Numpy と Pandas を用いた演算.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numpy と Pandas を用いた演算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 数値計算やデータフレーム操作に関するライブラリをインポートする\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## まずは Pandas の基本操作から"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = pd.DataFrame([[1,4,7,10,13,16],[2,5,8,11,14,17],[3,6,9,12,15,18],[21,24,27,20,23,26]],\n",
    "                   index = ['i1','i2','i3', 'i4'],\n",
    "                   columns = list(\"abcdef\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
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       "     a   b   c   d   e   f\n",
       "i1   1   4   7  10  13  16\n",
       "i2   2   5   8  11  14  17\n",
       "i3   3   6   9  12  15  18\n",
       "i4  21  24  27  20  23  26"
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   "source": [
    "df"
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "a     1\n",
       "b     4\n",
       "c     7\n",
       "d    10\n",
       "e    13\n",
       "f    16\n",
       "Name: i1, dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# インデックス名を指定した行の取り出し。\n",
    "df.ix['i1']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
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   "outputs": [
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       "a     2\n",
       "b     5\n",
       "c     8\n",
       "d    11\n",
       "e    14\n",
       "f    17\n",
       "Name: i2, dtype: int64"
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "# インデックス番号を指定した行の取り出し\n",
    "df.ix[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
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   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a</th>\n",
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       "     a   b   c   d   e   f\n",
       "i2   2   5   8  11  14  17\n",
       "i3   3   6   9  12  15  18\n",
       "i4  21  24  27  20  23  26"
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   "source": [
    "# インデックス番号を指定した行の取り出し\n",
    "df.ix[1:] # （ゼロスタートで）１行目以降を取り出す"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
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      "text/plain": [
       "    a  b  c   d   e   f\n",
       "i1  1  4  7  10  13  16"
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "# インデックス番号を指定した行の取り出し\n",
    "df.ix[:1] # （ゼロスタートで）１行目より手前を取り出す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
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   "outputs": [
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      "text/plain": [
       "    a  b  c   d   e   f\n",
       "i2  2  5  8  11  14  17\n",
       "i3  3  6  9  12  15  18"
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     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# インデックス番号を指定した行の取り出し\n",
    "df.ix[1:3] # （ゼロスタートで）１行目から、３行目の手前までを取り出す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 一つ目のパラメータで行を、二つ目のパラメータで列を指定して取り出す\n",
    "df.ix['i3','b']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "i1     1\n",
       "i2     2\n",
       "i3     3\n",
       "i4    21\n",
       "Name: a, dtype: int64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# : は全指定の意味\n",
    "df.ix[:, 'a']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>b</th>\n",
       "      <th>d</th>\n",
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       "  </thead>\n",
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      "text/plain": [
       "     b   d\n",
       "i2   5  11\n",
       "i4  24  20"
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     "execution_count": 11,
     "metadata": {},
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   ],
   "source": [
    "# 複数の指定も可能。飛び飛びの指定も可能。\n",
    "# 番号での指定も名前での指定も可能。\n",
    "df.ix[[1,3], ['b','d']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "i1     1\n",
       "i2     2\n",
       "i3     3\n",
       "i4    21\n",
       "Name: a, dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 列に関する操作は[カラム名]で渡す。\n",
    "df['a']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3, 21])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# arrayとして取得する。\n",
    "df['a'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# さらにindex名を指定することで値として取得できる。\n",
    "df['a']['i3']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# DataFrameをtableとみなして、位置指定から値を明示的に取る方法。\n",
    "df.iloc[2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# これも同じ\n",
    "df.ix[2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a     3\n",
