notebooks/01_Introducing_Python.ipynb

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      "<style>\n",
      "    h1{\n",
      "        text-align:center;\n",
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      "    h2{\n",
      "        text-align:center;\n",
      "        font-variant:small-caps;\n",
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      "</style>\n",
      "# Introducing Python\n",
      "# Python in HPC Tutorial\n",
      "\n",
      "## Supercomputing 2014\n",
      "\n",
      "Matt Knepley and Aron Ahmadia\n",
      "\n",
      "[![Creative Commons License](../figures/creative_commons_logo.png)](http://creativecommons.org/licenses/by/3.0/deed.en_US)  "
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     "source": [
      "---\n",
      "\n",
      "## About This Tutorial\n",
      "\n",
      "### PyHPC Tutorial on GitHub\n",
      "\n",
      "These presentation materials are part of a continuously updated tutorial on Python for High Performance Computing.  Future versions of this presentation will be found at:\n",
      "\n",
      "https://github.com/pyhpc/pyhpc-tutorial\n",
      "\n",
      "Please set all permanent bookmarks to this URL.\n",
      "\n",
      "### \n",
      "Checkout from git\n",
      "\n",
      "```\n",
      "git clone https://github.com/pyhpc/pyhpc-tutorial.git\n",
      "git checkout sc2014\n",
      "```\n",
      "\n",
      "### Viewing the read-only version of this presentation on nbviewer: \n",
      "\n",
      "* http://nbviewer.ipython.org/urls/raw.github.com/pyhpc/pyhpc-tutorial/master/notebooks/01_Introducing_Python.ipynb"
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      "---\n",
      "\n",
      "## Interacting with the Tutorial Slides\n",
      "\n",
      "This tutorial is an interactive worksheet designed to encourage you to try out the lessons during the demonstration.  If you are looking at the PDF version of these slides, we encourage you to download the updated version (see previous slide) and try the interactive version.\n",
      "\n",
      "To run the interactive version of this notebook, you will need a Python 2.7 environment including: \n",
      "\n",
      "* IPython version >= 13.0\n",
      "* numpy version >= 1.6\n",
      "* scipy >= 0.10\n",
      "* matplotlib >= 1.0.0\n",
      "\n",
      "Move to the directory containing the tarball and execute:\n",
      "\n",
      "    $ ipython notebook --pylab=inline\n",
      "\n",
      "If you are installing the packages yourself, Continuum Analytics provides both free community as well as professional versions of the Anaconda installer, which provides all the packages you will need for this portion of the tutorial. The installer is available from the [Anaconda download page at Continuum Analytics](https://store.continuum.io/cshop/anaconda).\n",
      "\n",
      "You are also welcome to use Enthought's Python Distribution (free for Academic users), available from the [EPD download page at Enthought](http://www.enthought.com/products/epd.php).\n",
      "\n",
      "Unfortunately, you will need to upgrade your EPD's IPython to 0.13 if you go this route, and this may be non-trivial, please see the [Enthought discussion thread here](https://mail.enthought.com/pipermail/epd-users/2012-August/000800.html)."
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      "---\n",
      "## Presentation mode\n",
      "The slideshow mode is only supported by an IPython development branch version. If you would like to write your own slideshows (the notebooks will work regardless of slideshow capabilities), you will need to install Matthias Bussonnier's slideshow_metadata branch.  Here are some sample command-line instructions.\n",
      "\n",
      "    #!/bin/bash\n",
      "    git clone carreau git://github.com/Carreau/ipython.git # Matthias' IPython fork\n",
      "    git checkout origin/slideshow_metadata                 # Select the right branch\n",
      "    python setup.py develop                                # Install the development version\n",
      "    ipython notebook                                       # Check out the slideshows!"
     ]
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      "---\n",
      "## Slideshow Setup Code"
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      "# The below command starts pylab inline mode, which simplifies syntax for many common \n",
      "# scientific computing commands.  All commands starting with % are IPython extensions.\n",
      "%pylab inline\n",
      "\n",
      "import numpy as np\n",
      "import scipy as sp\n",
      "\n",
      "# The following two lines of code load the slideshow extension and start it,\n",
      "# you only need to run these if you are writing or running your own slideshow\n",
      "\n",
      "#%load_ext slidemode\n",
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        "Populating the interactive namespace from numpy and matplotlib\n"
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      "---\n",
      "\n",
      "Introduction to Python (This Notebook)\n",
      "------------\n",
      "\n",
      "### Objectives\n",
      "\n",
      "1. You will understand how scripting languages fit into the toolbox of\n",
      "a computational scientist.\n",
      "2. You will see why Python is a powerful choice\n",
      "3. You will get a taste of Python for actual scientific computing\n",
      "\n",
      "The first part of this introduction is adapted from *Python\n",
      "Scripting for Computational Science* by \n",
      "[Hans Petter Langtangen](http://folk.uio.no/hpl/), Simula \n",
      "and also includes motivating material from \n",
      "[Nathan Collier](http://www.mendeley.com/profiles/nathan-collier/), KAUST.\n",
      "\n",
      "<a href=\"http://www.amazon.com/Hans-Petter-Langtangen/e/B001K6A0IA\"><img src=\"../figures/books.png\"/> </a>\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "Scripting vs Traditional programming\n",
      "------------------------------------\n",
      "\n",
      "In traditional programming, large applications were typically\n",
      "written at a low level. Scripting, by contrast, is programming at a\n",
      "very high level with expressive, dynamic languages.\n",
      "\n",
      "> Traditional programming: Fortran, C, C++, C#, Java\n",
      ">\n",
      "> Scripting: Python, Perl, Ruby, MATLAB\n",
      "\n",
      "In the past, a major gain for scripting languages was that they could automate many \n",
      "tasks that otherwise would be performed by hand.\n",
      "\n",
      "As domain-specific scripting languages such as MATLAB and Python evolved, scientists realized\n",
      "that there were also great benefits in programming at a high level, allowing them to naturally\n",
      "express their computations in fewer lines of code, resulting in greater productivity and less \n",
      "defects.\n",
      "\n",
      "Computational scientists are now demonstrating that high level languages can also be more performant than their low-level\n",
      "counterparts, and Python is at the forefront of this.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Python Scripting - Has this ever happened to you?\n",
      "------------------------------\n",
      "\n",
      "### Scenario 1\n",
      "You are working on data for a presentation your advisor is giving\n",
      "at a conference. At the last minute, you realize that there is a\n",
      "major bug in your code and you need to regenerate all the images\n",
      "and graphs that you have given him. You spend 30 minutes\n",
