Juliaクックブック.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "srand(1234);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ベクトル(リスト)の処理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルを作る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0-element Array{Any,1}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = []  # 何でも入るリスト"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0-element Array{Int64,1}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = Int[]  # Int型のみのリスト"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0-element Array{Int64,1}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = Vector{Int}()  #　Int[]と同じ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,2,3]  # 3要素からなるリスト"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### すべて同じ値のベクトルを作る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Int64,1}:\n",
       " 42\n",
       " 42\n",
       " 42\n",
       " 42\n",
       " 42\n",
       " 42\n",
       " 42\n",
       " 42\n",
       " 42\n",
       " 42"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fill(42, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{String,1}:\n",
       " \"foo\"\n",
       " \"foo\"\n",
       " \"foo\"\n",
       " \"foo\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fill(\"foo\", 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルに要素を追加する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "push!(x, 4) # 右に追加"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Int64,1}:\n",
       " 0\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unshift!(x, 0)  # 左に追加"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8-element Array{Int64,1}:\n",
       " 0\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 5\n",
       " 6\n",
       " 7"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "append!(x, [5,6,7])  # 別のベクトルを追加"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルの要素を削除する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 5"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,2,3,4,5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pop!(x)  # 右端を削除"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shift!(x)  # 左端を削除"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 2\n",
       " 3\n",
       " 4"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Int64,1}:\n",
       " 2\n",
       " 4"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "deleteat!(x, 2)  # 特定の場所の要素を削除"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルがソート済みかを判定する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "issorted([1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "issorted([1,3,2,4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルをソートする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Array{Int64,1}:\n",
       " 1\n",
       " 5\n",
       " 4\n",
       " 3\n",
       " 7\n",
       " 6\n",
       " 2"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,5,4,3,7,6,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 5\n",
       " 6\n",
       " 7"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort(x)  # ベクトルを新しく作る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Array{Int64,1}:\n",
       " 7\n",
       " 6\n",
       " 5\n",
       " 4\n",
       " 3\n",
       " 2\n",
       " 1"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort(x, rev=true)  # 逆順でソート"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 5\n",
       " 6\n",
       " 7"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort!(x)  # ベクトルを上書きする"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルの要素を逆順にする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,2,3,4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       " 4\n",
       " 3\n",
       " 2\n",
       " 1"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reverse(x)  # ベクトルを新しく作る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == [1,2,3,4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Int64,1}:\n",
       " 4\n",
       " 3\n",
       " 2\n",
       " 1"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reverse!(x)  # ベクトルを上書きする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == [1,2,3,4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルをシャッフルする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 5\n",
       " 6"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1,2,3,4,5,6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{Int64,1}:\n",
       " 2\n",
       " 1\n",
       " 3\n",
       " 6\n",
       " 4\n",
       " 5"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shuffle(x)  # ベクトルを新しく作る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == [1,2,3,4,5,6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{Int64,1}:\n",
       " 6\n",
       " 1\n",
       " 5\n",
       " 2\n",
       " 3\n",
       " 4"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shuffle!(x)  # ベクトルを上書きする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == [1,2,3,4,5,6]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルを結合する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{Int64,1}:\n",
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 5\n",
       " 6"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vcat([1,2,3], [4,5,6])  # 縦方向 => ベクトル"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×2 Array{Int64,2}:\n",
       " 1  4\n",
       " 2  5\n",
       " 3  6"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hcat([1,2,3], [4,5,6])  # 横方向 => 行列"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 辞書"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 辞書を作る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{Any,Any} with 0 entries"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Dict()  # 何でも入る空の辞書"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Int64} with 0 entries"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Dict{String,Int}()  # Stringがキー、Intが値の空の辞書"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Int64} with 2 entries:\n",
       "  \"two\" => 2\n",
       "  \"one\" => 1"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Dict(\"one\" => 1, \"two\" => 2)  # 初期値のある辞書"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 辞書があるキーを持つか判定する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "haskey(Dict(\"one\" => 1, \"two\" => 2), \"two\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "haskey(Dict(\"one\" => 1), \"two\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 辞書の値を取り出す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Int64} with 2 entries:\n",
       "  \"two\" => 2\n",
       "  \"one\" => 1"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = Dict(\"one\" => 1, \"two\" => 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[\"one\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "\u001b[91mKeyError: key \"three\" not found\u001b[39m",
     "output_type": "error",
     "traceback": [
      "\u001b[91mKeyError: key \"three\" not found\u001b[39m",
      "",
      "Stacktrace:",
      " [1] \u001b[1mgetindex\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Dict{String,Int64}, ::String\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./dict.jl:474\u001b[22m\u001b[22m"
     ]
    }
   ],
   "source": [
    "d[\"three\"]  # キーがなければエラー"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### デフォルト値を設定して辞書の値を取り出す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Int64} with 2 entries:\n",
       "  \"two\" => 2\n",
       "  \"one\" => 1"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = Dict(\"one\" => 1, \"two\" => 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get(d, \"one\", 0)  # 第三引数がデフォルト値"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get(d, \"three\", 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 辞書に値を代入する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Int64} with 2 entries:\n",
       "  \"two\" => 2\n",
       "  \"one\" => 1"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = Dict(\"one\" => 1, \"two\" => 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d[\"three\"] = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Int64} with 3 entries:\n",
       "  \"two\"   => 2\n",
       "  \"one\"   => 1\n",
       "  \"three\" => 3"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 辞書のキー・値を取り出す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dict{String,Int64} with 2 entries:\n",
       "  \"two\" => 2\n",
       "  \"one\" => 1"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = Dict(\"one\" => 1, \"two\" => 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Base.KeyIterator for a Dict{String,Int64} with 2 entries. Keys:\n",
       "  \"two\"\n",
       "  \"one\""
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "keys(d)  # イテレータとして取り出す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{String,1}:\n",
       " \"two\"\n",
       " \"one\""
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "collect(keys(d))  # ベクトルとして取り出す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Base.ValueIterator for a Dict{String,Int64} with 2 entries. Values:\n",
       "  2\n",
       "  1"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Int64,1}:\n",
       " 2\n",
       " 1"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "collect(values(d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 集合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 集合を作る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set{Int64}()"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Set{Int}()  # 空の集合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set([2, 3, 1])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Set([1,2,3])  # ベクトルから"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set(String[\"bar\", \"baz\", \"foo\"])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Set([\"foo\", \"bar\", \"baz\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 集合にある要素があるか判定する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 in Set([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4 in Set([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 ∈ Set([1,2,3])  # ∈ は in の別名"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 集合に要素を追加する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set([4, 2, 3, 1])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = Set([1,2,3])\n",
    "push!(s, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set([4, 2, 3, 5, 6, 1])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "union!(s, [5, 6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 和集合・積集合・差集合をとる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set([4, 2, 3, 5])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 = Set([1,2,3])\n",
    "s2 = Set([2,3,4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set([4, 2, 3, 5, 1])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "union(s1, s2)  # 和集合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set([4, 2, 3, 5, 1])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 ∪ s2  # \\cupは和集合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set([2, 3])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intersect(s1, s2)  # 積集合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set([2, 3])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 ∩ s2  # \\capは積集合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Set([1])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "setdiff(s1, s2)  # 差集合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 集合の要素をベクトルとして取り出す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 2\n",
       " 3\n",
       " 1"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = Set([1,2,3])\n",
    "collect(s)  # 順番は順不同"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 文字列処理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 文字数をカウントする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(\"foo\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "length(\"αβγ\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 文字のバイト数を得る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sizeof(\"foo\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sizeof(\"αβγ\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 文字列をUTF-8のバイト列に変換する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{UInt8,1}:\n",
       " 0x66\n",
       " 0x6f\n",
       " 0x6f"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "convert(Vector{UInt8}, \"foo\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6-element Array{UInt8,1}:\n",
       " 0xce\n",
       " 0xb1\n",
       " 0xce\n",
       " 0xb2\n",
       " 0xce\n",
       " 0xb3"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "convert(Vector{UInt8}, \"αβγ\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{UInt8,1}:\n",
       " 0x66\n",
       " 0x6f\n",
       " 0x6f"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vector{UInt8}(\"foo\")  # これもOK"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### UTF-8のバイト列を文字列に変換する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foo\""
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "convert(String, [0x66, 0x6f, 0x6f])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"αβγ\""
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "convert(String, [0xce, 0xb1, 0xce, 0xb2, 0xce, 0xb3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foo\""
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "String([0x66, 0x6f, 0x6f])  # これもOK"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 特定のパターンを置換する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"hello, there\""
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "replace(\"hello, world\", \"world\", \"there\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"abracadabra\""
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "replace(\"a5b4ra221ca1d856ab86r7a7\", r\"\\d+\", \"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 文字列を文字の配列に分割する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Char,1}:\n",
       " 'f'\n",
       " 'o'\n",
       " 'o'"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "collect(\"foo\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Char,1}:\n",
       " 'α'\n",
       " 'β'\n",
       " 'γ'"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "collect(\"αβγ\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 文字列を連結する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foobar\""
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"foo\" * \"bar\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foo123\""
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "string(\"foo\", 123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foo,bar,baz\""
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "join([\"foo\", \"bar\", \"baz\"], \",\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 文字列を分割する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{SubString{String},1}:\n",
       " \"foo\"\n",
       " \"bar\"\n",
       " \"baz\""
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "split(\"foo,bar,baz\", \",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{SubString{String},1}:\n",
       " \"123\"\n",
       " \"45\" \n",
       " \"567\""
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "split(\"123 45   567\", r\"\\s+\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 特定の幅で左詰め・右詰めする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"123  \""
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rpad(123, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"  123\""
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lpad(123, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " left aligned: 123  \n",
      "right aligned:   123\n"
     ]
    }
   ],
   "source": [
    "println(\" left aligned: \", rpad(123, 5))\n",
    "println(\"right aligned: \", lpad(123, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"  123\""
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@sprintf(\"%5d\", 123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 末尾の改行を除く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foo bar\""
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chomp(\"foo bar\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foo bar\""
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chomp(\"foo bar\\r\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 左右の空白を除く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foo bar\""
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "strip(\" foo bar \")   # 両側"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foo bar \""
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lstrip(\" foo bar \")  # 左のみ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\" foo bar\""
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rstrip(\" foo bar \")  # 右のみ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 大文字・小文字に変換する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"FOO\""
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "uppercase(\"foo\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"foo\""
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lowercase(\"FOO\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 入出力"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ファイルをテキストとして読み込む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Juliaは技術計算のための動的言語で、以下の様な機能を備えています。\\n\\n- 多重ディスパッチ\\n- JITコンパイル\\n- マクロなどのメタプログラミング\\n\""
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "readstring(\"data/julia.md\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{String,1}:\n",
       " \"Juliaは技術計算のための動的言語で、以下の様な機能を備えています。\"\n",
       " \"\"                                   \n",
       " \"- 多重ディスパッチ\"                         \n",
       " \"- JITコンパイル\"                         \n",
       " \"- マクロなどのメタプログラミング\"                  "
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "readlines(\"data/julia.md\")  # 改行で分割"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ファイルを行毎に読み込む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1: Juliaは技術計算のための動的言語で、以下の様な機能を備えています。\n",
      "2: \n",
      "3: - 多重ディスパッチ\n",
      "4: - JITコンパイル\n",
      "5: - マクロなどのメタプログラミング\n"
     ]
    }
   ],
   "source": [
    "i = 1\n",
    "for line in eachline(\"data/julia.md\")\n",
    "    println(i, \": \", line)\n",
    "    i += 1\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ファイルをバイナリデータとして読み込む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "193-element Array{UInt8,1}:\n",
       " 0x4a\n",
       " 0x75\n",
       " 0x6c\n",
       " 0x69\n",
       " 0x61\n",
       " 0xe3\n",
       " 0x81\n",
       " 0xaf\n",
       " 0xe6\n",
       " 0x8a\n",
       " 0x80\n",
       " 0xe8\n",
       " 0xa1\n",
       "    ⋮\n",
       " 0x83\n",
       " 0xa9\n",
       " 0xe3\n",
       " 0x83\n",
       " 0x9f\n",
       " 0xe3\n",
       " 0x83\n",
       " 0xb3\n",
       " 0xe3\n",
       " 0x82\n",
       " 0xb0\n",
       " 0x0a"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "read(\"data/julia.md\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ファイルが存在するかを調べる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isfile(\"data/julia.md\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isfile(\"data/python.md\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ファイルサイズを得る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "193"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filesize(\"data/julia.md\")  # 単位はバイト"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ファイルを開閉する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "IOStream(<file data/julia.md>)"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file = open(\"data/julia.md\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isopen(file)  # ファイルが開いているか判定する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Juliaは技術計算のための動的言語で、以下の様な機能を備えています。\""
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "readline(file)  # 1行読み込む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "close(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isopen(file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 開いているファイルの現在位置を得る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "IOStream(<file data/julia.md>)"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file = open(\"data/julia.md\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position(file)  # 最初の位置は0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "95"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sizeof(readline(file))  # 1行(改行含む)を読む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "96"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position(file)  # 1行分読み込み位置が進む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eof(file)  # 読み込み位置は末尾か判定"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "97"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sizeof(read(file))  # 残りすべてを読み込む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eof(file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 開いたファイルを必ず閉じる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Juliaは技術計算のための動的言語で、以下の様な機能を備えています。\n"
     ]
    },
    {
     "ename": "LoadError",
     "evalue": "\u001b[91mDivideError: integer division error\u001b[39m",
     "output_type": "error",
     "traceback": [
      "\u001b[91mDivideError: integer division error\u001b[39m",
      "",
      "Stacktrace:",
      " [1] \u001b[1mopen\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::##1#2, ::String\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./iostream.jl:152\u001b[22m\u001b[22m"
     ]
    }
   ],
   "source": [
    "# open ... do ... endはdoの中でエラーが起きても必ずファイルを閉じる\n",
    "open(\"data/julia.md\") do file\n",
    "    println(readline(file))\n",
    "    div(1, 0)  # エラー！\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### gzipの圧縮ファイルを読み込む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using CodecZlib  # https://github.com/bicycle1885/CodecZlib.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "TranscodingStreams.TranscodingStream{CodecZlib.GzipDecompression,IOStream}(<state=idle>)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "file = GzipDecompressionStream(open(\"data/julia.md.gz\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{String,1}:\n",
       " \"Juliaは技術計算のための動的言語で、以下の様な機能を備えています。\"\n",
       " \"\"                                   \n",
       " \"- 多重ディスパッチ\"                         \n",
       " \"- JITコンパイル\"                         \n",
       " \"- マクロなどのメタプログラミング\"                  "
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "readlines(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "close(file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### テキストをファイルに書き込む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "write(\"data/output.txt\", \"アブラカダブラ\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"アブラカダブラ\\n\""
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "readstring(\"data/output.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "file = open(\"data/output.txt\", \"w\")\n",
    "println(file, \"寿限無寿限無\")\n",
    "close(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"寿限無寿限無\\n\""
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "readstring(\"data/output.txt\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### オブジェクトをファイルにシリアライズする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "file = open(\"data/object.dat\", \"w\")\n",
    "serialize(file, \"テキスト\")\n",
    "serialize(file, 3.14)\n",
    "serialize(file, [10, 20, 30])\n",
    "serialize(file, Dict(\"愛里寿\" => \"センチュリオン\", \"ミカ\" => \"BT-42\"))\n",
    "close(file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "deserialize(file) = \"テキスト\"\n",
      "deserialize(file) = 3.14\n",
      "deserialize(file) = [10, 20, 30]\n",
      "deserialize(file) = Dict(\"ミカ\"=>\"BT-42\",\"愛里寿\"=>\"センチュリオン\")\n"
     ]
    }
   ],
   "source": [
    "file = open(\"data/object.dat\")\n",
    "while !eof(file)\n",
    "    @show deserialize(file)\n",
    "end\n",
    "close(file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 外部コマンド"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 外部コマンドを実行する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hello\n"
     ]
    }
   ],
   "source": [
    "run(`echo \"hello\"`)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### コマンドの出力を読み込む"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"julia.md\\njulia.md.gz\\nobject.dat\\noutput.txt\\n\""
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "readstring(`ls data`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43-element Array{UInt8,1}:\n",
       " 0x6a\n",
       " 0x75\n",
       " 0x6c\n",
       " 0x69\n",
       " 0x61\n",
       " 0x2e\n",
       " 0x6d\n",
       " 0x64\n",
       " 0x0a\n",
       " 0x6a\n",
       " 0x75\n",
       " 0x6c\n",
       " 0x69\n",
       "    ⋮\n",
       " 0x0a\n",
       " 0x6f\n",
       " 0x75\n",
       " 0x74\n",
       " 0x70\n",
       " 0x75\n",
       " 0x74\n",
       " 0x2e\n",
       " 0x74\n",
       " 0x78\n",
       " 0x74\n",
       " 0x0a"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "read(`ls data`)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Pipe(RawFD(-1) closed => RawFD(51) open, 0 bytes waiting), Process(`ls data`, ProcessExited(0)))"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe, proc = open(`ls data`)  # パイプとプロセス"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "julia.md\n",
      "julia.md.gz\n",
      "object.dat\n",
      "output.txt\n"
     ]
    }
   ],
   "source": [
    "while !eof(pipe)\n",
    "    println(readline(pipe))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Process(`ls data`, ProcessExited(0))"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "proc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 関数型プログラミング"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 条件を満たす要素を残す"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 1\n",
       " 3\n",
       " 5"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filter(isodd, [1,2,3,4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 3\n",
       " 4\n",
       " 5"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filter(x->x>2, [1,2,3,4,5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 条件を満たす要素があるか確認する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "any(isodd, [1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "any(isodd, [2,4,6,8])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### すべての要素が条件を満たすかを確認する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all(isodd, [1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all(isodd, [1,3,5,7])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 全要素に同じ関数を適用する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " 0.0     \n",
       " 0.841471\n",
       " 0.909297\n",
       " 0.14112 "
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "map(sin, [0.0, 1.0, 2.0, 3.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " 0.0     \n",
       " 0.841471\n",
       " 0.909297\n",
       " 0.14112 "
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin.([0.0, 1.0, 2.0, 3.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 関数を適用して畳み込みをする"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "foldl(+, 0, [1,2,3])  # 総和の計算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "foldl(+, [1,2,3])  # 第二引数は省略可"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":(if x == 1 # In[146], line 2:\n",
       "        print(1)\n",
       "    else  # In[146], line 2:\n",
       "        if x == 2 # In[146], line 2:\n",
       "            print(2)\n",
       "        else  # In[146], line 2:\n",
       "            if x == 3 # In[146], line 2:\n",
       "                print(3)\n",
       "            else  # In[146], line 2:\n",
       "                nothing\n",
       "            end\n",
       "        end\n",
       "    end)"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 分岐する式の作成\n",
    "foldr((x, r)->:(if x == $(x); print($(x)); else; $(r); end), :(nothing), [1,2,3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ベンチマーク・プロファイル"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 関数の実行時間を測定する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008851748"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort(randn(100000))  # コンパイルのため測定前に一度実行する\n",
    "@elapsed sort(randn(100000))  # 単位は秒"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Float64,1}:\n",
       " 0.00876565\n",
       " 0.0156572 \n",
       " 0.00870781\n",
       " 0.00845791\n",
       " 0.00924334\n",
       " 0.0104665 \n",
       " 0.00999714\n",
       " 0.0109102 \n",
       " 0.0105973 \n",
       " 0.00948196"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[@elapsed sort(randn(100000)) for _ in 1:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 関数のメモリ割り付けを測定する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1600240"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sort(randn(100000))  # コンパイルのため測定前に一度実行する\n",
    "@allocated sort(randn(100000))  # 単位はバイト"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Int64,1}:\n",
       " 1600240\n",
       " 1600240\n",
       " 1600240\n",
       " 1600240\n",
       " 1600240\n",
       " 1600240\n",
       " 1600240\n",
       " 1600240\n",
       " 1600240\n",
       " 1600240"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[@allocated sort(randn(100000)) for _ in 1:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 関数の実行時間とメモリ割り付けを同時に測定する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.008674 seconds (9 allocations: 1.526 MiB)\n"
     ]
    }
   ],
   "source": [
    "sort(randn(100000))  # コンパイルのため測定前に一度実行する\n",
    "@time sort(randn(100000));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.011001 seconds (5 allocations: 1.526 MiB)\n",
      "  0.010731 seconds (5 allocations: 1.526 MiB)\n",
      "  0.010590 seconds (5 allocations: 1.526 MiB)\n",
      "  0.008951 seconds (5 allocations: 1.526 MiB)\n",
      "  0.009545 seconds (5 allocations: 1.526 MiB)\n",
      "  0.008640 seconds (5 allocations: 1.526 MiB)\n",
      "  0.008199 seconds (5 allocations: 1.526 MiB)\n",
      "  0.008194 seconds (5 allocations: 1.526 MiB)\n",
      "  0.009020 seconds (5 allocations: 1.526 MiB)\n",
      "  0.008863 seconds (5 allocations: 1.526 MiB)\n"
     ]
    }
   ],
   "source": [
    "for _ in 1:10\n",
    "    @time sort(randn(100000))\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.52587890625"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "100000 * sizeof(Float64) * 2 / 1024^2  # 100000要素の倍精度浮動小数点数のメモリ割り当て量 (MiB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 詳細なベンチマークを行う"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using BenchmarkTools  # https://github.com/JuliaCI/BenchmarkTools.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  1.53 MiB\n",
       "  allocs estimate:  5\n",
       "  --------------\n",
       "  minimum time:     7.214 ms (0.00% GC)\n",
       "  median time:      8.233 ms (0.00% GC)\n",
       "  mean time:        8.661 ms (1.33% GC)\n",
       "  maximum time:     25.404 ms (0.00% GC)\n",
       "  --------------\n",
       "  samples:          577\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark sort(randn(100000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  400 bytes\n",
       "  allocs estimate:  3\n",
       "  --------------\n",
       "  minimum time:     421.925 ns (0.00% GC)\n",
       "  median time:      452.987 ns (0.00% GC)\n",
       "  mean time:        554.083 ns (3.35% GC)\n",
       "  maximum time:     19.120 μs (0.00% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     199"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark sort(randn(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### プロファイルを取る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bubblesort (generic function with 1 method)"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function bubblesort(x)\n",
    "    x = copy(x)\n",
    "    swapped = true\n",
    "    while swapped\n",
    "        swapped = false\n",
    "        for i in 1:endof(x)-1\n",
    "            if x[i+1] < x[i]\n",
    "                x[i+1], x[i] = x[i], x[i+1]\n",
    "                swapped = true\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    return x\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Float64,1}:\n",
       " -1.79628 \n",
       " -1.73885 \n",
       " -0.460956\n",
       " -0.450571\n",
       " -0.151273\n",
       "  0.342973\n",
       "  0.474332\n",
       "  0.617031\n",
       "  0.710638\n",
       "  0.768515"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bubblesort(randn(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = randn(10000)\n",
    "Profile.clear()\n",
    "@profile bubblesort(x);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "196 ./task.jl:335; (::IJulia.##11#14)()\n",
      " 1   ...Julia/src/eventloop.jl:5; eventloop(::ZMQ.Socket)\n",
      "  1 ...v0.6/IJulia/src/msg.jl:87; recv_ipython(::ZMQ.Socket)\n",
      "   1 ....6/JSON/src/Parser.jl:375; #parse#1(::Type{Dict{String,Any}}...\n",
      "    1 ....6/JSON/src/Parser.jl:158; parse_value(::JSON.Parser.Memory...\n",
      "     1 ....6/JSON/src/Parser.jl:201; parse_object(::JSON.Parser.Memor...\n",
      " 195 ...Julia/src/eventloop.jl:8; eventloop(::ZMQ.Socket)\n",
      "  195 ...rc/execute_request.jl:160; execute_request(::ZMQ.Socket, ::...\n",
      "   195 ./loading.jl:515; include_string(::String, ::String)\n",
      "    195 ./<missing>:?; anonymous\n",
      "     195 ./profile.jl:23; macro expansion\n",
      "      53  ./In[157]:6; bubblesort(::Array{Float64,1})\n",
      "      109 ./In[157]:7; bubblesort(::Array{Float64,1})\n",
      "      31  ./In[157]:8; bubblesort(::Array{Float64,1})\n",
      "      2   ./In[157]:9; bubblesort(::Array{Float64,1})\n"
     ]
    }
   ],
   "source": [
    "Profile.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 数値の計算"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 奇数・偶数を判定する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isodd(41)   # 奇数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iseven(42)  # 偶数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 素数判定する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using Primes  # https://github.com/JuliaMath/Primes.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isprime(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "isprime(43)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 素数列を生成する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using Primes  # https://github.com/JuliaMath/Primes.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15-element Array{Int64,1}:\n",
       "  2\n",
       "  3\n",
       "  5\n",
       "  7\n",
       " 11\n",
       " 13\n",
       " 17\n",
       " 19\n",
       " 23\n",
       " 29\n",
       " 31\n",
       " 37\n",
       " 41\n",
       " 43\n",
       " 47"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "primes(50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 商を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "div(42, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.4"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "42 / 5  # 整数 / 整数 = 浮動小数点数 になるので注意"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 剰余を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "42 % 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rem(42, 5)  # 上と同じ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 絶対値を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(-42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 排他的論理和を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xor(42, 35)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "42 ⊻ 35  # 上と同じ(\\xor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 線形代数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルの和を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " -1.0\n",