       "b     6\n",
       "c     9\n",
       "d    12\n",
       "e    15\n",
       "f    18\n",
       "Name: i3, dtype: int64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行の取得\n",
    "df.iloc[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>c</th>\n",
       "      <th>d</th>\n",
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       "     c   d\n",
       "i1   7  10\n",
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       "i3   9  12\n",
       "i4  27  20"
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     "execution_count": 18,
     "metadata": {},
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   "source": [
    "# 複数の列の取得\n",
    "df.iloc[:, 2:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numpy で生成した乱数を Pandas で使う"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df1 = pd.DataFrame(np.random.randint(10, size=(4,5)))"
   ]
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  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
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    "df1"
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    0   1   2   3  4\n",
       "0 NaN   2   9   4  4\n",
       "1   2   9   8   5  4\n",
       "2   8   5 NaN NaN  2\n",
       "3   9 NaN   4 NaN  9"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 条件を満たすものだけを抽出\n",
    "df1[df1>1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# # 条件をみたすものに-1を代入\n",
    "df1[df1>5] = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "   0  1  2  3  4\n",
       "0  1  2 -1  4  4\n",
       "1  2 -1 -1  5  4\n",
       "2 -1  5  0  1  2\n",
       "3 -1  1  4  1 -1"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 欠損値を含むデータを取り扱う"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 欠損値 (NaN) を含むランダムデータを作成する\n",
    "df2 = pd.DataFrame(np.random.randint(10, size=(8,7)))\n",
    "df2 = df2[df2>0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
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       "   0   1  2   3   4   5  6\n",
       "0  8   4  1   8   5   1  2\n",
       "1  1 NaN  9   4   2 NaN  3\n",
       "2  8   4  9   3   5   2  2\n",
       "3  5   7  6 NaN   6   2  8\n",
       "4  6   6  5   1   4   2  4\n",
       "5  4   3  9   8 NaN   4  7\n",
       "6  3 NaN  1   9 NaN   9  7\n",
       "7  3   7  6   6   2   2  2"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>4</td>\n",
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       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3  4  5  6\n",
       "0  8  4  1  8  5  1  2\n",
       "2  8  4  9  3  5  2  2\n",
       "4  6  6  5  1  4  2  4\n",
       "7  3  7  6  6  2  2  2"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NaNを含む行を削除\n",
    "df2.dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
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       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  2  6\n",
       "0  8  1  2\n",
       "1  1  9  3\n",
       "2  8  9  2\n",
       "3  5  6  8\n",
       "4  6  5  4\n",
       "5  4  9  7\n",
       "6  3  1  7\n",
       "7  3  6  2"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NaNを含む列を削除\n",
    "df2.dropna(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
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       "      <td>8</td>\n",
       "      <td>-1</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
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       "      <td>3</td>\n",
       "      <td>-1</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>-1</td>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3  4  5  6\n",
       "0  8  4  1  8  5  1  2\n",
       "1  1 -1  9  4  2 -1  3\n",
       "2  8  4  9  3  5  2  2\n",
       "3  5  7  6 -1  6  2  8\n",
       "4  6  6  5  1  4  2  4\n",
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       "6  3 -1  1  9 -1  9  7\n",
       "7  3  7  6  6  2  2  2"
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     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NaNを埋める\n",
    "df2.fillna(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3  4  5  6\n",
       "0  8  4  1  8  5  1  2\n",
       "1  1  4  9  4  2  1  3\n",
       "2  8  4  9  3  5  2  2\n",
       "3  5  7  6  3  6  2  8\n",
       "4  6  6  5  1  4  2  4\n",
       "5  4  3  9  8  4  4  7\n",
       "6  3  3  1  9  4  9  7\n",
       "7  3  7  6  6  2  2  2"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#直前の値で埋める\n",
    "df2.fillna(method='pad')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