      "regenerating the data and 6 hours regenerating the graphs because\n",
      "you had them in Excel and had done them by hand.\n",
      "\n",
      "### Scenario 2\n",
      "You are working on your thesis and as you near the finish you\n",
      "review some graphs you generated months earlier and you aren't\n",
      "sure if they are now completely up to date. You spend half a day\n",
      "locating the old code that you wrote on your second laptop and\n",
      "hours more again creating and polishing the charts.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true,
       "slide_step": false
      }
     },
     "source": [
      "---\n",
      "\n",
      "Buyer Beware\n",
      "------------\n",
      "<!--====-->\n",
      "\n",
      "Learning to automate many of these common tasks can greatly\n",
      "increase your productivity (and make your research\n",
      "reproducible). However, beware that there is no end to the number\n",
      "of different ways to do essentially the same thing. \n",
      "\n",
      "![Recall we want to script to SAVE time](../figures/careful.png)\n",
      "\n",
      "> Image credit [Bruno Oliveira](https://plus.google.com/102451193315916178828/posts/MGxauXypb1Y)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Why Python is useful\n",
      "-----------------------\n",
      "<!--====-->\n",
      "\n",
      "There are perhaps many reasons, here we list a few:\n",
      "\n",
      "* like other scripting languages, has an easier interface to learn\n",
      "* allow you to build your own work environment\n",
      "* scientific computing is more than crunching numbers\n",
      "* easier creation of GUIs, demos, and fancy HTML notebooks\n",
      "* create modern interfaces to old codes\n",
      "* allow you to explore, develop and test interactively\n",
      "* cleaner, shorter, easy to read, write, and maintain code"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Is Python > MATLAB?\n",
      "-------------------\n",
      "\n",
      "### Python == MATLAB\n",
      "\n",
      "* Simple and easy to use syntax (dynamic typing, array and linear algebra language)\n",
      "* Easy creation of interactive interfaces and GUIs\n",
      "* Merge simulation and visualization\n",
      "* Commercially supported (Continuum Analytics, Enthought)\n",
      "* Vibrant, enthusiastic academic communities for getting support and learning more\n",
      "* JIT support\n",
      "* Amazon EC2 support\n",
      "\n",
      "### MATLAB > Python\n",
      "\n",
      "* Several MATLAB toolboxes offer capabilities unavailable to the Python community\n",
      "* Superior documentation\n",
      "* Commercially robust and reliable scientific computing tools\n",
      "\n",
      "### Python > MATLAB\n",
      "\n",
      "* Python is free \n",
      "* Object-oriented programming is more convenient in Python\n",
      "* Extensive tools within and beyond scientific computing\n",
      "    + IPython notebook relies on a Python webserver as well as\n",
      "extensive asynchronous messaging support through PyZMQ\n",
      "* Python runs on all modern Cray and IBM supercomputers (and anywhere C does)\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Some Sample Applications\n",
      "========================"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Teaching the finite element method\n",
      "----------------------------------\n",
      "\n",
      "### Stiffness matrix computation\n",
      "\n",
      "![Stiffness matrix](../figures/fem.png)\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Monitor program progress\n",
      "------------------------\n",
      "\n",
      "### Python parses a datafile and makes plots of current progress\n",
      "\n",
      "![Log](../figures/log.png)\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Problem prototypes\n",
      "------------------\n",
      "\n",
      "### Nonlinear, time dependent problem\n",
      "\n",
      "![NonLinear problem](../figures/dsw.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Problem prototypes\n",
      "------------------\n",
      "\n",
      "### Method for fitting surface to data\n",
      "\n",
      "![Prototypes](../figures/molt.png)\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "\n",
      "---\n",
      "\n",
      "Structural program\n",
      "------------------\n",
      "\n",
      "### Python manages floors and columns\n",
      "\n",
      "![Structural program](../figures/struct.png)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Auto-generation of results\n",
      "--------------------------\n",
      "\n",
      "### Python runs C code, post-processes the results, and generates a LaTeX table\n",
      "\n",
      "![Result Generation](../figures/dpg.png)\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "\n",
      "---\n",
      "\n",
      "# A Tour of Python for Simple Scripting\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Script 1\n",
      "--------\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#!/usr/bin/env python\n",
      "import math\n",
      "r = math.pi / 2.0\n",
      "s = math.sin(r)\n",
      "print \"Hello world, sin(%f)=%f\" % (r,s)\n"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": false
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Hello world, sin(1.570796)=1.000000\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Script 2\n",
      "--------\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "infile = \"../examples/data/numbers\"\n",
      "outfile = \"../examples/data/f_numbers\"\n",
      "\n",
      "f = open(infile,'r')\n",
      "g = open(outfile,'w')\n",
      "\n",
      "def func(y):\n",
      "    if y >= 0.0:\n",
      "        return y**5.0*math.exp(-y)\n",
      "    else:\n",
      "        return 0.0\n",
      "    \n",
      "for line in f:\n",
      "    line = line.split()\n",
      "    x = float(line[0])\n",
      "    y = float(line[1])\n",
      "    fy = func(y)\n",
      "    g.write(\"%g %12.5e\\n\" % (x,fy))\n",
      "    \n",
      "f.close() \n",
      "g.close()\n"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Script 3\n",
      "--------\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys,os\n",
      "cmd = 'date'\n",
      "output = os.popen(cmd)\n",
      "lines = output.readlines()\n",
      "fail = output.close()\n",
      "if fail: print 'You do not have the date command'; sys.exit()\n",
      "for line in lines:\n",
      "    line = line.split()\n",
      "    print \"The current time is %s on %s %s, %s\" % (line[3],line[2],line[1],line[-1])"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The current time is 10:14:20 on 4 Sep, 2014\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Script 4\n",
      "--------\n",
      "    "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "source": [
      "---\n",
      "\n",
      "A bib-file (see examples/data/python.bib)\n",
      "----------\n",
      "<!--====-->\n",
      "\n",
      "    @Book{Langtangen2011,\n",
      "      author = \t  {Hans Petter Langtangen},\n",
      "      title = \t  {A Primer on Scientific Programming with Python},\n",
      "      publisher = {Springer},\n",
      "      year = \t  {2011}\n",
      "    }\n",
      "    @Book{Langtangen2010,\n",
      "      author = \t  {Hans Petter Langtangen},\n",
      "      title = \t  {Python Scripting for Computational Science},\n",
      "      publisher = {Springer},\n",
      "      year = \t  {2010}\n",
      "    }\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import re\n",
      "pattern1 = \"@Book{(.*),\"\n",
      "pattern2 = \"\\s+title\\s+=\\s+{(.*)},\"\n",