       "  3.0\n",
       "  0.0"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [1.0, 2.0, 3.0]\n",
    "y = [-1.0, 3.0, 0.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 0.0\n",
       " 5.0\n",
       " 3.0"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       "  2.0\n",
       " -1.0\n",
       "  3.0"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x - y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ベクトルのスカラー倍を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 3.2\n",
       " 6.4\n",
       " 9.6"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3.2x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 行ベクトルを作る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×3 RowVector{Float64,Array{Float64,1}}:\n",
       " 1.0  2.0  3.0"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 1.0\n",
       " 2.0\n",
       " 3.0"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x''  # 2回でもとに戻る"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 内積を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.0"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot(x, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.0"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x ⋅ x  # 上と同じ (\\cdot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.0"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x'x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 直積を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " 1.0  2.0  3.0\n",
       " 2.0  4.0  6.0\n",
       " 3.0  6.0  9.0"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x * x'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 対角行列を作る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " 1.0  0.0  0.0\n",
       " 0.0  2.0  0.0\n",
       " 0.0  0.0  3.0"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diagm([1.0, 2.0, 3.0])  # 通常の行列の型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Diagonal{Float64}:\n",
       " 1.0   ⋅    ⋅ \n",
       "  ⋅   2.0   ⋅ \n",
       "  ⋅    ⋅   3.0"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Diagonal([1.0, 2.0, 3.0])  # 対角行列の型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 行列積を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       "  0.726385    1.6588   1.13122 \n",
       "  1.01566     1.77963  0.710212\n",
       " -0.0650975  -1.22412  1.03047 "
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = randn(3, 3)\n",
    "B = randn(3, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " -1.28874  -3.78644  -1.10194 \n",
       " -1.70857  -4.33366  -0.816591\n",
       "  1.54023   2.93319   1.31487 "
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B  # 通常の行列積"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " -2.19284  -5.01086  -2.08284 \n",
       " -1.06601  -3.18224   0.516614\n",
       "  1.47724   2.94792   1.4728  "
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "At_mul_B(A, B)  # Aを転置して掛ける"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " -2.19284  -5.01086  -2.08284 \n",
       " -1.06601  -3.18224   0.516614\n",
       "  1.47724   2.94792   1.4728  "
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A'B  # 上と同じ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " -0.35104  -1.17308   0.938959\n",
       " -1.26934  -2.02604   2.15484 \n",
       "  2.2404    2.53849  -1.5252  "
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_mul_Bt(A, B)  # Bを転置して掛ける"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " -0.35104  -1.17308   0.938959\n",
       " -1.26934  -2.02604   2.15484 \n",
       "  2.2404    2.53849  -1.5252  "
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B'  # 上と同じ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " -2.22868   -3.02436    1.7201 \n",
       " -0.275315  -0.892186   2.39829\n",
       "  1.98846    2.34479   -1.18667"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "At_mul_Bt(A, B)  # AもBも転置して掛ける"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " -2.22868   -3.02436    1.7201 \n",
       " -0.275315  -0.892186   2.39829\n",
       "  1.98846    2.34479   -1.18667"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A'B'  # 上と同じ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 固有値・固有ベクトルを計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       "  5.0  2.0\n",
       " -2.0  3.0"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [5.0 2.0; -2.0 3.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Complex{Float64},1}:\n",
       " 4.0+1.73205im\n",
       " 4.0-1.73205im"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvals(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Complex{Float64},2}:\n",
       "  0.707107+0.0im        0.707107-0.0im     \n",
       " -0.353553+0.612372im  -0.353553-0.612372im"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvecs(X)  # 複素数の固有ベクトル"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " 12.0557\n",
       " 29.9443"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvals(X'X)  # 固有値はすべて正なので正定値行列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       "  0.229753  -0.973249\n",
       " -0.973249  -0.229753"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvecs(X'X)  # 正定値行列に対しては実数の固有ベクトル"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 線型方程式系を解く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       "  1.0\n",
       " -2.0\n",
       "  0.0"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = [3.0  2.0 -1.0\n",
    "     2.0 -2.0  4.0\n",
    "    -1.0  0.5 -1.0]\n",
    "b = [1.0, -2.0, 0.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       "  1.0\n",
       " -2.0\n",
       " -2.0"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = A \\ b  # A x = b の解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * x ≈ b  # 解の確認"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 統計"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 一様分布から乱数を得る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3867181118018075"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30-element Array{Float64,1}:\n",
       " 0.0233823 \n",
       " 0.584213  \n",
       " 0.996262  \n",
       " 0.0486294 \n",
       " 0.823912  \n",
       " 0.00980484\n",
       " 0.506794  \n",
       " 0.922409  \n",
       " 0.846705  \n",
       " 0.685258  \n",
       " 0.0148934 \n",
       " 0.101358  \n",
       " 0.578418  \n",
       " ⋮         \n",
       " 0.672831  \n",
       " 0.167329  \n",
       " 0.826931  \n",
       " 0.181764  \n",
       " 0.401678  \n",
       " 0.1965    \n",
       " 0.202258  \n",
       " 0.0961149 \n",
       " 0.245319  \n",
       " 0.919989  \n",
       " 0.549066  \n",
       " 0.184145  "
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand(30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 標準正規分布から乱数を得る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04586384215519224"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "randn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30-element Array{Float64,1}:\n",
       " -0.437116 \n",
       "  0.385278 \n",
       " -0.473007 \n",
       " -0.371043 \n",
       " -0.0256377\n",
       "  1.2682   \n",
       "  0.552556 \n",
       " -0.0252973\n",
       " -1.13349  \n",
       "  2.46311  \n",
       " -0.902314 \n",
       "  1.19349  \n",
       "  0.271862 \n",
       "  ⋮        \n",
       " -1.3191   \n",
       "  0.194445 \n",
       "  2.25805  \n",
       "  1.87969  \n",
       " -0.176167 \n",
       " -0.0395945\n",
       "  1.24096  \n",
       " -1.03593  \n",
       " -0.259864 \n",
       "  1.2209   \n",
       "  2.11896  \n",
       " -0.695827 "
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "randn(30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 様々な分布から乱数を得る"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import Distributions  ## https://github.com/JuliaStats/Distributions.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Float64,1}:\n",
       " 0.851551 \n",
       " 1.8048   \n",
       " 0.0905379\n",
       " 0.0643867\n",
       " 0.464794 \n",
       " 0.792174 \n",
       " 2.73824  \n",
       " 0.332647 \n",
       " 0.565023 \n",
       " 1.14877  "
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = Distributions.Gamma(1.0, 2.0)  # ガンマ分布\n",
    "rand(g, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Int64,1}:\n",
       " 10\n",
       " 12\n",
       " 13\n",
       "  8\n",
       " 12\n",
       "  7\n",
       "  7\n",
       " 12\n",
       "  4\n",
       " 11"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = Distributions.Poisson(10)  # ポアソン分布\n",
    "rand(p, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### サンプリングを行う"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand(1:20)  # 1-20の値から1個サンプリング"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Int64,1}:\n",
       " 10\n",
       "  8\n",
       " 17\n",
       "  7\n",
       " 17\n",
       "  3\n",
       " 10\n",
       " 18\n",
       "  7\n",
       " 10"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand(1:20, 10)  # 1~20の値から10個サンプリング"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using StatsBase  # https://github.com/JuliaStats/StatsBase.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10-element Array{Int64,1}:\n",
       "  7\n",
       " 18\n",
       " 17\n",
       "  8\n",
       " 20\n",
       " 12\n",
       " 14\n",
       "  5\n",
       "  4\n",
       " 19"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample(1:20, 10, replace=false)  # 非復元抽出"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 平均・分散を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008539475320023372"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(randn(100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.865934027580458"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "var(randn(100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 中央値を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0103736890230341"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median(exp.(randn(100)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 分位数を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = exp.(randn(100));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39879867876339664"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quantile(x, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6779346947809612"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quantile(x, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0: 0.10576604052523694\n",
      "0.1: 0.39879867876339664\n",
      "0.2: 0.5585514635406499\n",
      "0.3: 0.7252001881297099\n",
      "0.4: 0.9280416777324269\n",
      "0.5: 1.1110217625293453\n",
      "0.6: 1.4068712917385797\n",
      "0.7: 1.7752452712496667\n",
      "0.8: 2.9288228171021804\n",
      "0.9: 4.571210350690497\n",
      "1.0: 15.1433030232737\n"
     ]
    }
   ],
   "source": [
    "for q in linspace(0, 1, 11)\n",
    "    println(q, \": \", quantile(x, q))\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 行列の最大値・最小値を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×3 Array{Float64,2}:\n",
       " -0.80238    0.644167  -0.0853525\n",
       "  0.823909  -0.350321  -0.969769 \n",
       "  0.463137   2.23558   -0.64375  \n",
       "  1.85394    0.886008   1.16761  \n",
       " -0.821372   0.468997  -1.69867  "
      ]
     },
     "execution_count": 222,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = randn(5, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.235578644026364"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maximum(A)  # 全要素の最大値 (最小値はminimum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×1 Array{Float64,2}:\n",
       " 0.644167\n",
       " 0.823909\n",
       " 2.23558 \n",
       " 1.85394 \n",
       " 0.468997"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maximum(A, 2)  # 行最大"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1×3 Array{Float64,2}:\n",
       " 1.85394  2.23558  1.16761"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maximum(A, 1)  # 列最大"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 行列から平均を引く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×3 Array{Float64,2}:\n",
       " 10.9184   10.6914    8.21326\n",
       " 10.2181   10.8977   11.8139 \n",
       "  9.11668   9.83351  10.3405 \n",
       " 11.5015    8.74474   9.91524\n",
       " 11.31     10.1985    8.82895"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = randn(5, 3) + 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×3 Array{Float64,2}:\n",
       "  0.977356   0.75038    -1.72774 \n",
       " -0.758501  -0.0788276   0.837329\n",
       " -0.646876   0.0699516   0.576924\n",
       "  1.44766   -1.30908    -0.138582\n",
       "  1.19753    0.0860069  -1.28354 "
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A .- mean(A, 2)  # 行平均を引く"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×3 Array{Float64,2}:\n",
       "  0.305433   0.618205  -1.6091  \n",
       " -0.394858   0.824564   1.99153 \n",
       " -1.49624   -0.23966    0.51812 \n",
       "  0.888563  -1.32843    0.092875\n",
       "  0.697097   0.125321  -0.993418"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A .- mean(A, 1)  # 列平均を引く"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 共分散行列を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Array{Float64,2}:\n",
       " 3.0  5.8  1.1\n",
       " 1.0  4.2  0.1"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [3.0 5.8 1.1; 1.0 4.2 0.1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×3 Array{Float64,2}:\n",
       " 2.0  1.6   1.0\n",
       " 1.6  1.28  0.8\n",
       " 1.0  0.8   0.5"
      ]
     },
     "execution_count": 230,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov(X, 1)  # 各行がサンプル"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       " 5.59  4.99   \n",
       " 4.99  4.64333"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov(X, 2)  # 各列がサンプル"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×2 Array{Float64,2}:\n",
       " 1.0       0.979444\n",
       " 0.979444  1.0     "
      ]
     },
     "execution_count": 232,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cor(X, 2)  # ピアソンの相関係数の行列"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 最小二乗法を行う"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " -1.0\n",
       "  1.0\n",
       "  2.0\n",
       "  3.0"
      ]
     },
     "execution_count": 233,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = randn(20, 4)\n",
    "b = [-1.0, 1.0, 2.0, 3.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20-element Array{Float64,1}:\n",
       "  1.8996  \n",
       "  6.01268 \n",
       "  1.41041 \n",
       " -0.542336\n",
       " -2.5572  \n",
       " -0.450025\n",
       "  3.60568 \n",
       " -3.86358 \n",
       " -0.819904\n",
       "  1.11038 \n",
       " -6.1131  \n",
       "  1.69123 \n",
       " -2.1921  \n",
       "  5.05921 \n",
       " -1.56521 \n",
       "  2.39779 \n",
       "  3.91339 \n",
       "  0.451056\n",
       " -1.10424 \n",
       "  4.80995 "
      ]
     },
     "execution_count": 234,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = X * b + randn(20) * 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "正規方程式 $(X'X)\\beta = X'y$ の解"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " -1.02689 \n",
       "  0.976217\n",
       "  2.01937 \n",
       "  2.98385 "
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(X'X)\\X'*y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "また、$X=QR$と分解すると、$X$が最大列階数のとき正規方程式は\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "(X'X)\\beta &= X'y \\\\\n",
    "(QR)'(QR)\\beta &= (QR)'y \\\\\n",
    "R'(Q'Q)R\\beta &= R'Q'y \\\\\n",
    "R\\beta &= Q'y\n",
    "\\end{align}\n",
    "\n",
    "なので次のようにも計算できる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4-element Array{Float64,1}:\n",
       " -1.02689 \n",
       "  0.976217\n",
       "  2.01937 \n",
       "  2.98385 "
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q, R = qr(X)\n",
    "R\\(Q'y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 解析"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 関数の根を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using Roots  # https://github.com/JuliaMath/Roots.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fzero(log, 0, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fzero(x -> sin(x - 3), 2, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### データ点を補完する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using Interpolations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) = sin(x) * exp(-x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(::#17) (generic function with 1 method)"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xs = linspace(-3, 3, 8)\n",
    "itp = interpolate([f(x) for x in xs], BSpline(Cubic(Line())), OnCell())\n",
    "scl = scale(itp, xs)\n",
    "g = x->scl[x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3095598756531122"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.31573248343343835"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
