0. numpy_pandas_matplotlib_tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "=================================================================================================================\n",
    "# Tutorials: Numpy, Pandas, Matplotlib, and scikit-learn \n",
    "\n",
    "##### D.Vidotto, Data Mining: JBI030 2019/2020\n",
    "\n",
    "\n",
    "================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With this notebook, we are going to explore the main functionalities of `numpy`, `pandas`, `matplotlib` and `scikit-learn`. While we will see (some of) the most useful function for the Data Mining course, this notebook is by no means an exhaustive guide to such libraries. It should be taken as a starting point to a more in-depth self-study. Various tutorials can be find online. Particularly useful are the libraries *documentations*, that are linked at the end of this document. \n",
    "\n",
    "This notebook assumes that the reader has already a basic knowledge of Python and its built-in functions. Examples and functions reported in this notebook are taken from the book [Python for Data Analysis](http://shop.oreilly.com/product/0636920023784.do) (McKinney 2012, 2nd Edition, *O'Reilly Media*). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Numpy\n",
    "\n",
    "*NumPy* (short for \"numerical Python\") is a library that allows for scientific computing in Python. It contains functionalities for multidimensional arrays, high-level functions and random number generations. Most of the computational packages written in Python are built on top of NumPy and use NumPy arrays. \n",
    "\n",
    "In Numpy you can find: \n",
    "\n",
    "* numpy arrays, a special multidimensional arrays that support fast computations and high-level arithmetic operations\n",
    "* mathematical operations that work on entire numpy arrays without need to write cumbersome loops\n",
    "* linear algebra operations \n",
    "* random number generators \n",
    "\n",
    "In Python, we can load the module in this way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Numpy arrays \n",
    "\n",
    "**Creating arrays**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6. , 7.5, 8. , 0. , 1. ])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a numpy array from a Python list\n",
    "data1 = [6, 7.5, 8, 0, 1]\n",
    "arr1 = np.array(data1)\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 4],\n",
       "       [5, 6, 7, 8]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2-dimensional array\n",
    "data2 = [[1, 2, 3, 4], [5, 6, 7, 8]]\n",
    "arr2 = np.array(data2)\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arr2 dimension: 2; arr2 dimension-specific lengths: (2, 4)\n"
     ]
    }
   ],
   "source": [
    "arr2_dim = arr2.ndim\n",
    "arr2_shape = arr2.shape\n",
    "print(\"arr2 dimension: {}; arr2 dimension-specific lengths: {}\".format(arr2_dim, arr2_shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numpy arrays support various `dtypes` (data-types) (more on this below). If not manually specified, numpy tries to automatically infer the dtypes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also initialize arrays of 0's, 1's, and create sequences of numbers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10,)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(10).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones = np.ones((3, 6))\n",
    "ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 6)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3,  5,  7,  9, 11, 13])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Start at 1, end at 15, jumpy by 2: \n",
    "np.arange(1, 15, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.52631579,  1.05263158,  1.57894737,  2.10526316,\n",
       "        2.63157895,  3.15789474,  3.68421053,  4.21052632,  4.73684211,\n",
       "        5.26315789,  5.78947368,  6.31578947,  6.84210526,  7.36842105,\n",
       "        7.89473684,  8.42105263,  8.94736842,  9.47368421, 10.        ])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 20 equi-distant points between 0 and 10\n",
    "np.linspace(0, 10, 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**dtypes**. You can manually specify the **dtypes** of numpy arrays: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(dtype('float64'), dtype('int32'))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = np.array([1, 2, 3], dtype=np.float64)\n",
    "arr2 = np.array([1, 2, 3], dtype=np.int32)\n",
    "(arr1.dtype, arr2.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also convert an array's dtype:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([1, 2, 3, 4, 5])\n",
    "arr.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float_arr = arr.astype(np.float64)\n",
    "float_arr.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can find a list of supported **dtypes** [here](https://docs.scipy.org/doc/numpy/user/basics.types.html). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Arithmetic operations**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [4., 5., 6.]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  4.,  9.],\n",
       "       [16., 25., 36.]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Array multiplications\n",
    "arr * arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Difference between arrays\n",
    "arr - arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.5       , 0.33333333],\n",
       "       [0.25      , 0.2       , 0.16666667]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Division\n",
    "1 / arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 1.41421356, 1.73205081],\n",
       "       [2.        , 2.23606798, 2.44948974]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Exponentiation\n",
    "arr ** 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  4.,  1.],\n",
       "       [ 7.,  2., 12.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Array comparisons (returns booleans)\n",
    "arr2 = np.array([[0., 4., 1.], [7., 2., 12.]])\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False,  True, False],\n",
       "       [ True, False,  True]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2 > arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Indexing**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can assign multiple indices to a value: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4, 12, 12, 12,  8,  9])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[5:8] = 12\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A colon is used to take all the elements of the array: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([64, 64, 64, 64, 64, 64, 64, 64, 64, 64])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[:] = 64\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With two-dimensional arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: each dimension is also called **axis**; for instance, we can think of two-dimensional arrays as having the axis of the rows and the axis of the column. \n",
    "\n",
    "<img src=\"./img/numpy_pandas_matplotlib_tutorial/numpy_axes.png\" width=\"300\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Call the third element of the 2D array (note: it is itself an array)\n",
    "arr2d[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Third element of the first array\n",
    "arr2d[0][2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ...which is equivalent to: \n",
    "arr2d[0, 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Three-dimensional array: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[42, 42, 42],\n",
       "        [42, 42, 42]],\n",
       "\n",
       "       [[ 7,  8,  9],\n",
       "        [10, 11, 12]]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[0] = 42\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 9])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3d[1, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Slicing**.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr[1:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Take up to the second element of the 2d-array\n",
    "arr2d[:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Exclude first elements of first two arrays:\n",
    "arr2d[:2, 1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Return up to the second element of the second array: \n",
    "arr2d[1, :2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 6])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Take third elements of first two arrays: \n",
    "arr2d[:2, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [4],\n",
       "       [7]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Take first elements of all arrays: \n",
    "arr2d[:, :1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0],\n",
       "       [4, 0, 0],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Assign 0 to the first two arrays (excluding their first element)\n",
    "arr2d[:2, 1:] = 0\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0],\n",
       "       [4, 0, 0],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 1],\n",
       "       [0, 0, 4],\n",
       "       [9, 8, 7]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Take all elements in first and second axes, second axis in reversed order\n",
    "arr2d[:,::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Boolean Indexing**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'], dtype='<U4')"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "# Generate 28 random numbers and allocate them in a 2dimensional 7x4 array \n",
    "# (more on random number generation later): \n",
    "data = np.random.randn(7, 4)\n",
    "names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.91110064,  0.820531  ,  0.64707197,  1.26065103],\n",
       "       [-1.28708197,  0.9321176 ,  0.70584248, -0.17236889],\n",
       "       [ 0.183099  ,  0.96635551, -1.09458499,  1.48246256],\n",
       "       [ 0.05062965, -0.24421544,  0.37605325,  0.70758932],\n",
       "       [-0.74159525,  1.80924983, -0.3710081 , -0.22811887],\n",
       "       [ 0.07303507, -1.1131136 ,  1.14163873, -1.01840334],\n",
       "       [-0.55877829,  0.96607286,  0.07932958,  0.51920984]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True, False, False, False])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names == 'Bob'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.91110064,  0.820531  ,  0.64707197,  1.26065103],\n",
       "       [ 0.05062965, -0.24421544,  0.37605325,  0.70758932]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Which data rows (first axis) correspond to 'Bob'? \n",
    "data[names == 'Bob']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.64707197, 1.26065103],\n",
       "       [0.37605325, 0.70758932]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Exclude first two columns\n",
    "data[names == 'Bob', 2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.26065103, 0.70758932])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pick fourth column\n",
    "data[names == 'Bob', 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True,  True, False,  True,  True,  True])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Select everything but Bob\n",
    "names != 'Bob'        # Equivalent: data[~(names == 'Bob')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.91110064,  0.820531  ,  0.64707197,  1.26065103],\n",
       "       [ 0.183099  ,  0.96635551, -1.09458499,  1.48246256],\n",
       "       [ 0.05062965, -0.24421544,  0.37605325,  0.70758932],\n",
       "       [-0.74159525,  1.80924983, -0.3710081 , -0.22811887]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rows corresponding to multiple names\n",
    "mask = (names == 'Bob') | (names == 'Will')\n",
    "mask\n",
    "data[mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.91110064, 0.820531  , 0.64707197, 1.26065103],\n",
       "       [0.        , 0.9321176 , 0.70584248, 0.        ],\n",
       "       [0.183099  , 0.96635551, 0.        , 1.48246256],\n",
       "       [0.05062965, 0.        , 0.37605325, 0.70758932],\n",
       "       [0.        , 1.80924983, 0.        , 0.        ],\n",
       "       [0.07303507, 0.        , 1.14163873, 0.        ],\n",
       "       [0.        , 0.96607286, 0.07932958, 0.51920984]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set to 0 negative values: \n",
    "data[data < 0] = 0\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fancy Indexing**. Fancy indexing corresponds to indexing using arrays of integers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [2., 2., 2., 2.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [4., 4., 4., 4.],\n",
       "       [5., 5., 5., 5.],\n",
       "       [6., 6., 6., 6.],\n",
       "       [7., 7., 7., 7.]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initialize 2d empty array\n",
    "arr = np.empty((8, 4))\n",
    "# Fill each row with row index\n",
    "for i in range(8): \n",
    "    arr[i] = i \n",
    "arr   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 1.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [4., 4., 4., 4.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [6., 6., 6., 6.]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make a sub-selection of the rows, in a specific order, with an array of indices\n",
    "arr[[1, 0, 4, 3, 6]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5., 5., 5., 5.],\n",
       "       [3., 3., 3., 3.],\n",
       "       [1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Negative indices select rows from the end\n",
    "arr[[-3, -5, -7]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15],\n",
       "       [16, 17, 18, 19],\n",
       "       [20, 21, 22, 23],\n",
       "       [24, 25, 26, 27],\n",
       "       [28, 29, 30, 31]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(32).reshape((8, 4))\n",
    "# Reshape changes the dimensions of the arrays; more on this later\n",
    "arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Passing multiple indices of arrays creates *tuples of indices* (for example, the first element returned in the next query is the element (1,0); check this yourself!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4, 23, 29, 10])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pass multiple arrays of indices:\n",
    "arr[[1,5,7,2], [0,3,1,2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To select instead rows 1,5,7 and 2 and columns 0,3,1, and 2 you can do the following: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  7,  5,  6],\n",
       "       [20, 23, 21, 22],\n",
       "       [28, 31, 29, 30],\n",
       "       [ 8, 11,  9, 10]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[[1, 5, 7, 2]][:, [0, 3, 1, 2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Transposing arrays**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(15).reshape((3, 5))\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  5, 10],\n",
       "       [ 1,  6, 11],\n",
       "       [ 2,  7, 12],\n",
       "       [ 3,  8, 13],\n",
       "       [ 4,  9, 14]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Transpose: \n",
    "arr.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Element-Wise Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(10)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 1.        , 1.41421356, 1.73205081, 2.        ,\n",
       "       2.23606798, 2.44948974, 2.64575131, 2.82842712, 3.        ])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Element-wise square rootoperations\n",
    "np.sqrt(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+00, 2.71828183e+00, 7.38905610e+00, 2.00855369e+01,\n",
       "       5.45981500e+01, 1.48413159e+02, 4.03428793e+02, 1.09663316e+03,\n",
       "       2.98095799e+03, 8.10308393e+03])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Element-wise exponential\n",
    "np.exp(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.32557655,  0.4775606 , -0.05052346, -0.9665265 , -0.57482342,\n",
       "        1.18583366, -0.29431782,  0.95184903])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initialize two (random) arrays\n",
    "x = np.random.randn(8)\n",
    "y = np.random.randn(8)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.87756559, -0.78127901,  0.2226049 ,  1.65396048,  1.2209076 ,\n",
       "        0.26480292, -0.06218757,  0.68308963])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.32557655,  0.4775606 ,  0.2226049 ,  1.65396048,  1.2209076 ,\n",
       "        1.18583366, -0.06218757,  0.95184903])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Element-wise maximum of elements in x and y\n",
    "np.maximum(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.32557655, 0.4775606 , 0.05052346, 0.9665265 , 0.57482342,\n",
       "       1.18583366, 0.29431782, 0.95184903])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Absolute value\n",
    "np.abs(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.9665265040277623, 1.1858336559974487)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Max. and min. of an array\n",
    "(np.min(x), np.max(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other useful functions are: \n",
    "\n",
    "* function that take one array as argument, such as `square`, `log`, `ceil`, `floor`, `isnan`, `isfinite`, `sin` and `cos`\n",
    "* function that take two arrays as arguments, such as `add`, `subtract`, `multiply`, `divide`, `power`, `maximum`, `minimum`, `greater`, `less`\n",
    "\n",
    "You can find further information about them (and many more) in the [documentation](https://docs.scipy.org/doc/numpy/reference/routines.math.html). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Vectorized operations \n",
    "**2D Functions Evaluation**. *Vectorized operations* allows performing operations on arrays without writing loops, replacing them with specific array expressions. Let's see an example here. We will make use of the `meshgrid` function, which takes two 1D arrays -x and y- as inputs, and produces rectangular grids across all the (x,y) coorinates of its input vectors. The following figure might help to better understand the functioning of meshgrid: \n",
    "\n",
    "\n",
    "<img src=\"./img/numpy_pandas_matplotlib_tutorial/numpy_meshgrid.png\" width=\"500\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       ...,\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99],\n",
       "       [-5.  , -4.99, -4.98, ...,  4.97,  4.98,  4.99]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points = np.arange(-5, 5, 0.01)    # 1000 equally spaced points\n",
    "# np.meshgrid creates a rectangular grid out of an array of x values and an array of y values\n",
    "xs, ys = np.meshgrid(points, points)\n",
    "xs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-5.  , -5.  , -5.  , ..., -5.  , -5.  , -5.  ],\n",
       "       [-4.99, -4.99, -4.99, ..., -4.99, -4.99, -4.99],\n",
       "       [-4.98, -4.98, -4.98, ..., -4.98, -4.98, -4.98],\n",
       "       ...,\n",
       "       [ 4.97,  4.97,  4.97, ...,  4.97,  4.97,  4.97],\n",
       "       [ 4.98,  4.98,  4.98, ...,  4.98,  4.98,  4.98],\n",