      "for line in file('../examples/data/python.bib'):\n",
      "    match = re.search(pattern1,line)\n",
      "    if match: \n",
      "        print \"Found a book with the tag '%s'\" % match.group(1)\n",
      "    match = re.search(pattern2,line)\n",
      "    if match:\n",
      "        print \"The title is '%s'\" % match.group(1)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Found a book with the tag 'Langtangen2011'\n",
        "The title is 'A Primer on Scientific Programming with Python'\n",
        "Found a book with the tag 'Langtangen2010'\n",
        "The title is 'Python Scripting for Computational Science'\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "# A Tour of Python for Scientific Computing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Arrays\n",
      "-------------------\n",
      "<!--====-->\n",
      "\n",
      "**Python** has built-in:\n",
      "\n",
      "containers: lists (costless insertion and append), dictionaries (fast lookup)  \n",
      "high-level number objects: integers, floating point  \n",
      "\n",
      "**Numpy** is:\n",
      "\n",
      "extension package to Python for multi-dimensional arrays  \n",
      "closer to hardware (efficiency)  \n",
      "designed for scientific computation (convenience)  \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([0,1,2,3,4])\n",
      "a"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([0, 1, 2, 3, 4])"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print a.ndim # Dimensionality\n",
      "print a.shape # Shape"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1\n",
        "(5,)\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = np.array([[0, 1, 2], [3, 4, 5]])\n",
      "print b\n",
      "print b.ndim\n",
      "print b.shape"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[0 1 2]\n",
        " [3 4 5]]\n",
        "2\n",
        "(2, 3)\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Common Arrays\n",
      "-------------------\n",
      "<!--====-->\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.arange(10) # Like range [0, 1, ..., 9]\n",
      "print np.arange(1,9, 2) # [1, 3, 5, 7]"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0 1 2 3 4 5 6 7 8 9]\n",
        "[1 3 5 7]\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.linspace(0, 1, 6) # A linear space of [0,1] with 6 pts\n",
      "print np.linspace(0, 1, 6, endpoint=False) # [0,1["
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.   0.2  0.4  0.6  0.8  1. ]\n",
        "[ 0.          0.16666667  0.33333333  0.5         0.66666667  0.83333333]\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.ones((3,3)) # 3 X 3 2D array of 1's"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 1.  1.  1.]\n",
        " [ 1.  1.  1.]\n",
        " [ 1.  1.  1.]]\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.eye(3)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 1.  0.  0.]\n",
        " [ 0.  1.  0.]\n",
        " [ 0.  0.  1.]]\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.diag(arange(4))"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[0 0 0 0]\n",
        " [0 1 0 0]\n",
        " [0 0 2 0]\n",
        " [0 0 0 3]]\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.random.rand(4) # Uniform distribution\n",
      "print np.random.randn(4) # Gaussian distribution"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.9134486   0.7943014   0.40743464  0.8400922 ]\n",
        "[-0.05662066 -0.99363921  0.35042966 -0.29096857]\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(np.random.rand(10000), bins=np.linspace(0, 1, 20, endpoint=False));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10437fc10>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(np.random.randn(50000), bins=np.linspace(-5, 5, 100, endpoint=False));"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Lfmu1Ws/k5OTUX7p06b7A8S+//PKPEhMTz86aNetUXV3d4sD+o0ePPpiWlnY8MTHx7MaN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\nlAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1046f3b10>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "## Other Numpy Features to be aware of\n",
      "<!--====-->\n",
      "\n",
      "* Reshaping"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "arr = np.arange(1000000)\n",
      "arr2 = arr.reshape((10,100000))\n",
      "print(arr2)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[     0      1      2 ...,  99997  99998  99999]\n",
        " [100000 100001 100002 ..., 199997 199998 199999]\n",
        " [200000 200001 200002 ..., 299997 299998 299999]\n",
        " ..., \n",
        " [700000 700001 700002 ..., 799997 799998 799999]\n",
        " [800000 800001 800002 ..., 899997 899998 899999]\n",
        " [900000 900001 900002 ..., 999997 999998 999999]]\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "* Memory Views"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "arr2.view?"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "* Index Slicing"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.arange(0, 20, 2); y = x**2\n",
      "((y[1:] - y[:-1]) / (x[1:] - x[:-1])) # dy/dx"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "array([ 2,  6, 10, 14, 18, 22, 26, 30, 34])"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "* Fancy Indexing"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "evens = arr[arr%2 == 0]\n",
      "print(evens)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[     0      2      4 ..., 999994 999996 999998]\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "LinAlg, FFTs, and Random numbers\n",
      "-------------------\n",
      "<!--====-->"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.dot(arange(10), arange(10))"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "285"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.dot(arange(9).reshape(3,3),\n",
      "    arange(9).reshape(3,3))"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "array([[ 15,  18,  21],\n",
        "       [ 42,  54,  66],\n",
        "       [ 69,  90, 111]])"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.fft?"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": true,
       "slide_step": true
      }
     },
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.linalg?"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random?"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Quick Visualization / MatPlotLib\n",
      "-------------------\n",
      "<!--====-->\n",
      "\n",
      "How quickly can we plot 10K numbers?\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_ = hist(random.randn(100000), 100)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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dgLkwDDNjtSMR7ngFAJA0hDwAgIQh5AEAJAwhDwAgYQh5gKiHckpYPHz9H0DUQzklLB56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\nEgLmAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104c70290>"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "Basic Plotting\n",
      "-------------------\n",
      "<!--====-->\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_ = plot(range(100))\n",
      "_ = xlabel(\"measured\")\n",
      "_ = ylabel(\"calculated\")\n",
      "grid(True)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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1dXVKodvK19HY2Nhbp9OZExMT8+Uci7q6OuX06dO3h4aGfjdq1KjioqKi8XKN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\nEgQAALTp/wCzizQLLoFt8gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104c936d0>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = [val*.01 for val in range(100)]  # [0, .01, .02, ..., .98, .99]\n",
