notebook/07-Pandas计算工具介绍.ipynb

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   "source": [
    "> 教你学会 Pandas 不是我的目的，**教你轻松玩转 Pandas 才是我的目的**。我会通过一系列实例来带入 Pandas 的知识点，让你在学习 Pandas 的路上不再枯燥。\n",
    "\n",
    "> 声明：我所写的**轻松玩转 Pandas 教程都是免费的**，如果对你有帮助，你可以持续关注我。\n",
    "\n",
    "在 [06-Pandas时间序列详解](06-Pandas时间序列详解.ipynb) 介绍了使用 Pandas 中时间序列相关的处理，这节来看下如何使用 Pandas 中包含的一些计算工具吧。"
   ]
  },
  {
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   "outputs": [],
   "source": [
    "# 导入相关库\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pandas 中包含了非常丰富的计算工具，如一些统计函数、窗口函数、聚合等计算工具。\n",
    "\n",
    "## 统计函数\n",
    "\n",
    "最常见的计算工具莫过于一些统计函数了。这里我们首先构建一个包含了用户年龄与收入的 DataFrame。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:37.075528Z",
     "start_time": "2018-07-09T12:55:37.014367Z"
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   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>income</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Tom</th>\n",
       "      <td>18</td>\n",
       "      <td>1000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Bob</th>\n",
       "      <td>40</td>\n",
       "      <td>4500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mary</th>\n",
       "      <td>28</td>\n",
       "      <td>1800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>James</th>\n",
       "      <td>20</td>\n",
       "      <td>1800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Andy</th>\n",
       "      <td>30</td>\n",
       "      <td>3000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alice</th>\n",
       "      <td>35</td>\n",
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      "text/plain": [
       "       age  income\n",
       "name              \n",
       "Tom     18  1000.0\n",
       "Bob     40  4500.0\n",
       "Mary    28  1800.0\n",
       "James   20  1800.0\n",
       "Andy    30  3000.0\n",
       "Alice   35     NaN"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = pd.Index(data=[\"Tom\", \"Bob\", \"Mary\", \"James\", \"Andy\", \"Alice\"], name=\"name\")\n",
    "\n",
    "data = {\n",
    "    \"age\": [18, 40, 28, 20, 30, 35],\n",
    "    \"income\": [1000, 4500 , 1800, 1800, 3000, np.nan],\n",
    "}\n",
    "\n",
    "df = pd.DataFrame(data=data, index=index)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以通过 `cov` 函数来求出年龄与收入之间的协方差，计算的时候会丢弃缺失值。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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     "end_time": "2018-07-09T12:55:37.236958Z",
     "start_time": "2018-07-09T12:55:37.079540Z"
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   "outputs": [
    {
     "data": {
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       "11320.0"
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     "execution_count": 3,
     "metadata": {},
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   ],
   "source": [
    "df.age.cov(df.income)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "除了协方差之外，我们还可以通过 `corr` 函数来计算下它们之间的相关性，计算的时候会丢弃缺失值。\n",
    "\n",
    "默认情况下 `corr` 计算相关性时用到的方法是 `pearson`，当然了你也可以指定 `kendall` 或 `spearman`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:37.259017Z",
     "start_time": "2018-07-09T12:55:37.242974Z"
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    {
     "data": {
      "text/plain": [
       "0.94416508951340194"
      ]
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df.age.corr(df.income)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:40.710200Z",
     "start_time": "2018-07-09T12:55:37.265033Z"
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    {
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       "0.94868329805051366"
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df.age.corr(df.income, method=\"kendall\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:40.733260Z",
     "start_time": "2018-07-09T12:55:40.718220Z"
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    {
     "data": {
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       "0.97467943448089644"
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     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df.age.corr(df.income, method=\"spearman\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "除了相关性的计算外，还可以通过 `rank` 函数求出数据的排名顺序。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:40.805452Z",
     "start_time": "2018-07-09T12:55:40.736268Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "name\n",
       "Tom      1.0\n",
       "Bob      5.0\n",
       "Mary     2.5\n",
       "James    2.5\n",
       "Andy     4.0\n",
       "Alice    NaN\n",
       "Name: income, dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.income.rank()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果有相同的数，默认取其排名的平均值作为值。我们可以设置参数来得到不同的结果。可以设置的参数有：`min`、`max`、`first`、`dense`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:40.833527Z",
