learning_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3024049a",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Top"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d8392fd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standard\n",
    "import random\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2cf1a5e9-01e1-4cc2-88a5-4c89406fff52",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Seed random for less diff in notebook\n",
    "np.random.seed(31)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8374d1df",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Adjust figure size to be bigger:\n",
    "plt.rcParams['figure.figsize'] = [15, 6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "07f37f12",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set seaborn plot theme:\n",
    "sns.set_theme()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4c159f65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'3.6.9 (default, Jun 29 2022, 11:45:57) \\n[GCC 8.4.0]'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2bdcb040",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.19.5'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ba0f9e8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.1.5'"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1a01f5a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.11.2'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sns.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3133645e",
   "metadata": {},
   "source": [
    "# Notebook Tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "57c096d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "85afea23-7a4e-4ecd-88d7-f873d3c258b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Output history value '_', '__'\n",
    "1 + _"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2e6b3354",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_ - __"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14b6a769",
   "metadata": {},
   "source": [
    "# Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "551a25e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e5933449",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e23c0213",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cebedafa-7cef-4b6d-8026-f45e0f9a5dae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.28605382, 0.95810557, 0.77031293, 0.98687   , 0.20816546,\n",
       "       0.13691705, 0.9083738 , 0.06863852, 0.07533272, 0.54353469])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3baee9d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 4, 5, 2, 3, 2, 5, 3, 5, 4],\n",
       "       [4, 4, 3, 1, 1, 2, 3, 4, 5, 4],\n",
       "       [1, 5, 3, 2, 2, 2, 2, 2, 2, 5],\n",
       "       [5, 1, 2, 1, 2, 3, 6, 4, 2, 1],\n",
       "       [4, 1, 4, 3, 5, 2, 3, 3, 2, 1]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (row, col)\n",
    "M = np.random.randint(1, 7, (5, 10))\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4db44079",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "147"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ea661777",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16, 15, 17,  9, 13, 11, 19, 16, 16, 15])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "378f54ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([35, 31, 26, 27, 28])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.sum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69889297",
   "metadata": {},
   "source": [
    "## Broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0b3c208e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4]\n",
      "(5,)\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(5)\n",
    "print(a)\n",
    "print(a.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "2c967c4c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0]\n",
      " [1]\n",
      " [2]\n",
      " [3]\n",
      " [4]]\n",
      "(5, 1)\n"
     ]
    }
   ],
   "source": [
    "# Similar to transpose?\n",
    "b = a[:, np.newaxis]\n",
    "print(b)\n",
    "print(b.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8ed4e27d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2, 3, 4],\n",
       "       [1, 2, 3, 4, 5],\n",
       "       [2, 3, 4, 5, 6],\n",
       "       [3, 4, 5, 6, 7],\n",
       "       [4, 5, 6, 7, 8]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c72825f",
   "metadata": {},
   "source": [
    "## Masks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e44fc128",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Normal distribution\n",
    "x = np.random.randn(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b28ac9e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.019929128729231336"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "35ebc747",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0552964151939448"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2c79fdc2-516d-4ac7-89ae-6d3bf9b958e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-3.2089444841548556, 3.3444339815399284]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x.min(), x.max()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "d446e548",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x > -2).all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "44529b47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x > 2.5).any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "4fc81cff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((x > 2.5) * 1).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef87a99a",
   "metadata": {},
   "source": [
    "## Indexing (np)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "837257cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 6, 1, 5, 6, 4, 8, 4, 7, 4])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.random.randint(0, 10, size=10)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "752c728d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 4, 8])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[[4, 5, 6]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "9b486b3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.random.randn(100, 2)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ca2327ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 2)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Select 10 samples in the total array\n",
    "Xs = X[np.random.choice(X.shape[0], 10, replace=False)]\n",
    "Xs.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d7e5e7f",
   "metadata": {},
   "source": [
    "# Plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bf166dc",
   "metadata": {},
   "source": [
    "## Regular plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "bbe9ace6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa447135f60>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "39579d0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa446ee4b70>]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# '[marker][line][color]'\n",
    "plt.plot([1,2,3], 'o:g')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "f5b1e7e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa44706d198>]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([1,2,3], [4,5,6], 'D r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7959c969",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa44708e9e8>]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IALV07cq4lXIAciGkwS2YWafKdC8FaJ73UNpJSINbMLNOlZX9vmAAKXkPpZ2ENKBlZhMBAIqjcQjQMveTKw/dS4Gqm5yabdv7mfdQOkVIA6gR3UuBqmvnxKH3UDpFSAOakttsYjtnTmme5wUA1k5IA5qS22yiLZdr14nupSmfFwGRMjJum5Ni4lAHaNpJSAOu4gKhPqr+PAvulJFx25wUE4eeJ9pJSAOu0swFQqrZxNy2XLaiSuG4Ss/LalTpuWNtPPed4fdMHQlpQMtSfXjmtuWyFVWaPU/5vKQIiFV67libop77V/71dPzz628t/73qExtrtdbfs22IaQnVxRDSgNqtfFBdSwGxt3dj7D50tNTBnfr4qwe3xWf+5J6IKP+EUw58bqVl4qoYQhpQiRWpMs6c1iEcl/F5WY06PHfcmOe+M/yeqbuuRqPRSPHAFy9ejsXFJA+dhd7ejXHhwqXUZcB1bhTSjNf2K2s4zlVv78Z48f/NdORiznNXX0U99yvfY20Vu57XWH6uvS64NlQvEapvrru7KzZt2nDT77e0kvbqq6/Gd7/73Xj//ffjy1/+cvz1X/91Kz8OyECnVz5ckNAuxlUevMbXxu+KMqrCjpzcdDf7D3/729/G2NhYvPLKK3H06NH4wQ9+EGfOnCmyNiCBTl8g3GjmrY6qui2wDjx3t1bl17jnvjP8nqmjpkPaG2+8EZ/85CfjzjvvjPXr18eDDz4YP/7xj4usDaA2zJ6Xl+euvjz3neH3XC5CdTGa3u74zjvvRG9v7/LfN2/eHL/4xS8KKQqoNgfCqapObe3LfQuh1zjUl9d4MZoOaTfqN9LV1bXqf3+rg3J10du7MXUJsGpFjtevfn57fPXz2yMiYveho/Hqc3sL+9mwJMV77LHpueWxXYXHadaNXuO7Dx3NuubUXBNQNsZsezUd0u6+++74+c9/vvz3d955JzZv3rzqf6+7o255lEe7x6vXAkVL+R7bqce93ePktNq2VKvX+o25JqBsjNnWta2746c+9al4/vnnY35+Pj7ykY/E66+/Hn//93/f7I8Dasre9erLKSy0Q6e29q31cXK4oezk1GxE/L5W2x5bV/XXE/ChllbSDh48GPv27Yv3338/vvCFL8QnPvGJImuDyrty+lScnzgSW4b3x/ptA6nLScLFRvXlEBbaqVOtp8vY4rqMNeeu7K8nIRNWp6X7pO3evTt2795dVC1QK1dOn4pz42NxcsNA7Bwfi3sOHKxtUAOKoWEHuSt7yIROaSmkAc1ZCmiNhYWYvmt77JifiXOCGhVS17DQqe27N3ucnFeubG1uXl1fT1BnXY0btWnsAI1DHLisq5UBLSJidOu+GDnzckREdPX0ZBnUjFdakSIsGLP5hTRubi3jtYzP67Uhc4mQWV7eY1vXtsYhQHPOTxyJkxsGYvqu37eiHt26LyIiBudn4v6JI9H/7HOpyoO2ch6lfa4942rlilzkvMILuepOXQDUzZbh/bHz8qkYOfPy8gra0p93Xj4VW4b3J66QOlvqxleklWHhRrPptG5phf6ncW+cGx+LK6dPCcMVJXxDPQhp0GHrtw3EPQcORldPz1Vfz3WrI/XSjhAlLLTXtWdcGwsLy0GN6in760nIhNWx3RESWApq58bHYnB+RkCj0jQ9aJ9rz7guWQpq3lfIjdc8rI7GIYk4cElEee6TZrxWWycP9XfqPEpdxuzsk4fip3HvVWdclwzOz8T9cdYZ1xKoy3ilOozZ1mkcAhlbv23ABRTJOdRfXluG98fO8bHYMT8TEdd3i91y4GDK8iipskwgQpU5kwZAxziPUixnXCnajZrQAJ0npAGFaUdnQDqr3SHKeZTirQxqzrjSCk1oIB9CGlAY7dXLT4gqp6Wgdn+cFdBoyu2a0Ahq0FnOpAFUgJtE44wrrTg/cSRObhi4qgnN6NZ9EfG/TWgmjhhf0EFCGtAS7dXzcGx6zu8bmmSSQxMayI3tjis4TwNrN7SjPyZGHljuCLj057pf8ADlYau2JjSQGytpK5iJBsrEKiZQpKWgdm58TBMaSExIAwqjvXpnub8ZNM8kx40tN6GZOBJbBDRIpvYhzZs0FMdrBiiLm01yXDl9KmafPFTrGzlrQgPp1T6kmYkGqsAqJrRuqQ39yQ0DsXN8zFY/IBmNQwAqwCrm9TSDup7fyY3tGexzI2cgK0LaCmaiAapDx77r+Z3c2Gd733Mj54yZXKCOar/dcSUz0QBQP27knDfdt6kjIQ2AytAM6np+J7fnRs5AbroajUYjxQNfvHg5FheTPHQWens3xoULl1KXAativFI2vb0bY/eho5pBXUODrJtbeSZtKaR16j5h3mOvd+3kwhKTC3kwZlvX3d0VmzZtuOn3raQBALW3fCPn//vchzdyXrdOd8eEdN+m7jQOAWgDB93T0wzqen4nt9e45n8BUhDSANpAF730bIm6nt/JzS1td4wPPviwgcgHH+jsmAmTC9SRkAZQMKtoUC4rz6OtpAV/HkwuUEcahyTiwCVlYryujoPu+TBm05qcmi3VmJ998lD8NO69qgX/ksH5mbg/zra1Bb/xStkYs63TOASgQ5YOui+1OHfQnboq232ttOAHcmO7I0ABJqdmY3j0xHJAi/iwI5mtj5C/pc6OXT09V329Uy34b8R7B9SblTSAAlzbLtoWx3op2/a+dij7TbOXW/CPj33Ygj9hQIso32okUCwhDaANXFzViwvqztzX6srpU3F+4khsGd7flvC0FNTunzgSW9wjDUhISAMomHbRULylDownNwzEzvGxtq1yrd820NYmIbdS9tVIoDhCGkDBXEzVgwvqmyt6omJli/zpu7bHjvmZONfGoJZKJ1YjgXIQ0gCgCS6ob67IkHq7e5hVLagBROjuCAC0WSudCs9PHImTGwZidOu+GN26LyJi+c8nNwzE+YkjRZWZlU5um9ZJshw8T/UipAFAi5xDvLUb3eR9tbYM74+dl0/FyJmXl+9dtvTnnZdPxZbh/QVVmZdObplt5fmhczxP9SKkAUCL6n4GrZ1yvIcZQLt1NRqNRooHvnjxciwuJnnoLPT2bowLFy6lLgNWpUrj1f2s6qFKY7asrm2ssqTZxipXdXe8fKpSAS3FeC36+aE9cn2evMe2rru7KzZt2nDT7wtpiRjclEmVxqsGD52XIhhXacxWQVGvu3bfJy2V1OPV+2I55PQ8pR6zVXC7kGa7IwBt5RwFRVm6h1mVAhrAjWjBD5TWaldo3M8K0tJYJW+en3LwPNWL7Y6JWCamTHIdr81s/chpu0iVpT5HkeuYhRsxXikbY7Z1t9vuaCUNgMK50TMANE9IA0ql1a2LtosAALkT0oBSaXWFxhm0zhOMAWBtdHcEoK0EYwBYm5ZD2uHDh+P5558vohaANbFCA1CcyanZ1CUA/6vpkHbp0qV46qmnYmJiosh6AFbNCg1AcdzTEPLRdEg7fvx49PX1xVe+8pUi6wEAAChMGVeJm24cMjQ0FBFhqyMAQElMTs1etQuh1Y65UAbHpudKN55vG9Jee+21eOaZZ676Wn9/f7z00kstPfCtbt5WF729G1OXAKtmvFI2nRizr/zr6firB7e1/XGovk69xx6bnouvfn778t+/+vnty3/ffehovPrc3o7UQfmV7bqgbPXeNqQ99NBD8dBDDxX+wBcvXo7FxUbhP7cs3KmdMjFeKZtOjdl/fv2t+Myf3NP2x6HaOv0ee6vH8l7PapThuuDaVeLdh45GRD6rxN3dXbdctHKfNACAClvtlkYdc6mSVu+rmpqQBgBr4AwPZbPai1XjF/LRckj727/92yLqAIBSKPvsLEDdlHGVuOWbWQMAUA5lvFiFVpVxlVhIA4AmueClbMp4sQp1JKQBQJNc8ALQDkIaAABARoQ0AACAjAhpAAAAGRHSAAAAMiKkAQAAZERIAwAAyIiQBgCsyeTUbOoSACpNSAOAEksRmI5Nz3X8MQHqREgDgBITmACqZ13qAgCA/E1OzV4VCIdHT0RExJ7Bvhja0Z+oKoBqEtIAoGRSBKahHf3LP3t49ERMjDzQlscBQEgDgNIRmLjW5NSsFU2oEGfSAIA12TPYl7oEruFsIlSLkAYAJZYiMFmxAWgv2x0BoMQEpvpq99lEWyghHSENgDVx4QZ5aPfZxGPTc17rkIjtjgCsibMvANBeVtIAAEquqLOJ7ocHeehqNBqNFA988eLlWFxM8tBZ6O3dGBcuXEpdBqyK8cq1F25Lcr1wM2Ypk1zHq9s7cDO5jtky6e7uik2bNtz0+1bSALgt9+UCgM5xJg0AgOu4Hx6kI6QBsCYu3KAectzKDHUhpAGwJi7cAKC9hDQAAICMCGkAAAAZEdIAAAAyIqQBAABkREgDAADIiJAGAACQESENAAAgI0IaAABARoQ0AACAjAhpAAAAGRHSAJo0OTWbugQAoIKENIAmHZueS10CAFBBQhoAAEBG1qUuAKBMJqdmr1pBGx49ERERewb7YmhHf6KqAIAqEdIA1mBoR/9yGBsePRETIw8krggAqBrbHQEAADIipAE0ac9gX+oSAIAKEtIAmuQMGgDQDkIaAABARoQ0AACAjAhpAAAAGWk6pL355pvxyCOPxN69e+NLX/pSnDt3rsi6AAAAaqnpkPbEE0/E008/HUePHo3du3fHt7/97SLrAgAAqKWmQtrCwkJ84xvfiG3btkVExMc//vF4++23Cy0MAACgjpoKaT09PbF3796IiFhcXIwXXnghPv3pTxdaGAAAQB11NRqNxq3+D6+99lo888wzV32tv78/XnrppVhYWIiRkZH47//+7/iHf/iHuOOOO9paLAAAQNXdNqTdzLvvvhtf+9rX4s4774zvfOc70dPTs6Z/f/Hi5VhcbOqhK6G3d2NcuHApdRmwKsYrZWPMUibGK2VjzLauu7srNm3acPPvN/uDn3jiifjoRz8ahw8fXnNAAwAA4MbWNfOPfvWrX8Xx48dj69atMTQ0FBERmzdvjhdffLHI2gAAAGqnqZD2R3/0R/HWW28VXQsAAEDtNb3dEQAAgOIJaQAAABkR0gAAADIipAEAAGRESAMAAMiIkAYAAJARIQ0AACAjQhoAAEBGhDQAAICMCGkAAAAZEdIAAAAyIqQBAABkREgDAADIiJAGAG0yOTWbugQASkhIA4A2OTY9l7oEAEpISAMAAMjIutQFAECVTE7NXrWCNjx6IiIi9gz2xdCO/kRVAVAmQhoAFGhoR/9yGBsePRETIw8krgiAsrHdEQAAICNCGgC0yZ7BvtQlAFBCQhoAtIkzaAA0Q0gDAADIiJAGAACQESENAAAgI0IaAABARoQ0AACAjAhpAAAAGRHSAAAAMiKkAQAAZERIAwAAyMi6VA/c3d2V6qGz4XdAmRivlI0xS5kYr5SNMdua2/3+uhqNRqNDtQAAAHAbtjsCAABkREgDAADIiJAGAACQESENAAAgI0IaAABARoQ0AACAjAhpAAAAGRHSAAAAMiKkAQAAZERIS+TNN9+MRx55JPbu3Rtf+tKX4ty5c6lLglU5fPhwPP/886nLgBt69dVX4+GHH47PfOYz8U//9E+py4Hbunz5cnzuc5+Ls2fPpi4FbuuFF16IXbt2xa5du+LZZ59NXU6lCWmJPPHEE/H000/H0aNHY/fu3fHtb387dUlwS5cuXYqnnnoqJiYmUpcCN/Tb3/42xsbG4pVXXomjR4/GD37wgzhz5kzqsuCmZmZm4rHHHou5ubnUpcBtvfHGG/Gzn/0sfvSjH8Xk5GT88pe/jJ/85Cepy6osIS2BhYWF+MY3vhHbtm2LiIiPf/zj8fbbbyeuCm7t+PHj0dfXF1/5yldSlwI39MYbb8QnP/nJuPPOO2P9+vXx4IMPxo9//OPUZcFN/fCHP4xvfetbsXnz5tSlwG319vbGyMhI9PT0xB133BEf+9jH4je/+U3qsiprXeoC6qinpyf27t0bERGLi4vxwgsvxKc//enEVcGtDQ0NRUTY6ki23nnnnejt7V3+++bNm+MXv/hFworg1p5++unUJcCq/eEf/uHyn+fm5uJf/uVf4vvf/37CiqpNSGuz1157LZ555pmrvtbf3x8vvfRSLCwsxMjISHzwwQfx+OOPJ6oQrnarMQs5azQa132tq6srQSUA1fXrX/86Hn/88fjmN78ZfX19qcupLCGtzR566KF46KGHrvv6u+++G1/72tfizjvvjO9+97txxx13JKgOrnezMQu5u/vuu+PnP//58t/feecd28gACvTmm2/GgQMH4qmnnopdu3alLqfSnElL5IknnoiPfvSjcfjw4ejp6UldDkDpfepTn4p/+7d/i/n5+fjd734Xr7/+euzcuTN1WQCV8Pbbb8fXv/71+M53viOgdYCVtAR+9atfxfHjx2Pr1q3L53w2b94cL774YtrCAErs7rvvjoMHD8a+ffvi/fffjy984QvxiU98InVZAJXwve99L957770YHR1d/tqjjz4ajz32WMKqqqurcaNN/AAAACRhuyMAAEBGhDQAAICMCGkAAAAZEdIAAAAyIqQBAABkREgDAADIiJAGAACQESENAAAgI/8fCGJq8naxcDcAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Xs[:, 0], Xs[:, 1], 'D r')\n",
