text/Chapter05.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e9f88bf8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore') # 実行に影響のない　warninig　を非表示にします. 非推奨."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "d4c32d9e",
   "metadata": {},
   "source": [
    "# Chapter5: 潜在変数"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "68e7ea29",
   "metadata": {},
   "source": [
    "この章では混合ガウス分布についての解説と実装を通して、潜在変数について学ぶ。<br>\n",
    "そして、混合ガウス分布のパラメータ推定と関係の深いk-means法を取り扱ったのちに、混合ガウス分布について詳しい説明を行っていく。"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e8db45be",
   "metadata": {},
   "source": [
    "# 5.1 潜在変数"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "111f03e1",
   "metadata": {},
   "source": [
    "### 5.1.1 潜在変数とは"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a48559bd",
   "metadata": {},
   "source": [
    "潜在変数は実際に観測されることはないが、データを決定づける上で重要な変数のことを指す。<br>\n",
    "例えば、学生の学力を図るために「国語」、「数学」、「理科」、「社会」のテストを実施したとしよう。<br>\n",
    "この場合、５教科のテストの点数が観測変数であり、生徒がどの科目が得意なのかを表現する実際に観測できるデータである。<br>\n",
    "そして、点数を見てみると数学が得意な生徒は理科も得意であったり、国語が得意な生徒は社会も得意であったりという傾向がみられることがある。<br>\n",
    "このとき、数学や理科の点数には学生の「理系的能力」、国語や社会には学生の「文系的能力」という実際に測定できない能力が関係するのかもしれない。<br>\n",
    "このような実際には観測できないが観測データに影響を与えている変数を潜在変数と呼ぶ。<br>\n",
    "![](./figs/score.png)\n",
    "<br>\n",
    "そして、本章では観測データを用いることで潜在変数を推定するモデルについて取り扱っていく。<br>\n",
    "（例でいえば、テストの点数から「理系的能力」と「文系的能力」を推定するということである）"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "f09f8346",
   "metadata": {},
   "source": [
    "### 5.1.2 混合ガウス分布における潜在変数"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "952c2bf2",
   "metadata": {},
   "source": [
    "今回学ぶ潜在変数モデルは混合ガウス分布である。<br>\n",
    "混合ガウス分布ではデータが複数のガウス分布の合成であるとみなして、データの分布を求めるモデルである。<br>\n",
    "このとき、各データがどのガウス分布から生成されたものなのかということが潜在変数となる。<br>\n",
    "例えば、下の図のような人間の身長を考えよう。([出典](https://www.google.com/url?sa=i&url=https%3A%2F%2Fstatresearch.jp%2FBMI%2F&psig=AOvVaw2hy059Ws0tKUdnFTl8aDT9&ust=1687502895983000&source=images&cd=vfe&ved=0CBMQjhxqFwoTCICFk6Kk1v8CFQAAAAAdAAAAABAE))<br>\n",
    "身長は男女で差があるものであるが、男性の身長と女性の身長を分けて考えればそれぞれガウス分布に従う。<br>\n",
    "そのため、人間の身長の分布=男性の身長の分布+女性の身長の分布であるといえる。<br>\n",
    "そして、今回の場合における観測変数はAさんの身長であり、潜在変数はAさんの性別ということになる。<br>\n",
    "![](./figs/he.png)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "43f6feaa-360a-4212-bf2a-fa80c6a8bb4b",
   "metadata": {},
   "source": [
    "# 5.2 k-means法\n",
    "\n",
    "k-means法の目的は、データをk個のグループに分割する方法である。<br>\n",
    "\n",
    "グループが３つ(k=3)の場合、以下のデータでは、青・赤・緑に分類することができると考えられる。<br>\n",
    "\n",
    "「同じクラスに属するデータ点は似ている」という仮定に基づき、距離の近いデータ点を同じクラスに分類することが主な考え方だ。<br>\n",
    "各クラスの代表地点は上の図でいう印スター。<br>\n",
    "各データ点は、代表地点との距離の近さを基準として、各クラスに分類される。<br>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "03108065-4d36-4746-9b63-5ace62a112f9",
   "metadata": {},
   "source": [
    "### 5.2.1 k-means法の定式化\n",
    "次に、k-means法の式について見ていこうと思う。\n",
    "\n",
    "目的関数：<br>\n",
    "$$\n",
    "J = \\sum_{n=1}^N \\sum_{k=1}^K r_{nk} || \\mathbf{x}_n - \\mathbf{\\mu}_k  ||^2 \\tag{1}\n",
    "$$\n",
    "\n",
    "$\\mathbf{x}_n$：n番目のデータ点<br>\n",
    "$\\mu_k$：k番目のクラスターの重心点(代表地点)<br>\n",
    "2値指示変数：$r_{nk} \\in \\{0 , 1\\}$<br>\n",
    "2値指示変数とは、データ点$\\mathbf{x}_n$がクラスタkに属されるとき1を、そうでなければ0を割り当てる指示変数<br>\n",
    "\n",
    "目的関数Jを最小になるような$r_{nk}$と$\\mu_k$の値を求めることで、最適なクラスタリングができる仕組みになっている。<br>\n",
    "初めから各クラスの代表地点がわかるはずが無い。<br>\n",
    "よってk-means法のアルゴリズムは、以下のような流れで目的関数Jを最小にするような$r_{nk}$と$\\mu_k$の値の決定するようになっている。"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "8244277a-7896-4aef-a315-51a54ee96d1b",
   "metadata": {},
   "source": [
    "### 5.2.2 k-means法のアルゴリズムの流れ\n",
    "**1.重心点$\\mu_k$の初期値を決定する。**\n",
    "\n",
    "**2.重心点$\\mu_k$を固定しつつ、$r_{nk}$について、目的関数Jを最小化する。**<br>\n",
    "\n",
    "これは、n番目のデータ点と各クラスの重心点$\\mu_k$との距離を求めて、n番目のデータ点を最も距離の近いクラスの重心点に割り当てることである。<br>\n",
    "\n",
    "$$\n",
    "r_{nk}=  \\left\\{\n",
    "\\begin{array}{ll}\n",
    "1 & k = \\text{argmin}_j|| \\mathbf{x}_n - \\mathbf{\\mu}_k  ||^2 \\\\\n",
    "0\n",
    "\\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "**3.$r_{nk}$を固定しつつ、重心点$\\mu_k$について目的関数Jを最小化する。**<br>\n",
    "\n",
    "これは、k番目のクラスに割り当てられたすべてのデータ点$\\mathbf{x}_n$の平均値をとり、新しくk番目のクラスの重心点$\\mu_k$を決定することである。\n",
    "\n",
    "$\\mu_k$の決定を式で見てみる。<br>\n",
    "$\\mu_k$に関する偏微分を0とおくと、以下の通りになる。\n",
    "$$\n",
    "2\\sum_{n=1}^N r_{nk}(\\mathbf{x}_n - \\mathbf{\\mu}_k) = 0\n",
    "$$\n",
    "$$\n",
    "\\mathbf{\\mu}_k = \\frac{\\sum_{n=1}^N r_{nk}\\mathbf{x}_n }{\\sum_{n=1}^N r_{nk}}\n",
    "$$\n",
    "最後の式を見ると、k番目のクラスに割り当てられたすべてのデータ点$\\mathbf{x}_n$の平均値であると解釈が可能である。\n",
    "\n",
    "**4.目的関数Jが収束するまで、2と3を繰り返し計算する**"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a89a3f88-6733-423f-ad93-c145a2185fd6",
   "metadata": {},
   "source": [
    "### 5.2.3 sk-learnで実装"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "49ce0dfc-ef50-4a92-9427-45b5ad2ddaba",
   "metadata": {},
   "source": [
    "### データセットの準備"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d131c38c-5104-4000-a7ff-fa7a9ba19a58",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "709ff5da-9fd3-46aa-9e0c-2ac820a34e59",
   "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>alcohol</th>\n",
       "      <th>malic_acid</th>\n",
       "      <th>ash</th>\n",
       "      <th>alcalinity_of_ash</th>\n",
       "      <th>magnesium</th>\n",
       "      <th>total_phenols</th>\n",
       "      <th>flavanoids</th>\n",
       "      <th>nonflavanoid_phenols</th>\n",
       "      <th>proanthocyanins</th>\n",
       "      <th>color_intensity</th>\n",
       "      <th>hue</th>\n",
       "      <th>od280/od315_of_diluted_wines</th>\n",
       "      <th>proline</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127.0</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100.0</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101.0</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113.0</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118.0</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   alcohol  malic_acid   ash  alcalinity_of_ash  magnesium  total_phenols   \n",
       "0    14.23        1.71  2.43               15.6      127.0           2.80  \\\n",
       "1    13.20        1.78  2.14               11.2      100.0           2.65   \n",
       "2    13.16        2.36  2.67               18.6      101.0           2.80   \n",
       "3    14.37        1.95  2.50               16.8      113.0           3.85   \n",
       "4    13.24        2.59  2.87               21.0      118.0           2.80   \n",
       "\n",
       "   flavanoids  nonflavanoid_phenols  proanthocyanins  color_intensity   hue   \n",
       "0        3.06                  0.28             2.29             5.64  1.04  \\\n",
       "1        2.76                  0.26             1.28             4.38  1.05   \n",
       "2        3.24                  0.30             2.81             5.68  1.03   \n",
       "3        3.49                  0.24             2.18             7.80  0.86   \n",
       "4        2.69                  0.39             1.82             4.32  1.04   \n",
       "\n",
       "   od280/od315_of_diluted_wines  proline  class  \n",
       "0                          3.92   1065.0      0  \n",
       "1                          3.40   1050.0      0  \n",
       "2                          3.17   1185.0      0  \n",
       "3                          3.45   1480.0      0  \n",
       "4                          2.93    735.0      0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ワインデータのダウンロード\n",
    "wine = datasets.load_wine()\n",
    "data = pd.DataFrame(wine.data, columns=wine.feature_names)\n",
    "target = pd.DataFrame(wine.target, columns=[\"class\"])\n",
    "\n",
    "df = pd.concat([data, target], axis=1)\n",
    "\n",
    "df.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5a5af293-f175-4604-9069-2ddd9c6b6dcf",
   "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>color_intensity</th>\n",
       "      <th>proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.64</td>\n",
       "      <td>1065.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.38</td>\n",
       "      <td>1050.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.68</td>\n",
       "      <td>1185.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.80</td>\n",
       "      <td>1480.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.32</td>\n",
       "      <td>735.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   color_intensity  proline\n",
       "0             5.64   1065.0\n",
       "1             4.38   1050.0\n",
       "2             5.68   1185.0\n",
       "3             7.80   1480.0\n",
       "4             4.32    735.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df[[\"color_intensity\",\"proline\"]]\n",
    "y = wine.target\n",
    "\n",
    "X.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "164a591f-8acc-4096-8e8e-ec43b2f4fa07",
   "metadata": {},
   "outputs": [],
   "source": [
    "#k-means法で必要なライブラリ\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c1461ad4-a289-4d81-80fa-9f7d1baeb47e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 特徴量の標準化\n",
    "sc = StandardScaler()\n",
    "X_std = sc.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0fb09c41-59da-4cf5-9c34-502ecab84ba6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=4, random_state=7)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">KMeans</label><div class=\"sk-toggleable__content\"><pre>KMeans(n_clusters=4, random_state=7)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=4, random_state=7)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# K-Meansのモデルを作成\n",
    "model2 = KMeans(n_clusters=2, random_state=7)\n",
    "model3 = KMeans(n_clusters=3, random_state=7)\n",
    "model4 = KMeans(n_clusters=4, random_state=7)\n",
    "\n",
    "#モデルの訓練\n",
    "model2.fit(X_std)\n",
    "model3.fit(X_std)\n",
    "model4.fit(X_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "51bd6776-ac01-4328-ae8e-6bd21a665f34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(close=None, block=None)>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x864 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,12)) #プロットのサイズ指定\n",
    "\n",
    "color2 = np.array(['r','g'])\n",
    "color3 = np.array(['r','g','b'])\n",
    "color4 = np.array(['r','g','b','y'])\n",
    "# クラスタ数2のK-Meansの散布図\n",
    "plt.subplot(3, 1, 1)\n",
    "plt.scatter(X_std[:,0], X_std[:,1], c=color2[model2.labels_])\n",
    "plt.scatter(model2.cluster_centers_[:,0], model2.cluster_centers_[:,1],s=250, marker='*',c='red')\n",
    "plt.title('K-means(n_clusters=2)')\n",
    "\n",
    "# クラスタ数3のK-Meansの散布図\n",
    "plt.subplot(3, 1, 2)\n",
    "plt.scatter(X_std[:,0], X_std[:,1], c=color3[model3.labels_])\n",
    "plt.scatter(model3.cluster_centers_[:,0], model3.cluster_centers_[:,1],s=250, marker='*',c='red')\n",
    "plt.title('K-means(n_clusters=3)')\n",
    "\n",
    "# クラスタ数4のK-Meansの散布図\n",
    "plt.subplot(3, 1, 3)\n",
    "plt.scatter(X_std[:,0], X_std[:,1], c=color4[model4.labels_])\n",
    "plt.scatter(model4.cluster_centers_[:,0], model4.cluster_centers_[:,1],s=250, marker='*',c='red')\n",
    "plt.title('K-means(n_clusters=4)')\n",
    "\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "428bef40-baf5-4ec9-916c-91344ebe7d76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(close=None, block=None)>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8)) #プロットのサイズ指定\n",
    "\n",
    "# 色とプロリンの散布図\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.scatter(X_std[:,0], X_std[:,1],c=y)\n",
    "plt.title('training data y')\n",
    "\n",
    "# K-Meansの散布図\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.scatter(X_std[:,0], X_std[:,1], c=model3.labels_)\n",
    "plt.scatter(model3.cluster_centers_[:,0], model3.cluster_centers_[:,1],s=250, marker='*',c='red')\n",
    "plt.title('K-means(n_clusters=3)')\n",
    "\n",
    "plt.show"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e282a21f-646b-446d-bdc8-c36d6b41c57c",
   "metadata": {},
   "source": [
    "## 5.3 混合ガウス分布"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "2a4f4eac-7dc9-417c-8e70-221861106898",
   "metadata": {},
   "source": [
    "### 5.3.1 ガウス分布\n",
    "ガウス分布は、平均$\\mu$と分散$\\sigma$のパラメータを指定することで、分布の形状を決めることができる確率分布である。<br>\n",
    "\n",
    "以下では、平均$\\mu=0$、分散$\\sigma=1$とした時のガウス分布である。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3f5772fc-83db-418b-850b-5ebaa2ebd192",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# ガウス関数\n",
    "def gauss(x, a=1, mu=0, sigma=1):\n",
    "    return a * np.exp(-(x - mu)**2 / (2*sigma**2))\n",
    "\n",
    "x = np.arange(-4, 4, 0.1)\n",
    "f = gauss(x)\n",
    "\n",
    "# Figureを作成\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "\n",
    "ax = fig.add_subplot(111)\n",
    "ax.set_title(\"Gaussian Function\", fontsize=16)\n",
    "ax.set_xlabel(\"x\", fontsize=14)\n",
    "ax.set_ylabel(\"y\", fontsize=14)\n",
    "ax.grid()\n",
    "ax.set_xlim([-4, 4])\n",
    "ax.set_ylim([0, 1.2])\n",
    "\n",
    "f1 = gauss(x)\n",
    "\n",
    "# Axesにガウス関数を描画\n",
    "ax.plot(x, f, label=\"a=1.0, μ=0, σ=1\")\n",
    "ax.legend(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c2968650-7913-4dd2-b03f-efad1ee37259",
   "metadata": {},
   "source": [
    "### 5.3.2 混合ガウス分布とは\n",
    "\n",
    "例えば、ワインデータは、以下の図のように単一のガウス分布で表されているとは考えられない。<br>\n",
    "ワインデータは、k-means法でも見たようにいくつかのクラスタから構成されている。それぞれのクラスタはガウス分布に基づいていると仮定すると、ワインデータは単一のガウス分布が複数混合した分布と表すことができる。<br>\n",
    "\n",
    "このように、単一のガウス分布よりも、より豊かな確率密度のモデルを提供することが、混合ガウス分布の意図である。"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "1fb7a5c6-a61d-4cab-bb54-aa899fc582d9",
   "metadata": {},
   "source": [
    "### 5.3.3 混合ガウス分布の定義\n",
    "ここでは、離散的な潜在変数zを用いた混合ガウス分布を定式化したいと思う。\n",
    "\n",
    "混合ガウス分布は、ガウス分布の線形重ね合わせで表すことができ、以下の式となっている。\n",
    "$$\n",
    "p(\\mathbf{x})= \\sum_{k=1}^K \\pi_k N(\\mathbf{x}|\\mathbf{\\mu}_k,\\mathbf{\\sum}_k) \\tag{1,1}\n",
    "$$\n",
    "\n",
    "ここで、K次元の２値確率変数の$\\mathbf{z}$を導入する。\n",
    "$\\mathbf{z}$は、1-of-k符号化法(どれか1つの$z_k$だけが1で、それ以外が0)を取り、以下を満たす。\n",
    "\n",
    "$$\n",
    "z_{k} \\in \\{0 , 1\\}\n",
    "$$\n",
    "$$\n",
    "\\sum_{k} z_{k} = 1\n",
    "$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "44ed8a54-8c29-4c2f-96af-be5ed62fafaa",
   "metadata": {},
   "source": [
    "次に、潜在変数$\\mathbf{z}$を用いて、同時分布$p(\\mathbf{x},\\mathbf{z})$を定義したい。<br>\n",
    "$p(\\mathbf{x},\\mathbf{z})=p(\\mathbf{x}|\\mathbf{z})p(\\mathbf{z})$より、同時分布を得るためには、条件付き分布$p(\\mathbf{x}|\\mathbf{z})$と周辺分布$p(\\mathbf{z})$が分かれば良いので、それぞれについて定義していく。"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "d53175bd-a2bc-4e27-99e7-e61879c8fccb",
   "metadata": {},
   "source": [
    "周辺分布$p(\\mathbf{z})$は、以下のように混合係数$\\pi_k$によって定められる。\n",
    "\n",
    "$$\n",
    "p(z)=\\Pi_{k=1}^K\\pi_k^{z_k} \\tag{1,2}\n",
    "$$\n",
    "\n",
    "ただし、パラメータ$\\pi_k$は、確率であるための制約として以下を満たさなければならない。\n",
    "\n",
    "$$\n",
    "0\\leqq\\pi_k\\leqq1\n",
    "$$\n",
    "$$\n",
    "\\sum_{k=1}^{K}\\pi_k=1\n",
    "$$\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "f0853e22-9ec5-4168-92a2-6a312f34820c",
   "metadata": {},
   "source": [
    "同様に、潜在変数$\\mathbf{z}$が与えられた下での$\\mathbf{x}$の条件付き分布は次のガウス分布になる。\n",
    "$$\n",
    "p(\\mathbf{x}|\\mathbf{z})=\\Pi_{k=1}^{K}N(\\mathbf{x}|\\mathbf{\\mu}_k,\\sum_k)^{zk} \\tag{1,3}\n",
    "$$"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a795bb5c-1ada-4cd1-bf48-29401eea6c32",
   "metadata": {},
   "source": [
