{ "metadata": { "name": "", "signature": "sha256:62086092cb881dd61e4f97d6d5bb811b40f6d2b0e572601e0191f2ba03f4fc14" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#V-[Matplotlib](http://matplotlib.org/)\n", "\n", "\n", "Lecturer:*Jos\u00e9 Pedro Silva*^{[1](http://www-num.math.uni-wuppertal.de/en/amna/people/jose-pedro-silva.html)} - [silva_at_math.uni-wuppertal.de](mailto:silva_at_math.uni-wuppertal.de)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Index\n", "\n", "- [Simple Plot](#simple_plot)\n", "- [Colormap](#colormap)\n", "- [3D](#3d)\n", "- [Histogram](#histogram)\n", "- [Animation](#animation)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib as mpl\n", "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "heading", "level": 5, "metadata": {}, "source": [ "Simple Plot" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = linspace(0,1,100)\n", "y = x**2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(y)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "figure()\n", "plot(x,y)\n", "xlabel('x')\n", "ylabel('y')\n", "title('Quadratic function')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "figure()\n", "plot(x,y)\n", "xlabel('$x$')\n", "ylabel('$y$')\n", "title('$y=x^2$')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "fig = figure()\n", "\n", "axes = fig.add_axes([0.1, 0.1, 0.8, 0.8]) # left, bottom, width, height (range 0 to 1)\n", "axes.plot(x, y, 'r')\n", "axes.set_xlabel('x')\n", "axes.set_ylabel('y')\n", "axes.set_title('title');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can change the appearance, similar to MATLAB" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = linspace(0,1,10)\n", "y1 = x**2\n", "y2 = x**2 + 0.1\n", "y3 = x**2 + 0.2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "figure()\n", "plot(x, y1, color='blue', linestyle='dashed')\n", "plot(x, y2, color='red')\n", "plot(x, y3, color='green', linestyle='.',marker='*')\n", "xlabel('$x$')\n", "ylabel('$y$')\n", "title('$y=x^2$')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "figure()\n", "plot(x,y1,'--',x,y2,'r',x,y3,'*')\n", "xlabel('$x$')\n", "ylabel('$y$')\n", "title('$y=x^2$')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "or more definition based" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figure()\n", "plot(x, y1, color='green', linestyle='dashed')\n", "plot(x, y2, color='blue', linestyle='.', marker='o', markerfacecolor='blue', markersize=10, alpha = 0.3)\n", "xlabel('$x$')\n", "ylabel('$y$')\n", "title('$y=x^2$')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = subplots(2,2,figsize=(12,6))\n", "\n", "ax[0,0].plot(x, x+1, color=\"blue\", linewidth=0.25)\n", "ax[0,0].plot(x, x+2, color=\"blue\", linewidth=0.50)\n", "ax[0,0].plot(x, x+3, color=\"blue\", linewidth=1.00) # default\n", "ax[0,0].plot(x, x+4, color=\"blue\", linewidth=2.00)\n", "\n", "# possible linestype options \u2018-\u2018, \u2018\u2013\u2019, \u2018-.\u2019, \u2018:\u2019, \u2018.\u2019, \u2018steps\u2019\n", "ax[0,0].plot(x, x+5, color=\"red\", lw=2, linestyle='-')\n", "ax[0,0].plot(x, x+6, color=\"red\", lw=2, ls='--')\n", "ax[0,0].plot(x, x+7, color=\"red\", lw=2, ls='-.')\n", "ax[0,0].plot(x, x+8, color=\"red\", lw=2, ls=':')\n", "ax[0,0].plot(x, x+9, color=\"red\", lw=2, ls='.')\n", "\n", "# custom\n", "line, = ax[0,0].plot(x, x+10, color=\"black\", lw=1.50)\n", "line.set_dashes([5, 10, 15, 10]) # format: line length, space length, ...