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       "function(){k.stop();var d=z(this.node,\"filter\");if(d)return(d=w(d).match(A))&&a.select(d[1])});k.on(\"snap.util.attr.filter\",function(d){if(d instanceof v&&\"filter\"==d.type){k.stop();var f=d.node.id;f||(z(d.node,{id:d.id}),f=d.id);z(this.node,{filter:a.url(f)})}d&&\"none\"!=d||(k.stop(),this.node.removeAttribute(\"filter\"))});a.filter.blur=function(d,f){null==d&&(d=2);return a.format('<feGaussianBlur stdDeviation=\"{def}\"/>',{def:null==f?d:[d,f]})};a.filter.blur.toString=function(){return this()};a.filter.shadow=\n",
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       "{color:u,dx:d,dy:f,blur:k,opacity:p})};a.filter.shadow.toString=function(){return this()};a.filter.grayscale=function(d){null==d&&(d=1);return a.format('<feColorMatrix type=\"matrix\" values=\"{a} {b} {c} 0 0 {d} {e} {f} 0 0 {g} {b} {h} 0 0 0 0 0 1 0\"/>',{a:0.2126+0.7874*(1-d),b:0.7152-0.7152*(1-d),c:0.0722-0.0722*(1-d),d:0.2126-0.2126*(1-d),e:0.7152+0.2848*(1-d),f:0.0722-0.0722*(1-d),g:0.2126-0.2126*(1-d),h:0.0722+0.9278*(1-d)})};a.filter.grayscale.toString=function(){return this()};a.filter.sepia=\n",
       "function(d){null==d&&(d=1);return a.format('<feColorMatrix type=\"matrix\" values=\"{a} {b} {c} 0 0 {d} {e} {f} 0 0 {g} {h} {i} 0 0 0 0 0 1 0\"/>',{a:0.393+0.607*(1-d),b:0.769-0.769*(1-d),c:0.189-0.189*(1-d),d:0.349-0.349*(1-d),e:0.686+0.314*(1-d),f:0.168-0.168*(1-d),g:0.272-0.272*(1-d),h:0.534-0.534*(1-d),i:0.131+0.869*(1-d)})};a.filter.sepia.toString=function(){return this()};a.filter.saturate=function(d){null==d&&(d=1);return a.format('<feColorMatrix type=\"saturate\" values=\"{amount}\"/>',{amount:1-\n",
       "d})};a.filter.saturate.toString=function(){return this()};a.filter.hueRotate=function(d){return a.format('<feColorMatrix type=\"hueRotate\" values=\"{angle}\"/>',{angle:d||0})};a.filter.hueRotate.toString=function(){return this()};a.filter.invert=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncG type=\"table\" tableValues=\"{amount} {amount2}\"/><feFuncB type=\"table\" tableValues=\"{amount} {amount2}\"/></feComponentTransfer>',{amount:d,\n",
       "amount2:1-d})};a.filter.invert.toString=function(){return this()};a.filter.brightness=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\"/><feFuncG type=\"linear\" slope=\"{amount}\"/><feFuncB type=\"linear\" slope=\"{amount}\"/></feComponentTransfer>',{amount:d})};a.filter.brightness.toString=function(){return this()};a.filter.contrast=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncG type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncB type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/></feComponentTransfer>',\n",
       "{amount:d,amount2:0.5-d/2})};a.filter.contrast.toString=function(){return this()}});return C});\n",
       "\n",
       "]]> </script>\n",
       "<script> <![CDATA[\n",
       "\n",
       "(function (glob, factory) {\n",
       "    // AMD support\n",
       "    if (typeof define === \"function\" && define.amd) {\n",
       "        // Define as an anonymous module\n",
       "        define(\"Gadfly\", [\"Snap.svg\"], function (Snap) {\n",
       "            return factory(Snap);\n",
       "        });\n",
       "    } else {\n",
       "        // Browser globals (glob is window)\n",
       "        // Snap adds itself to window\n",
       "        glob.Gadfly = factory(glob.Snap);\n",
       "    }\n",
       "}(this, function (Snap) {\n",
       "\n",
       "var Gadfly = {};\n",
       "\n",
       "// Get an x/y coordinate value in pixels\n",
       "var xPX = function(fig, x) {\n",
       "    var client_box = fig.node.getBoundingClientRect();\n",
       "    return x * fig.node.viewBox.baseVal.width / client_box.width;\n",
       "};\n",
       "\n",
       "var yPX = function(fig, y) {\n",
       "    var client_box = fig.node.getBoundingClientRect();\n",
       "    return y * fig.node.viewBox.baseVal.height / client_box.height;\n",
       "};\n",
       "\n",
       "\n",
       "Snap.plugin(function (Snap, Element, Paper, global) {\n",
       "    // Traverse upwards from a snap element to find and return the first\n",
       "    // note with the \"plotroot\" class.\n",
       "    Element.prototype.plotroot = function () {\n",
       "        var element = this;\n",
       "        while (!element.hasClass(\"plotroot\") && element.parent() != null) {\n",
       "            element = element.parent();\n",
       "        }\n",
       "        return element;\n",
       "    };\n",
       "\n",
       "    Element.prototype.svgroot = function () {\n",
       "        var element = this;\n",
       "        while (element.node.nodeName != \"svg\" && element.parent() != null) {\n",
       "            element = element.parent();\n",
       "        }\n",
       "        return element;\n",
       "    };\n",
       "\n",
       "    Element.prototype.plotbounds = function () {\n",
       "        var root = this.plotroot()\n",
       "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
       "        return {\n",
       "            x0: bbox.x,\n",
       "            x1: bbox.x + bbox.width,\n",
       "            y0: bbox.y,\n",
       "            y1: bbox.y + bbox.height\n",
       "        };\n",
       "    };\n",
       "\n",
       "    Element.prototype.plotcenter = function () {\n",
       "        var root = this.plotroot()\n",
       "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
       "        return {\n",
       "            x: bbox.x + bbox.width / 2,\n",
       "            y: bbox.y + bbox.height / 2\n",
       "        };\n",
       "    };\n",
       "\n",
       "    // Emulate IE style mouseenter/mouseleave events, since Microsoft always\n",
       "    // does everything right.\n",
       "    // See: http://www.dynamic-tools.net/toolbox/isMouseLeaveOrEnter/\n",
       "    var events = [\"mouseenter\", \"mouseleave\"];\n",
       "\n",
       "    for (i in events) {\n",
       "        (function (event_name) {\n",
       "            var event_name = events[i];\n",
       "            Element.prototype[event_name] = function (fn, scope) {\n",
       "                if (Snap.is(fn, \"function\")) {\n",
       "                    var fn2 = function (event) {\n",
       "                        if (event.type != \"mouseover\" && event.type != \"mouseout\") {\n",
       "                            return;\n",
       "                        }\n",
       "\n",
       "                        var reltg = event.relatedTarget ? event.relatedTarget :\n",
       "                            event.type == \"mouseout\" ? event.toElement : event.fromElement;\n",
       "                        while (reltg && reltg != this.node) reltg = reltg.parentNode;\n",
       "\n",
       "                        if (reltg != this.node) {\n",
       "                            return fn.apply(this, event);\n",
       "                        }\n",
       "                    };\n",
       "\n",
       "                    if (event_name == \"mouseenter\") {\n",
       "                        this.mouseover(fn2, scope);\n",
       "                    } else {\n",
       "                        this.mouseout(fn2, scope);\n",
       "                    }\n",
       "                }\n",
       "                return this;\n",
       "            };\n",
       "        })(events[i]);\n",
       "    }\n",
       "\n",
       "\n",
       "    Element.prototype.mousewheel = function (fn, scope) {\n",
       "        if (Snap.is(fn, \"function\")) {\n",
       "            var el = this;\n",
       "            var fn2 = function (event) {\n",
       "                fn.apply(el, [event]);\n",
       "            };\n",
       "        }\n",
       "\n",
       "        this.node.addEventListener(\n",
       "            /Firefox/i.test(navigator.userAgent) ? \"DOMMouseScroll\" : \"mousewheel\",\n",
       "            fn2);\n",
       "\n",
       "        return this;\n",
       "    };\n",
       "\n",
       "\n",
       "    // Snap's attr function can be too slow for things like panning/zooming.\n",
       "    // This is a function to directly update element attributes without going\n",
       "    // through eve.\n",
       "    Element.prototype.attribute = function(key, val) {\n",
       "        if (val === undefined) {\n",
       "            return this.node.getAttribute(key);\n",
       "        } else {\n",
       "            this.node.setAttribute(key, val);\n",
       "            return this;\n",
       "        }\n",
       "    };\n",
       "\n",
       "    Element.prototype.init_gadfly = function() {\n",
       "        this.mouseenter(Gadfly.plot_mouseover)\n",
       "            .mouseleave(Gadfly.plot_mouseout)\n",
       "            .dblclick(Gadfly.plot_dblclick)\n",
       "            .mousewheel(Gadfly.guide_background_scroll)\n",
       "            .drag(Gadfly.guide_background_drag_onmove,\n",
       "                  Gadfly.guide_background_drag_onstart,\n",
       "                  Gadfly.guide_background_drag_onend);\n",
       "        this.mouseenter(function (event) {\n",
       "            init_pan_zoom(this.plotroot());\n",
       "        });\n",
       "        return this;\n",
       "    };\n",
       "});\n",
       "\n",
       "\n",
       "// When the plot is moused over, emphasize the grid lines.\n",
       "Gadfly.plot_mouseover = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    var keyboard_zoom = function(event) {\n",
       "        if (event.which == 187) { // plus\n",
       "            increase_zoom_by_position(root, 0.1, true);\n",
       "        } else if (event.which == 189) { // minus\n",
       "            increase_zoom_by_position(root, -0.1, true);\n",
       "        }\n",
       "    };\n",
       "    root.data(\"keyboard_zoom\", keyboard_zoom);\n",
       "    window.addEventListener(\"keyup\", keyboard_zoom);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    xgridlines.data(\"unfocused_strokedash\",\n",
       "                    xgridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "    ygridlines.data(\"unfocused_strokedash\",\n",
       "                    ygridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "\n",
       "    // emphasize grid lines\n",
       "    var destcolor = root.data(\"focused_xgrid_color\");\n",
       "    xgridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    destcolor = root.data(\"focused_ygrid_color\");\n",
       "    ygridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    // reveal zoom slider\n",
       "    root.select(\".zoomslider\")\n",
       "        .animate({opacity: 1.0}, 250);\n",
       "};\n",
       "\n",
       "// Reset pan and zoom on double click\n",
       "Gadfly.plot_dblclick = function(event) {\n",
       "  set_plot_pan_zoom(this.plotroot(), 0.0, 0.0, 1.0);\n",
       "};\n",
       "\n",
       "// Unemphasize grid lines on mouse out.\n",
       "Gadfly.plot_mouseout = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    window.removeEventListener(\"keyup\", root.data(\"keyboard_zoom\"));\n",
       "    root.data(\"keyboard_zoom\", undefined);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    var destcolor = root.data(\"unfocused_xgrid_color\");\n",
       "\n",
       "    xgridlines.attribute(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    destcolor = root.data(\"unfocused_ygrid_color\");\n",
       "    ygridlines.attribute(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    // hide zoom slider\n",
       "    root.select(\".zoomslider\")\n",
       "        .animate({opacity: 0.0}, 250);\n",
       "};\n",
       "\n",
       "\n",
       "var set_geometry_transform = function(root, tx, ty, scale) {\n",
       "    var xscalable = root.hasClass(\"xscalable\"),\n",
       "        yscalable = root.hasClass(\"yscalable\");\n",
       "\n",
       "    var old_scale = root.data(\"scale\");\n",
       "\n",
       "    var xscale = xscalable ? scale : 1.0,\n",
       "        yscale = yscalable ? scale : 1.0;\n",
       "\n",
       "    tx = xscalable ? tx : 0.0;\n",
       "    ty = yscalable ? ty : 0.0;\n",
       "\n",
       "    var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
       "\n",
       "    root.selectAll(\".geometry, image\")\n",
       "        .forEach(function (element, i) {\n",
       "            element.transform(t);\n",
       "        });\n",
       "\n",
       "    bounds = root.plotbounds();\n",
       "\n",
       "    if (yscalable) {\n",
       "        var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
       "        root.selectAll(\".xfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(xfixed_t);\n",
       "            });\n",
       "\n",
       "        root.select(\".ylabels\")\n",
       "            .transform(xfixed_t)\n",
       "            .selectAll(\"text\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var cx = element.asPX(\"x\"),\n",
       "                        cy = element.asPX(\"y\");\n",
       "                    var st = element.data(\"static_transform\");\n",
       "                    unscale_t = new Snap.Matrix();\n",
       "                    unscale_t.scale(1, 1/scale, cx, cy).add(st);\n",
       "                    element.transform(unscale_t);\n",
       "\n",
       "                    var y = cy * scale + ty;\n",
       "                    element.attr(\"visibility\",\n",
       "                        bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    if (xscalable) {\n",
       "        var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
       "        var xtrans = new Snap.Matrix().translate(tx, 0);\n",
       "        root.selectAll(\".yfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(yfixed_t);\n",
       "            });\n",
       "\n",
       "        root.select(\".xlabels\")\n",
       "            .transform(yfixed_t)\n",
       "            .selectAll(\"text\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var cx = element.asPX(\"x\"),\n",
       "                        cy = element.asPX(\"y\");\n",
       "                    var st = element.data(\"static_transform\");\n",
       "                    unscale_t = new Snap.Matrix();\n",
       "                    unscale_t.scale(1/scale, 1, cx, cy).add(st);\n",
       "\n",
       "                    element.transform(unscale_t);\n",
       "\n",
       "                    var x = cx * scale + tx;\n",
       "                    element.attr(\"visibility\",\n",
       "                        bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
       "                    }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    // we must unscale anything that is scale invariance: widths, raiduses, etc.\n",
       "    var size_attribs = [\"font-size\"];\n",
       "    var unscaled_selection = \".geometry, .geometry *\";\n",
       "    if (xscalable) {\n",
       "        size_attribs.push(\"rx\");\n",
       "        unscaled_selection += \", .xgridlines\";\n",
       "    }\n",
       "    if (yscalable) {\n",
       "        size_attribs.push(\"ry\");\n",
       "        unscaled_selection += \", .ygridlines\";\n",
       "    }\n",
       "\n",
       "    root.selectAll(unscaled_selection)\n",
       "        .forEach(function (element, i) {\n",
       "            // circle need special help\n",
       "            if (element.node.nodeName == \"circle\") {\n",
       "                var cx = element.attribute(\"cx\"),\n",
       "                    cy = element.attribute(\"cy\");\n",
       "                unscale_t = new Snap.Matrix().scale(1/xscale, 1/yscale,\n",
       "                                                        cx, cy);\n",
       "                element.transform(unscale_t);\n",
       "                return;\n",
       "            }\n",
       "\n",
       "            for (i in size_attribs) {\n",
       "                var key = size_attribs[i];\n",
       "                var val = parseFloat(element.attribute(key));\n",
       "                if (val !== undefined && val != 0 && !isNaN(val)) {\n",
       "                    element.attribute(key, val * old_scale / scale);\n",
       "                }\n",
       "            }\n",
       "        });\n",
       "};\n",
       "\n",
       "\n",
       "// Find the most appropriate tick scale and update label visibility.\n",
       "var update_tickscale = function(root, scale, axis) {\n",
       "    if (!root.hasClass(axis + \"scalable\")) return;\n",
       "\n",
       "    var tickscales = root.data(axis + \"tickscales\");\n",
       "    var best_tickscale = 1.0;\n",
       "    var best_tickscale_dist = Infinity;\n",
       "    for (tickscale in tickscales) {\n",
       "        var dist = Math.abs(Math.log(tickscale) - Math.log(scale));\n",
       "        if (dist < best_tickscale_dist) {\n",
       "            best_tickscale_dist = dist;\n",
       "            best_tickscale = tickscale;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
       "        root.data(axis + \"tickscale\", best_tickscale);\n",
       "        var mark_inscale_gridlines = function (element, i) {\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        var mark_inscale_labels = function (element, i) {\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        root.select(\".\" + axis + \"gridlines\").selectAll(\"path\").forEach(mark_inscale_gridlines);\n",
       "        root.select(\".\" + axis + \"labels\").selectAll(\"text\").forEach(mark_inscale_labels);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "var set_plot_pan_zoom = function(root, tx, ty, scale) {\n",
       "    var old_scale = root.data(\"scale\");\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    // compute the viewport derived from tx, ty, and scale\n",
       "    var x_min = -width * scale - (scale * width - width),\n",
       "        x_max = width * scale,\n",