    "plt.plot(X[:, 0], X[:, 1], '+ b')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5b0f7b2",
   "metadata": {},
   "source": [
    "## Scatter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "d811bff6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.scatter(Xs[:, 0], Xs[:, 1], color='red', s=200, alpha=0.3);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68eed8be",
   "metadata": {},
   "source": [
    "## Histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "aadbdc96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  2.,   1.,   1.,   2.,   5.,   8.,   7.,  16.,  21.,  29.,  46.,\n",
       "         82., 100., 125., 151., 189., 276., 349., 358., 424., 492., 527.,\n",
       "        577., 576., 605., 573., 619., 595., 520., 441., 423., 383., 317.,\n",
       "        277., 206., 177., 135., 108.,  86.,  62.,  37.,  23.,  20.,  11.,\n",
       "          7.,   7.,   1.,   1.,   1.,   1.]),\n",
       " array([-3.88575503, -3.73051558, -3.57527613, -3.42003668, -3.26479723,\n",
       "        -3.10955778, -2.95431832, -2.79907887, -2.64383942, -2.48859997,\n",
       "        -2.33336052, -2.17812107, -2.02288161, -1.86764216, -1.71240271,\n",
       "        -1.55716326, -1.40192381, -1.24668436, -1.0914449 , -0.93620545,\n",
       "        -0.780966  , -0.62572655, -0.4704871 , -0.31524765, -0.16000819,\n",
       "        -0.00476874,  0.15047071,  0.30571016,  0.46094961,  0.61618906,\n",
       "         0.77142852,  0.92666797,  1.08190742,  1.23714687,  1.39238632,\n",
       "         1.54762578,  1.70286523,  1.85810468,  2.01334413,  2.16858358,\n",
       "         2.32382303,  2.47906249,  2.63430194,  2.78954139,  2.94478084,\n",
       "         3.10002029,  3.25525974,  3.4104992 ,  3.56573865,  3.7209781 ,\n",
       "         3.87621755]),\n",
       " <BarContainer object of 50 artists>)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA28AAAFoCAYAAADAVcNtAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAgy0lEQVR4nO3dfZBV9X0/8Pe6uyxYl7Hau8QhDpkER+I4SlrHuOnM7tgHQDdbHCAt4gy101hIU6mMw8Qi6mi1oMVhNFbT6VidMGktGuVpyGpqpkwdTK38YZpqM2kEWh9md8FEHsI+sOzvD9v9xaKwLHe593Bfr7+8Z8/X87n7gXPvm/M951s3PDw8HAAAAKraWZUuAAAAgBMT3gAAAApAeAMAACgA4Q0AAKAAhDcAAIACEN4AAAAKQHgDAAAogIZKF/B//fSnh3L06PgvPXf++edk376D434cjk8fqoM+VAd9qA76UB30oTroQ3XQh+pwOvpw1ll1+eVf/qWP/XnVhbejR4dPS3j732NRefpQHfShOuhDddCH6qAP1UEfqoM+VIdK98G0SQAAgAIQ3gAAAApAeAMAACgA4Q0AAKAAhDcAAIACEN4AAAAKQHgDAAAoAOENAACgAIQ3AACAAhDeAAAACkB4AwAAKADhDQAAoACENwAAgAJoqHQBAHCmaJ48KRObxvbR2td/JAf2Hy5zRQCcSYQ3ACiTiU0N6bx105jGbnlwbg6UuR4AziymTQIAABSA8AYAAFAAwhsAAEABjCq8fe9738u8efMyZ86c3HvvvUmSHTt2pLOzM7Nmzcq6detG9n3jjTcyf/78zJ49O7fffnuOHDkyPpUDAADUkBOGt//+7//OXXfdlUcffTRbtmzJ66+/nu3bt2flypV59NFHs23btvzwhz/M9u3bkyQrVqzIHXfckeeffz7Dw8PZsGHDuL8JAACAM90Jnzb53e9+N9dee20+8YlPJEnWrVuXPXv2ZNq0abnwwguTJJ2dnenq6sr06dPT19eXmTNnJknmzZuXhx9+OIsWLRq/dwAAv+BUHtefJAODQ2WsBgDK54Sfbnv27EljY2P+8A//ML29vbn66qtz0UUXpVQqjezT0tKS7u7u9PT0fGh7qVRKd3f3+FQOAB/hVB7Xn3zwyH4AqEYnDG9DQ0N59dVXs379+px99tn54z/+40yaNOmY/erq6jI8PPyR20/G+eefc1L7n4pSqfm0HYuPpw/VQR+qgz5Uh0r1Qf8/zO+jOuhDddCH6lDpPpwwvP3Kr/xKWltbc9555yVJfvM3fzNdXV2pr68f2aenpyctLS2ZMmVK9u7dO7K9t7c3LS0tJ1XQvn0Hc/TosSGw3Eql5vT2Wg610vShOuhDddCH8ijHB+tY+3Cqx9b//8/fh+qgD9VBH6rD6ejDWWfVHfdi1gkfWHL11VfnpZdeyv79+zM0NJR//ud/zpw5c7Jr167s2bMnQ0ND2bp1a9ra2jJ16tQ0NTVl586dSZKNGzemra2tfO8GAACgRp3wytvll1+eL3/5y1m0aFEGBwfz67/+67n++uvz6U9/OjfffHP6+/vT3t6eOXPmJEnWrl2bVatW5dChQ7nkkkuyePHicX8TAFB0A4NDY75y19d/JAf2Hy5zRQBUm1E9jmvBggVZsGDBh7a1trZm8+bNx+w7Y8aMPPPMM+WpDgBqxITG+jE/aGXLg3NjQhXAmW9Ui3QDAABQWcIbAABAAQhvAAAABSC8AQAAFIDwBgAAUADCGwAAQAEIbwAAAAUwqnXeAOBkNU+elIlNY/uY6R8YStOE+jJXBADFJrwBMC4mNjWc0qLTpzIWAM5EwhsA/IKBwaGUSs2VLgMAjiG8AcAvmNBY76ofAFXJA0sAAAAKQHgDAAAoAOENAACgAIQ3AACAAhDeAAAACkB4AwAAKADhDQAAoACENwAAgAIQ3gAAAApAeAMAACgA4Q0AAKAAhDcAAIACEN4AAAAKQHgDAAAoAOENAACgAIQ3AACAAhDeAAAACkB4AwAAKADhDQAAoACENwAAgAIQ3gAAAAqgodIFAFC9midPysQmHxUAUA18IgPwsSY2NaTz1k1jGrvlwbllrgYAaptpkwAAAAXgyhsAFNzA4FBKpeYxj+/rP5ID+w+XsSIAxoPwBgAFN6GxfszTW5MPprgeKGM9AIwP0yYBAAAKQHgDAAAoAOENAACgAIQ3AACAAhjVA0sWL16cffv2paHhg93vueee/Nd//Vcee+yxDA4O5sYbb8wNN9yQJNmxY0dWr16d/v7+XHPNNVm+fPn4VQ8AAFAjThjehoeH8+abb+af/umfRsJbd3d3li9fnmeffTYTJkzIwoUL8/nPfz6f/OQns3Llyqxfvz4XXHBBlixZku3bt6e9vX3c3wgAAMCZ7ITh7c0330xdXV1uuumm7Nu3L7/7u7+bX/qlX8pVV12Vc889N0kye/bsdHV15corr8y0adNy4YUXJkk6OzvT1dUlvAEAAJyiE97ztn///rS2tuav/uqv8uSTT+app57KO++8k1KpNLJPS0tLuru709PT85HbAQAAODUnvPL2uc99Lp/73OeSJGeffXYWLFiQ1atXZ+nSpR/ar66uLsPDw8eMr6urO6mCzj//nJPa/1SUSs2n7Vh8PH2oDvpQHfSBSqnGP3vVWFMt0ofqoA/VodJ9OGF4e/XVVzM4OJjW1tYkH9wDN3Xq1Ozdu3dkn56enrS0tGTKlCkfuf1k7Nt3MEePHhsCy61Uak5v74FxPw7Hpw/VQR+qQzX2odIfUpw+1fhnr9pqqkX6UB30oTqcjj6cdVbdcS9mnXDa5IEDB/LAAw+kv78/Bw8ezHPPPZe//Mu/zMsvv5z33nsvhw8fzgsvvJC2trZcfvnl2bVrV/bs2ZOhoaFs3bo1bW1tZX1DAAAAteiEV96uvvrqvPbaa7nuuuty9OjRLFq0KL/2a7+W5cuXZ/HixRkcHMyCBQty2WWXJUnWrFmTm2++Of39/Wlvb8+cOXPG/U0AAACc6Ua1ztstt9ySW2655UPbOjs709nZecy+ra2t2bx5c1mKA+DUNU+elIlNozrdAwBVzKc5wBluYlNDOm/dNKaxWx6cW+ZqAICxOuE9bwAAAFSe8AYAAFAAwhsAAEABCG8AAAAFILwBAAAUgPAGAABQAMIbAABAAQhvAAAABSC8AQAAFIDwBgAAUADCGwAAQAEIbwAAAAUgvAEAABSA8AYAAFAAwhsAAEABCG8AAAAFILwBAAAUgPAGAABQAMIbAABAAQhvAAAABSC8AQAAFIDwBgAAUADCGwAAQAEIbwAAAAXQUOkCAIDKGhgcSqnUPKaxff1HcmD/4TJXBMBHEd4AoMZNaKxP562bxjR2y4Nzc6DM9QDw0UybBAAAKADhDQAAoACENwAAgAIQ3gAAAApAeAMAACgA4Q0AAKAAhDcAAIACsM4bQJVrnjwpE5ucrqlOFvgGOH18GwCochObGsa8gHLywSLKMF4s8A1w+pg2CQAAUADCGwAAQAEIbwAAAAUgvAEAABSA8AYAAFAAwhsAAEABjDq83X///bntttuSJG+88Ubmz5+f2bNn5/bbb8+RI0eSJO+8805uuOGGzJkzJ1/5yldy6NCh8akaAACgxowqvL388st57rnnRl6vWLEid9xxR55//vkMDw9nw4YNSZK77747ixYtSldXVy699NI8+uij41M1AABAjTlhePvZz36WdevWZenSpUmSt99+O319fZk5c2aSZN68eenq6srg4GD+9V//NbNnz/7QdgAAAE7dCcPbnXfemeXLl2fy5MlJkp6enpRKpZGfl0qldHd356c//WnOOeecNDQ0fGg7AAAAp67heD98+umnc8EFF6S1tTXPPvtskmR4ePiY/erq6j52+8k6//xzTnrMWJVKzaftWHw8fagO+lAd9IFac7w/8/4+VAd9qA76UB0q3Yfjhrdt27alt7c3c+fOzfvvv5+f//znqaury969e0f26e3tTUtLS84777wcPHgwQ0NDqa+vH9l+svbtO5ijR48NguVWKjWnt/fAuB+H49OH6qAP1eHj+lDpDwoYTx937nFeqg76UB30oTqcjj6cdVbdcS9mHXfa5BNPPJGtW7dm06ZNWbZsWX7jN34jq1evTlNTU3bu3Jkk2bhxY9ra2tLY2Jgrrrgi27Zt+9B2AAAATt2Y1nlbu3ZtVq9enWuuuSaHDx/O4sWLkyR33XVXNmzYkGuvvTavvvpqbrnllnLWCgAAULOOO23yF82bNy/z5s1LksyYMSPPPPPMMftMnTo169evL191AAAAJBnjlTcAAABOL+ENAACgAIQ3AACAAhj1PW8AAOU0MDg05nXe+vqP5MD+w+NRFkDVEt4AgIqY0Fifzls3jWnslgfnxqpXQK0xbRIAAKAAhDcAAIACEN4AAAAKQHgDAAAoAOENAACgAIQ3AACAAhDeAAAACkB4AwAAKADhDQAAoACENwAAgAIQ3gAAAAqgodIFANSC5smTMrHpxKfcUqn5NFQDABSR8AZwGkxsakjnrZvGNHbLg3PLXA0AUESmTQIAABSA8AYAAFAApk0CjNJo71sDABgPvoUAjJL71gCASjJtEgAAoACENwAAgAIQ3gAAAApAeAMAACgA4Q0AAKAAhDcAAIACEN4AAAAKQHgDAAAoAOENAACgAIQ3AACAAhDeAAAACkB4AwAAKADhDQAAoACENwAAgAJoqHQBAAAna2BwKKVS85jG9vUfyYH9h8tcEcD4E94AgMKZ0Fifzls3jWnslgfn5kCZ6wE4HUybBAAAKADhDQAAoACENwAAgAIYVXh76KGHcu2116ajoyNPPPFEkmTHjh3p7OzMrFmzsm7dupF933jjjcyfPz+zZ8/O7bffniNHjoxP5QAAADXkhOHtlVdeyfe///1s3rw53/72t7N+/fr8x3/8R1auXJlHH30027Ztyw9/+MNs3749SbJixYrccccdef755zM8PJwNGzaM+5sAAAA4050wvF155ZX55je/mYaGhuzbty9DQ0PZv39/pk2blgsvvDANDQ3p7OxMV1dX3n777fT19WXmzJlJknnz5qWrq2u83wMAAMAZb1TTJhsbG/Pwww+no6Mjra2t6enpSalUGvl5S0tLuru7j9leKpXS3d1d/qoBAABqzKjXeVu2bFluuummLF26NLt37z7m53V1dRkeHv7I7Sfj/PPPOan9T8VYF/ekvPShOugDUEuc80bP76o66EN1qHQfThjefvKTn2RgYCCf/exnM2nSpMyaNStdXV2pr68f2aenpyctLS2ZMmVK9u7dO7K9t7c3LS0tJ1XQvn0Hc/TosSGw3Eql5vT2WqKz0vShOujD6FT6hA2Uj3Pe6Ph8qA76UB1ORx/OOqvuuBezTjht8q233sqqVasyMDCQgYGBvPjii1m4cGF27dqVPXv2ZGhoKFu3bk1bW1umTp2apqam7Ny5M0mycePGtLW1le/dAAAA1KgTXnlrb2/Pa6+9luuuuy719fWZNWtWOjo6ct555+Xmm29Of39/2tvbM2fOnCTJ2rVrs2rVqhw6dCiXXHJJFi9ePO5vAgAA4Ew3qnveli1blmXLln1oW2trazZv3nzMvjNmzMgzzzxTnuoAAABIMsqnTQIAAFBZwhsAAEABCG8AAAAFILwBAAAUgPAGAABQAMIbAABAAYxqqQAAgDPFwOBQSqXmMY/v6z+SA/sPl7EigNER3oCa0jx5UiY2OfVBLZvQWJ/OWzeNefyWB+fmQBnrARgt32CAmjKxqWHMX9q2PDi3zNUAAIyee94AAAAKQHgDAAAoAOENAACgAIQ3AACAAhDeAAAACkB4AwAAKADhDQAAoACENwAAgAIQ3gAAAApAeAMAACgA4Q0AAKAAhDcAAIACEN4AAAAKQHgDAAAoAOENAACgAIQ3AACAAhDeAAAACkB4AwAAKADhDQAAoACENwAAgAIQ3gAAAApAeAMAACgA4Q0AAKAAhDcAAIACEN4AAAAKQHgDAAAoAOENAACgAIQ3AACAAhDeAAAACkB4AwAAKADhDQAAoACENwAAgAIYVXh75JFH0tHRkY6OjjzwwANJkh07dqSzszOzZs3KunXrRvZ94403Mn/+/MyePTu33357jhw5Mj6VAwAA1JCGE+2wY8eOvPTSS3nuuedSV1eXL3/5y9m6dWvWrl2b9evX54ILLsiSJUuyffv2tLe3Z8WKFbn33nszc+bMrFy5Mhs2bMiiRYtOx3sBABh3A4NDKZWaxzS2r/9IDuw/XOaKgFpxwvBWKpVy2223ZcKECUmSz3zmM9m9e3emTZuWCy+8MEnS2dmZrq6uTJ8+PX19fZk5c2aSZN68eXn44YeFNwDgjDGhsT6dt24a09gtD87NgTLXA9SOE06bvOiii0bC2O7du7Nt27bU1dWlVCqN7NPS0pLu7u709PR8aHupVEp3d3f5qwYAAKgxJ7zy9r9+/OMfZ8mSJfna176WhoaG7Nq160M/r6ury/Dw8DHj6urqTqqg888/56T2PxVjnfJAeelDddAHgNOjaOfbotV7ptKH6lDpPowqvO3cuTPLli3LypUr09HRkVdeeSV79+4d+XlPT09aWloyZcqUD23v7e1NS0vLSRW0b9/BHD16bAgst1KpOb29Ji5Umj5Uh1rqQ6VPugBFOt/W0udDNdOH6nA6+nDWWXXHvZh1wmmT7777br761a9m7dq16ejoSJJcfvnl2bVrV/bs2ZOhoaFs3bo1bW1tmTp1apqamrJz584kycaNG9PW1lamtwIAAFC7Tnjl7fHHH09/f3/WrFkzsm3hwoVZs2ZNbr755vT396e9vT1z5sxJkqxduzarVq3KoUOHcskll2Tx4sXjVz0AAECNOGF4W7VqVVatWvWRP9u8efMx22bMmJFnnnnm1CsDAABgxKgfWAJQLZonT8rEJqcvAKC2+PYDFM7EpoZTWmMJAKCITvjAEgAAACpPeAMAACgA4Q0AAKAAhDcAAIAC8MASAIDTZGBwKKVS85jG9vUfyYH9h8tcEVAkwhsAwGkyobH+lJ6We6DM9QDFYtokAABAAQhvAAAABSC8AQAAFIDwBgAAUADCGwAAQAEIbwAAAAUgvAEAABSA8AYAAFAAwhsAAEABCG8AAAAFILwBAAAUgPAGAABQAA2VLgCoPc2TJ2Vik9MPAMDJ8O0JOO0mNjWk89ZNYx6/5cG5ZawGAKAYTJsEAAAoAOENAACgAIQ3AACAAhDeAAAACkB4AwAAKADhDQAAoAAsFQAAUAADg0MplZrHNLav/0gO7D9c5oqA0014AwAogAmN9WNeI3PLg3NzoMz1AKefaZMAAAAFILwBAAAUgPAGAABQAO55A8akefKkTGxyCgEAOF188wLGZGJTwyndOA8AwMkxbRIAAKAAhDcAAIACEN4AAAAKQHgDAAAoAOENAACgAIQ3AACAAhj1UgEHDx7MwoUL841vfCOf/OQns2PHjqxevTr9/f255pprsnz58iTJG2+8kVWrVuXgwYO54oorcvfdd6ehwYoEAACVMjA4lFKpeUxjS6Xm9PUfyYH9h8tcFXCyRpWqXnvttaxatSq7d+9OkvT19WXlypVZv359LrjggixZsiTbt29Pe3t7VqxYkXvvvTczZ87MypUrs2HDhixatGg83wMAAMcxobF+zGtzJh+sz3mgjPUAYzOqaZMbNmzIXXfdlZaWliTJD37wg0ybNi0XXnhhGhoa0tnZma6urrz99tvp6+vLzJkzkyTz5s1LV1fXuBUPAABQK0Z15e2+++770Ouenp6USqWR1y0tLenu7j5me6lUSnd3d5lKBQAAqF1juhlteHj4mG11dXUfu/1knH/+OWMpaUzGOveb8tKHyhkYHMqExvok+gDA8fmcqCy//+pQ6T6MKbxNmTIle/fuHXnd09OTlpaWY7b39vaOTLUcrX37Dubo0WNDYLmVSs3p7TV7u9L0obJKpeYx3wOx5cG5Za4GgGrm87pyfF+qDqejD2edVXfci1ljWirg8ssvz65du7Jnz54MDQ1l69ataWtry9SpU9PU1JSdO3cmSTZu3Ji2traxVQ4AAMCIMV15a2pqypo1a3LzzTenv78/7e3tmTNnTpJk7dq1WbVqVQ4dOpRLLrkkixcvLmvBAAAAteikwtv3vve9kf9ubW3N5s2bj9lnxowZeeaZZ069MgAAAEaMadokAAAAp5fwBgAAUABjuucNAIDaMTA4NOZHpPf1H8mB/YfLXBHUJuENAIDjmtBYf0pLy3jIPZSH8AYF1zx5UiY2+asMAHCm840PCm5iU4OFtgEAaoAHlgAAABSA8AYAAFAAwhsAAEABCG8AAAAFILwBAAAUgPAGAABQAMIbAABAAQhvAAAABWCRbgAAxs3A4FBKpeYxje3rP5ID+w+XuSIoLuENAIBxM6GxPp23bhrT2C0Pzs2BMtcDRWbaJAAAQAEIbwAAAAUgvAEAABSA8AYAAFAAwhsAAEABCG8AAAAFYKkAqLDmyZMysclfRQAAjs83RqiwiU0NY17/JvlgDRwAAM58pk0CAAAUgPAGAABQAMIbAABAAbjnDQCAqjQwOJRSqXlMY/v6j+TA/sNlrggqS3gDAKAqTWisH/NDvbY8ODcHylwPVJppkwAAAAUgvAEAABSAaZNQBhbaBgBgvPm2CWVwKgttW2QbAIDRMG0SAACgAFx5AwDgjGOZAc5Ewhv8D/etAcCZ41SWGfj2mi+OOfglwh/jxzdV+B/uWwMAklMLfok15hg/whtnFFfPAAA4U/mWyxnF1TMAAM5UnjYJAABQAK68AQBAGXnSJeNlXMLbli1b8thjj2VwcDA33nhjbrjhhvE4DFXqZO87+78nNyctAKDITuWBJx52wvGUPbx1d3dn3bp1efbZZzNhwoQsXLgwn//85zN9+vRyH4oqdSr3nSWn/nheAICi+rirdqP5btQ/MJSmCfVjOq5/PC+Gsoe3HTt25Kqrrsq5556bJJk9e3a6urryJ3/yJ+U+FOOokk9tPNV/rQIAKKpT/R7kit+Zrezfznt6elIqlUZet7S05Ac/+MGox591Vl25SzrlY51zzsQ0jTHI9PcfycGDfWMae6pOpe4k+cN7XxjTuMdXzUrLL08a83GTnNL4WhtbyWN7z8UYW8ljF3FsJY/tPRdjbCWP7T0XY2wlj30qY0/n9/CiGu/f0Yn+/3XDw8PD5TzgN77xjRw+fDjLly9Pkjz99NP5t3/7t9xzzz3lPAwAAEBNKftSAVOmTMnevXtHXvf09KSlpaXchwEAAKgpZQ9vX/jCF/Lyyy/nvffey+HDh/PCCy+kra2t3IcBAACoKWW/523KlClZvnx5Fi9enMHBwSxYsCCXXXZZuQ8DAABQU8p+zxsAAADlV/ZpkwAAAJSf8AYAAFAAwhsAAEABCG8AAAAFILwBAAAUQM2Ht9dffz2XXnpppcuoWa+++