{ "cells": [ { "cell_type": "markdown", "id": "7d47fdc3-bc34-4780-aeb1-1fac7990b360", "metadata": {}, "source": [ "## Monte Carlo Hit & Miss Integration\n", " - April 4, 2024\n", "\n", "This tutorial will numerically evaluate a definite integral using the Monte Carlo Hit & Miss method." ] }, { "cell_type": "code", "execution_count": 1, "id": "certified-master", "metadata": {}, "outputs": [], "source": [ "# Import basic Python modules\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "0dad0e22-ac54-4474-8db9-98ac103e2ffb", "metadata": {}, "source": [ "In all Monte Carlo simulations, it is necessary to generate random or pseudo-random numbers. The Python command ```np.random.uniform()``` from the NumPy module generates random numbers uniformly distributed between zero and one. \n", "\n", "In the cell below, we use this command to generate a single sample." ] }, { "cell_type": "code", "execution_count": 2, "id": "major-sentence", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.626168801676552" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.uniform()" ] }, { "cell_type": "markdown", "id": "7ee20b3e-6c17-4b17-8505-ffa64446857c", "metadata": {}, "source": [ "To confirm that the numbers generated are uniformly distribted on the interval $[0, 1]$, we can generate a long list of these numbers and plot a histogram. ```np.random.uniform(a, b, n)``` returns $n$ random numbers uniformly distributed between $a$ and $b$.\n", "\n", "In the cell below, we use this command to generate $10^4$ random numbers between $0$ and $1$." ] }, { "cell_type": "code", "execution_count": 3, "id": "personal-onion", "metadata": {}, "outputs": [], "source": [ "nos = np.random.uniform(0, 1, int(1e4))" ] }, { "cell_type": "markdown", "id": "aacab746-3933-42c9-833f-53650aa03be3", "metadata": {}, "source": [ "Here's a histogram of the $10^4$ uniformly-distributed random numbers. " ] }, { "cell_type": "code", "execution_count": 4, "id": "aboriginal-invitation", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nbins = 50\n", "plt.hist(nos, nbins, color = 'c', edgecolor = 'k')\n", "plt.xlabel('x');\n", "plt.ylabel('counts');" ] }, { "cell_type": "markdown", "id": "6a1ac1cd-ac7e-4662-8ffb-b2bf00d41185", "metadata": {}, "source": [ "This tutorial will first attempt to evaluate an integral for which the solution is easily obtained. This approach has been taken purposely so that we can confirm that our numerical techniques are reliable. The function that we will integrate is a simple polynomial. Below, the function is plotted on the interval $x = [0, 1]$ and the exact value of the integral is evaluated over the same interval. We are going to use this polynomial over and over again in this tutorial, so we define it as a function." ] }, { "cell_type": "code", "execution_count": 5, "id": "plastic-protocol", "metadata": {}, "outputs": [], "source": [ "fcn = lambda x : (-65536*x**8 + 262144*x**7 - 409600*x**6 + 311296*x**5 - 114688*x**4 + 16384*x**3)/27" ] }, { "cell_type": "markdown", "id": "f697d2ae-2fa9-4388-8516-04b09ec755ac", "metadata": {}, "source": [ "Here's a plot of the function over the interval $0\\le x\\le 1$." ] }, { "cell_type": "code", "execution_count": 6, "id": "decimal-animation", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xx = np.arange(0, 1, 0.001)\n", "plt.plot(xx, fcn(xx), 'k-', linewidth = 1.2)\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)');" ] }, { "cell_type": "markdown", "id": "caa9848e-bec0-49ad-8d14-23fbec5b41ea", "metadata": {}, "source": [ "Here's how we can use the SymPy module to do symbolic integration in Python. We first need to import the SymPy module. We can then evaluate the indefinite integral