     "start_time": "2018-07-09T12:55:40.808460Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "name\n",
       "Tom      1.0\n",
       "Bob      5.0\n",
       "Mary     2.0\n",
       "James    3.0\n",
       "Andy     4.0\n",
       "Alice    NaN\n",
       "Name: income, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.income.rank(method=\"first\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 窗口函数\n",
    "\n",
    "有的时候，我们需要对不同窗口的中数据进行一个统计，常见的窗口类型为时间窗口。\n",
    "\n",
    "例如，下面是某个餐厅 7 天的营业额，我们想要计算每两天的收入总额，如何计算呢?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:40.897697Z",
     "start_time": "2018-07-09T12:55:40.837538Z"
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   "outputs": [
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       "      <th>1</th>\n",
       "      <td>2018-07-02</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2018-07-03</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2018-07-04</td>\n",
       "      <td>12000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2018-07-05</td>\n",
       "      <td>9000.0</td>\n",
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       "      <th>5</th>\n",
       "      <td>2018-07-06</td>\n",
       "      <td>16000.0</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2018-07-07</td>\n",
       "      <td>18000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "        date  turnover\n",
       "0 2018-07-01   12000.0\n",
       "1 2018-07-02   18000.0\n",
       "2 2018-07-03       NaN\n",
       "3 2018-07-04   12000.0\n",
       "4 2018-07-05    9000.0\n",
       "5 2018-07-06   16000.0\n",
       "6 2018-07-07   18000.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = {\n",
    "    \"turnover\": [12000, 18000, np.nan, 12000, 9000, 16000, 18000],\n",
    "    \"date\": pd.date_range(\"2018-07-01\", periods=7)\n",
    "}\n",
    "\n",
    "df2 = pd.DataFrame(data=data)\n",
    "df2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过 `rolling` 我们可以实现，设置 `window=2` 来保证窗口长度为 2，设置 `on=\"date\"` 来保证根据日期这一列来滑动窗口（默认不设置，表示根据索引来滑动）"
   ]
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   "execution_count": 10,
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       "      <th>1</th>\n",
       "      <td>2018-07-02</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2018-07-03</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2018-07-04</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2018-07-05</td>\n",
       "      <td>21000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2018-07-06</td>\n",
       "      <td>25000.0</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2018-07-07</td>\n",
       "      <td>34000.0</td>\n",
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      "text/plain": [
       "        date  turnover\n",
       "0 2018-07-01       NaN\n",
       "1 2018-07-02   30000.0\n",
       "2 2018-07-03       NaN\n",
       "3 2018-07-04       NaN\n",
       "4 2018-07-05   21000.0\n",
       "5 2018-07-06   25000.0\n",
       "6 2018-07-07   34000.0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df2.rolling(window=2, on=\"date\").sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "是不是发现，有很多结果是缺失值，导致这个结果的原因是因为在计算时，窗口中默认需要的最小数据个数与窗口长度一致，这里可以设置 `min_periods=1` 来修改下。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
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       "      <td>12000.0</td>\n",
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       "      <th>4</th>\n",
       "      <td>2018-07-05</td>\n",
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      "text/plain": [
       "        date  turnover\n",
       "0 2018-07-01   12000.0\n",
       "1 2018-07-02   30000.0\n",
       "2 2018-07-03   18000.0\n",
       "3 2018-07-04   12000.0\n",
       "4 2018-07-05   21000.0\n",
       "5 2018-07-06   25000.0\n",
       "6 2018-07-07   34000.0"
      ]
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     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df2.rolling(window=2, on=\"date\", min_periods=1).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "有时候，我想要计算每段时间的累加和，如何实现呢？先来看看第一种方式吧。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:41.056118Z",
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       "      <td>12000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2018-07-02</td>\n",
       "      <td>30000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2018-07-03</td>\n",
       "      <td>30000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2018-07-04</td>\n",
       "      <td>42000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2018-07-05</td>\n",
       "      <td>51000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2018-07-06</td>\n",