    "$p(\\mathbf{x})=\\sum_zp(\\mathbf{x},\\mathbf{z})=\\sum_zp(\\mathbf{x}|\\mathbf{z})p(\\mathbf{z})$に(1,2)(1,3)を代入すると、\n",
    "$$\n",
    "p(\\mathbf{x})=\\sum_zp(\\mathbf{x}|\\mathbf{z})p(\\mathbf{z})= \\sum_{k=1}^K \\pi_k N(\\mathbf{x}|\\mathbf{\\mu},\\mathbf{\\sum}_k) \n",
    "$$\n",
    "\n",
    "これは、(1,1)の混合ガウス分布と同じ式となるため、各観測データ点に対応する潜在変数が存在することが確認できた。"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "948a806c-b0b4-4e26-af19-0b23e466d287",
   "metadata": {},
   "source": [
    "### 5.3.4 負担率\n",
    "\n",
    "ベイズの定理より、$\\mathbf{z}$の事後分布を算出することができる。\n",
    "つまり、観測されたデータ$\\mathbf{x}$から$\\mathbf{z}$の分布を見直すことができるということである。\n",
    "$$\n",
    "\\gamma(z_{nk}) \\equiv p(z_k=1|\\mathbf{x}) =  \\frac{ \\pi_k  \\mathcal{N} \\left( x_n| \\mu _k , \\Sigma _k \\right)}{ \\sum_j \\pi_j  \\mathcal{N} \\left( x_n| \\mu _j , \\Sigma _j \\right)   }\n",
    "$$\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "264b2db5-be51-4768-92a0-86d428397b09",
   "metadata": {},
   "source": [
    "この事後分布は、$\\gamma(z_k)$とおき、負担率と呼ばれ、n番目のデータが各クラスタkへ所属する確率を表したものである。"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ded6e014-4654-4a61-91e1-b9027929c249",
   "metadata": {},
   "source": [
    "### 5.3.4 混合ガウス分布に最尤推定を適用\n",
    "\n",
    "観測したデータ集合　に混合ガウス分布を当てはめる問題を考える。\n",
    "この時の対数尤度関数は以下のように定義することができる。\n",
    "\n",
    "$$\\begin{eqnarray} \\text{ln}p(X|\\pi,\\mu,\\sum) = \\text{ln} \\prod _n\\big\\{ \\sum_k \\pi _k \\mathcal{N}\\left( x_n |\\mu _k , \\Sigma _k \\right)\\big\\} \\\\\n",
    "= \\sum _n \\text{ln}\\big\\{\\sum_k \\pi _k \\mathcal{N}\\left( x_n |\\mu _k , \\Sigma _k \\right)\\big\\}  \\end{eqnarray}\n",
    "$$\n",
    "<br>\n",
    "この対数尤度関数を最大化を行っていきたいが、log-sum部分があり、解析的には解くことが困難であるため、潜在変数を持つモデルの最尤推定を求めるための強力な方法として、EMアルゴリズムを用いる。\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e4e3aec9-7583-4804-b5ce-f50a7007443b",
   "metadata": {},
   "source": [
    "### 5.3.5 混合ガウス分布のEMアルゴリズム\n",
    "EMアルゴリズムはデータから分布のパラメータを推定する有名なアルゴリズムで，混合ガウス分布のパラメータ推定でもよく用いられる．<br>\n",
    "中身については以下の通りである．<br>\n",
    "\n",
    "1. $ \\pi , \\mu , \\Sigma$を初期化する\n",
    "2. [Eステップ]以下の式を計算する<br>\n",
    ">$ \\gamma(z_{nk}) =  \\frac{ \\pi_k  \\mathcal{N} \\left( x_n| \\mu _k , \\Sigma _k \\right)}{ \\sum_j \\pi_j  \\mathcal{N} \\left( x_n| \\mu _j , \\Sigma _j \\right)   }$<br>\n",
    ">$ \\\\N_k = \\sum_n \\gamma (z_{nk} )$<br>\n",
    "3. [Mステップ]パラメータの更新を行う<br>\n",
    ">$L= \\sum_n \\log \\sum_k \\pi _k  \\mathcal{N} \\left( x_n | \\mu _k , \\Sigma _k \\right)$<br>\n",
    ">$\\mu _k  =  \\frac{ \\sum_{n} \\gamma (z_{nk}) x_n }{N_k}$<br>\n",
    ">$ \\Sigma _k = \\frac{1}{N_k} \\sum_n   \\gamma (z_{nk} ) (x_n -\\mu_k ) (x_n - \\mu _k ) ^{T}$<br>\n",
    ">$ \\pi_ k =\\frac{N_k } {N}$\n",
    "4. 2，3を収束するまで繰り返す"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "14fa41f6-046b-4796-bd35-38218e8863e5",
   "metadata": {},
   "source": [
    "このアルゴリズムも数式だらけで難しく感じるが，実は先ほど学んだKmeans法と非常に類似したアルゴリズムである．<br>\n",
    "EMアルゴリズムでは与えられたデータ点がどのガウス分布から生成されたものかを推定している．<br>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "622b6f96-f215-46b8-9f70-7a043f67dc3e",
   "metadata": {},
   "source": [
    "## 5.4 sk-leanで実装"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4bf37468-7b94-406e-9ce5-0b1759761f41",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ライブラリのインポート\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.mixture import GaussianMixture\n",
    "from sklearn.mixture import BayesianGaussianMixture\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a518805f-fbf1-4f77-8249-1cc75388d6c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ワインデータのダウンロード\n",
    "wine = datasets.load_wine()\n",
    "X = wine.data[:,[9,12]]\n",
    "y = wine.target\n",
    "\n",
    "# 特徴量の標準化\n",
    "sc = StandardScaler()\n",
    "X_std = sc.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "281e526e-f8a3-476c-ab9d-5123bbd6f14e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GaussianMixture(n_components=3, random_state=1)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">GaussianMixture</label><div class=\"sk-toggleable__content\"><pre>GaussianMixture(n_components=3, random_state=1)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "GaussianMixture(n_components=3, random_state=1)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# covariance_typeに'diag'を指定しGMMのモデルを作成\n",
    "model = GaussianMixture(n_components=3, covariance_type='diag', random_state=1)\n",
    "\n",
    "#モデルの訓練\n",
    "model.fit(X_std)\n",
    "\n",
    "# covariance_typeに'full'を指定し GMMのモデルを作成\n",
    "model2 = GaussianMixture(n_components=3, covariance_type='full', random_state=1)\n",
    "\n",
    "#モデルの訓練\n",
    "model2.fit(X_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "440dc6a6-7663-4279-bb38-c868fce102ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(close=None, block=None)>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 576x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8)) #プロットのサイズ指定\n",
    "# 色とプロリンの散布図のGMM(diag)によるクラスタリング\n",
    "plt.subplot(2, 1, 1)\n",
    "\n",
    "x = np.linspace(X_std[:,0].min(), X_std[:,0].max(), 100)\n",
    "y = np.linspace(X_std[:,0].min(), X_std[:,0].max(), 100)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "XX = np.array([X.ravel(), Y.ravel()]).T\n",
    "Z = -model.score_samples(XX)\n",
    "Z = Z.reshape(X.shape)\n",
    "\n",
    "plt.contour(X, Y, Z, levels=[0.5, 1, 2 ,3 ,4, 5]) # 等高線のプロット\n",
    "plt.scatter(X_std[:,0], X_std[:,1], c=model.predict(X_std))\n",
    "plt.scatter(model.means_[:,0], model.means_[:,1],s=250, marker='*',c='red')\n",
    "plt.title('GMM(covariance_type=diag)')\n",
    "\n",
    "# 色とプロリンの散布図のGMM(full)によるクラスタリング\n",
    "plt.subplot(2, 1, 2)\n",
    "\n",
    "x = np.linspace(X_std[:,0].min(), X_std[:,0].max(), 100)\n",
    "y = np.linspace(X_std[:,0].min(), X_std[:,0].max(), 100)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "XX = np.array([X.ravel(), Y.ravel()]).T\n",
    "Z = -model2.score_samples(XX)\n",
    "Z = Z.reshape(X.shape)\n",
    "\n",
    "plt.contour(X, Y, Z, levels=[0.5, 1, 2 ,3 ,4, 5]) # 等高線のプロット\n",
    "plt.scatter(X_std[:,0], X_std[:,1], c=model2.predict(X_std))\n",
    "plt.scatter(model2.means_[:,0], model2.means_[:,1],s=250, marker='*',c='red')\n",
    "plt.title('GMM(covariance_type=full)')\n",
    "\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "08aee75e-8650-4bd9-9a92-950fe6f1ba66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0,\n",
       "       2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,\n",
       "       1, 1], dtype=int64)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(X_std) #予測"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e3e9569b",
   "metadata": {},
   "source": [
    "## 5.5 フルスクラッチコーディング\n",
    "<a id=\"1.5\"></a>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "f51f3d47",
   "metadata": {},
   "source": [
    "これまでscikit-learnで実装された機械学習モデルを用いて混合ガウス分布を推定してきた．<br>\n",
    "本節ではscikit-learnでどのように混合ガウス分布のパラメータを推定しているのかを理解するために、EMアルゴリズムをフルスクラッチで実装を行う．"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6da8794c",
   "metadata": {},
   "source": [
    "### 5.5.1 k-means法"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6a29f49c",
   "metadata": {},
   "source": [
    "まず，EMアルゴリズムの話に入る前に，分類問題でよく利用される教師なし学習手法のk-means法を実装してみよう．<br>\n",
    "kmeans法では各クラス$C_k$の代表地点$\\{\\boldsymbol\\mu_k\\}$を求めることで分類を行うアルゴリズムである．\n",
    "k-means法のアルゴリズムは以下の通りである．<br>\n",
    ">1. 各クラスの代表地点$\\{\\boldsymbol\\mu_k\\}$を初期化\n",
    ">2. 各点$x_n$を以下の式を満たすクラス$\\hat{k}$に割り当てる\n",
    ">>$\\hat{k}=\\mathop{\\arg\\min}\\limits_{k}||\\mathbf x_n-\\boldsymbol\\mu_k||^2$\n",
    ">3. $\\{\\boldsymbol\\mu_k\\}$を以下の式のように更新\n",
    ">>$\\boldsymbol\\mu_k=\\frac{1}{|C_k|}\\sum_{\\mathbf x\\in C_k} \\mathbf x$\n",
    ">4. (2)，(3)を繰り返し、$\\{\\boldsymbol\\mu_k\\}$の更新が止まれば終了\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "95a067ab",
   "metadata": {},
   "source": [
    "一見難しく感じるかもしれないが，「同じクラスに属するデータ点は似ている」という仮定に基づき，距離の近いデータ点を同じクラスに分類することが主な考え方である．<br>\n",
    "各クラスは代表地点を持ち，各データ点はどの代表地点に最も近いかという基準に基づいて分類がなされる．<br>\n",
    "各データ点をそれぞれのクラスに割り振った後に，各クラスに属するデータ点の重心を求めて代表地点の更新を行う．<br>\n",
    "この作業を一定回数，あるいは分類結果の変化が止まるまで繰り返すことがk-means法のアルゴリズムである．"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "b7705039",
   "metadata": {},
   "source": [
    "### 5.5.2 k-means法の実装"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "8de60995",
   "metadata": {},
   "source": [
    "### 課題1 k-means法を実装せよ<br>\n",
    "基本となるのは，(1)各データ点をどのクラスに分類するのか決定するdist関数と，(2)fit関数内の各クラスの代表地点を決定する部分である．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0ac45dca",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from copy import deepcopy\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "class My_KMeans:\n",
    "    def __init__(self, n_cluster=2, random_state=42,n_iter=300):\n",
    "        self.n_cluster = n_cluster\n",
    "        self.n_iter = n_iter\n",
    "        self.random_state = random_state\n",
    "        self.is_trained = False\n",
    "    #各クラスタの中心点を計算\n",
    "    def fit(self,X):\n",
    "        \n",
    "        #結果保存用\n",
    "        self.centroids_and_labels = []\n",
    "        self.features = len(X[0])\n",
    "        \n",
    "        #代表地点をランダムに選んだデータ点で初期化する\n",
    "        idx = np.random.choice(len(X), self.n_cluster, replace=False)\n",
    "        #各クラスタの中心の座標を格納\n",
    "        self.centroids = X[idx, :]\n",
    "        \n",
    "        #代表地点を基に各データ点にラベル付け\n",
    "        label = [self.dist(x) for x in X]\n",
    "\n",
    "        #n_iter回の更新、もしくは分類結果が変わらなくなれば終了\n",
    "        for n in range(self.n_iter):\n",
    "            self.labels = label\n",
    "            \n",
    "            #分類結果を基に代表地点を更新する（各クラスに属するデータ点の重心を求める）\n",
    "\n",
    "            #代表地点を格納\n",
    "            self.centroids = np.zeros((self.n_cluster,self.features))\n",
    "            #いくつのデータがクラスタに含まれるか数える\n",
    "            self.counts = np.zeros((self.n_cluster,1))\n",
    "\n",
    "            #代表地点を求める\n",
    "            #点の重心を求めるので座標を合計してからその平均をとればよい\n",
    "            for i,x in enumerate(X):\n",
    "                #コードを埋める\n",
    "                self.centroids[self.labels[i]] += \n",
    "                self.counts[self.labels[i]] += \n",
    "            #平均をとる\n",
    "            self.centroids /= self.counts\n",
    "            \n",
    "            #animation描画用に結果を保存しておく\n",
    "            self.centroids_and_labels.append([deepcopy(self.centroids),deepcopy(self.labels)])\n",
    "            \n",
    "            #更新された代表地点を基に再分類\n",
    "            label=[self.dist(x) for x in X]\n",
    "            \n",
    "            #分類結果が変わらなければ終了する\n",
    "            if label==self.labels:\n",
    "                break\n",
    "                \n",
    "        #学習を終了する\n",
    "        self.is_trained=True\n",
    "        \n",
    "    #与えられた点のクラスタを予測\n",
    "    def predict(self,X):\n",
    "        #学習済みでなければ処理をしない\n",
    "        assert self.is_trained,\"fitが実行されていません\"\n",
    "        \n",
    "        #予測値を格納した配列を作成\n",
    "        pred=[self.dist(x) for x in X]\n",
    "        return pred\n",
    "    \n",
    "    #xと各クラスタの中心点との距離を計算し、最も距離が近いクラスタのラベルを返す\n",
    "    def dist(self,x):\n",
    "        #xが属するクラスタのラベル\n",
    "        label=-1\n",
    "        #最小の距離を格納\n",
    "        min_distance=float('inf')\n",
    "        for i in range(self.n_cluster):\n",
    "            #距離を求める\n",
    "            #コードを埋める\n",
    "            distance=\n",
    "            #もしxからより近いクラスタを発見したら更新を行う\n",
    "            #if文を埋める\n",
    "            if :\n",
    "                label=\n",
    "                min_distance=\n",
    "        return label\n",
    "        "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "9973e725",
   "metadata": {},
   "source": [
    "上記の実装に成功していれば，下記のコードが正常に動くはずだ．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2bd6e7ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": "/* Put everything inside the global mpl namespace */\n/* global mpl */\nwindow.mpl = {};\n\nmpl.get_websocket_type = function () {\n    if (typeof WebSocket !== 'undefined') {\n        return WebSocket;\n    } else if (typeof MozWebSocket !== 'undefined') {\n        return MozWebSocket;\n    } else {\n        alert(\n            'Your browser does not have WebSocket support. ' +\n                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n                'Firefox 4 and 5 are also supported but you ' +\n                'have to enable WebSockets in about:config.'\n        );\n    }\n};\n\nmpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n    this.id = figure_id;\n\n    this.ws = websocket;\n\n    this.supports_binary = this.ws.binaryType !== undefined;\n\n    if (!this.supports_binary) {\n        var warnings = document.getElementById('mpl-warnings');\n        if (warnings) {\n            warnings.style.display = 'block';\n            warnings.textContent =\n                'This browser does not support binary websocket messages. ' +\n                'Performance may be slow.';\n        }\n    }\n\n    this.imageObj = new Image();\n\n    this.context = undefined;\n    this.message = undefined;\n    this.canvas = undefined;\n    this.rubberband_canvas = undefined;\n    this.rubberband_context = undefined;\n    this.format_dropdown = undefined;\n\n    this.image_mode = 'full';\n\n    this.root = document.createElement('div');\n    this.root.setAttribute('style', 'display: inline-block');\n    this._root_extra_style(this.root);\n\n    parent_element.appendChild(this.root);\n\n    this._init_header(this);\n    this._init_canvas(this);\n    this._init_toolbar(this);\n\n    var fig = this;\n\n    this.waiting = false;\n\n    this.ws.onopen = function () {\n        fig.send_message('supports_binary', { value: fig.supports_binary });\n        fig.send_message('send_image_mode', {});\n        if (fig.ratio !== 1) {\n            fig.send_message('set_device_pixel_ratio', {\n                device_pixel_ratio: fig.ratio,\n            });\n        }\n        fig.send_message('refresh', {});\n    };\n\n    this.imageObj.onload = function () {\n        if (fig.image_mode === 'full') {\n            // Full images could contain transparency (where diff images\n            // almost always do), so we need to clear the canvas so that\n            // there is no ghosting.