symbolically." ] }, { "cell_type": "code", "execution_count": 7, "id": "generous-central", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle - \\frac{65536 x^{9}}{243} + \\frac{32768 x^{8}}{27} - \\frac{409600 x^{7}}{189} + \\frac{155648 x^{6}}{81} - \\frac{114688 x^{5}}{135} + \\frac{4096 x^{4}}{27}$" ], "text/plain": [ "-65536*x**9/243 + 32768*x**8/27 - 409600*x**7/189 + 155648*x**6/81 - 114688*x**5/135 + 4096*x**4/27" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sym\n", "x = sym.Symbol('x')\n", "fint = sym.integrate(fcn(x), x)\n", "fint" ] }, { "cell_type": "markdown", "id": "62fccfce-0af0-45a0-9cca-1148981f4656", "metadata": {}, "source": [ "We can also evaluate the definite integram using SymPy." ] }, { "cell_type": "code", "execution_count": 8, "id": "hollow-compromise", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4096/8505\n", "The exact value of the integral of f(x) on 0 < x < 1 is 0.481599059376837\n" ] } ], "source": [ "fint = sym.integrate(fcn(x), (x, 0, 1))\n", "print(fint)\n", "print('The exact value of the integral of f(x) on 0 < x < 1 is', sym.N(fint))" ] }, { "cell_type": "markdown", "id": "684c9380-5c75-460a-9da4-a6c2d4cb46f6", "metadata": {}, "source": [ "We now implement is the Hit & Miss numerical integration technique. In this method pairs of random numbers $(x_i, y_i)$ will be generated. For the $x$-coordinate the $x_i$ values will be between $0$ and $1$ (the integration interval). Notice that our function of interest always lies between $y = 0..1$. Therefore, we will also restrict our $y_i$ values to be between $0$ and $1$. The randomly generated points $(x_i, y_i)$ have equal probability of landing anywhere in the box which has area $1$. The probability of a point landing beneath the function is equal to the area $A$ beneath the curve (which is just the integral of the function of interest) divided by the area of the box. Therefore, if we can determine the probability of a point landing beneath the curve, we can easily approximate the value of the definite integral. The probability will be estimated simply by spraying $n$ points into the box and counting how many land beneath the curve $Z_n$ (i.e. counting the Hits). Then, the probability $p$ is simply given by $p = Z_n/n$." ] }, { "cell_type": "code", "execution_count": 9, "id": "threaded-glenn", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The Hit & Miss estimate of the integral of f(x) on 0 < x < 1 is 0.4827\n" ] } ], "source": [ "n = int(1e4) # Generate 10^4 pairs of (x_i, y_i) values\n", "hits = 0 # Initialize the number of hits to zero\n", "misses = 0 # Initialize the number of misses to zero (it's not necessary to count the misses, but we'll do it anyways.\n", "\n", "# Define a set of empty lists to keep track of the coorodinates of the hits and misses \n", "# (again, not necessary if all you want is the numerical value of the integral)\n", "xH = [] \n", "yH = []\n", "xM = []\n", "yM = []\n", "\n", "# Start the main loop\n", "for i in range(n):\n", " xx = np.random.uniform() # Generate the x coordinate\n", " yy = np.random.uniform() # Generate the y coordinate\n", " if yy <= fcn(xx): # If the randomly-generated y-coorodinate y_i is below the cooresponding value of y = f(x_i), then count a hit \n", " hits += 1\n", " xH = xH + [xx]\n", " yH = yH + [yy]\n", " else: # else, count a miss\n", " misses += 1\n", " xM = xM + [xx]\n", " yM = yM + [yy]\n", "intEst = hits/n # Estimate the value of the integral\n", "print('The Hit & Miss estimate of the integral of f(x) on 0 < x < 1 is', intEst)" ] }, { "cell_type": "markdown", "id": "a3a13357-39ac-418e-8bba-590592045883", "metadata": {}, "source": [ "Because we tracked the coorodinates of hits and misses, we