mrmzZuXzs7OLF26NO+//36lS6pJO3fuzPz58zN37tz8/u//ft5+++1Kl1TzHnrooXz961+vdBk1Z8uWLbn22mvz27/92/nWt75V6XJq1sGDB/PFL34xb731VqVLqVmPPPJIOjo60tHRkQceeKDS5dS0hx56KNdee206OjryxBNPVLqcmnb//ffntttuq2gNNR3eDh8+nHvuuSeDg4OVLqVm/dmf/VkeeOCBbNmyJdOnT8/jjz9e6ZJq0ooVK3Lfffdl06ZN6ezszL333lvpkmrWgQMHsnLlyvzt3/5tpUupOd3d3Vm3bl3+7u/+Lps2bco//MM/5D//8z8rXVbNee2113L99ddn9+7dlS6lZu3YsSMvvfRSnnvuuWzcuDH//u//nu9+97uVLqsmvfLKK/n+97+fzZs359vf/nbWr1+fN998s9Jl1aSXX345zz33XKXLqO3wtmbNmtx4442VLqOmbdu2LdOnT8/g4GC6u7szefLkSpdUcwYGBvKnf/qnmTFjRpLk4osvzrvvvlvhqmrXiy++mE996lP5gz/4g0qXUnN27NiRq666Kueee27OPvvszJ49O11dXZUuq+Zs2LAhd911V1paWipdSs0qlUq57bbbMmHChDQ2NuYzn/lM3nnnnUqXVZOuvPLKfPOb30xDQ0P27duXoaGhnH322ZUuq+b87Gc/y7p167J06dJKl1K74e3FF19MX19f5syZU+lSalpjY2N+9KMfpb29Pf/yL/+Sjo6OSpdUcyZMmJC5c+cmSY4ePZpHHnkkv/Vbv1XhqmrXddddlz/6oz9KfX19pUupOT09PSmVSiOvW1pa0t3dXcGKatN9992XK664otJl1LSLLrooM2fOTJLs3r0727ZtS3t7e2WLqmGNjY15+OGH09HRkdbW1kyZMqXSJdWcO++8M8uXL6+KiwwNlS5gvH3nO9/J6tWrP7Tt05/+dA4ePJgnn3yyMkXVoI/rw5NPPpmLL744O3bsyFNPPZXly5fnqaeeqlCVZ77j9WFgYCC33XZbjhw5kiVLllSowtpxvF5QGcPDw8dsq6urq0AlUB1+/OMfZ8mSJfna176WT33qU5Uup6YtW7YsN910U5YuXZoNGzbk937v9ypdUs14+umnc8EFF6S1tTXPPvtspcs588PbNddck2uuueZD255++un89V//dW644YaRbXPnzs23vvWtnHPOOae7xJrwUX3o7+/PP/7jP45c5fmd3/md3H///ZUor2Z8VB+S5NChQ/nKV76Sc889N4899lgaGxsrUF1t+bheUDlTpkzJq6++OvK6p6fH1D1q1s6dO7Ns2bKsXLnSrJgK+slPfpKBgYF89rOfzaRJkzJr1qz86Ec/qnRZNWXbtm3p7e3N3Llz8/777+fnP/95/uIv/iIrV66sSD1nfHj7KF/60pfypS99aeT1xRdfnE2bNlWwotrU0NCQu+++O5/4xCdy6aWX5jvf+U5+9Vd/tdJl1aQVK1Zk2rRpueeee1xpoGZ94QtfyNe//vW89957mTRpUl544YX8+Z//eaXLgtPu3XffzVe/+tWsW7cura2tlS6npr311lt5+OGH8/d///dJPrjtZ/78+RWuqrb84hM+n3322bzyyisVC25JjYY3qkN9fX3WrVuXO++8M0NDQ5kyZUruu+++SpdVc15//fW8+OKLmT59eq677rokH9zr8zd/8zeVLQxOsylTpmT58uVZvHhxBgcHs2DBglx22WWVLgtOu8cffzz9/f1Zs2bNyLaFCxfm+uuvr2BVtam9vT2vvfZarrvuutTX12fWrFmuhNa4uuGPmuQPAABAVanZp00CAAAUifAGAABQAMIbAABAAQhvAAAABSC8AQAAFIDwBgAAUADCGwAAQAEIbwAAAAXw/wBmsEPHJjxhyAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.randn(10000)\n",
    "plt.hist(x, bins=50)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85c89933",
   "metadata": {},
   "source": [
    "## 3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "d880f382",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-1, 1, num=50)\n",
    "y = x[:, np.newaxis]\n",
    "z = np.sqrt(x * x + y * y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "b295b32f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fa446d95d68>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(z, extent=[-1, 1, -1, 1], cmap='hot')\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31a4680c",
   "metadata": {},
   "source": [
    "# Pandas"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3d47307",
   "metadata": {},
   "source": [
    "## Series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "dcd1c1e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# True/False plotting:\n",
    "pd.Series((np.random.rand(20) > 0.5) * 1).plot(marker='o')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3d39c9b",
   "metadata": {},
   "source": [
    "## DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "db05edc2",
   "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>Attributes</th>\n",
       "      <th>area</th>\n",
       "      <th>pop</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>States</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>423967</td>\n",
       "      <td>38332521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>695662</td>\n",
       "      <td>26448193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>141297</td>\n",
       "      <td>19651127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>170312</td>\n",
       "      <td>19552860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>149995</td>\n",
       "      <td>12882135</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Attributes    area       pop\n",
       "States                      \n",
       "California  423967  38332521\n",
       "Texas       695662  26448193\n",
       "New York    141297  19651127\n",
       "Florida     170312  19552860\n",
       "Illinois    149995  12882135"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "area = pd.Series({'California': 423967, 'Texas': 695662,\n",
    "                  'New York': 141297, 'Florida': 170312,\n",
    "                  'Illinois': 149995})\n",
    "pop = pd.Series({'California': 38332521, 'Texas': 26448193,\n",
    "                 'New York': 19651127, 'Florida': 19552860,\n",
    "                 'Illinois': 12882135})\n",
    "df = pd.DataFrame({'area':area, 'pop':pop})\n",
    "# Give meaningful names to axis\n",
    "df.rename_axis('Attributes', axis='columns', inplace=True)\n",
    "df.rename_axis('States', axis='index', inplace=True)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "f922b0eb",
   "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>Attributes</th>\n",
       "      <th>area</th>\n",
       "      <th>pop</th>\n",
       "      <th>density</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>States</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>423967</td>\n",
       "      <td>38332521</td>\n",
       "      <td>90.413926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>695662</td>\n",
       "      <td>26448193</td>\n",
       "      <td>38.018740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>141297</td>\n",
       "      <td>19651127</td>\n",
       "      <td>139.076746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>170312</td>\n",
       "      <td>19552860</td>\n",
       "      <td>114.806121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>149995</td>\n",
       "      <td>12882135</td>\n",
       "      <td>85.883763</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Attributes    area       pop     density\n",
       "States                                  \n",
       "California  423967  38332521   90.413926\n",
       "Texas       695662  26448193   38.018740\n",
       "New York    141297  19651127  139.076746\n",
       "Florida     170312  19552860  114.806121\n",
       "Illinois    149995  12882135   85.883763"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Operation on columns\n",
    "df['density'] = df['pop'] / df['area']\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4826232e-a519-4727-9866-b7e53ba01019",
   "metadata": {},
   "source": [
    "### Indexing (df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4685549",
   "metadata": {},
   "source": [
    "From: https://jakevdp.github.io/PythonDataScienceHandbook/03.02-data-indexing-and-selection.html\n",
    "\n",
    "* indexing refers to columns\n",
    "* slicing refers to rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "2e668d24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Attributes\n",
       "area       1.412970e+05\n",
       "pop        1.965113e+07\n",
       "density    1.390767e+02\n",
       "Name: New York, dtype: float64"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.iloc[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "3cf35bf2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Attributes\n",
       "area       1.703120e+05\n",
       "pop        1.955286e+07\n",
       "density    1.148061e+02\n",
       "Name: Florida, dtype: float64"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['Florida']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "2aabe274",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "States\n",
       "California    38332521\n",
       "Texas         26448193\n",
       "New York      19651127\n",
       "Florida       19552860\n",
       "Illinois      12882135\n",
       "Name: pop, dtype: int64"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['pop']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "b952416b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26448193"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Both:\n",
    "df.loc['Texas', 'pop']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "bab2e009",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "States\n",
       "New York    139.076746\n",
       "Florida     114.806121\n",
       "Illinois     85.883763\n",
       "Name: density, dtype: float64"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Combined:\n",
    "df.iloc[2:].loc[:, 'density']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e13f33f",
   "metadata": {},
   "source": [
    "## Multi Index DF"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91140d42",
   "metadata": {},
   "source": [
    "### Creation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "efaa24b6",
   "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></th>\n",
       "      <th>data1</th>\n",
       "      <th>data2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">a</th>\n",
       "      <th>1</th>\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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">b</th>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     data1  data2\n",
       "a 1      1      2\n",
       "  2      3      4\n",
       "b 1      5      6\n",
       "  2      7      8"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Multi index\n",
    "df1 = pd.DataFrame(np.reshape(np.arange(0, 4*2) + 1, (4, 2)),\n",
    "                  index=[['a', 'a', 'b', 'b'], [1, 2, 1, 2]],\n",
    "                  columns=['data1', 'data2'])\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "bd2ebfe1",
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\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>ColName1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">A</th>\n",
       "      <th colspan=\"2\" halign=\"left\">B</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ColName2</th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IndexName</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x3</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x4</th>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x5</th>\n",
       "      <td>17</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColName1    A       B    \n",
       "ColName2   d1  d2  d1  d2\n",
       "IndexName                \n",
       "x1          1   2   3   4\n",
       "x2          5   6   7   8\n",
       "x3          9  10  11  12\n",
       "x4         13  14  15  16\n",
       "x5         17  18  19  20"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Multi column\n",
    "df2 = pd.DataFrame(np.reshape(np.arange(0, 5*4) + 1, (5, 4)),\n",
    "                   index=['x' + str(i) for i in [1,2,3,4,5]],\n",
    "                   columns=[['A', 'A', 'B', 'B'], ['d1', 'd2', 'd1', 'd2']])\n",
    "df2.columns.names = ['ColName1', 'ColName2']\n",
    "df2.index.name = 'IndexName'\n",
    "df2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7df33d84",
   "metadata": {},
   "source": [
    "From: https://pandas.pydata.org/docs/user_guide/advanced.html#using-slicers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "35aac5ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Utility function to quickly create label array\n",
    "def mklbl(prefix, n):\n",
    "    return [\"%s%d\" % (prefix, i) for i in range(n)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "16d7d1f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['A0', 'A1', 'A2', 'A3', 'A4', 'A5']"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mklbl('A', 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "a05e4dd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiIndex([('A0', 'B0', 'C0'),\n",
       "            ('A0', 'B0', 'C1'),\n",
       "            ('A0', 'B0', 'C2'),\n",
       "            ('A0', 'B1', 'C0'),\n",
       "            ('A0', 'B1', 'C1'),\n",
       "            ('A0', 'B1', 'C2'),\n",
       "            ('A1', 'B0', 'C0'),\n",
       "            ('A1', 'B0', 'C1'),\n",
       "            ('A1', 'B0', 'C2'),\n",
       "            ('A1', 'B1', 'C0'),\n",
       "            ('A1', 'B1', 'C1'),\n",
       "            ('A1', 'B1', 'C2')],\n",
       "           names=['IdxLvl0', 'IdxLvl1', 'IdxLvl2'])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "miindex = pd.MultiIndex.from_product(\n",
    "    [mklbl('A', 2), mklbl('B', 2), mklbl('C', 3)],\n",
    "    names=['IdxLvl0', 'IdxLvl1', 'IdxLvl2']\n",
    ")\n",
    "miindex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "9aee83b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MultiIndex([('X0', 'Y0', 'Z0'),\n",
       "            ('X0', 'Y0', 'Z1'),\n",
       "            ('X0', 'Y0', 'Z2'),\n",
       "            ('X0', 'Y1', 'Z0'),\n",
       "            ('X0', 'Y1', 'Z1'),\n",