\n            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n        }\n        fig.context.drawImage(fig.imageObj, 0, 0);\n    };\n\n    this.imageObj.onunload = function () {\n        fig.ws.close();\n    };\n\n    this.ws.onmessage = this._make_on_message_function(this);\n\n    this.ondownload = ondownload;\n};\n\nmpl.figure.prototype._init_header = function () {\n    var titlebar = document.createElement('div');\n    titlebar.classList =\n        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n    var titletext = document.createElement('div');\n    titletext.classList = 'ui-dialog-title';\n    titletext.setAttribute(\n        'style',\n        'width: 100%; text-align: center; padding: 3px;'\n    );\n    titlebar.appendChild(titletext);\n    this.root.appendChild(titlebar);\n    this.header = titletext;\n};\n\nmpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._init_canvas = function () {\n    var fig = this;\n\n    var canvas_div = (this.canvas_div = document.createElement('div'));\n    canvas_div.setAttribute('tabindex', '0');\n    canvas_div.setAttribute(\n        'style',\n        'border: 1px solid #ddd;' +\n            'box-sizing: content-box;' +\n            'clear: both;' +\n            'min-height: 1px;' +\n            'min-width: 1px;' +\n            'outline: 0;' +\n            'overflow: hidden;' +\n            'position: relative;' +\n            'resize: both;' +\n            'z-index: 2;'\n    );\n\n    function on_keyboard_event_closure(name) {\n        return function (event) {\n            return fig.key_event(event, name);\n        };\n    }\n\n    canvas_div.addEventListener(\n        'keydown',\n        on_keyboard_event_closure('key_press')\n    );\n    canvas_div.addEventListener(\n        'keyup',\n        on_keyboard_event_closure('key_release')\n    );\n\n    this._canvas_extra_style(canvas_div);\n    this.root.appendChild(canvas_div);\n\n    var canvas = (this.canvas = document.createElement('canvas'));\n    canvas.classList.add('mpl-canvas');\n    canvas.setAttribute(\n        'style',\n        'box-sizing: content-box;' +\n            'pointer-events: none;' +\n            'position: relative;' +\n            'z-index: 0;'\n    );\n\n    this.context = canvas.getContext('2d');\n\n    var backingStore =\n        this.context.backingStorePixelRatio ||\n        this.context.webkitBackingStorePixelRatio ||\n        this.context.mozBackingStorePixelRatio ||\n        this.context.msBackingStorePixelRatio ||\n        this.context.oBackingStorePixelRatio ||\n        this.context.backingStorePixelRatio ||\n        1;\n\n    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n\n    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n        'canvas'\n    ));\n    rubberband_canvas.setAttribute(\n        'style',\n        'box-sizing: content-box;' +\n            'left: 0;' +\n            'pointer-events: none;' +\n            'position: absolute;' +\n            'top: 0;' +\n            'z-index: 1;'\n    );\n\n    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n    if (this.ResizeObserver === undefined) {\n        if (window.ResizeObserver !== undefined) {\n            this.ResizeObserver = window.ResizeObserver;\n        } else {\n            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n            this.ResizeObserver = obs.ResizeObserver;\n        }\n    }\n\n    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n        var nentries = entries.length;\n        for (var i = 0; i < nentries; i++) {\n            var entry = entries[i];\n            var width, height;\n            if (entry.contentBoxSize) {\n                if (entry.contentBoxSize instanceof Array) {\n                    // Chrome 84 implements new version of spec.\n                    width = entry.contentBoxSize[0].inlineSize;\n                    height = entry.contentBoxSize[0].blockSize;\n                } else {\n                    // Firefox implements old version of spec.\n                    width = entry.contentBoxSize.inlineSize;\n                    height = entry.contentBoxSize.blockSize;\n                }\n            } else {\n                // Chrome <84 implements even older version of spec.\n                width = entry.contentRect.width;\n                height = entry.contentRect.height;\n            }\n\n            // Keep the size of the canvas and rubber band canvas in sync with\n            // the canvas container.\n            if (entry.devicePixelContentBoxSize) {\n                // Chrome 84 implements new version of spec.\n                canvas.setAttribute(\n                    'width',\n                    entry.devicePixelContentBoxSize[0].inlineSize\n                );\n                canvas.setAttribute(\n                    'height',\n                    entry.devicePixelContentBoxSize[0].blockSize\n                );\n            } else {\n                canvas.setAttribute('width', width * fig.ratio);\n                canvas.setAttribute('height', height * fig.ratio);\n            }\n            /* This rescales the canvas back to display pixels, so that it\n             * appears correct on HiDPI screens. */\n            canvas.style.width = width + 'px';\n            canvas.style.height = height + 'px';\n\n            rubberband_canvas.setAttribute('width', width);\n            rubberband_canvas.setAttribute('height', height);\n\n            // And update the size in Python. We ignore the initial 0/0 size\n            // that occurs as the element is placed into the DOM, which should\n            // otherwise not happen due to the minimum size styling.\n            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n                fig.request_resize(width, height);\n            }\n        }\n    });\n    this.resizeObserverInstance.observe(canvas_div);\n\n    function on_mouse_event_closure(name) {\n        /* User Agent sniffing is bad, but WebKit is busted:\n         * https://bugs.webkit.org/show_bug.cgi?id=144526\n         * https://bugs.webkit.org/show_bug.cgi?id=181818\n         * The worst that happens here is that they get an extra browser\n         * selection when dragging, if this check fails to catch them.\n         */\n        var UA = navigator.userAgent;\n        var isWebKit = /AppleWebKit/.test(UA) && !/Chrome/.test(UA);\n        if(isWebKit) {\n            return function (event) {\n                /* This prevents the web browser from automatically changing to\n                 * the text insertion cursor when the button is pressed. We\n                 * want to control all of the cursor setting manually through\n                 * the 'cursor' event from matplotlib */\n                event.preventDefault()\n                return fig.mouse_event(event, name);\n            };\n        } else {\n            return function (event) {\n                return fig.mouse_event(event, name);\n            };\n        }\n    }\n\n    canvas_div.addEventListener(\n        'mousedown',\n        on_mouse_event_closure('button_press')\n    );\n    canvas_div.addEventListener(\n        'mouseup',\n        on_mouse_event_closure('button_release')\n    );\n    canvas_div.addEventListener(\n        'dblclick',\n        on_mouse_event_closure('dblclick')\n    );\n    // Throttle sequential mouse events to 1 every 20ms.\n    canvas_div.addEventListener(\n        'mousemove',\n        on_mouse_event_closure('motion_notify')\n    );\n\n    canvas_div.addEventListener(\n        'mouseenter',\n        on_mouse_event_closure('figure_enter')\n    );\n    canvas_div.addEventListener(\n        'mouseleave',\n        on_mouse_event_closure('figure_leave')\n    );\n\n    canvas_div.addEventListener('wheel', function (event) {\n        if (event.deltaY < 0) {\n            event.step = 1;\n        } else {\n            event.step = -1;\n        }\n        on_mouse_event_closure('scroll')(event);\n    });\n\n    canvas_div.appendChild(canvas);\n    canvas_div.appendChild(rubberband_canvas);\n\n    this.rubberband_context = rubberband_canvas.getContext('2d');\n    this.rubberband_context.strokeStyle = '#000000';\n\n    this._resize_canvas = function (width, height, forward) {\n        if (forward) {\n            canvas_div.style.width = width + 'px';\n            canvas_div.style.height = height + 'px';\n        }\n    };\n\n    // Disable right mouse context menu.\n    canvas_div.addEventListener('contextmenu', function (_e) {\n        event.preventDefault();\n        return false;\n    });\n\n    function set_focus() {\n        canvas.focus();\n        canvas_div.focus();\n    }\n\n    window.setTimeout(set_focus, 100);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'mpl-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'mpl-button-group';\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'mpl-button-group';\n            continue;\n        }\n\n        var button = (fig.buttons[name] = document.createElement('button'));\n        button.classList = 'mpl-widget';\n        button.setAttribute('role', 'button');\n        button.setAttribute('aria-disabled', 'false');\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n\n        var icon_img = document.createElement('img');\n        icon_img.src = '_images/' + image + '.png';\n        icon_img.srcset = '_images/' + image + '_large.png 2x';\n        icon_img.alt = tooltip;\n        button.appendChild(icon_img);\n\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    var fmt_picker = document.createElement('select');\n    fmt_picker.classList = 'mpl-widget';\n    toolbar.appendChild(fmt_picker);\n    this.format_dropdown = fmt_picker;\n\n    for (var ind in mpl.extensions) {\n        var fmt = mpl.extensions[ind];\n        var option = document.createElement('option');\n        option.selected = fmt === mpl.default_extension;\n        option.innerHTML = fmt;\n        fmt_picker.appendChild(option);\n    }\n\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n};\n\nmpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n    // which will in turn request a refresh of the image.\n    this.send_message('resize', { width: x_pixels, height: y_pixels });\n};\n\nmpl.figure.prototype.send_message = function (type, properties) {\n    properties['type'] = type;\n    properties['figure_id'] = this.id;\n    this.ws.send(JSON.stringify(properties));\n};\n\nmpl.figure.prototype.send_draw_message = function () {\n    if (!this.waiting) {\n        this.waiting = true;\n        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    var format_dropdown = fig.format_dropdown;\n    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n    fig.ondownload(fig, format);\n};\n\nmpl.figure.prototype.handle_resize = function (fig, msg) {\n    var size = msg['size'];\n    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n        fig._resize_canvas(size[0], size[1], msg['forward']);\n        fig.send_message('refresh', {});\n    }\n};\n\nmpl.figure.prototype.handle_rubberband = function (fig, msg) {\n    var x0 = msg['x0'] / fig.ratio;\n    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n    var x1 = msg['x1'] / fig.ratio;\n    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n    x0 = Math.floor(x0) + 0.5;\n    y0 = Math.floor(y0) + 0.5;\n    x1 = Math.floor(x1) + 0.5;\n    y1 = Math.floor(y1) + 0.5;\n    var min_x = Math.min(x0, x1);\n    var min_y = Math.min(y0, y1);\n    var width = Math.abs(x1 - x0);\n    var height = Math.abs(y1 - y0);\n\n    fig.rubberband_context.clearRect(\n        0,\n        0,\n        fig.canvas.width / fig.ratio,\n        fig.canvas.height / fig.ratio\n    );\n\n    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n};\n\nmpl.figure.prototype.handle_figure_label = function (fig, msg) {\n    // Updates the figure title.\n    fig.header.textContent = msg['label'];\n};\n\nmpl.figure.prototype.handle_cursor = function (fig, msg) {\n    fig.canvas_div.style.cursor = msg['cursor'];\n};\n\nmpl.figure.prototype.handle_message = function (fig, msg) {\n    fig.message.textContent = msg['message'];\n};\n\nmpl.figure.prototype.handle_draw = function (fig, _msg) {\n    // Request the server to send over a new figure.\n    fig.send_draw_message();\n};\n\nmpl.figure.prototype.handle_image_mode = function (fig, msg) {\n    fig.image_mode = msg['mode'];\n};\n\nmpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n    for (var key in msg) {\n        if (!(key in fig.buttons)) {\n            continue;\n        }\n        fig.buttons[key].disabled = !msg[key];\n        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n    }\n};\n\nmpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n    if (msg['mode'] === 'PAN') {\n        fig.buttons['Pan'].classList.add('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    } else if (msg['mode'] === 'ZOOM') {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.add('active');\n    } else {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    }\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Called whenever the canvas gets updated.\n    this.send_message('ack', {});\n};\n\n// A function to construct a web socket function for onmessage handling.\n// Called in the figure constructor.\nmpl.figure.prototype._make_on_message_function = function (fig) {\n    return function socket_on_message(evt) {\n        if (evt.data instanceof Blob) {\n            var img = evt.data;\n            if (img.type !== 'image/png') {\n                /* FIXME: We get \"Resource interpreted as Image but\n                 * transferred with MIME type text/plain:\" errors on\n                 * Chrome.  But how to set the MIME type?  It doesn't seem\n                 * to be part of the websocket stream */\n                img.type = 'image/png';\n            }\n\n            /* Free the memory for the previous frames */\n            if (fig.imageObj.src) {\n                (window.URL || window.webkitURL).revokeObjectURL(\n                    fig.imageObj.src\n                );\n            }\n\n            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n                img\n            );\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        } else if (\n            typeof evt.data === 'string' &&\n            evt.data.slice(0, 21) === 'data:image/png;base64'\n        ) {\n            fig.imageObj.src = evt.data;\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        }\n\n        var msg = JSON.parse(evt.data);\n        var msg_type = msg['type'];\n\n        // Call the  \"handle_{type}\" callback, which takes\n        // the figure and JSON message as its only arguments.\n        try {\n            var callback = fig['handle_' + msg_type];\n        } catch (e) {\n            console.log(\n                \"No handler for the '\" + msg_type + \"' message type: \",\n                msg\n            );\n            return;\n        }\n\n        if (callback) {\n            try {\n                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n                callback(fig, msg);\n            } catch (e) {\n                console.log(\n                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n                    e,\n                    e.stack,\n                    msg\n                );\n            }\n        }\n    };\n};\n\nfunction getModifiers(event) {\n    var mods = [];\n    if (event.ctrlKey) {\n        mods.push('ctrl');\n    }\n    if (event.altKey) {\n        mods.push('alt');\n    }\n    if (event.shiftKey) {\n        mods.push('shift');\n    }\n    if (event.metaKey) {\n        mods.push('meta');\n    }\n    return mods;\n}\n\n/*\n * return a copy of an object with only non-object keys\n * we need this to avoid circular references\n * https://stackoverflow.com/a/24161582/3208463\n */\nfunction simpleKeys(original) {\n    return Object.keys(original).reduce(function (obj, key) {\n        if (typeof original[key] !== 'object') {\n            obj[key] = original[key];\n        }\n        return obj;\n    }, {});\n}\n\nmpl.figure.prototype.mouse_event = function (event, name) {\n    if (name === 'button_press') {\n        this.canvas.focus();\n        this.canvas_div.focus();\n    }\n\n    // from https://stackoverflow.com/q/1114465\n    var boundingRect = this.canvas.getBoundingClientRect();\n    var x = (event.clientX - boundingRect.left) * this.ratio;\n    var y = (event.clientY - boundingRect.top) * this.ratio;\n\n    this.send_message(name, {\n        x: x,\n        y: y,\n        button: event.button,\n        step: event.step,\n        modifiers: getModifiers(event),\n        guiEvent: simpleKeys(event),\n    });\n\n    return false;\n};\n\nmpl.figure.prototype._key_event_extra = function (_event, _name) {\n    // Handle any extra behaviour associated with a key event\n};\n\nmpl.figure.prototype.key_event = function (event, name) {\n    // Prevent repeat events\n    if (name === 'key_press') {\n        if (event.key === this._key) {\n            return;\n        } else {\n            this._key = event.key;\n        }\n    }\n    if (name === 'key_release') {\n        this._key = null;\n    }\n\n    var value = '';\n    if (event.ctrlKey && event.key !