       "       [ 4.99,  4.99,  4.99, ...,  4.99,  4.99,  4.99]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ys"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's suppose we want to calculat the function $\\sqrt{(x^2 + y^2)}$ along this grid. We can do as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "z = np.sqrt(xs ** 2 + ys ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the results with a *contour* plot, which can be drawn with `matplotlib.pyplot` (more details about this module in the next sections). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5BcOS9gZuAC41s229f2+/mXcOYMlRB43saSVWczlZ+thLE6/z3BG7V9CSatR5QXEd3zGxcdMBrFi+pdLH8CBp0EnajVbIXWdmN6Zsi1feq4hpgm3UfeQUfCEPyYJOkmh9cN56M7sqVTsmVWc15zXkZhFu496/x9CLqi4/Kc/RnQy8CzhF0v3tn7Pmc4dNehUphaWPvVR5yHl4zHF4PQiF/pJVdGZ2FxDvnh7A00DyEDSdNnis8KoW3wc7f8lfjMhJXdNWLyHnIeB6eQq8+KSTfLi4vCT44zHkunmZ0tZ1UKr6IFv6aZ9igq7qHdWUas5LgIwrp7aGdIoJujB/uYZG6nanPjiF0SLoHEk5YFKHxXzlVolOI6av0ysi6EqZtqZSUkCkei5R1flWRNCVIMVAKbUKKvE5hfmJoGuo0sMgxfOr42AV09fpRNCNUMe0te5qrvSQ62jK8wyjZR90pR6BwmzUHXZxrs6n7IMud1HNVa+051z6i2NViKAborQOVdqA9yr3qq7EWVK81zWhOgdE00Nu6WMvuXh/bJgdSRuB54FXgB1mtmrQsllXdCUeearQ9JDrKGk7lDbbmIdfNbPjhoUcZB50Vaq6I+U+vclVXWEX+9eXmLoWrqQqJuRn+/aF0868lkla13V7rv39Md0MuE2SAZ/t8/fXRNAVLEKuv7rO1+X8eXUOPl5966jpKPDPzGyzpAOBNZI2mNm3+i2Y7dQ15/NzMa1Jr4SDQNPP05nZ5va/TwM3AScOWjbboKtSCR2ohIEcwiCS9pK0pPN/4AzgoUHLR9CFxqrjYBDVe2XeANwl6QHgO8CtZva1QQvHObqa1dHxo5oLpTOzHwDHjrt8VHSh0XI/KFR5miXn8+C9oqLrkfv5OU8Dd9GGTQP/tn3l8hpbklbOr76WIsugK+lIU5ph4TZoudShF28PK1+WQZerqs/Ppazmxg24UeumDr1QpjhHF+Zl0YZN8wq5fvcXwqxF0IWpVRVKKcKu6mq4ymo+9/PKdYigK0Td09aqw2jWlWJotgi6LlUeGUu6cLTOAKrzsTy9Yu1FKS/8RdAVoM4BmqLKisouzFd2QVfKESZHETghV9kFXUgjdcilfvxZKOn0RW4i6MJIXkKmjnbEeboyRdDVoMojeQzMAHGJySgRdGEoL9Vch7f2hDxE0LXFETGEckXQhYG8Vk9VtytOB5Qngi5jMSDzE6+8phFBF7LktdosUQnXrkbQhb4iSEJJIugqFlOVENKLoAvZiqozjCuCLuwiAiRe6ClNBF0IoXgRdCGE4mUVdNu3x3f5hBAmlzToJK2W9D1Jj0r6UMq2hJC7pr2NUdICSfdJumXUssmCTtIC4NPAmcDRwIWSjk7VntzEyfIQuARYP86CI4NO0u9I2m/eTdrVicCjZvYDM9sO/CVwXgWPEwoWrxA3k6TlwNnA1eMsP85JrzcAayXdC1wDfN3MZnEV7MHAj7pubwLe2ruQpIuAiwAW7L/vDB42lCS+8No3bde0U+plktZ13Z4zs7mu258ELgeWjHNnIys6M/s94Ejgc8C7gX+Q9FFJR4zd5HkwszkzW2VmqxYs2auOhwwhpLe1M+7bP6+FnKRzgKfN7J5x72ysc3TtCu6p9s8OYD/gekkfm6ztO9kMHNJ1e3n7d2EMzx2xe+omhJDKycC5kjbSOuV1iqRrh60wzjm6SyTdA3wM+FvgF83sfcAvAf9iHo1dCxwp6XBJi4ALgJvncX8hNNpLh25P3YRamNkVZrbczFbQyo1vmNk7h60zzjm61wO/bmaP9zzYq+0SctrG7pB0MfB1YAFwjZk9PGydRYt2TPtwIYQGGxl0ZvbhIX8b66XdIet/FfjqfO4jhNBcZnYncOeo5bJ6Z0SoR7ySGedASxNBF0IoXgRdxZ4/TKmbUKyoPMO4IuhCCMWLoAt9RbUUShJBl7EmnzDPNYhzPJWxYvmW1E2Ytwi6MFCuYRJCrwi6tqZcVV6CqgO4yZVyqSLowlBR1YUSRNCFrETwhmlE0NWgyhPQdUyzIlz8i1Mvw0XQhbF4CLs62hDn58qUXdCV8FJ3mJyHoJ2vHC8tKUV2QRd2VVcVkipsSgi5kFYEXZhI3aFT5+PFtLVcEXRdqjyhW9K0pa7wiUouvVJOFUXQFaLuaqTqECot5Eo60OVonI9SD6GvThjN8rtVUwVcztPWuLRktKjoCpJqsG5fuXwmAVVaFRf8yLKiW7F8Cxs3HZC6GRN7/jCx5PFZfPe3T9NUeB7CLedqLowny6Cr0kuHbp/2m8VDm4fw8iTOz6UXU9fCRHUymdheg5XyiitE0NUuju5hluKFiPFE0BUoqpTx1LGd4sDmQwRdHyUcJSPsQviZbIMu5/MHcZRPLw4E+ZK0WNJ3JD0g6WFJ/2XUOtkGXRgtBnNaVR/QSph5TOkl4BQzOxY4Dlgt6aRhK8TlJaFx4gAwmucZk5kZ8JP2zd3aP0MvUI2gG6Dq6+nqunj4uSN2Z+ljL1X+OLmIkKvXgu1M28+XSVrXdXvOzOY6NyQtAO4B3gR82szuHnZnEXQNEGFXv5i2zttWM1s16I9m9gpwnKR9gZskHWNmDw1aPutzdJ7La2+ikoltUCIzexa4A1g9bLmsgy538eprfeoMudz3q/cCQtIB7UoOSXsApwMbhq0TQTdEadODplY0TX3eBXsjcIekB4G1wBozu2XYCnGOLrG6P9GkaefrSgy50g7AkzKzB4HjJ1kn+4rOe5ntUYmDv58UzzP3aWupsg+6qtVx9EwxOEoPu9KfX1VKLRwi6Bqs1DBI9bzqOGA1fdo6rQg6J1JNeUoLu9KeT5iNIoKu6nK79KNoKeGQ8nlENedbEUFXipQnsnMPu9JDrg6lnp+DuLxkbE34LolOWOR0+UnuAR3qUUxFV8rRyEN1kEt4eGhnXfsrpq3zExWdQx6+FtFzdech4EpTSqEwSATdBJowfe3lKfC8BVxUc/koZuoKZR2VPExhuz13xO7JgiblYw/ibf+E4ZIEnaSPS9og6UFJN3U+iSAHdR5dPQ6mTujUETweA65EJRUIg6Sq6NYAx5jZm4HvA1ckakeYhypCr84gnVadB6CYts5GknN0ZnZb181vA+fP6r5XLN/Cxk0HzOru+qrzXJ2HFybG0S+Yhp3X8xxkw3isssNoHl6MeC/wpUF/lHQRcBHA7gcuqatNruQSdr1yDTMv6qjmmjBthQqnrpJul/RQn5/zupa5EtgBXDfofsxszsxWmdmq3fbds6rmTqzuKUVUEunFPshXZRWdmZ027O+S3g2cA5za/vqymalj+hqape6Qi3Nzs5XqVdfVwOXAuWb20xRtmIWo6pqh1O3elGkrpHvV9U+BJcAaSfdL+sysH6DUnVjqoPMqxfaOam72Ur3q+qYUj1uFFO+WyPXFidyUfFAptRAYpKh3RjRJyYOwyaKaq0bRQVfXUStV54ywq05s27IUHXRNEANy9lJt07oOmE2btkIDgq70qg4i7Gap9JBrquKDrk4RdnlrwjZsYjUHDQm6puzcJgzUKjx/mJJuu6jmJiPpEEl3SHpE0sOSLhm1TiOCrk6pO22E3WSatL0KOuDvAC4zs6OBk4D3Szp62AoRdAVq0uCdDw/bKfWBMUdm9qSZ3dv+//PAeuDgYet4+PSSWtT5/lcPH7neGcRxYXF/TQu5VNXcghdt2o/hXyZpXdftOTOb611I0grgeODuYXfWmKCrm4ewg3gXRS8PAQdRyY1hq5mtGraApL2BG4BLzWzbsGUbNXWt+6jmpTN7GdypNXU7FHRu7jWSdqMVcteZ2Y2jlo+KriGaPJX1FnBeDoC5kiTgc8B6M7tqnHUaVdFBc6u6Dm+Dvmrenm/d/aHEag44GXgXcEr704/ul3TWsBWioquBl/N1HU2o7rwFXJgdM7sLmGgHN66igzRHOW+VHaS/ULYKnp9TVHPpNDLoIDpBN8/hMC7vz8Hjga5JYupaI29T2F45Tmk9h1tHipCLA/nOGh10Kb5Ex3vYwc7h4TH0cgi3jqjkfGh00KWSQ9h1eAm9nMIttajmdtX4oEv11Yg5hV1Hb9hUHXy5h1tMWf1ofNCllGPYdesXRNOEX+6B1k9MWX2JoCPtF17nHna9SgytSaUKuajmBmvs5SW9UnaSOPqXI/alTxF0IcxIypCLam64CLouqau6qAbyFSHnWwRdj9SdJsIuP7HP/IugcygGTj5S76vUB+ZcRND14aHzpB5AYbTU+8hDP81FBN0AHjpR6oEU+ovzqfmJoHMuBpQvXvaHhwNxTrIKun0Wvljr43npTF4GV9N52Q9198vTD9pQ6+NVIaugS8FT2HkZaE3kZdt76Y+5yS7oUhxdPHUuLwOuKZp+gCmhmoMMgw4i7Jo88OrkbTt76oO5yTLoQlQaVfO2bVOEXCnVHGQcdE2v6jq8DcjceTyAeOx3uck26FLx2Ok8Ds7ceN2GqfpbSdUcZB50qXaGx7ADv4PVu9hmOyst5CDzoIMIu35i4I7H+4HBcx/LTfZBl5Lnjuh9EKeUw7aJKetwkq6R9LSkh8ZZvoigy2XnpJDDoK5LLtsiQm4snwdWj7twEUEHMYUdJZdBXoWcnnsu/Sk1M/sW8ONxl48vx5mBlF+uM6nuAV/Sl/L0k0u4daQMuaoKBb24nUUbNk2z6jJJ67puz5nZ3LTtKCroTj9oA2ueWpnksXMKu45OEJQUeLmFW0eJITdPW81s1azurJipa0fKnZbrtKMztcs1JHJvf679JidJg07SZZJM0rKU7Zil3Dttd2h4Do4c2jiO1P3FaTU3c8mCTtIhwBnAE7O+79Q7L3XnnSUvweelHbOUup+kHifzIemLwN8DR0naJOm3hi2f8hzdJ4DLga9Ucecpz9dBnufsxjEoZGZ1nq+UEBsldcjlzswunGT5JEEn6Txgs5k9IClFE2pRatj105SAmgUPIZdzNTeNyoJO0u3AQX3+dCXwu7SmrePcz0XARQBL37jHRG1IXdXBzzp1UwIvDBchl0Zl5+jM7DQzO6b3B/gBcDjwgKSNwHLgXkn9QhEzmzOzVWa2aq/9Jp8eedmpHjp4SMtDH/AyHupW+4sRZvZdMzvQzFaY2QpgE3CCmT1V1WN62bkeOnqo34rlW2LfJ1bcdXSDRNiFFDztby9jIIXkQdeu7LambkedPHX+UB1P+7nJIQcOgq5OnnZ2TGfK5mnfeur3qTQq6MDfTvc0IML8eTuAeevvqTQu6MDfzvc0MML0Yj/61cigA59hFwMlXx73nbc+nlJjgw58dgSPAyYM5vUA5bFvp9TooPPK6+AJO/O6jyLkdtX4oPPcKbwOpKbzfCDy3J9TanzQge/O4XlQNY33feG5H6cWQdfmvZN4H2Sl877tvfff1CLouuTQWSLw6pXD9s6h36YWQdcjl07jffDlLoeAg3z6a2oRdH3k0nlyGYw5yWmb5tJPPSjq6w5nycOHdo6re2DGB3xOJ5dw64iQm0xUdEPk2Jlyqkg8yHF75dgvU4uKboScKrtu8RHug+UWbN0i5KYTQTeGXMMOYlrbLeeAgwi5+YigG1POYdfRxNDLPdw6IuTmJ4JuAiWEXUfJoVdKuHVEyM1fBN2EOp2ulMCD/EOvtGDrFiE3G1kF3X4Lfpq6Ca8pqbrr1i80PIVfyaHWy0vInb/Pvfxe6kb0kLQa+BSwALjazP5w2PJZBR20Nvr1205I3Qyg3LDrNShcqgzAJgVaLy8BB63x5o2kBcCngdNpfV3qWkk3m9kjg9bJLuggws6LScJo46YDGh1e4/IUco6dCDxqZj8AkPSXwHnAwKCTmdXUtvmTtAV4vIK7Xgbk9pWL0ebq5dZeqK7Nh5nZxCW8pK/RatOkFgMvdt2eM7O59n2eD6w2s99u334X8FYzu3jQnWVV0U2zocchaZ2ZrarivqsSba5ebu0Ff202s9Wp2wDxFrAQQn42A4d03V7e/t1AEXQhhNysBY6UdLikRcAFwM3DVshq6lqhudQNmEK0uXq5tRfybPNEzGyHpIuBr9O6vOQaM3t42DpZvRgRQgjTiKlrCKF4EXQhhOJF0PWQdJkkkzTNtT+1kvRxSRskPSjpJkn7pm5TP5JWS/qepEclfSh1e0aRdE9AgNAAAAKmSURBVIikOyQ9IulhSZekbtM4JC2QdJ+kW1K3xZsIui6SDgHOAJ5I3ZYxrQGOMbM3A98Hrkjcnl10vV3nTOBo4EJJR6dt1Ug7gMvM7GjgJOD9GbQZ4BJgfepGeBRBt7NPAJcDWbxCY2a3mdmO9s1v07qeyJvX3q5jZtuBztt13DKzJ83s3vb/n6cVHgenbdVwkpYDZwNXp26LRxF0bZLOAzab2QOp2zKl9wJ/nboRfRwM/Kjr9iach0Y3SSuA44G707ZkpE/SOki/mrohHjXqOjpJtwMH9fnTlcDv0pq2ujKszWb2lfYyV9Kabl1XZ9tKJ2lv4AbgUjPblro9g0g6B3jazO6R9I7U7fGoUUFnZqf1+72kXwQOBx6QBK0p4L2STjSzp2ps4i4GtblD0ruBc4BTzedFkRO/XccDSbvRCrnrzOzG1O0Z4WTgXEln0Xoz/D6SrjWzdyZulxtxwXAfkjYCq8zM9SdXtD988Crg7Wbm8jOQJC2k9ULJqbQCbi3wL0ddyZ6SWke7Pwd+bGaXpm7PJNoV3QfN7JzUbfEkztHl7U+BJcAaSfdL+kzqBvVqv1jSebvOeuCvPIdc28nAu4BT2tv1/na1FDIVFV0IoXhR0YUQihdBF0IoXgRdCKF4EXQhhOJF0IUQihdBF0IoXgRdCKF4EXShUpLe0v68vMWS9mp/vtsxqdsVmiUuGA6Vk/Rfab0Hcw9gk5n9t8RNCg0TQRcq1/5KurW0vnn9l83slcRNCg0TU9dQh/2BvWm9L3dx4raEBoqKLlRO0s20Pln4cOCNZnZx4iaFhmnU59GF+kn618DLZvaF9vdH/J2kU8zsG6nbFpojKroQQvHiHF0IoXgRdCGE4kXQhRCKF0EXQiheBF0IoXgRdCGE4kXQhRCK9/8B5PyGYnHOPWoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(5,5))\n",
    "contour = plt.contourf(xs, ys, z, cmap=\"viridis\")\n",
    "plt.title(r\"$\\sqrt{x^2 + y^2}$ in 2D\", fontsize=15)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.colorbar(contour)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Vectorized Conditional Operations**. The `where` function of Numpy can be used in two ways:\n",
    "\n",
    " 1. First, as a [*ternary operator*](https://book.pythontips.com/en/latest/ternary_operators.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.1, 2.2, 1.3, 1.4, 2.5])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1.1, 1.2, 1.3, 1.4, 1.5])\n",
    "y = np.array([2.1, 2.2, 2.3, 2.4, 2.5])\n",
    "# cond is an array of booleans\n",
    "cond = np.array([True, False, True, True, False])\n",
    "result = np.where(cond, x, y)\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, `where` returns the elements in the second argument when the conditions are True, otherwise it returns the elements of the third argument (importantly, neither the second nor the third argument need to be arrays; they can be scalars). \n",
    "\n",
    "2. Second, it can be used to find the indices of the array for which the condition is True:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2, 3, 4]),)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(x >= 1.25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Mathematical and Statistical Vectorized Operations**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.30396709, -0.61542252,  0.31554751, -0.21808124],\n",
       "       [-0.16895233,  1.87108191, -1.39124697,  1.10805514],\n",
       "       [ 0.09943259, -1.34923242, -0.49618346,  1.97231423],\n",
       "       [ 1.07100434, -0.32634419, -0.4949362 , -0.7182656 ],\n",
       "       [-1.71621568, -0.26912039,  0.38202512, -0.79030374]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Generate a 5x4 array of random numbers\n",
    "arr = np.random.randn(5,4)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.0215438399307334"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the mean of the array\n",
    "arr.mean()    # Or equivalenty: np.mean(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.19650271,  0.35473444,  0.05658274, -0.11713541, -0.59840367])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find the mean of each row\n",
    "arr.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.430876798614668"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sum of the elements of the array\n",
    "np.sum(arr)    # Equivalent: arr.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.589236 , -0.6890376, -1.684794 ,  1.3537188])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sum of each column\n",
    "np.sum(arr, axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other important statistical functions that can be computed (across the whole array, or a specific axis) are:\n",
    "\n",
    "* std, var: for standard deviation and variance\n",
    "* min, max: for minimum and maximum\n",
    "* argming, argmax: for indices of minimum and maximum elements\n",
    "* cumsum, cumprod: for cumulative sums and products "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Vectorized Operations on Boolean Arrays**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "54"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(100)\n",
    "# Find out how many positive values are in the array just generated\n",
    "(arr > 0).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Sorting**. `sort(array)` creates a new array, while `array.sort()` sorts the array *in-place*. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.59985538, -0.5363037 , -0.49080731, -0.17782413, -0.12335404,\n",
       "        0.73170567])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(6)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.59985538, -0.5363037 , -0.49080731, -0.17782413, -0.12335404,\n",
       "        0.73170567])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.59985538, -0.5363037 , -0.49080731, -0.17782413, -0.12335404,\n",
       "        0.73170567])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.59985538, -0.5363037 , -0.49080731, -0.17782413, -0.12335404,\n",
       "        0.73170567])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr.sort()\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.54659826,  0.73677231,  0.07286615],\n",
       "       [ 0.20046333,  0.22517163, -0.43703929],\n",
       "       [-0.92290609, -0.33085181, -2.32980796],\n",
       "       [-1.01167085,  0.48268025, -0.53480326],\n",
       "       [-0.25060509, -2.51024086, -1.54729316]])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# With 2D arrays\n",
    "arr2d = np.random.randn(5,3)\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.54659826,  0.07286615,  0.73677231],\n",
       "       [-0.43703929,  0.20046333,  0.22517163],\n",
       "       [-2.32980796, -0.92290609, -0.33085181],\n",
       "       [-1.01167085, -0.53480326,  0.48268025],\n",
       "       [-2.51024086, -1.54729316, -0.25060509]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sort values along axis 1 \n",
    "arr2d.sort(axis=1)\n",
    "arr2d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Unique**. `unique()` returns unique values of an array; if `return_counts=True`, it also returns the number of occurrences of each value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Bob', 'Joe', 'Will'], dtype='<U4')"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names = np.array(['Bob', 'Joe', 'Will', 'Bob', 'Will', 'Joe', 'Joe'])\n",
    "np.unique(names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Values in array: ['Bob' 'Joe' 'Will'], appearing [2 3 2] times\n"
     ]
    }
   ],
   "source": [
    "values, counts = np.unique(names, return_counts=True)\n",
    "print(\"Values in array: {}, appearing {} times\".format(values, counts))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 Linear Algebra\n",
    "\n",
    "**Matrix Multiplication** We are going to perform the operation $XY$, where $X$ and $Y$ are two matrices (that is, 2-dimensional arrays). Matrix multiplication can be executed with the `dot` function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 28.,  64.],\n",
       "       [ 67., 181.]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.array([[1., 2., 3.], [4., 5., 6.]])\n",
    "Y = np.array([[6., 23.], [-1, 7], [8, 9]])\n",
    "X.dot(Y)    # Equivalent to: np.dot(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`dot` can also be used to perform the dot product between two vectors (1D-arrays). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Other Linear Algebra routines**. Other functions for linear algebra operations are within the `numpy.linalg` module. Here, we will see how to compute an inverse, the determinant and the SVD decomposition of a 2D-array. Other functions can be found in the [documentation](https://docs.scipy.org/doc/numpy/reference/routines.linalg.html). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.40603046,  3.60630988,  3.44710811, -4.31291117, -0.15974462],\n",
       "       [-0.01622577,  2.54784641,  1.96153807, -2.83278349,  0.08487118],\n",
       "       [ 0.45300825, -3.88409027, -3.47649132,  3.71025929,  0.46459172],\n",
       "       [-1.7308636 ,  6.89464836,  6.89991643, -7.64340925, -0.16761347],\n",
       "       [ 0.0366432 ,  1.20988444,  1.34953598, -1.11947286,  0.43556486]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy.linalg import inv, det, svd\n",
    "# set random.seed for reproducibility \n",
    "np.random.seed(1)\n",
    "# Create a 5x5 2d array\n",
    "X = np.random.randn(5,5)\n",
    "inv(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.990422171694092"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "det(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-0.42501696,  0.27320454, -0.05174593, -0.8551932 ,  0.10337701],\n",
       "        [ 0.61604378,  0.44274302,  0.21688757, -0.24590141, -0.56299286],\n",
       "        [-0.56593484,  0.43017644, -0.25681173,  0.36882926, -0.54099787],\n",
       "        [ 0.12772785,  0.73740115,  0.00952864,  0.24596981,  0.61590032],\n",
       "        [ 0.3213316 , -0.02292756, -0.94033988, -0.10789303,  0.01844844]]),\n",
       " array([4.64691667, 1.87569862, 1.55964124, 1.18214521, 0.06163067]),\n",
       " array([[-0.73808752,  0.61257924,  0.02487562,  0.22311156, -0.17197649],\n",
       "        [-0.39029396, -0.23151367, -0.68668778, -0.15860288,  0.54532289],\n",
       "        [ 0.04216404, -0.08907188, -0.58419304, -0.15950219, -0.78966191],\n",
       "        [-0.36856741, -0.70350222,  0.17489546,  0.55294433, -0.1814024 ],\n",
       "        [-0.40654359, -0.2613406 ,  0.39493185, -0.77063479, -0.12874107]]))"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svd(X)   # It returns left-singular vectors, singular values, and right-singular vectors "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.5 Random Number Generation \n",
    "The `numpy.random` module can be used for random numbers generation. So far, we have encounted the `randn` function from this module. `randn` allows to generate values from a standardized normal distribution, on arrays of desired size (for example, random.randn(5,5) will create a 5x5 2D array of standardized normal draws). It is possible to generate non-standardized normal values (controlling mean and standard deviation) with `random.normal`:    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate a sample of 1000 values from a normal N(10, 1) and visualize its hisogram\n",
    "x= np.random.normal(loc=10, scale=1, size=1000)\n",
    "plt.hist(x, 30)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is important to set the *seed* of the random number generator in order to obtain reproducible results. Compare the following results: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.42754695,  0.03619746,  2.02999749, -0.63440471, -0.52510339],\n",
       "       [ 0.38773466, -0.35479876,  1.17705226, -0.64110782,  1.32269399],\n",
       "       [ 0.19417502,  2.56545278, -0.46411491, -0.20269391,  0.14565182],\n",
       "       [-2.18102797,  0.60226513,  0.48084611,  0.10931836, -1.54439578],\n",
       "       [-1.54656104,  0.58661852,  1.17517869,  1.59446463, -0.89544152]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 5x5 2D-array from standard normal distribution (similar to ranom.randn)\n",
    "x = np.random.normal(size=(5, 5))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.03079803, -0.2719388 , -1.97573014, -0.58893118,  0.85178964],\n",
       "       [ 1.6346025 ,  0.27915545,  1.64055365,  0.41087294,  0.19136392],\n",
       "       [-0.17144119,  0.18693705, -0.25485295, -0.14091075, -0.66189183],\n",
       "       [ 0.2590319 ,  0.01444842, -1.47958003, -0.2407005 , -0.85567139],\n",
       "       [-2.04820046,  0.48388365,  1.55868825,  2.36973019,  1.56241953]])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.normal(size=(5, 5))\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now set the seed: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.62434536, -0.61175641, -0.52817175, -1.07296862,  0.86540763],\n",
       "       [-2.3015387 ,  1.74481176, -0.7612069 ,  0.3190391 , -0.24937038],\n",
       "       [ 1.46210794, -2.06014071, -0.3224172 , -0.38405435,  1.13376944],\n",
       "       [-1.09989127, -0.17242821, -0.87785842,  0.04221375,  0.58281521],\n",
       "       [-1.10061918,  1.14472371,  0.90159072,  0.50249434,  0.90085595]])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "x = np.random.normal(size=(5, 5))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.62434536, -0.61175641, -0.52817175, -1.07296862,  0.86540763],\n",
       "       [-2.3015387 ,  1.74481176, -0.7612069 ,  0.3190391 , -0.24937038],\n",
       "       [ 1.46210794, -2.06014071, -0.3224172 , -0.38405435,  1.13376944],\n",
       "       [-1.09989127, -0.17242821, -0.87785842,  0.04221375,  0.58281521],\n",
       "       [-1.10061918,  1.14472371,  0.90159072,  0.50249434,  0.90085595]])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "x = np.random.normal(size=(5, 5))\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other imprtant functions of the `numpy.random` module are: \n",
    "* permutation, shuffle: random permutation of a sequency (shuffle is *in-place*)\n",
    "* rand: draws from a [0,1) uniform distribution\n",
    "* randint: draw random integers\n",
    "* binomial, beta, gamma, uniform, etc: draws from corresponding probability distributions\n",
    "\n",
    "More information can be found in the [documentation](https://docs.scipy.org/doc/numpy-1.14.0/reference/routines.random.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.6 Other types of array manipulation\n",
    "**Reshape**. It is possible to 'resize' the dimensions of an array to a desired one (as long as the new shape is compatible with the original one). By default, the reshape occurs 'by row' (a.k.a. 'row major' or 'C-order'), but it can be required to occur by column ('column-major' or 'F-order').  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1],\n",
       "       [2, 3],\n",
       "       [4, 5],\n",
       "       [6, 7]])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reshape 1D array into a matrix: \n",
    "x = np.arange(8)\n",
    "x.reshape((4,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 4],\n",
       "       [1, 5],\n",
       "       [2, 6],\n",
       "       [3, 7]])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.reshape((4,2),order='F')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3],\n",
       "       [4, 5, 6, 7]])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reshape 2d array \n",
    "x = x.reshape((4,2)).reshape((2,4))\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In multi-dimensional arrays, one of the dimensions can be set equal to -1, in which case it will be deduced from the array size: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2],\n",
       "       [ 3,  4,  5],\n",
       "       [ 6,  7,  8],\n",
       "       [ 9, 10, 11],\n",
       "       [12, 13, 14]])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(15)\n",
    "x.reshape((5, -1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transforming a multi-dimensional array into a one-dimensional one is done with the `ravel` function: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2],\n",
       "       [ 3,  4,  5],\n",
       "       [ 6,  7,  8],\n",
       "       [ 9, 10, 11],\n",
       "       [12, 13, 14]])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(15).reshape((5,3))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.ravel()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Concatenation/Split**. `concatenate` takes as input a sequence of arrays and joins them along the desired axis; `vstack` and `hstack` perform concatenations across the first and second axis, respectively. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 4,  5,  6],\n",
       "       [ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr1 = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "arr2 = np.array([[7, 8, 9], [10, 11, 12]])\n",
    "np.concatenate([arr1, arr2], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  7,  8,  9],\n",
       "       [ 4,  5,  6, 10, 11, 12]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate([arr1, arr2], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 4,  5,  6],\n",
       "       [ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vstack((arr1, arr2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  7,  8,  9],\n",
       "       [ 4,  5,  6, 10, 11, 12]])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack((arr1, arr2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`split`, instead, slices the array along an axis. It takes the array as input, along with the indices at which to perform the split. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.68372786, -0.12289023],\n",
