{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Plotting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many Python plotting libraries depending on your purpose. However, the standard general-purpose library is `matplotlib`. This is often used through its `pyplot` interface." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from matplotlib import pyplot" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "nbconvert": { "hide_code": true } }, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import rcParams\n", "rcParams['figure.figsize']=(12,9)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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RICOvnntOmj1bco36fi5dZs/2f14AkKmdqFtBgXTffdRONB0jFsirMWOkf/5nafp06yTR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\nQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import sin, pi\n", "\n", "x = []\n", "y = []\n", "for i in range(201):\n", " x_point = 0.01*i\n", " x.append(x_point)\n", " y.append(sin(pi*x_point)**2)\n", "\n", "pyplot.plot(x, y)\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have defined two sequences - in this case lists, but tuples would also work. One contains the $x$-axis coordinates, the other the data points to appear on the $y$-axis. A basic plot is produced using the `plot` command of `pyplot`. However, this plot will not automatically appear on the screen, as after plotting the data you may wish to add additional information. Nothing will actually happen until you either save the figure to a file (using `pyplot.savefig()`) or explicitly ask for it to be displayed (with the `show` command). When the plot is displayed the program will typically pause until you dismiss the plot." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If using the notebook you can include the command `%matplotlib inline` or `%matplotlib notebook` before plotting to make the plots appear automatically inside the notebook. If code is included in a program which is run inside `spyder` through an IPython console, the figures may appear in the console automatically. Either way, it is good practice to always include the `show` command to explicitly display the plot." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plotting interface is straightforward, but the results are not particularly nice. The following commands illustrate some of the ways of improving the plot:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cAcwDRgPnBEEwqcxz7gDqBUFwh3OuEfALsFMQBIUbfS2tYEdQQQGMGmWt+jp2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\nH0aNggsusDcMKZpIBNq0gR9/hNq1XUcjIvGSmwtbtsCxx9r9oI9O1wp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import sin, pi\n", "\n", "x = []\n", "y = []\n", "for i in range(201):\n", " x_point = 0.01*i\n", " x.append(x_point)\n", " y.append(sin(pi*x_point)**2)\n", "\n", "pyplot.plot(x, y, marker='+', markersize=8, linestyle=':', \n", " linewidth=3, color='b', label=r'$\\sin^2(\\pi x)$')\n", "pyplot.legend(loc='lower right')\n", "pyplot.xlabel(r'$x$')\n", "pyplot.ylabel(r'$y$')\n", "pyplot.title('A basic plot')\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Whilst most of the commands are self-explanatory, a note should be made of the strings line `r'$x$'`. These strings are in LaTeX format, which is *the* standard typesetting method for professional-level mathematics. The `$` symbols surround mathematics. The `r` before the definition of the string is Python notation, not LaTeX. It says that the following string will be \"raw\": that backslash characters should be left alone. Then, special LaTeX commands have a backslash in front of them: here we use `\\pi` and `\\sin`. Most basic symbols can be easily guessed (eg `\\theta` or `\\int`), but there are [useful lists of symbols](http://www.artofproblemsolving.com/wiki/index.php/LaTeX:Symbols), and a [reverse search site](http://detexify.kirelabs.org/classify.html) available. We can also use `^` to denote superscripts (used here), `_` to denote subscripts, and use `{}` to group terms." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By combining these basic commands with other plotting types (`semilogx` and `loglog`, for example), most simple plots can be produced quickly." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are some more examples:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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L+GX3wAOhY1L41hBEnSeeeEKNGzfWNddcowLhVmeJZc8/H/7GSVnDd+fOofun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\nAACAk2g7QURkZGSoSZMmWr16deZY5cq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import sin, pi, exp, log\n", "\n", "x = []\n", "y1 = []\n", "y2 = []\n", "for i in range(201):\n", " x_point = 1.0 + 0.01*i\n", " x.append(x_point)\n", " y1.append(exp(sin(pi*x_point)))\n", " y2.append(log(pi+x_point*sin(x_point)))\n", "\n", "pyplot.loglog(x, y1, linestyle='--', linewidth=4, \n", " color='k', label=r'$y_1=e^{\\sin(\\pi x)}$')\n", "pyplot.loglog(x, y2, linestyle='-.', linewidth=4, \n", " color='r', label=r'$y_2=\\log(\\pi+x\\sin(x))$')\n", "pyplot.legend(loc='lower right')\n", "pyplot.xlabel(r'$x$')\n", "pyplot.ylabel(r'$y$')\n", "pyplot.title('A basic logarithmic plot')\n", "pyplot.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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OEcWP0A0AAHIWH6zjQ3LrhlYtXLpQG4ZvUOfWTgU2BuQOcwoEAjrw7QOlgdKm/TYlXOa2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\nfOSJJ57QsGHDtHr1ao0cOVJ///vfdcU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import sin, pi, exp, log\n", "\n", "x = []\n", "y1 = []\n", "y2 = []\n", "for i in range(201):\n", " x_point = 1.0 + 0.01*i\n", " x.append(x_point)\n", " y1.append(exp(sin(pi*x_point)))\n", " y2.append(log(pi+x_point*sin(x_point)))\n", "\n", "pyplot.semilogy(x, y1, linestyle='None', marker='o', \n", " color='g', label=r'$y_1=e^{\\sin(\\pi x)}$')\n", "pyplot.semilogy(x, y2, linestyle='None', marker='^', \n", " color='r', label=r'$y_2=\\log(\\pi+x\\sin(x))$')\n", "pyplot.legend(loc='lower right')\n", "pyplot.xlabel(r'$x$')\n", "pyplot.ylabel(r'$y$')\n", "pyplot.title('A different logarithmic plot')\n", "pyplot.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will look at more complex plots later, but the [matplotlib documentation](http://matplotlib.org/api/pyplot_summary.html) contains a lot of details, and the [gallery](http://matplotlib.org/gallery.html) contains a lot of examples that can be adapted to fit. There is also an [extremely useful document](http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-4-Matplotlib.ipynb) as part of [Johansson's lectures on scientific Python](https://github.com/jrjohansson/scientific-python-lectures), and an [introduction by Nicolas Rougier](http://www.labri.fr/perso/nrougier/teaching/matplotlib/matplotlib.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise: Logistic map" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The logistic map builds a sequence of numbers $\\{ x_n \\}$ using the relation\n", "\n", "$$ x_{n+1} = r x_n \\left( 1 - x_n \\right), $$\n", "\n", "where $0 \\le x_0 \\le 1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1\n", "\n", "Write a program that calculates the first $N$ members of the sequence, given as input $x_0$ and $r$ (and, of course, $N$)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2\n", "\n", "Fix $x_0=0.5$. Calculate the first 2,000 members of the sequence for $r=1.5$ and $r=3.5$. Plot the last 100 members of the sequence in both cases.\n", "\n", "What does this suggest about the long-term behaviour of the sequence?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 3\n", "\n", "Fix $x_0 = 0.5$. For each value of $r$ between $1$ and $4$, in steps of $0.01$, calculate the first 2,000 members of the sequence. Plot the last 1,000 members of the sequence on a plot where the $x$-axis is the value of $r$ and the $y$-axis is the values in the sequence. Do not plot lines - just plot markers (e.g., use the `'k.'` plotting style)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4\n", "\n", "For iterative maps such as the logistic map, one of three things can occur:\n", "\n", "1. The sequence settles down to a *fixed point*.\n", "2. The sequence rotates through a finite number of values. This is called a *limit cycle*.\n", "3. The sequence generates an infinite number of values. This is called *deterministic chaos*.\n", "\n", "Using just your plot, or new plots from this data, work out approximate values of $r$ for which there is a transition from fixed points to limit cycles, from limit cycles of a given number of values to more values, and the transition to chaos." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" }, "nbconvert": { "title": "Plotting basics" } }, "nbformat": 4, "nbformat_minor": 0 }