== 'Control') {\n        value += 'ctrl+';\n    }\n    else if (event.altKey && event.key !== 'Alt') {\n        value += 'alt+';\n    }\n    else if (event.shiftKey && event.key !== 'Shift') {\n        value += 'shift+';\n    }\n\n    value += 'k' + event.key;\n\n    this._key_event_extra(event, name);\n\n    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n    return false;\n};\n\nmpl.figure.prototype.toolbar_button_onclick = function (name) {\n    if (name === 'download') {\n        this.handle_save(this, null);\n    } else {\n        this.send_message('toolbar_button', { name: name });\n    }\n};\n\nmpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n    this.message.textContent = tooltip;\n};\n\n///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n// prettier-ignore\nvar _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\nmpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o\", \"download\"]];\n\nmpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\", \"webp\"];\n\nmpl.default_extension = \"png\";/* global mpl */\n\nvar comm_websocket_adapter = function (comm) {\n    // Create a \"websocket\"-like object which calls the given IPython comm\n    // object with the appropriate methods. Currently this is a non binary\n    // socket, so there is still some room for performance tuning.\n    var ws = {};\n\n    ws.binaryType = comm.kernel.ws.binaryType;\n    ws.readyState = comm.kernel.ws.readyState;\n    function updateReadyState(_event) {\n        if (comm.kernel.ws) {\n            ws.readyState = comm.kernel.ws.readyState;\n        } else {\n            ws.readyState = 3; // Closed state.\n        }\n    }\n    comm.kernel.ws.addEventListener('open', updateReadyState);\n    comm.kernel.ws.addEventListener('close', updateReadyState);\n    comm.kernel.ws.addEventListener('error', updateReadyState);\n\n    ws.close = function () {\n        comm.close();\n    };\n    ws.send = function (m) {\n        //console.log('sending', m);\n        comm.send(m);\n    };\n    // Register the callback with on_msg.\n    comm.on_msg(function (msg) {\n        //console.log('receiving', msg['content']['data'], msg);\n        var data = msg['content']['data'];\n        if (data['blob'] !== undefined) {\n            data = {\n                data: new Blob(msg['buffers'], { type: data['blob'] }),\n            };\n        }\n        // Pass the mpl event to the overridden (by mpl) onmessage function.\n        ws.onmessage(data);\n    });\n    return ws;\n};\n\nmpl.mpl_figure_comm = function (comm, msg) {\n    // This is the function which gets called when the mpl process\n    // starts-up an IPython Comm through the \"matplotlib\" channel.\n\n    var id = msg.content.data.id;\n    // Get hold of the div created by the display call when the Comm\n    // socket was opened in Python.\n    var element = document.getElementById(id);\n    var ws_proxy = comm_websocket_adapter(comm);\n\n    function ondownload(figure, _format) {\n        window.open(figure.canvas.toDataURL());\n    }\n\n    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n\n    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n    // web socket which is closed, not our websocket->open comm proxy.\n    ws_proxy.onopen();\n\n    fig.parent_element = element;\n    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n    if (!fig.cell_info) {\n        console.error('Failed to find cell for figure', id, fig);\n        return;\n    }\n    fig.cell_info[0].output_area.element.on(\n        'cleared',\n        { fig: fig },\n        fig._remove_fig_handler\n    );\n};\n\nmpl.figure.prototype.handle_close = function (fig, msg) {\n    var width = fig.canvas.width / fig.ratio;\n    fig.cell_info[0].output_area.element.off(\n        'cleared',\n        fig._remove_fig_handler\n    );\n    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n\n    // Update the output cell to use the data from the current canvas.\n    fig.push_to_output();\n    var dataURL = fig.canvas.toDataURL();\n    // Re-enable the keyboard manager in IPython - without this line, in FF,\n    // the notebook keyboard shortcuts fail.\n    IPython.keyboard_manager.enable();\n    fig.parent_element.innerHTML =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n    fig.close_ws(fig, msg);\n};\n\nmpl.figure.prototype.close_ws = function (fig, msg) {\n    fig.send_message('closing', msg);\n    // fig.ws.close()\n};\n\nmpl.figure.prototype.push_to_output = function (_remove_interactive) {\n    // Turn the data on the canvas into data in the output cell.\n    var width = this.canvas.width / this.ratio;\n    var dataURL = this.canvas.toDataURL();\n    this.cell_info[1]['text/html'] =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Tell IPython that the notebook contents must change.\n    IPython.notebook.set_dirty(true);\n    this.send_message('ack', {});\n    var fig = this;\n    // Wait a second, then push the new image to the DOM so\n    // that it is saved nicely (might be nice to debounce this).\n    setTimeout(function () {\n        fig.push_to_output();\n    }, 1000);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'btn-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'btn-group';\n    var button;\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'btn-group';\n            continue;\n        }\n\n        button = fig.buttons[name] = document.createElement('button');\n        button.classList = 'btn btn-default';\n        button.href = '#';\n        button.title = name;\n        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    // Add the status bar.\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message pull-right';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n\n    // Add the close button to the window.\n    var buttongrp = document.createElement('div');\n    buttongrp.classList = 'btn-group inline pull-right';\n    button = document.createElement('button');\n    button.classList = 'btn btn-mini btn-primary';\n    button.href = '#';\n    button.title = 'Stop Interaction';\n    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n    button.addEventListener('click', function (_evt) {\n        fig.handle_close(fig, {});\n    });\n    button.addEventListener(\n        'mouseover',\n        on_mouseover_closure('Stop Interaction')\n    );\n    buttongrp.appendChild(button);\n    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n};\n\nmpl.figure.prototype._remove_fig_handler = function (event) {\n    var fig = event.data.fig;\n    if (event.target !== this) {\n        // Ignore bubbled events from children.\n        return;\n    }\n    fig.close_ws(fig, {});\n};\n\nmpl.figure.prototype._root_extra_style = function (el) {\n    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n};\n\nmpl.figure.prototype._canvas_extra_style = function (el) {\n    // this is important to make the div 'focusable\n    el.setAttribute('tabindex', 0);\n    // reach out to IPython and tell the keyboard manager to turn it's self\n    // off when our div gets focus\n\n    // location in version 3\n    if (IPython.notebook.keyboard_manager) {\n        IPython.notebook.keyboard_manager.register_events(el);\n    } else {\n        // location in version 2\n        IPython.keyboard_manager.register_events(el);\n    }\n};\n\nmpl.figure.prototype._key_event_extra = function (event, _name) {\n    // Check for shift+enter\n    if (event.shiftKey && event.which === 13) {\n        this.canvas_div.blur();\n        // select the cell after this one\n        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n        IPython.notebook.select(index + 1);\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    fig.ondownload(fig, null);\n};\n\nmpl.find_output_cell = function (html_output) {\n    // Return the cell and output element which can be found *uniquely* in the notebook.\n    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n    // IPython event is triggered only after the cells have been serialised, which for\n    // our purposes (turning an active figure into a static one), is too late.\n    var cells = IPython.notebook.get_cells();\n    var ncells = cells.length;\n    for (var i = 0; i < ncells; i++) {\n        var cell = cells[i];\n        if (cell.cell_type === 'code') {\n            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n                var data = cell.output_area.outputs[j];\n                if (data.data) {\n                    // IPython >= 3 moved mimebundle to data attribute of output\n                    data = data.data;\n                }\n                if (data['text/html'] === html_output) {\n                    return [cell, data, j];\n                }\n            }\n        }\n    }\n};\n\n// Register the function which deals with the matplotlib target/channel.\n// The kernel may be null if the page has been refreshed.\nif (IPython.notebook.kernel !== null) {\n    IPython.notebook.kernel.comm_manager.register_target(\n        'matplotlib',\n        mpl.mpl_figure_comm\n    );\n}\n",
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"431.8518823589666\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": "/* Put everything inside the global mpl namespace */\n/* global mpl */\nwindow.mpl = {};\n\nmpl.get_websocket_type = function () {\n    if (typeof WebSocket !== 'undefined') {\n        return WebSocket;\n    } else if (typeof MozWebSocket !== 'undefined') {\n        return MozWebSocket;\n    } else {\n        alert(\n            'Your browser does not have WebSocket support. ' +\n                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n                'Firefox 4 and 5 are also supported but you ' +\n                'have to enable WebSockets in about:config.'\n        );\n    }\n};\n\nmpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n    this.id = figure_id;\n\n    this.ws = websocket;\n\n    this.supports_binary = this.ws.binaryType !== undefined;\n\n    if (!this.supports_binary) {\n        var warnings = document.getElementById('mpl-warnings');\n        if (warnings) {\n            warnings.style.display = 'block';\n            warnings.textContent =\n                'This browser does not support binary websocket messages. ' +\n                'Performance may be slow.';\n        }\n    }\n\n    this.imageObj = new Image();\n\n    this.context = undefined;\n    this.message = undefined;\n    this.canvas = undefined;\n    this.rubberband_canvas = undefined;\n    this.rubberband_context = undefined;\n    this.format_dropdown = undefined;\n\n    this.image_mode = 'full';\n\n    this.root = document.createElement('div');\n    this.root.setAttribute('style', 'display: inline-block');\n    this._root_extra_style(this.root);\n\n    parent_element.appendChild(this.root);\n\n    this._init_header(this);\n    this._init_canvas(this);\n    this._init_toolbar(this);\n\n    var fig = this;\n\n    this.waiting = false;\n\n    this.ws.onopen = function () {\n        fig.send_message('supports_binary', { value: fig.supports_binary });\n        fig.send_message('send_image_mode', {});\n        if (fig.ratio !== 1) {\n            fig.send_message('set_device_pixel_ratio', {\n                device_pixel_ratio: fig.ratio,\n            });\n        }\n        fig.send_message('refresh', {});\n    };\n\n    this.imageObj.onload = function () {\n        if (fig.image_mode === 'full') {\n            // Full images could contain transparency (where diff images\n            // almost always do), so we need to clear the canvas so that\n            // there is no ghosting.\n            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n        }\n        fig.context.drawImage(fig.imageObj, 0, 0);\n    };\n\n    this.imageObj.onunload = function () {\n        fig.ws.close();\n    };\n\n    this.ws.onmessage = this._make_on_message_function(this);\n\n    this.ondownload = ondownload;\n};\n\nmpl.figure.prototype._init_header = function () {\n    var titlebar = document.createElement('div');\n    titlebar.classList =\n        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n    var titletext = document.createElement('div');\n    titletext.classList = 'ui-dialog-title';\n    titletext.setAttribute(\n        'style',\n        'width: 100%; text-align: center; padding: 3px;'\n    );\n    titlebar.appendChild(titletext);\n    this.root.appendChild(titlebar);\n    this.header = titletext;\n};\n\nmpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._init_canvas = function () {\n    var fig = this;\n\n    var canvas_div = (this.canvas_div = document.createElement('div'));\n    canvas_div.setAttribute('tabindex', '0');\n    canvas_div.setAttribute(\n        'style',\n        'border: 1px solid #ddd;' +\n            'box-sizing: content-box;' +\n            'clear: both;' +\n            'min-height: 1px;' +\n            'min-width: 1px;' +\n            'outline: 0;' +\n            'overflow: hidden;' +\n            'position: relative;' +\n            'resize: both;' +\n            'z-index: 2;'\n    );\n\n    function on_keyboard_event_closure(name) {\n        return function (event) {\n            return fig.key_event(event, name);\n        };\n    }\n\n    canvas_div.addEventListener(\n        'keydown',\n        on_keyboard_event_closure('key_press')\n    );\n    canvas_div.addEventListener(\n        'keyup',\n        on_keyboard_event_closure('key_release')\n    );\n\n    this._canvas_extra_style(canvas_div);\n    this.root.appendChild(canvas_div);\n\n    var canvas = (this.canvas = document.createElement('canvas'));\n    canvas.classList.add('mpl-canvas');\n    canvas.setAttribute(\n        'style',\n        'box-sizing: content-box;' +\n            'pointer-events: none;' +\n            'position: relative;' +\n            'z-index: 0;'\n    );\n\n    this.context = canvas.getContext('2d');\n\n    var backingStore =\n        this.context.backingStorePixelRatio ||\n        this.context.webkitBackingStorePixelRatio ||\n        this.context.mozBackingStorePixelRatio ||\n        this.context.msBackingStorePixelRatio ||\n        this.context.oBackingStorePixelRatio ||\n        this.context.backingStorePixelRatio ||\n        1;\n\n    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n\n    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n        'canvas'\n    ));\n    rubberband_canvas.setAttribute(\n        'style',\n        'box-sizing: content-box;' +\n            'left: 0;' +\n            'pointer-events: none;' +\n            'position: absolute;' +\n            'top: 0;' +\n            'z-index: 1;'\n    );\n\n    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n    if (this.ResizeObserver === undefined) {\n        if (window.ResizeObserver !== undefined) {\n            this.ResizeObserver = window.ResizeObserver;\n        } else {\n            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n            this.ResizeObserver = obs.ResizeObserver;\n        }\n    }\n\n    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n        var nentries = entries.length;\n        for (var i = 0; i < nentries; i++) {\n            var entry = entries[i];\n            var width, height;\n            if (entry.contentBoxSize) {\n                if (entry.contentBoxSize instanceof Array) {\n                    // Chrome 84 implements new version of spec.