Python Course Lecture 7b Functional Programming and Interactive Analysis.ipynb

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   "source": [
    "from IPython.display import HTML\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
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   "metadata": {
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   "source": [
    "# Python Course Lecture 7b:Intro to Functional Programming and its Applications: \n",
    "  - **Data Aggregation** in Pandas\n",
    "  - **Parallel Processing** using multiprocessing.map()\n",
    "  - **Graphical Interfaces** using ipywidgets.interact()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "# Different Tasks and Languages Encourage Different Programming Paradigms"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Python is a Multi-Paradigm Language.  \n",
    "This means that Python supports programming according to different manners of thinking:\n",
    "  - **Procedural Programming**: Telling the computer what to do in a step-by-step manner.\n",
    "  - **Functional Programming**: Telling the computer a set of transformations to perform.\n",
    "  - **Object-Oriented Programming**: Telling the computer how certain data should be stored and handled by describing its qualities.\n",
    "  - **Declarative Programming**: Telling the computer what result you want."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "# Paradigm Example: Building a Sandwich"
   ]
  },
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   "source": [
    "## Procedural: Building a Sandwich\n",
    "\"Grasp the drawer handle and pull it towards you 10cm. Take a knife, located in the 3rd compartment from the drawer into your hand. Push the drawer handle until it resists pressure. Place the bread on the table. Twice now: Hold the knife above the bread, then move it down 1cm from its end, pulling away the smallest segment and laying it flat on the table.  Open the refrigerator. Take some cheese from the refrigerator. Close the refrigerator...\"\n"
   ]
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   "source": [
    "## Functional: Building a Sandwich\n",
    "  - **Getting** means opening something and removing the specified object, then closing that something.\n",
    "  - **Slicing** means pushing a knife through something and removing the small segment that is removed.\n",
    "  - **Stacking** means placing all things on top of one another in the order specified, resulting in a single thing.\n",
    "\n",
    "\"**Get** a Knife. **Get** and **Slice** and **Stack** the Bread and Cheese\""
   ]
  },
  {
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   "source": [
    "## Object-Oriented: Building a Sandwich\n",
    "  - **Containers** can be opened and closed. They can also contain Things that can be added or removed.\n",
    "  - **Things** can be Taken.\n",
    "  - **Food** is a **Thing**.  It can be sliced and eaten.\n",
    "  - **SharpObjects** are **Things**. They can slice things.\n",
    "  - The **Drawer** and **Refrigerator** are **Containers**. \n",
    "  - The **Bread** and **Cheese** are **Food**.\n",
    "  - The **Drawer** **Contains** the **Knife**.  \n",
    "  \n",
    "  "
   ]
  },
  {
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   "metadata": {
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   },
   "source": [
    "## Declarative: Building a Sandwich\n",
    "\n",
    "\"Give me a cheese sandwich, please.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Functional Programming in Python: \n",
    "## \"Applying Functions to Data\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Review: Making Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
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     "execution_count": 32,
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   "source": [
    "def add(args):\n",
    "    return sum(args)\n",
    "\n",
    "add([1, 2, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Python Functions can be Renamed.  They are also Objects!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
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       "6"
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     "execution_count": 33,
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   "source": [
    "total = add\n",
    "total([1, 2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "function"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(total)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Lambda Functions: Make a Function in a single line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
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     "execution_count": 26,
     "metadata": {},
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   ],
   "source": [
    "add2 = lambda x: x + 2\n",
    "add2(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 25,
     "metadata": {},
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   ],
   "source": [
    "mult = lambda x,y: x*y\n",
    "mult(3, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Python Functions can be put in other functions\n",