       "            ('X0', 'Y1', 'Z2'),\n",
       "            ('X1', 'Y0', 'Z0'),\n",
       "            ('X1', 'Y0', 'Z1'),\n",
       "            ('X1', 'Y0', 'Z2'),\n",
       "            ('X1', 'Y1', 'Z0'),\n",
       "            ('X1', 'Y1', 'Z1'),\n",
       "            ('X1', 'Y1', 'Z2')],\n",
       "           names=['ColLvl0', 'ColLvl1', 'ColLvl2'])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "micolumns = pd.MultiIndex.from_product(\n",
    "    [mklbl('X', 2), mklbl('Y', 2), mklbl('Z', 3)],\n",
    "    names=[\"ColLvl0\", \"ColLvl1\", \"ColLvl2\"]\n",
    ")\n",
    "micolumns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "37f571e8",
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\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></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl0</th>\n",
       "      <th colspan=\"6\" halign=\"left\">X0</th>\n",
       "      <th colspan=\"6\" halign=\"left\">X1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl1</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y0</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y1</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y0</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IdxLvl0</th>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th>IdxLvl2</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A0</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "      <td>16</td>\n",
       "      <td>17</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>20</td>\n",
       "      <td>21</td>\n",
       "      <td>22</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>24</td>\n",
       "      <td>25</td>\n",
       "      <td>26</td>\n",
       "      <td>27</td>\n",
       "      <td>28</td>\n",
       "      <td>29</td>\n",
       "      <td>30</td>\n",
       "      <td>31</td>\n",
       "      <td>32</td>\n",
       "      <td>33</td>\n",
       "      <td>34</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>36</td>\n",
       "      <td>37</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>40</td>\n",
       "      <td>41</td>\n",
       "      <td>42</td>\n",
       "      <td>43</td>\n",
       "      <td>44</td>\n",
       "      <td>45</td>\n",
       "      <td>46</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>48</td>\n",
       "      <td>49</td>\n",
       "      <td>50</td>\n",
       "      <td>51</td>\n",
       "      <td>52</td>\n",
       "      <td>53</td>\n",
       "      <td>54</td>\n",
       "      <td>55</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>58</td>\n",
       "      <td>59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>60</td>\n",
       "      <td>61</td>\n",
       "      <td>62</td>\n",
       "      <td>63</td>\n",
       "      <td>64</td>\n",
       "      <td>65</td>\n",
       "      <td>66</td>\n",
       "      <td>67</td>\n",
       "      <td>68</td>\n",
       "      <td>69</td>\n",
       "      <td>70</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A1</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>72</td>\n",
       "      <td>73</td>\n",
       "      <td>74</td>\n",
       "      <td>75</td>\n",
       "      <td>76</td>\n",
       "      <td>77</td>\n",
       "      <td>78</td>\n",
       "      <td>79</td>\n",
       "      <td>80</td>\n",
       "      <td>81</td>\n",
       "      <td>82</td>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>84</td>\n",
       "      <td>85</td>\n",
       "      <td>86</td>\n",
       "      <td>87</td>\n",
       "      <td>88</td>\n",
       "      <td>89</td>\n",
       "      <td>90</td>\n",
       "      <td>91</td>\n",
       "      <td>92</td>\n",
       "      <td>93</td>\n",
       "      <td>94</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>96</td>\n",
       "      <td>97</td>\n",
       "      <td>98</td>\n",
       "      <td>99</td>\n",
       "      <td>100</td>\n",
       "      <td>101</td>\n",
       "      <td>102</td>\n",
       "      <td>103</td>\n",
       "      <td>104</td>\n",
       "      <td>105</td>\n",
       "      <td>106</td>\n",
       "      <td>107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>108</td>\n",
       "      <td>109</td>\n",
       "      <td>110</td>\n",
       "      <td>111</td>\n",
       "      <td>112</td>\n",
       "      <td>113</td>\n",
       "      <td>114</td>\n",
       "      <td>115</td>\n",
       "      <td>116</td>\n",
       "      <td>117</td>\n",
       "      <td>118</td>\n",
       "      <td>119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>120</td>\n",
       "      <td>121</td>\n",
       "      <td>122</td>\n",
       "      <td>123</td>\n",
       "      <td>124</td>\n",
       "      <td>125</td>\n",
       "      <td>126</td>\n",
       "      <td>127</td>\n",
       "      <td>128</td>\n",
       "      <td>129</td>\n",
       "      <td>130</td>\n",
       "      <td>131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>132</td>\n",
       "      <td>133</td>\n",
       "      <td>134</td>\n",
       "      <td>135</td>\n",
       "      <td>136</td>\n",
       "      <td>137</td>\n",
       "      <td>138</td>\n",
       "      <td>139</td>\n",
       "      <td>140</td>\n",
       "      <td>141</td>\n",
       "      <td>142</td>\n",
       "      <td>143</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl0                   X0                            X1                 \\\n",
       "ColLvl1                   Y0             Y1             Y0             Y1   \n",
       "ColLvl2                   Z0   Z1   Z2   Z0   Z1   Z2   Z0   Z1   Z2   Z0   \n",
       "IdxLvl0 IdxLvl1 IdxLvl2                                                     \n",
       "A0      B0      C0         0    1    2    3    4    5    6    7    8    9   \n",
       "                C1        12   13   14   15   16   17   18   19   20   21   \n",
       "                C2        24   25   26   27   28   29   30   31   32   33   \n",
       "        B1      C0        36   37   38   39   40   41   42   43   44   45   \n",
       "                C1        48   49   50   51   52   53   54   55   56   57   \n",
       "                C2        60   61   62   63   64   65   66   67   68   69   \n",
       "A1      B0      C0        72   73   74   75   76   77   78   79   80   81   \n",
       "                C1        84   85   86   87   88   89   90   91   92   93   \n",
       "                C2        96   97   98   99  100  101  102  103  104  105   \n",
       "        B1      C0       108  109  110  111  112  113  114  115  116  117   \n",
       "                C1       120  121  122  123  124  125  126  127  128  129   \n",
       "                C2       132  133  134  135  136  137  138  139  140  141   \n",
       "\n",
       "ColLvl0                            \n",
       "ColLvl1                            \n",
       "ColLvl2                   Z1   Z2  \n",
       "IdxLvl0 IdxLvl1 IdxLvl2            \n",
       "A0      B0      C0        10   11  \n",
       "                C1        22   23  \n",
       "                C2        34   35  \n",
       "        B1      C0        46   47  \n",
       "                C1        58   59  \n",
       "                C2        70   71  \n",
       "A1      B0      C0        82   83  \n",
       "                C1        94   95  \n",
       "                C2       106  107  \n",
       "        B1      C0       118  119  \n",
       "                C1       130  131  \n",
       "                C2       142  143  "
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3 = pd.DataFrame(\n",
    "        np.arange(len(miindex) * len(micolumns)).reshape(\n",
    "            (len(miindex), len(micolumns))\n",
    "        ),\n",
    "        index=miindex,\n",
    "        columns=micolumns,\n",
    "    )\n",
    "df3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b18b7bb4",
   "metadata": {},
   "source": [
    "### Indexing (mi df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "c8a5e563",
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\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>ColName1</th>\n",
       "      <th colspan=\"2\" halign=\"left\">A</th>\n",
       "      <th colspan=\"2\" halign=\"left\">B</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ColName2</th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IndexName</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x3</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x4</th>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x5</th>\n",
       "      <td>17</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColName1    A       B    \n",
       "ColName2   d1  d2  d1  d2\n",
       "IndexName                \n",
       "x1          1   2   3   4\n",
       "x2          5   6   7   8\n",
       "x3          9  10  11  12\n",
       "x4         13  14  15  16\n",
       "x5         17  18  19  20"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "aa0ae6f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ColName1  ColName2\n",
       "A         d1           9\n",
       "          d2          10\n",
       "B         d1          11\n",
       "          d2          12\n",
       "Name: x3, dtype: int64"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# by index name\n",
    "df2.loc['x3']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "5bb2b7d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ColName1  ColName2\n",
       "A         d1          13\n",
       "          d2          14\n",
       "B         d1          15\n",
       "          d2          16\n",
       "Name: x4, dtype: int64"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# by integer position (array style)\n",
    "df2.iloc[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "fa7cea91",
   "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>ColName2</th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IndexName</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x3</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x4</th>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x5</th>\n",
       "      <td>17</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColName2   d1  d2\n",
       "IndexName        \n",
       "x1          1   2\n",
       "x2          5   6\n",
       "x3          9  10\n",
       "x4         13  14\n",
       "x5         17  18"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1st level column indexing\n",
    "df2['A']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "c2eba5da",
   "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>ColName2</th>\n",
       "      <th>d1</th>\n",
       "      <th>d2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IndexName</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x3</th>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x4</th>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x5</th>\n",
       "      <td>17</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColName2   d1  d2\n",
       "IndexName        \n",
       "x1          1   2\n",
       "x2          5   6\n",
       "x3          9  10\n",
       "x4         13  14\n",
       "x5         17  18"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Equivalent:\n",
    "df2.loc[:, 'A']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "7f328c42",
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\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>ColName1</th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ColName2</th>\n",
       "      <th>d1</th>\n",
       "      <th>d1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IndexName</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x2</th>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x3</th>\n",
       "      <td>9</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x4</th>\n",
       "      <td>13</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x5</th>\n",
       "      <td>17</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColName1    A   B\n",
       "ColName2   d1  d1\n",
       "IndexName        \n",
       "x1          1   3\n",
       "x2          5   7\n",
       "x3          9  11\n",
       "x4         13  15\n",
       "x5         17  19"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2nd level column indexing\n",
    "df2.loc[:, (slice(None), 'd1')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "4e694723",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead tr th {\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></th>\n",
       "      <th>ColLvl0</th>\n",