\n                    width = entry.contentBoxSize[0].inlineSize;\n                    height = entry.contentBoxSize[0].blockSize;\n                } else {\n                    // Firefox implements old version of spec.\n                    width = entry.contentBoxSize.inlineSize;\n                    height = entry.contentBoxSize.blockSize;\n                }\n            } else {\n                // Chrome <84 implements even older version of spec.\n                width = entry.contentRect.width;\n                height = entry.contentRect.height;\n            }\n\n            // Keep the size of the canvas and rubber band canvas in sync with\n            // the canvas container.\n            if (entry.devicePixelContentBoxSize) {\n                // Chrome 84 implements new version of spec.\n                canvas.setAttribute(\n                    'width',\n                    entry.devicePixelContentBoxSize[0].inlineSize\n                );\n                canvas.setAttribute(\n                    'height',\n                    entry.devicePixelContentBoxSize[0].blockSize\n                );\n            } else {\n                canvas.setAttribute('width', width * fig.ratio);\n                canvas.setAttribute('height', height * fig.ratio);\n            }\n            /* This rescales the canvas back to display pixels, so that it\n             * appears correct on HiDPI screens. */\n            canvas.style.width = width + 'px';\n            canvas.style.height = height + 'px';\n\n            rubberband_canvas.setAttribute('width', width);\n            rubberband_canvas.setAttribute('height', height);\n\n            // And update the size in Python. We ignore the initial 0/0 size\n            // that occurs as the element is placed into the DOM, which should\n            // otherwise not happen due to the minimum size styling.\n            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n                fig.request_resize(width, height);\n            }\n        }\n    });\n    this.resizeObserverInstance.observe(canvas_div);\n\n    function on_mouse_event_closure(name) {\n        /* User Agent sniffing is bad, but WebKit is busted:\n         * https://bugs.webkit.org/show_bug.cgi?id=144526\n         * https://bugs.webkit.org/show_bug.cgi?id=181818\n         * The worst that happens here is that they get an extra browser\n         * selection when dragging, if this check fails to catch them.\n         */\n        var UA = navigator.userAgent;\n        var isWebKit = /AppleWebKit/.test(UA) && !/Chrome/.test(UA);\n        if(isWebKit) {\n            return function (event) {\n                /* This prevents the web browser from automatically changing to\n                 * the text insertion cursor when the button is pressed. We\n                 * want to control all of the cursor setting manually through\n                 * the 'cursor' event from matplotlib */\n                event.preventDefault()\n                return fig.mouse_event(event, name);\n            };\n        } else {\n            return function (event) {\n                return fig.mouse_event(event, name);\n            };\n        }\n    }\n\n    canvas_div.addEventListener(\n        'mousedown',\n        on_mouse_event_closure('button_press')\n    );\n    canvas_div.addEventListener(\n        'mouseup',\n        on_mouse_event_closure('button_release')\n    );\n    canvas_div.addEventListener(\n        'dblclick',\n        on_mouse_event_closure('dblclick')\n    );\n    // Throttle sequential mouse events to 1 every 20ms.\n    canvas_div.addEventListener(\n        'mousemove',\n        on_mouse_event_closure('motion_notify')\n    );\n\n    canvas_div.addEventListener(\n        'mouseenter',\n        on_mouse_event_closure('figure_enter')\n    );\n    canvas_div.addEventListener(\n        'mouseleave',\n        on_mouse_event_closure('figure_leave')\n    );\n\n    canvas_div.addEventListener('wheel', function (event) {\n        if (event.deltaY < 0) {\n            event.step = 1;\n        } else {\n            event.step = -1;\n        }\n        on_mouse_event_closure('scroll')(event);\n    });\n\n    canvas_div.appendChild(canvas);\n    canvas_div.appendChild(rubberband_canvas);\n\n    this.rubberband_context = rubberband_canvas.getContext('2d');\n    this.rubberband_context.strokeStyle = '#000000';\n\n    this._resize_canvas = function (width, height, forward) {\n        if (forward) {\n            canvas_div.style.width = width + 'px';\n            canvas_div.style.height = height + 'px';\n        }\n    };\n\n    // Disable right mouse context menu.\n    canvas_div.addEventListener('contextmenu', function (_e) {\n        event.preventDefault();\n        return false;\n    });\n\n    function set_focus() {\n        canvas.focus();\n        canvas_div.focus();\n    }\n\n    window.setTimeout(set_focus, 100);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'mpl-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'mpl-button-group';\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'mpl-button-group';\n            continue;\n        }\n\n        var button = (fig.buttons[name] = document.createElement('button'));\n        button.classList = 'mpl-widget';\n        button.setAttribute('role', 'button');\n        button.setAttribute('aria-disabled', 'false');\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n\n        var icon_img = document.createElement('img');\n        icon_img.src = '_images/' + image + '.png';\n        icon_img.srcset = '_images/' + image + '_large.png 2x';\n        icon_img.alt = tooltip;\n        button.appendChild(icon_img);\n\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    var fmt_picker = document.createElement('select');\n    fmt_picker.classList = 'mpl-widget';\n    toolbar.appendChild(fmt_picker);\n    this.format_dropdown = fmt_picker;\n\n    for (var ind in mpl.extensions) {\n        var fmt = mpl.extensions[ind];\n        var option = document.createElement('option');\n        option.selected = fmt === mpl.default_extension;\n        option.innerHTML = fmt;\n        fmt_picker.appendChild(option);\n    }\n\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n};\n\nmpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n    // which will in turn request a refresh of the image.\n    this.send_message('resize', { width: x_pixels, height: y_pixels });\n};\n\nmpl.figure.prototype.send_message = function (type, properties) {\n    properties['type'] = type;\n    properties['figure_id'] = this.id;\n    this.ws.send(JSON.stringify(properties));\n};\n\nmpl.figure.prototype.send_draw_message = function () {\n    if (!this.waiting) {\n        this.waiting = true;\n        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    var format_dropdown = fig.format_dropdown;\n    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n    fig.ondownload(fig, format);\n};\n\nmpl.figure.prototype.handle_resize = function (fig, msg) {\n    var size = msg['size'];\n    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n        fig._resize_canvas(size[0], size[1], msg['forward']);\n        fig.send_message('refresh', {});\n    }\n};\n\nmpl.figure.prototype.handle_rubberband = function (fig, msg) {\n    var x0 = msg['x0'] / fig.ratio;\n    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n    var x1 = msg['x1'] / fig.ratio;\n    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n    x0 = Math.floor(x0) + 0.5;\n    y0 = Math.floor(y0) + 0.5;\n    x1 = Math.floor(x1) + 0.5;\n    y1 = Math.floor(y1) + 0.5;\n    var min_x = Math.min(x0, x1);\n    var min_y = Math.min(y0, y1);\n    var width = Math.abs(x1 - x0);\n    var height = Math.abs(y1 - y0);\n\n    fig.rubberband_context.clearRect(\n        0,\n        0,\n        fig.canvas.width / fig.ratio,\n        fig.canvas.height / fig.ratio\n    );\n\n    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n};\n\nmpl.figure.prototype.handle_figure_label = function (fig, msg) {\n    // Updates the figure title.\n    fig.header.textContent = msg['label'];\n};\n\nmpl.figure.prototype.handle_cursor = function (fig, msg) {\n    fig.canvas_div.style.cursor = msg['cursor'];\n};\n\nmpl.figure.prototype.handle_message = function (fig, msg) {\n    fig.message.textContent = msg['message'];\n};\n\nmpl.figure.prototype.handle_draw = function (fig, _msg) {\n    // Request the server to send over a new figure.\n    fig.send_draw_message();\n};\n\nmpl.figure.prototype.handle_image_mode = function (fig, msg) {\n    fig.image_mode = msg['mode'];\n};\n\nmpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n    for (var key in msg) {\n        if (!(key in fig.buttons)) {\n            continue;\n        }\n        fig.buttons[key].disabled = !msg[key];\n        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n    }\n};\n\nmpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n    if (msg['mode'] === 'PAN') {\n        fig.buttons['Pan'].classList.add('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    } else if (msg['mode'] === 'ZOOM') {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.add('active');\n    } else {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    }\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Called whenever the canvas gets updated.\n    this.send_message('ack', {});\n};\n\n// A function to construct a web socket function for onmessage handling.\n// Called in the figure constructor.\nmpl.figure.prototype._make_on_message_function = function (fig) {\n    return function socket_on_message(evt) {\n        if (evt.data instanceof Blob) {\n            var img = evt.data;\n            if (img.type !== 'image/png') {\n                /* FIXME: We get \"Resource interpreted as Image but\n                 * transferred with MIME type text/plain:\" errors on\n                 * Chrome.  But how to set the MIME type?  It doesn't seem\n                 * to be part of the websocket stream */\n                img.type = 'image/png';\n            }\n\n            /* Free the memory for the previous frames */\n            if (fig.imageObj.src) {\n                (window.URL || window.webkitURL).revokeObjectURL(\n                    fig.imageObj.src\n                );\n            }\n\n            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n                img\n            );\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        } else if (\n            typeof evt.data === 'string' &&\n            evt.data.slice(0, 21) === 'data:image/png;base64'\n        ) {\n            fig.imageObj.src = evt.data;\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        }\n\n        var msg = JSON.parse(evt.data);\n        var msg_type = msg['type'];\n\n        // Call the  \"handle_{type}\" callback, which takes\n        // the figure and JSON message as its only arguments.\n        try {\n            var callback = fig['handle_' + msg_type];\n        } catch (e) {\n            console.log(\n                \"No handler for the '\" + msg_type + \"' message type: \",\n                msg\n            );\n            return;\n        }\n\n        if (callback) {\n            try {\n                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n                callback(fig, msg);\n            } catch (e) {\n                console.log(\n                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n                    e,\n                    e.stack,\n                    msg\n                );\n            }\n        }\n    };\n};\n\nfunction getModifiers(event) {\n    var mods = [];\n    if (event.ctrlKey) {\n        mods.push('ctrl');\n    }\n    if (event.altKey) {\n        mods.push('alt');\n    }\n    if (event.shiftKey) {\n        mods.push('shift');\n    }\n    if (event.metaKey) {\n        mods.push('meta');\n    }\n    return mods;\n}\n\n/*\n * return a copy of an object with only non-object keys\n * we need this to avoid circular references\n * https://stackoverflow.com/a/24161582/3208463\n */\nfunction simpleKeys(original) {\n    return Object.keys(original).reduce(function (obj, key) {\n        if (typeof original[key] !== 'object') {\n            obj[key] = original[key];\n        }\n        return obj;\n    }, {});\n}\n\nmpl.figure.prototype.mouse_event = function (event, name) {\n    if (name === 'button_press') {\n        this.canvas.focus();\n        this.canvas_div.focus();\n    }\n\n    // from https://stackoverflow.com/q/1114465\n    var boundingRect = this.canvas.getBoundingClientRect();\n    var x = (event.clientX - boundingRect.left) * this.ratio;\n    var y = (event.clientY - boundingRect.top) * this.ratio;\n\n    this.send_message(name, {\n        x: x,\n        y: y,\n        button: event.button,\n        step: event.step,\n        modifiers: getModifiers(event),\n        guiEvent: simpleKeys(event),\n    });\n\n    return false;\n};\n\nmpl.figure.prototype._key_event_extra = function (_event, _name) {\n    // Handle any extra behaviour associated with a key event\n};\n\nmpl.figure.prototype.key_event = function (event, name) {\n    // Prevent repeat events\n    if (name === 'key_press') {\n        if (event.key === this._key) {\n            return;\n        } else {\n            this._key = event.key;\n        }\n    }\n    if (name === 'key_release') {\n        this._key = null;\n    }\n\n    var value = '';\n    if (event.ctrlKey && event.key !== 'Control') {\n        value += 'ctrl+';\n    }\n    else if (event.altKey && event.key !== 'Alt') {\n        value += 'alt+';\n    }\n    else if (event.shiftKey && event.key !== 'Shift') {\n        value += 'shift+';\n    }\n\n    value += 'k' + event.key;\n\n    this._key_event_extra(event, name);\n\n    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n    return false;\n};\n\nmpl.figure.prototype.toolbar_button_onclick = function (name) {\n    if (name === 'download') {\n        this.handle_save(this, null);\n    } else {\n        this.send_message('toolbar_button', { name: name });\n    }\n};\n\nmpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n    this.message.textContent = tooltip;\n};\n\n///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n// prettier-ignore\nvar _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\nmpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o\", \"download\"]];\n\nmpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\", \"webp\"];\n\nmpl.default_extension = \"png\";/* global mpl */\n\nvar comm_websocket_adapter = function (comm) {\n    // Create a \"websocket\"-like object which calls the given IPython comm\n    // object with the appropriate methods. Currently this is a non binary\n    // socket, so there is still some room for performance tuning.\n    var ws = {};\n\n    ws.binaryType = comm.kernel.ws.binaryType;\n    ws.readyState = comm.kernel.ws.readyState;\n    function updateReadyState(_event) {\n        if (comm.kernel.ws) {\n            ws.readyState = comm.kernel.ws.readyState;\n        } else {\n            ws.readyState = 3; // Closed state.\n        }\n    }\n    comm.kernel.ws.addEventListener('open', updateReadyState);\n    comm.kernel.ws.addEventListener('close', updateReadyState);\n    comm.kernel.ws.addEventListener('error', updateReadyState);\n\n    ws.close = function () {\n        comm.close();\n    };\n    ws.send = function (m) {\n        //console.log('sending', m);\n        comm.send(m);\n    };\n    // Register the callback with on_msg.