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       "      <td>4</td>\n",
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       "      <td>4</td>\n",
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       "      <th>2</th>\n",
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       "      <td>2</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
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       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3  4  5  6\n",
       "0  8  4  1  8  5  1  2\n",
       "1  1  4  9  4  2  2  3\n",
       "2  8  4  9  3  5  2  2\n",
       "3  5  7  6  1  6  2  8\n",
       "4  6  6  5  1  4  2  4\n",
       "5  4  3  9  8  2  4  7\n",
       "6  3  7  1  9  2  9  7\n",
       "7  3  7  6  6  2  2  2"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#直後の値で埋める\n",
    "df2.fillna(method='bfill')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <tr style=\"text-align: right;\">\n",
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       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>4</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.5</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>3</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>3.333333</td>\n",
       "      <td>4.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>2.666667</td>\n",
       "      <td>9.0</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3         4    5  6\n",
       "0  8  4  1  8  5.000000  1.0  2\n",
       "1  1  4  9  4  2.000000  1.5  3\n",
       "2  8  4  9  3  5.000000  2.0  2\n",
       "3  5  7  6  2  6.000000  2.0  8\n",
       "4  6  6  5  1  4.000000  2.0  4\n",
       "5  4  3  9  8  3.333333  4.0  7\n",
       "6  3  5  1  9  2.666667  9.0  7\n",
       "7  3  7  6  6  2.000000  2.0  2"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# misssing valueの前後の線形の値で埋める\n",
    "df2.apply(pd.Series.interpolate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 重複のあるデータを取り扱う"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df3 = pd.DataFrame(np.random.randint(2, size=(10,4)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3\n",
       "0  0  0  0  0\n",
       "1  1  1  0  0\n",
       "2  0  1  0  1\n",
       "3  1  0  0  0\n",
       "4  0  1  0  0\n",
       "5  1  1  1  1\n",
       "6  0  0  0  1\n",
       "7  0  0  0  0\n",
       "8  1  0  0  0\n",
       "9  1  0  1  0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "2    False\n",
       "3    False\n",
       "4    False\n",
       "5    False\n",
       "6    False\n",
       "7     True\n",
       "8     True\n",
       "9    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 重複を調べる\n",
    "df3.duplicated()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    False\n",
       "1    False\n",
       "2     True\n",
       "3     True\n",
       "4     True\n",
       "5     True\n",
       "6     True\n",
       "7     True\n",
       "8     True\n",
       "9     True\n",
       "dtype: bool"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 重複を調査するcolumnを指定することも可能\n",
    "df3.duplicated(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
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       "      <th>0</th>\n",
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       "      <th>3</th>\n",
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       "    <tr>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3\n",
       "0  0  0  0  0\n",
       "1  1  1  0  0\n",
       "2  0  1  0  1\n",
       "3  1  0  0  0\n",
       "4  0  1  0  0\n",
       "5  1  1  1  1\n",
       "6  0  0  0  1\n",
       "9  1  0  1  0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 重複を除去する\n",
    "df3.drop_duplicates()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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      "text/plain": [
       "   0  1  2  3\n",
       "0  0  0  0  0\n",
       "1  1  1  0  0"
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     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 指定した列の重複を除去する\n",
    "df3.drop_duplicates(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
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       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3\n",
       "7  0  0  0  0\n",
       "9  1  0  1  0"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 指定した列の重複を除去し最後のを残す\n",
    "df3.drop_duplicates(0, take_last=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 行列演算を行う"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = pd.DataFrame(np.random.randint(10, size=(2,2)))\n",
