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| "metadata": { | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 3 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython3", | |
| "version": "3.9.2-final" | |
| }, | |
| "orig_nbformat": 2, | |
| "kernelspec": { | |
| "name": "python39264bitvenvvenv093c0f58795b4f9dae044164cc15dc82", | |
| "display_name": "Python 3.9.2 64-bit ('venv': venv)" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2, | |
| "cells": [ | |
| { | |
| "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 f(x):\n", | |
| " return x ** 2 * math.exp(-x) * math.log(x + 2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "n = 100\nA[n] = 0.16495\nerrors[n] = 0.08733850797328749\n\nn = 1000\nA[n] = 0.16276\nerrors[n] = 0.027699443720046076\n\nn = 5000\nA[n] = 0.15923\nerrors[n] = 0.012422848361788853\n\nn = 10000\nA[n] = 0.15849\nerrors[n] = 0.008789146260587544\n\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "N = (100, 1000, 5000, 10000)\n", | |
| "A = {}\n", | |
| "errors = {}\n", | |
| "random.seed(1)\n", | |
| "\n", | |
| "lower_lim, upper_lim = 0.0, 1.0\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) * f(x) 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": 17, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<BarContainer object of 4 artists>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 17 | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": "<Figure size 432x288 with 1 Axes>", | |
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\n" | |
| }, | |
| "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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