\n", "\n", "# Marker Symbols\n", "ax[1,0].plot(x, x, lw=2, ls='*', marker='+')\n", "ax[1,0].plot(x, x+1, lw=2, ls='*', marker='o')\n", "ax[1,0].plot(x, x+2, lw=2, ls='*', marker='v')\n", "ax[1,0].plot(x, x+3, lw=2, ls='*', marker='^')\n", "ax[1,0].plot(x, x+4, lw=2, ls='*', marker='<')\n", "ax[1,0].plot(x, x+5, lw=2, ls='*', marker='>')\n", "ax[1,0].plot(x, x+6, lw=2, ls='*', marker='1')\n", "ax[1,0].plot(x, x+7, lw=2, ls='*', marker='2')\n", "ax[1,0].plot(x, x+8, lw=2, ls='*', marker='3')\n", "ax[1,0].plot(x, x+9, lw=2, ls='*', marker='4')\n", "ax[1,0].plot(x, x+10, lw=2, ls='*', marker='s')\n", "ax[1,0].plot(x, x+11, lw=2, ls='*', marker='p')\n", "ax[1,0].plot(x, x+12, lw=2, ls='*', marker='*')\n", "ax[1,0].plot(x, x+13, lw=2, ls='*', marker='h')\n", "ax[1,0].plot(x, x+14, lw=2, ls='*', marker='H')\n", "ax[1,0].plot(x, x+15, lw=2, ls='*', marker='+')\n", "ax[1,0].plot(x, x+16, lw=2, ls='*', marker='x')\n", "ax[1,0].plot(x, x+17, lw=2, ls='*', marker='D')\n", "ax[1,0].plot(x, x+18, lw=2, ls='*', marker='d')\n", "\n", "\n", "# marker size and color\n", "ax[0,1].plot(x, x+4, color=\"purple\", lw=1, ls='-', marker='o', markersize=2)\n", "ax[0,1].plot(x, x+5, color=\"purple\", lw=1, ls='-', marker='o', markersize=4)\n", "ax[0,1].plot(x, x+6, color=\"green\", lw=1, ls='-', marker='o', markersize=8, markerfacecolor=\"red\")\n", "ax[0,1].plot(x, x+7, color=\"blue\", lw=1, ls='-', marker='s', markersize=8, \n", " markerfacecolor=\"yellow\", markeredgewidth=2, markeredgecolor=\"green\");" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Subplots" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(2, 3)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = plt.subplots(2, 3)\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Colormap" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "cmap with _r is a reversed one" ] }, { "cell_type": "code", "collapsed": false, "input": [ "data = random.randn(50,50)\n", "fig, ax = subplots(1,3)\n", "\n", "plt1 = ax[0].imshow(data,cmap='Greens')\n", "fig.colorbar(plt1,ax=ax[0],fraction=0.05)\n", "plt2 = ax[1].imshow(data,cmap='BuGn')\n", "fig.colorbar(plt2,ax=ax[1],fraction=0.1)\n", "plt3 = ax[2].imshow(data,cmap='Blues')\n", "fig.colorbar(plt3,ax=ax[2])\n", "fig.tight_layout()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "code", "collapsed": false, "input": [ "scatter(data[0,:], data[1,:], s=100,alpha=0.1)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 34, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "svg": [ "\n", "\n", "\n", "\n" ], "text": [ "" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "3D" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from mpl_toolkits.mplot3d import Axes3D" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 35 }, { "cell_type": "code", "collapsed": false, "input": [ "x = linspace(-1,1,50)\n", "y = linspace(-1,1,50)\n", "X,Y = meshgrid(x,y)\n", "Z = exp(-X**2-Y**2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 36 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Using matplotlib backend: Qt4Agg\n" ] } ], "prompt_number": 41 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ax = subplots(2,2,subplot_kw=dict(projection='3d'))\n", "ax[0,0].plot_surface(X,Y,Z,cstride=1)\n", "ax[0,1].plot_wireframe(X,Y,Z)\n", "ax[1,0].plot_surface(X,Y,Z,cmap=cm.coolwarm,rstride=5,cstride=5)\n", "cset = ax[1,0].contour(X, Y, Z, zdir='z', offset=-0.25, cmap=cm.coolwarm)\n", "cset = ax[1,0].contour(X, Y, Z, zdir='x', offset=-1.5, cmap=cm.coolwarm)\n", "cset = ax[1,0].contour(X, Y, Z, zdir='y', offset=1.5, cmap=cm.coolwarm)\n", "\n", "ax[1,0].set_xlim([-1.5, 1])\n", "ax[1,0].set_ylim([-1, 1.5])\n", "ax[1,0].set_zlim([-0.25, 1.25])\n", "\n", "ax[1,1].plot_wireframe(X,Y,Z,rstride=4,cstride=4)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 