    "Demo: The **apply()** function (included in Python2, not 3) calls a function on data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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     "data": {
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       "6"
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     "execution_count": 6,
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   "source": [
    "def apply(fun, data):\n",
    "    return fun(data)\n",
    "    \n",
    "apply(sum, [1, 2, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
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   "source": [
    "## Pandas Aggregation: Another example of Functions applying Functions\n",
    "From last week's homework:\n",
    "```python\n",
    "LogRT.agg({'Mean': np.mean, 'STD': np.std})\n",
    "```"
   ]
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   "execution_count": 98,
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       "<table border=\"1\">\n",
       " <thead>\n",
       " <tr style=\"text-align: right;\">\n",
       " <th></th>\n",
       " <th>STD</th>\n",
       "  <th>Mean</th>\n",
       " </tr>\n",
       "  <tr>\n",
       "      <th>UserID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>156772</th>\n",
       "      <td>0.287129</td>\n",
       "      <td>7.161207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156839</th>\n",
       "      <td>0.525333</td>\n",
       "      <td>6.513287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156856</th>\n",
       "      <td>0.316302</td>\n",
       "      <td>6.942405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>156857</th>\n",
       "      <td>0.424438</td>\n",
       "      <td>7.176462</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
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       "<IPython.core.display.HTML object>"
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   "source": [
    "HTML('<table border=\"1\">\\n <thead>\\n <tr style=\"text-align: right;\">\\n <th></th>\\n <th>STD</th>\\n  <th>Mean</th>\\n </tr>\\n  <tr>\\n      <th>UserID</th>\\n      <th></th>\\n      <th></th>\\n    </tr>\\n  </thead>\\n  <tbody>\\n    <tr>\\n      <th>156772</th>\\n      <td>0.287129</td>\\n      <td>7.161207</td>\\n    </tr>\\n    <tr>\\n      <th>156839</th>\\n      <td>0.525333</td>\\n      <td>6.513287</td>\\n    </tr>\\n    <tr>\\n      <th>156856</th>\\n      <td>0.316302</td>\\n      <td>6.942405</td>\\n    </tr>\\n    <tr>\\n      <th>156857</th>\\n      <td>0.424438</td>\\n      <td>7.176462</td>\\n    </tr>\\n  </tbody>\\n</table>')"
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  {
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   },
   "source": [
    "## map()\n",
    "Applying a Function on each element in a collection is called **Mapping** a Function to Data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def square(x): \n",
    "    return x ** 2\n",
    "\n",
    "list(map(square, range(10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
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   ],
   "source": [
    "[el ** 2 for el in range(10)]  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## lambda is often used for simple maps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(map(lambda x: x ** 2, range(10)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Mapping can be used for parallel processing.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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    "collapsed": false
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   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'square' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-2-1bb6f93bb389>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mmaxval\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mget_ipython\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmagic\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'timeit list(map(square, range(maxval)))'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mmultiprocessing\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mPool\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mworkers\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mPool\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# Make a collection of 3 \"workers\" to do the work independently\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/nickdg/anaconda3/lib/python3.5/site-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mmagic\u001b[1;34m(self, arg_s)\u001b[0m\n\u001b[0;32m   2161\u001b[0m         \u001b[0mmagic_name\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0m_\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmagic_arg_s\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0marg_s\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpartition\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m' '\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2162\u001b[0m         \u001b[0mmagic_name\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmagic_name\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlstrip\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprefilter\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mESC_MAGIC\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2163\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrun_line_magic\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmagic_name\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmagic_arg_s\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2164\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2165\u001b[0m     \u001b[1;31m#-------------------------------------------------------------------------\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/nickdg/anaconda3/lib/python3.5/site-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mrun_line_magic\u001b[1;34m(self, magic_name, line)\u001b[0m\n\u001b[0;32m   2082\u001b[0m                 \u001b[0mkwargs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'local_ns'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msys\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_getframe\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstack_depth\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mf_locals\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2083\u001b[0m             \u001b[1;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbuiltin_trap\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2084\u001b[1;33m                 \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2085\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2086\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<decorator-gen-59>\u001b[0m in \u001b[0;36mtimeit\u001b[1;34m(self, line, cell)\u001b[0m\n",
      "\u001b[1;32m/home/nickdg/anaconda3/lib/python3.5/site-packages/IPython/core/magic.py\u001b[0m in \u001b[0;36m<lambda>\u001b[1;34m(f, *a, **k)\u001b[0m\n\u001b[0;32m    191\u001b[0m     \u001b[1;31m# but it's overkill for just that one bit of state.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    192\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mmagic_deco\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 193\u001b[1;33m         \u001b[0mcall\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    194\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    195\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/nickdg/anaconda3/lib/python3.5/site-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[1;34m(self, line, cell)\u001b[0m\n\u001b[0;32m   1039\u001b[0m             \u001b[0mnumber\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1040\u001b[0m             \u001b[1;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1041\u001b[1;33m                 \u001b[0mtime_number\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtimer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtimeit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1042\u001b[0m                 \u001b[0mworst_tuning\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mworst_tuning\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtime_number\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1043\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0mtime_number\u001b[0m \u001b[1;33m>=\u001b[0m \u001b[1;36m0.2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m/home/nickdg/anaconda3/lib/python3.5/site-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[1;34m(self, number)\u001b[0m\n\u001b[0;32m    135\u001b[0m         \u001b[0mgc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdisable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    136\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 137\u001b[1;33m             \u001b[0mtiming\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minner\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mit\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtimer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    138\u001b[0m         \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    139\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mgcold\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<magic-timeit>\u001b[0m in \u001b[0;36minner\u001b[1;34m(_it, _timer)\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'square' is not defined"
     ]
    }
   ],
   "source": [
    "maxval = 10\n",
    "%timeit list(map(square, range(maxval)))\n",
    "\n",
    "from multiprocessing import Pool\n",
    "workers = Pool(3) # Make a collection of 3 \"workers\" to do the work independently\n",
    "%timeit workers.map(square, range(maxval))\n",
    "workers.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Intro to Interactive Jupyter Widgets\n",
    "\n",
    "Now, we'll use the functional approach to make interactive plots in our Jupyter Notebooks.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import ipywidgets\n",
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Widgets are Parts of a Graphical Interface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ipywidgets.Text('This is Text')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ipywidgets.IntSlider(3, min=-10, max=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Project: Interact with Sine-waves\n",