       "        y_min = -height * scale - (scale * height - height),\n",
       "        y_max = height * scale;\n",
       "\n",
       "    var x0 = bounds.x0 - scale * bounds.x0,\n",
       "        y0 = bounds.y0 - scale * bounds.y0;\n",
       "\n",
       "    var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
       "        ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
       "\n",
       "    tx += x0;\n",
       "    ty += y0;\n",
       "\n",
       "    // when the scale change, we may need to alter which set of\n",
       "    // ticks is being displayed\n",
       "    if (scale != old_scale) {\n",
       "        update_tickscale(root, scale, \"x\");\n",
       "        update_tickscale(root, scale, \"y\");\n",
       "    }\n",
       "\n",
       "    set_geometry_transform(root, tx, ty, scale);\n",
       "\n",
       "    root.data(\"scale\", scale);\n",
       "    root.data(\"tx\", tx);\n",
       "    root.data(\"ty\", ty);\n",
       "};\n",
       "\n",
       "\n",
       "var scale_centered_translation = function(root, scale) {\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    var tx0 = root.data(\"tx\"),\n",
       "        ty0 = root.data(\"ty\");\n",
       "\n",
       "    var scale0 = root.data(\"scale\");\n",
       "\n",
       "    // how off from center the current view is\n",
       "    var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),\n",
       "        yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);\n",
       "\n",
       "    // rescale offsets\n",
       "    xoff = xoff * scale / scale0;\n",
       "    yoff = yoff * scale / scale0;\n",
       "\n",
       "    // adjust for the panel position being scaled\n",
       "    var x_edge_adjust = bounds.x0 * (1 - scale),\n",
       "        y_edge_adjust = bounds.y0 * (1 - scale);\n",
       "\n",
       "    return {\n",
       "        x: xoff + x_edge_adjust + (width - width * scale) / 2,\n",
       "        y: yoff + y_edge_adjust + (height - height * scale) / 2\n",
       "    };\n",
       "};\n",
       "\n",
       "\n",
       "// Initialize data for panning zooming if it isn't already.\n",
       "var init_pan_zoom = function(root) {\n",
       "    if (root.data(\"zoompan-ready\")) {\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    // The non-scaling-stroke trick. Rather than try to correct for the\n",
       "    // stroke-width when zooming, we force it to a fixed value.\n",
       "    var px_per_mm = root.node.getCTM().a;\n",
       "\n",
       "    // Drag events report deltas in pixels, which we'd like to convert to\n",
       "    // millimeters.\n",
       "    root.data(\"px_per_mm\", px_per_mm);\n",
       "\n",
       "    root.selectAll(\"path\")\n",
       "        .forEach(function (element, i) {\n",
       "        sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
       "        if (sw > 0) {\n",
       "            element.attribute(\"stroke-width\", sw);\n",
       "            element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
       "        }\n",
       "    });\n",
       "\n",
       "    // Store ticks labels original tranformation\n",
       "    root.selectAll(\".xlabels > text, .ylabels > text\")\n",
       "        .forEach(function (element, i) {\n",
       "            var lm = element.transform().localMatrix;\n",
       "            element.data(\"static_transform\",\n",
       "                new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
       "        });\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\");\n",
       "    var ygridlines = root.select(\".ygridlines\");\n",
       "    var xlabels = root.select(\".xlabels\");\n",
       "    var ylabels = root.select(\".ylabels\");\n",
       "\n",
       "    if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
       "    if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
       "    if (root.data(\"scale\") === undefined) root.data(\"scale\", 1.0);\n",
       "    if (root.data(\"xtickscales\") === undefined) {\n",
       "\n",
       "        // index all the tick scales that are listed\n",
       "        var xtickscales = {};\n",
       "        var ytickscales = {};\n",
       "        var add_x_tick_scales = function (element, i) {\n",
       "            xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "        var add_y_tick_scales = function (element, i) {\n",
       "            ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "\n",
       "        if (xgridlines) xgridlines.selectAll(\"path\").forEach(add_x_tick_scales);\n",
       "        if (ygridlines) ygridlines.selectAll(\"path\").forEach(add_y_tick_scales);\n",
       "        if (xlabels) xlabels.selectAll(\"text\").forEach(add_x_tick_scales);\n",
       "        if (ylabels) ylabels.selectAll(\"text\").forEach(add_y_tick_scales);\n",
       "\n",
       "        root.data(\"xtickscales\", xtickscales);\n",
       "        root.data(\"ytickscales\", ytickscales);\n",
       "        root.data(\"xtickscale\", 1.0);\n",
       "    }\n",
       "\n",
       "    var min_scale = 1.0, max_scale = 1.0;\n",
       "    for (scale in xtickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    for (scale in ytickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    root.data(\"min_scale\", min_scale);\n",
       "    root.data(\"max_scale\", max_scale);\n",
       "\n",
       "    // store the original positions of labels\n",
       "    if (xlabels) {\n",
       "        xlabels.selectAll(\"text\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"x\", element.asPX(\"x\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    if (ylabels) {\n",
       "        ylabels.selectAll(\"text\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"y\", element.asPX(\"y\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    // mark grid lines and ticks as in or out of scale.\n",
       "    var mark_inscale = function (element, i) {\n",
       "        element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
       "    };\n",
       "\n",
       "    if (xgridlines) xgridlines.selectAll(\"path\").forEach(mark_inscale);\n",
       "    if (ygridlines) ygridlines.selectAll(\"path\").forEach(mark_inscale);\n",
       "    if (xlabels) xlabels.selectAll(\"text\").forEach(mark_inscale);\n",
       "    if (ylabels) ylabels.selectAll(\"text\").forEach(mark_inscale);\n",
       "\n",
       "    // figure out the upper ond lower bounds on panning using the maximum\n",
       "    // and minum grid lines\n",
       "    var bounds = root.plotbounds();\n",
       "    var pan_bounds = {\n",
       "        x0: 0.0,\n",
       "        y0: 0.0,\n",
       "        x1: 0.0,\n",
       "        y1: 0.0\n",
       "    };\n",
       "\n",
       "    if (xgridlines) {\n",
       "        xgridlines\n",
       "            .selectAll(\"path\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
       "                        pan_bounds.x0 = bounds.x1 - bbox.x;\n",
       "                    }\n",
       "                    if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
       "                        pan_bounds.x1 = bounds.x0 - bbox.x;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        ygridlines\n",
       "            .selectAll(\"path\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
       "                        pan_bounds.y0 = bounds.y1 - bbox.y;\n",
       "                    }\n",
       "                    if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
       "                        pan_bounds.y1 = bounds.y0 - bbox.y;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    // nudge these values a little\n",
       "    pan_bounds.x0 -= 5;\n",
       "    pan_bounds.x1 += 5;\n",
       "    pan_bounds.y0 -= 5;\n",
       "    pan_bounds.y1 += 5;\n",
       "    root.data(\"pan_bounds\", pan_bounds);\n",
       "\n",
       "    root.data(\"zoompan-ready\", true)\n",
       "};\n",
       "\n",
       "\n",
       "// drag actions, i.e. zooming and panning\n",
       "var pan_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        root.data(\"dx\", 0);\n",
       "        root.data(\"dy\", 0);\n",
       "        root.data(\"tx0\", root.data(\"tx\"));\n",
       "        root.data(\"ty0\", root.data(\"ty\"));\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        dx /= px_per_mm;\n",
       "        dy /= px_per_mm;\n",
       "\n",
       "        var tx0 = root.data(\"tx\"),\n",
       "            ty0 = root.data(\"ty\");\n",
       "\n",
       "        var dx0 = root.data(\"dx\"),\n",
       "            dy0 = root.data(\"dy\");\n",
       "\n",
       "        root.data(\"dx\", dx);\n",
       "        root.data(\"dy\", dy);\n",
       "\n",
       "        dx = dx - dx0;\n",
       "        dy = dy - dy0;\n",
       "\n",
       "        var tx = tx0 + dx,\n",
       "            ty = ty0 + dy;\n",
       "\n",
       "        set_plot_pan_zoom(root, tx, ty, root.data(\"scale\"));\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        set_plot_pan_zoom(root, root.data(\"tx0\"), root.data(\"ty0\"), root.data(\"scale\"));\n",
       "    }\n",
       "};\n",
       "\n",
       "var zoom_box;\n",
       "var zoom_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        var bounds = root.plotbounds();\n",
       "        var width = bounds.x1 - bounds.x0,\n",
       "            height = bounds.y1 - bounds.y0;\n",
       "        var ratio = width / height;\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        x = xscalable ? x / px_per_mm : bounds.x0;\n",
       "        y = yscalable ? y / px_per_mm : bounds.y0;\n",
       "        var w = xscalable ? 0 : width;\n",
       "        var h = yscalable ? 0 : height;\n",
       "        zoom_box = root.rect(x, y, w, h).attr({\n",
       "            \"fill\": \"#000\",\n",
       "            \"opacity\": 0.25\n",
       "        });\n",
       "        zoom_box.data(\"ratio\", ratio);\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        var bounds = root.plotbounds();\n",
       "        if (yscalable) {\n",
       "            y /= px_per_mm;\n",
       "            y = Math.max(bounds.y0, y);\n",
       "            y = Math.min(bounds.y1, y);\n",
       "        } else {\n",
       "            y = bounds.y1;\n",
       "        }\n",
       "        if (xscalable) {\n",
       "            x /= px_per_mm;\n",
       "            x = Math.max(bounds.x0, x);\n",
       "            x = Math.min(bounds.x1, x);\n",
       "        } else {\n",
       "            x = bounds.x1;\n",
       "        }\n",
       "\n",
       "        dx = x - zoom_box.attr(\"x\");\n",
       "        dy = y - zoom_box.attr(\"y\");\n",
       "        if (xscalable && yscalable) {\n",
       "            var ratio = zoom_box.data(\"ratio\");\n",
       "            var width = Math.min(Math.abs(dx), ratio * Math.abs(dy));\n",
       "            var height = Math.min(Math.abs(dy), Math.abs(dx) / ratio);\n",
       "            dx = width * dx / Math.abs(dx);\n",
       "            dy = height * dy / Math.abs(dy);\n",
       "        }\n",
       "        var xoffset = 0,\n",
       "            yoffset = 0;\n",
       "        if (dx < 0) {\n",
       "            xoffset = dx;\n",
       "            dx = -1 * dx;\n",
       "        }\n",
       "        if (dy < 0) {\n",
       "            yoffset = dy;\n",
       "            dy = -1 * dy;\n",
       "        }\n",
       "        if (isNaN(dy)) {\n",
       "            dy = 0.0;\n",
       "        }\n",
       "        if (isNaN(dx)) {\n",
       "            dx = 0.0;\n",
       "        }\n",
       "        zoom_box.transform(\"T\" + xoffset + \",\" + yoffset);\n",
       "        zoom_box.attr(\"width\", dx);\n",
       "        zoom_box.attr(\"height\", dy);\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var zoom_bounds = zoom_box.getBBox();\n",
       "        if (zoom_bounds.width * zoom_bounds.height <= 0) {\n",
       "            return;\n",
       "        }\n",
       "        var plot_bounds = root.plotbounds();\n",
       "        var zoom_factor = 1.0;\n",
       "        if (yscalable) {\n",
       "            zoom_factor = (plot_bounds.y1 - plot_bounds.y0) / zoom_bounds.height;\n",
       "        } else {\n",
       "            zoom_factor = (plot_bounds.x1 - plot_bounds.x0) / zoom_bounds.width;\n",
       "        }\n",
       "        var tx = (root.data(\"tx\") - zoom_bounds.x) * zoom_factor + plot_bounds.x0,\n",
       "            ty = (root.data(\"ty\") - zoom_bounds.y) * zoom_factor + plot_bounds.y0;\n",
       "        set_plot_pan_zoom(root, tx, ty, root.data(\"scale\") * zoom_factor);\n",
       "        zoom_box.remove();\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        zoom_box.remove();\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var scalable = root.hasClass(\"xscalable\") || root.hasClass(\"yscalable\");\n",
       "    var zoomable = !event.altKey && !event.ctrlKey && event.shiftKey && scalable;\n",
       "    var panable = !event.altKey && !event.ctrlKey && !event.shiftKey && scalable;\n",
       "    var drag_action = zoomable ? zoom_action :\n",
       "                      panable  ? pan_action :\n",
       "                                 undefined;\n",
       "    root.data(\"drag_action\", drag_action);\n",
       "    if (drag_action) {\n",
       "        var cancel_drag_action = function(event) {\n",
       "            if (event.which == 27) { // esc key\n",
       "                drag_action.cancel(root);\n",
       "                root.data(\"drag_action\", undefined);\n",
       "            }\n",
       "        };\n",
       "        window.addEventListener(\"keyup\", cancel_drag_action);\n",
       "        root.data(\"cancel_drag_action\", cancel_drag_action);\n",
       "        drag_action.start(root, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.update(root, dx, dy, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onend = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    window.removeEventListener(\"keyup\", root.data(\"cancel_drag_action\"));\n",
       "    root.data(\"cancel_drag_action\", undefined);\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.end(root, event);\n",
       "    }\n",
       "    root.data(\"drag_action\", undefined);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_scroll = function(event) {\n",
       "    if (event.shiftKey) {\n",
       "        increase_zoom_by_position(this.plotroot(), 0.001 * event.wheelDelta);\n",
       "        event.preventDefault();\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_button_mouseover = function(event) {\n",
       "    this.select(\".button_logo\")\n",
       "         .animate({fill: this.data(\"mouseover_color\")}, 100);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_button_mouseout = function(event) {\n",
       "     this.select(\".button_logo\")\n",
       "         .animate({fill: this.data(\"mouseout_color\")}, 100);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_zoomout_click = function(event) {\n",
       "    increase_zoom_by_position(this.plotroot(), -0.1, true);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_zoomin_click = function(event) {\n",
       "    increase_zoom_by_position(this.plotroot(), 0.1, true);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_track_click = function(event) {\n",
       "    // TODO\n",
       "};\n",
       "\n",
       "\n",
       "// Map slider position x to scale y using the function y = a*exp(b*x)+c.\n",
       "// The constants a, b, and c are solved using the constraint that the function\n",
       "// should go through the points (0; min_scale), (0.5; 1), and (1; max_scale).\n",
       "var scale_from_slider_position = function(position, min_scale, max_scale) {\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return a * Math.exp(b * position) + c;\n",
       "}\n",
       "\n",
       "// inverse of scale_from_slider_position\n",
       "var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return 1 / b * Math.log((scale - c) / a);\n",
       "}\n",
       "\n",
       "var increase_zoom_by_position = function(root, delta_position, animate) {\n",
       "    var scale = root.data(\"scale\"),\n",
       "        min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\");\n",
       "    var position = slider_position_from_scale(scale, min_scale, max_scale);\n",
       "    position += delta_position;\n",
       "    scale = scale_from_slider_position(position, min_scale, max_scale);\n",
       "    set_zoom(root, scale, animate);\n",
       "}\n",
       "\n",
       "var set_zoom = function(root, scale, animate) {\n",
       "    var min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\"),\n",
       "        old_scale = root.data(\"scale\");\n",
       "    var new_scale = Math.max(min_scale, Math.min(scale, max_scale));\n",
       "    if (animate) {\n",
       "        Snap.animate(\n",
       "            old_scale,\n",
       "            new_scale,\n",
       "            function (new_scale) {\n",
       "                update_plot_scale(root, new_scale);\n",
       "            },\n",
       "            200);\n",
       "    } else {\n",
       "        update_plot_scale(root, new_scale);\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "var update_plot_scale = function(root, new_scale) {\n",
       "    var trans = scale_centered_translation(root, new_scale);\n",
       "    set_plot_pan_zoom(root, trans.x, trans.y, new_scale);\n",
       "\n",
       "    root.selectAll(\".zoomslider_thumb\")\n",
       "        .forEach(function (element, i) {\n",
