{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "from math import log\n",
    "import pandas as pd\n",
    "import operator\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 前置知识\n",
    "pandas\n",
    "    选择行列：https://blog.csdn.net/qq_38328378/article/details/81166518\n",
    "    统计数量与频率iris['Species'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 载入数据并查看"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>Sepal.Length</th>\n",
       "      <th>Sepal.Width</th>\n",
       "      <th>Petal.Length</th>\n",
       "      <th>Petal.Width</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Sepal.Length  Sepal.Width  Petal.Length  Petal.Width Species\n",
       "1           5.1          3.5           1.4          0.2  setosa\n",
       "2           4.9          3.0           1.4          0.2  setosa\n",
       "3           4.7          3.2           1.3          0.2  setosa\n",
       "4           4.6          3.1           1.5          0.2  setosa\n",
       "5           5.0          3.6           1.4          0.2  setosa"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "csv_path=os.path.join(\"datas\", \"iris\",\"iris.csv\")\n",
    "iris=pd.read_csv(csv_path,sep=',',header=0,index_col=0)\n",
    "iris.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method NDFrame.describe of      Sepal.Length  Sepal.Width  Petal.Length  Petal.Width    Species\n",
       "1             5.1          3.5           1.4          0.2     setosa\n",
       "2             4.9          3.0           1.4          0.2     setosa\n",
       "3             4.7          3.2           1.3          0.2     setosa\n",
       "4             4.6          3.1           1.5          0.2     setosa\n",
       "5             5.0          3.6           1.4          0.2     setosa\n",
       "6             5.4          3.9           1.7          0.4     setosa\n",
       "7             4.6          3.4           1.4          0.3     setosa\n",
       "8             5.0          3.4           1.5          0.2     setosa\n",
       "9             4.4          2.9           1.4          0.2     setosa\n",
       "10            4.9          3.1           1.5          0.1     setosa\n",
       "11            5.4          3.7           1.5          0.2     setosa\n",
       "12            4.8          3.4           1.6          0.2     setosa\n",
       "13            4.8          3.0           1.4          0.1     setosa\n",
       "14            4.3          3.0           1.1          0.1     setosa\n",
       "15            5.8          4.0           1.2          0.2     setosa\n",
       "16            5.7          4.4           1.5          0.4     setosa\n",
       "17            5.4          3.9           1.3          0.4     setosa\n",
       "18            5.1          3.5           1.4          0.3     setosa\n",
       "19            5.7          3.8           1.7          0.3     setosa\n",
       "20            5.1          3.8           1.5          0.3     setosa\n",
       "21            5.4          3.4           1.7          0.2     setosa\n",
       "22            5.1          3.7           1.5          0.4     setosa\n",
       "23            4.6          3.6           1.0          0.2     setosa\n",
       "24            5.1          3.3           1.7          0.5     setosa\n",
       "25            4.8          3.4           1.9          0.2     setosa\n",
       "26            5.0          3.0           1.6          0.2     setosa\n",
       "27            5.0          3.4           1.6          0.4     setosa\n",
       "28            5.2          3.5           1.5          0.2     setosa\n",
       "29            5.2          3.4           1.4          0.2     setosa\n",
       "30            4.7          3.2           1.6          0.2     setosa\n",
       "..            ...          ...           ...          ...        ...\n",
       "121           6.9          3.2           5.7          2.3  virginica\n",
       "122           5.6          2.8           4.9          2.0  virginica\n",
       "123           7.7          2.8           6.7          2.0  virginica\n",
       "124           6.3          2.7           4.9          1.8  virginica\n",
       "125           6.7          3.3           5.7          2.1  virginica\n",
       "126           7.2          3.2           6.0          1.8  virginica\n",
       "127           6.2          2.8           4.8          1.8  virginica\n",
       "128           6.1          3.0           4.9          1.8  virginica\n",
       "129           6.4          2.8           5.6          2.1  virginica\n",
       "130           7.2          3.0           5.8          1.6  virginica\n",
       "131           7.4          2.8           6.1          1.9  virginica\n",
       "132           7.9          3.8           6.4          2.0  virginica\n",
       "133           6.4          2.8           5.6          2.2  virginica\n",
       "134           6.3          2.8           5.1          1.5  virginica\n",
       "135           6.1          2.6           5.6          1.4  virginica\n",
       "136           7.7          3.0           6.1          2.3  virginica\n",
       "137           6.3          3.4           5.6          2.4  virginica\n",