can plot them!" ] }, { "cell_type": "code", "execution_count": 10, "id": "opposed-tolerance", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(xH, yH, 'ro', fillstyle = 'none', markersize = 1.5, label = \"hits\") # Scatter plot of the hits (red points)\n", "plt.plot(xM, yM, 'bo', fillstyle = 'none', markersize = 1.5, label = \"misses\") # Scatter plot of the misses (blue points)\n", "xx = np.arange(0, 1, 0.001)\n", "plt.plot(xx, fcn(xx), 'k-', linewidth = 3) # Line plot of the function (black line)\n", "plt.gca().set_aspect('equal') # Force the plot to be a square\n", "plt.legend(loc=\"upper left\") # Position the legend\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)');" ] }, { "cell_type": "markdown", "id": "3a7c66b1-08eb-4221-8f0f-1965bfd682f7", "metadata": {}, "source": [ "If you don't need to keep track of the actual coordinates of each hit and miss, then you can get away with a more compact loop that just counts the number of hits." ] }, { "cell_type": "code", "execution_count": 11, "id": "eca00a9a-1754-4176-ada7-03b41fb597f0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The Hit & Miss estimate of the integral of f(x) on 0 < x < 1 is 0.4848\n" ] } ], "source": [ "n = int(1e4)\n", "hits = 0\n", "for i in range(n):\n", " xx = np.random.uniform()\n", " yy = np.random.uniform()\n", " if yy <= fcn(xx):\n", " hits += 1\n", "print('The Hit & Miss estimate of the integral of f(x) on 0 < x < 1 is', hits/n)" ] }, { "cell_type": "markdown", "id": "eabf3401-4f05-4757-9b1e-599edfdeef7e", "metadata": {}, "source": [ "Now, we will numerically approximate the integral using $n = 10^4$ five thousand times and plot the resulting distribution of our determination of the integral. The distribution is expected to be Gaussian.\n", "\n", "To keep track of how long this block of codes takes to complete, we'll use the ```datetime.now()``` function to display the time before and after the loop." ] }, { "cell_type": "code", "execution_count": 30, "id": "healthy-small", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2024-04-05 08:50:52.200455\n", "0%\n", "10%\n", "20%\n", "30%\n", "40%\n", "50%\n", "60%\n", "70%\n", "80%\n", "90%\n", "2024-04-05 08:52:17.478698\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from datetime import datetime # Import the datetime module\n", "print(datetime.now()) # Print the start time\n", "\n", "n = int(1e4) \n", "m = int(5e3)\n", "intList = [] # Prepare an empty list to store the values of the integral estimations\n", "for j in range(m):\n", " hits = 0 # Initialize hits to zero\n", " if j % int(m/10) == 0:\n", " print(int(j/(m/100)), '%', sep = '')\n", " xx = np.random.uniform(0, 1, n) # Generatre n random x_i values\n", " yy = np.random.uniform(0, 1, n) # Generatre n random y_i values\n", " for i in range(n):\n", " if yy[i] <= fcn(xx[i]): # Check for a hit\n", " hits += 1\n", " intList = intList + [hits/n] # Estimate the value of the integral\n", "print(datetime.now()) # Print the end time\n", "nbins = 20\n", "plt.hist(intList, nbins, color = 'c', edgecolor = 'k') # Plot the distribution of values\n", "plt.xlabel('integral')\n", "plt.ylabel('counts');" ] }, { "cell_type": "markdown", "id": "69d19397-96f7-44e6-90f3-179f761eb658", "metadata": {}, "source": [ "The width of the distribution can be calculated from the standard deviation of the list of $5000$ approximations of the integral and is an estimate in the uncertainty of our determination of the definite integral.\n", "\n", "The standard deviation can be calculated easily using the statistics module." ] }, { "cell_type": "code", "execution_count": 31, "id": "shared-destruction", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.005064775980588549" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import statistics\n", "statistics.stdev(intList)" ] }, { "cell_type": "markdown", "id": "c4bb46db-116f-412c-8d8a-4e6b9d151fc1", "metadata": {}, "source": [ "Finally, the last thing we'll attempt to do is to understand how our uncertainly (standard deviation) depends on $n$. So far, all of our calculations have used $n = 10^4$. Now we'll determine the standard deviation for values of n that range from $100$ to $10^5$. This block of code took my laptop over an hour to complete... If you've got a lot time to kill, trying running the same loop in Maple!" ] }, { "cell_type": "code", "execution_count": 27, "id": "right-finland", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2024-04-05 07:55:55.809046\n", "1 of 10\n", "2 of 10\n", "3 of 10\n", "4 of 10\n", "5 of 10\n", "6 of 10\n", "7 of 10\n", "8 of 10\n", "9 of 10\n", "10 of 10\n", "2024-04-05 08:48:48.756214\n" ] } ], "source": [ "print(datetime.now()) # Start time\n", "nList = [100, 200, 500, 1000, 2000, 5000, 1e4, 2e4, 5e4, 1e5] # List of n values to try\n", "m = int(5e3) # Do 5000 iterations for each value of n\n", "sigmaList = []\n", "for k in range(len(nList)): # Loop of the values of n\n", " intList = [] # Empty list that will be used to store the integral values\n", " print(k+1, 'of', len(nList)) # Keep track of progress\n", " n = int(nList[k]) # Select the current value of n\n", " for j in range(m):\n", " hits = 0 # Initialize the number of hits\n", " xx = np.random.uniform(0, 1, n) # Generate n x_i values\n", " yy = np.random.uniform(0, 1, n) # Generate n y_i values\n", " for i in range(len(xx)):\n", " if yy[i] <= fcn(xx[i]): # Test for a hit\n", " hits += 1\n", " intList = intList + [hits/n] # Estimate the value of the integral and add it to the list\n", " sigmaList = sigmaList + [statistics.stdev(intList)] # Find the standard deviation and add it to the list\n", "print(datetime.now()) # End time" ] }, { "cell_type": "markdown", "id": "c5911c46-916b-461d-8041-8563b7e3b95e", "metadata": {}, "source": [ "Below we plot the uncertainty in the numerical integral estimation as a function of $n$ (the number of trials in the Monte Carlo simulation). As expected, the uncertainty decreases as the number of trials increases. The sigma values are proportional to $1/\\sqrt{n}$." ] }, { "cell_type": "code", "execution_count": 28, "id": "orange-service", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(nList, sigmaList, 'bo', fillstyle = 'none')\n", "plt.xlabel('n')\n", "plt.ylabel(r'$\\sigma$ (std)')\n", "plt.axis((-5e3, 1.2e5, 0, 0.055));" ] }, { "cell_type": "markdown", "id": "07935e9f-1001-4b28-802e-bff1bfd6e578", "metadata": {}, "source": [ "To get a better appreciation of the dependence of $\\sigma$ on $n$, below we plot $\\sigma$ as a function of $1/\\sqrt{n}$ and observe the linear relationship between the two. Beautiful! All of this generated from uniformly distributed random numbers! Take a moment to reflect on what we've accomplished. We've used Monte Carlo simulations to study the behaviour of Monte Carlo simulations! The objective of a Monte Carlo calculation is always to study the characteristics of some system (often a physical system) by simulating data using random numbers." ] }, { "cell_type": "code", "execution_count": 29, "id": "proud-essay", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(1/np.sqrt(nList), sigmaList, 'bo', fillstyle = 'none')\n", "plt.xlabel(r'$1/\\sqrt{n}$')\n", "plt.ylabel(r'$\\sigma$ (std)')\n", "plt.axis((0, .12, 0, 0.055));" ] }, { "cell_type": "code", "execution_count": null, "id": "e3d8cc5f-7039-4d68-8535-ee2b5686c593", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 5 }