       "            var min_pos = element.data(\"min_pos\"),\n",
       "                max_pos = element.data(\"max_pos\"),\n",
       "                min_scale = root.data(\"min_scale\"),\n",
       "                max_scale = root.data(\"max_scale\");\n",
       "            var xmid = (min_pos + max_pos) / 2;\n",
       "            var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);\n",
       "            element.transform(new Snap.Matrix().translate(\n",
       "                Math.max(min_pos, Math.min(\n",
       "                         max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));\n",
       "    });\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var min_pos = this.data(\"min_pos\"),\n",
       "        max_pos = this.data(\"max_pos\"),\n",
       "        min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\"),\n",
       "        old_scale = root.data(\"old_scale\");\n",
       "\n",
       "    var px_per_mm = root.data(\"px_per_mm\");\n",
       "    dx /= px_per_mm;\n",
       "    dy /= px_per_mm;\n",
       "\n",
       "    var xmid = (min_pos + max_pos) / 2;\n",
       "    var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +\n",
       "                   dx / (max_pos - min_pos);\n",
       "\n",
       "    // compute the new scale\n",
       "    var new_scale = scale_from_slider_position(xpos, min_scale, max_scale);\n",
       "    new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));\n",
       "\n",
       "    update_plot_scale(root, new_scale);\n",
       "    event.stopPropagation();\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_thumb_dragstart = function(x, y, event) {\n",
       "    this.animate({fill: this.data(\"mouseover_color\")}, 100);\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    // keep track of what the scale was when we started dragging\n",
       "    root.data(\"old_scale\", root.data(\"scale\"));\n",
       "    event.stopPropagation();\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_thumb_dragend = function(event) {\n",
       "    this.animate({fill: this.data(\"mouseout_color\")}, 100);\n",
       "    event.stopPropagation();\n",
       "};\n",
       "\n",
       "\n",
       "var toggle_color_class = function(root, color_class, ison) {\n",
       "    var guides = root.selectAll(\".guide.\" + color_class + \",.guide .\" + color_class);\n",
       "    var geoms = root.selectAll(\".geometry.\" + color_class + \",.geometry .\" + color_class);\n",
       "    if (ison) {\n",
       "        guides.animate({opacity: 0.5}, 250);\n",
       "        geoms.animate({opacity: 0.0}, 250);\n",
       "    } else {\n",
       "        guides.animate({opacity: 1.0}, 250);\n",
       "        geoms.animate({opacity: 1.0}, 250);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.colorkey_swatch_click = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    var color_class = this.data(\"color_class\");\n",
       "\n",
       "    if (event.shiftKey) {\n",
       "        root.selectAll(\".colorkey text\")\n",
       "            .forEach(function (element) {\n",
       "                var other_color_class = element.data(\"color_class\");\n",
       "                if (other_color_class != color_class) {\n",
       "                    toggle_color_class(root, other_color_class,\n",
       "                                       element.attr(\"opacity\") == 1.0);\n",
       "                }\n",
       "            });\n",
       "    } else {\n",
       "        toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "return Gadfly;\n",
       "\n",
       "}));\n",
       "\n",
       "\n",
       "//@ sourceURL=gadfly.js\n",
       "\n",
       "(function (glob, factory) {\n",
       "    // AMD support\n",
       "      if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
       "        require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
       "            factory(Snap, Gadfly);\n",
       "        });\n",
       "      } else {\n",
       "          factory(glob.Snap, glob.Gadfly);\n",
       "      }\n",
       "})(window, function (Snap, Gadfly) {\n",
       "    var fig = Snap(\"#img-5cbf6b2f\");\n",
       "fig.select(\"#img-5cbf6b2f-4\")\n",
       "   .drag(function() {}, function() {}, function() {});\n",
       "fig.select(\"#img-5cbf6b2f-6\")\n",
       "   .data(\"color_class\", \"color_f1\")\n",
       ".click(Gadfly.colorkey_swatch_click)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-7\")\n",
       "   .data(\"color_class\", \"color_f2\")\n",
       ".click(Gadfly.colorkey_swatch_click)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-9\")\n",
       "   .data(\"color_class\", \"color_f1\")\n",
       ".click(Gadfly.colorkey_swatch_click)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-10\")\n",
       "   .data(\"color_class\", \"color_f2\")\n",
       ".click(Gadfly.colorkey_swatch_click)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-14\")\n",
       "   .init_gadfly();\n",
       "fig.select(\"#img-5cbf6b2f-17\")\n",
       "   .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-17\")\n",
       "   .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-131\")\n",
       "   .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-131\")\n",
       "   .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-317\")\n",
       "   .data(\"mouseover_color\", \"#CD5C5C\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-317\")\n",
       "   .data(\"mouseout_color\", \"#6A6A6A\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-317\")\n",
       "   .click(Gadfly.zoomslider_zoomin_click)\n",
       ".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
       ".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-321\")\n",
       "   .data(\"max_pos\", 111.58)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-321\")\n",
       "   .data(\"min_pos\", 94.58)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-321\")\n",
       "   .click(Gadfly.zoomslider_track_click);\n",
       "fig.select(\"#img-5cbf6b2f-323\")\n",
       "   .data(\"max_pos\", 111.58)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-323\")\n",
       "   .data(\"min_pos\", 94.58)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-323\")\n",
       "   .data(\"mouseover_color\", \"#CD5C5C\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-323\")\n",
       "   .data(\"mouseout_color\", \"#6A6A6A\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-323\")\n",
       "   .drag(Gadfly.zoomslider_thumb_dragmove,\n",
       "     Gadfly.zoomslider_thumb_dragstart,\n",
       "     Gadfly.zoomslider_thumb_dragend)\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-325\")\n",
       "   .data(\"mouseover_color\", \"#CD5C5C\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-325\")\n",
       "   .data(\"mouseout_color\", \"#6A6A6A\")\n",
       ";\n",
       "fig.select(\"#img-5cbf6b2f-325\")\n",
       "   .click(Gadfly.zoomslider_zoomout_click)\n",
       ".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
       ".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
       ";\n",
       "    });\n",
       "]]> </script>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot(...)"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Gadfly\n",
    "plot(layer([f, g], -3, 3), layer(x=xs, y=f.(xs), Geom.point))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1変数関数の微分を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import ForwardDiff  # https://github.com/JuliaDiff/ForwardDiff.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f′ (generic function with 1 method)"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) = sin(x) * exp(-x)\n",
    "f′(x) = ForwardDiff.derivative(f, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3095598756531122"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.11079376530669924"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f′(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\"\n",
       "     xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     xmlns:gadfly=\"http://www.gadflyjl.org/ns\"\n",
       "     version=\"1.2\"\n",
       "     width=\"141.42mm\" height=\"100mm\" viewBox=\"0 0 141.42 100\"\n",
       "     stroke=\"none\"\n",
       "     fill=\"#000000\"\n",
       "     stroke-width=\"0.3\"\n",
       "     font-size=\"3.88\"\n",
       ">\n",
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       "    <text x=\"73.33\" y=\"88.39\" text-anchor=\"middle\" dy=\"0.6em\">x</text>\n",
       "  </g>\n",
       "  <g class=\"guide xlabels\" font-size=\"2.82\" font-family=\"'PT Sans Caption','Helvetica Neue','Helvetica',sans-serif\" fill=\"#6C606B\" id=\"img-81c4d93a-3\">\n",
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       "  </g>\n",
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       "A.undrag=function(){for(var b=r.length;b--;)r[b].el==this&&(this.unmousedown(r[b].start),r.splice(b,1),k.unbind(\"snap.drag.*.\"+this.id));!r.length&&a.unmousemove(e).unmouseup(l);return this}});C.plugin(function(a,v,y,C){y=y.prototype;var A=/^\\s*url\\((.+)\\)/,w=String,z=a._.$;a.filter={};y.filter=function(d){var f=this;\"svg\"!=f.type&&(f=f.paper);d=a.parse(w(d));var k=a._.id(),u=z(\"filter\");z(u,{id:k,filterUnits:\"userSpaceOnUse\"});u.appendChild(d.node);f.defs.appendChild(u);return new v(u)};k.on(\"snap.util.getattr.filter\",\n",
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       "amount2:1-d})};a.filter.invert.toString=function(){return this()};a.filter.brightness=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\"/><feFuncG type=\"linear\" slope=\"{amount}\"/><feFuncB type=\"linear\" slope=\"{amount}\"/></feComponentTransfer>',{amount:d})};a.filter.brightness.toString=function(){return this()};a.filter.contrast=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncG type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncB type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/></feComponentTransfer>',\n",
       "{amount:d,amount2:0.5-d/2})};a.filter.contrast.toString=function(){return this()}});return C});\n",
       "\n",
       "]]> </script>\n",
       "<script> <![CDATA[\n",
       "\n",
       "(function (glob, factory) {\n",
       "    // AMD support\n",
       "    if (typeof define === \"function\" && define.amd) {\n",
       "        // Define as an anonymous module\n",
       "        define(\"Gadfly\", [\"Snap.svg\"], function (Snap) {\n",
       "            return factory(Snap);\n",
       "        });\n",
       "    } else {\n",
       "        // Browser globals (glob is window)\n",
       "        // Snap adds itself to window\n",
       "        glob.Gadfly = factory(glob.Snap);\n",
       "    }\n",
       "}(this, function (Snap) {\n",
       "\n",
       "var Gadfly = {};\n",
       "\n",
       "// Get an x/y coordinate value in pixels\n",
       "var xPX = function(fig, x) {\n",
       "    var client_box = fig.node.getBoundingClientRect();\n",
       "    return x * fig.node.viewBox.baseVal.width / client_box.width;\n",
       "};\n",
       "\n",
       "var yPX = function(fig, y) {\n",
       "    var client_box = fig.node.getBoundingClientRect();\n",
       "    return y * fig.node.viewBox.baseVal.height / client_box.height;\n",
       "};\n",
       "\n",
       "\n",
       "Snap.plugin(function (Snap, Element, Paper, global) {\n",
       "    // Traverse upwards from a snap element to find and return the first\n",
       "    // note with the \"plotroot\" class.\n",
       "    Element.prototype.plotroot = function () {\n",
       "        var element = this;\n",
       "        while (!element.hasClass(\"plotroot\") && element.parent() != null) {\n",
       "            element = element.parent();\n",
       "        }\n",
       "        return element;\n",
       "    };\n",
       "\n",
       "    Element.prototype.svgroot = function () {\n",
       "        var element = this;\n",
       "        while (element.node.nodeName != \"svg\" && element.parent() != null) {\n",
       "            element = element.parent();\n",
       "        }\n",
       "        return element;\n",
       "    };\n",
       "\n",
       "    Element.prototype.plotbounds = function () {\n",
       "        var root = this.plotroot()\n",
       "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
       "        return {\n",
       "            x0: bbox.x,\n",
       "            x1: bbox.x + bbox.width,\n",
       "            y0: bbox.y,\n",
       "            y1: bbox.y + bbox.height\n",
       "        };\n",
       "    };\n",
       "\n",
       "    Element.prototype.plotcenter = function () {\n",
       "        var root = this.plotroot()\n",
       "        var bbox = root.select(\".guide.background\").node.getBBox();\n",
       "        return {\n",
       "            x: bbox.x + bbox.width / 2,\n",
       "            y: bbox.y + bbox.height / 2\n",
       "        };\n",
       "    };\n",
       "\n",
       "    // Emulate IE style mouseenter/mouseleave events, since Microsoft always\n",
       "    // does everything right.\n",
       "    // See: http://www.dynamic-tools.net/toolbox/isMouseLeaveOrEnter/\n",
       "    var events = [\"mouseenter\", \"mouseleave\"];\n",
       "\n",
       "    for (i in events) {\n",
       "        (function (event_name) {\n",
       "            var event_name = events[i];\n",
       "            Element.prototype[event_name] = function (fn, scope) {\n",
       "                if (Snap.is(fn, \"function\")) {\n",
       "                    var fn2 = function (event) {\n",
       "                        if (event.type != \"mouseover\" && event.type != \"mouseout\") {\n",
       "                            return;\n",
       "                        }\n",
       "\n",
       "                        var reltg = event.relatedTarget ? event.relatedTarget :\n",
       "                            event.type == \"mouseout\" ? event.toElement : event.fromElement;\n",
       "                        while (reltg && reltg != this.node) reltg = reltg.parentNode;\n",
       "\n",
       "                        if (reltg != this.node) {\n",
       "                            return fn.apply(this, event);\n",
       "                        }\n",
       "                    };\n",
       "\n",
       "                    if (event_name == \"mouseenter\") {\n",
       "                        this.mouseover(fn2, scope);\n",
       "                    } else {\n",
       "                        this.mouseout(fn2, scope);\n",
       "                    }\n",
       "                }\n",
       "                return this;\n",
       "            };\n",
       "        })(events[i]);\n",
       "    }\n",
       "\n",
       "\n",
       "    Element.prototype.mousewheel = function (fn, scope) {\n",
       "        if (Snap.is(fn, \"function\")) {\n",
       "            var el = this;\n",
       "            var fn2 = function (event) {\n",
       "                fn.apply(el, [event]);\n",
       "            };\n",
       "        }\n",
       "\n",
       "        this.node.addEventListener(\n",
       "            /Firefox/i.test(navigator.userAgent) ? \"DOMMouseScroll\" : \"mousewheel\",\n",
       "            fn2);\n",
       "\n",
       "        return this;\n",
       "    };\n",
       "\n",
       "\n",
       "    // Snap's attr function can be too slow for things like panning/zooming.\n",
       "    // This is a function to directly update element attributes without going\n",
       "    // through eve.\n",
       "    Element.prototype.attribute = function(key, val) {\n",
       "        if (val === undefined) {\n",
       "            return this.node.getAttribute(key);\n",
       "        } else {\n",
       "            this.node.setAttribute(key, val);\n",
       "            return this;\n",
       "        }\n",
       "    };\n",
       "\n",
       "    Element.prototype.init_gadfly = function() {\n",
       "        this.mouseenter(Gadfly.plot_mouseover)\n",
       "            .mouseleave(Gadfly.plot_mouseout)\n",
       "            .dblclick(Gadfly.plot_dblclick)\n",
       "            .mousewheel(Gadfly.guide_background_scroll)\n",
       "            .drag(Gadfly.guide_background_drag_onmove,\n",
       "                  Gadfly.guide_background_drag_onstart,\n",
       "                  Gadfly.guide_background_drag_onend);\n",
       "        this.mouseenter(function (event) {\n",
       "            init_pan_zoom(this.plotroot());\n",
       "        });\n",
       "        return this;\n",
       "    };\n",
       "});\n",
       "\n",
       "\n",
       "// When the plot is moused over, emphasize the grid lines.\n",
       "Gadfly.plot_mouseover = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    var keyboard_zoom = function(event) {\n",
       "        if (event.which == 187) { // plus\n",
       "            increase_zoom_by_position(root, 0.1, true);\n",
       "        } else if (event.which == 189) { // minus\n",
       "            increase_zoom_by_position(root, -0.1, true);\n",
       "        }\n",
       "    };\n",
       "    root.data(\"keyboard_zoom\", keyboard_zoom);\n",
       "    window.addEventListener(\"keyup\", keyboard_zoom);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    xgridlines.data(\"unfocused_strokedash\",\n",
       "                    xgridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "    ygridlines.data(\"unfocused_strokedash\",\n",
       "                    ygridlines.attribute(\"stroke-dasharray\").replace(/(\\d)(,|$)/g, \"$1mm$2\"));\n",
       "\n",
       "    // emphasize grid lines\n",