       "      <td>67000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2018-07-07</td>\n",
       "      <td>85000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        date  turnover\n",
       "0 2018-07-01   12000.0\n",
       "1 2018-07-02   30000.0\n",
       "2 2018-07-03   30000.0\n",
       "3 2018-07-04   42000.0\n",
       "4 2018-07-05   51000.0\n",
       "5 2018-07-06   67000.0\n",
       "6 2018-07-07   85000.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.rolling(window=len(df2), on=\"date\", min_periods=1).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "还有另外一种方式，直接使用 `expanding` 来生成窗口。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:41.092215Z",
     "start_time": "2018-07-09T12:55:41.060130Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    12000.0\n",
       "1    30000.0\n",
       "2    30000.0\n",
       "3    42000.0\n",
       "4    51000.0\n",
       "5    67000.0\n",
       "6    85000.0\n",
       "Name: turnover, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.expanding(min_periods=1)[\"turnover\"].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "除了可以使用 `sum` 函数外，还有很多其他的函数可以使用，如：`count`、`mean`、`median`、`min`、`max`、`std`、`var`、`quantile`、`apply`、`cov`、`corr`等等。\n",
    "\n",
    "|方法|描述|\n",
    "|:--:|:--:|\n",
    "|count()|非空观测值数量|\n",
    "|sum()|值的总和|\n",
    "|mean()|价值的平均值|\n",
    "|median()|值的算术中值|\n",
    "|min()|最小值|\n",
    "|max()|最大|\n",
    "|std()|贝塞尔修正样本标准差|\n",
    "|var()|无偏方差|\n",
    "|skew()|样品偏斜度（三阶矩）|\n",
    "|kurt()|样品峰度（四阶矩）|\n",
    "|quantile()|样本分位数（百分位上的值）|\n",
    "|apply()|通用适用|\n",
    "|cov()|无偏协方差（二元）|\n",
    "|corr()|相关（二进制）|\n",
    "\n",
    "不过上面的方式只能生成一个结果，有时候想要同时求出多个结果（如求和和均值），如何实现呢？\n",
    "\n",
    "借助 `agg` 函数可以快速实现。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:41.158391Z",
     "start_time": "2018-07-09T12:55:41.098231Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sum</th>\n",
       "      <th>mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12000.0</td>\n",
       "      <td>12000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30000.0</td>\n",
       "      <td>15000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18000.0</td>\n",
       "      <td>18000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12000.0</td>\n",
       "      <td>12000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21000.0</td>\n",
       "      <td>10500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>25000.0</td>\n",
       "      <td>12500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>34000.0</td>\n",
       "      <td>17000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       sum     mean\n",
       "0  12000.0  12000.0\n",
       "1  30000.0  15000.0\n",
       "2  18000.0  18000.0\n",
       "3  12000.0  12000.0\n",
       "4  21000.0  10500.0\n",
       "5  25000.0  12500.0\n",
       "6  34000.0  17000.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.rolling(window=2, min_periods=1)[\"turnover\"].agg([np.sum, np.mean])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果传入一个字典，可以为生成的统计结果重命名。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-09T12:55:41.184460Z",
     "start_time": "2018-07-09T12:55:41.162402Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>tur_sum</th>\n",
       "      <th>tur_mean</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12000.0</td>\n",
       "      <td>12000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30000.0</td>\n",
       "      <td>15000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18000.0</td>\n",
       "      <td>18000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>12000.0</td>\n",
       "      <td>12000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>21000.0</td>\n",
       "      <td>10500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>25000.0</td>\n",
       "      <td>12500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>34000.0</td>\n",
       "      <td>17000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   tur_sum  tur_mean\n",
       "0  12000.0   12000.0\n",
       "1  30000.0   15000.0\n",
       "2  18000.0   18000.0\n",
       "3  12000.0   12000.0\n",
       "4  21000.0   10500.0\n",
       "5  25000.0   12500.0\n",
       "6  34000.0   17000.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.rolling(window=2, min_periods=1)[\"turnover\"].agg({\"tur_sum\": np.sum, \"tur_mean\": np.mean})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------\n",
    "\n",
    "\n",
    "想要学习更多关于人工智能的知识，请关注公众号：**AI派**\n",
    "\n",
    "![qrcode_for_gh_60cef389e81c_258.jpg](http://www.naodongopen.com/wp-content/uploads/2018/06/qrcode_for_gh_60cef389e81c_258.jpg)\n",
    "\n",
    "这里我将整篇文章的内容整理成了pdf，想要pdf文件的可以在公众号后台回复关键字：**pandas**。"
   ]
  }
 ],
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