       "138           6.4          3.1           5.5          1.8  virginica\n",
       "139           6.0          3.0           4.8          1.8  virginica\n",
       "140           6.9          3.1           5.4          2.1  virginica\n",
       "141           6.7          3.1           5.6          2.4  virginica\n",
       "142           6.9          3.1           5.1          2.3  virginica\n",
       "143           5.8          2.7           5.1          1.9  virginica\n",
       "144           6.8          3.2           5.9          2.3  virginica\n",
       "145           6.7          3.3           5.7          2.5  virginica\n",
       "146           6.7          3.0           5.2          2.3  virginica\n",
       "147           6.3          2.5           5.0          1.9  virginica\n",
       "148           6.5          3.0           5.2          2.0  virginica\n",
       "149           6.2          3.4           5.4          2.3  virginica\n",
       "150           5.9          3.0           5.1          1.8  virginica\n",
       "\n",
       "[150 rows x 5 columns]>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.describe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Sepal.Length', 'Sepal.Width', 'Petal.Length', 'Petal.Width',\n",
       "       'Species'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spec=iris.columns\n",
    "spec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "versicolor    50\n",
      "virginica     50\n",
      "setosa        50\n",
      "Name: Species, dtype: int64\n",
      "Index(['versicolor', 'virginica', 'setosa'], dtype='object')\n",
      "50\n"
     ]
    }
   ],
   "source": [
    "print(iris['Species'].value_counts(),iris['Species'].value_counts().index,iris['Species'].value_counts()[2],sep='\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 构建信息函数，其实就是熵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.584962500721156"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def ent(daframe,colum):\n",
    "    \"\"\"输入dataframe以及需要计算熵的列索引，输出熵\"\"\"\n",
    "    coun=daframe[colum].value_counts()\n",
    "    rat=coun/sum(coun)\n",
    "    return sum(-rat*rat.apply(np.log2))\n",
    "ent(iris,'Species')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0    0.066667\n",
       "6.3    0.060000\n",
       "5.1    0.060000\n",
       "6.7    0.053333\n",
       "5.7    0.053333\n",
       "5.5    0.046667\n",
       "5.8    0.046667\n",
       "6.4    0.046667\n",
       "6.0    0.040000\n",
       "4.9    0.040000\n",
       "6.1    0.040000\n",
       "5.4    0.040000\n",
       "5.6    0.040000\n",
       "6.5    0.033333\n",
       "4.8    0.033333\n",
       "7.7    0.026667\n",
       "6.9    0.026667\n",
       "5.2    0.026667\n",
       "6.2    0.026667\n",
       "4.6    0.026667\n",
       "7.2    0.020000\n",
       "6.8    0.020000\n",
       "4.4    0.020000\n",
       "5.9    0.020000\n",
       "6.6    0.013333\n",
       "4.7    0.013333\n",
       "7.6    0.006667\n",
       "7.4    0.006667\n",
       "4.3    0.006667\n",
       "7.9    0.006667\n",
       "7.3    0.006667\n",
       "7.0    0.006667\n",
       "4.5    0.006667\n",
       "5.3    0.006667\n",
       "7.1    0.006667\n",
       "Name: Sepal.Length, dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coun=iris['Sepal.Length'].value_counts()\n",
    "rat=coun/sum(coun)\n",
    "rat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 构建gain函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.584962500721156 Sepal.Length\n",
      "1.584962500721156 Sepal.Width\n",
      "1.584962500721156 Petal.Length\n",
      "1.584962500721156 Petal.Width\n",
      "1.584962500721156 Species\n"
     ]
    }
   ],
   "source": [
    "def Gain(daframe,D):\n",
    "    \"\"\"输入：\n",
    "        dataframe，通常是上一次分支后的\n",
    "        D，当前列\n",
    "        a，计划试探的列\"\"\"\n",
    "    coun=iris[D].value_counts()\n",
    "    rat=coun/sum(coun)\n",
    "    gain=ent(daframe,'Species')\n",
    "    for i in range(len(coun)):\n",
    "        #为dataframe中D的每一个取值拆分出叫做temp的，包含该取值的dataframe\n",
    "        temp=daframe[daframe[D]==coun.index[i]]\n",
    "        #print(temp)\n",
    "        gain-=rat.iloc[i]*ent(temp,D)\n",
    "        #print(ent(temp,D))\n",
    "        #print(gain)\n",
    "    return gain\n",
    "#由于这些是连续值，所以算出来都是0，但是计算ent和gain任务算是完成了\n",
    "for i in spec:\n",
    "    print(Gain(iris,i),i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        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>Sepal.Length</th>\n",
       "      <th>Sepal.Width</th>\n",
       "      <th>Petal.Length</th>\n",
       "      <th>Petal.Width</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Sepal.Length  Sepal.Width  Petal.Length  Petal.Width Species\n",
       "5           5.0          3.6           1.4          0.2  setosa\n",
       "6           5.4          3.9           1.7          0.4  setosa\n",
       "7           4.6          3.4           1.4          0.3  setosa"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.iloc[4:7,0:len(iris.columns)+1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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