{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "\n",
       ".rendered_html {\n",
       "    font-family: \"proxima-nova\", helvetica;\n",
       "    font-size: 130%;\n",
       "    line-height: 1.5;\n",
       "}\n",
       "\n",
       ".rendered_html h1 {\n",
       "    margin: 0.25em 0em 0.5em;\n",
       "    color: #015C9C;\n",
       "    text-align: center;\n",
       "    line-height: 1.2; \n",
       "    page-break-before: always;\n",
       "}\n",
       "\n",
       ".rendered_html h2 {\n",
       "    margin: 1.1em 0em 0.5em;\n",
       "    color: #26465D;\n",
       "    line-height: 1.2;\n",
       "}\n",
       "\n",
       ".rendered_html h3 {\n",
       "    margin: 1.1em 0em 0.5em;\n",
       "    color: #002845;\n",
       "    line-height: 1.2;\n",
       "}\n",
       "\n",
       ".rendered_html li {\n",
       "    line-height: 1.5; \n",
       "}\n",
       "\n",
       "/*.prompt {\n",
       "    font-size: 120%; \n",
       "}*/\n",
       "\n",
       ".CodeMirror-lines {\n",
       "    font-size: 110%; \n",
       "}\n",
       "\n",
       "/*.output_area {\n",
       "    font-size: 120%; \n",
       "}*/\n",
       "\n",
       "/*#notebook {\n",
       "    background-image: url('files/images/witewall_3.png');\n",
       "}*/\n",
       "\n",
       "h1.bigtitle {\n",
       "    margin: 4cm 1cm 4cm 1cm;\n",
       "    font-size: 300%;\n",
       "}\n",
       "\n",
       "h3.point {\n",
       "    font-size: 200%;\n",
       "    text-align: center;\n",
       "    margin: 2em 0em 2em 0em;\n",
       "    #26465D\n",
       "}\n",
       "\n",
       ".logo {\n",
       "    margin: 20px 0 20px 0;\n",
       "}\n",
       "\n",
       "a.anchor-link {\n",
       "    display: none;\n",
       "}\n",
       "\n",
       "h1.title { \n",
       "    font-size: 250%;\n",
       "}\n",
       "\n",
       "</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%load_ext load_style\n",
    "%load_style talk.css"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IPython notebook widgets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "from `version 2.0`, IPython includes an architecture for **interactive widgets** that tie together Python code running in the kernel and JavaScript/HTML/CSS running in the browser. These widgets enable users to **explore their code and data interactively**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from ipywidgets import interactive, interact, fixed\n",
    "from IPython.html import widgets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### simple function that just prints its argument"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### if x is a integer, a widget slider will be created"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "interact(f, x=10); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### you can also use a python `decorator` syntax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from datetime import datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "@interact(x=10)\n",
    "def f(x):\n",
    "    print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### If x is Boolean (True / False), a checkbox is created"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "interact(f, x=True); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### If x is a string: text box"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hi there!\n"
     ]
    }
   ],
   "source": [
    "interact(f, x='Hi there!');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Widgets can be called with arguments to customize them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    }
   ],
   "source": [
    "interact(f, x=widgets.IntSlider(min=-10,max=10,step=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An example with plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4D5YkSSrKs8/CLbfA88/nXUl9cJG7JEkNbskS+PrXs5s5b7ll3tXUBwOWJEkN7tJLYaut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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112cc0ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "@interact(degree=2)\n",
    "def f(degree):\n",
    "    x = np.linspace(0,1,100)\n",
    "    f, ax = plt.subplots(figsize=(10,5))\n",
    "    plt.plot(x, x**degree)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An example using [sympy](http://sympy.org/en/index.html) to factor polynomials"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy import Symbol, Eq, factor, init_printing\n",
    "init_printing(use_latex='mathjax')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = Symbol('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def factorit(n):\n",
    "    display(Eq(x**n-1, factor(x**n-1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x^{12} - 1 = \\left(x - 1\\right) \\left(x + 1\\right) \\left(x^{2} + 1\\right) \\left(x^{2} - x + 1\\right) \\left(x^{2} + x + 1\\right) \\left(x^{4} - x^{2} + 1\\right)$$"
      ],
      "text/plain": [
       " 12                       ⎛ 2    ⎞ ⎛ 2        ⎞ ⎛ 2        ⎞ ⎛ 4    2    ⎞\n",
       "x   - 1 = (x - 1)⋅(x + 1)⋅⎝x  + 1⎠⋅⎝x  - x + 1⎠⋅⎝x  + x + 1⎠⋅⎝x  - x  + 1⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "factorit(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x^{24} - 1 = \\left(x - 1\\right) \\left(x + 1\\right) \\left(x^{2} + 1\\right) \\left(x^{4} + 1\\right) \\left(x^{2} - x + 1\\right) \\left(x^{2} + x + 1\\right) \\left(x^{4} - x^{2} + 1\\right) \\left(x^{8} - x^{4} + 1\\right)$$"
      ],
      "text/plain": [
       " 24                       ⎛ 2    ⎞ ⎛ 4    ⎞ ⎛ 2        ⎞ ⎛ 2        ⎞ ⎛ 4    2\n",
       "x   - 1 = (x - 1)⋅(x + 1)⋅⎝x  + 1⎠⋅⎝x  + 1⎠⋅⎝x  - x + 1⎠⋅⎝x  + x + 1⎠⋅⎝x  - x \n",
       "\n",
       "    ⎞ ⎛ 8    4    ⎞\n",
       " + 1⎠⋅⎝x  - x  + 1⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(factorit, n=(2,40));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Another example with Pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xdf = pd.DataFrame({'A':np.random.randn(5), 'B':np.random.randn(5)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11c258a58>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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E0xw4AA0bQlgY1KzpXVuHzh2iwfgG/OD6gUalG1kSX2pIOUiIJGht9v5/9lnz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1133b9940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xdf.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_df(label):\n",
    "    xdf[label].plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "w = interactive(plot_df, label=['A','B'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YGAlsSYLqsjFxkoC6zMR5JDAMmJXpIw7AL/BZYomp08bESfx12hUYZ76dfAvg\n8UzdJepvvTFxEn9dZpVrfWqxmIhIimlgWEQkxZQERERSTElARCTFlARERFJMSUBEJMWUBEREUkxJ\nQEQkxZQERERS7P8Bg6NTvNQIaa0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c3082e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[NbConvertApp] Converting notebook IPython_widgets.ipynb to html\n",
      "[NbConvertApp] Writing 442485 bytes to IPython_widgets.html\n"
     ]
    }
   ],
   "source": [
    "!ipython nbconvert IPython_widgets.ipynb --to html"
   ]
  }
 ],
 "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": "3.5.1"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}