    "B = pd.DataFrame(np.random.randint(10, size=(2,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1\n",
       "0  4  4\n",
       "1  3  6"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1\n",
       "0  6  3\n",
       "1  1  5"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1\n",
       "0  4  3\n",
       "1  4  6"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行列の転置\n",
    "A.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1\n",
       "0  6  1\n",
       "1  3  5"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行列の転置\n",
    "B.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    0   1\n",
       "0  10   7\n",
       "1   4  11"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行列の要素ごとの和\n",
    "A + B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>24</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    0   1\n",
       "0  24  12\n",
       "1   3  30"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行列の要素ごとの積（「行列の積」ではない）\n",
    "A * B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>28</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>24</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    0   1\n",
       "0  28  32\n",
       "1  24  39"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行列の積をとりたい場合は DataFrame.dot。ただし、行列の積をとるためには元データの columns と 引数の index のラベルが一致している必要がある\n",
    "A.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>33</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>19</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    0   1\n",
       "0  33  42\n",
       "1  19  34"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.dot(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 簡単な統計量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df4 = pd.DataFrame(np.random.randint(10, size=(5,10)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
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       "  <tbody>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
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       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
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       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0  1  2  3  4  5  6  7  8  9\n",
       "0  7  5  5  9  4  8  6  4  4  5\n",
       "1  8  6  0  9  9  5  0  9  6  3\n",
       "2  1  8  2  0  1  5  7  1  2  4\n",
       "3  1  3  3  5  2  2  6  6  0  2\n",
       "4  1  8  3  2  1  8  6  1  7  0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
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       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.600000</td>\n",
       "      <td>6.00000</td>\n",
       "      <td>2.60000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>3.400000</td>\n",
       "      <td>5.60000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>4.200000</td>\n",
       "      <td>3.800000</td>\n",
       "      <td>2.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>3.577709</td>\n",
       "      <td>2.12132</td>\n",
       "      <td>1.81659</td>\n",
       "      <td>4.062019</td>\n",
       "      <td>3.361547</td>\n",
       "      <td>2.50998</td>\n",
       "      <td>2.828427</td>\n",
       "      <td>3.420526</td>\n",
       "      <td>2.863564</td>\n",
       "      <td>1.923538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.00000</td>\n",
       "      <td>0.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.00000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>2.00000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.00000</td>\n",
       "      <td>3.00000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.000000</td>\n",
       "      <td>8.00000</td>\n",
       "      <td>3.00000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>8.00000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>4.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>8.000000</td>\n",
       "      <td>8.00000</td>\n",
       "      <td>5.00000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>8.00000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              0        1        2         3         4        5         6  \\\n",
       "count  5.000000  5.00000  5.00000  5.000000  5.000000  5.00000  5.000000   \n",
       "mean   3.600000  6.00000  2.60000  5.000000  3.400000  5.60000  5.000000   \n",
       "std    3.577709  2.12132  1.81659  4.062019  3.361547  2.50998  2.828427   \n",
       "min    1.000000  3.00000  0.00000  0.000000  1.000000  2.00000  0.000000   \n",