       "      <th colspan=\"5\" halign=\"left\">X0</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl1</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y0</th>\n",
       "      <th colspan=\"2\" halign=\"left\">Y1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IdxLvl0</th>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th>IdxLvl2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">A0</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>24</td>\n",
       "      <td>25</td>\n",
       "      <td>26</td>\n",
       "      <td>27</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl0                  X0                \n",
       "ColLvl1                  Y0          Y1    \n",
       "ColLvl2                  Z0  Z1  Z2  Z0  Z1\n",
       "IdxLvl0 IdxLvl1 IdxLvl2                    \n",
       "A0      B0      C0        0   1   2   3   4\n",
       "                C1       12  13  14  15  16\n",
       "                C2       24  25  26  27  28"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# iloc irrelevant of the levels\n",
    "df3.iloc[:3, :5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "5e76415b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3.iloc[2, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "d03edb51",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Shortcut for indexer:\n",
    "idx = pd.IndexSlice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "5c3f1f52",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>ColLvl1</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y0</th>\n",
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       "      <th colspan=\"3\" halign=\"left\">Y0</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y1</th>\n",
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       "    <tr>\n",
       "      <th></th>\n",
       "      <th>ColLvl2</th>\n",
       "      <th>Z0</th>\n",
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       "      <th>Z2</th>\n",
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       "      <th>Z2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th>IdxLvl2</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "      <td>16</td>\n",
       "      <td>17</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>20</td>\n",
       "      <td>21</td>\n",
       "      <td>22</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>24</td>\n",
       "      <td>25</td>\n",
       "      <td>26</td>\n",
       "      <td>27</td>\n",
       "      <td>28</td>\n",
       "      <td>29</td>\n",
       "      <td>30</td>\n",
       "      <td>31</td>\n",
       "      <td>32</td>\n",
       "      <td>33</td>\n",
       "      <td>34</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>36</td>\n",
       "      <td>37</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>40</td>\n",
       "      <td>41</td>\n",
       "      <td>42</td>\n",
       "      <td>43</td>\n",
       "      <td>44</td>\n",
       "      <td>45</td>\n",
       "      <td>46</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>48</td>\n",
       "      <td>49</td>\n",
       "      <td>50</td>\n",
       "      <td>51</td>\n",
       "      <td>52</td>\n",
       "      <td>53</td>\n",
       "      <td>54</td>\n",
       "      <td>55</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>58</td>\n",
       "      <td>59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>60</td>\n",
       "      <td>61</td>\n",
       "      <td>62</td>\n",
       "      <td>63</td>\n",
       "      <td>64</td>\n",
       "      <td>65</td>\n",
       "      <td>66</td>\n",
       "      <td>67</td>\n",
       "      <td>68</td>\n",
       "      <td>69</td>\n",
       "      <td>70</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl0          X0                      X1                    \n",
       "ColLvl1          Y0          Y1          Y0          Y1        \n",
       "ColLvl2          Z0  Z1  Z2  Z0  Z1  Z2  Z0  Z1  Z2  Z0  Z1  Z2\n",
       "IdxLvl1 IdxLvl2                                                \n",
       "B0      C0        0   1   2   3   4   5   6   7   8   9  10  11\n",
       "        C1       12  13  14  15  16  17  18  19  20  21  22  23\n",
       "        C2       24  25  26  27  28  29  30  31  32  33  34  35\n",
       "B1      C0       36  37  38  39  40  41  42  43  44  45  46  47\n",
       "        C1       48  49  50  51  52  53  54  55  56  57  58  59\n",
       "        C2       60  61  62  63  64  65  66  67  68  69  70  71"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Slicing\n",
    "# TBD Strange: A0 is dropped\n",
    "df3.loc[idx['A0']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "03891e35",
   "metadata": {},
   "outputs": [
    {
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A0</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "      <td>16</td>\n",
       "      <td>17</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>20</td>\n",
       "      <td>21</td>\n",
       "      <td>22</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>24</td>\n",
       "      <td>25</td>\n",
       "      <td>26</td>\n",
       "      <td>27</td>\n",
       "      <td>28</td>\n",
       "      <td>29</td>\n",
       "      <td>30</td>\n",
       "      <td>31</td>\n",
       "      <td>32</td>\n",
       "      <td>33</td>\n",
       "      <td>34</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>36</td>\n",
       "      <td>37</td>\n",
       "      <td>38</td>\n",
       "      <td>39</td>\n",
       "      <td>40</td>\n",
       "      <td>41</td>\n",
       "      <td>42</td>\n",
       "      <td>43</td>\n",
       "      <td>44</td>\n",
       "      <td>45</td>\n",
       "      <td>46</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>48</td>\n",
       "      <td>49</td>\n",
       "      <td>50</td>\n",
       "      <td>51</td>\n",
       "      <td>52</td>\n",
       "      <td>53</td>\n",
       "      <td>54</td>\n",
       "      <td>55</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>58</td>\n",
       "      <td>59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>60</td>\n",
       "      <td>61</td>\n",
       "      <td>62</td>\n",
       "      <td>63</td>\n",
       "      <td>64</td>\n",
       "      <td>65</td>\n",
       "      <td>66</td>\n",
       "      <td>67</td>\n",
       "      <td>68</td>\n",
       "      <td>69</td>\n",
       "      <td>70</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl0                  X0                      X1                    \n",
       "ColLvl1                  Y0          Y1          Y0          Y1        \n",
       "ColLvl2                  Z0  Z1  Z2  Z0  Z1  Z2  Z0  Z1  Z2  Z0  Z1  Z2\n",
       "IdxLvl0 IdxLvl1 IdxLvl2                                                \n",
       "A0      B0      C0        0   1   2   3   4   5   6   7   8   9  10  11\n",
       "                C1       12  13  14  15  16  17  18  19  20  21  22  23\n",
       "                C2       24  25  26  27  28  29  30  31  32  33  34  35\n",
       "        B1      C0       36  37  38  39  40  41  42  43  44  45  46  47\n",
       "                C1       48  49  50  51  52  53  54  55  56  57  58  59\n",
       "                C2       60  61  62  63  64  65  66  67  68  69  70  71"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Slicing\n",
    "# TBD Strange: A0 is NOT dropped\n",
    "df3.loc[idx['A0', :, :]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "28336e09",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>IdxLvl0</th>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">A0</th>\n",
       "      <th>B0</th>\n",
       "      <td>12</td>\n",
       "      <td>13</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "      <td>16</td>\n",
       "      <td>17</td>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>20</td>\n",
       "      <td>21</td>\n",
       "      <td>22</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <td>48</td>\n",
       "      <td>49</td>\n",
       "      <td>50</td>\n",
       "      <td>51</td>\n",
       "      <td>52</td>\n",
       "      <td>53</td>\n",
       "      <td>54</td>\n",
       "      <td>55</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>58</td>\n",
       "      <td>59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">A1</th>\n",
       "      <th>B0</th>\n",
       "      <td>84</td>\n",
       "      <td>85</td>\n",
       "      <td>86</td>\n",
       "      <td>87</td>\n",
       "      <td>88</td>\n",
       "      <td>89</td>\n",
       "      <td>90</td>\n",
       "      <td>91</td>\n",
       "      <td>92</td>\n",
       "      <td>93</td>\n",
       "      <td>94</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <td>120</td>\n",
       "      <td>121</td>\n",
       "      <td>122</td>\n",
       "      <td>123</td>\n",
       "      <td>124</td>\n",
       "      <td>125</td>\n",
       "      <td>126</td>\n",
       "      <td>127</td>\n",
       "      <td>128</td>\n",
       "      <td>129</td>\n",
       "      <td>130</td>\n",
       "      <td>131</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl0           X0                            X1                         \n",
       "ColLvl1           Y0             Y1             Y0             Y1          \n",
       "ColLvl2           Z0   Z1   Z2   Z0   Z1   Z2   Z0   Z1   Z2   Z0   Z1   Z2\n",
       "IdxLvl0 IdxLvl1                                                            \n",
       "A0      B0        12   13   14   15   16   17   18   19   20   21   22   23\n",
       "        B1        48   49   50   51   52   53   54   55   56   57   58   59\n",
       "A1      B0        84   85   86   87   88   89   90   91   92   93   94   95\n",
       "        B1       120  121  122  123  124  125  126  127  128  129  130  131"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Slicing\n",
    "# TBD Strange: C1 is dropped\n",
    "df3.loc[idx[:, :, 'C1']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "3c8deef5",
   "metadata": {},
   "outputs": [
    {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl0</th>\n",
       "      <th colspan=\"6\" halign=\"left\">X0</th>\n",
       "      <th colspan=\"6\" halign=\"left\">X1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl1</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y0</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y1</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y0</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IdxLvl0</th>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th>IdxLvl2</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">A1</th>\n",
       "      <th>B0</th>\n",
       "      <th>C1</th>\n",
       "      <td>84</td>\n",
       "      <td>85</td>\n",
       "      <td>86</td>\n",
       "      <td>87</td>\n",
       "      <td>88</td>\n",
       "      <td>89</td>\n",
       "      <td>90</td>\n",
       "      <td>91</td>\n",
       "      <td>92</td>\n",
       "      <td>93</td>\n",
       "      <td>94</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <th>C1</th>\n",
       "      <td>120</td>\n",
       "      <td>121</td>\n",
       "      <td>122</td>\n",
       "      <td>123</td>\n",
       "      <td>124</td>\n",
       "      <td>125</td>\n",
       "      <td>126</td>\n",
       "      <td>127</td>\n",
       "      <td>128</td>\n",
       "      <td>129</td>\n",
       "      <td>130</td>\n",
       "      <td>131</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl0                   X0                            X1                 \\\n",
       "ColLvl1                   Y0             Y1             Y0             Y1   \n",
       "ColLvl2                   Z0   Z1   Z2   Z0   Z1   Z2   Z0   Z1   Z2   Z0   \n",
       "IdxLvl0 IdxLvl1 IdxLvl2                                                     \n",
       "A1      B0      C1        84   85   86   87   88   89   90   91   92   93   \n",
       "        B1      C1       120  121  122  123  124  125  126  127  128  129   \n",
       "\n",
       "ColLvl0                            \n",
       "ColLvl1                            \n",
       "ColLvl2                   Z1   Z2  \n",
       "IdxLvl0 IdxLvl1 IdxLvl2            \n",
       "A1      B0      C1        94   95  \n",
       "        B1      C1       130  131  "
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Slicing\n",
    "df3.loc[idx['A1', :, 'C1']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "af29adcc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th colspan=\"3\" halign=\"left\">Y1</th>\n",
