6667 3.1442 0.005 0.265\n", + "2000 1.0000 3.1463 0.006 0.385\n", + "2000 1.3333 3.1392 0.005 0.495\n", + "2000 1.6667 3.1386 0.006 0.598\n", + "2000 2.0000 3.1403 0.006 0.688\n", + "2000 2.3333 3.1404 0.010 0.766\n", + "2000 2.6667 3.1358 0.013 0.821\n", + "2000 3.0000 3.1525 0.017 0.858\n" + ] + } + ], "source": [ - "# YOUR CODE HERE\n", - "raise NotImplementedError()" + "# To calculate the rejection rate, we need to know the positions. I will copy\n", + "# and adapt the above code and the code in the markov_pebble function as is\n", + "# provided at the beginning of this document.\n", + "\n", + "N = 2000 # number of trials\n", + "m = 200 # number of repetitions\n", + "delta_range = np.linspace(0, 3, 10) # throwing ranges\n", + "\n", + "p0 = np.array([0., 0.]) # starting position in origin\n", + "hits = np.zeros((len(delta_range), m), dtype=int)\n", + "rejections = np.zeros((len(delta_range), m), dtype=int)\n", + "\n", + "for index_delta, delta in enumerate(delta_range):\n", + " for i in range(m):\n", + " prev_position = None\n", + " for position in markov_pebble_generator(p0,delta,N):\n", + " if np.all(position == prev_position):\n", + " rejections[index_delta][i] += 1\n", + " if is_in_circle(position):\n", + " hits[index_delta][i] += 1\n", + " prev_position = position\n", + "\n", + "## Print the results\n", + "print(\"{:4} {:6} {:8} {:<10} {:<10}\"\n", + " .format('N','delta','4*hits/trials','E[(4*hits/trials - pi)^2]', 'rejection rate'))\n", + "for index_delta, delta in enumerate(delta_range):\n", + " pi_estimates = hits[index_delta]/N*4\n", + " print(\"{:4} {:1.4f} {:1.4f} {:1.3f} {:1.3f}\"\n", + " .format(N, delta, np.mean(pi_estimates), np.mean((pi_estimates - np.pi)**2), np.mean(rejections[index_delta]/N)))" ] }, { @@ -694,7 +739,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "deletable": false, "nbgrader": { @@ -709,10 +754,40 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The rejection rate is around 1/2 for delta = 1.3333, which also yields near lowest mean square deviation to pi.\n", + "The rule of thumb works quite nicely in this case, although it does not yields the best result.\n" + ] + } + ], "source": [ - "# YOUR CODE HERE\n", - "raise NotImplementedError()" + "plt.figure()\n", + "plt.title(\"Mean square deviation and rejection rate of $\\\\pi$ guesses by the Metropolis algorithm for {} trials of each {} repetitions\".format(N, m))\n", + "plt.plot(delta_range, np.mean((hits/N*4 - np.pi)**2, axis=1), label=\"$\\mathbb{E}[(\\\\frac{4hits}{trials} - \\\\pi)^2]$\")\n", + "plt.plot(delta_range, np.mean(rejections/N, axis=1), label=\"rejection rate\")\n", + "plt.xlabel(\"throwing range $\\\\delta$\")\n", + "plt.legend()\n", + "plt.rc('legend', fontsize=13)\n", + "plt.show()\n", + "\n", + "print(\"The rejection rate is around 1/2 for delta = 1.3333, which also yields near lowest mean square deviation to pi.\")\n", + "print(\"The rule of thumb works quite nicely in this case, although it does not yields the best result.\")" ] } ],