       "25%    1.000000  5.00000  2.00000  2.000000  1.000000  5.00000  6.000000   \n",
       "50%    1.000000  6.00000  3.00000  5.000000  2.000000  5.00000  6.000000   \n",
       "75%    7.000000  8.00000  3.00000  9.000000  4.000000  8.00000  6.000000   \n",
       "max    8.000000  8.00000  5.00000  9.000000  9.000000  8.00000  7.000000   \n",
       "\n",
       "              7         8         9  \n",
       "count  5.000000  5.000000  5.000000  \n",
       "mean   4.200000  3.800000  2.800000  \n",
       "std    3.420526  2.863564  1.923538  \n",
       "min    1.000000  0.000000  0.000000  \n",
       "25%    1.000000  2.000000  2.000000  \n",
       "50%    4.000000  4.000000  3.000000  \n",
       "75%    6.000000  6.000000  4.000000  \n",
       "max    9.000000  7.000000  5.000000  "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 基本統計量の表示\n",
    "df4.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    18\n",
       "1    30\n",
       "2    13\n",
       "3    25\n",
       "4    17\n",
       "5    28\n",
       "6    25\n",
       "7    21\n",
       "8    19\n",
       "9    14\n",
       "dtype: int64"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 列の合計値\n",
    "df4.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.6\n",
       "1    6.0\n",
       "2    2.6\n",
       "3    5.0\n",
       "4    3.4\n",
       "5    5.6\n",
       "6    5.0\n",
       "7    4.2\n",
       "8    3.8\n",
       "9    2.8\n",
       "dtype: float64"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 列の平均値\n",
    "df4.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    12.8\n",
       "1     4.5\n",
       "2     3.3\n",
       "3    16.5\n",
       "4    11.3\n",
       "5     6.3\n",
       "6     8.0\n",
       "7    11.7\n",
       "8     8.2\n",
       "9     3.7\n",
       "dtype: float64"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 列の不偏分散\n",
    "df4.var()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    10.24\n",
       "1     3.60\n",
       "2     2.64\n",
       "3    13.20\n",
       "4     9.04\n",
       "5     5.04\n",
       "6     6.40\n",
       "7     9.36\n",
       "8     6.56\n",
       "9     2.96\n",
       "dtype: float64"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 列の標本分散\n",
    "df4.var(ddof=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.577709\n",
       "1    2.121320\n",
       "2    1.816590\n",
       "3    4.062019\n",
       "4    3.361547\n",
       "5    2.509980\n",
       "6    2.828427\n",
       "7    3.420526\n",
       "8    2.863564\n",
       "9    1.923538\n",
       "dtype: float64"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 列の不偏標準偏差\n",
    "df4.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3.200000\n",
       "1    1.897367\n",
       "2    1.624808\n",
       "3    3.633180\n",
       "4    3.006659\n",
       "5    2.244994\n",
       "6    2.529822\n",
       "7    3.059412\n",
       "8    2.561250\n",
       "9    1.720465\n",
       "dtype: float64"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 列の標本標準偏差\n",
    "df4.std(ddof=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    57\n",
       "1    55\n",
       "2    31\n",
       "3    30\n",
       "4    37\n",
       "dtype: int64"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行の合計値\n",
    "df4.sum(axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    5.7\n",
       "1    5.5\n",
       "2    3.1\n",
       "3    3.0\n",
       "4    3.7\n",
       "dtype: float64"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行の平均値\n",
    "df4.mean(axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 行列の正規化（標準化）\n",
    "\n",
    "正規化 (normalize) とは、異なる基準のデータを一定の基準にしたがって変形し利用しやすくすることです。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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     "execution_count": 59,
     "metadata": {},
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   "source": [
    "df4"
   ]
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  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "      <td>-0.628587</td>\n",
       "      <td>0.623850</td>\n",
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       "      <th>3</th>\n",
       "      <td>-0.726722</td>\n",
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       "      <td>-0.415900</td>\n",
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       "      <th>4</th>\n",
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      "text/plain": [
       "          0         1         2         3         4         5         6  \\\n",