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       "    <tr>\n",
       "      <th></th>\n",
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       "      <th>ColLvl2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
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       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IdxLvl0</th>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th>IdxLvl2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A0</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>20</td>\n",
       "      <td>21</td>\n",
       "      <td>22</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>30</td>\n",
       "      <td>31</td>\n",
       "      <td>32</td>\n",
       "      <td>33</td>\n",
       "      <td>34</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>42</td>\n",
       "      <td>43</td>\n",
       "      <td>44</td>\n",
       "      <td>45</td>\n",
       "      <td>46</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>54</td>\n",
       "      <td>55</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>58</td>\n",
       "      <td>59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>66</td>\n",
       "      <td>67</td>\n",
       "      <td>68</td>\n",
       "      <td>69</td>\n",
       "      <td>70</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A1</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>78</td>\n",
       "      <td>79</td>\n",
       "      <td>80</td>\n",
       "      <td>81</td>\n",
       "      <td>82</td>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>90</td>\n",
       "      <td>91</td>\n",
       "      <td>92</td>\n",
       "      <td>93</td>\n",
       "      <td>94</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>102</td>\n",
       "      <td>103</td>\n",
       "      <td>104</td>\n",
       "      <td>105</td>\n",
       "      <td>106</td>\n",
       "      <td>107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>114</td>\n",
       "      <td>115</td>\n",
       "      <td>116</td>\n",
       "      <td>117</td>\n",
       "      <td>118</td>\n",
       "      <td>119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>126</td>\n",
       "      <td>127</td>\n",
       "      <td>128</td>\n",
       "      <td>129</td>\n",
       "      <td>130</td>\n",
       "      <td>131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>138</td>\n",
       "      <td>139</td>\n",
       "      <td>140</td>\n",
       "      <td>141</td>\n",
       "      <td>142</td>\n",
       "      <td>143</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl0                   X1                         \n",
       "ColLvl1                   Y0             Y1          \n",
       "ColLvl2                   Z0   Z1   Z2   Z0   Z1   Z2\n",
       "IdxLvl0 IdxLvl1 IdxLvl2                              \n",
       "A0      B0      C0         6    7    8    9   10   11\n",
       "                C1        18   19   20   21   22   23\n",
       "                C2        30   31   32   33   34   35\n",
       "        B1      C0        42   43   44   45   46   47\n",
       "                C1        54   55   56   57   58   59\n",
       "                C2        66   67   68   69   70   71\n",
       "A1      B0      C0        78   79   80   81   82   83\n",
       "                C1        90   91   92   93   94   95\n",
       "                C2       102  103  104  105  106  107\n",
       "        B1      C0       114  115  116  117  118  119\n",
       "                C1       126  127  128  129  130  131\n",
       "                C2       138  139  140  141  142  143"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Indexing (columns)\n",
    "# TBD Strange: X1 is NOT dropped\n",
    "df3.loc[idx[:, :, :], idx['X1', :, :]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "ba616c46",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Z2</th>\n",
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       "      <th>Z2</th>\n",
       "    </tr>\n",
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       "      <th>IdxLvl0</th>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th>IdxLvl2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A0</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>18</td>\n",
       "      <td>19</td>\n",
       "      <td>20</td>\n",
       "      <td>21</td>\n",
       "      <td>22</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>30</td>\n",
       "      <td>31</td>\n",
       "      <td>32</td>\n",
       "      <td>33</td>\n",
       "      <td>34</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>42</td>\n",
       "      <td>43</td>\n",
       "      <td>44</td>\n",
       "      <td>45</td>\n",
       "      <td>46</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>54</td>\n",
       "      <td>55</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>58</td>\n",
       "      <td>59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>66</td>\n",
       "      <td>67</td>\n",
       "      <td>68</td>\n",
       "      <td>69</td>\n",
       "      <td>70</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A1</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>78</td>\n",
       "      <td>79</td>\n",
       "      <td>80</td>\n",
       "      <td>81</td>\n",
       "      <td>82</td>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>90</td>\n",
       "      <td>91</td>\n",
       "      <td>92</td>\n",
       "      <td>93</td>\n",
       "      <td>94</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>102</td>\n",
       "      <td>103</td>\n",
       "      <td>104</td>\n",
       "      <td>105</td>\n",
       "      <td>106</td>\n",
       "      <td>107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>114</td>\n",
       "      <td>115</td>\n",
       "      <td>116</td>\n",
       "      <td>117</td>\n",
       "      <td>118</td>\n",
       "      <td>119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>126</td>\n",
       "      <td>127</td>\n",
       "      <td>128</td>\n",
       "      <td>129</td>\n",
       "      <td>130</td>\n",
       "      <td>131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>138</td>\n",
       "      <td>139</td>\n",
       "      <td>140</td>\n",
       "      <td>141</td>\n",
       "      <td>142</td>\n",
       "      <td>143</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl1                   Y0             Y1          \n",
       "ColLvl2                   Z0   Z1   Z2   Z0   Z1   Z2\n",
       "IdxLvl0 IdxLvl1 IdxLvl2                              \n",
       "A0      B0      C0         6    7    8    9   10   11\n",
       "                C1        18   19   20   21   22   23\n",
       "                C2        30   31   32   33   34   35\n",
       "        B1      C0        42   43   44   45   46   47\n",
       "                C1        54   55   56   57   58   59\n",
       "                C2        66   67   68   69   70   71\n",
       "A1      B0      C0        78   79   80   81   82   83\n",
       "                C1        90   91   92   93   94   95\n",
       "                C2       102  103  104  105  106  107\n",
       "        B1      C0       114  115  116  117  118  119\n",
       "                C1       126  127  128  129  130  131\n",
       "                C2       138  139  140  141  142  143"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Simplified\n",
    "# TBD Strange: X1 is dropped\n",
    "df3.loc[:, idx['X1']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "bcb9558d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A0</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>13</td>\n",
       "      <td>16</td>\n",
       "      <td>19</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>25</td>\n",
       "      <td>28</td>\n",
       "      <td>31</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>37</td>\n",
       "      <td>40</td>\n",
       "      <td>43</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>49</td>\n",
       "      <td>52</td>\n",
       "      <td>55</td>\n",
       "      <td>58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>61</td>\n",
       "      <td>64</td>\n",
       "      <td>67</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A1</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>73</td>\n",
       "      <td>76</td>\n",
       "      <td>79</td>\n",
       "      <td>82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>85</td>\n",
       "      <td>88</td>\n",
       "      <td>91</td>\n",
       "      <td>94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>97</td>\n",
       "      <td>100</td>\n",
       "      <td>103</td>\n",
       "      <td>106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>109</td>\n",
       "      <td>112</td>\n",
       "      <td>115</td>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>121</td>\n",
       "      <td>124</td>\n",
       "      <td>127</td>\n",
       "      <td>130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>133</td>\n",
       "      <td>136</td>\n",
       "      <td>139</td>\n",
       "      <td>142</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl0                   X0        X1     \n",
       "ColLvl1                   Y0   Y1   Y0   Y1\n",
       "ColLvl2                   Z1   Z1   Z1   Z1\n",
       "IdxLvl0 IdxLvl1 IdxLvl2                    \n",
       "A0      B0      C0         1    4    7   10\n",
       "                C1        13   16   19   22\n",
       "                C2        25   28   31   34\n",
       "        B1      C0        37   40   43   46\n",
       "                C1        49   52   55   58\n",
       "                C2        61   64   67   70\n",
       "A1      B0      C0        73   76   79   82\n",
       "                C1        85   88   91   94\n",
       "                C2        97  100  103  106\n",
       "        B1      C0       109  112  115  118\n",
       "                C1       121  124  127  130\n",
       "                C2       133  136  139  142"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Z1 not dropped...\n",
    "df3.loc[:, idx[:, :, 'Z1']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "1bc829e0-d7c7-4373-98dc-1c3e8260cb21",
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\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></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl0</th>\n",
       "      <th colspan=\"6\" halign=\"left\">X0</th>\n",
       "      <th colspan=\"6\" halign=\"left\">X1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl1</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y0</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y1</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y0</th>\n",
       "      <th colspan=\"3\" halign=\"left\">Y1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>ColLvl2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "      <th>Z0</th>\n",
       "      <th>Z1</th>\n",
       "      <th>Z2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IdxLvl0</th>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th>IdxLvl2</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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"2\" valign=\"top\">A0</th>\n",
       "      <th>B0</th>\n",
       "      <th>C2</th>\n",
       "      <td>24</td>\n",
       "      <td>25</td>\n",
       "      <td>26</td>\n",
       "      <td>27</td>\n",
       "      <td>28</td>\n",
       "      <td>29</td>\n",
       "      <td>30</td>\n",
       "      <td>31</td>\n",
       "      <td>32</td>\n",
       "      <td>33</td>\n",
       "      <td>34</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <th>C2</th>\n",
       "      <td>60</td>\n",
       "      <td>61</td>\n",
       "      <td>62</td>\n",
       "      <td>63</td>\n",
       "      <td>64</td>\n",
       "      <td>65</td>\n",
       "      <td>66</td>\n",
       "      <td>67</td>\n",
       "      <td>68</td>\n",
       "      <td>69</td>\n",
       "      <td>70</td>\n",
       "      <td>71</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl0                  X0                      X1                    \n",
       "ColLvl1                  Y0          Y1          Y0          Y1        \n",
       "ColLvl2                  Z0  Z1  Z2  Z0  Z1  Z2  Z0  Z1  Z2  Z0  Z1  Z2\n",
       "IdxLvl0 IdxLvl1 IdxLvl2                                                \n",
       "A0      B0      C2       24  25  26  27  28  29  30  31  32  33  34  35\n",
       "        B1      C2       60  61  62  63  64  65  66  67  68  69  70  71"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Strange:\n",
