{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy and Matplotlib examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First import NumPy and Matplotlib:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "module://ipykernel.pylab.backend_inline\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "print(matplotlib.backends.backend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython.display import set_matplotlib_formats\n",
    "set_matplotlib_formats('png', 'pdf')\n",
    "matplotlib.rcParams['figure.figsize'] = (2,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{matplotlib.figure.Figure: <function IPython.core.pylabtools.<lambda>>}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ip.display_formatter.formatters['application/pdf'].type_printers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we show some very basic examples of how they can be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.random.uniform(size=(100,100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "evs = np.linalg.eigvals(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100,)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evs.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Here is a very long heading that pandoc will wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap and wrap"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a cell that has both text and PNG output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([97,  2,  0,  0,  0,  0,  0,  0,  0,  1]),\n",
       " array([ -2.59479443,   2.67371141,   7.94221725,  13.21072308,\n",
       "         18.47922892,  23.74773476,  29.0162406 ,  34.28474644,\n",
       "         39.55325228,  44.82175812,  50.09026395]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "xCsMGOIVBgzxCgOGeIUBQ7z6LzWkj3n7AHKHAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b0ecf10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(evs.real)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "import math \n",
    "import numpy as np\n",
    "def matrix_calc(L=None):\n",
    "    \"\"\"docstring\"\"\"\n",
    "    if L is None:",
    "       L = np.random.random(size=(1,1))",
    "    raise Exception(\"message\")\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This string contains a ~~strikethrough~~, struckthrough. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This string contains a `'` single tick inside backticks, leading to a ``\\textquotesingle`` in latex."
   ]
  }
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