      "linear = [val for val in x] \n",
      "square = [val**2 for val in x]\n",
      "_ = plot(x, linear, x, square)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9Ae9EvIPMB5nYOHIjFHYKsUsi0hmlUgmlUqn1eapt7hKJRND0ZIcPHx64fv36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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104eb7090>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "num_vals = 10\n",
      "x = [float(val)/num_vals for val in range(num_vals)]  # [0, .01, .02, ..., .98, .99]\n",
      "linear = [val for val in x] \n",
      "square = [val**2 for val in x]\n",
      "_= plot(x, linear, 'g:+', x, square, 'r--o')"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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PDw8/qVAoApVKpVij0XTasmXLzKioqF1N25SVlUkMg/2nT58eBgBU2B3XPNk8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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104e043d0>"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "num_vals = 10\n",
      "x = [float(val)/num_vals for val in range(num_vals)]  # [0, .01, .02, ..., .98, .99]\n",
      "linear = [val for val in x] \n",
      "square = [val**2 for val in x]\n",
      "_ = plot(x, linear, 'g:+', x, square, 'r--o')\n",
      "_ = legend(('linear', 'square'), loc='upper left')"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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E1LL14lZc+f0K1zHsw969wOTJwObNVNhtCPXcid0orSyFu7M71zHsB2PAv/8N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\nsUP/D9RbnB8qZhKAAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104c96750>"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_ = plot(linear)\n",
      "_ = axes([0.2, 0.5, 0.25, 0.25])\n",
      "_ = plot(square)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VsqtXrzoRvUVqairbuXNnW0xNTU1Ovc5sNrPRo0ezCxcudDlGrVazCRMmtCXv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\nPBwlckII8XCUyAkhxMNRIieEEA/3/wECFQ1t/nO+HwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1049f0e90>"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "SciPy: Collection of High-Level Tools\n",
      "--------------------------------------\n",
      "\n",
      "* mathematical algorithms and convenience functions built on the Numpy,\n",
      "* organized into subpackages covering different scientific computing domains,\n",
      "* a data-processing and system-prototyping environment rivaling sytems such as MATLAB, IDL, Octave, R-Lab, and SciLab\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "SciPy: Collection of High-Level Tools\n",
      "--------------------------------------\n",
      "\n",
      "* File IO (scipy.io)\n",
      "* Special functions (scipy.special)\n",
      "* Integration (scipy.integrate)\n",
      "* Optimization (scipy.optimize)\n",
      "* Interpolation (scipy.interpolate)\n",
      "* Fourier Transforms (scipy.fftpack)\n",
      "* Signal Processing (scipy.signal)\n",
      "* Linear Algebra (scipy.linalg)\n",
      "* Sparse Eigenvalue Problems with ARPACK\n",
      "* Statistics (scipy.stats)\n",
      "* Multi-dimensional image processing (scipy.ndimage)\n",
      "* Weave (scipy.weave)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "scipy.io\n",
      "--------\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy\n",
      "from scipy import io as spio\n",
      "a = np.ones((3, 3))\n",
      "spio.savemat('file.mat', {'a': a}) # savemat expects a dictionary\n",
      "data = spio.loadmat('file.mat', struct_as_record=True)\n",
      "data['a']\n"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/Users/knepley/MacSoftware/lib/python2.7/site-packages/scipy/io/matlab/mio.py:267: FutureWarning: Using oned_as default value ('column') This will change to 'row' in future versions\n",
        "  oned_as=oned_as)\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "array([[ 1.,  1.,  1.],\n",
        "       [ 1.,  1.,  1.],\n",
        "       [ 1.,  1.,  1.]])"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "source": [
      "Also see:\n",
      "\n",
      "* Images\n",
      "* IDL Files\n",
      "* Matrix Market Files\n",
      "* Wav files"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "scipy.special\n",
      "--------\n",
      "\n",
      "* Bessel function, such as scipy.special.jn() (nth integer order Bessel function)\n",
      "* Elliptic function (scipy.special.ellipj() for the Jacobian elliptic function, ...)\n",
      "* Gamma function: scipy.special.gamma(), also note scipy.special.gammaln() which will give the log of Gamma to a higher numerical precision.\n",
      "* Erf, the area under a Gaussian curve: scipy.special.erf()\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.special import jn\n",
      "x = np.linspace(0, 1, 10)\n",
      "print [jn(val, 1.0) for val in x]\n"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0.76519768655796649, 0.77042135015704238, 0.75775886140714455, 0.73087640216944849, 0.69324418101264496, 0.64801456180958794, 0.59794997367362868, 0.54539073261127002, 0.49225331977915776, 0.44005058574493355]\n"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import *\n",
      "from scipy.special import jn, jn_zeros\n",
      "def drumhead_height(n, k, distance, angle, t):\n",
      "    nth_zero = jn_zeros(n, k)\n",
      "    return cos(t)*cos(n*angle)*jn(n, distance*nth_zero)\n",
      "theta = r_[0:2*pi:50j]\n",
      "radius = r_[0:1:50j]\n",
      "x = array([r*cos(theta) for r in radius])\n",
      "y = array([r*sin(theta) for r in radius])\n",
      "z = array([drumhead_height(1, 1, r, theta, 0.5) for r in radius])"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from mpl_toolkits.mplot3d import Axes3D\n",
      "from matplotlib import cm\n",
      "fig = pylab.figure()\n",
      "ax = Axes3D(fig)\n",
      "ax.plot_surface(x, y, z, rstride=1, cstride=1, cmap=cm.jet)\n",
      "_ = ax.set_xlabel('X')\n",
      "_ = ax.set_ylabel('Y')\n",
      "_ = ax.set_zlabel('Z')"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wIsLK078J9wN9gDvj67kbkbJwDSII5kXEwFMQX2YYUB1fPwihuxwhdJsRYhiN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\nrZkg0ZHrUslQawOl+h7GWzwTKV5J1IufeNYzY7XGaMmwK04c0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yUYDNLe3m50\nSTkzX7RaLBabMaekpIRgMEhNTQ0NDQ2Mjo7mu0wRWYCSWyTnTCYTFy9exOVyMTAwUFCbiWbyLtqW\nLVuIRqOYzWb6+/tpbm7mzZs3eahORDKhKz75Kfr7+7Farbx8+dLoUnIqk/i1FStWYDabAXC5XMTj\ncaampvJap4ikp8YnOTc8PMyjR4949uwZly9fnjc/8Xe1bds2xsbGiEQifP36lbt379LU1DRjzuTk\nZOoe3+DgIMlkUtvciPxCtNQpOZVMJnG73Vy5cgWbzcbJkydpb2/n1q1bRpeWEyaTic7OTvbs2ZOK\nX9uwYcOM+LX/tt0xmUyYzWbu3LljcNUi8iO9ziA51d3dzZMnT/D5fMC/Acnbt2/H6/Uq5V5E8kmv\nM0h+HD16NNX0AEpLSxkaGlLTkxnu3bvHpk2bKCsr4/nz52nn+f1+qqursdvtXLhwIY8VSiFT4xOR\nvHM4HPT09FBbW5t2TiKRSO3YMTo6is/n49WrV3msUgqV7vGJSN5VV1cvOufHsAAgFRbwY0qOyFLo\nik+kyB05cgSLxYLD4Ug75/jx49jtdmpqanjx4kVe6sokLEBkKdT4RIpca2srfr8/7fG+vj7Gx8cZ\nGxuju7sbt9ud0Xnr6upwOBxzxoMHDzL6fyM3rpXCpqVOkSK3a9cuIpFI2uO9vb0cPnwYgB07djA9\nPc3k5CQWi2XB8w4MDGRVVyZhASJLoSs+EVnQfEuOExMTOTt/uleqMgkLEFkKNT4RWdTs5pTtMmRP\nTw82m41QKERjYyMulwuAt2/f0tjYCMwMC9i4cSP79+/Xgy2SE1rqFJEFzV5ynJiYYM2aNVmds6Wl\nhZaWljmfW61WHj58mPrb5XKlmqJIrix2xVeioaFRFONPYGS+Y01NTY03btzoB0pCodBfq1atClss\nFqPr1dBYbKSlKz6RInfw4EHf06dPne/fv//DZrNFPR5PRzweLwdoa2v7u6Ghoa+vr6+hqqpqfPny\n5Z+vX7/eanTNItlYLKtTRESkoOjhFhERKSpqfCIiUlTU+EREpKio8YmISFH5B4fVn7Cc4dEJAAAA\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104e1de50>"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "scipy.linalg\n",
      "--------\n",
      "\n",
      "* Matrix class (all routines still work with 2D NumPy arrays)\n",
      "* Basic Linear Algebra\n",
      "* Decompositions\n",
      "* Matrix Functions\n",
