{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random\n", "import math\n", "import matplotlib.pyplot as plt\n", "\n", "def estimate_pi(total_points):\n", " circle_points = 0\n", " for _ in range(total_points):\n", " x = random.uniform(-1, 1) # Random x coordinate\n", " y = random.uniform(-1, 1) # Random y coordinate\n", "\n", " # Distance from the origin (using Pythagorean theorem)\n", " distance = math.sqrt(x ** 2 + y ** 2)\n", "\n", " # Check if the point is inside the circle\n", " if distance <= 1:\n", " circle_points += 1\n", " \n", " # Estimate Pi\n", " # area(D)/area(total) = r^2.pi/ (2x2) = pi/4 --> pi = 4 x area(D)/area(total)\n", " pi_estimate = 4 * circle_points / total_points\n", "\n", " return pi_estimate\n", "\n", "# Number of points to be tested\n", "points = [10, 100, 1000, 5000, 10000, 50000, 100000, 500000, 1000000, 10000000]\n", "\n", "# List to store Pi estimations\n", "pi_estimates = []\n", "\n", "# Estimate Pi for different number of points\n", "for point in points:\n", " pi_est = estimate_pi(point)\n", " pi_estimates.append(pi_est)\n", "\n", "# Plot the results\n", "plt.figure(figsize=(10, 5))\n", "plt.plot(points, pi_estimates, marker='o')\n", "plt.xscale('log')\n", "plt.xlabel('Number of Points')\n", "plt.ylabel('Estimated Pi')\n", "plt.title('Estimation of Pi using Monte Carlo Method')\n", "plt.grid(True)\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import random\n", "import matplotlib.pyplot as plt\n", "\n", "# Define the function to be integrated\n", "def f(x):\n", " return x**2\n", "\n", "# Define the Monte Carlo estimator for the integral\n", "def monte_carlo_integral(f, a, b, total_points):\n", " function_sum = 0\n", " for _ in range(total_points):\n", " x = random.uniform(a, b) # Random x in the interval [a, b]\n", "\n", " # Sum the function's value at each point\n", " function_sum += f(x)\n", "\n", " # The average of the function values times the width of the interval gives an estimate of the integral\n", " integral_estimate = ((b - a) / total_points) * function_sum\n", "\n", " return integral_estimate\n", "\n", "# Number of points to be tested\n", "points = [10, 100, 1000, 5000, 10000, 50000, 100000, 500000, 1000000,10000000]\n", "\n", "# List to store integral estimations\n", "integral_estimates = []\n", "\n", "# Estimate integral for different number of points\n", "for point in points:\n", " integral_est = monte_carlo_integral(f, 0, 1, point)\n", " integral_estimates.append(integral_est)\n", "\n", "# Plot the results\n", "plt.figure(figsize=(10, 5))\n", "plt.plot(points, integral_estimates, marker='o')\n", "plt.xscale('log')\n", "plt.xlabel('Number of Points')\n", "plt.ylabel('Estimated Integral')\n", "plt.title('Estimation of Integral using Monte Carlo Method')\n", "plt.grid(True)\n", "plt.show()\n" ] } ], "metadata": { "kernelspec": { "display_name": "TAA", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.16" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }