{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# PHYS201 PHYSICS IIA - *Python Lab 4*\n", "\n", "*Alexei Gilchrist*, 2014\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Remember to execute the cells as you go!*" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "1 Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this lab we will explore sequences of random numbers. Random numbers play a crucial role in computational science. Apart from obvious application in statistics, probability theory, and gambling, random numbers are used as the basis of techniques for numerical integration and optimisation, two tasks that have a wide range of application. They are used heavily in cryptographic protocols. Statistical physics abandons tracking each and every atom and instead treats with statistical quantities - but to be able to simulate such systems we need to sample from random numbers with a given distribution. Quantum mechanics predicts the results of measurements as probabilities - again to simulate quantum systems on a computer we need to be able to handle random numbers. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To give you an idea of their importance, there are various sources where you can obtain random numbers as a commodity, often having to buy them when you want large amounts:\n", "\n", "* [Random.org](http://www.random.org) - random numbers generated from atmospheric noise\n", "* [Hotbits](http://www.fourmilab.ch/hotbits/) - from radioactive decay\n", "* [ANU Quantum Random Numbers Server](http://qrng.anu.edu.au/index.php) - from quantum vacuum fluctuations\n", "* [randomnumbers.info](http://www.randomnumbers.info) - from photons at a beamsplitter\n", "* [QRNG Service](http://qrng.physik.hu-berlin.de) - from photon arrival times\n", "* [A Million Random Digits with 100000 Normal Deviates (Paperback)](http://www.amazon.com/Million-Random-Digits-Normal-Deviates/dp/0833030477) - I suggest you read the book reviews before buying :)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll only be taking a very shallow look at the subject of randomness, this lab is geared to getting you more familiar with using Python to solve problems than to teach you probability theory.\n", "\n", "*Bits of the material below originally appeared in a course at the University of Queensland, run by Prof. P. Drummond and A. Gilchrist.*" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "2 Pseudo random number generators (PRNG)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import Image \n", "Image('http://imgs.xkcd.com/comics/random_number.png') " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "png": 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"prompt_number": 16, "text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generating random numbers in software is really convenient, but the first thing to realise about these random number generators is, well, they are not. The numbers produced are the result of a deterministic algorithm and, while it looks random and hard to predict, if you knew the input parameters then you would be able to reproduce the numbers exactly. This is why they are called *pseudo-random number generators* or PRNGs. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are various properties that a PRNG should have:\n", "\n", "* **Uniformity**. The sequence of pseudo random numbers should sample its space uniformly leaving no holes or sparsenesses or overly sampled regions. \n", "* **Uncorrelated Sequences**. A sequence of pseudo random numbers should not show any correlations with another sequence of pseudo random numbers. \n", "* **Long Period**. Sequences from PRNGs generally repeat themselves after some period. It is essential that this period is sufficiently long for the desired purpose. In fact it has been discovered as a good rule-of-thumb that if the period of a PRNG is $m$ then it is best to use only the first $\\sqrt{m}$ elements of the sequence to avoid any correlations. \n", "* **Efficiency**. The PRNG should be computationally efficient. In large Monte Carlo simulations one can literally use up billions random numbers. Thus computational overheads in calculating sequences should be minimized. " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "2.1 Linear Congruential Generators" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Linear Congruential Generators (LCG) were introduced by D.H. Lehmer in 1948.\n", "The sequence is given by\n", "\n", "\$$\n", "x_{n+1}=(ax_{n}+c)mod\\: m\n", "\$$\n", "\n", "where the *modulus* $m$ has $m>0$, the *multiplier* $a$ has $0 Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a function lcg that takes five parameters m, a, c, x0, and N, and returns a numpy array with N elements where the first element is x0 and each one thereafter is the next one in the sequence for a linear congruential generators with m, a, c. Test it by reproducing the two sequences above." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "2.2 Numpy's random module" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The numpy.random module contains various functions to generate and manipulate random numbers. Numpy uses the [Mersenne Twister](http://en.wikipedia.org/wiki/Mersenne_twister) algorithm to generate pseudo-random numbers. You can find more information in the official documentation [numpy.random documentation](http://docs.scipy.org/doc/numpy/reference/routines.random.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Mersenne Twister has a long period:$2^{19937}-1$. To get an idea of how large this is, evaluate the following:" ] }, { "cell_type": "code", "collapsed": false, "input": [ " 2**19937-1" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This number lies between a *googol*$10^{100}$and a *googolplex*$10^{\\mathrm{googol}}=10^{10^{100}}$. The terms where coined in 1938 by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. Initially a googleplex was \"one, followed by writing zeroes until you get tired\", then it got formalised to$10^{10^{100}}$. Carl Sagan has estimated that it's physically impossible to write it down as stated as it requires more space and time than the Universe. Incidentally, where do you think Google got it's name? " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll import the module" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from numpy import random" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and now we can generate uniformly random numbers using the rand() function which takes the size of the array to return as argument" ] }, { "cell_type": "code", "collapsed": false, "input": [ "random.rand(10)" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate a 5x5 array of random numbers distributed between 100 and 150 based on random.rand()" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "3 Testing randomness" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "3.1 Visual inspection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the simplest ways of testing randomness is by visual inspection. Our eyes are very good at picking up visual patterns so we can make use of that ability in checking random sequences which should *not* have a pattern. If we see a pattern then it's a poor random number generator! For example we can check to see how each number$x_n$is correlated with the number$m$-th along the sequence$x_{x+m}$, by plotting$x_n$vs$x_{n+m}$. Idealy there should not be a pattern. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check nearest neighbour corellations for numpy's rand function:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "v=random.rand(5000)\n", "plt.plot(v[:-1],v[1:],'.')" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare this with a some poor choice of LCG (this has the same number of points plotted as the above graph!)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "x0 = 1\n", "m = 2**31-1+3\n", "v = [x0]\n", "for jj in range(5000):\n", " x1 = 16807*x0%(m)\n", " v.append(x1/float(m))\n", " x0=x1\n", "\n", "plt.plot(v[:-1],v[1:],'.')" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fact that it doesn't fill the space in the same way means that only relatively small set of values is being produced." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This simple visual analysis has also been used to demonstrate that the rand() function from PHP on Microsoft Windows was a rather bad implementation (at least in 2008, details in [PhP rand on MS Windows](http://www.random.org/analysis/#visual)):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "Image('http://www.random.org/analysis/randbitmap-wamp.png') " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "png": 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mbv/1Jz+OkQf8Ybxfttt+oFaWR5Xz5nV7uwSXXaUj7e/lu92BOXHQAd7kY9ys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6OvvIV8QJu05Dduk+4CZ4GTNQP+02RWj3GCg6U+yQgS1kw8CqNOn4kxhjSdl5QUKfDsGF+/4/PL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"prompt_number": 17, "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider two LCGs$A$and$B$:\n", "\n", "*$A$has parameters$m=2^{31}-1$,$a=16807$,$c=0$,$x_0=1$\n", "*$B$has parameters$m=2^{31}$,$a=2^{16}+3$,$c=0$,$x_0=1$\n", "\n", "Using your lcg method, make sure that the 10,001'th number is 1043618065 for A, and 1623524161 for B. Show this below." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following piece of code generates an array with 1000 random numbers and plots$x_n$,$x_{n+1}$, and$x_{n+2}$as a 3-D scatter plot. Note the ax.azim setting which sets the viewpoint angle. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "from mpl_toolkits.mplot3d import Axes3D\n", "v = random.rand(1000)\n", "\n", "fig = plt.figure(figsize=(6,6))\n", "ax = fig.add_subplot(111, projection='3d', aspect='equal')\n", "ax.scatter(v[0:-2],v[1:-1],v[2:], zdir='z', s=2)\n", "ax.azim = 45\n", "ax.elev = 20" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot each of the two LCGs$A$and$B$above viewed from angles 20,40,60, and 80 degrees and check if there are any problems with the LCGs - which is a bad implementation?" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note: the bad algorithm is called RANDU and was brought out by IBM in the early 1960s and its use became widespread. The choice of modulus and multiplier was primarily to simplify the computation, but the result was to produce a poor PRNG. The other more modern algorithm is quite popular and has been extensively studied and seems to provide reasonable pseudo-random number sequence." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "3.2 Histogram" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another quick an ready test is to plot the sequence of numbers in a histogram. If the random numbers are uniformly distributed than we expect a uniform (ish) histogram." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use plt.hist with 10 bins, to plot the numbers produced random.rand(). How many numbers do you need to use to get a histogram that is approximately flat in the graph?" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "3.3 Statistical tests" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many statistical tests that can be applied to random number generators. Bear in mind though that ultimately the numbers are *not* random so it will always be possible to design a test which the sequence would fail. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This level of analysis if beyond this unit though so we'll move along..." ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "4 Other Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are various techniques for changing variables so that uniformly distributed random numbers end up with another distribution. There are also tricks that can be used to efficiently generate various special distributions such as the Normal distribution. The random module can generate numbers from a large number of distributions, for instance beta, exponential, gamma, poisson, normal, ... Take a look at the documentation for more details.\n", "\n", "Here is an example of the Poisson distribution:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.hist(random.poisson(lam=2.0,size=3000),10)" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Von Neuman rejection method is a very general way of producing random numbers according to some given distribution. It's also really simple to understand, though it may be very inefficient for some distributions. Say we want to produce random numbers according to some function$f(x)$, with$a\\le x\\le b$. Also, let's say that the maximum of the function in this interval is$c$:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can generate the random numbers distributed as$f(x)$in the following way:\n", "\n", "* generate a uniform random number$x$in the range$a$to$b$\n", "* generate a uniform random number$y$in the range 0 to$c$\n", "* if$y\\le f(x)$we keep the$x$otherwise we reject it.\n", "* repeat until you have enough numbers\n", "\n", "You can see that the first two steps generate a random point$(x,y)$in a box of size$c\\times(b-a)$. We only keep the point if it is at or below the function." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the following function:$f(x) = \\sin^2(x)+\\cos^2(3x)$which looks like" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.arange(0,2*np.pi,0.1)\n", "plt.plot(x,np.sin(x)**2+np.cos(3*x)**2)" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use the Von Neuman rejection method to produce a list of 100,000 numbers that are distributed according to$f(x)$. Show that this is the case using a histogram with 60 bins." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "5 Central Limit Theorem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An important result in statistics is the *Central Limit Theorem* which states that the average of independent random numbers each drawn from distributions which have a mean and variance, will seem to be drawn from a nomal distribution as more and more numbers are included in the average.\n", "\n", "For example, pick 10 random numbers that are uniformly distributed and calculate the mean (add them all together and divide by ten) - this is one sample. Repeat the process till you have a large number of samples. Now if you look at the distribution of samples, with a histogram for instance, then it will look like a Normal distribution." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Demonstrate the central limit theorem with numbers drawn from (a) the uniform distribution, and (b) the power distribution$p(x) = 5x^{4}\$. You already know how to draw from the uniform distribution, the power distribution is shown below." ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.hist(random.power(5,1000))" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "6 One time pads" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The final application of random numbers we turn to is cryptography. Here, probably the only really secure cryptographic protocol is one-time pads. The idea behind one-time pads is quite simple. Lets assume a message is made of the characters a-z and spaces so that there are a total of 27 possible characters. \n", "\n", "* We take the message and reduce it to a sequence of integers so that 'a'=0, 'b'=1, ... , ' '=26. \n", "* To encode a message that is 15 characters long we generate 15 random integers between 0 and 26. This random sequence is the cryptographic key - *keep it safe*.\n", "* To each character we add the corersponding random integer in the key modulo 27 - this has the potential to map any character to any other character and so will encrypt the message with random shifts.\n", "* Now convert the integers back to letters (this step is not really necessary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could start to implement the algorithm by figuring out how to convert characters to integers and vice versa. The index method on python lists is perfect for this. First put the alphabet we are using in a list:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "alphabet = list('abcdefghijklmnopqrstuvwxyz ')" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can convert a character to the position integer:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "alphabet.index('c')" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and an integer to a character:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "alphabet[2]" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now if we wanted to encode the message 'attack now' which is length 10, we can easily generate a suitable one time pad of the right length with:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "message = 'attack now'\n", "pad = random.randint(0,26,len(message))\n", "print pad" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Write *two* matched methods - one to encode a message given a key (of the same length), and one to decode the encrypted message given the same key. Illustrate the methods by encrypting 'attack now' and decrypting it." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ " Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can get an idea of why one-time pads are secure from the following. Imagine we are trying to crack the encoded message you generated in the previous exercise. Illustrate the following with your decoding method:\n", "\n", "* Figure out what the key should be to 'decode' the message to say 'make peace' \n", "* Figure out another sequence that will decode the message to some other 10-letter phrase that you want\n", "\n", "If every random sequece is equaly likely, then every message that fits in 10 spaces is equaly likely too!" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }