lab_00_part_II_python_scientific_programming_modules.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scientific Programming Python Modules"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we get started, here are some useful links:\n",
    "\n",
    "* [The Juyter homepage](http://jupyter.org/)\n",
    "* [Jupyter documentation](https://jupyter-notebook.readthedocs.io/en/stable/), \n",
    "in particular have a look at the **Community documentation** section\n",
    "* [A gallery of interesting Jupyter Notebooks](https://github.com/jupyter/jupyter/wiki/A-gallery-of-interesting-Jupyter-Notebooks)\n",
    "* [Links to the best IPython and Jupyter Notebooks](http://nb.bianp.net/sort/views/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Important Python Libraries for Scientific Computing \n",
    "\n",
    "[NumPy](http://www.numpy.org/) is the (probably most) fundamental package for scientific computing with Python. In particluar, it provides a powerful N-dimensional array object\n",
    "and many many ways to generate, manipulate and process them.\n",
    "\n",
    "[SciPy](https://scipy.org/) is \"a Python-based ecosystem of open-source software for mathematics, science, and engineering. In particular, these are some of the core packages:\"\n",
    " \n",
    "* NumPy\n",
    "* [SciPy Library](https://scipy.org/scipylib/index.html), a fundamental library for scientific computing\n",
    "* [Matplotlib](http://matplotlib.org/), a comprehensive plotting library\n",
    "* [Sympy](http://www.sympy.org/), a Python library for symbolic mathematics\n",
    "* [pandas](http://pandas.pydata.org/), a sophisticated Python data analysis libray\n",
    "\n",
    "We will mainly use **NumPy, SciPy** and **Matplotlib**, but I encourage you to have a look at the Sympy and pandas as well. \n",
    "\n",
    "Finally, we only glance at the most basic functions. If you have\n",
    "some spare time, you can find is a nice collection of more detailed jupyter notebooks at\n",
    "https://github.com/jrjohansson/scientific-python-lectures, in particular Lecture 0 to Lecture 5 are of interest for this course."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy\n",
    "\n",
    "The official NumPy documentation provides a [\"quickstart\" tutorial](https://docs.scipy.org/doc/numpy/user/quickstart.html)\n",
    "(it covers relatively much ground) as part of its [NumPy User Guide](https://docs.scipy.org/doc/numpy/user/index.html).\n",
    "\n",
    "There you will also find the particular useful website for Matlab users \n",
    "https://docs.scipy.org/doc/numpy-dev/user/numpy-for-matlab-users.html\n",
    "which explains the key differences between the Matlab and NumPy way to\n",
    "accomlish things. There, you will find a large list on many NumPy equivalents for common Matlab operations. **Extremely useful!**\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okay, let's get started by importing the numpy module. Remember, as in real life, we don't want to pollute our environment, so **don't**\n",
    "import everything directly into you global namespace. Rather, we use the possibility to give modules a shortcut name when we import them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create some arrays. One way is to simply pass a list of numbers\n",
    "to the array constructor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4]\n",
      "<class 'numpy.ndarray'>\n",
      "[ 1.  2.  3.  4.]\n",
      "<class 'numpy.ndarray'>\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1,2,3,4]) # Mind the brackets inside!\n",
    "print(a)\n",
    "# Check is type\n",
    "print(type(a))\n",
    "# Since we only used integers, a is an array of datatype ...\n",
    "a.dtype\n",
    "\n",
    "# repeat the same thing with floats\n",
    "a = np.array([1.0,2.0,3.0,4.0]) # Mind the brackets inside!\n",
    "print(a)\n",
    "# Check is type\n",
    "print(type(a))\n",
    "# Since we only used integers, a is an array of datatype ...\n",
    "a.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to create a bunch of 0s or 1s, you can do this using"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  0.  0.  0.  0.]\n",
      "[ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.]\n"
     ]
    }
   ],
   "source": [
    "zeros = np.zeros(5)\n",
    "print(zeros)\n",
    "\n",
    "ones = np.ones(10)\n",
    "print(ones)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to create longer sequence you can simply use the `arange` function which very similiar to the built-in `range` function (just\n",
    "that it returns a NumPy array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24\n",
      " 25 26 27 28 29]\n"
     ]
    }
   ],
   "source": [
    "b = np.arange(30)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Miniexercise:** Curious about the possible arguments of `arange`? Use the `?` to look up\n",
    "its documentation and create an array 20 to 20000 with step size equal to 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to generate evenly space sequence of numbers over a given\n",
    "interval $[a,b]$, the `linspace` function is your best friend!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          0.34906585  0.6981317   1.04719755  1.3962634   1.74532925\n",
      "  2.0943951   2.44346095  2.7925268   3.14159265]\n"
     ]
    }
   ],
   "source": [
    "grid = np.linspace(0, np.pi,10)\n",
    "print(grid)\n",
    "np.linspace?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that linspace takes the *number of samples to generate* instead of a step size. As always you can explore the documentation on `linspace`\n",
    "via\n",
    "```Python\n",
    "np.linspace?\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Time to look at more complex arrays. Let's go to higher dimensions!\n",
    "\n",
    "You can create a simple 2d array by simply passing a list of lists:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =\n",
      "[[1 2 3]\n",
      " [4 5 6]]\n",
      "The rank/dimension is\n",
      "2\n",
      "Shape of a\n",
      "(2, 3)\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[1,2,3],\n",
    "              [4,5,6]]) # A (dense) matrix or an array of rank 2\n",
    "print(\"a =\")\n",
    "print(a)\n",
    "\n",
    "# More information on a\n",
    "print(\"The rank/dimension is\")\n",
    "print(a.ndim) \n",
    "\n",
    "# The shape of a is\n",
    "print(\"Shape of a\")\n",
    "print(a.shape) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So you could say, we defined $2\\times 3$ Matrix (2 rows, each consists\n",
    "of 3 colums).\n",
    "\n",
    "Note that `shape` attribute of an array is a tuple which returns the\n",
    "number of elements of each so-called `axis`. The \"0\" axis corresponds\n",
    "the number of elements in the *outer-most* list. The 1st axis in the corresponds to the second outer-most list, and so on.\n",
    "\n",
    "Let's try it out with a rank-3 array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 2, 4)\n"
     ]
    }
   ],
   "source": [
    "b = np.array([ [[1,2,3,4],[5,6,7,8]],\n",
    "               [[9,10,11,12],[13,14,15,16]], \n",
    "               [[17,18,19,20],[21,22,23,24]]]) # This is an array of rank 3\n",
    "\n",
    "# Determine its shape and confirm it!\n",
    "print(b.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Useful Operations on Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0, 110, 220, 330, 440])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1 = np.array([0, 10, 20, 30, 40])\n",
    "a2 = np.arange(5)\n",
    "\n",
    "a1 + 100*a2  # elementwise scaling and addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([100, 110, 120, 130, 140])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1 + 100 # elementwise addition of a scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,  10,  40,  90, 160])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1*a2 # elementwise product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 10,  40,  90],\n",
       "       [160, 250, 360],\n",
       "       [490, 640, 810]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = np.array([[1, 2, 3],\n",
    "               [4, 5, 6],\n",
    "               [7, 8, 9]])\n",
    "A2 = np.array([[10, 20, 30],\n",
    "               [40, 50, 60],\n",
    "               [70, 80, 90]])\n",
    "A1*A2 # elementwise product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 300,  360,  420],\n",
       "       [ 660,  810,  960],\n",
       "       [1020, 1260, 1500]])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1.dot(A2) # matrix product (if you're using the pure array interface)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 300,  360,  420],\n",
       "       [ 660,  810,  960],\n",
       "       [1020, 1260, 1500]])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(A1, A2) # Achieves the same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n",
      "[[11 22 33]\n",
      " [44 55 66]\n",
      " [77 88 99]]\n",
      "[[ 1011.  1022.  1033.]\n",
      " [ 1044.  1055.  1066.]\n",
      " [ 1077.  1088.  1099.]]\n"
     ]
    }
   ],
   "source": [
    "print(A1)\n",
    "A1 += A2\n",
    "print(A1)\n",
    "print(A1 + 1000.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a more linear algebra friendly interface, have a look at the\n",
    "Section *‘array’ or ‘matrix’? Which should I use?* at \n",
    "https://docs.scipy.org/doc/numpy/user/numpy-for-matlab-users.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes it is necessary to flatten them out (from the most-inner to the most-outer axis), storing everying in a single consecutive array of rank 1. The `ravel` function does the job for you. Note that is *doesn't* change the original array, but\n",
    "rather returns the flatten array as a copy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing flatten rank 3 array\n",
      "[ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24]\n",
      "Print original array\n",
      "[[[ 1  2  3  4]\n",
      "  [ 5  6  7  8]]\n",
      "\n",
      " [[ 9 10 11 12]\n",
      "  [13 14 15 16]]\n",
      "\n",
      " [[17 18 19 20]\n",
      "  [21 22 23 24]]]\n"
     ]
    }
   ],
   "source": [
    "bflat = b.ravel()\n",
    "print(\"Printing flatten rank 3 array\\n\" + str(bflat))\n",
    "print(\"Print original array\\n\" + str(b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also reshape arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reshaped array\n",
      "[[ 1  2  3  4  5  6  7  8  9 10 11 12]\n",
      " [13 14 15 16 17 18 19 20 21 22 23 24]]\n",
      "Original array\n",
      "[[[ 1  2  3  4]\n",
      "  [ 5  6  7  8]]\n",
      "\n",
      " [[ 9 10 11 12]\n",
      "  [13 14 15 16]]\n",
      "\n",
      " [[17 18 19 20]\n",
      "  [21 22 23 24]]]\n"
     ]
    }
   ],
   "source": [
    "b_reshaped = b.reshape(2, 12) # Returns a reshape array\n",
    "print(\"Reshaped array\")\n",
    "print(b_reshaped)\n",
    "print(\"Original array\")\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also reshape the original array using the `resize` function "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original array\n",
      "[[ 1  2  3  4  5  6  7  8  9 10 11 12]\n",
      " [13 14 15 16 17 18 19 20 21 22 23 24]]\n"
     ]
    }
   ],
   "source": [
    "b.resize(2,12)\n",
    "print(\"Original array\")\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to lists, there are lot of possibilities to slice an array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0 10 20 30 40]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(a1)\n",
    "a1[1] # Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 30])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1[2:4] # Extracting subarray from index 2 to 3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1[1:4:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note** You will encounter more sophisticated slicing of arrays/matrices later in the course!\n",
    "\n",
    "Opposed to standard lists, the slicing operations do not return \n",
    "a copy, but rather a *view* of the original array to avoid\n",
    "unneccessary copying!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  3 20  3 40]\n",
      "[    0 10000    20 10000    40]\n",
      "[ 0  3 20  3 40]\n"
     ]
    }
   ],
   "source": [
    "print(a1)\n",
    "a1[1:4:2] = 10000\n",
    "print(a1) \n",
    "a1[1:4:2] = np.pi\n",
    "print(a1) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happened in the second case? a1's datatype is integer and thus $\\pi$ was\n",
    "converted/rounded to avoid changing the underlying number datatype\n",
    "of a1. You can a converted copy by using the `astype` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int64\n",
      "float64\n"
     ]
    }
   ],
   "source": [
    "print(a1.dtype)\n",
    "a1_float = a1.astype(float)\n",
    "print(a1_float.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or you can specify the datatype when creating the array (and you only\n",
    "use integers):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  2.  3.]\n",
      "[ 1.  2.  3.]\n"
     ]
    }
   ],
   "source": [
    "a3 = np.array([1,2, 3], dtype=float)\n",
    "print(a3)\n",
    "# If any of the number are floats you get float as dtype \n",
    "a4 = np.array([1.0 ,2, 3]) \n",
    "print(a4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's slice some matrices/arrays with rank $ > 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3  4  5]\n",
      " [ 6  7  8  9 10 11]\n",
      " [12 13 14 15 16 17]\n",
      " [18 19 20 21 22 23]]\n",
      "8\n",
      "[ 6  7  8  9 10 11]\n",
      "[ 2  8 14 20]\n",
      "Extracting continuously connected subblocks\n",
      "[[ 8  9]\n",
      " [14 15]]\n",
      "[[ 2  3]\n",
      " [ 8  9]\n",
      " [14 15]\n",
      " [20 21]]\n",
      "[[ 6  7  8  9 10 11]\n",
      " [12 13 14 15 16 17]]\n"
     ]
    }
   ],
   "source": [
    "#Print current A1\n",
    "A1 = np.arange(24).reshape(4,6)\n",
    "print(A1)\n",
    "print(A1[1,2]) # Get \n",
    "\n",
    "# Similar effect, but  first version is preferred\n",
    "#print(A1[1][2])\n",
    "\n",
    "# Get 2nd row\n",
    "print(A1[1,:])\n",
    "\n",
    "# Get 3rd column\n",
    "print(A1[:,2])\n",
    "\n",
    "# Extract (continuous) subblocks\n",
    "print(\"Extracting continuously connected subblocks\")\n",
    "print(A1[1:3,2:4])\n",
    "print(A1[:,2:4])\n",
    "print(A1[1:3,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Miniexercise**: Who dares to try something simular for a rank 3 array? Define one by starting from a suitable defined arange and reshaping and try to get a view on\n",
    "* Single elements\n",
    "* Rank 1 subarrays\n",
    "* Rank 2 subarrays\n",
    "* Rank 3 subarrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0  1]\n",
      "  [ 2  3]\n",
      "  [ 4  5]\n",
      "  [ 6  7]]\n",
      "\n",
      " [[ 8  9]\n",
      "  [10 11]\n",
      "  [12 13]\n",
      "  [14 15]]\n",
      "\n",
      " [[16 17]\n",
      "  [18 19]\n",
      "  [20 21]\n",
      "  [22 23]]]\n",
      "[[ 0  2  4  6]\n",
      " [ 8 10 12 14]\n",
      " [16 18 20 22]]\n",
      "[[ 2  4]\n",
      " [10 12]\n",
      " [18 20]]\n"
     ]
    }
   ],
   "source": [
    "A2 = A1.reshape(3,4,2)\n",
    "print(A2)\n",
    "A2[2, 3, 1]\n",
    "print(A2[:,:,0])\n",
    "print(A2[:,1:3,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining grids and evaluating functions on arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NumPy has implemented its own 'array'-aware version of many mathematical functions. Evaluating a function on an array basically\n",
    "means this function is applied element-wise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.00000000e+00   1.06293486e-01   2.11382624e-01   3.14076712e-01\n",
      "   4.13212186e-01   5.07665800e-01   5.96367359e-01   6.78311836e-01\n",
      "   7.52570770e-01   8.18302776e-01   8.74763085e-01   9.21311978e-01\n",
      "   9.57422038e-01   9.82684125e-01   9.96812007e-01   9.99645611e-01\n",
      "   9.91152831e-01   9.71429893e-01   9.40700267e-01   8.99312130e-01\n",
      "   8.47734428e-01   7.86551556e-01   7.16456740e-01   6.38244184e-01\n",
      "   5.52800065e-01   4.61092501e-01   3.64160575e-01   2.63102564e-01\n",
      "   1.59063496e-01   5.32221748e-02  -5.32221748e-02  -1.59063496e-01\n",
      "  -2.63102564e-01  -3.64160575e-01  -4.61092501e-01  -5.52800065e-01\n",
      "  -6.38244184e-01  -7.16456740e-01  -7.86551556e-01  -8.47734428e-01\n",
      "  -8.99312130e-01  -9.40700267e-01  -9.71429893e-01  -9.91152831e-01\n",
      "  -9.99645611e-01  -9.96812007e-01  -9.82684125e-01  -9.57422038e-01\n",
      "  -9.21311978e-01  -8.74763085e-01  -8.18302776e-01  -7.52570770e-01\n",
      "  -6.78311836e-01  -5.96367359e-01  -5.07665800e-01  -4.13212186e-01\n",
      "  -3.14076712e-01  -2.11382624e-01  -1.06293486e-01  -2.44929360e-16]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(0, 2*np.pi, 60)\n",
    "f = np.sin(x)\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Don't trust me? Let's get started with Matplotlib and plot the result!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matplotlib\n",
    "\n",
    "First of course, you have to import the right module! Luckily for (former ;) ) Matlab users, there is simplified interface called\n",
    "`pyplot` which tries to resembles the basic Matlab plotting function rather closely. \n",
    "\n",
    "There is a nice tutorial on `pyplot` as part of the [offical Matplotlib tutorials](http://matplotlib.org/tutorials/index.html),\n",
    "see [Pyplot tutorial](http://matplotlib.org/tutorials/introductory/pyplot.html#sphx-glr-tutorials-introductory-pyplot-py). Later on, you might want to have a look at the [Matplotlib Gallery](http://matplotlib.org/gallery/index.html#)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(x,f)\n",
    "# You need this command to show the final figure\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to switch to an interactive plotting, just execute on of the Jupyter notebook's magic command:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make a fancier plot by plotting both $\\sin$ and $\\cos$ and giving the figure\n",
    "labels, a legend and some markers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"930\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,f, marker='o', color='cyan', linestyle='dashed', linewidth=2.0, label = '$\\sin$')\n",
    "# Similar result with the slightly less verbose command\n",
    "#plt.plot(x,f, 'co--', linewidth=2.0, label = '$\\sin$')\n",
    "plt.plot(x, np.cos(x), marker='*', color='magenta', linestyle=':',linewidth=2, label = '$\\cos$')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$f(x)$')\n",
    "plt.title('My first Matplotlib plot!')\n",
    "# You need this to show the legend\n",
    "plt.legend()\n",
    "#You need this command to show the final figure\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As always, you can look up the possibile arguments using"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.plot?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Important:** When you activated interactive plotting using \n",
    "```Python \n",
    "%matplotlib notebook\n",
    "```\n",
    "make sure that you stop the interaction mode/event loop for the current figure before you plot a new figure, otherwise the next plot command won't result in a proper figure! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<!--<link href='http://fonts.googleapis.com/css?family=Fenix' rel='stylesheet' type='text/css'>-->\n",
       "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
       "<!-- <link href='http://fonts.googleapis.com/css?family=Source+Code+Pro:300,400' rel='stylesheet' type='text/css'>* -->\n",
       "<link href=\"https://fonts.googleapis.com/css?family=Source+Code+Pro\" rel=\"stylesheet\"> \n",
       "<link href=\"https://fonts.googleapis.com/css?family=News+Cycle\" rel=\"stylesheet\"> \n",
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "        font-family: 'News Cycle', sans-serif;\n",
       "    }\n",
       "\n",
       "    div.cell{\n",
       "        /*max-width:600px;*/\n",
       "        /*margin-left:16% !important;*/\n",
       "        /*margin-right:auto;*/\n",
       "    }\n",
       "    div.text_cell {\n",
       "        max-width: 105ex /* instead of 100%, */\n",
       "        }\n",
       "    h1 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    h2 {\n",
       "        /*font-family: 'Fenix', serif;*/\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "        color: #5889C5;\n",
       "        /*color: #5889C5;*/\n",
       "    }\n",
       "    h3{\n",
       "\t\t/*font-family: 'Fenix', serif;*/\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "        color: #5889C5;\n",
       "        /*color: #5889C5;*/\n",
       "        /*margin-top:12px;*/\n",
       "        /*margin-bottom: 3px;*/\n",
       "       }\n",
       "\th4{\n",
       "\t\t/*font-family: 'Fenix', serif;*/\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "        color: #5889C5;\n",
       "       }\n",
       "    h5 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "        color: #5889C5;\n",
       "    }\t   \n",
       "    div.text_cell_render{\n",
       "        /*font-family: News Cycle, Geneva,Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;*/\n",
       "        font-family: 'Alegreya Sans','News Cycle',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 135%;\n",
       "        font-size: 120%;\n",
       "        /*width:600px;*/\n",
       "        /*margin-left:auto;*/\n",
       "        /*margin-right:auto;*/\n",
       "    }\n",
       "    .CodeMirror{\n",
       "            font-family: 'Source Code Pro', monospace;\n",
       "            /*font-style: italic;*/\n",
       "            /*font-weight: bold;*/\n",
       "            /*font-size: 120%;*/\n",
       "    }\n",
       "    /*.prompt{\n",
       "        display: None;\n",
       "    }*/\n",
       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 50pt;\n",
       "\t\tline-height: 100%;\n",
       "        color: #5889C5;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\t\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-size: 16pt;\n",
       "        color: #5889C5;\n",
       "        font-style: italic;\n",
       "        margin-bottom: .5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    \n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "        }  \n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\",\"begingroup.js\"],\n",
       "                           Macros: {\n",
       "                               RR: \"{\\\\mathbb{R}\",\n",
       "                               mcO: \"\\\\mathcal{O}\"\n",
       "                           }\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    #styles = open(\"../styles/custom.css\", \"r\").read()\n",
    "    styles = open(\"../styles/custom1.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "#     return HTML(\"\")\n",
    "\n",
    "# Comment out next line and execute this cell to restore the default notebook style \n",
    "css_styling()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}