       "       [-0.93576943, -0.26788808],\n",
       "       [ 0.53035547, -0.69166075],\n",
       "       [-0.39675353, -0.6871727 ],\n",
       "       [-0.84520564, -0.67124613]])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(5, 2)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.68372786, -0.12289023]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first, second, third = np.split(arr, [1,3])\n",
    "first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.93576943, -0.26788808],\n",
       "       [ 0.53035547, -0.69166075]])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "second"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.39675353, -0.6871727 ],\n",
       "       [-0.84520564, -0.67124613]])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "third"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Stacking helpers**. `r_` and `c_` are *objects* that can make stacking more concise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  1.        ],\n",
       "       [ 2.        ,  3.        ],\n",
       "       [ 4.        ,  5.        ],\n",
       "       [-0.0126646 , -1.11731035],\n",
       "       [ 0.2344157 ,  1.65980218],\n",
       "       [ 0.74204416, -0.19183555]])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(6)\n",
    "arr1 = arr.reshape((3,2))\n",
    "arr2 = np.random.randn(3,2)\n",
    "np.r_[arr1, arr2]    # Compare with np.vstack((arr1, arr2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  1.        , -0.0126646 , -1.11731035],\n",
       "       [ 2.        ,  3.        ,  0.2344157 ,  1.65980218],\n",
       "       [ 4.        ,  5.        ,  0.74204416, -0.19183555]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.c_[arr1, arr2]   # Compare with np.hstack((arr1, arr2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Repeating elements**. `repeat` replicates the elements of an array for a specific number of times; `tile` stacks copies of an array across an axis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(3)\n",
    "arr.repeat(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.88762896, -0.74715829,  1.6924546 ],\n",
       "       [ 0.05080775, -0.63699565,  0.19091548]])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(2,3)\n",
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.88762896, -0.74715829,  1.6924546 , -0.88762896, -0.74715829,\n",
       "         1.6924546 ],\n",
       "       [ 0.05080775, -0.63699565,  0.19091548,  0.05080775, -0.63699565,\n",
       "         0.19091548]])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tile(arr,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.7 Broadcasting\n",
    "*Broadcasting* is a Numpy features that allows for arithmetics between arrays of different shapes. For instance, if we multiply an array by a scalar: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  4,  8, 12, 16])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.arange(5)\n",
    "arr * 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we say that 4 has been *broadcast* (or stretched) to all other elements of *arr*. Another operation that can be performed via broadcasting is subtracting, for example, each column of an array by its column mean: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0.])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr = np.random.randn(4,3)\n",
    "demeaned = arr - arr.mean(axis=0)\n",
    "demeaned.mean(axis=0).round()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a rule, two arrays are compatible for broadcasting if for each *trailing dimension* (i.e., the last dimension) the axis lengths match, or if either of the lengths is 1. Broadcasting will then be executed along the other dimensions, or across the length-1 dimensions. \n",
    "\n",
    "Let's now subtract the row mean from the same array: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_means = arr.mean(axis=1)\n",
    "row_means.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "# row_means must have trailing dimension of 1 for broadcasting: \n",
    "row_means = row_means.reshape((4,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0., -0.])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "demeaned = arr - row_means.reshape((4,1))\n",
    "demeaned.mean(axis=1).round()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Broadcasting is not a simple concept to understand, especially when working with arrays of several dimensions. The NumPy [documentation](https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html) gives more details about the topic. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Pandas\n",
    "\n",
    "Pandas is a Python library designed for data wrangling and analysis. Pandas adopts idioms from Numpy, being built on top of it. The biggest difference between Numpy and Pandas is that the former is mostly conceived to work with homogeneous, numerical arrays, while the latter is designed for tabular, heterogeneous data. Pandas tables are similar to Excel spreadsheets (formed by rows and columns), for which a great range of methods and operations are provided. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Pandas Data Structures \n",
    "The two main objects in Pandas are `Series` (one-dimensional sequences), and `DataFrame` (two-dimensional arrays of heterogeneous types). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Series**. A pandas Series can be created in this way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    4\n",
       "1    7\n",
       "2   -5\n",
       "3    3\n",
       "dtype: int64"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj = pd.Series([4, 7, -5, 3])\n",
    "obj "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Series is composed by two objects: the Series's values, and an index. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4,  7, -5,  3]), RangeIndex(start=0, stop=4, step=1))"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(obj.values, obj.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The index serves to identify the values (they can be seen as *labels*); indices can be given custom labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "d    4\n",
       "b    7\n",
       "a   -5\n",
       "c    3\n",
       "dtype: int64"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj = pd.Series([4, 7, -5, 3], index=['d', 'b', 'a', 'c'])\n",
    "obj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is possible to perform Numpy operations (notice that it preserves the index's names): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "d      54.598150\n",
       "b    1096.633158\n",
       "a       0.006738\n",
       "c      20.085537\n",
       "dtype: float64"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(obj)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is possible to generate a Series from a Python dictionary: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ohio      35000\n",
       "Texas     71000\n",
       "Oregon    16000\n",
       "Utah       5000\n",
       "dtype: int64"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = {'Ohio': 35000, 'Texas': 71000, 'Oregon': 16000, 'Utah': 5000}\n",
    "obj2 = pd.Series(data)\n",
    "obj2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**DataFrame**. DataFrames, as mentioned above, represent tabular data, where each columns can be of a different value type. We can create a Pandas DataFrame from a Python dictionary (unlike Series, the keys of the dictionary will represent the column names, rather than the index name; nevertheless, also dataframes have an index object incorporated): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>state</th>\n",
       "      <th>year</th>\n",
       "      <th>pop</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Ohio</td>\n",
       "      <td>2000</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Ohio</td>\n",
       "      <td>2001</td>\n",
       "      <td>1.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Ohio</td>\n",
       "      <td>2002</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Nevada</td>\n",
       "      <td>2001</td>\n",
       "      <td>2.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Nevada</td>\n",
       "      <td>2002</td>\n",
       "      <td>2.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Nevada</td>\n",
       "      <td>2003</td>\n",
       "      <td>3.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    state  year  pop\n",
       "0    Ohio  2000  1.5\n",
       "1    Ohio  2001  1.7\n",
       "2    Ohio  2002  3.6\n",
       "3  Nevada  2001  2.4\n",
       "4  Nevada  2002  2.9\n",
       "5  Nevada  2003  3.2"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = {'state': ['Ohio', 'Ohio', 'Ohio', 'Nevada', 'Nevada', 'Nevada'],\n",
    "        'year': [2000, 2001, 2002, 2001, 2002, 2003],\n",
    "        'pop': [1.5, 1.7, 3.6, 2.4, 2.9, 3.2]}\n",
    "frame = pd.DataFrame(data)\n",
    "frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can visualize the first five rows of a DataFrame with the `head()` method: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>state</th>\n",
       "      <th>year</th>\n",
       "      <th>pop</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Ohio</td>\n",
       "      <td>2000</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Ohio</td>\n",
       "      <td>2001</td>\n",
       "      <td>1.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Ohio</td>\n",
       "      <td>2002</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Nevada</td>\n",
       "      <td>2001</td>\n",
       "      <td>2.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Nevada</td>\n",
       "      <td>2002</td>\n",
       "      <td>2.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    state  year  pop\n",
       "0    Ohio  2000  1.5\n",
       "1    Ohio  2001  1.7\n",
       "2    Ohio  2002  3.6\n",
       "3  Nevada  2001  2.4\n",
       "4  Nevada  2002  2.9"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The order of the columns can be changed according to a given sequence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>state</th>\n",
       "      <th>pop</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2000</td>\n",
       "      <td>Ohio</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2001</td>\n",
       "      <td>Ohio</td>\n",
       "      <td>1.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2002</td>\n",
       "      <td>Ohio</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2001</td>\n",
       "      <td>Nevada</td>\n",
       "      <td>2.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2002</td>\n",
       "      <td>Nevada</td>\n",
       "      <td>2.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   year   state  pop\n",
       "0  2000    Ohio  1.5\n",
       "1  2001    Ohio  1.7\n",
       "2  2002    Ohio  3.6\n",
       "3  2001  Nevada  2.4\n",
       "4  2002  Nevada  2.9"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(data, columns=['year', 'state', 'pop']).head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to give to `DataFrame` a name for the indices; furthermore, if a column name is given that is not in the Python dictionary, such column will appear as a sequence of *missing values*: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>state</th>\n",
       "      <th>pop</th>\n",
       "      <th>debt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>one</th>\n",
       "      <td>2000</td>\n",
       "      <td>Ohio</td>\n",
       "      <td>1.5</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>two</th>\n",
       "      <td>2001</td>\n",
       "      <td>Ohio</td>\n",
       "      <td>1.7</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>three</th>\n",
       "      <td>2002</td>\n",
       "      <td>Ohio</td>\n",
       "      <td>3.6</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>four</th>\n",
       "      <td>2001</td>\n",
       "      <td>Nevada</td>\n",
       "      <td>2.4</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>five</th>\n",
       "      <td>2002</td>\n",
       "      <td>Nevada</td>\n",
       "      <td>2.9</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>six</th>\n",
       "      <td>2003</td>\n",
       "      <td>Nevada</td>\n",
       "      <td>3.2</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       year   state  pop debt\n",
       "one    2000    Ohio  1.5  NaN\n",
       "two    2001    Ohio  1.7  NaN\n",
       "three  2002    Ohio  3.6  NaN\n",
       "four   2001  Nevada  2.4  NaN\n",
       "five   2002  Nevada  2.9  NaN\n",
       "six    2003  Nevada  3.2  NaN"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame2 = pd.DataFrame(data, columns=['year', 'state', 'pop', 'debt'],\n",
    "                      index=['one', 'two', 'three', 'four',\n",
    "                             'five', 'six'])\n",
    "frame2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can obtain the column names with the `.columns` attribute, and retrieve a single column (in which case it is returned in form of a Series):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['year', 'state', 'pop', 'debt'], dtype='object')"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame2.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "one        Ohio\n",
       "two        Ohio\n",
       "three      Ohio\n",
       "four     Nevada\n",
       "five     Nevada\n",
       "six      Nevada\n",
       "Name: state, dtype: object"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame2['state']    # Equivalently: frame2.state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can manually assign values to a column: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>state</th>\n",
       "      <th>pop</th>\n",
       "      <th>debt</th>\n",
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       "      <th>one</th>\n",
       "      <td>2000</td>\n",
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       "      <th>two</th>\n",
       "      <td>2001</td>\n",
       "      <td>Ohio</td>\n",
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       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>three</th>\n",
       "      <td>2002</td>\n",
       "      <td>Ohio</td>\n",
       "      <td>3.6</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>four</th>\n",
       "      <td>2001</td>\n",
       "      <td>Nevada</td>\n",
       "      <td>2.4</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>five</th>\n",
       "      <td>2002</td>\n",
       "      <td>Nevada</td>\n",
       "      <td>2.9</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>six</th>\n",
       "      <td>2003</td>\n",
       "      <td>Nevada</td>\n",
       "      <td>3.2</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       year   state  pop  debt\n",
       "one    2000    Ohio  1.5   0.0\n",
       "two    2001    Ohio  1.7   1.0\n",
       "three  2002    Ohio  3.6   2.0\n",
       "four   2001  Nevada  2.4   3.0\n",
       "five   2002  Nevada  2.9   4.0\n",
       "six    2003  Nevada  3.2   5.0"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame2['debt'] = np.arange(6.)\n",
    "frame2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also instantiate a DataFrame from Numpy arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ohio</th>\n",
       "      <th>Texas</th>\n",
       "      <th>California</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ohio  Texas  California\n",
       "a     0      1           2\n",
       "c     3      4           5\n",
       "d     6      7           8"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame = pd.DataFrame(np.arange(9).reshape((3,3)), \n",
    "                    index=['a','c','d'], \n",
    "                    columns=['Ohio', 'Texas', 'California'])\n",
    "frame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Pandas DataFrame can also be converted into a Numpy 2D-array with `to_numpy`; notice that with this operation information about axes labels is lost. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame.to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Main Functionalities \n",
    "**Reindexing**. It refers to creating a new Pandas object, with data conformed to a new index. If some entries result without index, they will be instantiated (by default) as missing values. Consider this example with a Pandas DataFrame (but analogous examples can be made with a Series): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ohio  Texas  California\n",
       "a     0      1           2\n",
       "c     3      4           5\n",
       "d     6      7           8"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame = pd.DataFrame(np.arange(9).reshape((3, 3)),\n",
    "                     index=['a', 'c', 'd'],\n",
    "                     columns=['Ohio', 'Texas', 'California'])\n",
    "frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ohio</th>\n",
       "      <th>Texas</th>\n",
       "      <th>California</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>3.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ohio  Texas  California\n",
       "a   0.0    1.0         2.0\n",
       "b   NaN    NaN         NaN\n",
       "c   3.0    4.0         5.0\n",
       "d   6.0    7.0         8.0"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame2 = frame.reindex(['a', 'b', 'c', 'd'])\n",
    "frame2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Dropping entries from an axis**. It is possible to drop values from an existing axis. In the case of Series, this is the Series index: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    0.0\n",
       "b    1.0\n",
       "c    2.0\n",
       "d    3.0\n",
       "e    4.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj = pd.Series(np.arange(5.), index=['a', 'b', 'c', 'd', 'e'])\n",
    "obj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    0.0\n",
       "b    1.0\n",
       "e    4.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's drop the values indexed 'd' and 'c': \n",
    "obj.drop(['d', 'c'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can delete index values in DataFrames from both axes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three  four\n",
       "Ohio        0    1      2     3\n",
       "Colorado    4    5      6     7\n",
       "Utah        8    9     10    11\n",
       "New York   12   13     14    15"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(np.arange(16).reshape((4, 4)),\n",
    "                    index=['Ohio', 'Colorado', 'Utah', 'New York'],\n",
    "                    columns=['one', 'two', 'three', 'four'])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three  four\n",
       "Utah        8    9     10    11\n",
       "New York   12   13     14    15"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Drop two rows (notice that index names are in a Python list): \n",
    "data.drop(['Colorado', 'Ohio'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>three</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  three\n",
       "Ohio        0      2\n",
       "Colorado    4      6\n",
       "Utah        8     10\n",
       "New York   12     14"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Drop two columns: \n",
    "data.drop(['two','four'], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The object is not modified in-place; if we call \"data\" again: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three  four\n",
       "Ohio        0    1      2     3\n",
       "Colorado    4    5      6     7\n",
       "Utah        8    9     10    11\n",
       "New York   12   13     14    15"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The modification can occur in-place by setting to True the specific argument: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three  four\n",
       "Colorado    4    5      6     7\n",
       "Utah        8    9     10    11\n",
       "New York   12   13     14    15"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.drop('Ohio', inplace=True)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Indexing, Slicing, Filtering**. Indexing occurs in a similar manner to what we have seen for Numpy arrays. The difference is that you can also perform it with the index names. Here's an example with series: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    0.0\n",
       "b    1.0\n",
       "c    2.0\n",
       "d    3.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj = pd.Series(np.arange(4.), index=['a', 'b', 'c', 'd'])\n",
    "obj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "c    2.0\n",
       "d    3.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj[2:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "b    1.0\n",
       "a    0.0\n",
       "d    3.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj[['b', 'a', 'd']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "b    1.0\n",
       "d    3.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj[[1, 3]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    0.0\n",
       "b    1.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get only values smaller than two: \n",
    "obj[obj < 2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When slicing with labels, the end-point is inclusive:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "b    1.0\n",