\n    comm.on_msg(function (msg) {\n        //console.log('receiving', msg['content']['data'], msg);\n        var data = msg['content']['data'];\n        if (data['blob'] !== undefined) {\n            data = {\n                data: new Blob(msg['buffers'], { type: data['blob'] }),\n            };\n        }\n        // Pass the mpl event to the overridden (by mpl) onmessage function.\n        ws.onmessage(data);\n    });\n    return ws;\n};\n\nmpl.mpl_figure_comm = function (comm, msg) {\n    // This is the function which gets called when the mpl process\n    // starts-up an IPython Comm through the \"matplotlib\" channel.\n\n    var id = msg.content.data.id;\n    // Get hold of the div created by the display call when the Comm\n    // socket was opened in Python.\n    var element = document.getElementById(id);\n    var ws_proxy = comm_websocket_adapter(comm);\n\n    function ondownload(figure, _format) {\n        window.open(figure.canvas.toDataURL());\n    }\n\n    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n\n    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n    // web socket which is closed, not our websocket->open comm proxy.\n    ws_proxy.onopen();\n\n    fig.parent_element = element;\n    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n    if (!fig.cell_info) {\n        console.error('Failed to find cell for figure', id, fig);\n        return;\n    }\n    fig.cell_info[0].output_area.element.on(\n        'cleared',\n        { fig: fig },\n        fig._remove_fig_handler\n    );\n};\n\nmpl.figure.prototype.handle_close = function (fig, msg) {\n    var width = fig.canvas.width / fig.ratio;\n    fig.cell_info[0].output_area.element.off(\n        'cleared',\n        fig._remove_fig_handler\n    );\n    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n\n    // Update the output cell to use the data from the current canvas.\n    fig.push_to_output();\n    var dataURL = fig.canvas.toDataURL();\n    // Re-enable the keyboard manager in IPython - without this line, in FF,\n    // the notebook keyboard shortcuts fail.\n    IPython.keyboard_manager.enable();\n    fig.parent_element.innerHTML =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n    fig.close_ws(fig, msg);\n};\n\nmpl.figure.prototype.close_ws = function (fig, msg) {\n    fig.send_message('closing', msg);\n    // fig.ws.close()\n};\n\nmpl.figure.prototype.push_to_output = function (_remove_interactive) {\n    // Turn the data on the canvas into data in the output cell.\n    var width = this.canvas.width / this.ratio;\n    var dataURL = this.canvas.toDataURL();\n    this.cell_info[1]['text/html'] =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Tell IPython that the notebook contents must change.\n    IPython.notebook.set_dirty(true);\n    this.send_message('ack', {});\n    var fig = this;\n    // Wait a second, then push the new image to the DOM so\n    // that it is saved nicely (might be nice to debounce this).\n    setTimeout(function () {\n        fig.push_to_output();\n    }, 1000);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'btn-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'btn-group';\n    var button;\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'btn-group';\n            continue;\n        }\n\n        button = fig.buttons[name] = document.createElement('button');\n        button.classList = 'btn btn-default';\n        button.href = '#';\n        button.title = name;\n        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    // Add the status bar.\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message pull-right';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n\n    // Add the close button to the window.\n    var buttongrp = document.createElement('div');\n    buttongrp.classList = 'btn-group inline pull-right';\n    button = document.createElement('button');\n    button.classList = 'btn btn-mini btn-primary';\n    button.href = '#';\n    button.title = 'Stop Interaction';\n    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n    button.addEventListener('click', function (_evt) {\n        fig.handle_close(fig, {});\n    });\n    button.addEventListener(\n        'mouseover',\n        on_mouseover_closure('Stop Interaction')\n    );\n    buttongrp.appendChild(button);\n    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n};\n\nmpl.figure.prototype._remove_fig_handler = function (event) {\n    var fig = event.data.fig;\n    if (event.target !== this) {\n        // Ignore bubbled events from children.\n        return;\n    }\n    fig.close_ws(fig, {});\n};\n\nmpl.figure.prototype._root_extra_style = function (el) {\n    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n};\n\nmpl.figure.prototype._canvas_extra_style = function (el) {\n    // this is important to make the div 'focusable\n    el.setAttribute('tabindex', 0);\n    // reach out to IPython and tell the keyboard manager to turn it's self\n    // off when our div gets focus\n\n    // location in version 3\n    if (IPython.notebook.keyboard_manager) {\n        IPython.notebook.keyboard_manager.register_events(el);\n    } else {\n        // location in version 2\n        IPython.keyboard_manager.register_events(el);\n    }\n};\n\nmpl.figure.prototype._key_event_extra = function (event, _name) {\n    // Check for shift+enter\n    if (event.shiftKey && event.which === 13) {\n        this.canvas_div.blur();\n        // select the cell after this one\n        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n        IPython.notebook.select(index + 1);\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    fig.ondownload(fig, null);\n};\n\nmpl.find_output_cell = function (html_output) {\n    // Return the cell and output element which can be found *uniquely* in the notebook.\n    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n    // IPython event is triggered only after the cells have been serialised, which for\n    // our purposes (turning an active figure into a static one), is too late.\n    var cells = IPython.notebook.get_cells();\n    var ncells = cells.length;\n    for (var i = 0; i < ncells; i++) {\n        var cell = cells[i];\n        if (cell.cell_type === 'code') {\n            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n                var data = cell.output_area.outputs[j];\n                if (data.data) {\n                    // IPython >= 3 moved mimebundle to data attribute of output\n                    data = data.data;\n                }\n                if (data['text/html'] === html_output) {\n                    return [cell, data, j];\n                }\n            }\n        }\n    }\n};\n\n// Register the function which deals with the matplotlib target/channel.\n// The kernel may be null if the page has been refreshed.\nif (IPython.notebook.kernel !== null) {\n    IPython.notebook.kernel.comm_manager.register_target(\n        'matplotlib',\n        mpl.mpl_figure_comm\n    );\n}\n",
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"431.8518823589666\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(10)\n",
    "# テストデータ\n",
    "X = np.array([[0, 0], [1, 1], [1, 0], [0, 1], [2, 2], [2, 1], [1, 2], [3, 3], [3, 2], [2, 3]])\n",
    "points1 = np.random.randn(80, 2)\n",
    "points2 = np.random.randn(80, 2) + np.array([4,0])\n",
    "points3 = np.random.randn(80, 2) + np.array([5,8])\n",
    "\n",
    "X = np.r_[points1, points2, points3]\n",
    "#実行\n",
    "model = My_KMeans(n_cluster=4,n_iter=20)\n",
    "model.fit(X)\n",
    "# 結果を結果をplot\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()\n",
    "colors=['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd', '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']\n",
    "fig, ax = plt.subplots()\n",
    "ims=[]\n",
    "#結果を可視化可視化(ラベル付き) \n",
    "for n,(centroids,label) in enumerate(model.centroids_and_labels):\n",
    "    u_labels = np.unique(label)\n",
    "    new=[ax.text(1.3, 3.2,f\"n={n}\")]\n",
    "    for i in u_labels:\n",
    "        new.append(plt.scatter(X[label == i , 0] , X[label == i , 1] ,color=colors[i%10], label = i))\n",
    "    for i in range(model.n_cluster):\n",
    "        new.append(plt.scatter(centroids[i][0] , centroids[i][1] ,color=colors[i%10], marker=\"*\"))\n",
    "    ims.append(new)\n",
    "ani = animation.ArtistAnimation(fig, ims, interval=500)\n",
    "plt.plot()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "0cd09898",
   "metadata": {},
   "source": [
    "### 5.5.3 混合ガウス分布"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a44166ba",
   "metadata": {},
   "source": [
    "混合ガウス分布についておさらいしておこう．<br>\n",
    "混合ガウス分布は以下の式で表されている．<br>\n",
    "$$\\begin{eqnarray} p(X) = \\prod _n \\sum_k \\pi _k \\mathcal{N}\\left( x_n |\\mu _k , \\Sigma _k \\right) \\end{eqnarray}$$\n",
    "<br>\n",
    "混合ガウス分布において決定しなくてはならないパラメータは以下の通りである．\n",
    "- $\\{\\mu _k\\}$　各ガウス分布の平均<br>\n",
    "- $ \\{\\Sigma _k\\}$　各ガウス分布の共分散行列<br>\n",
    "- $\\{\\pi_ k\\}$　ガウス分布の混合比率"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "aef14287",
   "metadata": {},
   "source": [
    "### 5.5.4 EMアルゴリズム"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "90698fe0",
   "metadata": {},
   "source": [
    "EMアルゴリズムはデータから分布のパラメータを推定する有名なアルゴリズムで，混合ガウス分布のパラメータ推定でもよく用いられる．<br>\n",
    "中身については以下の通りである．<br>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "1cda98f8",
   "metadata": {},
   "source": [
    ">1. $ \\pi , \\mu , \\Sigma$を初期化する\n",
    ">2. [Eステップ]以下の式を計算する<br>\n",
    ">>$ \\gamma(z_{nk}) =  \\frac{ \\pi_k  \\mathcal{N} \\left( x_n| \\mu _k , \\Sigma _k \\right)}{ \\sum_j \\pi_j  \\mathcal{N} \\left( x_n| \\mu _j , \\Sigma _j \\right)   }$<br>\n",
    ">>$ \\\\N_k = \\sum_n \\gamma (z_{nk} )$<br>\n",
    ">3. [Mステップ]パラメータの更新を行う<br>\n",
    ">>$L= \\sum_n \\log \\sum_k \\pi _k  \\mathcal{N} \\left( x_n | \\mu _k , \\Sigma _k \\right)$<br>\n",
    ">>$\\mu _k  =  \\frac{ \\sum_{n} \\gamma (z_{nk}) x_n }{N_k}$<br>\n",
    ">>$ \\Sigma _k = \\frac{1}{N_k} \\sum_n   \\gamma (z_{nk} ) (x_n -\\mu_k ) (x_n - \\mu _k ) ^{T}$<br>\n",
    ">>$ \\pi_ k =\\frac{N_k } {N}$\n",
    ">4. 2，3を収束するまで繰り返す"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "177fd063",
   "metadata": {},
   "source": [
    "このアルゴリズムも数式だらけで難しく感じるが，実は先ほど学んだKmeans法と非常に類似したアルゴリズムである．<br>\n",
    "EMアルゴリズムでは与えられたデータ点がどのガウス分布から生成されたものかを推定している．<br>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "3aaa9a81",
   "metadata": {},
   "source": [
    "### 5.5.5 EMアルゴリズムの実装"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "3db1ae57",
   "metadata": {},
   "source": [
    "### **[オプション課題]** 課題2 クラスmy_GMMを完成させることで混合ガウス分布を推定するEMアルゴリズムを実装せよ．"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3ee53c3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from copy import deepcopy\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "def Gaus(x,mu,S): #正規分布の値を取得\n",
    "    #xがデータ点，muが正規分布の平均値，Sが共分散行列である\n",
    "    #正規分布の値を求める\n",
    "    #コードを埋める\n",
    "    g = \n",
    "    return g\n",
    "\n",
    "#混合ガウスモデル\n",
    "class my_GMM:\n",
    "    def __init__(self, n_cluster=3, random_state=42,epsilon=0.1):\n",
    "        self.n_cluster = n_cluster\n",
    "        self.epsilon = epsilon\n",
    "        self.random_state = random_state\n",
    "        self.is_trained = False\n",
    "        \n",
    "    def fit(self,X):\n",
    "        self.X = X\n",
    "        \n",
    "        #パラメータの初期化\n",
    "        \n",
    "        #合計が1になるように初期化\n",
    "        self.pi = np.ones(self.n_cluster)/self.n_cluster\n",
    "        \n",
    "        #平均はランダムに選んだデータ点で初期化する\n",
    "        idx = np.random.choice(len(self.X), self.n_cluster, replace=False)\n",
    "        self.mu = X[idx, :]\n",
    "        \n",
    "        #共分散行列は単位行列にする\n",
    "        self.S = np.array([np.eye(len(self.X[0])) for _ in range(self.n_cluster)])\n",
    "        LF=0\n",
    "        \n",
    "        #アニメーション描画用\n",
    "        self.params=[]\n",
    "        \n",
    "        for _ in range(300):\n",
    "            self.params.append([deepcopy(self.pi),deepcopy(self.mu),deepcopy(self.S)])\n",
    "            \n",
    "            #Eステップ\n",
    "            new_LF = self.E_Step()\n",
    "\n",
    "            #更新量が基準以下になれば終了\n",
    "            if abs(new_LF-LF)<self.epsilon:\n",
    "                return \n",
    "            LF = new_LF\n",
    "            #Mステップ\n",
    "            self.M_Step()\n",
    "            \n",
    "    #事後分布の計算(Eステップ)\n",
    "    def E_Step(self):\n",
    "        #割引率の計算\n",
    "        #コードを埋める\n",
    "        gam = \n",
    "        #正規化定数\n",
    "        #コードを埋める\n",
    "        nom = \n",
    "        gam/= nom\n",
    "        self.gam = gam\n",
    "        #誤差関数の計算\n",
    "        LF = sum(np.log(nom))[0]\n",
    "        return LF\n",
    "    \n",
    "    #パラメーターの更新式（Mステップ）\n",
    "    def M_Step(self):\n",
    "        #各ガウス分布から生成されたと推測されるのサンプル数\n",
    "        #コードを埋める\n",
    "        N_k = \n",
    "        N = np.sum(N_k)\n",
    "        #各ガウス分布の平均値\n",
    "        #コードを埋める\n",
    "        mu = \n",
    "        S =[]\n",
    "        #各kについてΣを求める\n",
    "        for k in range(self.n_cluster):\n",
    "            #データ点について和をとる\n",
    "            new=np.zeros((len(self.X[0]),(len(self.X[0]))))\n",
    "            for n in range(len(self.X)):\n",
    "                #共分散行列\n",
    "                #コードを埋める\n",
    "                cov=\n",
    "                #重みづけ\n",
    "                #コードを埋める\n",
    "                new+=\n",
    "            S.append(new)\n",
    "        S=np.array(S)\n",
    "\n",
    "        #混合率を求める\n",
    "        #コードを埋める\n",
    "        pi = \n",
    "        #パラメータを更新\n",
    "        self.pi, self.mu, self.S = pi , mu, S\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "751e80b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "# テストデータ\n",
    "X = np.array([[0, 0], [1, 1], [1, 0], [0, 1], [2, 2], [2, 1], [1, 2], [3, 3], [3, 2], [2, 3]])\n",
    "points1 = np.random.randn(80, 2)\n",
    "points2 = np.random.randn(80, 2) + np.array([4,0])\n",
    "points3 = np.random.randn(80, 2) + np.array([5,8])\n",
    "\n",
    "X = np.r_[points1, points2, points3]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f4d6496c",
   "metadata": {},
   "outputs": [],
   "source": [
    "model=my_GMM(n_cluster=5)\n",
    "model.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "59448a35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1e7cb72ff40>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.scatter(X[:,0],X[:,1])\n",