       "    var destcolor = root.data(\"focused_xgrid_color\");\n",
       "    xgridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    destcolor = root.data(\"focused_ygrid_color\");\n",
       "    ygridlines.attribute(\"stroke-dasharray\", \"none\")\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    // reveal zoom slider\n",
       "    root.select(\".zoomslider\")\n",
       "        .animate({opacity: 1.0}, 250);\n",
       "};\n",
       "\n",
       "// Reset pan and zoom on double click\n",
       "Gadfly.plot_dblclick = function(event) {\n",
       "  set_plot_pan_zoom(this.plotroot(), 0.0, 0.0, 1.0);\n",
       "};\n",
       "\n",
       "// Unemphasize grid lines on mouse out.\n",
       "Gadfly.plot_mouseout = function(event) {\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    window.removeEventListener(\"keyup\", root.data(\"keyboard_zoom\"));\n",
       "    root.data(\"keyboard_zoom\", undefined);\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\"),\n",
       "        ygridlines = root.select(\".ygridlines\");\n",
       "\n",
       "    var destcolor = root.data(\"unfocused_xgrid_color\");\n",
       "\n",
       "    xgridlines.attribute(\"stroke-dasharray\", xgridlines.data(\"unfocused_strokedash\"))\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    destcolor = root.data(\"unfocused_ygrid_color\");\n",
       "    ygridlines.attribute(\"stroke-dasharray\", ygridlines.data(\"unfocused_strokedash\"))\n",
       "              .selectAll(\"path\")\n",
       "              .animate({stroke: destcolor}, 250);\n",
       "\n",
       "    // hide zoom slider\n",
       "    root.select(\".zoomslider\")\n",
       "        .animate({opacity: 0.0}, 250);\n",
       "};\n",
       "\n",
       "\n",
       "var set_geometry_transform = function(root, tx, ty, scale) {\n",
       "    var xscalable = root.hasClass(\"xscalable\"),\n",
       "        yscalable = root.hasClass(\"yscalable\");\n",
       "\n",
       "    var old_scale = root.data(\"scale\");\n",
       "\n",
       "    var xscale = xscalable ? scale : 1.0,\n",
       "        yscale = yscalable ? scale : 1.0;\n",
       "\n",
       "    tx = xscalable ? tx : 0.0;\n",
       "    ty = yscalable ? ty : 0.0;\n",
       "\n",
       "    var t = new Snap.Matrix().translate(tx, ty).scale(xscale, yscale);\n",
       "\n",
       "    root.selectAll(\".geometry, image\")\n",
       "        .forEach(function (element, i) {\n",
       "            element.transform(t);\n",
       "        });\n",
       "\n",
       "    bounds = root.plotbounds();\n",
       "\n",
       "    if (yscalable) {\n",
       "        var xfixed_t = new Snap.Matrix().translate(0, ty).scale(1.0, yscale);\n",
       "        root.selectAll(\".xfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(xfixed_t);\n",
       "            });\n",
       "\n",
       "        root.select(\".ylabels\")\n",
       "            .transform(xfixed_t)\n",
       "            .selectAll(\"text\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var cx = element.asPX(\"x\"),\n",
       "                        cy = element.asPX(\"y\");\n",
       "                    var st = element.data(\"static_transform\");\n",
       "                    unscale_t = new Snap.Matrix();\n",
       "                    unscale_t.scale(1, 1/scale, cx, cy).add(st);\n",
       "                    element.transform(unscale_t);\n",
       "\n",
       "                    var y = cy * scale + ty;\n",
       "                    element.attr(\"visibility\",\n",
       "                        bounds.y0 <= y && y <= bounds.y1 ? \"visible\" : \"hidden\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    if (xscalable) {\n",
       "        var yfixed_t = new Snap.Matrix().translate(tx, 0).scale(xscale, 1.0);\n",
       "        var xtrans = new Snap.Matrix().translate(tx, 0);\n",
       "        root.selectAll(\".yfixed\")\n",
       "            .forEach(function (element, i) {\n",
       "                element.transform(yfixed_t);\n",
       "            });\n",
       "\n",
       "        root.select(\".xlabels\")\n",
       "            .transform(yfixed_t)\n",
       "            .selectAll(\"text\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var cx = element.asPX(\"x\"),\n",
       "                        cy = element.asPX(\"y\");\n",
       "                    var st = element.data(\"static_transform\");\n",
       "                    unscale_t = new Snap.Matrix();\n",
       "                    unscale_t.scale(1/scale, 1, cx, cy).add(st);\n",
       "\n",
       "                    element.transform(unscale_t);\n",
       "\n",
       "                    var x = cx * scale + tx;\n",
       "                    element.attr(\"visibility\",\n",
       "                        bounds.x0 <= x && x <= bounds.x1 ? \"visible\" : \"hidden\");\n",
       "                    }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    // we must unscale anything that is scale invariance: widths, raiduses, etc.\n",
       "    var size_attribs = [\"font-size\"];\n",
       "    var unscaled_selection = \".geometry, .geometry *\";\n",
       "    if (xscalable) {\n",
       "        size_attribs.push(\"rx\");\n",
       "        unscaled_selection += \", .xgridlines\";\n",
       "    }\n",
       "    if (yscalable) {\n",
       "        size_attribs.push(\"ry\");\n",
       "        unscaled_selection += \", .ygridlines\";\n",
       "    }\n",
       "\n",
       "    root.selectAll(unscaled_selection)\n",
       "        .forEach(function (element, i) {\n",
       "            // circle need special help\n",
       "            if (element.node.nodeName == \"circle\") {\n",
       "                var cx = element.attribute(\"cx\"),\n",
       "                    cy = element.attribute(\"cy\");\n",
       "                unscale_t = new Snap.Matrix().scale(1/xscale, 1/yscale,\n",
       "                                                        cx, cy);\n",
       "                element.transform(unscale_t);\n",
       "                return;\n",
       "            }\n",
       "\n",
       "            for (i in size_attribs) {\n",
       "                var key = size_attribs[i];\n",
       "                var val = parseFloat(element.attribute(key));\n",
       "                if (val !== undefined && val != 0 && !isNaN(val)) {\n",
       "                    element.attribute(key, val * old_scale / scale);\n",
       "                }\n",
       "            }\n",
       "        });\n",
       "};\n",
       "\n",
       "\n",
       "// Find the most appropriate tick scale and update label visibility.\n",
       "var update_tickscale = function(root, scale, axis) {\n",
       "    if (!root.hasClass(axis + \"scalable\")) return;\n",
       "\n",
       "    var tickscales = root.data(axis + \"tickscales\");\n",
       "    var best_tickscale = 1.0;\n",
       "    var best_tickscale_dist = Infinity;\n",
       "    for (tickscale in tickscales) {\n",
       "        var dist = Math.abs(Math.log(tickscale) - Math.log(scale));\n",
       "        if (dist < best_tickscale_dist) {\n",
       "            best_tickscale_dist = dist;\n",
       "            best_tickscale = tickscale;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    if (best_tickscale != root.data(axis + \"tickscale\")) {\n",
       "        root.data(axis + \"tickscale\", best_tickscale);\n",
       "        var mark_inscale_gridlines = function (element, i) {\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        var mark_inscale_labels = function (element, i) {\n",
       "            var inscale = element.attr(\"gadfly:scale\") == best_tickscale;\n",
       "            element.attribute(\"gadfly:inscale\", inscale);\n",
       "            element.attr(\"visibility\", inscale ? \"visible\" : \"hidden\");\n",
       "        };\n",
       "\n",
       "        root.select(\".\" + axis + \"gridlines\").selectAll(\"path\").forEach(mark_inscale_gridlines);\n",
       "        root.select(\".\" + axis + \"labels\").selectAll(\"text\").forEach(mark_inscale_labels);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "var set_plot_pan_zoom = function(root, tx, ty, scale) {\n",
       "    var old_scale = root.data(\"scale\");\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    // compute the viewport derived from tx, ty, and scale\n",
       "    var x_min = -width * scale - (scale * width - width),\n",
       "        x_max = width * scale,\n",
       "        y_min = -height * scale - (scale * height - height),\n",
       "        y_max = height * scale;\n",
       "\n",
       "    var x0 = bounds.x0 - scale * bounds.x0,\n",
       "        y0 = bounds.y0 - scale * bounds.y0;\n",
       "\n",
       "    var tx = Math.max(Math.min(tx - x0, x_max), x_min),\n",
       "        ty = Math.max(Math.min(ty - y0, y_max), y_min);\n",
       "\n",
       "    tx += x0;\n",
       "    ty += y0;\n",
       "\n",
       "    // when the scale change, we may need to alter which set of\n",
       "    // ticks is being displayed\n",
       "    if (scale != old_scale) {\n",
       "        update_tickscale(root, scale, \"x\");\n",
       "        update_tickscale(root, scale, \"y\");\n",
       "    }\n",
       "\n",
       "    set_geometry_transform(root, tx, ty, scale);\n",
       "\n",
       "    root.data(\"scale\", scale);\n",
       "    root.data(\"tx\", tx);\n",
       "    root.data(\"ty\", ty);\n",
       "};\n",
       "\n",
       "\n",
       "var scale_centered_translation = function(root, scale) {\n",
       "    var bounds = root.plotbounds();\n",
       "\n",
       "    var width = bounds.x1 - bounds.x0,\n",
       "        height = bounds.y1 - bounds.y0;\n",
       "\n",
       "    var tx0 = root.data(\"tx\"),\n",
       "        ty0 = root.data(\"ty\");\n",
       "\n",
       "    var scale0 = root.data(\"scale\");\n",
       "\n",
       "    // how off from center the current view is\n",
       "    var xoff = tx0 - (bounds.x0 * (1 - scale0) + (width * (1 - scale0)) / 2),\n",
       "        yoff = ty0 - (bounds.y0 * (1 - scale0) + (height * (1 - scale0)) / 2);\n",
       "\n",
       "    // rescale offsets\n",
       "    xoff = xoff * scale / scale0;\n",
       "    yoff = yoff * scale / scale0;\n",
       "\n",
       "    // adjust for the panel position being scaled\n",
       "    var x_edge_adjust = bounds.x0 * (1 - scale),\n",
       "        y_edge_adjust = bounds.y0 * (1 - scale);\n",
       "\n",
       "    return {\n",
       "        x: xoff + x_edge_adjust + (width - width * scale) / 2,\n",
       "        y: yoff + y_edge_adjust + (height - height * scale) / 2\n",
       "    };\n",
       "};\n",
       "\n",
       "\n",
       "// Initialize data for panning zooming if it isn't already.\n",
       "var init_pan_zoom = function(root) {\n",
       "    if (root.data(\"zoompan-ready\")) {\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    // The non-scaling-stroke trick. Rather than try to correct for the\n",
       "    // stroke-width when zooming, we force it to a fixed value.\n",
       "    var px_per_mm = root.node.getCTM().a;\n",
       "\n",
       "    // Drag events report deltas in pixels, which we'd like to convert to\n",
       "    // millimeters.\n",
       "    root.data(\"px_per_mm\", px_per_mm);\n",
       "\n",
       "    root.selectAll(\"path\")\n",
       "        .forEach(function (element, i) {\n",
       "        sw = element.asPX(\"stroke-width\") * px_per_mm;\n",
       "        if (sw > 0) {\n",
       "            element.attribute(\"stroke-width\", sw);\n",
       "            element.attribute(\"vector-effect\", \"non-scaling-stroke\");\n",
       "        }\n",
       "    });\n",
       "\n",
       "    // Store ticks labels original tranformation\n",
       "    root.selectAll(\".xlabels > text, .ylabels > text\")\n",
       "        .forEach(function (element, i) {\n",
       "            var lm = element.transform().localMatrix;\n",
       "            element.data(\"static_transform\",\n",
       "                new Snap.Matrix(lm.a, lm.b, lm.c, lm.d, lm.e, lm.f));\n",
       "        });\n",
       "\n",
       "    var xgridlines = root.select(\".xgridlines\");\n",
       "    var ygridlines = root.select(\".ygridlines\");\n",
       "    var xlabels = root.select(\".xlabels\");\n",
       "    var ylabels = root.select(\".ylabels\");\n",
       "\n",
       "    if (root.data(\"tx\") === undefined) root.data(\"tx\", 0);\n",
       "    if (root.data(\"ty\") === undefined) root.data(\"ty\", 0);\n",
       "    if (root.data(\"scale\") === undefined) root.data(\"scale\", 1.0);\n",
       "    if (root.data(\"xtickscales\") === undefined) {\n",
       "\n",
       "        // index all the tick scales that are listed\n",
       "        var xtickscales = {};\n",
       "        var ytickscales = {};\n",
       "        var add_x_tick_scales = function (element, i) {\n",
       "            xtickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "        var add_y_tick_scales = function (element, i) {\n",
       "            ytickscales[element.attribute(\"gadfly:scale\")] = true;\n",
       "        };\n",
       "\n",
       "        if (xgridlines) xgridlines.selectAll(\"path\").forEach(add_x_tick_scales);\n",
       "        if (ygridlines) ygridlines.selectAll(\"path\").forEach(add_y_tick_scales);\n",
       "        if (xlabels) xlabels.selectAll(\"text\").forEach(add_x_tick_scales);\n",
       "        if (ylabels) ylabels.selectAll(\"text\").forEach(add_y_tick_scales);\n",
       "\n",
       "        root.data(\"xtickscales\", xtickscales);\n",
       "        root.data(\"ytickscales\", ytickscales);\n",
       "        root.data(\"xtickscale\", 1.0);\n",
       "    }\n",
       "\n",
       "    var min_scale = 1.0, max_scale = 1.0;\n",
       "    for (scale in xtickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    for (scale in ytickscales) {\n",
       "        min_scale = Math.min(min_scale, scale);\n",
       "        max_scale = Math.max(max_scale, scale);\n",
       "    }\n",
       "    root.data(\"min_scale\", min_scale);\n",
       "    root.data(\"max_scale\", max_scale);\n",
       "\n",
       "    // store the original positions of labels\n",
       "    if (xlabels) {\n",
       "        xlabels.selectAll(\"text\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"x\", element.asPX(\"x\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    if (ylabels) {\n",
       "        ylabels.selectAll(\"text\")\n",
       "               .forEach(function (element, i) {\n",
       "                   element.data(\"y\", element.asPX(\"y\"));\n",
       "               });\n",
       "    }\n",
       "\n",
       "    // mark grid lines and ticks as in or out of scale.\n",
       "    var mark_inscale = function (element, i) {\n",
       "        element.attribute(\"gadfly:inscale\", element.attribute(\"gadfly:scale\") == 1.0);\n",
       "    };\n",
       "\n",
       "    if (xgridlines) xgridlines.selectAll(\"path\").forEach(mark_inscale);\n",
       "    if (ygridlines) ygridlines.selectAll(\"path\").forEach(mark_inscale);\n",
       "    if (xlabels) xlabels.selectAll(\"text\").forEach(mark_inscale);\n",
       "    if (ylabels) ylabels.selectAll(\"text\").forEach(mark_inscale);\n",
       "\n",
       "    // figure out the upper ond lower bounds on panning using the maximum\n",
       "    // and minum grid lines\n",
       "    var bounds = root.plotbounds();\n",
       "    var pan_bounds = {\n",
       "        x0: 0.0,\n",
       "        y0: 0.0,\n",
       "        x1: 0.0,\n",
       "        y1: 0.0\n",
       "    };\n",
       "\n",
       "    if (xgridlines) {\n",
       "        xgridlines\n",
       "            .selectAll(\"path\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.x1 - bbox.x < pan_bounds.x0) {\n",
       "                        pan_bounds.x0 = bounds.x1 - bbox.x;\n",
       "                    }\n",
       "                    if (bounds.x0 - bbox.x > pan_bounds.x1) {\n",
       "                        pan_bounds.x1 = bounds.x0 - bbox.x;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    if (ygridlines) {\n",
       "        ygridlines\n",
       "            .selectAll(\"path\")\n",
       "            .forEach(function (element, i) {\n",
       "                if (element.attribute(\"gadfly:inscale\") == \"true\") {\n",
       "                    var bbox = element.node.getBBox();\n",
       "                    if (bounds.y1 - bbox.y < pan_bounds.y0) {\n",
       "                        pan_bounds.y0 = bounds.y1 - bbox.y;\n",
       "                    }\n",
       "                    if (bounds.y0 - bbox.y > pan_bounds.y1) {\n",
       "                        pan_bounds.y1 = bounds.y0 - bbox.y;\n",
       "                    }\n",
       "                    element.attr(\"visibility\", \"visible\");\n",
       "                }\n",
       "            });\n",
       "    }\n",
       "\n",
       "    // nudge these values a little\n",
       "    pan_bounds.x0 -= 5;\n",
       "    pan_bounds.x1 += 5;\n",
       "    pan_bounds.y0 -= 5;\n",
       "    pan_bounds.y1 += 5;\n",
       "    root.data(\"pan_bounds\", pan_bounds);\n",
       "\n",
       "    root.data(\"zoompan-ready\", true)\n",
       "};\n",
       "\n",
       "\n",
       "// drag actions, i.e. zooming and panning\n",
       "var pan_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        root.data(\"dx\", 0);\n",
       "        root.data(\"dy\", 0);\n",
       "        root.data(\"tx0\", root.data(\"tx\"));\n",