    "The **ipywidgets.interact()** function is a quick-and-dirty way to generate widgets for controlling functions.  By default, it will try to choose an appropriate widget given the argument's type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98544972998846014"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sin(x):\n",
    "    return np.sin(x)\n",
    "\n",
    "interact(sin, x=1.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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D3LlM6j7ZYQfgoYdsErxzZ6BTJ9tfpiqffw7ccIP9Ddx/v23NzInzzMQxdo/N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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f073e3af278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_sin(amplitude):\n",
    "    x = np.linspace(0, 5 * np.pi, 100)\n",
    "    y = amplitude * np.sin(x)\n",
    "    plt.plot(x, y)\n",
    "    plt.ylim(-3, 3)\n",
    "    \n",
    "interact(plot_sin, amplitude=1.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BwYza58612VFZWf6fKxmRS+wdOgAVKgSzo87dd1tf+DBvyZbOghy1c7Qefr/6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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f073e26e908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_sin(amplitude):\n",
    "    x = np.linspace(0, 5 * np.pi, 100)\n",
    "    y = amplitude * np.sin(x)\n",
    "    plt.plot(x, y)\n",
    "    plt.ylim(-3, 3)\n",
    "    \n",
    "interact(plot_sin, amplitude=ipywidgets.FloatSlider(0., min=-3, max=3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f073e99e2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_sin(amplitude=0.):\n",
    "    x = np.linspace(0, 5 * np.pi, 100)\n",
    "    y = amplitude * np.sin(x)\n",
    "    plt.plot(x, y)\n",
    "    plt.ylim(-3, 3)\n",
    "    \n",
    "interact(plot_sin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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x6qtWnps927uhqQMG2Mbq8+ZxuGsQMbFH1Cef2CiF2bNtmnm6br/d6vf/+Ef6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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f073e298438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_sin(amplitude, theta, offset):\n",
    "    x = np.linspace(0, 5 * np.pi, 100)\n",
    "    y = amplitude * np.sin(x + theta) + offset\n",
    "    plt.plot(x, y)\n",
    "    plt.ylim(-3, 3)\n",
    "    \n",
    "interact(plot_sin, amplitude=1., theta=0., offset=0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ERAHDxE5EFDBM7EREAcPETkQUMEzsREQBw8RORBQwTOxERAHDxE5EFDBM7ERE\nAcPETkQUMEzsREQBw8RORBQwTOxERAHDxE5EFDBM7EREAcPETkQUMEzsREQBw8RORBQwTOxERAHD\nxE5EFDBM7EREAcPETkQUMEzsREQBw8RORBQwUSV2EXlKRJaKyGIRmSIiJ3kVGBERlU60LfZ+qnqe\nqp4PYBKAXh7E5FQoFHIdQrEwTu8kQowA4/RaosRZGlEldlXdXeDTYwDkRxeOe4nyy2ac3kmEGAHG\n6bVEibM0ykZ7ABF5GsDfAewA0DjqiIiIKCpFtthF5BMRWVbgsTz8b3MAUNXHVLUWgJEAOsU6YCIi\nOjJRVW8OJHIqgMmqWq+Q73tzIiKiJKOqUpLnR9UVIyJnquq68Kc3AcjyKjAiIiqdqFrsIjIGQB3Y\noGk2gHtU9TuPYiMiolLwrCuGiIj8IeYzT0WkmYisEpE1IvJIrM9XGiJSU0Smi0hmeHC4s+uYjkRE\nUkRkkYhMcB1LYUSkkoi8LyJZ4de1oeuYDkdEHhSRFeGCgJEiUs51TAAgIv8Vka0isqzA1yqLyFQR\nWS0iH4tIJZcxhmM6XJz9wr/3JSIyVkSOcxljOKZD4izwvW4iki8iJ7iI7aBYDhuniHQKv6bLReT5\noo4T08QuIikABgNoCqAugNtF5OxYnrOU9gPoqqp1AVwK4D6fxhnRBcBK10EU4SXYYPo5AM7DEcZf\nXBGRGrBKrgtU9VzYmFOG26h+NQT2vimoO4BpqnoWgOkAesQ9qkMdLs6pAOqqan0Aa+HfOCEiNQFc\nDetK9oND4hSRdADNAdQLF6e8UNRBYt1ibwBgrapmq2oegFEAbozxOUtMVbeo6pLwx7thSegUt1Ed\nXvgP8ToAb7qOpTDhFtrlqjoEAFR1v6ruchxWYcoAOEZEygKoAGCz43gAAKo6E8CPB335RgDDwh8P\ngxUsOHW4OFV1mqpGJivOBVAz7oEdpJDXEwAGAngozuEUqpA47wXwvKruDz/n+6KOE+vEfgqAjQU+\n/xY+TZgRIlIbQH0AX7qNpFCRP0Q/D46cBuB7ERkS7jJ6Q0TKuw7qYKq6GcAAABsAbAKwQ1WnuY3q\niKqp6lbAGiMAqjmOpzjaA/jIdRCHIyItAGxU1eWuYylCHQBXiMhcEflMRC4q6ge4umMBIlIRwBgA\nXQ5aLsEXROR6AFvDdxcSfvhRWQAXAHhVVS8AsAfWjeArInI8rBWcBqAGgIoi8je3UZWIny/uEJGe\nAPJU9R1Edee9AAAB5klEQVTXsRws3NB4FL9f38rP76fKqnoJgIcBjC7qB2Kd2DcBqFXg85rhr/lO\n+FZ8DIC3VfUD1/EUohGAFiLyNYB3ATQWkeGOYzqcb2EtoQXhz8fAEr3fXAXga1XdrqoHAIwDcJnj\nmI5kq4hUB4DwSqo5juMplIi0hXUZ+vVCeQaA2gCWisg3sNy0UET8eBe0Efa3CVWdDyBfRE480g/E\nOrHPB3CmiKSFqw0yAPi1kuMtACtV9SXXgRRGVR9V1VqqejrstZyuqn93HdfBwt0FG0WkTvhLTeDP\nwd4NAC4RkaNFRGBx+mmQ9+C7sgkA2oY/vhOAXxogv4tTRJrBugtbqGqus6gO9WucqrpCVU9S1dNV\n9TRYY+R8VfXDxfLg3/t4AFcCQPg9laqqPxzpADFN7OFW0P2wUfJMAKNU1U9vHACAiDQCcAeAK8Nr\nyy8K/3FS6XUGMFJElsCqYp51HM8hVHUe7G5iMYClsDfTG06DChORdwDMBlBHRDaISDsAzwO4WkRW\nwy5CRZa9xVohcb4CoCKAT8LvpdecBolC4yxI4YOumELifAvA6SKyHMA7sEUXj3wcTlAiIgoWDp4S\nEQUMEzsRUcAwsRMRBQwTOxFRwDCxExEFDBM7EVHAMLETEQUMEzsRUcD8P3d/GrR2/ixWAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f073e0e2080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_fun(fun, amplitude=1., theta=0., offset=0.):\n",
    "    x = np.linspace(0, 5 * np.pi, 100)\n",
    "    y = amplitude * fun(x + theta) + offset\n",
    "    plt.plot(x, y, label=fun.__name__); plt.ylim(-3, 3); plt.legend()\n",
    "    \n",
    "interact(plot_fun, fun={'sin': np.sin, 'cos': np.cos})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conclusion:  Functional Programming is as simple as apply(fun, data)!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}