    "\n",
    "#df3.loc['A0'].loc[idx[:, 'C2'], :]\n",
    "df3.loc[idx['A0', :, 'C2']]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "165ca2f6",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Cross Section\n",
    "\n",
    "Note: xs (cross section drop by default): \n",
    "https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.xs.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "664615e6",
   "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></th>\n",
       "      <th>ColLvl1</th>\n",
       "      <th>Y0</th>\n",
       "      <th>Y1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IdxLvl0</th>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th>IdxLvl2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A0</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>13</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>25</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>37</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>49</td>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>61</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"6\" valign=\"top\">A1</th>\n",
       "      <th rowspan=\"3\" valign=\"top\">B0</th>\n",
       "      <th>C0</th>\n",
       "      <td>73</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>85</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>97</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th rowspan=\"3\" valign=\"top\">B1</th>\n",
       "      <th>C0</th>\n",
       "      <td>109</td>\n",
       "      <td>112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C1</th>\n",
       "      <td>121</td>\n",
       "      <td>124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C2</th>\n",
       "      <td>133</td>\n",
       "      <td>136</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl1                   Y0   Y1\n",
       "IdxLvl0 IdxLvl1 IdxLvl2          \n",
       "A0      B0      C0         1    4\n",
       "                C1        13   16\n",
       "                C2        25   28\n",
       "        B1      C0        37   40\n",
       "                C1        49   52\n",
       "                C2        61   64\n",
       "A1      B0      C0        73   76\n",
       "                C1        85   88\n",
       "                C2        97  100\n",
       "        B1      C0       109  112\n",
       "                C1       121  124\n",
       "                C2       133  136"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3.xs(key=('X0', 'Z1'), axis='columns', level=['ColLvl0', 'ColLvl2'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "f0e2de50",
   "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>ColLvl1</th>\n",
       "      <th>Y0</th>\n",
       "      <th>Y1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>IdxLvl1</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>B0</th>\n",
       "      <td>26</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B1</th>\n",
       "      <td>62</td>\n",
       "      <td>65</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "ColLvl1  Y0  Y1\n",
       "IdxLvl1        \n",
       "B0       26  29\n",
       "B1       62  65"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Both combined:\n",
    "df3.xs(key=('A0', 'C2'), axis='index', level=['IdxLvl0', 'IdxLvl2']). \\\n",
    "    xs(key=('X0', 'Z2'), axis='columns', level=['ColLvl0', 'ColLvl2'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc3c85b4-3d26-4012-bb53-7c1ddbd7bcaa",
   "metadata": {},
   "source": [
    "## Combining"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "681b97ea-0966-4957-9ebf-ec04e30d19c2",
   "metadata": {},
   "outputs": [],
   "source": [
    "class display(object):\n",
    "    \"\"\"Display HTML representation of multiple objects\"\"\"\n",
    "    template = \"\"\"<div style=\"float: left; padding: 10px;\">\n",
    "    <p style='font-family:\"Courier New\", Courier, monospace'>{0}</p>{1}\n",
    "    </div>\"\"\"\n",
    "    def __init__(self, *args):\n",
    "        self.args = args\n",
    "        \n",
    "    def _repr_html_(self):\n",
    "        return '\\n'.join(self.template.format(a, eval(a)._repr_html_())\n",
    "                         for a in self.args)\n",
    "    \n",
    "    def __repr__(self):\n",
    "        return '\\n\\n'.join(a + '\\n' + repr(eval(a))\n",
    "                           for a in self.args)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "bacfd72d-16aa-4008-aaef-b8904677fbd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_df(cols, ind):\n",
    "    \"\"\"Quickly make a DataFrame\"\"\"\n",
    "    return pd.DataFrame(\n",
    "        {c: [str(c) + str(i) for i in ind] for c in cols},\n",
    "        ind)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b430a138-81fb-4d4c-bd4f-e73d9dba08a4",
   "metadata": {},
   "source": [
    "### Concat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "f8c0e2bf-30fa-4f81-b06b-6728492d8b73",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df1</p><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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df2</p><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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A3</td>\n",
       "      <td>B3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A4</td>\n",
       "      <td>B4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>pd.concat([df1, df2])</p><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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A3</td>\n",
       "      <td>B3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A4</td>\n",
       "      <td>B4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>"
      ],
      "text/plain": [
       "df1\n",
       "    A   B\n",
       "1  A1  B1\n",
       "2  A2  B2\n",
       "\n",
       "df2\n",
       "    A   B\n",
       "3  A3  B3\n",
       "4  A4  B4\n",
       "\n",
       "pd.concat([df1, df2])\n",
       "    A   B\n",
       "1  A1  B1\n",
       "2  A2  B2\n",
       "3  A3  B3\n",
       "4  A4  B4"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = make_df('AB', [1,2])\n",
    "df2 = make_df('AB', [3,4])\n",
    "display('df1', 'df2', 'pd.concat([df1, df2])')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "285be8f7-d001-40a0-8621-3890aa7ce629",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df1</p><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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>A1</td>\n",
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       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df2</p><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>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
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       "      <td>C1</td>\n",
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       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>pd.concat([df1, df2], axis=1)</p><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>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C1</td>\n",
       "      <td>D1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>"
      ],
      "text/plain": [
       "df1\n",
       "    A   B\n",
       "1  A1  B1\n",
       "2  A2  B2\n",
       "\n",
       "df2\n",
       "    C   D\n",
       "1  C1  D1\n",
       "2  C2  D2\n",
       "\n",
       "pd.concat([df1, df2], axis=1)\n",
       "    A   B   C   D\n",
       "1  A1  B1  C1  D1\n",
       "2  A2  B2  C2  D2"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = make_df('AB', [1,2])\n",
    "df2 = make_df('CD', [1,2])\n",
    "display('df1', 'df2', 'pd.concat([df1, df2], axis=1)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "c9f4fdf8-7c00-448f-9dd4-e97acf92511c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df1</p><div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\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>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A0</td>\n",
       "      <td>B0</td>\n",
       "      <td>C0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df2</p><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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
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       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A3</td>\n",
       "      <td>B3</td>\n",
       "      <td>C3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A4</td>\n",
       "      <td>B4</td>\n",
       "      <td>C4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>pd.concat([df1, df2])</p><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",
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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>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>A0</td>\n",
       "      <td>B0</td>\n",
       "      <td>C0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>C1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A3</td>\n",
       "      <td>B3</td>\n",
       "      <td>C3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>A4</td>\n",
       "      <td>B4</td>\n",
       "      <td>C4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>"
      ],
      "text/plain": [
       "df1\n",
       "    A   B   C\n",
       "0  A0  B0  C0\n",
       "1  A1  B1  C1\n",
       "2  A2  B2  C2\n",
       "\n",
       "df2\n",
       "    A   B   C\n",
       "2  A2  B2  C2\n",
       "3  A3  B3  C3\n",
       "4  A4  B4  C4\n",
       "\n",
       "pd.concat([df1, df2])\n",
       "    A   B   C\n",
       "0  A0  B0  C0\n",
       "1  A1  B1  C1\n",
       "2  A2  B2  C2\n",
       "2  A2  B2  C2\n",
       "3  A3  B3  C3\n",
       "4  A4  B4  C4"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = make_df('ABC', [0,1,2])\n",
    "df2 = make_df('ABC', [2,3,4])\n",
    "display('df1', 'df2', 'pd.concat([df1, df2])')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "84be20bf-2f89-4960-8b0a-5d29ccb03dc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df1</p><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",
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       "      <td>A1</td>\n",
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       "      <th>3</th>\n",
       "      <td>A3</td>\n",
       "      <td>B3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df2</p><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>B</th>\n",
       "      <th>C</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>B4</td>\n",
       "      <td>C4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df3</p><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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>A3</td>\n",
       "      <td>B3</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>B4</td>\n",
       "      <td>C4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>"
      ],
      "text/plain": [
       "df1\n",
       "    A   B\n",
       "1  A1  B1\n",
       "3  A3  B3\n",
       "\n",
       "df2\n",
       "    B   C\n",
       "2  B2  C2\n",
       "4  B4  C4\n",
       "\n",
       "df3\n",
       "     A   B    C\n",
       "1   A1  B1  NaN\n",
       "2  NaN  B2   C2\n",
       "3   A3  B3  NaN\n",
       "4  NaN  B4   C4"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = make_df('AB', [1,3])\n",
    "df2 = make_df('BC', [2,4])\n",
    "df3 = pd.concat([df1, df2]).sort_index()\n",
    "display('df1', 'df2', 'df3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "0f7548f7-6aba-4a56-b160-00fb7afb8647",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df1</p><div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "\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>A</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df2</p><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>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>B2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>B3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df3</p><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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>B3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>"
      ],
      "text/plain": [
       "df1\n",
       "    A\n",
       "1  A1\n",
       "2  A2\n",
       "\n",
       "df2\n",
       "    B\n",
       "2  B2\n",
       "3  B3\n",
       "\n",
       "df3\n",
       "     A    B\n",
       "1   A1  NaN\n",
       "2   A2   B2\n",
       "3  NaN   B3"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = make_df('A', [1,2])\n",
    "df2 = make_df('B', [2,3])\n",