       "c    2.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj['b':'c']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    0.0\n",
       "b    5.0\n",
       "c    5.0\n",
       "d    3.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's assign 5 to labels 'b' and 'c': \n",
    "obj['b':'c'] = 5\n",
    "obj"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In DataFrames, indexing names select columns:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three  four\n",
       "Ohio        0    1      2     3\n",
       "Colorado    4    5      6     7\n",
       "Utah        8    9     10    11\n",
       "New York   12   13     14    15"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(np.arange(16).reshape((4, 4)),\n",
    "                    index=['Ohio', 'Colorado', 'Utah', 'New York'],\n",
    "                    columns=['one', 'two', 'three', 'four'])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>three</th>\n",
       "      <th>one</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>14</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          three  one\n",
       "Ohio          2    0\n",
       "Colorado      6    4\n",
       "Utah         10    8\n",
       "New York     14   12"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[['three', 'one']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can select the first two rows of the DataFrame in this way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three  four\n",
       "Ohio        0    1      2     3\n",
       "Colorado    4    5      6     7"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is possible to filter data with a boolean array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three  four\n",
       "Colorado    4    5      6     7\n",
       "Utah        8    9     10    11\n",
       "New York   12   13     14    15"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data['three'] > 5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A comparison by scalar yields a boolean DataFrame: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            one    two  three   four\n",
       "Ohio       True   True   True   True\n",
       "Colorado   True  False  False  False\n",
       "Utah      False  False  False  False\n",
       "New York  False  False  False  False"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data < 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three  four\n",
       "Ohio        0    0      0     0\n",
       "Colorado    0    5      6     7\n",
       "Utah        8    9     10    11\n",
       "New York   12   13     14    15"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's assign 0 to all values smaller than 5\n",
    "data[data<5] = 0\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**loc and iloc**. `loc` and `iloc` allow for indexing across rows and columns of a DataFrame. In particular, with `loc` we can perform selection by axis labels, while with `iloc` we can perform selection by integers. We can see some examples in the next snippets of code. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "      <th>four</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three  four\n",
       "Ohio        0    1      2     3\n",
       "Colorado    4    5      6     7\n",
       "Utah        8    9     10    11\n",
       "New York   12   13     14    15"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(np.arange(16).reshape((4, 4)),\n",
    "                    index=['Ohio', 'Colorado', 'Utah', 'New York'],\n",
    "                    columns=['one', 'two', 'three', 'four'])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "two      1\n",
       "three    2\n",
       "Name: Ohio, dtype: int64"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.loc['Ohio', ['two', 'three']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          two  three\n",
       "Ohio        1      2\n",
       "Colorado    5      6"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.loc[['Ohio','Colorado'], ['two', 'three']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "four    11\n",
       "one      8\n",
       "two      9\n",
       "Name: Utah, dtype: int64"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.iloc[2, [3,0,1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "one       8\n",
       "two       9\n",
       "three    10\n",
       "four     11\n",
       "Name: Utah, dtype: int64"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A single integer select the corresponding row\n",
    "data.iloc[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>four</th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>11</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          four  one  two\n",
       "Colorado     7    4    5\n",
       "Utah        11    8    9"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.iloc[[1,2],[3,0,1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ohio        1\n",
       "Colorado    5\n",
       "Utah        9\n",
       "Name: two, dtype: int64"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Slicing with labels\n",
    "data.loc[:'Utah','two']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "      <th>three</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          one  two  three\n",
       "Colorado    4    5      6\n",
       "Utah        8    9     10\n",
       "New York   12   13     14"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Slicing with integers (followed by boolean selection)\n",
    "data.iloc[:,:3][data.three > 5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Function Application**. As mentioned above, you can perform NumPy operations on Pandas objects. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "        vertical-align: top;\n",
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       "\n",
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       "        text-align: right;\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>b</th>\n",
       "      <th>d</th>\n",
       "      <th>e</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>0.885141</td>\n",
       "      <td>0.754398</td>\n",
       "      <td>1.252868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>0.512930</td>\n",
       "      <td>0.298093</td>\n",
       "      <td>0.488518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>0.075572</td>\n",
       "      <td>1.131629</td>\n",
       "      <td>1.519817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oregon</th>\n",
       "      <td>2.185575</td>\n",
       "      <td>1.396496</td>\n",
       "      <td>1.444114</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               b         d         e\n",
       "Utah    0.885141  0.754398  1.252868\n",
       "Ohio    0.512930  0.298093  0.488518\n",
       "Texas   0.075572  1.131629  1.519817\n",
       "Oregon  2.185575  1.396496  1.444114"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame = pd.DataFrame(np.random.randn(4, 3), columns=list('bde'),\n",
    "                     index=['Utah', 'Ohio', 'Texas', 'Oregon'])\n",
    "frame\n",
    "# Absolute value of the dataframe\n",
    "np.abs(frame)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also compute custom functions by means of the `apply` method. When operations are 1-dimensional, by default they will be performed on each column of a DataFrame.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "b    2.261147\n",
       "d    2.528126\n",
       "e    2.963931\n",
       "dtype: float64"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the range of each column\n",
    "f = lambda x: x.max() - x.min()\n",
    "frame.apply(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can require the function to become row-specific by passing the argument axis='columns' to `apply`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Utah      2.007266\n",
       "Ohio      0.811023\n",
       "Texas     1.595389\n",
       "Oregon    3.629689\n",
       "dtype: float64"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# By passing axis='columns', the function is calculated for each row: \n",
    "frame.apply(f, axis='columns')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Sorting**. You can sort a Series by index label: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    1\n",
       "b    2\n",
       "c    3\n",
       "d    0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj = pd.Series(range(4), index=['d', 'a', 'b', 'c'])\n",
    "obj.sort_index()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DataFrame's can be sorted by either axis  (rows by default): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
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       "      <th>three</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
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      "text/plain": [
       "       d  a  b  c\n",
       "one    4  5  6  7\n",
       "three  0  1  2  3"
      ]
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     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame = pd.DataFrame(np.arange(8).reshape((2, 4)),\n",
    "                     index=['three', 'one'],\n",
    "                     columns=['d', 'a', 'b', 'c'])\n",
    "# Sort by row index\n",
    "frame.sort_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "      <th>c</th>\n",
       "      <th>d</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>three</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
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       "      <th>one</th>\n",
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      "text/plain": [
       "       a  b  c  d\n",
       "three  1  2  3  0\n",
       "one    5  6  7  4"
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     "execution_count": 175,
     "metadata": {},
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   "source": [
    "# Sort by column index\n",
    "frame.sort_index(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is possible to sort by value with `sort_values`. In DataFrame's, this requires specifying the column name(s) by which the  sorting must occur: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "d    0\n",
       "a    1\n",
       "b    2\n",
       "c    3\n",
       "dtype: int64"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sort Series by value \n",
    "obj.sort_values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>b</th>\n",
       "      <th>a</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <th>1</th>\n",
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       "      <td>1</td>\n",
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       "      <th>2</th>\n",
       "      <td>-3</td>\n",
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       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
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      "text/plain": [
       "   b  a\n",
       "0  4  0\n",
       "1  7  1\n",
       "2 -3  0\n",
       "3  2  1"
      ]
     },
     "execution_count": 177,
     "metadata": {},
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   ],
   "source": [
    "frame = pd.DataFrame({'b': [4, 7, -3, 2], 'a': [0, 1, 0, 1]})\n",
    "frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>b</th>\n",
       "      <th>a</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-3</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
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       "      <th>0</th>\n",
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       "      <th>1</th>\n",
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       "      <td>1</td>\n",
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       "</table>\n",
       "</div>"
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      "text/plain": [
       "   b  a\n",
       "2 -3  0\n",
       "3  2  1\n",
       "0  4  0\n",
       "1  7  1"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sort DataFrame by the 'b' column:\n",
    "frame.sort_values(by='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>b</th>\n",
       "      <th>a</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
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       "      <th>3</th>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
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      "text/plain": [
       "   b  a\n",
       "2 -3  0\n",
       "0  4  0\n",
       "3  2  1\n",
       "1  7  1"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sort DataFrame by multiple columns (a first, and then b): \n",
    "frame.sort_values(by=['a','b'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Descriptive Statistics\n",
    "Pandas allows computing summary statistics on Series and DataFrame's; these include sums, cumulative sums, means, etc.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>1.40</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>7.10</td>\n",
       "      <td>-4.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>0.75</td>\n",
       "      <td>-1.3</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    one  two\n",
       "a  1.40  NaN\n",
       "b  7.10 -4.5\n",
       "c   NaN  NaN\n",
       "d  0.75 -1.3"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# DataFrame with some missing values (denoted by NaN)\n",
    "df = pd.DataFrame([[1.4, np.nan], [7.1, -4.5],\n",
    "                   [np.nan, np.nan], [0.75, -1.3]],\n",
    "                  index=['a', 'b', 'c', 'd'],\n",
    "                  columns=['one', 'two'])\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Univariate Descriptive Statistics**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "one    9.25\n",
       "two   -5.80\n",
       "dtype: float64"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Column sums (by default, missing values are ignored)\n",
    "df.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    1.40\n",
       "b    2.60\n",
       "c    0.00\n",
       "d   -0.55\n",
       "dtype: float64"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Row sums\n",
    "df.sum(axis='columns')    # or axis=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>a</th>\n",
       "      <td>1.40</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>8.50</td>\n",
       "      <td>-4.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>9.25</td>\n",
       "      <td>-5.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    one  two\n",
       "a  1.40  NaN\n",
       "b  8.50 -4.5\n",
       "c   NaN  NaN\n",
       "d  9.25 -5.8"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cumulative sums by columns:\n",
    "df.cumsum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, missing values are ignored by default. This option can be modified with the `skipna` argument; let's see an example with row means:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a      NaN\n",
       "b    1.300\n",
       "c      NaN\n",
       "d   -0.275\n",
       "dtype: float64"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.mean(axis='columns', skipna=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`describe` prodcues multiple summary statistics of the DataFrame, such as sample size, mean, standard deviations, quartiles, and min/max:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>one</th>\n",
       "      <th>two</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.083333</td>\n",
       "      <td>-2.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.493685</td>\n",
       "      <td>2.262742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.750000</td>\n",
       "      <td>-4.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.075000</td>\n",
       "      <td>-3.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.400000</td>\n",
       "      <td>-2.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>4.250000</td>\n",
       "      <td>-2.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>7.100000</td>\n",
       "      <td>-1.300000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            one       two\n",
       "count  3.000000  2.000000\n",
       "mean   3.083333 -2.900000\n",
       "std    3.493685  2.262742\n",
       "min    0.750000 -4.500000\n",
       "25%    1.075000 -3.700000\n",
       "50%    1.400000 -2.900000\n",
       "75%    4.250000 -2.100000\n",
       "max    7.100000 -1.300000"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For non-numeric data, `describe` computes the mode (and its frequency):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     16\n",
       "unique     3\n",
       "top        a\n",
       "freq       8\n",
       "dtype: object"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj = pd.Series(['a', 'a', 'b', 'c'] * 4)\n",
    "obj.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several others univariate descriptive statistics that can be computed; you can find a list of them in the [Pandas documentation](https://pandas.pydata.org/pandas-docs/stable/reference/frame.html#computations-descriptive-stats)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Correlation and Covariance**. We can also calculate  correlations and covariances among columns. Let's first create a DataFrame with $n=100$ observations and four variables, two correlated and two uncorrelated ones. For this, we will use the Numpy library. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.624345</td>\n",
       "      <td>-0.611756</td>\n",
       "      <td>-0.528172</td>\n",
       "      <td>-0.575075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.072969</td>\n",
       "      <td>0.865408</td>\n",
       "      <td>-2.301539</td>\n",
       "      <td>-12.978850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.744812</td>\n",
       "      <td>-0.761207</td>\n",
       "      <td>0.319039</td>\n",
       "      <td>0.765024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.249370</td>\n",
       "      <td>1.462108</td>\n",
       "      <td>-2.060141</td>\n",
       "      <td>-11.181281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.322417</td>\n",
       "      <td>-0.384054</td>\n",
       "      <td>1.133769</td>\n",
       "      <td>5.389749</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B         C          D\n",
       "0  1.624345 -0.611756 -0.528172  -0.575075\n",
       "1 -1.072969  0.865408 -2.301539 -12.978850\n",
       "2  1.744812 -0.761207  0.319039   0.765024\n",
       "3 -0.249370  1.462108 -2.060141 -11.181281\n",
       "4 -0.322417 -0.384054  1.133769   5.389749"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "# Three uncorrelated normal variables \n",
    "X = np.random.randn(100,3)\n",
    "# Create a fourth variable, correlated to the third one: \n",
    "new_x = X[:,2] * 5 + np.random.randn(100)\n",
    "# Let's put everything in a DataFrame\n",
    "data = pd.DataFrame(np.hstack((X,new_x.reshape((100,1)))), columns=['A','B','C','D'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's calculate the correlation between A and C, and between C and D: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.01877783682931588"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['A'].corr(data['C'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9731427321485518"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['C'].corr(data['D'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, we can obtain covariances: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.017036286795916282"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['A'].cov(data['C'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.087914773647226"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['C'].cov(data['D'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When applied to the whole DataFrame, rather than to Series, we obtain correlation and covariance matrices: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.109183</td>\n",
       "      <td>-0.018778</td>\n",
       "      <td>-0.009587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>-0.109183</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.061937</td>\n",
       "      <td>-0.087876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>-0.018778</td>\n",
       "      <td>-0.061937</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.973143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>-0.009587</td>\n",
       "      <td>-0.087876</td>\n",
       "      <td>0.973143</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B         C         D\n",
       "A  1.000000 -0.109183 -0.018778 -0.009587\n",
       "B -0.109183  1.000000 -0.061937 -0.087876\n",
       "C -0.018778 -0.061937  1.000000  0.973143\n",
       "D -0.009587 -0.087876  0.973143  1.000000"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Correlation matrix:\n",
    "data.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>1.007324</td>\n",
       "      <td>-0.102195</td>\n",
       "      <td>-0.017036</td>\n",
       "      <td>-0.044717</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>-0.102195</td>\n",
       "      <td>0.869721</td>\n",
       "      <td>-0.052214</td>\n",
       "      <td>-0.380839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>-0.017036</td>\n",
       "      <td>-0.052214</td>\n",