    "plt.scatter(model.mu[:,0],model.mu[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "013b8bb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": "/* Put everything inside the global mpl namespace */\n/* global mpl */\nwindow.mpl = {};\n\nmpl.get_websocket_type = function () {\n    if (typeof WebSocket !== 'undefined') {\n        return WebSocket;\n    } else if (typeof MozWebSocket !== 'undefined') {\n        return MozWebSocket;\n    } else {\n        alert(\n            'Your browser does not have WebSocket support. ' +\n                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n                'Firefox 4 and 5 are also supported but you ' +\n                'have to enable WebSockets in about:config.'\n        );\n    }\n};\n\nmpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n    this.id = figure_id;\n\n    this.ws = websocket;\n\n    this.supports_binary = this.ws.binaryType !== undefined;\n\n    if (!this.supports_binary) {\n        var warnings = document.getElementById('mpl-warnings');\n        if (warnings) {\n            warnings.style.display = 'block';\n            warnings.textContent =\n                'This browser does not support binary websocket messages. ' +\n                'Performance may be slow.';\n        }\n    }\n\n    this.imageObj = new Image();\n\n    this.context = undefined;\n    this.message = undefined;\n    this.canvas = undefined;\n    this.rubberband_canvas = undefined;\n    this.rubberband_context = undefined;\n    this.format_dropdown = undefined;\n\n    this.image_mode = 'full';\n\n    this.root = document.createElement('div');\n    this.root.setAttribute('style', 'display: inline-block');\n    this._root_extra_style(this.root);\n\n    parent_element.appendChild(this.root);\n\n    this._init_header(this);\n    this._init_canvas(this);\n    this._init_toolbar(this);\n\n    var fig = this;\n\n    this.waiting = false;\n\n    this.ws.onopen = function () {\n        fig.send_message('supports_binary', { value: fig.supports_binary });\n        fig.send_message('send_image_mode', {});\n        if (fig.ratio !== 1) {\n            fig.send_message('set_device_pixel_ratio', {\n                device_pixel_ratio: fig.ratio,\n            });\n        }\n        fig.send_message('refresh', {});\n    };\n\n    this.imageObj.onload = function () {\n        if (fig.image_mode === 'full') {\n            // Full images could contain transparency (where diff images\n            // almost always do), so we need to clear the canvas so that\n            // there is no ghosting.\n            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n        }\n        fig.context.drawImage(fig.imageObj, 0, 0);\n    };\n\n    this.imageObj.onunload = function () {\n        fig.ws.close();\n    };\n\n    this.ws.onmessage = this._make_on_message_function(this);\n\n    this.ondownload = ondownload;\n};\n\nmpl.figure.prototype._init_header = function () {\n    var titlebar = document.createElement('div');\n    titlebar.classList =\n        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n    var titletext = document.createElement('div');\n    titletext.classList = 'ui-dialog-title';\n    titletext.setAttribute(\n        'style',\n        'width: 100%; text-align: center; padding: 3px;'\n    );\n    titlebar.appendChild(titletext);\n    this.root.appendChild(titlebar);\n    this.header = titletext;\n};\n\nmpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n\nmpl.figure.prototype._init_canvas = function () {\n    var fig = this;\n\n    var canvas_div = (this.canvas_div = document.createElement('div'));\n    canvas_div.setAttribute('tabindex', '0');\n    canvas_div.setAttribute(\n        'style',\n        'border: 1px solid #ddd;' +\n            'box-sizing: content-box;' +\n            'clear: both;' +\n            'min-height: 1px;' +\n            'min-width: 1px;' +\n            'outline: 0;' +\n            'overflow: hidden;' +\n            'position: relative;' +\n            'resize: both;' +\n            'z-index: 2;'\n    );\n\n    function on_keyboard_event_closure(name) {\n        return function (event) {\n            return fig.key_event(event, name);\n        };\n    }\n\n    canvas_div.addEventListener(\n        'keydown',\n        on_keyboard_event_closure('key_press')\n    );\n    canvas_div.addEventListener(\n        'keyup',\n        on_keyboard_event_closure('key_release')\n    );\n\n    this._canvas_extra_style(canvas_div);\n    this.root.appendChild(canvas_div);\n\n    var canvas = (this.canvas = document.createElement('canvas'));\n    canvas.classList.add('mpl-canvas');\n    canvas.setAttribute(\n        'style',\n        'box-sizing: content-box;' +\n            'pointer-events: none;' +\n            'position: relative;' +\n            'z-index: 0;'\n    );\n\n    this.context = canvas.getContext('2d');\n\n    var backingStore =\n        this.context.backingStorePixelRatio ||\n        this.context.webkitBackingStorePixelRatio ||\n        this.context.mozBackingStorePixelRatio ||\n        this.context.msBackingStorePixelRatio ||\n        this.context.oBackingStorePixelRatio ||\n        this.context.backingStorePixelRatio ||\n        1;\n\n    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n\n    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n        'canvas'\n    ));\n    rubberband_canvas.setAttribute(\n        'style',\n        'box-sizing: content-box;' +\n            'left: 0;' +\n            'pointer-events: none;' +\n            'position: absolute;' +\n            'top: 0;' +\n            'z-index: 1;'\n    );\n\n    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n    if (this.ResizeObserver === undefined) {\n        if (window.ResizeObserver !== undefined) {\n            this.ResizeObserver = window.ResizeObserver;\n        } else {\n            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n            this.ResizeObserver = obs.ResizeObserver;\n        }\n    }\n\n    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n        var nentries = entries.length;\n        for (var i = 0; i < nentries; i++) {\n            var entry = entries[i];\n            var width, height;\n            if (entry.contentBoxSize) {\n                if (entry.contentBoxSize instanceof Array) {\n                    // Chrome 84 implements new version of spec.\n                    width = entry.contentBoxSize[0].inlineSize;\n                    height = entry.contentBoxSize[0].blockSize;\n                } else {\n                    // Firefox implements old version of spec.\n                    width = entry.contentBoxSize.inlineSize;\n                    height = entry.contentBoxSize.blockSize;\n                }\n            } else {\n                // Chrome <84 implements even older version of spec.\n                width = entry.contentRect.width;\n                height = entry.contentRect.height;\n            }\n\n            // Keep the size of the canvas and rubber band canvas in sync with\n            // the canvas container.\n            if (entry.devicePixelContentBoxSize) {\n                // Chrome 84 implements new version of spec.\n                canvas.setAttribute(\n                    'width',\n                    entry.devicePixelContentBoxSize[0].inlineSize\n                );\n                canvas.setAttribute(\n                    'height',\n                    entry.devicePixelContentBoxSize[0].blockSize\n                );\n            } else {\n                canvas.setAttribute('width', width * fig.ratio);\n                canvas.setAttribute('height', height * fig.ratio);\n            }\n            /* This rescales the canvas back to display pixels, so that it\n             * appears correct on HiDPI screens. */\n            canvas.style.width = width + 'px';\n            canvas.style.height = height + 'px';\n\n            rubberband_canvas.setAttribute('width', width);\n            rubberband_canvas.setAttribute('height', height);\n\n            // And update the size in Python. We ignore the initial 0/0 size\n            // that occurs as the element is placed into the DOM, which should\n            // otherwise not happen due to the minimum size styling.\n            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n                fig.request_resize(width, height);\n            }\n        }\n    });\n    this.resizeObserverInstance.observe(canvas_div);\n\n    function on_mouse_event_closure(name) {\n        /* User Agent sniffing is bad, but WebKit is busted:\n         * https://bugs.webkit.org/show_bug.cgi?id=144526\n         * https://bugs.webkit.org/show_bug.cgi?id=181818\n         * The worst that happens here is that they get an extra browser\n         * selection when dragging, if this check fails to catch them.\n         */\n        var UA = navigator.userAgent;\n        var isWebKit = /AppleWebKit/.test(UA) && !/Chrome/.test(UA);\n        if(isWebKit) {\n            return function (event) {\n                /* This prevents the web browser from automatically changing to\n                 * the text insertion cursor when the button is pressed. We\n                 * want to control all of the cursor setting manually through\n                 * the 'cursor' event from matplotlib */\n                event.preventDefault()\n                return fig.mouse_event(event, name);\n            };\n        } else {\n            return function (event) {\n                return fig.mouse_event(event, name);\n            };\n        }\n    }\n\n    canvas_div.addEventListener(\n        'mousedown',\n        on_mouse_event_closure('button_press')\n    );\n    canvas_div.addEventListener(\n        'mouseup',\n        on_mouse_event_closure('button_release')\n    );\n    canvas_div.addEventListener(\n        'dblclick',\n        on_mouse_event_closure('dblclick')\n    );\n    // Throttle sequential mouse events to 1 every 20ms.\n    canvas_div.addEventListener(\n        'mousemove',\n        on_mouse_event_closure('motion_notify')\n    );\n\n    canvas_div.addEventListener(\n        'mouseenter',\n        on_mouse_event_closure('figure_enter')\n    );\n    canvas_div.addEventListener(\n        'mouseleave',\n        on_mouse_event_closure('figure_leave')\n    );\n\n    canvas_div.addEventListener('wheel', function (event) {\n        if (event.deltaY < 0) {\n            event.step = 1;\n        } else {\n            event.step = -1;\n        }\n        on_mouse_event_closure('scroll')(event);\n    });\n\n    canvas_div.appendChild(canvas);\n    canvas_div.appendChild(rubberband_canvas);\n\n    this.rubberband_context = rubberband_canvas.getContext('2d');\n    this.rubberband_context.strokeStyle = '#000000';\n\n    this._resize_canvas = function (width, height, forward) {\n        if (forward) {\n            canvas_div.style.width = width + 'px';\n            canvas_div.style.height = height + 'px';\n        }\n    };\n\n    // Disable right mouse context menu.\n    canvas_div.addEventListener('contextmenu', function (_e) {\n        event.preventDefault();\n        return false;\n    });\n\n    function set_focus() {\n        canvas.focus();\n        canvas_div.focus();\n    }\n\n    window.setTimeout(set_focus, 100);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'mpl-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'mpl-button-group';\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'mpl-button-group';\n            continue;\n        }\n\n        var button = (fig.buttons[name] = document.createElement('button'));\n        button.classList = 'mpl-widget';\n        button.setAttribute('role', 'button');\n        button.setAttribute('aria-disabled', 'false');\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n\n        var icon_img = document.createElement('img');\n        icon_img.src = '_images/' + image + '.png';\n        icon_img.srcset = '_images/' + image + '_large.png 2x';\n        icon_img.alt = tooltip;\n        button.appendChild(icon_img);\n\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    var fmt_picker = document.createElement('select');\n    fmt_picker.classList = 'mpl-widget';\n    toolbar.appendChild(fmt_picker);\n    this.format_dropdown = fmt_picker;\n\n    for (var ind in mpl.extensions) {\n        var fmt = mpl.extensions[ind];\n        var option = document.createElement('option');\n        option.selected = fmt === mpl.default_extension;\n        option.innerHTML = fmt;\n        fmt_picker.appendChild(option);\n    }\n\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n};\n\nmpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n    // which will in turn request a refresh of the image.\n    this.send_message('resize', { width: x_pixels, height: y_pixels });\n};\n\nmpl.figure.prototype.send_message = function (type, properties) {\n    properties['type'] = type;\n    properties['figure_id'] = this.id;\n    this.ws.send(JSON.stringify(properties));\n};\n\nmpl.figure.prototype.send_draw_message = function () {\n    if (!this.waiting) {\n        this.waiting = true;\n        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    var format_dropdown = fig.format_dropdown;\n    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n    fig.ondownload(fig, format);\n};\n\nmpl.figure.prototype.handle_resize = function (fig, msg) {\n    var size = msg['size'];\n    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n        fig._resize_canvas(size[0], size[1], msg['forward']);\n        fig.send_message('refresh', {});\n    }\n};\n\nmpl.figure.prototype.handle_rubberband = function (fig, msg) {\n    var x0 = msg['x0'] / fig.ratio;\n    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n    var x1 = msg['x1'] / fig.ratio;\n    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n    x0 = Math.floor(x0) + 0.5;\n    y0 = Math.floor(y0) + 0.5;\n    x1 = Math.floor(x1) + 0.5;\n    y1 = Math.floor(y1) + 0.5;\n    var min_x = Math.min(x0, x1);\n    var min_y = Math.min(y0, y1);\n    var width = Math.abs(x1 - x0);\n    var height = Math.abs(y1 - y0);\n\n    fig.rubberband_context.clearRect(\n        0,\n        0,\n        fig.canvas.width / fig.ratio,\n        fig.canvas.height / fig.ratio\n    );\n\n    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n};\n\nmpl.figure.prototype.handle_figure_label = function (fig, msg) {\n    // Updates the figure title.\n    fig.header.textContent = msg['label'];\n};\n\nmpl.figure.prototype.handle_cursor = function (fig, msg) {\n    fig.canvas_div.style.cursor = msg['cursor'];\n};\n\nmpl.figure.prototype.handle_message = function (fig, msg) {\n    fig.message.textContent = msg['message'];\n};\n\nmpl.figure.prototype.handle_draw = function (fig, _msg) {\n    // Request the server to send over a new figure.\n    fig.send_draw_message();\n};\n\nmpl.figure.prototype.handle_image_mode = function (fig, msg) {\n    fig.image_mode = msg['mode'];\n};\n\nmpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n    for (var key in msg) {\n        if (!(key in fig.buttons)) {\n            continue;\n        }\n        fig.buttons[key].disabled = !msg[key];\n        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n    }\n};\n\nmpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n    if (msg['mode'] === 'PAN') {\n        fig.buttons['Pan'].classList.add('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    } else if (msg['mode'] === 'ZOOM') {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.add('active');\n    } else {\n        fig.buttons['Pan'].classList.remove('active');\n        fig.buttons['Zoom'].classList.remove('active');\n    }\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Called whenever the canvas gets updated.\n    this.send_message('ack', {});\n};\n\n// A function to construct a web socket function for onmessage handling.\n// Called in the figure constructor.\nmpl.figure.prototype._make_on_message_function = function (fig) {\n    return function socket_on_message(evt) {\n        if (evt.data instanceof Blob) {\n            var img = evt.data;\n            if (img.type !== 'image/png') {\n                /* FIXME: We get \"Resource interpreted as Image but\n                 * transferred with MIME type text/plain:\" errors on\n                 * Chrome.  But how to set the MIME type?  