45, "text": [ "" ] } ], "prompt_number": 45 }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Histogram" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib.ticker import NullFormatter\n", "\n", "# the random data\n", "x = np.random.randn(1000)\n", "y = np.random.randn(1000)\n", "\n", "nullfmt = NullFormatter() # no labels\n", "\n", "# definitions for the axes\n", "left, width = 0.1, 0.65\n", "bottom, height = 0.1, 0.65\n", "bottom_h = left_h = left+width+0.02\n", "\n", "rect_scatter = [left, bottom, width, height]\n", "rect_histx = [left, bottom_h, width, 0.2]\n", "rect_histy = [left_h, bottom, 0.2, height]\n", "\n", "# start with a rectangular Figure\n", "plt.figure(1, figsize=(8,8))\n", "\n", "axScatter = plt.axes(rect_scatter)\n", "axHistx = plt.axes(rect_histx)\n", "axHisty = plt.axes(rect_histy)\n", "\n", "# no labels\n", "axHistx.xaxis.set_major_formatter(nullfmt)\n", "axHisty.yaxis.set_major_formatter(nullfmt)\n", "\n", "# the scatter plot:\n", "axScatter.scatter(x, y)\n", "\n", "# now determine nice limits by hand:\n", "binwidth = 0.25\n", "xymax = np.max( [np.max(np.fabs(x)), np.max(np.fabs(y))] )\n", "lim = ( int(xymax/binwidth) + 1) * binwidth\n", "\n", "axScatter.set_xlim( (-lim, lim) )\n", "axScatter.set_ylim( (-lim, lim) )\n", "\n", "bins = np.arange(-lim, lim + binwidth, binwidth)\n", "axHistx.hist(x, bins=bins)\n", "axHisty.hist(y, bins=bins, orientation='horizontal')\n", "\n", "axHistx.set_xlim( axScatter.get_xlim() )\n", "axHisty.set_ylim( axScatter.get_ylim() )\n", "\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 47 }, { "cell_type": "markdown", "metadata": {}, "source": [ "we can run any example from the online gallery [examples](http://matplotlib.org/gallery.html)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import os\n", "os.system('wget http://matplotlib.org/mpl_examples/images_contours_and_fields/interpolation_methods.py')\n", "\n", "%run 'interpolation_methods.py'" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 52 }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Animation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.integrate import odeint\n", "from matplotlib import animation\n", "\n", "g = 9.82; L = 0.5; m = 0.1\n", "\n", "def dx(x, t):\n", " x1, x2, x3, x4 = x[0], x[1], x[2], x[3]\n", " \n", " dx1 = 6.0/(m*L**2) * (2 * x3 - 3 * cos(x1-x2) * x4)/(16 - 9 * cos(x1-x2)**2)\n", " dx2 = 6.0/(m*L**2) * (8 * x4 - 3 * cos(x1-x2) * x3)/(16 - 9 * cos(x1-x2)**2)\n", " dx3 = -0.5 * m * L**2 * ( dx1 * dx2 * sin(x1-x2) + 3 * (g/L) * sin(x1))\n", " dx4 = -0.5 * m * L**2 * (-dx1 * dx2 * sin(x1-x2) + (g/L) * sin(x2))\n", " return [dx1, dx2, dx3, dx4]\n", "\n", "x0 = [pi/2, pi/2, 0, 0] # initial state\n", "t = linspace(0, 10, 250) # time coordinates\n", "x = odeint(dx, x0, t) # solve the ODE problem\n", "\n", "fig, ax = plt.subplots(figsize=(5,5))\n", "\n", "ax.set_ylim([-1.5, 0.5])\n", "ax.set_xlim([1, -1])\n", "t = linspace(0, 10, 250) # time coordinates\n", "\n", "\n", "pendulum1, = ax.plot([], [], color=\"red\", lw=2)\n", "pendulum2, = ax.plot([], [], color=\"blue\", lw=2)\n", "\n", "def init():\n", " pendulum1.set_data([], [])\n", " pendulum2.set_data([], [])\n", "\n", "def update(n): \n", " # n = frame counter\n", " # calculate the positions of the pendulums\n", " x1 = + L * sin(x[n, 0])\n", " y1 = - L * cos(x[n, 0])\n", " x2 = x1 + L * sin(x[n, 1])\n", " y2 = y1 - L * cos(x[n, 1])\n", " \n", " # update the line data\n", " pendulum1.set_data([0 ,x1], [0 ,y1])\n", " pendulum2.set_data([x1,x2], [y1,y2])\n", "\n", "anim = animation.FuncAnimation(fig, update, init_func=init, frames=len(t), blit=True)\n", "anim.save('../data/animation.mp4', fps=20)\n", "plt.close(fig)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 53 }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.display import HTML\n", "from tempfile import NamedTemporaryFile\n", "import shutil\n", "\n", "WEBM_VIDEO_TAG = \"\"\"