    "df3 = pd.concat([df1, df2], axis=1)\n",
    "display('df1', 'df2', 'df3')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0085d046-8cd6-455d-b1cb-d61290017cc1",
   "metadata": {},
   "source": [
    "### Join"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "8615acb7-1f72-4639-8987-c4cf1d2b4ee5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df1</p><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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df2</p><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>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>C3</td>\n",
       "      <td>D3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>C4</td>\n",
       "      <td>D4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df3</p><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>1</th>\n",
       "      <td>A1</td>\n",
       "      <td>B1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A2</td>\n",
       "      <td>B2</td>\n",
       "      <td>C2</td>\n",
       "      <td>D2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>C3</td>\n",
       "      <td>D3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>C4</td>\n",
       "      <td>D4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>"
      ],
      "text/plain": [
       "df1\n",
       "    A   B\n",
       "1  A1  B1\n",
       "2  A2  B2\n",
       "\n",
       "df2\n",
       "    C   D\n",
       "2  C2  D2\n",
       "3  C3  D3\n",
       "4  C4  D4\n",
       "\n",
       "df3\n",
       "     A    B    C    D\n",
       "1   A1   B1  NaN  NaN\n",
       "2   A2   B2   C2   D2\n",
       "3  NaN  NaN   C3   D3\n",
       "4  NaN  NaN   C4   D4"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = make_df('AB', [1,2])\n",
    "df2 = make_df('CD', [2,3,4])\n",
    "df3 = df1.join(df2, how='outer')\n",
    "display('df1', 'df2', 'df3')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc81de5c-b381-4e92-a638-bd8ea049aca1",
   "metadata": {},
   "source": [
    "### Merge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "5d1277e0-ed19-43e8-81c9-9eef071ae2cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df1</p><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>employee</th>\n",
       "      <th>group</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Bob</td>\n",
       "      <td>Accounting</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Jake</td>\n",
       "      <td>Engineering</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Lisa</td>\n",
       "      <td>Engineering</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sue</td>\n",
       "      <td>HR</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>\n",
       "<div style=\"float: left; padding: 10px;\">\n",
       "    <p style='font-family:\"Courier New\", Courier, monospace'>df2</p><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>employee</th>\n",
       "      <th>hire_date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Lisa</td>\n",
       "      <td>2004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Bob</td>\n",
       "      <td>2008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Jake</td>\n",
       "      <td>2012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sue</td>\n",
       "      <td>2014</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>\n",
       "    </div>"
      ],
      "text/plain": [
       "df1\n",
       "  employee        group\n",
       "0      Bob   Accounting\n",
       "1     Jake  Engineering\n",
       "2     Lisa  Engineering\n",
       "3      Sue           HR\n",
       "\n",
       "df2\n",
       "  employee  hire_date\n",
       "0     Lisa       2004\n",
       "1      Bob       2008\n",
       "2     Jake       2012\n",
       "3      Sue       2014"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = pd.DataFrame({'employee': ['Bob', 'Jake', 'Lisa', 'Sue'],\n",
    "                    'group': ['Accounting', 'Engineering', 'Engineering', 'HR']})\n",
    "df2 = pd.DataFrame({'employee': ['Lisa', 'Bob', 'Jake', 'Sue'],\n",
    "                    'hire_date': [2004, 2008, 2012, 2014]})\n",
    "display('df1', 'df2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "40849b6f-5a7f-4987-ab12-64e466d281eb",
   "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>employee</th>\n",
       "      <th>group</th>\n",
       "      <th>hire_date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Bob</td>\n",
       "      <td>Accounting</td>\n",
       "      <td>2008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Jake</td>\n",
       "      <td>Engineering</td>\n",
       "      <td>2012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Lisa</td>\n",
       "      <td>Engineering</td>\n",
       "      <td>2004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sue</td>\n",
       "      <td>HR</td>\n",
       "      <td>2014</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  employee        group  hire_date\n",
       "0      Bob   Accounting       2008\n",
       "1     Jake  Engineering       2012\n",
       "2     Lisa  Engineering       2004\n",
       "3      Sue           HR       2014"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.merge(df2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a7b350a-4d3f-4e20-b6ea-c9bf9659f947",
   "metadata": {},
   "source": [
    "## Other functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ca30f3b4-6ba3-4e18-a6be-f967164c7cc3",
   "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>Points</th>\n",
       "      <th>Player</th>\n",
       "      <th>Duration</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3</td>\n",
       "      <td>B</td>\n",
       "      <td>49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>A</td>\n",
       "      <td>82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>A</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>B</td>\n",
       "      <td>68</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>A</td>\n",
       "      <td>59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>1</td>\n",
       "      <td>C</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>3</td>\n",
       "      <td>B</td>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>3</td>\n",
       "      <td>A</td>\n",
       "      <td>37</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>1</td>\n",
       "      <td>B</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>1</td>\n",
       "      <td>B</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Points Player  Duration\n",
       "0        3      B        49\n",
       "1        1      A        82\n",
       "2        1      A        41\n",
       "3        1      B        68\n",
       "4        1      A        59\n",
       "..     ...    ...       ...\n",
       "95       1      C        81\n",
       "96       3      B        83\n",
       "97       3      A        37\n",
       "98       1      B        88\n",
       "99       1      B        99\n",
       "\n",
       "[100 rows x 3 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.seed(1234) # for repeatability\n",
    "df = pd.DataFrame({\n",
    "    'Points': [random.choice([1,3]) for x in range(100)],\n",
    "    'Player': [random.choice([\"A\",\"B\",\"C\"]) for x in range(100)],\n",
    "    'Duration': [random.randint(20, 100) for x in range(100)]})\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ded5d00-32e7-44e2-9254-b43f3634c135",
   "metadata": {},
   "source": [
    "### Pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b4ac007-47a6-4b90-8a39-8bb0970b2f64",
   "metadata": {},
   "source": [
    "This helps when chaining long DataFrame expression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ff920a14-cdc2-489f-abb9-6668fb6d1bdc",
   "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>Points</th>\n",
       "      <th>Player</th>\n",
       "      <th>Duration</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>3</td>\n",
       "      <td>B</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>3</td>\n",
       "      <td>B</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>3</td>\n",
       "      <td>A</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>3</td>\n",
       "      <td>C</td>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Points Player  Duration\n",
       "20       3      B        96\n",
       "23       3      B        41\n",
       "27       3      A        80\n",
       "29       3      C        79"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.iloc[20:30][df.iloc[20:30][\"Points\"] == 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "327a2fdf-f2ef-4b3a-ae9d-a645dc7d0b5b",
   "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>Points</th>\n",
       "      <th>Player</th>\n",
       "      <th>Duration</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>3</td>\n",
       "      <td>B</td>\n",
       "      <td>96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>3</td>\n",
       "      <td>B</td>\n",
       "      <td>41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>3</td>\n",
       "      <td>A</td>\n",
       "      <td>80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>3</td>\n",
       "      <td>C</td>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Points Player  Duration\n",
       "20       3      B        96\n",
       "23       3      B        41\n",
       "27       3      A        80\n",
       "29       3      C        79"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#It saves the initial repetition of pre-filtering of the DataFrame.\n",
    "df.iloc[20:30].pipe(lambda x: x[x[\"Points\"] == 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f57245c-59e7-4801-9b43-44295e40917e",
   "metadata": {},
   "source": [
    "### Query"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "58f5508f-9a65-4c86-acfd-5bcf2d9522ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Player\n",
       "A    11\n",
       "B    19\n",
       "C    15\n",
       "dtype: int64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.query(\"Points == 3\").groupby(\"Player\").size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a66e0bba-f011-4f5c-b72d-466eced8bb94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Player'>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.query(\"Points == 3\").groupby(\"Player\").size().plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "91572a50-7ae6-4440-9785-6b5c277fb163",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Player'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.query(\"Points == 3\").groupby(\"Player\").size().loc[lambda x: x > 14].plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ec19df7-1eda-4ab6-9b92-7ee6ae936411",
   "metadata": {},
   "source": [
    "# FFT"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0aa10e6f-6ede-4558-8b4a-23d3229b7e4e",
   "metadata": {},
   "source": [
    "## Test signal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "7df9e29e-176e-463d-9126-47d853a7fa66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sampling rate\n",
    "#sr = 48000\n",
    "sr = 30\n",
    "t = np.arange(0, 1, 1/sr)\n",
    "len(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "3c503e92-30c7-456f-8a3f-503c149203cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate multi-freq signal\n",
    "x = 0.0\n",
    "\n",
    "#f = .5\n",
    "#x += 1 * np.sin(2*np.pi*f*t)\n",
    "\n",
    "f = 1\n",
    "x += 3 * np.sin(2*np.pi*f*t)\n",
    "\n",
    "f = 4\n",
    "x += 2 * np.sin(2*np.pi*f*t)\n",
    "\n",
    "f = 7   \n",
    "x += 0.5 * np.sin(2*np.pi*f*t)\n",
    "\n",
    "# put some DC offset\n",
    "x += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "f997bdfd-0d3f-4274-80e5-ff05caec182a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa446b77e48>]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "bfa6b7b1-20d9-4106-9c33-aace6b33248a",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.fft.rfft(x) / len(x)\n",
    "# Convert to accurate value for non DC components:\n",
    "X[1:] *= 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "9f275dec-3631-44e8-8603-a0ecf86172e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "freq = np.fft.rfftfreq(len(x), 1/sr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "f9f6191e-a1ac-46a7-af6b-f2967c93c759",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<StemContainer object of 3 artists>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.stem(freq, abs(X))\n",
    "#plt.xlim(-.5, 10.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0eeccbee-6342-45f0-a491-fd00ae90f15a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}