       "0  0.950329 -0.471405  1.321157  0.984732  0.178489  0.956183  0.353553   \n",
       "1  1.229837  0.000000 -1.431253  0.984732  1.665900 -0.239046 -1.767767   \n",
       "2 -0.726722  0.942809 -0.330289 -1.230915 -0.713957 -0.239046  0.707107   \n",
       "3 -0.726722 -1.414214  0.220193  0.000000 -0.416475 -1.434274  0.353553   \n",
       "4 -0.726722  0.942809  0.220193 -0.738549 -0.713957  0.956183  0.353553   \n",
       "\n",
       "          7         8         9  \n",
       "0 -0.058471  0.069843  1.143726  \n",
       "1  1.403293  0.768273  0.103975  \n",
       "2 -0.935529 -0.628587  0.623850  \n",
       "3  0.526235 -1.327018 -0.415900  \n",
       "4 -0.935529  1.117488 -1.455651  "
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 一般的には平均 0 、分散 (及び標準偏差) が 1 になるように値を変換することを指します。\n",
    "df4.apply(lambda x: (x-x.mean())/x.std(), axis=0).fillna(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "          0    1    2         3      4    5         6      7         8    9\n",
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       "1  1.000000  0.6  0.0  1.000000  1.000  0.5  0.000000  1.000  0.857143  0.6\n",
       "2  0.000000  1.0  0.4  0.000000  0.000  0.5  1.000000  0.000  0.285714  0.8\n",
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       "4  0.000000  1.0  0.6  0.222222  0.000  1.0  0.857143  0.000  1.000000  0.0"
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     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 最大値を1、最小値を0にするような正規化もできます。\n",
    "df4.apply(lambda x: (x-x.min())/(x.max() - x.min()), axis=0).fillna(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.444444</td>\n",
       "      <td>0.200000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.36</td>\n",
       "      <td>0.529412</td>\n",
       "      <td>0.178571</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.428571</td>\n",
       "      <td>0.315789</td>\n",
       "      <td>0.214286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.055556</td>\n",
       "      <td>0.266667</td>\n",
       "      <td>0.153846</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.058824</td>\n",
       "      <td>0.178571</td>\n",
       "      <td>0.28</td>\n",
       "      <td>0.047619</td>\n",
       "      <td>0.105263</td>\n",
       "      <td>0.285714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.055556</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.230769</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.117647</td>\n",
       "      <td>0.071429</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.285714</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.142857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.055556</td>\n",
       "      <td>0.266667</td>\n",
       "      <td>0.230769</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.058824</td>\n",
       "      <td>0.285714</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.047619</td>\n",
       "      <td>0.368421</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2     3         4         5     6         7  \\\n",
       "0  0.388889  0.166667  0.384615  0.36  0.235294  0.285714  0.24  0.190476   \n",
       "1  0.444444  0.200000  0.000000  0.36  0.529412  0.178571  0.00  0.428571   \n",
       "2  0.055556  0.266667  0.153846  0.00  0.058824  0.178571  0.28  0.047619   \n",
       "3  0.055556  0.100000  0.230769  0.20  0.117647  0.071429  0.24  0.285714   \n",
       "4  0.055556  0.266667  0.230769  0.08  0.058824  0.285714  0.24  0.047619   \n",
       "\n",
       "          8         9  \n",
       "0  0.210526  0.357143  \n",
       "1  0.315789  0.214286  \n",
       "2  0.105263  0.285714  \n",
       "3  0.000000  0.142857  \n",
       "4  0.368421  0.000000  "
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 合計値が１になるような正規化もできます。\n",
    "df4.apply(lambda x: x/x.sum(), axis=0).fillna(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 相関行列\n",
    "\n",
    "相関行列とは、各要素間の相関係数を並べたものであり、その性質から必ず対称行列である。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# まずランダムな行列を作ってみる\n",
    "df5 = pd.DataFrame(np.random.rand(5, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.226256</td>\n",
       "      <td>0.179995</td>\n",
       "      <td>0.501218</td>\n",
       "      <td>0.042712</td>\n",
       "      <td>0.518461</td>\n",
       "      <td>0.250401</td>\n",
       "      <td>0.538263</td>\n",
       "      <td>0.277074</td>\n",
       "      <td>0.381640</td>\n",