       "      <td>0.817127</td>\n",
       "      <td>4.087915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>-0.044717</td>\n",
       "      <td>-0.380839</td>\n",
       "      <td>4.087915</td>\n",
       "      <td>21.595389</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B         C          D\n",
       "A  1.007324 -0.102195 -0.017036  -0.044717\n",
       "B -0.102195  0.869721 -0.052214  -0.380839\n",
       "C -0.017036 -0.052214  0.817127   4.087915\n",
       "D -0.044717 -0.380839  4.087915  21.595389"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Covariance matrix (variances in the diagonal): \n",
    "data.cov()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also observe the correlations for a specific column: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    1.000000\n",
       "B   -0.109183\n",
       "C   -0.018778\n",
       "D   -0.009587\n",
       "dtype: float64"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.corrwith(data['A'])    # Equivalent: data.corr()['A']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Unique values, counts, membership**. We can also obtain information about unique values and their counts observed for each object. Here, we will show an example with a Series. To begin with, `unique` returns the unique elements, while `value_counts()` counts the number of appearances of such values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['c', 'a', 'd', 'b'], dtype=object)"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj = pd.Series(['c', 'a', 'd', 'a', 'a', 'b', 'b', 'c', 'c'])\n",
    "# Obtain unique values in the Series\n",
    "uniques = obj.unique()\n",
    "uniques"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    3\n",
       "c    3\n",
       "b    2\n",
       "d    1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Count how many times each object appears\n",
    "obj.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "d    1\n",
       "c    3\n",
       "b    2\n",
       "a    3\n",
       "dtype: int64"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To avoid sorting by count, you can use the value_counts method: \n",
    "pd.value_counts(obj.values, sort=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, `isin` returns a boolean to assess what values are contained in a specific list/set: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    c\n",
       "1    a\n",
       "2    d\n",
       "3    a\n",
       "4    a\n",
       "5    b\n",
       "6    b\n",
       "7    c\n",
       "8    c\n",
       "dtype: object"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     True\n",
       "1    False\n",
       "2    False\n",
       "3    False\n",
       "4    False\n",
       "5     True\n",
       "6     True\n",
       "7     True\n",
       "8     True\n",
       "dtype: bool"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obj.isin(['b','c'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also count how many times values appears in the columns of a DataFrame. We see now an example in which we combine `apply` and `value_counts`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Qu1</th>\n",
       "      <th>Qu2</th>\n",
       "      <th>Qu3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Qu1  Qu2  Qu3\n",
       "0    1    2    1\n",
       "1    3    3    5\n",
       "2    4    1    2\n",
       "3    3    2    4\n",
       "4    4    3    4"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame({'Qu1': [1, 3, 4, 3, 4],\n",
    "                     'Qu2': [2, 3, 1, 2, 3],\n",
    "                     'Qu3': [1, 5, 2, 4, 4]})\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Qu1</th>\n",
       "      <th>Qu2</th>\n",
       "      <th>Qu3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Qu1  Qu2  Qu3\n",
       "1  1.0  1.0  1.0\n",
       "2  0.0  2.0  1.0\n",
       "3  2.0  2.0  0.0\n",
       "4  2.0  0.0  2.0\n",
       "5  0.0  0.0  1.0"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result = data.apply(pd.value_counts).fillna(0)\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The row labels in the results report the distinct values observed in the DataFrame; the values are the respective counts of these values. Because some values were not observed within some column (for instance, value 2 in column 1), the `fillna` method was used to replace the missing data indicator (NaN) with the value 0 (to denote no counts); more on missing values in Section 2.6.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Scatter matrix**. Pandas has also a `plotting` module which allows for data visualization. Let's use it to represent a scatterplot matrix, which represents the column vs. column bivariate plots in the off-diagonals, and the columns histograms in the diagonal. We use the `data` DataFrame created above. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.624345</td>\n",
       "      <td>-0.611756</td>\n",
       "      <td>-0.528172</td>\n",
       "      <td>-0.575075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.072969</td>\n",
       "      <td>0.865408</td>\n",
       "      <td>-2.301539</td>\n",
       "      <td>-12.978850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.744812</td>\n",
       "      <td>-0.761207</td>\n",
       "      <td>0.319039</td>\n",
       "      <td>0.765024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.249370</td>\n",
       "      <td>1.462108</td>\n",
       "      <td>-2.060141</td>\n",
       "      <td>-11.181281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.322417</td>\n",
       "      <td>-0.384054</td>\n",
       "      <td>1.133769</td>\n",
       "      <td>5.389749</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B         C          D\n",
       "0  1.624345 -0.611756 -0.528172  -0.575075\n",
       "1 -1.072969  0.865408 -2.301539 -12.978850\n",
       "2  1.744812 -0.761207  0.319039   0.765024\n",
       "3 -0.249370  1.462108 -2.060141 -11.181281\n",
       "4 -0.322417 -0.384054  1.133769   5.389749"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "# Three uncorrelated normal variables \n",
    "X = np.random.randn(100,3)\n",
    "# Create a fourth variable, correlated to the third one: \n",
    "new_x = X[:,2] * 5 + np.random.randn(100)\n",
    "# Let's put everything in a DataFrame\n",
    "data = pd.DataFrame(np.hstack((X,new_x.reshape((100,1)))), columns=['A','B','C','D'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 360x360 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas.plotting import scatter_matrix\n",
    "# alpha regulates the transparency\n",
    "scatter_matrix(data, figsize=(5,5),alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.4 Importing/Exporting files\n",
    "With Pandas, we can import/export files in form of Pandas objects. Here, we will see how to do this with `csv` files. For more information about what formats are supported, you can see the [documentation](https://pandas.pydata.org/pandas-docs/stable/user_guide/io.html).\n",
    "\n",
    "Let's start by exporting the DataFrame just created in `csv` format into the \"data\" folder; the file will be called 'pandas_test.csv'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Export `data` into data/pandas_test.csv with to_csv (without index labels): \n",
    "data.to_csv('data/tutorial/pandas_test.csv', index_label=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can assess in the 'data' folder that the file has been created. We do it here with the `os` library:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['pandas_test.csv']"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os \n",
    "os.listdir(\"data/tutorial\") "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now import the 'pandas_test.csv' file as a DataFrame called 'imported_test': "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.624345</td>\n",
       "      <td>-0.611756</td>\n",
       "      <td>-0.528172</td>\n",
       "      <td>-0.575075</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.072969</td>\n",
       "      <td>0.865408</td>\n",
       "      <td>-2.301539</td>\n",
       "      <td>-12.978850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.744812</td>\n",
       "      <td>-0.761207</td>\n",
       "      <td>0.319039</td>\n",
       "      <td>0.765024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.249370</td>\n",
       "      <td>1.462108</td>\n",
       "      <td>-2.060141</td>\n",
       "      <td>-11.181281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.322417</td>\n",
       "      <td>-0.384054</td>\n",
       "      <td>1.133769</td>\n",
       "      <td>5.389749</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          A         B         C          D\n",
       "0  1.624345 -0.611756 -0.528172  -0.575075\n",
       "1 -1.072969  0.865408 -2.301539 -12.978850\n",
       "2  1.744812 -0.761207  0.319039   0.765024\n",
       "3 -0.249370  1.462108 -2.060141 -11.181281\n",
       "4 -0.322417 -0.384054  1.133769   5.389749"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Impoort csv files with read_csv:\n",
    "imported_test = pd.read_csv(\"data/tutorial/pandas_test.csv\")\n",
    "imported_test.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.5 Pandas dtypes\n",
    "Pandas Series and DataFrame's columns inherit the Numpy data types (`dtypes`). More details can be found in the [documentation](https://pandas.pydata.org/pandas-docs/stable/getting_started/basics.html#dtypes). You can query the specifiy types with the `dtypes` attribute: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    float64\n",
       "B    float64\n",
       "C    float64\n",
       "D    float64\n",
       "dtype: object"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series([1,2,3]).dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Strings (and thus categorical objects) are identified as *objects* ('O' stands for \"objects\"):  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('O')"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(['a','b','c']).dtypes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `astype` method can be used to convert dtypes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>2</th>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
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       "      <th>3</th>\n",
       "      <td>0</td>\n",
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       "      <td>-2</td>\n",
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       "      <td>1</td>\n",
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      "text/plain": [
       "   A  B  C   D\n",
       "0  1  0  0   0\n",
       "1 -1  0 -2 -12\n",
       "2  1  0  0   0\n",
       "3  0  1 -2 -11\n",
       "4  0  0  1   5"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.astype('int32').head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    2.0\n",
       "2    3.0\n",
       "dtype: float32"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series([1,2,3]).astype('float32')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Strings can be converted into a `category` dtype: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    a\n",
       "1    b\n",
       "2    c\n",
       "3    a\n",
       "4    c\n",
       "dtype: category\n",
       "Categories (3, object): [a, b, c]"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(['a','b','c','a','c']).astype('category')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`select_dtypes` can be used to select columns of a DataFrame having a specific dtype: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>string_1</th>\n",
       "      <th>int_1</th>\n",
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       "      <th>int_2</th>\n",
       "      <th>float_2</th>\n",
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       "  <tbody>\n",
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       "      <th>0</th>\n",
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       "      <td>d</td>\n",
       "      <td>4</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>e</td>\n",
       "      <td>5</td>\n",
       "      <td>1.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>c</td>\n",
       "      <td>3</td>\n",
       "      <td>0.5</td>\n",
       "      <td>f</td>\n",
       "      <td>6</td>\n",
       "      <td>2.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  string_1  int_1  float_1 string_2  int_2  float_2\n",
       "0        a      1     -0.5        d      4      1.0\n",
       "1        b      2      0.0        e      5      1.5\n",
       "2        c      3      0.5        f      6      2.5"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame({\n",
    "    'string_1':['a','b','c'],\n",
    "    'int_1':[1,2,3],\n",
    "    'float_1':[-0.5,0.,0.5],\n",
    "    'string_2':['d','e','f'],\n",
    "    'int_2':[4,5,6],\n",
    "    'float_2':[1.0, 1.5, 2.5]\n",
    "})\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>float_1</th>\n",
       "      <th>float_2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>-0.5</td>\n",
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       "      <th>1</th>\n",
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       "      <th>2</th>\n",
       "      <td>0.5</td>\n",
       "      <td>2.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   float_1  float_2\n",
       "0     -0.5      1.0\n",
       "1      0.0      1.5\n",
       "2      0.5      2.5"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.select_dtypes(['float'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>string_1</th>\n",
       "      <th>int_1</th>\n",
       "      <th>string_2</th>\n",
       "      <th>int_2</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>1</td>\n",
       "      <td>d</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>2</td>\n",
       "      <td>e</td>\n",
       "      <td>5</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>c</td>\n",
       "      <td>3</td>\n",
       "      <td>f</td>\n",
       "      <td>6</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  string_1  int_1 string_2  int_2\n",
       "0        a      1        d      4\n",
       "1        b      2        e      5\n",
       "2        c      3        f      6"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.select_dtypes(['object','int'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.6 Missing Values\n",
    "In Pandas, missing values are denoted with `NaN` (not a number, `np.nan` in Numpy). Pandas has special methods dedicated to missing values. `isnull` can be used to detect missing values: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "2     True\n",
       "3    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "string_data = pd.Series(['apples','artichokes',np.nan,'avocado'])\n",
    "string_data.isnull()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# How many missing values in the Series?\n",
    "string_data.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Beside np.nan, the Python `None` value can also be used to indicate missing values: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     True\n",
       "1    False\n",
       "2     True\n",
       "3    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "string_data[0] = None\n",
    "string_data.isnull()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Dropping missing data**. It is possible to filter out missing values with the `dropna` method. Here, we see an example with a DataFrame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0    1    2\n",
       "0  1.0  6.5  3.0\n",
       "1  1.0  NaN  NaN\n",
       "2  NaN  NaN  NaN\n",
       "3  NaN  6.5  3.0"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import nan as NA\n",
    "data = pd.DataFrame([[1., 6.5, 3.], [1., NA, NA],\n",
    "                     [NA, NA, NA], [NA, 6.5, 3.]])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <tr style=\"text-align: right;\">\n",
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       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0    1    2\n",
       "0  1.0  6.5  3.0"
      ]
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     "execution_count": 220,
     "metadata": {},
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    }
   ],
   "source": [
    "cleaned = data.dropna()\n",
    "cleaned"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 221,
     "metadata": {},
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   ],
   "source": [
    "# Drop only rows that are completely NA's: \n",
    "data.dropna(how='all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
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       "     0    1    2   3\n",
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     "execution_count": 222,
     "metadata": {},
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   "source": [
    "# Drop only columns that are completely NA's: \n",
    "data[3] = NA\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
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       "     0    1    2\n",
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       "3  NaN  6.5  3.0"
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   "source": [
    "data.dropna(how='all', axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Filling missing data**. An alternative to dropping missing values, is to replace them. (This operation is known as *imputation* in statistics; we will see in the next lectures that `scikit-learn` has specific functions dedicated to data imputation). A way to do this is to replace them with a specific value with the `fillna` method: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
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       "     0    1    2    3\n",
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       "2  0.0  0.0  0.0  0.0\n",
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    "data.fillna(0)"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is possible to specify a different value for each column: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
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       "      <td>105.0</td>\n",
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       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
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      "text/plain": [
       "     0    1    2      3\n",
       "0  1.0  6.5  3.0  105.0\n",
       "1  1.0  0.5  0.0  105.0\n",
       "2  NaN  0.5  0.0  105.0\n",
       "3  NaN  6.5  3.0  105.0"
      ]
     },
     "execution_count": 225,
     "metadata": {},
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   ],
   "source": [
    "data.fillna({1:0.5,2:0,3:105})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As reported in the [Pandas documentation](https://pandas.pydata.org/pandas-docs/stable/user_guide/missing_data.html#filling-missing-values-fillna), various options can be used to replace missing values. \n",
    "\n",
    "Now, suppose you imported a dataset in which missing data are flagged as a number (for instance, -999) and you want to convert these values into `np.nan`'s. You can do this with `replace`: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      1.0\n",
       "1   -999.0\n",
       "2      2.0\n",
       "3   -999.0\n",
       "4   -999.0\n",
       "5      3.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# -999 is used to denote missing values \n",
    "data = pd.Series([1., -999., 2., -999., -999., 3.])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    NaN\n",
       "2    2.0\n",
       "3    NaN\n",
       "4    NaN\n",
       "5    3.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.replace(-999, np.nan)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.7 Data Transformations \n",
    "**Discretization and Binning**. \"Discretization\" is the act of converting numeric values into labels/integers; \"binning\" is a way to achieve this: it is the act of assigning continuous numbers to different bins. This can be achieved with the `cut` function, which takes the object to be converted and the binning values as input arguments; the returned object is a Categorical object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(18, 25], (18, 25], (18, 25], (25, 35], (18, 25], ..., (25, 35], (60, 100], (35, 60], (35, 60], (25, 35]]\n",
       "Length: 12\n",
       "Categories (4, interval[int64]): [(18, 25] < (25, 35] < (35, 60] < (60, 100]]"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ages = [20, 22, 25, 27, 21, 23, 37, 31, 61, 45, 41, 32]\n",
    "bins = [18, 25, 35, 60, 100]\n",
    "cats = pd.cut(ages, bins)\n",
    "cats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can observe the new labels with the `codes` attribute, and the created categories with `categories`: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "IntervalIndex([(18, 25], (25, 35], (35, 60], (60, 100]],\n",
       "              closed='right',\n",
       "              dtype='interval[int64]')"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cats.categories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 1, 0, 0, 2, 1, 3, 2, 2, 1], dtype=int8)"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cats.codes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18, 25]     5\n",
       "(35, 60]     3\n",
       "(25, 35]     3\n",
