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| "source": [ | |
| "# Assignment 4: Monte Carlo Integral\n", | |
| "## Part B\n", | |
| "## CSE 424\n", | |
| "\n", | |
| "**By: Rifaz Nahiyan (011152054)**" | |
| ], | |
| "cell_type": "markdown", | |
| "metadata": {} | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import math, random\n", | |
| "import matplotlib.pyplot as plt" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def f1(x):\n", | |
| " return math.sqrt(4*x)\n", | |
| "\n", | |
| "def f2(x):\n", | |
| " return 8 - x" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "n = 100\nA[n] = 19.45101\nerrors[n] = 5.038073062075747e+22\n\nn = 1000\nA[n] = 18.26014\nerrors[n] = 3.069686280377852e+22\n\nn = 5000\nA[n] = 18.60785\nerrors[n] = 1.3984444899831184e+22\n\nn = 100000\nA[n] = 18.65662\nerrors[n] = 3.1315297909007073e+21\n\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "N = (100, 1000, 5000, 10000*10)\n", | |
| "A = {}\n", | |
| "errors = {}\n", | |
| "#random.seed(1)\n", | |
| "\n", | |
| "lower_lim, upper_lim = 0.0, 8.0\n", | |
| "\n", | |
| "for n in N:\n", | |
| " xrands = [random.uniform(lower_lim, upper_lim)\n", | |
| " for _ in range(n)]\n", | |
| " areas = [(upper_lim - lower_lim) * (f1(x) if x < 4.0 else f2(x))\n", | |
| " for x in xrands]\n", | |
| "\n", | |
| " # Estimate area\n", | |
| " # est_area is just mean of areas\n", | |
| " est_area = round(sum(areas)/n, 5)\n", | |
| " A[n] = est_area\n", | |
| "\n", | |
| " # Estimate error\n", | |
| " sq_areas = [a ** a for a in areas]\n", | |
| " mean_sq_area = round(sum(sq_areas)/n, 5)\n", | |
| " sq_mean_area = est_area * est_area\n", | |
| " error = ((upper_lim - lower_lim)\n", | |
| " * math.sqrt(mean_sq_area - sq_mean_area)) \\\n", | |
| " / math.sqrt(n)\n", | |
| " errors[n] = error\n", | |
| "\n", | |
| " print(f'{n = }')\n", | |
| " print(f'{A[n] = }')\n", | |
| " print(f'{errors[n] = }\\n')\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
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| "metadata": {}, | |
| "execution_count": 14 | |
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| { | |
| "output_type": "display_data", | |
| "data": { | |
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| |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "x, y = errors.keys(), errors.values()\n", | |
| "x = list(map(str, x))\n", | |
| "plt.xlabel('Number of trials')\n", | |
| "plt.ylabel('Error')\n", | |
| "plt.bar(x, y)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ] | |
| } |
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