      "* Special matrices\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A = sp.mat('[1 3 5; 2 5 1; 2 3 8]')\n",
      "A"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "matrix([[1, 3, 5],\n",
        "        [2, 5, 1],\n",
        "        [2, 3, 8]])"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A.I"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "matrix([[-1.48,  0.36,  0.88],\n",
        "        [ 0.56,  0.08, -0.36],\n",
        "        [ 0.16, -0.12,  0.04]])"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy import linalg\n",
      "linalg.inv(A)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": true,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "array([[-1.48,  0.36,  0.88],\n",
        "       [ 0.56,  0.08, -0.36],\n",
        "       [ 0.16, -0.12,  0.04]])"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "linalg.svd(A)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 62,
       "text": [
        "(array([[-0.52956045,  0.04298197, -0.84718255],\n",
        "        [-0.34647857, -0.92256717,  0.16977167],\n",
        "        [-0.77428569,  0.38343496,  0.50344742]]),\n",
        " array([ 11.13385134,   4.2134737 ,   0.53291053]),\n",
        " array([[-0.24888863, -0.50691635, -0.82528193],\n",
        "        [-0.24570758, -0.79117262,  0.56006577],\n",
        "        [ 0.93684696, -0.34217203, -0.07236068]]))"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "linalg.toeplitz([1,2,3],[1,2,4,5,6])"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": true
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "array([[1, 2, 4, 5, 6],\n",
        "       [2, 1, 2, 4, 5],\n",
        "       [3, 2, 1, 2, 4]])"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "## Pattern Formation Exercise\n",
      "\n",
      "This exercise has been adapted from an example by [David Ketcheson](http://www.davidketcheson.info/), KAUST"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true,
       "slide_step": true
      }
     },
     "source": [
      "### 5 Point Laplace Operator\n",
      "We start by constructing a dense matrix representing our stencil operator applied to a vector"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def five_pt_laplacian(m, a, b):\n",
      "    \"\"\"Construct a matrix that applies the 5-point Laplacian discretization\"\"\"\n",
      "    e=np.ones(m**2)\n",
      "    e2=([0]+[1]*(m-1))*m\n",
      "    h=(b-a)/(m+1)\n",
      "    A=np.diag(-4*e,0)+np.diag(e2[1:],-1)+np.diag(e2[1:],1)+np.diag(e[m:],m)+np.diag(e[m:],-m)\n",
      "    A/=h**2\n",
      "    return A\n",
      "\n",
      "five_pt_laplacian(8, 0.0, 1.0)"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": false
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 64,
       "text": [
        "array([[-324.,   81.,    0., ...,    0.,    0.,    0.],\n",
        "       [  81., -324.,   81., ...,    0.,    0.,    0.],\n",
        "       [   0.,   81., -324., ...,    0.,    0.,    0.],\n",
        "       ..., \n",
        "       [   0.,    0.,    0., ..., -324.,   81.,    0.],\n",
        "       [   0.,    0.,    0., ...,   81., -324.,   81.],\n",
        "       [   0.,    0.,    0., ...,    0.,   81., -324.]])"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "Alternatively we can constuct a sparse representation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.sparse import spdiags\n",
      "\n",
      "def five_pt_laplacian_sparse(m, a, b):\n",
      "    \"\"\"Construct a sparse matrix that applies the 5-point laplacian discretization\"\"\"\n",
      "    e=np.ones(m**2)\n",
      "    e2=([1]*(m-1)+[0])*m\n",
      "    e3=([0]+[1]*(m-1))*m\n",
      "    h=(b-a)/(m+1)\n",
      "    A=spdiags([-4*e,e2,e3,e,e],[0,-1,1,-m,m],m**2,m**2)\n",
      "    A/=h**2\n",
      "    return A\n",
      "\n",
      "A = five_pt_laplacian_sparse(8, 0.0, 1.0)\n",
      "A?"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false,
       "slide_step": false
      }
     },
     "outputs": [],
     "prompt_number": 65
    },
    {
     "cell_type": "markdown",
     "metadata": {
      "slideshow": {
       "slide_start": true
      }
     },
     "source": [
      "---\n",
      "\n",
      "## Pattern Formation Exercise"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "from IPython.display import clear_output\n",
      "\n",
      "\"\"\"Pattern formation code\n",
      "\n",
      "    Solves the pair of PDEs:\n",
      "       u_t = D_1 \\nabla^2 u + f(u,v)\n",
      "       v_t = D_2 \\nabla^2 v + g(u,v)\n",
      "\"\"\"\n",
      "\n",
      "#import matplotlib\n",
      "#matplotlib.use('TkAgg')\n",
      "import numpy as np\n",
      "#import matplotlib.pyplot as plt\n",
      "from scipy.sparse import spdiags,linalg,eye\n",
      "from time import sleep\n",
      "\n",
      "#Parameter values\n",
      "Du=0.500; Dv=1;\n",
      "delta=0.0045; tau1=0.02; tau2=0.2; alpha=0.899; beta=-0.91; gamma=-alpha;\n",
      "#delta=0.0045; tau1=0.02; tau2=0.2; alpha=1.9; beta=-0.91; gamma=-alpha;\n",
      "#delta=0.0045; tau1=2.02; tau2=0.; alpha=2.0; beta=-0.91; gamma=-alpha;\n",
      "#delta=0.0021; tau1=3.5; tau2=0; alpha=0.899; beta=-0.91; gamma=-alpha;\n",
      "#delta=0.0045; tau1=0.02; tau2=0.2; alpha=1.9; beta=-0.85; gamma=-alpha;\n",
      "#delta=0.0001; tau1=0.02; tau2=0.2; alpha=0.899; beta=-0.91; gamma=-alpha;\n",
      "#delta=0.0005; tau1=2.02; tau2=0.; alpha=2.0; beta=-0.91; gamma=-alpha; nx=150;\n",
      "\n",
      "#Define the reaction functions\n",
      "def f(u,v):\n",
      "    return alpha*u*(1-tau1*v**2) + v*(1-tau2*u);\n",
      "\n",
      "def g(u,v):\n",
      "    return beta*v*(1+alpha*tau1/beta*u*v) + u*(gamma+tau2*v);\n",
      "\n",
      "\n",
      "def five_pt_laplacian(m,a,b):\n",
      "    \"\"\"Construct a matrix that applies the 5-point laplacian discretization\"\"\"\n",
      "    e=np.ones(m**2)\n",
      "    e2=([0]+[1]*(m-1))*m\n",
      "    h=(b-a)/(m+1)\n",
      "    A=np.diag(-4*e,0)+np.diag(e2[1:],-1)+np.diag(e2[1:],1)+np.diag(e[m:],m)+np.diag(e[m:],-m)\n",
      "    A/=h**2\n",
      "    return A\n",
      "\n",
      "def five_pt_laplacian_sparse(m,a,b):\n",
      "    \"\"\"Construct a sparse matrix that applies the 5-point laplacian discretization\"\"\"\n",
      "    e=np.ones(m**2)\n",
      "    e2=([1]*(m-1)+[0])*m\n",
      "    e3=([0]+[1]*(m-1))*m\n",
      "    h=(b-a)/(m+1)\n",
      "    A=spdiags([-4*e,e2,e3,e,e],[0,-1,1,-m,m],m**2,m**2)\n",
      "    A/=h**2\n",
      "    return A\n",
      "\n",
      "# Set up the grid\n",
      "a=-1.; b=1.\n",
      "m=100; h=(b-a)/m; \n",
      "x = np.linspace(-1,1,m)\n",
      "y = np.linspace(-1,1,m)\n",
      "Y,X = np.meshgrid(y,x)\n",
      "\n",
      "# Initial data\n",
      "u=np.random.randn(m,m)/2.;\n",
      "v=np.random.randn(m,m)/2.;\n",
      "hold(False)\n",
      "plt.pcolormesh(x,y,u)\n",
      "plt.colorbar; plt.axis('image'); \n",
      "plt.draw()\n",
      "u=u.reshape(-1)\n",
      "v=v.reshape(-1)\n",
      "\n",
      "A=five_pt_laplacian_sparse(m,-1.,1.);\n",
      "II=eye(m*m,m*m)\n",
      "\n",
      "t=0.\n",
      "dt=h/delta/5.;\n",
      "fig, ax = plt.subplots()\n",
      "plt.colorbar\n",
      "\n",
      "#Now step forward in time\n",
      "for k in range(120):\n",
      "    #Simple (1st-order) operator splitting:\n",
      "    u = linalg.spsolve(II-dt*delta*Du*A,u)\n",
      "    v = linalg.spsolve(II-dt*delta*Dv*A,v)\n",
      "\n",
      "    unew=u+dt*f(u,v);\n",
      "    v   =v+dt*g(u,v);\n",
      "    u=unew;\n",
      "    t=t+dt;\n",
      "\n",
      "    #Plot every 3rd frame\n",