       "(60, 100]    1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.value_counts(cats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By passing an integers instead of an array, equal-length bins will be created:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(19.959, 30.25]    6\n",
       "(30.25, 40.5]      3\n",
       "(40.5, 50.75]      2\n",
       "(50.75, 61.0]      1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 232,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cats2 = pd.cut(ages, 4)\n",
    "pd.value_counts(cats2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, `qcut` bins the data based on quantiles. Here, we will split a Numpy array into four quartiles: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.848, 2.056]         25\n",
       "(-0.000277, 0.848]     25\n",
       "(-0.643, -0.000277]    25\n",
       "(-2.415, -0.643]       25\n",
       "dtype: int64"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.random.randn(100)\n",
    "cats = pd.qcut(data,4)\n",
    "pd.value_counts(cats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Permutations and Random Sampling**. By using the `permutation` function (from the `numpy.random` module) in combination with the `iloc` function we can *permute* the entries of a Pandas object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
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       "    0   1   2   3\n",
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   "source": [
    "df = pd.DataFrame(np.arange(5 * 4).reshape((5,4)))\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [
    {
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       "      <td>16</td>\n",
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       "      <td>19</td>\n",
       "    </tr>\n",
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       "      <th>0</th>\n",
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       "      <td>3</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    0   1   2   3\n",
       "2   8   9  10  11\n",
       "1   4   5   6   7\n",
       "4  16  17  18  19\n",
       "0   0   1   2   3\n",
       "3  12  13  14  15"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(1)\n",
    "permuted_indices = np.random.permutation(5)\n",
    "df.iloc[permuted_indices]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to use the Pandas `sample` method for subsampling without replacement..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "    0   1   2   3\n",
       "2   8   9  10  11\n",
       "1   4   5   6   7\n",
       "4  16  17  18  19"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Note: random_state sets the seed of the random number generator in Pandas\n",
    "df.sample(n=3, random_state=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "...and with replacement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    0   1   2   3\n",
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       "3  12  13  14  15\n",
       "1   4   5   6   7"
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     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "df.sample(n=3, replace=True, random_state=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Creating Dummy variables**. Dummy variables are an alternative way to represent categorical data. Variables with 'k' distinct values will be replaced by 'k' variables, equal to 1 whenever the row instance has the original variable equal to the reference value of the new variable, and 0 otherwise. As we will see, this method is also known as One-Hot encoding in Machine Learning: `scikit-learn` also offers a functionality that allows converting categorical variables to one-hot encoded ones. \n",
    "\n",
    "In Pandas, the function that allows perform one-hot encoding is `get_dummies`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>key</th>\n",
       "      <th>data1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>b</td>\n",
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       "      <td>b</td>\n",
       "      <td>1</td>\n",
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       "      <th>2</th>\n",
       "      <td>a</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>c</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>a</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>b</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  key  data1\n",
       "0   b      0\n",
       "1   b      1\n",
       "2   a      2\n",
       "3   c      3\n",
       "4   a      4\n",
       "5   b      5"
      ]
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'key': ['b', 'b', 'a', 'c', 'a', 'b'],\n",
    "                   'data1': range(6)})\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
       "      <th>b</th>\n",
       "      <th>c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   a  b  c\n",
       "0  0  1  0\n",
       "1  0  1  0\n",
       "2  1  0  0\n",
       "3  0  0  1\n",
       "4  1  0  0\n",
       "5  0  1  0"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Dummy variables for the 'key' column:\n",
    "pd.get_dummies(df['key'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now replace 'key' in the original dataset, including the dummy names in the columns: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>data1</th>\n",
       "      <th>key_a</th>\n",
       "      <th>key_b</th>\n",
       "      <th>key_c</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   data1  key_a  key_b  key_c\n",
       "0      0      0      1      0\n",
       "1      1      0      1      0\n",
       "2      2      1      0      0\n",
       "3      3      0      0      1\n",
       "4      4      1      0      0\n",
       "5      5      0      1      0"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummies = pd.get_dummies(df['key'], prefix='key')\n",
    "df_with_dummy = df.drop('key', axis=1).join(dummies)\n",
    "df_with_dummy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.8 Hierarchical Indexing\n",
    "Pandas objects can share more than one index within each axis. Here's an example with a Series. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a  1   -0.549746\n",
       "   2   -1.402873\n",
       "   3    1.582752\n",
       "b  1   -1.045147\n",
       "   3    0.257594\n",
       "c  1   -1.959395\n",
       "   2   -1.507808\n",
       "d  2   -0.315292\n",
       "   3    0.858179\n",
       "dtype: float64"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.Series(np.random.randn(9),\n",
    "                 index=[['a', 'a', 'a', 'b', 'b', 'c', 'c', 'd', 'd'],\n",
    "                        [1, 2, 3, 1, 3, 1, 2, 2, 3]])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiIndex([('a', 1),\n",
       "            ('a', 2),\n",
       "            ('a', 3),\n",
       "            ('b', 1),\n",
       "            ('b', 3),\n",
       "            ('c', 1),\n",
       "            ('c', 2),\n",
       "            ('d', 2),\n",
       "            ('d', 3)],\n",
       "           )"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1   -1.045147\n",
       "3    0.257594\n",
       "dtype: float64"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Select data by first index\n",
    "data['b']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "b  1   -1.045147\n",
       "   3    0.257594\n",
       "c  1   -1.959395\n",
       "   2   -1.507808\n",
       "dtype: float64"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Slice by first index\n",
    "data['b':'c']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a   -1.402873\n",
       "c   -1.507808\n",
       "d   -0.315292\n",
       "dtype: float64"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Select by second index\n",
    "data.loc[:,2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `unstack` method can be used to rearrange data (one axis per index): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "      <th>b</th>\n",
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       "      <td>NaN</td>\n",
       "      <td>0.257594</td>\n",
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       "    <tr>\n",
       "      <th>c</th>\n",
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       "      <td>NaN</td>\n",
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       "          1         2         3\n",
       "a -0.549746 -1.402873  1.582752\n",
       "b -1.045147       NaN  0.257594\n",
       "c -1.959395 -1.507808       NaN\n",
       "d       NaN -0.315292  0.858179"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.unstack()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Summary Statistics by level**. You can calculate summary statistics, aggregated by the desired axis level. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>state</th>\n",
       "      <th colspan=\"2\" halign=\"left\">Ohio</th>\n",
       "      <th>Colorado</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>color</th>\n",
       "      <th>Green</th>\n",
       "      <th>Red</th>\n",
       "      <th>Green</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>key1</th>\n",
       "      <th>key2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">a</th>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">b</th>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "state      Ohio     Colorado\n",
       "color     Green Red    Green\n",
       "key1 key2                   \n",
       "a    1        0   1        2\n",
       "     2        3   4        5\n",
       "b    1        6   7        8\n",
       "     2        9  10       11"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame = pd.DataFrame(np.arange(12).reshape((4, 3)),\n",
    "                     index=[['a', 'a', 'b', 'b'], [1, 2, 1, 2]],\n",
    "                     columns=[['Ohio', 'Ohio', 'Colorado'],\n",
    "                              ['Green', 'Red', 'Green']])\n",
    "# Name the indexes:\n",
    "frame.index.names = ['key1', 'key2']\n",
    "frame.columns.names = ['state', 'color']\n",
    "frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>color</th>\n",
       "      <th>Green</th>\n",
       "      <th>Red</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>key1</th>\n",
       "      <th>key2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">a</th>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">b</th>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "color      Green  Red\n",
       "key1 key2            \n",
       "a    1         0    1\n",
       "     2         3    4\n",
       "b    1         6    7\n",
       "     2         9   10"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame['Ohio']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "        text-align: left;\n",
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       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th>state</th>\n",
       "      <th colspan=\"2\" halign=\"left\">Ohio</th>\n",
       "      <th>Colorado</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>color</th>\n",
       "      <th>Green</th>\n",
       "      <th>Red</th>\n",
       "      <th>Green</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>key2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12</td>\n",
       "      <td>14</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "state  Ohio     Colorado\n",
       "color Green Red    Green\n",
       "key2                    \n",
       "1         6   8       10\n",
       "2        12  14       16"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sum of values by key2 \n",
    "frame.sum(level='key2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>color</th>\n",
       "      <th>Green</th>\n",
       "      <th>Red</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>key1</th>\n",
       "      <th>key2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">a</th>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">b</th>\n",
       "      <th>1</th>\n",
       "      <td>14</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "color      Green  Red\n",
       "key1 key2            \n",
       "a    1         2    1\n",
       "     2         8    4\n",
       "b    1        14    7\n",
       "     2        20   10"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sum of values by color\n",
    "frame.sum(level='color', axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.9 Combining and Merging DataFrames\n",
    "`merge` links the rows of two datasets by using one or more keys. This recalls the \"join\" operation of the SQL language, which is used for relational databases. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>key</th>\n",
       "      <th>data1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>b</td>\n",
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       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>a</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>c</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>a</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>a</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>b</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  key  data1\n",
       "0   b      0\n",
       "1   b      1\n",
       "2   a      2\n",
       "3   c      3\n",
       "4   a      4\n",
       "5   a      5\n",
       "6   b      6"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame({'key': ['b', 'b', 'a', 'c', 'a', 'a', 'b'],\n",
    "                    'data1': range(7)})\n",
    "df2 = pd.DataFrame({'key': ['a', 'b', 'd'],\n",
    "                    'data2': range(3)})\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>key</th>\n",
       "      <th>data2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>d</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  key  data2\n",
       "0   a      0\n",
       "1   b      1\n",
       "2   d      2"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>b</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>a</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>a</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>a</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  key  data1  data2\n",
       "0   b      0      1\n",
       "1   b      1      1\n",
       "2   b      6      1\n",
       "3   a      2      0\n",
       "4   a      4      0\n",
       "5   a      5      0"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.merge(df1,df2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, Pandas uses matching column names to decide onto which column to join. It is also possible to make the key explicit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>key</th>\n",
       "      <th>data1</th>\n",
       "      <th>data2</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>b</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>a</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>a</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>a</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  key  data1  data2\n",
       "0   b      0      1\n",
       "1   b      1      1\n",
       "2   b      6      1\n",
       "3   a      2      0\n",
       "4   a      4      0\n",
       "5   a      5      0"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.merge(df1,df2, on='key')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If two objects have different colun names, we can specify them: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lkey</th>\n",
       "      <th>data1</th>\n",
       "      <th>rkey</th>\n",
       "      <th>data2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>b</td>\n",
       "      <td>0</td>\n",
       "      <td>b</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>1</td>\n",
       "      <td>b</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>b</td>\n",
       "      <td>6</td>\n",
       "      <td>b</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>a</td>\n",
       "      <td>2</td>\n",
       "      <td>a</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>a</td>\n",
       "      <td>4</td>\n",
       "      <td>a</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>a</td>\n",
       "      <td>5</td>\n",
       "      <td>a</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  lkey  data1 rkey  data2\n",
       "0    b      0    b      1\n",
       "1    b      1    b      1\n",
       "2    b      6    b      1\n",
       "3    a      2    a      0\n",
       "4    a      4    a      0\n",
       "5    a      5    a      0"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = pd.DataFrame({'lkey': ['b', 'b', 'a', 'c', 'a', 'a', 'b'],\n",
    "                    'data1': range(7)})\n",
    "df4 = pd.DataFrame({'rkey': ['a', 'b', 'd'],\n",
    "                    'data2': range(3)})\n",
    "pd.merge(df3, df4, left_on='lkey', right_on='rkey')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Values 'c' and 'd' have been dropped by `merge`; this is because by default, an inner join is performed. It is also possible to specify left, right, and outer joins:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lkey</th>\n",
       "      <th>data1</th>\n",
       "      <th>rkey</th>\n",
       "      <th>data2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>b</td>\n",
       "      <td>0.0</td>\n",
       "      <td>b</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>1.0</td>\n",
       "      <td>b</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>b</td>\n",
       "      <td>6.0</td>\n",
       "      <td>b</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>a</td>\n",
       "      <td>2.0</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>a</td>\n",
       "      <td>4.0</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>a</td>\n",
       "      <td>5.0</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>c</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>d</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  lkey  data1 rkey  data2\n",
       "0    b    0.0    b    1.0\n",
       "1    b    1.0    b    1.0\n",
       "2    b    6.0    b    1.0\n",
       "3    a    2.0    a    0.0\n",
       "4    a    4.0    a    0.0\n",
       "5    a    5.0    a    0.0\n",
       "6    c    3.0  NaN    NaN\n",
       "7  NaN    NaN    d    2.0"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.merge(df3,df4, left_on='lkey', right_on='rkey',how='outer')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also perform a join by multiple column names: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>key1</th>\n",
       "      <th>key2</th>\n",
       "      <th>lval</th>\n",
       "      <th>rval</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>foo</td>\n",
       "      <td>one</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>foo</td>\n",
       "      <td>one</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>bar</td>\n",
       "      <td>one</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  key1 key2  lval  rval\n",
       "0  foo  one     1     4\n",
       "1  foo  one     1     5\n",
       "2  bar  one     3     6"
      ]
     },
     "execution_count": 257,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "left = pd.DataFrame({'key1': ['foo', 'foo', 'bar'],\n",
    "                     'key2': ['one', 'two', 'one'],\n",
    "                     'lval': [1, 2, 3]})\n",
    "right = pd.DataFrame({'key1': ['foo', 'foo', 'bar', 'bar'],\n",
    "                      'key2': ['one', 'one', 'one', 'two'],\n",
    "                      'rval': [4, 5, 6, 7]})\n",
    "pd.merge(left, right, on=['key1', 'key2'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to merge by index with the `left_index` and/or `right_index` argument.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>key</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>a</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>a</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>b</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>c</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  key  value\n",
       "0   a      0\n",
       "1   b      1\n",
       "2   a      2\n",
       "3   a      3\n",
       "4   b      4\n",
       "5   c      5"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "left1 = pd.DataFrame({'key': ['a', 'b', 'a', 'a', 'b', 'c'],\n",
    "                      'value': range(6)})\n",
    "right1 = pd.DataFrame({'group_val': [3.5, 7]}, index=['a', 'b'])\n",
    "left1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>group_val</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   group_val\n",
       "a        3.5\n",
       "b        7.0"
      ]
     },
     "execution_count": 259,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "right1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>key</th>\n",
       "      <th>value</th>\n",
       "      <th>group_val</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>0</td>\n",
       "      <td>3.5</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>a</td>\n",
       "      <td>2</td>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>a</td>\n",
       "      <td>3</td>\n",
       "      <td>3.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>1</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>b</td>\n",