\"\"\"\n", "\n", "M4V_VIDEO_TAG = \"\"\"

\"\"\"\n", "\n", "FPS = 20 # Frames per second in the generated movie\n", "\n", "def anim_to_html(anim, filename=None):\n", " if not hasattr(anim, '_encoded_video'):\n", " with NamedTemporaryFile(suffix='.webm') as f:\n", " webm_writer = animation.FFMpegWriter(fps=FPS, codec=\"libvpx\") # you'll need libvpx to encode .webm videos\n", " vpx_args = [\"-quality\", \"good\", # many arguments are not needed in this example, but I left them for reference\n", " \"-cpu-used\", \"0\",\n", " \"-b:v\", \"500k\",\n", " \"-qmin\", \"10\",\n", " \"-qmax\", \"42\",\n", " \"-maxrate\", \"500k\",\n", " \"-bufsize\", \"1000k\",\n", " \"-threads\", \"4\",\n", " \"-vf\", \"scale=-1:240\",\n", " \"-codec:a\", \"libvorbis\",\n", " \"-b:a\", \"128k\"]\n", " anim.save(f.name, writer=webm_writer, extra_args=vpx_args)\n", " if filename is not None: # in case you want to keep a copy of the generated movie\n", " shutil.copyfile(f.name, filename)\n", " video = open(f.name, \"rb\").read()\n", " anim._encoded_video = video.encode(\"base64\")\n", " \n", " return WEBM_VIDEO_TAG.format(anim._encoded_video)\n", "\n", "def display_animation(anim, filename):\n", " plt.close(anim._fig)\n", " return HTML(anim_to_html(anim, filename))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 55 }, { "cell_type": "code", "collapsed": false, "input": [ "display_animation(anim,filename='../data/animation.mp4')" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "

" ], "metadata": {}, "output_type": "pyout", "prompt_number": 56, "text": [ "" ] } ], "prompt_number": 56 }, { "cell_type": "code", "collapsed": false, "input": [ "%load_ext version_information\n", "%version_information matplotlib" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "

Software	Version
Python	2.7.8 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]
IPython	2.3.1
OS	Linux 3.16.0 26 generic x86_64 with debian jessie sid
matplotlib	1.4.2
Wed Dec 10 11:49:04 2014 CET

" ], "json": [ "{\"Software versions\": [{\"version\": \"2.7.8 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\", \"module\": \"Python\"}, {\"version\": \"2.3.1\", \"module\": \"IPython\"}, {\"version\": \"Linux 3.16.0 26 generic x86_64 with debian jessie sid\", \"module\": \"OS\"}, {\"version\": \"1.4.2\", \"module\": \"matplotlib\"}]}" ], "latex": [ "\\begin{tabular}{|l|l|}\\hline\n", "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n", "Python & 2.7.8 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] \\\\ \\hline\n", "IPython & 2.3.1 \\\\ \\hline\n", "OS & Linux 3.16.0 26 generic x86\\_64 with debian jessie sid \\\\ \\hline\n", "matplotlib & 1.4.2 \\\\ \\hline\n", "\\hline \\multicolumn{2}{|l|}{Wed Dec 10 11:49:04 2014 CET} \\\\ \\hline\n", "\\end{tabular}\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 57, "text": [ "Software versions\n", "Python 2.7.8 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\n", "IPython 2.3.1\n", "OS Linux 3.16.0 26 generic x86_64 with debian jessie sid\n", "matplotlib 1.4.2\n", "Wed Dec 10 11:49:04 2014 CET" ] } ], "prompt_number": 57 }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"./styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", "\n", "\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to top](#Top)" ] } ], "metadata": {} } ] }