       "      <td>0.206244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.058678</td>\n",
       "      <td>0.581003</td>\n",
       "      <td>0.778982</td>\n",
       "      <td>0.003519</td>\n",
       "      <td>0.347807</td>\n",
       "      <td>0.707787</td>\n",
       "      <td>0.521578</td>\n",
       "      <td>0.328937</td>\n",
       "      <td>0.394446</td>\n",
       "      <td>0.817811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.626644</td>\n",
       "      <td>0.040506</td>\n",
       "      <td>0.117516</td>\n",
       "      <td>0.857788</td>\n",
       "      <td>0.701137</td>\n",
       "      <td>0.275158</td>\n",
       "      <td>0.807031</td>\n",
       "      <td>0.518195</td>\n",
       "      <td>0.981660</td>\n",
       "      <td>0.825709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.204449</td>\n",
       "      <td>0.719918</td>\n",
       "      <td>0.911821</td>\n",
       "      <td>0.955502</td>\n",
       "      <td>0.270247</td>\n",
       "      <td>0.281635</td>\n",
       "      <td>0.148356</td>\n",
       "      <td>0.671398</td>\n",
       "      <td>0.441276</td>\n",
       "      <td>0.380514</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.083750</td>\n",
       "      <td>0.181657</td>\n",
       "      <td>0.208537</td>\n",
       "      <td>0.896279</td>\n",
       "      <td>0.705320</td>\n",
       "      <td>0.808194</td>\n",
       "      <td>0.221535</td>\n",
       "      <td>0.217418</td>\n",
       "      <td>0.090762</td>\n",
       "      <td>0.379003</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6  \\\n",
       "0  0.226256  0.179995  0.501218  0.042712  0.518461  0.250401  0.538263   \n",
       "1  0.058678  0.581003  0.778982  0.003519  0.347807  0.707787  0.521578   \n",
       "2  0.626644  0.040506  0.117516  0.857788  0.701137  0.275158  0.807031   \n",
       "3  0.204449  0.719918  0.911821  0.955502  0.270247  0.281635  0.148356   \n",
       "4  0.083750  0.181657  0.208537  0.896279  0.705320  0.808194  0.221535   \n",
       "\n",
       "          7         8         9  \n",
       "0  0.277074  0.381640  0.206244  \n",
       "1  0.328937  0.394446  0.817811  \n",
       "2  0.518195  0.981660  0.825709  \n",
       "3  0.671398  0.441276  0.380514  \n",
       "4  0.217418  0.090762  0.379003  "
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.331614</td>\n",
       "      <td>0.008597</td>\n",
       "      <td>-0.361545</td>\n",
       "      <td>-0.282089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.331614</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.438151</td>\n",
       "      <td>-0.057235</td>\n",
       "      <td>-0.123217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.008597</td>\n",
       "      <td>-0.438151</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.345468</td>\n",
       "      <td>0.090937</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.361545</td>\n",
       "      <td>-0.057235</td>\n",
       "      <td>-0.345468</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.104524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.282089</td>\n",
       "      <td>-0.123217</td>\n",
       "      <td>0.090937</td>\n",
       "      <td>0.104524</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4\n",
       "0  1.000000  0.331614  0.008597 -0.361545 -0.282089\n",
       "1  0.331614  1.000000 -0.438151 -0.057235 -0.123217\n",
       "2  0.008597 -0.438151  1.000000 -0.345468  0.090937\n",
       "3 -0.361545 -0.057235 -0.345468  1.000000  0.104524\n",
       "4 -0.282089 -0.123217  0.090937  0.104524  1.000000"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 行間の相関行列\n",
    "pd.DataFrame(np.corrcoef(df5.dropna().as_matrix().tolist()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.546697</td>\n",
       "      <td>-0.530846</td>\n",
       "      <td>0.354762</td>\n",
       "      <td>0.446902</td>\n",
       "      <td>-0.654766</td>\n",
       "      <td>0.700749</td>\n",
       "      <td>0.461793</td>\n",
       "      <td>0.924027</td>\n",
       "      <td>0.370019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.546697</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.948513</td>\n",
       "      <td>-0.076822</td>\n",
       "      <td>-0.942433</td>\n",
       "      <td>0.081172</td>\n",
       "      <td>-0.584482</td>\n",
       "      <td>0.450873</td>\n",
       "      <td>-0.285252</td>\n",
       "      <td>-0.000772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.530846</td>\n",