       "      <td>4</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  key  value  group_val\n",
       "0   a      0        3.5\n",
       "2   a      2        3.5\n",
       "3   a      3        3.5\n",
       "1   b      1        7.0\n",
       "4   b      4        7.0"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.merge(left1, right1, left_on='key', right_index=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Concatenation**. `concat` allows for merging along an axis: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    0\n",
       "b    1\n",
       "c    2\n",
       "d    3\n",
       "e    4\n",
       "f    5\n",
       "g    6\n",
       "dtype: int64"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 = pd.Series([0, 1], index=['a', 'b'])\n",
    "s2 = pd.Series([2, 3, 4], index=['c', 'd', 'e'])\n",
    "s3 = pd.Series([5, 6], index=['f', 'g'])\n",
    "pd.concat([s1, s2, s3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>a</th>\n",
       "      <td>0.0</td>\n",
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       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c</th>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>d</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>e</th>\n",
       "      <td>NaN</td>\n",
       "      <td>4.0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>f</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>g</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0    1    2\n",
       "a  0.0  NaN  NaN\n",
       "b  1.0  NaN  NaN\n",
       "c  NaN  2.0  NaN\n",
       "d  NaN  3.0  NaN\n",
       "e  NaN  4.0  NaN\n",
       "f  NaN  NaN  5.0\n",
       "g  NaN  NaN  6.0"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([s1, s2, s3], axis=1, sort=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`concat` also allows performing inner joins:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1\n",
       "a  0  0\n",
       "b  1  1"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s4 = pd.concat([s1,s3])\n",
    "pd.concat([s1,s4], axis=1, join='inner')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are other functions in Pandas that allow for the merging and reshaping of dataset; among them we have: \n",
    "* [`stack` and `unstack`](https://pandas.pydata.org/pandas-docs/stable/user_guide/reshaping.html#reshaping-by-stacking-and-unstacking)to rotate from data columns to rows (and undo this operation)\n",
    "* [`pivot`](https://pandas.pydata.org/pandas-docs/stable/user_guide/reshaping.html#reshaping-by-pivoting-dataframe-objects) and [`melt`](https://pandas.pydata.org/pandas-docs/stable/user_guide/reshaping.html#reshaping-by-melt) to transform datasets from \"long\" to \"wide\" format (and vice versa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.10 Aggregated Data\n",
    "Pandas allows calculating summary statistics, aggregated by the values of a (categorical) column in the DataFrame. In particular, (1) data are  split into groups, given by a specific key; (2) group-specific statistics are calculated, and returned in the aggregated form. The method that allows performing such operation is `groupby`. For example, we are now going to calculate the mean of a variable called 'data1', aggregated by a variable called 'key1'.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "key1\n",
       "a   -0.529688\n",
       "b   -0.264862\n",
       "Name: data1, dtype: float64"
      ]
     },
     "execution_count": 264,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame({'key1' : ['a', 'a', 'b', 'b', 'a'],\n",
    "                   'key2' : ['one', 'two', 'one', 'two', 'one'],\n",
    "                   'data1' : np.random.randn(5),\n",
    "                   'data2' : np.random.randn(5)})\n",
    "# Group values of 'data1' by the values of 'key1'\n",
    "grouped = df['data1'].groupby(df['key1'])\n",
    "# Calculate aggregated means\n",
    "grouped.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This can be equivalently computed with: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "key1\n",
       "a   -0.529688\n",
       "b   -0.264862\n",
       "Name: data1, dtype: float64"
      ]
     },
     "execution_count": 265,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = df.groupby([\"key1\"]).data1\n",
    "g.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to pass several keys: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "key1  key2\n",
       "a     one     0.351622\n",
       "      two    -2.292309\n",
       "b     one    -1.415552\n",
       "      two     0.885829\n",
       "Name: data1, dtype: float64"
      ]
     },
     "execution_count": 266,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means = df['data1'].groupby([df['key1'], df['key2']]).mean()\n",
    "means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "      <th>two</th>\n",
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       "    <tr>\n",
       "      <th>key1</th>\n",
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       "  <tbody>\n",
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       "      <th>a</th>\n",
       "      <td>0.351622</td>\n",
       "      <td>-2.292309</td>\n",
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       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-1.415552</td>\n",
       "      <td>0.885829</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "key2       one       two\n",
       "key1                    \n",
       "a     0.351622 -2.292309\n",
       "b    -1.415552  0.885829"
      ]
     },
     "execution_count": 267,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For better visualization, we can unstack the two indexes:\n",
    "means.unstack()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also group values of multiple columns, or of an entire DataFrame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>data1</th>\n",
       "      <th>data2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>key1</th>\n",
       "      <th>key2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">a</th>\n",
       "      <th>one</th>\n",
       "      <td>0.351622</td>\n",
       "      <td>-0.247494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>two</th>\n",
       "      <td>-2.292309</td>\n",
       "      <td>-0.903123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">b</th>\n",
       "      <th>one</th>\n",
       "      <td>-1.415552</td>\n",
       "      <td>0.175323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>two</th>\n",
       "      <td>0.885829</td>\n",
       "      <td>0.194431</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              data1     data2\n",
       "key1 key2                    \n",
       "a    one   0.351622 -0.247494\n",
       "     two  -2.292309 -0.903123\n",
       "b    one  -1.415552  0.175323\n",
       "     two   0.885829  0.194431"
      ]
     },
     "execution_count": 268,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(['key1', 'key2']).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also observe group-specific sample sizes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "key1  key2\n",
       "a     one     2\n",
       "      two     1\n",
       "b     one     1\n",
       "      two     1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 269,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(['key1', 'key2']).size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several functions that can be computed with grouped data: count, sum, mean, median, std, quantile, and so on. An overall summary of the key statistics is given by `describe`: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"8\" halign=\"left\">data1</th>\n",
       "      <th colspan=\"8\" halign=\"left\">data2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>key1</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>a</th>\n",
       "      <td>3.0</td>\n",
       "      <td>-0.529688</td>\n",
       "      <td>1.551993</td>\n",
       "      <td>-2.292309</td>\n",
       "      <td>-1.110483</td>\n",
       "      <td>0.071343</td>\n",
       "      <td>0.351622</td>\n",
       "      <td>0.631902</td>\n",
       "      <td>3.0</td>\n",
       "      <td>-0.466037</td>\n",
       "      <td>0.475485</td>\n",
       "      <td>-0.903123</td>\n",
       "      <td>-0.719186</td>\n",
       "      <td>-0.535249</td>\n",
       "      <td>-0.247494</td>\n",
       "      <td>0.040260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>2.0</td>\n",
       "      <td>-0.264862</td>\n",
       "      <td>1.627323</td>\n",
       "      <td>-1.415552</td>\n",
       "      <td>-0.840207</td>\n",
       "      <td>-0.264862</td>\n",
       "      <td>0.310484</td>\n",
       "      <td>0.885829</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.184877</td>\n",
       "      <td>0.013512</td>\n",
       "      <td>0.175323</td>\n",
       "      <td>0.180100</td>\n",
       "      <td>0.184877</td>\n",
       "      <td>0.189654</td>\n",
       "      <td>0.194431</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     data1                                                              \\\n",
       "     count      mean       std       min       25%       50%       75%   \n",
       "key1                                                                     \n",
       "a      3.0 -0.529688  1.551993 -2.292309 -1.110483  0.071343  0.351622   \n",
       "b      2.0 -0.264862  1.627323 -1.415552 -0.840207 -0.264862  0.310484   \n",
       "\n",
       "               data2                                                    \\\n",
       "           max count      mean       std       min       25%       50%   \n",
       "key1                                                                     \n",
       "a     0.631902   3.0 -0.466037  0.475485 -0.903123 -0.719186 -0.535249   \n",
       "b     0.885829   2.0  0.184877  0.013512  0.175323  0.180100  0.184877   \n",
       "\n",
       "                          \n",
       "           75%       max  \n",
       "key1                      \n",
       "a    -0.247494  0.040260  \n",
       "b     0.189654  0.194431  "
      ]
     },
     "execution_count": 270,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(['key1']).describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to fill missing entries with group specific values. To do this, we pass the `mean` function as argument of `fillna`, in combination with `apply`. (Note: in the following example, we use an external Python list as grouping variable. This is perfectly legitimate.)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ohio          0.777351\n",
       "New York      0.171338\n",
       "Vermont      -0.442851\n",
       "Florida       1.704904\n",
       "Oregon        0.924346\n",
       "Nevada       -1.304861\n",
       "California   -0.380575\n",
       "Idaho        -0.743627\n",
       "dtype: float64"
      ]
     },
     "execution_count": 271,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "states = ['Ohio', 'New York', 'Vermont', 'Florida',\n",
    "          'Oregon', 'Nevada', 'California', 'Idaho']\n",
    "group_key = ['East'] * 4 + ['West'] * 4\n",
    "data = pd.Series(np.random.randn(8), index=states)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "East    0.884531\n",
       "West    0.271885\n",
       "dtype: float64"
      ]
     },
     "execution_count": 272,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[['Vermont', 'Nevada', 'Idaho']] = np.nan\n",
    "data\n",
    "data.groupby(group_key).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ohio          0.777351\n",
       "New York      0.171338\n",
       "Vermont       0.884531\n",
       "Florida       1.704904\n",
       "Oregon        0.924346\n",
       "Nevada        0.271885\n",
       "California   -0.380575\n",
       "Idaho         0.271885\n",
       "dtype: float64"
      ]
     },
     "execution_count": 273,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fill_mean = lambda g: g.fillna(g.mean())\n",
    "data.groupby(group_key).apply(fill_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Matplotlib \n",
    "*matplotlib* is a Python package that allows for data plotting and visualization. We will only explore some of its functionalities here, but the package contains many more options and possibilities. It is highly recommended to explore its documentation to discover the many potentials that matplotlib can offer. \n",
    "\n",
    "Besides importing the package, for plots visualization in Jupyter Notebooks we need to specify the magic keyword `%matplotlib inline` (or `%matplotlib notebook` for interactive plotting). We will make particular use of the `matplotlib.pyplot` module, which is the main tool used for data visualization.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Overview**. \n",
    "We are now going to create a Numpy array, and visualize it with pyplot. As we can see, plotting a set of data points is as easy as calling `plot`, and give the desired array as argument. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 275,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.arange(10)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot 'data'\n",
    "plt.plot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figures and Subplots**. \"Behind the scense\", `plot` creates a *figure* object. It is possible to initialize it with the `figure` function as follows: \n",
    "\n",
    "```\n",
    "fig = plt.figure()\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Among the option of `figure`, there is `figsize`, which allows setting (width, height) of a plot.\n",
    "\n",
    "To see several plots, you can use the `add_subplot` function. It takes three arguments: number of plots in a column, number of plots in a row, and plot indicator. For example, \n",
    "\n",
    "```\n",
    "ax1 = fig.add_subplot(2, 2, 1)\n",
    "``` \n",
    "\n",
    "means that the figure should be 2x2 (thus, four plots in total) and we are going to operate on the first subplot. Let's plot 3 blank figures: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(2, 2, 1)\n",
    "ax2 = fig.add_subplot(2, 2, 2)\n",
    "ax3 = fig.add_subplot(2, 2, 3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we will plot the cumulative sum of a random Numpy array, and add it to the last plot: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(2, 2, 1)\n",
    "ax2 = fig.add_subplot(2, 2, 2)\n",
    "\n",
    "ax3 = fig.add_subplot(2, 2, 3)\n",
    "plt.plot(np.random.randn(50).cumsum(), \"k--\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`k--` is a style option; it says that the type of line we are drawing must be black (abbreviated with `k`) and dashed (the `--` symbol). We can add arbitrary plots by calling the `ax1` and `ax2` objects created above, and giving them some plotting method (in what follows, an histogram and a scatterplot). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RyTXu7mYW6TppM2sLzAR+7u7bzazmsajH7+57gZNj1xBnAcc19RiRS+zuPvxgj5vZ5cAFwDBPcRF+Y7GETFM5ZIZseZ++MLPO7r7RzDpT3ZqMJDNrSXVSf9Tdn45tzpj493P3CjNbAAwE2ptZfqzV3uhnKKO6YszsXOBaYIS7fxV2PCHTVA6ZIVvep2eBcbHb44BI/o/VqpvmDwAfuPsfaj2UKfEX7a/2M7MC4CyqrxMsAC6O7dZ4/O6eMT/AWqr7K5fHfv43xFhGU93XtRv4AngphBjOo7o66GOqu4fCfG8eBzYClbG/y4/D/rxE5SdK71Nz30ugI9XVJGuAucDhYccZJ/bBVF9sfK9Wnjgvg+I/CXgnFv8K4ObY9mOAt2M58Emg1cGOoykFRESyTEZ1xYiISOOU2EVEsowSu4hIlgml3LGwsNCLi4vDOLXkgKVLl27xgyxRJ5LtAknsZvYpsAPYC1R5I2vzFRcXU1paGsSpRQ5wkMWkRXJCkC32M909k1cBFxHJCupjb8Ty5cvZtWtX2GGIiCQsqMTuwMtmttTMJjS0g5lNMLNSMyvdvHlzQKdNrWXLltGvXz+Ki4vZskX/GRGRzBBUYh/s7qdQPef0T83sjPo7uPtUdx/g7gOKijLjutbcuXMBuOKKKygsLATgnnvuYf78+ezbty/M0ERE4goksbt7Wex3OdWzkZ0axHHDtnDhQo4//njuuOMOAL7++mtuv/12hg0bxuDBg5XcRSSSkk7sZtbGzA7dfxs4m+o5DiLpkUce4aSTTmLDhg0H3a+qqorXXnuNIUOG1Gxr3bo169at4+abb2bx4sWq7BGRSAqixd4JeM3M3qV6kprn3f3vARw3cBUVFVx11VW8//77XHzxxezevTvuvnv37uXee+9l3LhxdbYXFBTws5/9jBYtWjBnzpxUhywi0mRJlzu6+ydA3wBiSbkpU6awdetWJk+ezJ133sk777xDSUlJg/u2atXqgKS+X8eOHRk8eDBvvfVWKsMVEWmWUGZ3HDBggIfRjbFq1SpeeeUVJk2aRHl5OUcccUTcfZ9//nl69+7Nscce2+DjW7ZsoWPHjtRemUWiwcyWNjZITiSb5VQde58+fZg0aRIARxxxBPv27eOxxx5j48aNdfarqqpi7Nix/O53v4t7rMLCQiV1EYmknEjsK1as4JJLLmHTpk11tn/22WdcfvnlTJ48uc725cuXs2PHDr7zne8c9Li33347P/rRjwKPV0QkGTmR2GfPns0TTzxBXl5ene3FxcX85Cc/4YEHHmDFin8V8ixcuBCg0cS+Y8cOZsyYwT//+c/AYxYRaa6cSOxz586lX79+NDQw6pe//CWHHnoo1157bc22f/zjH/Ts2ZMuXboc9LgjRoygsrKSl156KfCYRUSaK+sT+5dffskbb7zB8OHDG3y8Y8eO3HTTTbz44ou88cYbQHVLvHb9ejwlJSUUFhZyzTXX8Mc//jHIsEVEmi3rE/urr75KZWVl3MQOMHHiRHr06FFTJXPTTTdx1VVXNXrsvLw8rr76ajp27EhVVRWVlZUsWbIksNhFRJoj68sdZ86cyc0338ySJUv4xje+EXe/iooKDjnkkIPu05jf//73XH311ZSVlTXajSOpo3JHyXVZ32IfM2YMK1eubDRht2/fPqmkDjBs2DAA5s2bl9RxRESSkdWJvbKyMq0TdZ100kkUFhbWzAopIhKGrE7sM2fO5IgjjuDjjz9Oy/latGjBsGHDmDt3LmF0cYmIQJYn9nnz5lFVVUU6F84ePnw4n3/+OatXr07bOUVEagtyzdPIKCsrY9SoUXz22WcMHTr0gIFJqTRy5Eh69uxJjx490nZOEZHasiqxL1u2jMcee4wzzzyTr776ivLycr773e+mNYaioqJGR6yKiKRSVnXFvPjii/z+97/n29/+Nu+//z7Lli3jiiuuSHscK1eu5Prrr6eysjLt5xYRyarE/sYbb9CnTx86dOhAixYt6NevX1q7Yfb74IMPmDJligYriUgosiax79u3j8WLFzNo0KCwQ2Ho0KG0aNGCF154IexQRCQHZU1i//DDD9m2bRvf/va3ww6Fww8/nDPOOINZs2aFHYqI5KCsSezr16+nsLAwEokd4KKLLmLVqlUqexSRtMuaxH722WdTXl5Oz549ww4FgNGjR9OhQwc++uijsEMRkRwTuXLHXbt2UVBQ0KznRmmpuiOPPJLy8nLy8yP3JxaRLBepFvvDDz/M8ccfz+bNm2u2lZWVMWHCBKZPn8727dsbfN7//d//0bt3b55//vl0hZqQ/Px83J2qqqqwQxGRHBKpxH7yySezadMmfvjDH9ZM3vXhhx/y17/+lcsvv5wjjjiC4cOHM2TIEHbt2gWAu7N48WI++ugjDjvssDDDP8D27ds57rjjuPfee8MORURySOQS+z333MNLL73E7bffDlSXDu7cuZPFixczYcIEtm3bxr59+9i9ezcAY8eO5frrryc/P58BA6I1Bfdhhx1GQUEBM2fOBNDEYCKSFpHrAP6P//gPFi5cyOTJk2nXrh2TJk2iTZs2lJSUUFJSUmffyspKCgoKWLFiBaeddlqz++ZTacyYMUyePJlvfetb5Ofns3jx4rBDEpEsF0hiN7NzgbuBPGCau09J4lj85S9/IS8vj969ex9035YtW/LQQw8xceLEyHXD7HfZZZcxY8YM2rVrR//+/cMOR0RyQNJL45lZHvARcBawAVgCjHX3VfGek86l8aKmtLSUq6++mieffJKioqKww8lKWhpPcl0QfeynAmvd/RN33wPMAEYGcNys1LZtWxYtWsTdd98ddigikqWCSOxdgfW17m+IbavDzCaYWamZldYuZ8w1xx13HBdddBH33Xdf3PJNEZFkpK0qxt2nuvsAdx+Q610Q119/Pf/85z+5//77ww5FRLJQEIm9DOhW6/6RsW0SR//+/Tn77LO57bbb2LhxY9jhiEiWCaIqZgnQ08yOpjqh/zvwgwCOm9UeeughnnrqKTp37gzA3r17Q5k7XkSyT9ItdnevAiYCLwEfAE+4+8pkj5vtunTpws9+9jMApk2bRu/evfn6669DjkpEskEgfezu/oK793L3Hu7+6yCOmUuKi4v5+OOPmTFjRtihiEgWiNSUArlq2LBhnHDCCdx9992adkBEkqbEHgFmxs9//nOWL1/OokWLwg5HRDKcEntEXHrppRQWFnLXXXeFHYqIZLjITQKWqwoKCpg6dSrHHHMMO3bsYPXq1Xz99dcMHDhQi3WISJOoxR4ho0ePpm/fvrz99tuceuqpnHHGGdxzzz1hhyUiGUaJPYJOPvlk5syZQ0lJCffeey979+4NO6Q6qqqq6Nu3L8OGDeOTTz4JOxwRqUeJPYI6duzIBRdcwDXXXMOnn37KnDlzwg6pjtLSUt577z3mz5/Pyy+/HHY4IlKPEnuEjRgxgh49erByZbTGe7388suYGS1atODNN98MOxwRqUdX5SIsPz+fFStW0Lp165SdY9++fbh7k6YzeOWVVzjllFPo0qULb731VspiE5HmUYs94vYn9fLy8pQcf+zYsZx11lkJ779jxw7efPNNzjrrLEpKSli9ejXbtm1LSWwi0jxK7Bngrrvuori4mKDnsf/000958sknWbBgAUuWLEnoOVu3buW8887j/PPPp6SkBDNjxYoVgcYlIslRYs8A55xzDrt37+Z//ud/Aj2umXHFFVfQpk0b7r333rj77dmzh9dffx2A7t2788wzzzB48GAGDx5MRUUFp59+eqBxiUhylNgzwPHHH8/48eP505/+FGh5Yffu3Zk2bRqXX345r7/+OpWVlQ3uN3nyZM4880z+/ve/1+kSOuSQQyK7iLhILlNizxC33nor+fn53HTTTc16fmlpKVu2bKm5/+abb/L222/j7vz6179m9erVtGzZ8oDnzZs3jwsuuIATTjiB0aNH06lTJx588MGax5999lnGjBmjyctEIkRVMRmia9euXHXVVdx3331s2bKFwsLChJ/r7vzgBz+gW7duXH311axbt47HH3+cDRs2sGbNGtq1awdAZWUlLVq0qFMhc+WVV9K3b19efvllzjjjDFavXs23vvWtmsfLy8t5+umnWbNmDb169QruBYtIs6nFnkF+8YtfsHbt2iYldYC3336bNWvWcOmll/Lggw/yk5/8hEWLFnHllVfSokX1R2DNmjV0796d2bNn1zxvy5YtfPzxx5x22mkUFRWxcOFCZs2axYknnlizz2mnnQagskeRCFFizyCHHnoohYWFuDvjx49PeNTnI488QuvWrbn44ot5+OGH6d+/PwUFBYwfP75mn2OOOYaWLVsybdq0mm37k3VJSQkAnTp1YtSoUXWO3adPH9q2bauBSiIRosSegTZt2sQbb7zBOeecw8UXX8xrr70Wt497z549zJgxg5EjR3LYYYfRpk0bFi5cyPvvv09RUVHNfnl5eVxyySXMnTuXrVu3AtWJPS8vj/79+8eNJS8vj9NPP505c+ZQVVUV7AsVkWZRYs9AnTt35t1332Xy5MnMnTuX008/nb59+/Lqq68esO/ixYvZunUrP/rRj2q2tWnThh49ehyw7/e//32qqqp45plngOoLrCeeeCJt2rQ5aDwTJkygV69edS7Oikh4LIxqhgEDBnhpaWnaz5uNvvzySx5//HHWr1/PZZddRs+ePQ/Y55NPPqFbt24NVr3U5u706NGD3r178+KLL1JRUcHGjRs5/vjjUxV+SpjZUncfEHYcImFRYpc6Zs6cSbt27Rg+fHiTn1tWVoaZ0aVLlxREljgldsl16orJEtu3b+eRRx6pM4DpueeeY9SoUU2aZ2bMmDEMHz6cuXPnctttt7Fr166Enrdz50569+7NHXfc0eTYRSRYSuxZYvv27YwbN47nnnuuZtvzzz/PvHnz6NChQ5OOtWLFCs4991z+8Ic/0KpVq4Se07ZtWy666CKmT5/Ojh07mnQ+EQmWEnuWOPLII+natSuLFy+u2TZv3jy+853vNNq3Xt+jjz7K3r17OfbYY2vq3BPx05/+lB07dhx03hkRST0l9iwycODAmsS+fv161qxZw9ChQ5t8nO9973sAHH300U163qmnnsrIkSO58cYbuf/++5t8XhEJRlKJ3cxuMbMyM1se+zkvqMCk6QYOHMi6devYuHEj8+fPB2DYsGFNPk6/fv147LHH+POf/9yk55kZf/vb3xgxYkRNTfvrr7/Or371K8aPH09FRUWTYxGRpgtirpg/uvvvAjiOJGngwIEALFu2jG984xsMHz68zvD/RJkZY8eObVYMrVq1YtasWTVdOL/85S9ZuHAh7k5xcTGTJ09u1nFFJHFJlTua2S3AzqYmdpU7pkZlZSWbN28Ovdywto8++oiioiLGjx/PokWL+PTTT1M+1a/KHSXXBdHHPtHM3jOzB80sbvmFmU0ws1IzKw16JSCp1rJlS7p06cJXX33F119/HXY4APTq1YsOHTpw4403sm3bNp599tmax7Zt20ZZWVmI0Ylkp0Zb7GY2F/i3Bh66EXgT2AI48Cugs7tf0dhJ1WJPnX/84x8MGTKEvLw8Pvvss0i13lesWME3v/lNoLq76LTTTqN9+/Zs2LAh4bLKRKjFLrmu0T52d09oCKKZ/RV4rtEdJaW++OILAPbu3Uvnzp1Djqau/Ul99uzZXHbZZVRVVXHJJZeEHJVI9km2KqZ25hgNaFXjkO2/gFpUVISZhRzNgX77298yevRoevfuzeeff859990XaGtdRJKvivmtmZ1MdVfMp8CVSUckSenWrRt33HEH559/ftihNOi8886joqKCG264gbZt27J7924eeughTjzxRAYNGhR2eCJZQZOASah2795N9+7dOeWUU3jhhRcCOab62CXXaeSphKpVq1ZMnDiRF198kVWrVoUdjkhWUGKX0P3nf/4nrVu31hwzIgFRYpfQFRYWMmLECGbNmsW+ffvCDkck4ymxSySMGjWKnj17osFrIsnTxVPJOrp4KrlOLXaJlJ07d4YdgkjGU2KXyHjiiSc4/PDDWbduXdihiGQ0JXaJjJNPPpnKyso6y/uJSNMpsUtk9OrVi169ejFnzpywQxHJaJXur00AAANaSURBVErsEikXXnghCxYs0ILYIklQYpdIufDCC9mzZw+vvvpq2KGIZCwldomUQYMG8V//9V+cffbZYYcikrGU2CVS8vPz+fOf/0x+fj6bNm3illtuicxqUCKZQoldIuupp57i1ltvpVu3btxwww2sX78+7JBEMoISu0TWxIkTWbBgAYMHD+Y3v/kNxxxzDNdeey1hjJYWySRK7BJpQ4YMYdasWaxdu5Zx48bx1VdfRXJlKJEoSXYFJZG0OProo5k2bZpa6yIJUItdMopa6yKNU2IXEckySuwiIllGiV1EJMuEstCGmW0G4s3NWghsSWM46Zbtrw/Cf43d3b0oxPOLhCqUxH4wZlaazavfZPvrg9x4jSJRpq4YEZEso8QuIpJlopjYp4YdQIpl++uD3HiNIpEVuT52ERFJThRb7CIikgQldhGRLBOZxG5m55rZh2a21syuCzueIJhZNzNbYGarzGylmU2KbT/czF4xszWx3x3CjjUZZpZnZu+Y2XOx+0eb2Vux9/JvZnZI2DGK5JJIJHYzywP+BHwX6AOMNbM+4UYViCrgv929D1AC/DT2uq4D5rl7T2Be7H4mmwR8UOv+b4A/uvuxwDbgx6FEJZKjIpHYgVOBte7+ibvvAWYAI0OOKWnuvtHdl8Vu76A6+XWl+rVNj+02HRgVToTJM7MjgfOBabH7BgwFnortktGvTyQTRSWxdwVqr3u2IbYta5hZMdAPeAvo5O4bYw9tAjqFFFYQ7gKuBfbF7ncEKty9KnY/695LkaiLSmLPambWFpgJ/Nzdt9d+zKvrTTOy5tTMLgDK3X1p2LGIyL9EZQWlMqBbrftHxrZlPDNrSXVSf9Tdn45t/sLMOrv7RjPrDJSHF2FSBgEjzOw8oDVwGHA30N7M8mOt9qx5L0UyRVRa7EuAnrFqikOAfweeDTmmpMX6mx8APnD3P9R66FlgXOz2OOCZdMcWBHe/3t2PdPdiqt+z+e5+KbAAuDi2W8a+PpFMFYnEHmvZTQReovoC4xPuvjLcqAIxCPghMNTMlsd+zgOmAGeZ2RpgeOx+NvkFcJWZraW6z/2BkOMRySmaUkBEJMtEosUuIiLBUWIXEckySuwiIllGiV1EJMsosYuIZBkldhGRLKPELiKSZf4frpg7DUzdDIAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(2, 2, 1)\n",