      "    if k/3==float(k)/3:\n",
      "        U=u.reshape((m,m))\n",
      "        ax.pcolormesh(x,y,U)\n",
      "        #ax.colorbar\n",
      "        ax.axis('image')\n",
      "        ax.set_title(str(t))\n",
      "        #ax.draw()\n",
      "        clear_output()\n",
      "        display(fig)\n",
      "\n",
      "plt.close()"
     ],
     "language": "python",
     "metadata": {
      "slideshow": {
       "slide_start": false
      }
     },
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QzRP7eGUecmQNlxa7AbF2nAh0MrLmyThq7SCxKFo5jqmUFQ5eWXSXMw5dMmIe\nf9ON6U1nqsU6ek0nnUfA4TgAqEOJczOuzh7MmQu9MV3GIr5wUaEXOSN1FfjsdqBplVyD+2SpzOYB\nvD6yCjT1qvQz/LlTxhDFjqnMsNxEy/cJOLug+kGdad8jDPMwMDDwhNBiHmSO38rpWRWtiefvoCwD\nLTA8mrYqIhQek+7xCUQjni5Hrk7DROXFdElpdlBfeO52rcr1gtu4OEwxd1Xle3ECH0Hc6CVUcTg5\n41AxIU95Xyhj4N5vilGz1e90DEbVIM5m+MhPjyFTxIVoRMdQ79Q2eh6n56ximgg3buUqVuGCcfD/\nA1VgMd6tZmGcgYFBR8F8PAwMDDwhtKYtpDWcZUWoTEw6BZEqvR//PWe6kqb39NuBRXAFZlqCKI+l\nY7oAlSmSJ+LRxetHWkujjcnSTdrJYBSmOvMrZ94qRzLO0pVwsyiGT0V00xfVIgyucFWlAHXj9cbN\nptTE6iYuidO1dPMEjYnVUpDqnMQ0K2axiptoVTM+4yRmYGDQ0Wjzd2jNmjXTHn/88d/5/f6whx56\naOlTTz31HK3fuHFj7te+9rV3+/fv/wUAwB133PHW008//TO3DWulMFWtFFQ5xaiSIQPoB0hZF1XX\naB3qGSu8g5JBOJAdS5LMg1rTank3NrFSdUyRngGHEO64ReFkctOZdRGqeB6cgagUplrTLB99VR3M\nTdeqUZ2zEBXz0Jk93bTDqV0q6NqK0KU84IxD5bYfhAOY02kBWses4bFsaF0wpv1LoE0fD7/fH7Zg\nwYJF69atm5ySklI2duzYT/Py8lYOGTKEZhiF66+//t8rV67Ma1tTDQwMQglt+nhs37792oyMjML0\n9PRiAIA5c+a8/u67736NfzwCgYBPeQJNa1q5p+vmcSp9CE8IpQOLaRFORvEoyRDi4AzIDYFutgzU\n8taqhnGnyOp0xMRFc3JXxTzcJGnm0MXq4E5QrliGLiSZinU5sQAdA1EpfJzc3FVtVIHL615/3jaV\nbCvNnEKeMw56Hh6XVMNkuAhlFfyYLqEYP18b0KZTlJWVpaSlpZXgfmpqaum2bdtyqIzP5wts2bJl\nfHZ29t6UlJSyX/3qV08MHTr0YOuzASwkn5xeADCqLY0zMDBQ4+RGgC83tvk0bfp4+Hw+7TgFADB6\n9OhdJSUlaVFRUefz8/Onz5w5c8Xhw4cHqWQXkjVMmws8NFA1CutO4DQgkuORUpkQCVIPgm7vyvO6\nGX11eQwWQkSlAAAgAElEQVT5sn25q1q2H8ycVbUkHxEU09AxD69sgINTTJ0ORYW2BmV1OreKVfC6\ncM0xzjKojMbqxBmHG5KjYunUiJScC9Ar167b/ozz9TVok7UlJSWlrKSkJA33S0pK0lJTU0upTExM\nTG1UVNR5AIDp06fnNzU1RZw+fTqen8vAwODqQps+HmPGjNlx5MiRgcXFxemNjY2dly9ffldeXt5K\nKlNZWZmAOo/t27dfGwgEfPHx8aow0QYGBlcR2jRtCQ8Pb160aNGCqVOnrvX7/WEPPvjgX4YMGVKw\nePHi+QAA8+fPX/zmm2/e+cILLzwSHh7eHBUVdf7111+fc6nztgv4nanu1EXQXwyEG+Zq8YgTzafb\n3FSr8+SRXJNOLVSznXaBatrB12zopi2gqAsGwczD2tu3UXdtnaKUy+icxHRTG80l+c9UbgncYKAy\nIPBXqx260BcIXFJtcUXg8/kCgdvt/c1vixLvMQejwI0hPxouS4zlkkzqUJ5roOm7zXOW4oMZaIt8\nlHQtAAD8AR4DAIC3ln9DVDxJzlOyS25gjlFV2D1c2MSz7uqWX1+GBKOO6OiPx6XadTlxFXw8+OJP\nlWWRW13oq4XWQbQW9iJ1v/W5t4g6NPN/N1QjNn/PFQpXvzyIIfitD04Lz2gn/22dbVT3z8rR1o+I\nm1ihOrakWz3Kz+cGwZhIdYpKN7/32g7d+dx8PNzUSeC/rUoZ7hQBTMdOrtCYY9zTDQwMPCHkmUdQ\nJFi1qMtDzMYAccA5L01stcgBMTMhTY7sOCKrVuHpRnqnRqriXurgRPV1vakyL7uJW8HPqbq2m5Ha\nyYVdR/PdTCnc1HllIE4mW5dwYhxubsuNc6AqlWk7wjAPAwMDTwgt5kEGMT7+NMm6CJXOQmUIwTru\nzq3TeUjZRrKYDhnHKdTAYhRtVzoPCj4iq3QebniWk17EDXSjp27CHExsVhXzcEozqXI9d/NK6hSU\nXAaClHGSbSdQtaQT41BZUtoLZkm+gYFBR8N8PAwMDDwhtKYtBI4EXhfAmK4BcYogpvLzYHSxNspe\nMlsJfQAAoPyidCIpxhoafYoH29VRXjcKRt26Dg6dgpKvq4hpLcOVdhTNfBUBOgZXKY7V4o807eJz\nSdX9OcX1oFBF+3Kadrnwq7ic4N4T7TUNoVN1p9vSTefbAYZ5GBgYeEJoMQ+FwhRRL1lCC4UpMo0G\nVvJtuq9bpCnZiqUcBYASEOv+qj6XCYIwi6AVvh8gOCcxrmB0EdpMCV38TATzau1BqhJliXmPkJTQ\nyGvYv6gkLpXnKSaMJICsq1iWmABJ55qPbdXdnypBlBsz7BX0lAraJ/MS8MoKsFu5Pps+y3ZfzmCY\nh4GBgUeEFvMgc7RWYzgeUKVDvMBKAFvn4eaLi1/o7qIoJ4tkDsNgsbFHHjiCNXZiqNY6DzfdqpMN\nhnGoEN+yzJC7I4kIrhHKkmWqLFXMo0KWn8tyP5HZKdnNnhGiDGBEhmNECPtKZ9J2WrlF+0cXbd0D\n2ps5uIGrpOFBgquQglGZtQGGeRgYGHhCaDEPhc7DWsCuUhFwXUcLl3EJXaJrltulro/4lhZaQzXA\nPhyat8oDp3iSY94ogOCyCbsZHnSrWFURt2UiZ4zMNk2WM22Jr0wSNGKEpBGYVjPKSocJ0CxNAydG\niPMV3iz6ZU+NTWHq10lFSr48sF5SmCJbb2SndUQ9EV5Dx6JUehHO1twsWlNAZ2EKBjoWEcxidbxF\nbBc9r5Mjme7aKuZxGUI5GOZhYGDgCebjYWBg4AkhP23BQxaZplOTOlZyxzCA1o5glKqivFSUlkQK\ns+x+S4sIcGyXTPL0CR5BCk4jKaqigl0KwTiAuZEl0wSMKnuLLB8WxfRBb1siU2EtAACMgZ3yJyII\nfozl7AXQIGOYVMnIMcWQDgAA+2Pt/vno9okAALA+dzIAADS+LhWob5Jp1IbRcgOPFcuSOtpxM66q\nT9vIuZ2mK8Gm6uRor3haqvPw9Vu6ANh8uqKylvPztgGGeRgYGHhCaDEPAv7xtNaSUlMtMo6zsqQj\nCjdboeI0msjgMWmZ3Q/C3LgFxtsya2S5Ew+gCdIeoW201VHJzQpVnmpRjvQ+4rh1nSzvFsUdg14B\nAIB74BVLZGqDYB7Rey6KA8dlBe3fcNHribGig4f1PQoAAOMzt1giObANAABGxQtb9urvzAAAgD0Z\n4+zzoEPa+1KDW4ttL7RlHM3dugRTbYRXPzJkAUExDq/hFFkcW9VKcuwq/CeJVMhcBhjmYWBg4Amh\nxTxIazjjwHG+6awtE4HbyCYo8+BzxGYmCwByzRsUJgnzIjKOnfsm2DLIPALoHYZOUKq4Gl4YhxsX\ndtWohaO3ZByZpEqoH+CrozcAAMCd8CYAAMw6nW+J+P4tN/C2SL9awNvBPisSRY8j9r3fMEQog9Iz\nigEAYAAIdvLmzcctmfxUGdkag+/+M12Up+jrhyyE96sqapkq6lk7O5DxLqejuCvGEQyL5FDpeTQR\n9bl6yA3jaIf/fMM8DAwMPMF8PAwMDDwhZKctCJ5bvpaYauP5tIWigdVhGUtkpP5us5yurAah7IPX\nicwm3MAFHapkd8EkC9XBTcZ5nt9UepMOIyLTxM1PhnUtSt9mInNAlhiag0/zAGyFMlfSUaWqfAb9\nKssBAKDnODFF6hV2yhLpMVREjX71iQfEgXBpM30t1ZKxVu5aCmnVtNBNmoggpo5udJiulKO6fDa6\naUsw0Pyr4q2GOZRURuWy4BGGeRgYGHhCaDEPwgq4+gsNeVXk425lvOUjJAWarTA42BC7amtvsUbj\nPcgDAIDDK+XK0H/SE2A2OFyXobqIk4m2vZI1qWJadG1RwChb4prkHQBgm1F77T0nKo7YMpaClDMO\nuhaIZ9tD0NXL+AxkE2MbGgEAYMaYDyyRzrHiWFh/cbGXF0ivNUouXpEsxFrEhP3tdsQOwnyrYlm8\nDuGKcahWCzsFvKbg74cqUyD7T0BHN/qckFXHOZRUBv8P2iHciWEeBgYGnhBazCPB3kRnaxx/8NtO\nNQ6n5egZrzLVdmelNGWW5dhu3CvkMtO3vrhHHFgqKwrpVdAdnbpSA6jjTPD0AW5ibKrgxhlKXgsd\nsAbYNYPhUIsSvpQV1ByLp2Yri6EbkXFiHipg90hzbjhp+tQxGwEAoDFeuLtXDxJD4nvfnG0L4SLl\n99LlBvaBSsek6x88puhnZBGq1atcRgue/Er3nLiOKkhWgdv4XHR5aLGMdiHTHdoMwzwMDAw8IbSY\nRz97EyNqlDIROk22psc4B6d3gwRDruGqmyG+k6/CPZbI0osPiY3fyU/+e1hDzRJOug46ajjpOtxY\nW3SpG1UyjN3gvDbNlkiSvuZ9/DKeKDIOenoWt7XVqEW3uW5AldaTx1QpskVwQL3pemH1ORUpFtqV\nTLIbvedz6c5eLA/sR0sMfeJuIqy5cBbztJCNtsMprSh9xjEtj6EI1UPEMVGVrsKJVdDb7MJKlbGP\n/6cbJzEDA4OOgvl4GBgYeEJoTVtIgN50aVIdIvWVuLaF+njFIE3DKQqZ9oBcntIgV5YujRRTlP+B\n71giVQtl3gFUlFrTlWJyIu6spAr7p1OUcvDVolQ2GIci+TvsA0J1Y0CYZiOl2VQbb5ivNlZNW/hb\nokp/gahTyMgpTHS0WME7acJHAABwkNjN99wqbc1b5TyqUPZpPU08xZWnqumcB2cxJdw4eTFlKA2o\njO9kkixxFpZCZNJYXS9WAtjPtZtoR6dIMT+M7NpoiYSFi3mkvzmsRdl4gQS4OSe3z8h91VqmIGGY\nh4GBgSeEFPM4c6M9mveYIUb8HLnfJBdpRtCRsa8skbHcZFdV3ClsUX8D4RL9B3gMAADKf0LoySJZ\n1qMj2D5Z6lzQdSa3KCarMtXyfTdKQJXzUZOziBNUCjRuqqXR2JxMtTrnKpSlEd+wbdJJLSNZqMHH\n97PjgmxKFg5t28dMEgcw4HQBDaSsiqGC4ApTjclWCyfGoTG7I1NIJyJIqvDdHI6l7dufmiyityVL\nBXdP6aPfA6otmW7ynjHCWyTYjIMDI7/VSg1sFaEwx2XQGkxiVvplOrQVhnkYGBh4Qkgxjw2Qa23f\n/pCMPSGjfEVgeAjKPAbKUuo3Pup3rVX1ijTJLq0Uuo6Lv5I//Av5/RlkHFi6YRwqnYeTe/rl6F4W\nQx9HeHuwglpp18OE3ZHdpHu6m/SDKnaiuw2dqzcC24jdK3Ugg/sdtkSGwkEAANg+XDIP1A0UqHRL\nqkVzCM44VIsKOXQxQ7iTF9i6jXRZIrvIsUXwVU7NEXFKRsFuAAAYhI57ANBP6tb6yBSdvSTz6EYY\nFjKOKHnPYbLDwxQPsFFSxSqpcDlOkpcdksnL9sjGbutrN9Z+CsHBMA8DAwNPCCnmsRam2jvSnXxU\npoiNGSeH1mpiVsCv6Ra+pB4Adv5L0hG0pOBit+ZdYIPrOHjUJgBn13OVA5iOcfBRz+sSbfyd9Ac/\nKXeJNx3OazFhd69YyTyoPsOJeagSBXl5S1TnQQYifdeSwY42htHbIV0K9w5vfe1mN8wD4aZ/dVHc\nELIB1JKCSwG+KksZpb77rApLZHLn9QAAMB6EXidLvmsZMtIaAECfBuGTH31CxpHl2QDoti6pO3tO\nfWNFB4/qW2CJZGWKkBKoVzlv6ecM8zAwMLjCMB8PAwMDTwipact6jNwLdqb61chxJapIcqODMBQA\nAA7vk3E4VhBBXKeyAw+gAxgNaoHn5o5FKiUdL6OIjFM3tkPQBABQU3CpVMMIXAfsmsNyOndUrhDK\n7Cujc5WQn1PaC6DOZYrKUL52SDUl8bN9VU5hhDxfTI09/YiJFffTNU6U9dEyBy59FJYeUffa8mdJ\nwacpblJbyGdIgp7BWFnK3L8Dbv8MAABusxdHkaRa4gXsVSinjvZMzXbU4o51qikJHsNnoZraoAwq\nr4mVu+8Y8a5PnS7aVU6UqW+BNxjmYWBg4AkhxTyO7rMDcR7tJlgFSNdbqJZNpXmCcLTdykoAgDOo\nBEWlaLEsVeZYruhUMQ9ddLC2JntC8N/r4nhi8FEZCGOPHQxlz3Hh6r07WZjlMEkTTZngqIhTvRFd\nmIyKeQSh0EP4yb4fWrpWq+GlX1WmWjeedbJx+PgzSFWuKJJuFzZnTG0xk1DfceVC0W+FvlUl1XLj\n2MfZH090RrdrmAztSvm6JEYL4axJ+6GtMMzDwMDAE0KKedj6CQC4IG1jmBgIrWBUZYH+NtZcnlZi\nFG4MUeUmSZOKOVxJBzAOFQNpZseKRfEpCcP2vrDJbpx3AwDYsUynDPnYlsHRCtU+3JxKj3GdBQWf\ni2OpGlVxJJSxKc5E2eGs0KzceCq2ZTtaPLZgzNsquuPEOFQL7GTfY6S24URksggIglHpUb8xrmSP\nLbNNlsg4+AJCAJvRYb+ovAB4UzUR7K1rICmtU8hIVcfQSQcVDQoOhnkYGBh4QpuHzzVr1kx7/PHH\nf+f3+8MeeuihpU899dRzXOaxxx77Q35+/vSoqKjzf/vb3+4fNWrUbuXJqD6jgpXFrAQAqG9iB8tI\nJX5+OePQLVZTsQovegzVYqq2QLVsH00P8p5PkRira8TovX6ycJob2V90d1qGbW7JrDrW8nTcT45v\nA6itLTgSSmOCUi+Cv0Ptv1yKfpQoEqxtfAfwuWv1Au0VnV4BdApTMI8h/QXDQAewaxskzSDEw4ob\ni6M/X4hIt7Gkywc4kFXw9KkAdpQx/gypXgTbIfWE/crLNRdzhzYxD7/fH7ZgwYJFa9asmXbw4MGh\nr7322t0FBQVDqMzq1atnFBYWZhw5cmTgkiVL5j3yyCMvtK3JBgYGoYA2fTy2b99+bUZGRmF6enpx\nRERE05w5c15/9913v0ZlVq5cmTd37txlAAA5OTnbqqur4yorKxPUZzQwMLha0KZpS1lZWUpaWprF\nhVNTU0u3bduWcymZ0tLS1ISEhErgWLvQ3vblAvTIbT0jqadUEw8iX9MpRRFuonx5pcNcSdfWFIM6\n8NQExPS2Rq7rGS6495s/uRMAAJLBpqoxOcsBACAFp3e4DIJasvkUhCrggNVxWVUwahlKpWaMiDux\nA66xRHbAmJa3YS8TIdD1p5v1RW5soyxCG05bMm0JXAGcJRsb/blcm/KlLdOqr3C6oYrUxiO2qRSm\n/HaowhR/z+OvEJl6OYXp+gXAxrMAG38EbUabPh4+n89VHOpAIECXFTn/bvRCe7vYc7MMDAw0yO0O\nkPuQvf/MUmdZHdr08UhJSSkrKSmx4ueXlJSkpaamlupkSktLU1NSUqhm00a1YhtLi1TQaFKqNH8c\nl9NFPBi4iRzm9BuVApetrqVf2/o+onxNBDw5liqGzZfm3W+JYDyIvBzhUt0vWrKSz8mlkBvyUVSX\n1hNHQZpUSMZdCUhCtC5MhHyjq6hLP5IKUzTXW7dDk23xWB1eX18Xz5LHhk21xztcAWytCkZzrMrM\nzdMi6JiHSmHqhnlwhauiW2pk27qiaf54a5lg0Sadx5gxY3YcOXJkYHFxcXpjY2Pn5cuX35WXl7eS\nyuTl5a38+9//fh8AwNatW8fFxcVVK6csBgYGVxXaxDzCw8ObFy1atGDq1Klr/X5/2IMPPviXIUOG\nFCxevHg+AMD8+fMXz5gxY/Xq1atnZGRkFEZHR9e99NJLDziekH5N+WIfC00O2xxuokY5IViW4cY0\ny2V0i7LcgJ+HKiuk4qBQOlz9WeinD4SPtST+9C2MOiXiXM4YvhoAAMb0te2N4agHwVEKTX8qpzF8\nkzDYeV+76sw1wvFqnVz4+CbcAQAA+V/MsoVwTRle3mKaPM0nhc6Zzw00z40l/u4Ufd6qimFxRS0z\nqip9JZ5HZY7lrEQVM5YzD54mVPV7hYe/1Z34DFWrNIJEm/08pk+fnj99+vR8emz+/PmL6f6iRYsW\ntPU6BgYGoYXQck9XBQmv5wfaGoErmNGdynNdg8oLio9kKiYS7PX5eVRr3um1AWxlxXZR7JbKht/Z\nOVAOV4swBr96SKijDsUOAgCAG2I3WjIjcwQNSJdBRxNkZnGfwuoSkPP24/HCtHKUZN7eJoN7oo5j\n/WEZeusf5ATrZWk5Cqq81hDtlUjcaR9sFiGrLpJVfLiIrxmHeKyiIz5XV6lYQTBOYpxx0P9cnXu7\nhPXvhLoPk7fFwMCgo2A+HgYGBp4QWtMWyh5VyidP4DTfq6JSl3ORy7hJUegVTtyUXgvnemg1l1HU\n9o+yRX4lQmPVF4iIXW/MmgsAABtn3GCJXCPtpugUlRwvzLkx8a2TL2Fgagz3j1HeAAB2XhTOYFXv\ny3wKa2QFWeRr+7jhdEWlKNWtbHZSmKqek05pLY9hsGUrtYWtoaxOFvd6DtPbyxgZymmHLju906NU\nhTQJ5jyK/2prLbZUdndVOfwFCcM8DAwMPCG0mIcKFgNRKQr5CK9Jy6iV8eK45YZ56Fykg+l6nawu\n2hjWoQKVLGYul+xhqVzHuFMUJ963baz548R2/uDbAQCgU7oYrmJ6tGYe9edETNfGYmkeps5meFk0\nw36GbaBncGIcKnahSvkZjMJU97xlHa4SxtQWxbZEyVChZEaWldFHMjyahR0voQuM5gVt/I9t4pHf\n2gDDPAwMDDwhtJgH1XMEZdFU6RjqHUoV8+Dn0SVtctOwYJiHaqR081j471SmYx51jDr2otOTHPF3\nf0WWJEz4+7JMF8XFXsIeezaO+lhL4EiGIzW9FDIMjPRusQvKMpzirqgSiut0HhwqMzfve/oeyH4J\nSLM2LqQgTOrQDBGdHpOO5fQXJvHIInIaVVwTvs/JNDZLp+/zYukHBcduB52iYR4GBgaeEFrMQwuV\nk5iTXgPA2ZlKBd1ybi+R0XWObDodjNPjUKnW+SIxlbzO6sMtMsgCyJrFEjn6luCaetvJ7NKgTKKG\nHdPdu06voUg6HRScQiWo3hHZ5lKpyCBRwg4fFg522wYJ57eRUUKpM7YfSZ6DzIM7Y9ER3ylivco9\nHWV5fhy6zcqm5tYiTfxAG2CYh4GBgSeYj4eBgYEnhNa0pV3NWi48Z1qlkIxl+/SYbtrClbI6hSBX\nDLpZGayi9zqui+CpE3UOcnxqAWCbT3EqozORBgPd9JBfQ5WAyyt4f3KFMkCrOCm18vmTGYnMuACb\nBk0EAIAsmVgsbbgdYDqxjs1XVCkpeFBjUMjwaYrqPA6pPpvbYWqig2EeBgYGnhBazIOiVcvcpHuk\nyaejmIx0JW7hySMjbmEWYxzYehERjCTVDVqCDuIY7QyzPZzBChpUjSehUo30TixEd886cJlgR24+\nMrsxZbupU7E4zgKDVI762L42QKaOtTk42O0nMbsl8zg8XChO104Sq4VpjNgZI1cBAEB0s4xvilUq\nxlDH9lUMnKfxpO7lPNWnPE8TUc62erPa4T/fMA8DAwNPCC3mQQciFskJ6vnIBGCbDlVzcTwmR4xw\nuT+QiGQ4lMRPCn9uERfsMereyxNT4fx4BznRp3K7GYUwcAX1puKmTBXcRINvr8fKz+2GVbgxd+ue\nlwvGwVkGQOvRGkddJQNxE3WMsa1m0p6tkr2K/NaQnyoiovXqX2WJxEQKF/7JWRtbXukE2OCOZG6c\nw1QR9hxSfqp0HlaPR7auCxaGeRgYGHhCaDEPuqQZR3r0hMavaoDmi0LmIb+ndLBKlyXm2xgpyzFE\nZqT4ZA9KFhmzW0XFBoA4qdCIgZaLwRqgs7VdPUIsay+ReRT3QxYAAJR/1M/+AcboXCUbVoD3sYuc\ntRi8w83ydK/hAIJhO26YR5RCRsVGGJBxuLHKoQwdzVuxEJUejVvDcJ84z5VL+XzZ5jiZH+eJOy2R\nrrHCzT0sVgz/N2SJ+APhJL2OxUKQTagWq3FLCsqqUkkyvUiTgnlYPa5YYRAsDPMwMDDwBPPxMDAw\n8ITQnbagaRRNpSo2Gy0PYkopkhIQxsnyOsFVMbM5OvQAAAyGwwAAkC6nCzhd6Wkv/7SmK1GSvoZJ\nHtlIpi21co5VKU2/h+Vqy22T7MybaM47MUTGy/ibpLybJihurFiWqlgdTomPdLEt3KzL0b0KXlJ0\nunEAc7EqlipH+XTFTaYLLVRtx22uvKYnLBZFodSwrxC/qe/Sw5J49fFviCtEyXmH1LFOGmWHT4vE\nOCdoxsWpCJ2++Nkx1bTlLCvrWt4BRTwm4+quqAwShnkYGBh4QmgxD6rEQUct3sI4sp0uS1SG5toa\nomv7bgEAgBzYBgB2UuLBcMiSQQVpnwZhLo0+LR16dA44KpffLnLoiBVMJqeviO8wMsxeijkAjgIA\nwJvfEgmPDnQZ2/p8n2TJDR5/w80w6mYlsG6k15lhddfissEoU10oR1Xw4h8HoFlJqlq1zBkI/TG6\n7cusWPuHtLroOfkCv7RA5DhriBW20cYo20aaO2YDAABE77jY8hL0/cPtc2xfxTw0ileL8+EC6T6t\nZYKFYR4GBgaeEFrMI05xrCerI9ZP1GsMGi30GBNhk1U1HgTzGCUDaA7wi5E/9nij/XscQPCrrmIX\nDouOdKkFY4vENSb022nfRj+hR4mSkaqW3iNGoMMVI+zfY+yIEhnVq9VCO7dwio3h1a3czXGdOTeY\nWCgM7blYEtmMZbJVLTx0YkdUxiE6ncVAwHIqq28WepCX5t8v9hNsf4LzkcJkPXmC8HfvsU2ejzIH\nbobFffpKMObRpEgHajk4oH6wf2uZYGGYh4GBgSeEFvPoQbbRSQytLumyHGd/Vr+aLNjFDSDmjrmy\nBAAYJUM/9SqUtAL9vuh80mkO7KZXVEurkY1w7TcAZDaIhXGNmWsBwLbM/HrOYFtoj5wPv4w+9OhF\nZCdZdoaODbixyLg5j5vrBsNgLiOCykqqswzporHhMYVuqkCykL8JNnmxVij0Xn34W5bImUGCTqO1\nbnKOYCB9u1Afdgl8x/Cd0kQSi5C3k0B0iF2Reki1Ws1w21oIQNh4EDDMw8DAwBPMx8PAwMATQmva\nQhWm2DJcmCrXoeBUBQBgsgysgGXO+e1WXSSuIcDpikKJ1CqDuSoDObA6XXSmOlYqrjmiuzDnTkoS\nyt1tybYj2cfXTREbG+WBErSnnQYbwUxh3DhueZl2eHUo8wCqmEblaTBTEu3aFhXcmJV5ZDZ8Kehz\nkmbcIjkFfUWuw6q2JfK/KZJpVU0SZt0Tcio7NXutJTMqVp4Hp++6gHF4r9LZsitVNuNM+HpR7A/L\nIpU7wQsM8zAwMPCE0GIeNFoXspB0UeDKV+pePkYmYh7pF8rRSJJNETCcJE/oG6nYxrKLQoZnMVAF\n0+JKLB4uH8AelL4QxdAkkTx6FInp//EYyTwwroiV8oAuF+bDrlePKQ6vSagukzIUWQJ1Fmu35Oc6\ncNOsKr5IEzumciQ70fJYuTS/LycxXmT4j+3lkwAAoOQuYUctsqwDAFP7CRYyqZ9gqr12SgMAXZ2L\n7zq7ZAsX9OGiaJghyj2WZyWAYR4GBgZXFKHFPOiIL5lH50ThDYOL1vqRmBe4oA2dslpEaeJsAFkF\nveMurETTlirKEh5TjX7RrI7HmwSwTW2SgSQ1iPtJjyy2RLpmiOCn9Ylos8Z4Je1l/lQtAPPCOK6g\n6dWVnuJyQhWt3inKGV2KxqPSyxi2tYSdrEgXpVyHWV4sPCCXzH7MEjncX5jy94NwJsy5Riy3GHmN\nTbMTS+TLrmEepzIFrf8IRMT3HS0C2/zF4X70MMzDwMDAE0KLedABTY70XbsJ60JXaWWgEb2sbZV1\ng1tFUPMcrjjGrSyqdVIIZBA0fACPgq1yqWasJLpGLIaK6W3fT1ysUMXXx1FvOYD2iwDWXnBj7ugA\nx7B2RRtc6gGg9YJ4xRIDZFWb0kWJkSCO2YqejZOnAQDAjmmCKeRESeYBNvPISBNLL/qkCWc1DB9R\na3laAhyHJACwGUxLnYc3GOZhYGDgCebjYWBg4AmhNW2hkDTf3yya6O8sygaizbSCEKumJNzEighT\nyICQRsMAABr4SURBVPA6Xa9gnc7pTHUtBzNjWND2x2DMrm2FLsnTpX7jNdeh17YHM73g0y5dW4MK\nDKL4nS69aGXLqoJ0URJHMrQPnDsgHMnWj7sFAAA2jZloiaTHCyE0KuB0vpm8gDiFKYdkAAAoOZ0G\nbYVhHgYGBp4QWsyDxjGQvjDnTgmbbVVf4TB1goRAOiGjFGQmSDOYnTHBjtGhu0OnGB2qvNK6AdXN\nYBvWsmyQ5t1a4hlXe14quM6BBjhytbdCUndeNyNtMD7jbs4X7KvJR/i2MBEAfRuDWXbtRIEpUJkq\n05OWk/Qi5+R9YGKxz0XRuNVOm3o4QyhBD6fK2DAYha8buWazfPEuSGUsZTceYZiHgYGBJ4QW81CN\nuKWiicWp6QAAcKiTHf8C44Km9Rb+uf362omGLZ0EjfUI0FL34GelKukO122o4kxypzCVGgNNu9Jx\npzJKMKgSsOee54rlkGHdhioZdjDgLtZBBblwcV4VdNdor+urwJmGqs+8sDVVm92cB/vIaRGdCthm\nssCuVrIQyTgsxlBhi1iZS5GwIPPoQf69keC2Y2Q2wzwMDAw8IXSZB27LD3VVWAoAAOzOsZ1beCrI\nzpl2DNMUXHX0pTzAF8iRc1uMw43uQuV6zqNWq36PLuwybctRGAAAAAdhqC2Da+SK8QCOQJdzxOa6\nDlXjg2ETwfzeq0VGBTeu9JyNtNeCP5V3Ib83N/9qqmvKNmOid2Qc9PToZ4hOZsg8aIgL3Mb3MAba\nDMM8DAwMPMEz8zh9+nT8XXfdtfzYsWNfSU9PL37jjTe+HhcX10qHm56eXhwbG1sTFhbmj4iIaNq+\nffu1bWuygYFBKMDzx+PZZ5/9wZQpUz78/ve///xzzz331LPPPvuDZ5999gdczufzBTZu3JgbHx9/\nWnWeFqCfHmSYSMXkNOaY384puWG8KFWOVjmZYg1Av2ipfcTpC11iwONu8FWxKqhidfDEUAiaxEr4\n5sCpDKG52g2jAABgJ13duEOWR/EAdpkbhanuUbqZ9riR0QUDdlMXzLW8or0iowUz7VBNN7y0Q5UG\ng/0O37VzziJK3WxbffcU8DxtWblyZd7cuXOXAQDMnTt32YoVK2Y6yQYCAV3+LwMDg6sQnplHZWVl\nQkJCQiUAQEJCQmVlZWWCSs7n8wUmT568LiwszD9//vzFDz/88IuOJ/1wob0dkwuQmGt/KVFRZOeg\nhmPVgoWsmCa0P9WdbA1RtdQQ5aQJBjK0p4gFGfkFuR4O7G5SSnIHMlUyYh4TlaT0C8hITltA0KV1\ncBMAAJxY3dcW2orC2DAdWVMp6YJBMI5fOubAGYcbhWmwSlk3CGakd5Ogijt50fbx8+gc7HisWDcM\nRpMWVGVq5WwYSxU7CQeA0o0AZzZq2uEO2jdvypQpH1ZUVCTy4z//+c//m+77fL6Az+dThm3ZvHnz\nhKSkpPKTJ0/2njJlyoeZmZmfT5w4cZNKFr660N4+pZQwMDBoK1JzAUbm2vsbn/F0Gu3H48MPP5zi\nVJeQkFBZUVGRmJiYWFFeXp7Up08fRaYagKSkpHIAgN69e5+cNWvWO9u3b7/W8eNRS7arWYlf1xIi\nI7erSoUZ961pd1lVlX1bOmGNjxJR17OG28Ef+56UTUa3dp4wGMDZjKualqIjmGQcyDYAADbFCz3x\nKhBBJPOPiwVO8A45z6e4Id2ULV2HatQLBm5Yho4N6NiFGxkuG4x+xS10bIIfc5MAHI91ZcfdXNvp\n3Pw8QcQMwYk/iuqcvVT6DX6sHXQfnnUeeXl5K5ctWzYXAGDZsmVzZ86cuYLLnD9/Pqq2tjYGAKCu\nri76gw8+uDkrK2s/lzMwMLj64AsEvAWJPH36dPzXv/71N7788su+1FR7/Pjx5IcffvjFVatW3fLF\nF1/0v/32298GAGhubg7/xje+8coPf/jDXyob4vMF4G7SFhx8cfqiWsiD1ox0WdLgSJIzJd1cBAAA\nE+EjAADIATu3CybBHgQil0ryaeFY5lPFQkU2omIeqOOQWh+0qNA4ke/BbQAA8ErjPeK0v5KzwaXk\nPEV40+iLrEpwzaN5q5JY8xibupFNp4/AOh4dXKfzUFmG3Lhmu22fW+hisrrJyaJLEu5GJuoS13Rq\nI7SMGI8MA0V53F0A+/8Am4Gu6ConMSx7kbqf+jwZNTwrTOPj40+vW7duMj+enJx8fNWqVbcAAPTv\n3/+LPXv2tD3emYGBQcjBeJgaGBh4QmitbaEMFdkvV5yqWHGZLIvJMeloVb5bhLN/Y4oo94weZYnk\nAAaTFYtKBseLxFJp8bZWtqdcIxPjF9rcsGZBvf3hdtdVhwkuiMpZDC6LYe4BAN6ryRPNf0EGN35d\nVhTRG8Ib0cWmcDLRUhmdmZHLOCk86TGuuKXtC0ZhyhGM49Slzu1U50aZSad59ewYT/BEwa+lSgzl\nRpErgRMHqgzlMyLVtAVPqUuXytGRClMDA4P/txFazEMVa6PVYKegJ1hXSL78xfJzjLrHvaI4PG6E\nJXI4V2x/NEIIDQWRAjLD9g+340KGyZW7YSLB1HkyylRJ7dMhGAQAAHuk6/nhbfa14F1Zvi/L/Xgf\nBeR++CpanZLNjdORm7gbTuyCHuOlGycxN+bPWCLDlZCqCFz8ZaAMCLdRyczvCxSyqjijTgpp2lYe\nqwOhst87JRRXgCtH6Wk441DF4uVdp0sh0g7/+YZ5GBgYeEJoMQ9XoCORZkRslqNCgUwWfUTu23ml\nAaSr2rFRws392HC56M5eewfd04VffExn4esbJq/fSKK4V1YKr7CLh6TNDBe4fUyuha7n5djWI7Kk\nLug88pdqTu4mTSSHzrmLm2HPExkn5qE6D28XHakxbSauYOjD9ok8zvtxhFWRHOsg7TuMRH6C7VMZ\n3X0guJ5I5dgWqzhGf0uhowOyjhtJVYnJwtk+fSW4rkOXBaAd/+MN8zAwMPCEq5B5qJqssgKgr7sc\neZrlaFEQb4sUyGOb5X66LFNskbNJwpnrLDre4OXppWTQMst1HlUmRbSNOAKWsn06erlxYmoL43Cj\nz1DpEVS6DgS2A0NTpcryK0RmiCh6SFlkdulEBPscM21SawICF3pVyPOUEuZSLLcxnmc9Z3gAtjWL\nsxKdXsQNdPonFzqPABPRqYuCkdHlKGoHGOZhYGDgCebjYWBg4AmhNW0JU2y3styp1iGoFGDcVMdN\neeT35XL6Uo5TmohWIq1MZNSsjDMk6/J4jUqFEKfDKucjN9MWHZzib+imJKr+4dMdPkUBsJWeQ1qW\nWUQkR5ZflaVcsNAt0467kBwlTOIY1LqzDErhJ/dbL/vqlDSNH69MsuosZfUBeeAAKsiJuRy363G6\nglOaMlum1VRGpWzmpl4VeLoL1XnaO3GXhJt0qe0AwzwMDAw8IbSYBwVfRYgDNI35oXTgcYJu9GXK\nVdotGPK+XjdKOLlvq0yaCDerLN0oR1VKTD7KqYI4uDHDIrB/0cQ6kNSNFgV6/U+TJVky2edGEUDW\nWgYAchkACc7SR7K0KNmOSMk8aLLmerlSFZM2VybYCtOSBLE0oHhSOgAAHAKRHKx0X4bdEDSXb5UM\nc4ekRC2CRKBCW6YwtdijjpGplgHUszrufMa3yc9VymIEN8c6HaOXVNUZJzEDA4OOQmgxD51bLjrC\nUOLQrJqD8xNwN2el15Hi5Lpjl4Jq9HZyK9fFnQgGOgaicnRyiupFR0Ps13RZypF6CJGRAdFglqwa\nL2KkjIctlogdN0UwjmSZT7MniTUZ0yDYX2TDRQAACJNd6Cdd0RApxrr6yJYMBMCOWXtchqnHRYqF\nIwZYMgdHiARb++cJ3UfpNslKNoONj6Wpeassy7F/CokQshFkrG7Yn4r5uolSJhFMmsgr9F9tmIeB\ngYEneI4k1t7w+XwB+CZpCyZ7xo88X5oPYDsNWT9TzTm527Uu/ublhJul2cEMGboRjesxcIRUuZ7z\nhWzUZRydu9JFeas8fK8tMejmfQAAMBXWAoDNOLKIIiG9QXjLRZ8QrKJV1HraDB04mYwkdRhNSzrz\n1cR3BgCAqrCelojFRkAwjoPy/vaAHaZh23nBrs6tkaG21skKutTAujXUj6BLvIql8gV2xEnR0iXJ\nOnRT70ZEcJtHC6P3ziOI6aKNIVmjUcZ+7C2SmGEeBgYGnmA+HgYGBp4QWgpTSsV4dCQsKaVDWAyc\nTgW4kw53KKN1TvsA3iNicegiZAUDN212A7w+UmdcXJJji2D85gdE0f0hscL4zs5vWSI4XRkjlxL3\nK2fpPQHsINK6pFpO8SbcKgrZ72PDRdyVWEw3Cnbq0Uk9RRDsit7dAQCgGPpZMvujhHfblttFcq5N\nt4tocEf/Ncw+OcZkWSeVqvtxPQ91CuQJu9r4r9Y6o+qlT606Hozi9RIwzMPAwMATQkth+ghpC08v\niYpSmkLvgkNJt7W35yadYlvghl2ohodg0juqVsPWONTR8yITk6tfw6Xj12wi8m1R5E5aAwAAd8Fy\nALDZBgBAv0I5sqOnN64wViUL53EmumjqdMxDNQpzPzieHpSCK1y7kzqhU4WyfkLRuhOuAQCAdcTr\nbaVMo3FspVwe/Kas2EjOY/m/IQNBZXUUEWLKVJ3CtAvbpyw9hslwWbrNFacARmFqYGBwZRFaOg9V\nBCWdroND5bLLB2o6agWcYi2oFqtdSeiSNnNzoCpKN/6eRyaj9yV1HL2kafab8vATNmWYl/xnAAC4\nD14GAIAJRTtFxU5yGtRt0BSdAC1HRu7op4tw5UbXoVqcCOwYT16uOqZiR7KNKfGCQqUM/AAAACZO\nsDOkTpQh6JbnifSmb42UaU6XkhvLl+Vn0jRbjyZa+vza8O+nI7XtqNfQwTAPAwMDTwhd5oGDJI4O\nPJo6RRiTBWhtbFHNgVUe61RWBZ0OJehZ4yXOZ0E1zPBl4Sp9Bo+BmmqLpMlj0uGr29NCufRY1B8s\nkfmwGAAA+n4gnaC2yQqajhNHc84uqB5B5dTlFvSd0Bm+nNYA0t/g+1HnUAK01JsBWDFve2yzGcPs\nCe8BAMDQHBltv69wXV+68CFLpqqXZHaYwRkdy05pWK0bttVeMAvjDAwMOgrm42FgYOAJoTVtodSM\nO4epaChCtUDVabqiWtrCpynBLnVpr6UxvD3KKU0w5l+Ulcq6NPLbO0XR+Qlh1v1e1G9FCb+1RHr8\nRVJ1jINxXHEpnK6grxk+Q0r/nZ6hm35zY5alctxUS6eyuI1tw+kKNf/XsDo8H42jLLeHFYlI14/P\nEX3WuVOjJfKnBd8BAIAqVExjv3xGzoPuB7ocX26SNTmlWrjM/92GeRgYGHhCaDEPlXc56pdUClNs\nPY4klLlwV2j8HVXaOTkSuRkRaTu8KAJVI6or8zJuuHF3l52HoT5zSdX9soh/CQBs5WiP/yGmxA9k\nieZYbAe9X1SMOjl5AbQ246pYAZ4Tn2WwoVr58+bKUXpuJwZCt8+ykl4LHcAkE0usE0IPPbjUEqnu\nJJat/vHOx+QBeYP0WRbLEhc9Yx11nnNKp6DrH92C7XYMm2qYh4GBgSeEFvOgrcGvLzcFUnCzmspP\nSmeqBYdjOu901ejgBk5sRqWDcQqCBqBwu9ckFZIhKTBauRVfFACuG/EhAADMkS7nKW9Kv/LV5PfS\nTNkkR+MIlRkWwd8kFSvAEs/jxj1dB5XZnbMKlc4DdRwqUy3WMeZRf9YWaZLvQGwVtEDfPrYNe9Zt\n7wAAwKFkEUv1g9w8UXGK/ADbjGv3VGyU94ubpE+6OKftCMM8DAwMPMF8PAwMDDwhdKctSLncTA9U\n+WOd6K9qmoA0WjclCcYcG4zCVTVV46ZIOj1zUqrSWQuunEyXpZy2dLrJ5uc3yCWgN5z8RBxYLyt2\n2Kc5cqLlpXB1RjyZCkTwKQnSfroWCdvDze+qew/Gk5LSfCczsGrawk20GoXpabkotoo8U3zNukqF\n6UDsMzssCEy8XvTrR7EiLOO2cdeK0x5ItIVwCoPnpiZjBJ+CuEm94Ca2djt4rBrmYWBg4Amhyzx4\n0icdVKM4H4F0plr+m0sdu1Q7dKZbzm50a21U7MlpPQ5dMoGKUszNNFwUQxMOWiJWgGIcNQtEcYSs\nW6HJBgDsyBTxRHmI27GSXXRlgYgBoDXjULEMfq9eFabcSYyyNs6SZF0TYR61chuZBk8HBtA6nZPM\nlAkpxJEsXHbv4Aki3URGZ+FQtjODMI8i1sZqtk/B+4w+70h2TGXOdcNKgoRhHgYGBp4QWsyDsgw3\nIz6P66AbxXVuzrprBhNUTLca18013bjLO/VLNNnuLcv0lmWyZRME6IUTbmQRcsSl2TwxIidfv0uD\nUFnJA+TvY2XZlTAYnnygq3zOEYR5hMs3McLjG9kk+6VZlvUNLY8DOCfY1MVg4/sArXVAKJNC9Suy\nH2Jkj/bEEGtkYbPlvEfTiQComQdCxdp4Oga+qNrpWBthmIeBgYEnhBbzoK1x0hu4cUGnv28v5zCE\nF3ahk1Fd002buW6AsjacVqPuQyb4CSMnPI+xNDF3tSxpSiJkGjylkUo11YpdEBlLN4D7F1rLqHyf\nLgVd+i5VdFqMIsojuurSZamAzAvbn4J9n0aERNbLFikxAQCgC1ntGCcDwPRuKdLKnZ9CpRPiehB8\n91XpW924t7uEYR4GBgaeYD4eBgYGnhC60xYnU5Ju/QqFlxWzbta0uEEw0xbd9d1cE2koZcc4bYlr\nKVoNPaztQyDWXIy/UTgx9TgiiHo6UfrFy+zxu+Q0g+eGVzW5reCzsrbCTftUekVe0u5Nl2UOpsG9\nUZZ5tkzhcKEZxX6uAincTGJV8hQJPD8ZgPO7pIr50YXtq9QAXuaHDjDMw8DAwBM8f3/++c9/zl64\ncOHCzz//PPPTTz8dO3r06F0quTVr1kx7/PHHf+f3+8MeeuihpU899dRzrlrDv6IqluHFySvYWB3B\nQMcUSjYCpOW6a0cwjmnYP9Qpqzurk1ThKAywRDaBSKMYKbXOufM3AgDAsOuPWjKxMoJY7gF5ACOJ\nUY+pCwAbqwFydakx+MioUtp5cZvWuafrzPe6tJcIkvJj42mA3ExSh27oWbKcIIqtSSMtkXVwEwAA\nbAGRtrL4YrqooC7oeK+876iplrcxmLQVKoVpME54l4Bn5pGVlbX/nXfemTVp0qSPnGT8fn/YggUL\nFq1Zs2bawYMHh7722mt3FxQUDPF6zasapRs7ugWXDRu5n8L/MmzkaWcNAKAN35/MzMzPLyWzffv2\nazMyMgrT09OLAQDmzJnz+rvvvvu1IUOGFFyyNapYFqp9p2NeZHRo6+S+GwAkKI4Ho0tRQTXKcNYm\nHcFO7OtriaxNF7P4Q7FiTr5STtjTM4ssmeRM4VSGDmVx0pupq2X0BIiERjiy8AtYs/Arjk30MzqB\n+80KmuEP4pUMUzzUcNahYWQ/rFVd69/j9bGNDdAZChYegWULR1sy1VKZdEI+0BJpoy0htlrr2GlR\nNhZLdzoazwOBzEP1zrvReTgdcyPTBlxWnUdZWVlKWlqalbUzNTW1tKysLEX3GwMDg6sD2u/QlClT\nPqyoqEjkx3/xi1/812233fbepU7u8/mCy6L9oJesSVcR1j3T0S2wgE5QBaz0ilefKbq00FWMN57h\nywQNtB+PDz/8cEpbTp6SklJWUlJicbmSkpK01NTUUpWslyzdBgYGHYd2mbY4/eOPGTNmx5EjRwYW\nFxenNzY2dl6+fPldeXl5K9vjmgYGBh0Lzx+Pd955Z1ZaWlrJ1q1bx91yyy2rpk+fng8AcPz48eRb\nbrllFQBAeHh486JFixZMnTp17dChQw/eddddyx2VpQYGBlcXAoHAFf974403Zg8dOvSzTp06+Xfu\n3DnaSS4/P3/a4MGDP8/IyDjy7LPPPtURbfXyV1VVFT958uQPBw4ceHjKlCkfnDlzJk4l95WvfKU4\nKytr38iRI3ePHTt2e0e3+1J/bp7Ho48++oeMjIwjI0aM2Ltr165RHd3m9ry/DRs25MbGxp4dOXLk\n7pEjR+7+6U9/+nRHt9nt3wMPPPDXPn36VA4fPny/k0ywz65DbqSgoCDz0KFDg3Jzczc4fTyam5vD\nBgwYUFhUVJTe2NgYkZ2dvefgwYNDOvohuPl78sknn3/uuee+HwgE4Nlnn33qqaeeelYll56eXlRV\nVRXf0e118+fmeaxatWrG9OnTVwcCAdi6dWtOTk7O1o5ud3ve34YNG3Jvu+22lR3dVi9/H3300cRd\nu3aNcvp4eHl2HeKenpmZ+fmgQYMO62Soj0hEREQT+ohcqTa2BStXrsybO3fuMgCAuXPnLluxYsVM\nJ9nAVaIodvM86H3n5ORsq66ujqusrFR5t4Qc3L5vV8vz4pg4ceKmHj16nHGq9/LsQnZty9XsI1JZ\nWZmQkJBQCQCQkJBQ6fQQfD5fYPLkyevGjBmz48UXX3z4yrYyOLh5HiqZ0tJSGjsrZOHm/nw+X2DL\nli3js7Oz986YMWP1wYMHh175ll4eeHl2l21V7RX3EbnCcLq/n//85/9N930+X8DpXjZv3jwhKSmp\n/OTJk72nTJnyYWZm5ucTJ07cdLna3Ba4fR58ZA7154hw087Ro0fvKikpSYuKijqfn58/febMmSsO\nHz486Eq070og2Gd32T4eV9JHpCOgu7+EhITKioqKxMTExIry8vKkPn1IHkKCpKSkcgCA3r17n5w1\na9Y727dvvzZUPx5ungeXKS0tTU1JSSm7ku30Cjf3FxMTY0UjmD59ev53vvOdP50+fTo+Pj7+ql/9\n4uXZdfi0xWkOeTX7iOTl5a1ctmzZXACAZcuWzZ05c+YKLnP+/Pmo2traGACAurq66A8++ODmrKys\n/Ve6rW7h5nnk5eWt/Pvf/34fAMDWrVvHxcXFVeP0LdTh5v4qKysT8H3dvn37tYFAwPe/4cMB4PHZ\ndYTm9+23356Vmppa0qVLl/qEhISKadOm5QcCASgrK0ueMWPGKpRbvXr19EGDBh0aMGBA4S9+8Ysf\ndrTG2u1fVVVV/E033bSOm2rp/R09erR/dnb2nuzs7D3Dhg07cDXcn+p5/PnPf57/5z//eT7KfPe7\n3100YMCAwhEjRuzVmeFD8e9S97do0aLvDhs27EB2dvaer371q1s++eSTcR3dZrd/c+bMeS0pKel4\nREREY2pqaslf/vKXb7X12fkCgatiSmpgYBBi6PBpi4GBwdUJ8/EwMDDwBPPxMDAw8ATz8TAwMPAE\n8/EwMDDwBPPxMDAw8IT/H9z4V24pCuVrAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x104e0ab50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+mFOMKj1XNRpNrM7SueBoMirTHvIlg7vjBvO6zH2Iyni+bbIdn5f8GPEKMc0m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obu/PHHHwumpKQE3PwVc1fc7vP2Z7lfN0b9+vW/KlSo0KVbfT879y7X9rb8mTUiKSkp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\n++HhhhtuZCv+H/58mUSBKpLeAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1049f7750>"
       ]
      }
     ],
     "prompt_number": 66
    }
   ],
   "metadata": {}
  }
 ]
}