       "      <td>0.948513</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.306073</td>\n",
       "      <td>-0.994661</td>\n",
       "      <td>-0.094762</td>\n",
       "      <td>-0.472527</td>\n",
       "      <td>0.383875</td>\n",
       "      <td>-0.263352</td>\n",
       "      <td>-0.129336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.354762</td>\n",
       "      <td>-0.076822</td>\n",
       "      <td>-0.306073</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.295043</td>\n",
       "      <td>-0.072207</td>\n",
       "      <td>-0.340681</td>\n",
       "      <td>0.507647</td>\n",
       "      <td>0.160830</td>\n",
       "      <td>-0.027219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.446902</td>\n",
       "      <td>-0.942433</td>\n",
       "      <td>-0.994661</td>\n",
       "      <td>0.295043</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.155644</td>\n",
       "      <td>0.401186</td>\n",
       "      <td>-0.452233</td>\n",
       "      <td>0.163044</td>\n",
       "      <td>0.059461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.654766</td>\n",
       "      <td>0.081172</td>\n",
       "      <td>-0.094762</td>\n",
       "      <td>-0.072207</td>\n",
       "      <td>0.155644</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.321037</td>\n",
       "      <td>-0.618987</td>\n",
       "      <td>-0.632376</td>\n",
       "      <td>0.192210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.700749</td>\n",
       "      <td>-0.584482</td>\n",
       "      <td>-0.472527</td>\n",
       "      <td>-0.340681</td>\n",
       "      <td>0.401186</td>\n",
       "      <td>-0.321037</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.069271</td>\n",
       "      <td>0.767520</td>\n",
       "      <td>0.587976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.461793</td>\n",
       "      <td>0.450873</td>\n",
       "      <td>0.383875</td>\n",
       "      <td>0.507647</td>\n",
       "      <td>-0.452233</td>\n",
       "      <td>-0.618987</td>\n",
       "      <td>-0.069271</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.568691</td>\n",
       "      <td>0.194874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.924027</td>\n",
       "      <td>-0.285252</td>\n",
       "      <td>-0.263352</td>\n",
       "      <td>0.160830</td>\n",
       "      <td>0.163044</td>\n",
       "      <td>-0.632376</td>\n",
       "      <td>0.767520</td>\n",
       "      <td>0.568691</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.598632</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.370019</td>\n",
       "      <td>-0.000772</td>\n",
       "      <td>-0.129336</td>\n",
       "      <td>-0.027219</td>\n",
       "      <td>0.059461</td>\n",
       "      <td>0.192210</td>\n",
       "      <td>0.587976</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.598632</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6  \\\n",
       "0  1.000000 -0.546697 -0.530846  0.354762  0.446902 -0.654766  0.700749   \n",
       "1 -0.546697  1.000000  0.948513 -0.076822 -0.942433  0.081172 -0.584482   \n",
       "2 -0.530846  0.948513  1.000000 -0.306073 -0.994661 -0.094762 -0.472527   \n",
       "3  0.354762 -0.076822 -0.306073  1.000000  0.295043 -0.072207 -0.340681   \n",
       "4  0.446902 -0.942433 -0.994661  0.295043  1.000000  0.155644  0.401186   \n",
       "5 -0.654766  0.081172 -0.094762 -0.072207  0.155644  1.000000 -0.321037   \n",
       "6  0.700749 -0.584482 -0.472527 -0.340681  0.401186 -0.321037  1.000000   \n",
       "7  0.461793  0.450873  0.383875  0.507647 -0.452233 -0.618987 -0.069271   \n",
       "8  0.924027 -0.285252 -0.263352  0.160830  0.163044 -0.632376  0.767520   \n",
       "9  0.370019 -0.000772 -0.129336 -0.027219  0.059461  0.192210  0.587976   \n",
       "\n",
       "          7         8         9  \n",
       "0  0.461793  0.924027  0.370019  \n",
       "1  0.450873 -0.285252 -0.000772  \n",
       "2  0.383875 -0.263352 -0.129336  \n",
       "3  0.507647  0.160830 -0.027219  \n",
       "4 -0.452233  0.163044  0.059461  \n",
       "5 -0.618987 -0.632376  0.192210  \n",
       "6 -0.069271  0.767520  0.587976  \n",
       "7  1.000000  0.568691  0.194874  \n",
       "8  0.568691  1.000000  0.598632  \n",
       "9  0.194874  0.598632  1.000000  "
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 列間の相関行列\n",
    "pd.DataFrame(np.corrcoef(df5.dropna().T.as_matrix().tolist()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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