    "ax2 = fig.add_subplot(2, 2, 2)\n",
    "\n",
    "ax3 = fig.add_subplot(2, 2, 3)\n",
    "plt.plot(np.random.randn(50).cumsum(), \"k--\")\n",
    "\n",
    "\n",
    "# alpha defines the figure transparency\n",
    "_ = ax1.hist(np.random.randn(100), bins=20, color='k', alpha=0.3)\n",
    "ax2.scatter(np.arange(30), np.arange(30) + 3 * np.random.randn(30))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can find a list of types of plots [here](https://matplotlibguide.readthedocs.io/en/latest/Matplotlib/types.html). \n",
    "\n",
    "**Note**: it is possible to directly initialize the grid of subplots directly; this can be done via \n",
    "```\n",
    "fig, axes = plt.subplots(2,2)\n",
    "```\n",
    "for example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Colors, Markers, Line Styles**. The `plot` function accepts an array of coordinates for the x-axis, an array of coordinates for the y-axis (of course, they need to have the same size), and (optionally) a `linestyle` and a `color` arguments that define the lines. The latter two arguments can be specified in abbreviated form. For instance, a green dashed line can be drawn with: \n",
    "```\n",
    "ax.plot(x, y, linestyle='--', color='g')\n",
    "```\n",
    "which, abbreviated, can be specified as \n",
    "```\n",
    "ax.plot(x, y, 'g--')\n",
    "```\n",
    "The `o` marker, instead, can be used to draw points. Points and lines can also be combined together, as in the next example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The following command is equivalent to: \n",
    "# plt.plot(np.random.randn(50).cumsum(). linestyle='dashed', marker='o')\n",
    "plt.plot(np.random.randn(50).cumsum(), 'ko--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next example, we are going to see other three functionalities: \n",
    "* `drawstyle` can be used to modify the default interpolation behaviour\n",
    "* each plot can be given a label \n",
    "* labels given to each plot can then be visualized in a legend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.random.randn(50).cumsum()\n",
    "plt.plot(data, 'go--', label=\"Default\")\n",
    "plt.plot(data, 'b-', drawstyle=\"steps-post\", label=\"steps-post\")   # 'b': blue color\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another useful option for lines is `linewidth`, which specifies its width. The corresponding argument for points is `markersize`. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ticks and Axis Labels**. `xticks`, `xlim`, `xlabels` (and equivalentyl `yticks`, `ylim` and `ylabels`) can be used to customize, respectively, values in the (x/y)-axis ticks, their boundaries (useful for 'zooming in' and 'zooming out'), and the axes names. Let's see them 'in action': "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.plot(np.random.randn(1000).cumsum())\n",
    "\n",
    "# Set ticks for the x-axis\n",
    "ticks = ax.set_xticks([0, 250, 500, 750, 1000])\n",
    "labels = ax.set_xticklabels(['one', 'two', 'three', 'four', 'five'], \n",
    "                           rotation=30, fontsize=15)\n",
    "\n",
    "\n",
    "# Set plot title\n",
    "ax.set_title('Plotting with matplotlib is fun!')\n",
    "\n",
    "# Set x-axis label\n",
    "ax.set_xlabel('Stages')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Legends** We have seen above how to add legends. Let's see another example here, this time by plotting three lines. The option `loc='best'` finds automatically the best position to place the legend. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from numpy.random import randn\n",
    "fig = plt.figure(); ax = fig.add_subplot(1, 1, 1)\n",
    "ax.plot(randn(1000).cumsum(), 'r', label='one')\n",
    "ax.plot(randn(1000).cumsum(), 'g--', label='two')\n",
    "ax.plot(randn(1000).cumsum(), 'b.', label='three')\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Other objects**. Matplotlib allows adding [text and annotations](https://matplotlib.org/3.1.1/tutorials/text/text_intro.html) to a plot, as well as [drawing shapes](https://matplotlib.org/api/patches_api.html) (called *patches* in matplotlib) such as arrows, rectangles, circles, etc. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Barplots**. `plot.bar` and `plot.barh` produce vertical and horizontal bar plots; they use the index (or label) as first argument, and the 'heights' as second argument. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    0.019719\n",
       "b    0.323321\n",
       "c    0.563458\n",
       "d    0.208472\n",
       "e    0.752634\n",
       "f    0.469752\n",
       "g    0.957480\n",
       "h    0.383559\n",
       "i    0.754386\n",
       "j    0.488029\n",
       "k    0.141284\n",
       "l    0.940198\n",
       "m    0.668404\n",
       "n    0.911867\n",
       "o    0.946628\n",
       "p    0.136088\n",
       "dtype: float64"
      ]
     },
     "execution_count": 284,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.Series(np.random.rand(16), index=list('abcdefghijklmnop'))\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2,1, figsize=(5,7))\n",
    "data.plot.bar(ax=axes[0], color='b', alpha=0.7)\n",
    "data.plot.barh(ax=axes[1], color='y', alpha=0.7)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Contours and heatmaps**. We can draw **contours** and **heatmaps**, which allow us to represent a third dimension in a 2D-plot. We saw an example of a contour above. We replicate it here: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = np.arange(-5, 5, 0.01)    # 1000 equally spaced points\n",
    "# Create a grid of coordinates for x-axis and y-axis \n",
    "x, y = np.meshgrid(points, points)\n",
    "# Compute third dimensions across previous coordinates\n",
    "z = np.sqrt(x ** 2 + y ** 2)\n",
    "# Plot a contour plot\n",
    "plt.figure(figsize=(5,5))\n",
    "# contourf plots a `filled contour` (the function contour draws empty contours)\n",
    "contour = plt.contourf(x, y, z, cmap=\"plasma\")\n",
    "plt.title(r\"$\\sqrt{x^2 + y^2}$\", fontsize=15)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "# colorbar adds a legend to the contour\n",
    "plt.colorbar(contour)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also visualize heatmaps of a matrix, by means of the `imshow` function: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mat = np.random.randn(10,5)\n",
    "plt.figure(figsize=(6,7))\n",
    "plt.imshow(mat, cmap=\"winter\")\n",
    "plt.ylabel(\"Matrix rows\")\n",
    "plt.xlabel(\"Matrix columns\")\n",
    "plt.title(\"Matrix values\")\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**seaborn**. Another nice tool for data visualization is the `seaborn` package. It is particularly useful to represent data directly from objects such as Pandas dataframes. A particularly useful feature is that it allows plotting all columns of a DataFrame with a single command, as well as aggregated data. We won't discuss `seaborn` here, but you should definitely give a look to its [website](https://seaborn.pydata.org/index.html) for some examples.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. scikit-learn\n",
    "`scikit-learn` is probably the most famous library for Machine Learning with Python. It contains a wide range of models, evaluation measures, model selection methods, and many other functionalities. Furthermore, it has a comprhenesive documentation (linked in the end of the document), which includes accurate theoretical explanations, along with detailed functions description. We are going to see some `scikit-learn`'s features here; in the rest of the course, we will use the library more in detail.    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Estimators \n",
    "`scikit-learn` provides modules for a large number of algorithms, including *supervised* and *unsupervised* learning. These algorithms allow estimating (also called *training* or *fitting*) Machine Learning models on arrays in Numpy format (and therefore also Pandas). \n",
    "\n",
    "*Supervised learning* models (both classifiers and regressors) share a very similar interface with each other; they have an *initializer*, a *fit* method for model training, a *predict* method to perform predictions, and a *score* method for model evaluation (*note*: this method returns a default score, but other metrics are possible, as we will see). Such methods take as argument either a data matrix of inputs X alone, or along with an array of outputs y (plus other hyperparameters). Such objects are called **estimators** in scikit-learn, and a blueprint of their interface can be represented as follows: \n",
    "\n",
    "```\n",
    "class SupervisedEstimator(...):\n",
    "    # Estimator initializer\n",
    "    def __init__(self, X, y):\n",
    "    ...\n",
    "    return self\n",
    "    \n",
    "    # Fit to the training data given input X and output y\n",
    "    def fit(self, X, y):\n",
    "    ...\n",
    "    return self\n",
    "    \n",
    "    # Perform prediction on input X \n",
    "    def predict(self, X): \n",
    "    ...\n",
    "    return y_pred\n",
    "    \n",
    "    # Measure performance against true labels y  \n",
    "    def score(self, X, y): \n",
    "    ...\n",
    "    return score\n",
    "```\n",
    "\n",
    "\n",
    "\n",
    "Therefore, when training a model and, for instance, performing predictions with it, we should: \n",
    "1. initialize the estimator\n",
    "1. training the model with `fit` \n",
    "1. performing the predictions with `predict` \n",
    "\n",
    "***\n",
    "\n",
    "Besides estimators, scikit-learn also provides **transformers**, that perform data transformations. For example, the `SimpleImputer` algorithm is used to impute missing values. They share an interface similar to the one of the estimators, except that they replace the `predict` method with a `transform` method. They also allow performing fit and transformation in one go with the `fit_transform` method. \n",
    "\n",
    "***\n",
    "\n",
    "Both estimators and transformers, once fitted to the data, contain algorithm-specific attributes. Attributes are useful, for instance, to retrieve the estimated model coefficients, or estimated probabilities (in case of classifiers). Attribute names end with a underscore (`_`) in scikit learn. \n",
    "\n",
    "Check, for example, the [linear regression algorithm documentation page](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html): can you recognize which ones are the function arguments, the function methods, and the function attributes?  \n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Other Features\n",
    "**Unsupervised Learning**. Besides supervised learning estimators, scikit-learn also contains a huge number of unsupervised learning ones. For example, the [`sklearn.cluster`](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.cluster) module offers algorithms for clustering, while [`sklearn.decomposition`](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.decomposition) offers algorithms for matrix decomposition (such as PCA, for instance). \n",
    "\n",
    "**Pipelines**. As we will see, scikit-learn allows estimating several transformers (plus one optional estimator) into one object, called `Pipeline`. This can be found in the [`sklearn.pipeline` module](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.pipeline). \n",
    "\n",
    "**Model and feature selection**. sklearn also includes several functions for model and feature selection, such as cross-validation, train-test split methods, and grid/random parameter search, as well as model-based feature selection algorithms. Model selection functions are in the [`sklearn.model_selection`](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.model_selection) module, while feature selection functions are in the [`sklearn.feature_selection`](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.feature_selection) module. \n",
    "\n",
    "**Metrics**. Besides the default metrics contained in the estimators' `score` method, we can also compute other non-default metrics (such as root mean square error, $f_1$ score, etc.). Metrics are in the [`sklearn.metrics`](https://scikit-learn.org/stable/modules/classes.html#sklearn-metrics-metrics) module.\n",
    "\n",
    "**Datasets and Data Generation routines** `scikit-learn` also comes with a [`sklearn.datasets`](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.datasets) module, which allows to [load datasets](https://scikit-learn.org/stable/datasets/index.html) into your Python session, and use them to compare model performance. Furthermore, scikit-learn also performs [toy data generation](https://scikit-learn.org/stable/datasets/index.html#generated-datasets), which can be used to generate data for various tasks and sample sizes. The [`make_classification`](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_classification.html#sklearn.datasets.make_classification) function, for example, generates data with a desired sample size, a desired number of classes, and a desired number of features, for classification tasks.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Final example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this final example, we are going to use all the libraries we have explored in this tutorial to perform a small prediction task on a simulated dataset. In particular: \n",
    "\n",
    "* we will generate two continuous variables, an input x and an output y, with Numpy\n",
    "* we will include them in a Pandas DataFrame, and explore its descriptive statistics \n",
    "* we will transform the data using a scikit-learn transformer (StandardScaler, that standardizes the data)\n",
    "* we will train a linear regression model on such data with scikit-learn\n",
    "* we will compare model's predictions against the true values using matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd \n",
    "import matplotlib.pyplot as plt\n",
    "from pandas.plotting import scatter_matrix\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression \n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1. Data Generation**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 289,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1)\n",
    "# Generate continuous x and y, with sample size 100 \n",
    "x = np.random.randn(100)\n",
    "y = 2 + 3.5 * x + np.random.randn(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**2. Summary Statistics**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 290,
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.528172</td>\n",
       "      <td>0.554891</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.072969</td>\n",
       "      <td>-1.161812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.865408</td>\n",
       "      <td>3.934015</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y\n",
       "0  1.624345  7.238080\n",
       "1 -0.611756  1.083360\n",
       "2 -0.528172  0.554891\n",
       "3 -1.072969 -1.161812\n",
       "4  0.865408  3.934015"
      ]
     },
     "execution_count": 290,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a Pandas DataFrame and compute summary statistics\n",
    "data = pd.DataFrame({\"x\":x, \"y\":y})\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.060583</td>\n",
       "      <td>2.364835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.889615</td>\n",
       "      <td>3.331800</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-2.301539</td>\n",
       "      <td>-5.886003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.613818</td>\n",
       "      <td>0.244235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.064074</td>\n",
       "      <td>2.622106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.637410</td>\n",
       "      <td>4.618883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2.185575</td>\n",
       "      <td>11.840214</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                x           y\n",
       "count  100.000000  100.000000\n",
       "mean     0.060583    2.364835\n",
       "std      0.889615    3.331800\n",
       "min     -2.301539   -5.886003\n",
       "25%     -0.613818    0.244235\n",
       "50%      0.064074    2.622106\n",
       "75%      0.637410    4.618883\n",
       "max      2.185575   11.840214"
      ]
     },
     "execution_count": 291,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_matrix(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**3. Standardize the input x with a scikit-learn transformer**.\n",
    "Remember: scikit-learn transformers need to be initialized, before being used for estimation and transformation/prediction. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New mean: -0.00; new standard deviation: 1.00\n"
     ]
    }
   ],
   "source": [
    "# 1. Initialization\n",
    "scl = StandardScaler()\n",
    "# 2. Fit with the `fit` method\n",
    "scl.fit(x.reshape(-1,1))\n",
    "# 3. Transform the data \n",
    "x_standardized = scl.transform(x.reshape(-1,1))\n",
    "# 4. new mean and std. deviation of x (compare with the results of Pandas describe() method above)\n",
    "print(\"New mean: {0:.2f}; new standard deviation: {1:.2f}\".format(x_standardized.mean(), x_standardized.std()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**4. Train a Linear Regression model and perform predictions**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 294,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1. Initialization\n",
    "lin_reg = LinearRegression()\n",
    "# 2. Train the model\n",
    "lin_reg.fit(x_standardized,y)\n",
    "# 3. Perform predictions\n",
    "y_pred = lin_reg.predict(x_standardized)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also evaluate the predictions with `score`, which by default returns the *coefficient of determination* $R^2$ for regression estimators:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model R^2: 0.92\n"
     ]
    }
   ],
   "source": [
    "print(\"Model R^2: {0:.2f}\".format(lin_reg.score(x_standardized,y)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also observe the estimated intercept and slope with the corresponding attributes (compare with the true values, 2 and 3.5, used in the data generating step: they are not exactly equal; can you detect the reason?): "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 296,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model intercept: 2.36; slope for x_standardized: 3.18\n"
     ]
    }
   ],
   "source": [
    "print(\"Model intercept: {0:.2f}; slope for x_standardized: {1:.2f}\".format(lin_reg.intercept_, \n",
    "                                                                           lin_reg.coef_[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**5. Plot true values vs. model predictions**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 297,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5))\n",
    "plt.plot(x_standardized, y, \"bo\", markersize=8, label=\"True (generated) values\")\n",
    "plt.plot(x_standardized, y_pred, \"r-\", linewidth=1.5, label=\"Model predictions\")\n",
    "plt.title(\"Linear Regression: Observations vs. Model fit\")\n",
    "plt.xlabel(\"x\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Other Useful Resources \n",
    "\n",
    "* [Numpy official tutorial](https://numpy.org/devdocs/user/quickstart.html) \n",
    "* [Numpy documentation](https://docs.scipy.org/doc/numpy/user/index.html)\n",
    "* [Pandas documentation](https://pandas.pydata.org/pandas-docs/stable/user_guide/index.html) \n",
    "* [Matplotlib documentation](https://matplotlib.org/contents.html)\n",
    "* [scikit-learn documentation](https://scikit-learn.org/stable/user_guide.html)\n",
    "\n",
    "Other useful libraries for Data Science are: \n",
    "* [Scipy](https://docs.scipy.org/doc/scipy/reference/) for scientic computing with Python \n",
    "* [statsmodels](https://www.statsmodels.org/stable/index.html) for useful statistical routines \n",
    "\n",
    "Packages cheat-sheets: \n",
    "* [Numpy](https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Numpy_Python_Cheat_Sheet.pdf)\n",
    "* [Pandas](https://github.com/pandas-dev/pandas/blob/master/doc/cheatsheet/Pandas_Cheat_Sheet.pdf)\n",
    "* [Matplotlib](https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Python_Matplotlib_Cheat_Sheet.pdf)\n",
    "* [scikit-learn](https://s3.amazonaws.com/assets.datacamp.com/blog_assets/Scikit_Learn_Cheat_Sheet_Python.pdf)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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