{
 "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": [
      "\n",
      "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.kernel.zmq.pylab.backend_inline].\n",
      "For more information, type 'help(pylab)'.\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.random.uniform(size=(100,100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "evs = np.linalg.eigvals(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100,)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evs.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a cell that has both text and PNG output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([95,  4,  0,  0,  0,  0,  0,  0,  0,  1]),\n",
       " array([ -2.93566063,   2.35937011,   7.65440086,  12.9494316 ,\n",
       "        18.24446235,  23.53949309,  28.83452384,  34.12955458,\n",
       "        39.42458533,  44.71961607,  50.01464682]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1zjvvaMuWLerr6/PM/JK0efNmlZWVpS+M8NLslmUpGo3q0KFDisfjkrw1/7p162Tbtrq6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108c8f1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(evs.real)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 0
}