It doesn't seem\n                 * to be part of the websocket stream */\n                img.type = 'image/png';\n            }\n\n            /* Free the memory for the previous frames */\n            if (fig.imageObj.src) {\n                (window.URL || window.webkitURL).revokeObjectURL(\n                    fig.imageObj.src\n                );\n            }\n\n            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n                img\n            );\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        } else if (\n            typeof evt.data === 'string' &&\n            evt.data.slice(0, 21) === 'data:image/png;base64'\n        ) {\n            fig.imageObj.src = evt.data;\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        }\n\n        var msg = JSON.parse(evt.data);\n        var msg_type = msg['type'];\n\n        // Call the  \"handle_{type}\" callback, which takes\n        // the figure and JSON message as its only arguments.\n        try {\n            var callback = fig['handle_' + msg_type];\n        } catch (e) {\n            console.log(\n                \"No handler for the '\" + msg_type + \"' message type: \",\n                msg\n            );\n            return;\n        }\n\n        if (callback) {\n            try {\n                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n                callback(fig, msg);\n            } catch (e) {\n                console.log(\n                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n                    e,\n                    e.stack,\n                    msg\n                );\n            }\n        }\n    };\n};\n\nfunction getModifiers(event) {\n    var mods = [];\n    if (event.ctrlKey) {\n        mods.push('ctrl');\n    }\n    if (event.altKey) {\n        mods.push('alt');\n    }\n    if (event.shiftKey) {\n        mods.push('shift');\n    }\n    if (event.metaKey) {\n        mods.push('meta');\n    }\n    return mods;\n}\n\n/*\n * return a copy of an object with only non-object keys\n * we need this to avoid circular references\n * https://stackoverflow.com/a/24161582/3208463\n */\nfunction simpleKeys(original) {\n    return Object.keys(original).reduce(function (obj, key) {\n        if (typeof original[key] !== 'object') {\n            obj[key] = original[key];\n        }\n        return obj;\n    }, {});\n}\n\nmpl.figure.prototype.mouse_event = function (event, name) {\n    if (name === 'button_press') {\n        this.canvas.focus();\n        this.canvas_div.focus();\n    }\n\n    // from https://stackoverflow.com/q/1114465\n    var boundingRect = this.canvas.getBoundingClientRect();\n    var x = (event.clientX - boundingRect.left) * this.ratio;\n    var y = (event.clientY - boundingRect.top) * this.ratio;\n\n    this.send_message(name, {\n        x: x,\n        y: y,\n        button: event.button,\n        step: event.step,\n        modifiers: getModifiers(event),\n        guiEvent: simpleKeys(event),\n    });\n\n    return false;\n};\n\nmpl.figure.prototype._key_event_extra = function (_event, _name) {\n    // Handle any extra behaviour associated with a key event\n};\n\nmpl.figure.prototype.key_event = function (event, name) {\n    // Prevent repeat events\n    if (name === 'key_press') {\n        if (event.key === this._key) {\n            return;\n        } else {\n            this._key = event.key;\n        }\n    }\n    if (name === 'key_release') {\n        this._key = null;\n    }\n\n    var value = '';\n    if (event.ctrlKey && event.key !== 'Control') {\n        value += 'ctrl+';\n    }\n    else if (event.altKey && event.key !== 'Alt') {\n        value += 'alt+';\n    }\n    else if (event.shiftKey && event.key !== 'Shift') {\n        value += 'shift+';\n    }\n\n    value += 'k' + event.key;\n\n    this._key_event_extra(event, name);\n\n    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n    return false;\n};\n\nmpl.figure.prototype.toolbar_button_onclick = function (name) {\n    if (name === 'download') {\n        this.handle_save(this, null);\n    } else {\n        this.send_message('toolbar_button', { name: name });\n    }\n};\n\nmpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n    this.message.textContent = tooltip;\n};\n\n///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n// prettier-ignore\nvar _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\nmpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o\", \"download\"]];\n\nmpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\", \"webp\"];\n\nmpl.default_extension = \"png\";/* global mpl */\n\nvar comm_websocket_adapter = function (comm) {\n    // Create a \"websocket\"-like object which calls the given IPython comm\n    // object with the appropriate methods. Currently this is a non binary\n    // socket, so there is still some room for performance tuning.\n    var ws = {};\n\n    ws.binaryType = comm.kernel.ws.binaryType;\n    ws.readyState = comm.kernel.ws.readyState;\n    function updateReadyState(_event) {\n        if (comm.kernel.ws) {\n            ws.readyState = comm.kernel.ws.readyState;\n        } else {\n            ws.readyState = 3; // Closed state.\n        }\n    }\n    comm.kernel.ws.addEventListener('open', updateReadyState);\n    comm.kernel.ws.addEventListener('close', updateReadyState);\n    comm.kernel.ws.addEventListener('error', updateReadyState);\n\n    ws.close = function () {\n        comm.close();\n    };\n    ws.send = function (m) {\n        //console.log('sending', m);\n        comm.send(m);\n    };\n    // Register the callback with on_msg.\n    comm.on_msg(function (msg) {\n        //console.log('receiving', msg['content']['data'], msg);\n        var data = msg['content']['data'];\n        if (data['blob'] !== undefined) {\n            data = {\n                data: new Blob(msg['buffers'], { type: data['blob'] }),\n            };\n        }\n        // Pass the mpl event to the overridden (by mpl) onmessage function.\n        ws.onmessage(data);\n    });\n    return ws;\n};\n\nmpl.mpl_figure_comm = function (comm, msg) {\n    // This is the function which gets called when the mpl process\n    // starts-up an IPython Comm through the \"matplotlib\" channel.\n\n    var id = msg.content.data.id;\n    // Get hold of the div created by the display call when the Comm\n    // socket was opened in Python.\n    var element = document.getElementById(id);\n    var ws_proxy = comm_websocket_adapter(comm);\n\n    function ondownload(figure, _format) {\n        window.open(figure.canvas.toDataURL());\n    }\n\n    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n\n    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n    // web socket which is closed, not our websocket->open comm proxy.\n    ws_proxy.onopen();\n\n    fig.parent_element = element;\n    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n    if (!fig.cell_info) {\n        console.error('Failed to find cell for figure', id, fig);\n        return;\n    }\n    fig.cell_info[0].output_area.element.on(\n        'cleared',\n        { fig: fig },\n        fig._remove_fig_handler\n    );\n};\n\nmpl.figure.prototype.handle_close = function (fig, msg) {\n    var width = fig.canvas.width / fig.ratio;\n    fig.cell_info[0].output_area.element.off(\n        'cleared',\n        fig._remove_fig_handler\n    );\n    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n\n    // Update the output cell to use the data from the current canvas.\n    fig.push_to_output();\n    var dataURL = fig.canvas.toDataURL();\n    // Re-enable the keyboard manager in IPython - without this line, in FF,\n    // the notebook keyboard shortcuts fail.\n    IPython.keyboard_manager.enable();\n    fig.parent_element.innerHTML =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n    fig.close_ws(fig, msg);\n};\n\nmpl.figure.prototype.close_ws = function (fig, msg) {\n    fig.send_message('closing', msg);\n    // fig.ws.close()\n};\n\nmpl.figure.prototype.push_to_output = function (_remove_interactive) {\n    // Turn the data on the canvas into data in the output cell.\n    var width = this.canvas.width / this.ratio;\n    var dataURL = this.canvas.toDataURL();\n    this.cell_info[1]['text/html'] =\n        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n};\n\nmpl.figure.prototype.updated_canvas_event = function () {\n    // Tell IPython that the notebook contents must change.\n    IPython.notebook.set_dirty(true);\n    this.send_message('ack', {});\n    var fig = this;\n    // Wait a second, then push the new image to the DOM so\n    // that it is saved nicely (might be nice to debounce this).\n    setTimeout(function () {\n        fig.push_to_output();\n    }, 1000);\n};\n\nmpl.figure.prototype._init_toolbar = function () {\n    var fig = this;\n\n    var toolbar = document.createElement('div');\n    toolbar.classList = 'btn-toolbar';\n    this.root.appendChild(toolbar);\n\n    function on_click_closure(name) {\n        return function (_event) {\n            return fig.toolbar_button_onclick(name);\n        };\n    }\n\n    function on_mouseover_closure(tooltip) {\n        return function (event) {\n            if (!event.currentTarget.disabled) {\n                return fig.toolbar_button_onmouseover(tooltip);\n            }\n        };\n    }\n\n    fig.buttons = {};\n    var buttonGroup = document.createElement('div');\n    buttonGroup.classList = 'btn-group';\n    var button;\n    for (var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            /* Instead of a spacer, we start a new button group. */\n            if (buttonGroup.hasChildNodes()) {\n                toolbar.appendChild(buttonGroup);\n            }\n            buttonGroup = document.createElement('div');\n            buttonGroup.classList = 'btn-group';\n            continue;\n        }\n\n        button = fig.buttons[name] = document.createElement('button');\n        button.classList = 'btn btn-default';\n        button.href = '#';\n        button.title = name;\n        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n        button.addEventListener('click', on_click_closure(method_name));\n        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n        buttonGroup.appendChild(button);\n    }\n\n    if (buttonGroup.hasChildNodes()) {\n        toolbar.appendChild(buttonGroup);\n    }\n\n    // Add the status bar.\n    var status_bar = document.createElement('span');\n    status_bar.classList = 'mpl-message pull-right';\n    toolbar.appendChild(status_bar);\n    this.message = status_bar;\n\n    // Add the close button to the window.\n    var buttongrp = document.createElement('div');\n    buttongrp.classList = 'btn-group inline pull-right';\n    button = document.createElement('button');\n    button.classList = 'btn btn-mini btn-primary';\n    button.href = '#';\n    button.title = 'Stop Interaction';\n    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n    button.addEventListener('click', function (_evt) {\n        fig.handle_close(fig, {});\n    });\n    button.addEventListener(\n        'mouseover',\n        on_mouseover_closure('Stop Interaction')\n    );\n    buttongrp.appendChild(button);\n    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n};\n\nmpl.figure.prototype._remove_fig_handler = function (event) {\n    var fig = event.data.fig;\n    if (event.target !== this) {\n        // Ignore bubbled events from children.\n        return;\n    }\n    fig.close_ws(fig, {});\n};\n\nmpl.figure.prototype._root_extra_style = function (el) {\n    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n};\n\nmpl.figure.prototype._canvas_extra_style = function (el) {\n    // this is important to make the div 'focusable\n    el.setAttribute('tabindex', 0);\n    // reach out to IPython and tell the keyboard manager to turn it's self\n    // off when our div gets focus\n\n    // location in version 3\n    if (IPython.notebook.keyboard_manager) {\n        IPython.notebook.keyboard_manager.register_events(el);\n    } else {\n        // location in version 2\n        IPython.keyboard_manager.register_events(el);\n    }\n};\n\nmpl.figure.prototype._key_event_extra = function (event, _name) {\n    // Check for shift+enter\n    if (event.shiftKey && event.which === 13) {\n        this.canvas_div.blur();\n        // select the cell after this one\n        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n        IPython.notebook.select(index + 1);\n    }\n};\n\nmpl.figure.prototype.handle_save = function (fig, _msg) {\n    fig.ondownload(fig, null);\n};\n\nmpl.find_output_cell = function (html_output) {\n    // Return the cell and output element which can be found *uniquely* in the notebook.\n    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n    // IPython event is triggered only after the cells have been serialised, which for\n    // our purposes (turning an active figure into a static one), is too late.\n    var cells = IPython.notebook.get_cells();\n    var ncells = cells.length;\n    for (var i = 0; i < ncells; i++) {\n        var cell = cells[i];\n        if (cell.cell_type === 'code') {\n            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n                var data = cell.output_area.outputs[j];\n                if (data.data) {\n                    // IPython >= 3 moved mimebundle to data attribute of output\n                    data = data.data;\n                }\n                if (data['text/html'] === html_output) {\n                    return [cell, data, j];\n                }\n            }\n        }\n    }\n};\n\n// Register the function which deals with the matplotlib target/channel.\n// The kernel may be null if the page has been refreshed.\nif (IPython.notebook.kernel !== null) {\n    IPython.notebook.kernel.comm_manager.register_target(\n        'matplotlib',\n        mpl.mpl_figure_comm\n    );\n}\n",
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:image/png;base64,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\" width=\"431.8518823589666\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "from copy import deepcopy\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "\n",
    "\n",
    "data=model.X\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(data[:,0],data[:,1])\n",
    "#関数に投入するデータを作成\n",
    "x =  np.arange(min(data[:,0])-1, max(data[:,0])+1, 0.5)\n",
    "y =  np.arange(min(data[:,1])-1, max(data[:,1])+1, 0.5)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "z = np.c_[X.ravel(),Y.ravel()]\n",
    "ims=[]\n",
    "\n",
    "for n,params in enumerate(model.params):\n",
    "    text=[ax.text(1.3, 11.2,f\"n={n}\")]\n",
    "    #混合比,平均,共分散行列\n",
    "    pi,mu,S = params\n",
    "    #分散共分散行列の行列式\n",
    "    dets = [np.linalg.det(s) for s in S]\n",
    "    #分散共分散行列の逆行列\n",
    "    invs = [np.linalg.inv(s) for s in S]\n",
    "    #二次元正規分布の確率密度を返す関数\n",
    "    def gaussian(x):        \n",
    "        n = x.ndim\n",
    "        i=0\n",
    "        p= sum([pi[i]*np.diag(np.exp(-(x - mu[i])@invs[i]@((x - mu[i]).T)/2.0)) / (np.sqrt((2 * np.pi) ** n * dets[i])) for i in range(model.n_cluster)])\n",
    "        return p\n",
    "    Z = gaussian(z)\n",
    "    shape = X.shape\n",
    "    Z = Z.reshape(shape)\n",
    "    CS = ax.contourf(x,y, Z, alpha=0.4)\n",
    "    ims.append(CS.collections+text)\n",
    "ani = animation.ArtistAnimation(fig, ims, interval=200)\n",
    "#ani.save('MyGMM.gif', writer='imagemagick')\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "0778352e",
   "metadata": {},
   "source": [
    "## [練習問題](../exercise/questions.md#chapter-5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}