       "        root.data(\"ty0\", root.data(\"ty\"));\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        dx /= px_per_mm;\n",
       "        dy /= px_per_mm;\n",
       "\n",
       "        var tx0 = root.data(\"tx\"),\n",
       "            ty0 = root.data(\"ty\");\n",
       "\n",
       "        var dx0 = root.data(\"dx\"),\n",
       "            dy0 = root.data(\"dy\");\n",
       "\n",
       "        root.data(\"dx\", dx);\n",
       "        root.data(\"dy\", dy);\n",
       "\n",
       "        dx = dx - dx0;\n",
       "        dy = dy - dy0;\n",
       "\n",
       "        var tx = tx0 + dx,\n",
       "            ty = ty0 + dy;\n",
       "\n",
       "        set_plot_pan_zoom(root, tx, ty, root.data(\"scale\"));\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        set_plot_pan_zoom(root, root.data(\"tx0\"), root.data(\"ty0\"), root.data(\"scale\"));\n",
       "    }\n",
       "};\n",
       "\n",
       "var zoom_box;\n",
       "var zoom_action = {\n",
       "    start: function(root, x, y, event) {\n",
       "        var bounds = root.plotbounds();\n",
       "        var width = bounds.x1 - bounds.x0,\n",
       "            height = bounds.y1 - bounds.y0;\n",
       "        var ratio = width / height;\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        x = xscalable ? x / px_per_mm : bounds.x0;\n",
       "        y = yscalable ? y / px_per_mm : bounds.y0;\n",
       "        var w = xscalable ? 0 : width;\n",
       "        var h = yscalable ? 0 : height;\n",
       "        zoom_box = root.rect(x, y, w, h).attr({\n",
       "            \"fill\": \"#000\",\n",
       "            \"opacity\": 0.25\n",
       "        });\n",
       "        zoom_box.data(\"ratio\", ratio);\n",
       "    },\n",
       "    update: function(root, dx, dy, x, y, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var px_per_mm = root.data(\"px_per_mm\");\n",
       "        var bounds = root.plotbounds();\n",
       "        if (yscalable) {\n",
       "            y /= px_per_mm;\n",
       "            y = Math.max(bounds.y0, y);\n",
       "            y = Math.min(bounds.y1, y);\n",
       "        } else {\n",
       "            y = bounds.y1;\n",
       "        }\n",
       "        if (xscalable) {\n",
       "            x /= px_per_mm;\n",
       "            x = Math.max(bounds.x0, x);\n",
       "            x = Math.min(bounds.x1, x);\n",
       "        } else {\n",
       "            x = bounds.x1;\n",
       "        }\n",
       "\n",
       "        dx = x - zoom_box.attr(\"x\");\n",
       "        dy = y - zoom_box.attr(\"y\");\n",
       "        if (xscalable && yscalable) {\n",
       "            var ratio = zoom_box.data(\"ratio\");\n",
       "            var width = Math.min(Math.abs(dx), ratio * Math.abs(dy));\n",
       "            var height = Math.min(Math.abs(dy), Math.abs(dx) / ratio);\n",
       "            dx = width * dx / Math.abs(dx);\n",
       "            dy = height * dy / Math.abs(dy);\n",
       "        }\n",
       "        var xoffset = 0,\n",
       "            yoffset = 0;\n",
       "        if (dx < 0) {\n",
       "            xoffset = dx;\n",
       "            dx = -1 * dx;\n",
       "        }\n",
       "        if (dy < 0) {\n",
       "            yoffset = dy;\n",
       "            dy = -1 * dy;\n",
       "        }\n",
       "        if (isNaN(dy)) {\n",
       "            dy = 0.0;\n",
       "        }\n",
       "        if (isNaN(dx)) {\n",
       "            dx = 0.0;\n",
       "        }\n",
       "        zoom_box.transform(\"T\" + xoffset + \",\" + yoffset);\n",
       "        zoom_box.attr(\"width\", dx);\n",
       "        zoom_box.attr(\"height\", dy);\n",
       "    },\n",
       "    end: function(root, event) {\n",
       "        var xscalable = root.hasClass(\"xscalable\"),\n",
       "            yscalable = root.hasClass(\"yscalable\");\n",
       "        var zoom_bounds = zoom_box.getBBox();\n",
       "        if (zoom_bounds.width * zoom_bounds.height <= 0) {\n",
       "            return;\n",
       "        }\n",
       "        var plot_bounds = root.plotbounds();\n",
       "        var zoom_factor = 1.0;\n",
       "        if (yscalable) {\n",
       "            zoom_factor = (plot_bounds.y1 - plot_bounds.y0) / zoom_bounds.height;\n",
       "        } else {\n",
       "            zoom_factor = (plot_bounds.x1 - plot_bounds.x0) / zoom_bounds.width;\n",
       "        }\n",
       "        var tx = (root.data(\"tx\") - zoom_bounds.x) * zoom_factor + plot_bounds.x0,\n",
       "            ty = (root.data(\"ty\") - zoom_bounds.y) * zoom_factor + plot_bounds.y0;\n",
       "        set_plot_pan_zoom(root, tx, ty, root.data(\"scale\") * zoom_factor);\n",
       "        zoom_box.remove();\n",
       "    },\n",
       "    cancel: function(root) {\n",
       "        zoom_box.remove();\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onstart = function(x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var scalable = root.hasClass(\"xscalable\") || root.hasClass(\"yscalable\");\n",
       "    var zoomable = !event.altKey && !event.ctrlKey && event.shiftKey && scalable;\n",
       "    var panable = !event.altKey && !event.ctrlKey && !event.shiftKey && scalable;\n",
       "    var drag_action = zoomable ? zoom_action :\n",
       "                      panable  ? pan_action :\n",
       "                                 undefined;\n",
       "    root.data(\"drag_action\", drag_action);\n",
       "    if (drag_action) {\n",
       "        var cancel_drag_action = function(event) {\n",
       "            if (event.which == 27) { // esc key\n",
       "                drag_action.cancel(root);\n",
       "                root.data(\"drag_action\", undefined);\n",
       "            }\n",
       "        };\n",
       "        window.addEventListener(\"keyup\", cancel_drag_action);\n",
       "        root.data(\"cancel_drag_action\", cancel_drag_action);\n",
       "        drag_action.start(root, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onmove = function(dx, dy, x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.update(root, dx, dy, x, y, event);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_drag_onend = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    window.removeEventListener(\"keyup\", root.data(\"cancel_drag_action\"));\n",
       "    root.data(\"cancel_drag_action\", undefined);\n",
       "    var drag_action = root.data(\"drag_action\");\n",
       "    if (drag_action) {\n",
       "        drag_action.end(root, event);\n",
       "    }\n",
       "    root.data(\"drag_action\", undefined);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.guide_background_scroll = function(event) {\n",
       "    if (event.shiftKey) {\n",
       "        increase_zoom_by_position(this.plotroot(), 0.001 * event.wheelDelta);\n",
       "        event.preventDefault();\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_button_mouseover = function(event) {\n",
       "    this.select(\".button_logo\")\n",
       "         .animate({fill: this.data(\"mouseover_color\")}, 100);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_button_mouseout = function(event) {\n",
       "     this.select(\".button_logo\")\n",
       "         .animate({fill: this.data(\"mouseout_color\")}, 100);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_zoomout_click = function(event) {\n",
       "    increase_zoom_by_position(this.plotroot(), -0.1, true);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_zoomin_click = function(event) {\n",
       "    increase_zoom_by_position(this.plotroot(), 0.1, true);\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_track_click = function(event) {\n",
       "    // TODO\n",
       "};\n",
       "\n",
       "\n",
       "// Map slider position x to scale y using the function y = a*exp(b*x)+c.\n",
       "// The constants a, b, and c are solved using the constraint that the function\n",
       "// should go through the points (0; min_scale), (0.5; 1), and (1; max_scale).\n",
       "var scale_from_slider_position = function(position, min_scale, max_scale) {\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return a * Math.exp(b * position) + c;\n",
       "}\n",
       "\n",
       "// inverse of scale_from_slider_position\n",
       "var slider_position_from_scale = function(scale, min_scale, max_scale) {\n",
       "    var a = (1 - 2 * min_scale + min_scale * min_scale) / (min_scale + max_scale - 2),\n",
       "        b = 2 * Math.log((max_scale - 1) / (1 - min_scale)),\n",
       "        c = (min_scale * max_scale - 1) / (min_scale + max_scale - 2);\n",
       "    return 1 / b * Math.log((scale - c) / a);\n",
       "}\n",
       "\n",
       "var increase_zoom_by_position = function(root, delta_position, animate) {\n",
       "    var scale = root.data(\"scale\"),\n",
       "        min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\");\n",
       "    var position = slider_position_from_scale(scale, min_scale, max_scale);\n",
       "    position += delta_position;\n",
       "    scale = scale_from_slider_position(position, min_scale, max_scale);\n",
       "    set_zoom(root, scale, animate);\n",
       "}\n",
       "\n",
       "var set_zoom = function(root, scale, animate) {\n",
       "    var min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\"),\n",
       "        old_scale = root.data(\"scale\");\n",
       "    var new_scale = Math.max(min_scale, Math.min(scale, max_scale));\n",
       "    if (animate) {\n",
       "        Snap.animate(\n",
       "            old_scale,\n",
       "            new_scale,\n",
       "            function (new_scale) {\n",
       "                update_plot_scale(root, new_scale);\n",
       "            },\n",
       "            200);\n",
       "    } else {\n",
       "        update_plot_scale(root, new_scale);\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "var update_plot_scale = function(root, new_scale) {\n",
       "    var trans = scale_centered_translation(root, new_scale);\n",
       "    set_plot_pan_zoom(root, trans.x, trans.y, new_scale);\n",
       "\n",
       "    root.selectAll(\".zoomslider_thumb\")\n",
       "        .forEach(function (element, i) {\n",
       "            var min_pos = element.data(\"min_pos\"),\n",
       "                max_pos = element.data(\"max_pos\"),\n",
       "                min_scale = root.data(\"min_scale\"),\n",
       "                max_scale = root.data(\"max_scale\");\n",
       "            var xmid = (min_pos + max_pos) / 2;\n",
       "            var xpos = slider_position_from_scale(new_scale, min_scale, max_scale);\n",
       "            element.transform(new Snap.Matrix().translate(\n",
       "                Math.max(min_pos, Math.min(\n",
       "                         max_pos, min_pos + (max_pos - min_pos) * xpos)) - xmid, 0));\n",
       "    });\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_thumb_dragmove = function(dx, dy, x, y, event) {\n",
       "    var root = this.plotroot();\n",
       "    var min_pos = this.data(\"min_pos\"),\n",
       "        max_pos = this.data(\"max_pos\"),\n",
       "        min_scale = root.data(\"min_scale\"),\n",
       "        max_scale = root.data(\"max_scale\"),\n",
       "        old_scale = root.data(\"old_scale\");\n",
       "\n",
       "    var px_per_mm = root.data(\"px_per_mm\");\n",
       "    dx /= px_per_mm;\n",
       "    dy /= px_per_mm;\n",
       "\n",
       "    var xmid = (min_pos + max_pos) / 2;\n",
       "    var xpos = slider_position_from_scale(old_scale, min_scale, max_scale) +\n",
       "                   dx / (max_pos - min_pos);\n",
       "\n",
       "    // compute the new scale\n",
       "    var new_scale = scale_from_slider_position(xpos, min_scale, max_scale);\n",
       "    new_scale = Math.min(max_scale, Math.max(min_scale, new_scale));\n",
       "\n",
       "    update_plot_scale(root, new_scale);\n",
       "    event.stopPropagation();\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_thumb_dragstart = function(x, y, event) {\n",
       "    this.animate({fill: this.data(\"mouseover_color\")}, 100);\n",
       "    var root = this.plotroot();\n",
       "\n",
       "    // keep track of what the scale was when we started dragging\n",
       "    root.data(\"old_scale\", root.data(\"scale\"));\n",
       "    event.stopPropagation();\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.zoomslider_thumb_dragend = function(event) {\n",
       "    this.animate({fill: this.data(\"mouseout_color\")}, 100);\n",
       "    event.stopPropagation();\n",
       "};\n",
       "\n",
       "\n",
       "var toggle_color_class = function(root, color_class, ison) {\n",
       "    var guides = root.selectAll(\".guide.\" + color_class + \",.guide .\" + color_class);\n",
       "    var geoms = root.selectAll(\".geometry.\" + color_class + \",.geometry .\" + color_class);\n",
       "    if (ison) {\n",
       "        guides.animate({opacity: 0.5}, 250);\n",
       "        geoms.animate({opacity: 0.0}, 250);\n",
       "    } else {\n",
       "        guides.animate({opacity: 1.0}, 250);\n",
       "        geoms.animate({opacity: 1.0}, 250);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "Gadfly.colorkey_swatch_click = function(event) {\n",
       "    var root = this.plotroot();\n",
       "    var color_class = this.data(\"color_class\");\n",
       "\n",
       "    if (event.shiftKey) {\n",
       "        root.selectAll(\".colorkey text\")\n",
       "            .forEach(function (element) {\n",
       "                var other_color_class = element.data(\"color_class\");\n",
       "                if (other_color_class != color_class) {\n",
       "                    toggle_color_class(root, other_color_class,\n",
       "                                       element.attr(\"opacity\") == 1.0);\n",
       "                }\n",
       "            });\n",
       "    } else {\n",
       "        toggle_color_class(root, color_class, this.attr(\"opacity\") == 1.0);\n",
       "    }\n",
       "};\n",
       "\n",
       "\n",
       "return Gadfly;\n",
       "\n",
       "}));\n",
       "\n",
       "\n",
       "//@ sourceURL=gadfly.js\n",
       "\n",
       "(function (glob, factory) {\n",
       "    // AMD support\n",
       "      if (typeof require === \"function\" && typeof define === \"function\" && define.amd) {\n",
       "        require([\"Snap.svg\", \"Gadfly\"], function (Snap, Gadfly) {\n",
       "            factory(Snap, Gadfly);\n",
       "        });\n",
       "      } else {\n",
       "          factory(glob.Snap, glob.Gadfly);\n",
       "      }\n",
       "})(window, function (Snap, Gadfly) {\n",
       "    var fig = Snap(\"#img-ff04feb6\");\n",
       "fig.select(\"#img-ff04feb6-4\")\n",
       "   .drag(function() {}, function() {}, function() {});\n",
       "fig.select(\"#img-ff04feb6-6\")\n",
       "   .data(\"color_class\", \"color_f1\")\n",
       ".click(Gadfly.colorkey_swatch_click)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-7\")\n",
       "   .data(\"color_class\", \"color_f2\")\n",
       ".click(Gadfly.colorkey_swatch_click)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-9\")\n",
       "   .data(\"color_class\", \"color_f1\")\n",
       ".click(Gadfly.colorkey_swatch_click)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-10\")\n",
       "   .data(\"color_class\", \"color_f2\")\n",
       ".click(Gadfly.colorkey_swatch_click)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-14\")\n",
       "   .init_gadfly();\n",
       "fig.select(\"#img-ff04feb6-17\")\n",
       "   .plotroot().data(\"unfocused_ygrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-17\")\n",
       "   .plotroot().data(\"focused_ygrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-154\")\n",
       "   .plotroot().data(\"unfocused_xgrid_color\", \"#D0D0E0\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-154\")\n",
       "   .plotroot().data(\"focused_xgrid_color\", \"#A0A0A0\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-314\")\n",
       "   .data(\"mouseover_color\", \"#CD5C5C\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-314\")\n",
       "   .data(\"mouseout_color\", \"#6A6A6A\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-314\")\n",
       "   .click(Gadfly.zoomslider_zoomin_click)\n",
       ".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
       ".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-318\")\n",
       "   .data(\"max_pos\", 111.58)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-318\")\n",
       "   .data(\"min_pos\", 94.58)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-318\")\n",
       "   .click(Gadfly.zoomslider_track_click);\n",
       "fig.select(\"#img-ff04feb6-320\")\n",
       "   .data(\"max_pos\", 111.58)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-320\")\n",
       "   .data(\"min_pos\", 94.58)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-320\")\n",
       "   .data(\"mouseover_color\", \"#CD5C5C\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-320\")\n",
       "   .data(\"mouseout_color\", \"#6A6A6A\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-320\")\n",
       "   .drag(Gadfly.zoomslider_thumb_dragmove,\n",
       "     Gadfly.zoomslider_thumb_dragstart,\n",
       "     Gadfly.zoomslider_thumb_dragend)\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-322\")\n",
       "   .data(\"mouseover_color\", \"#CD5C5C\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-322\")\n",
       "   .data(\"mouseout_color\", \"#6A6A6A\")\n",
       ";\n",
       "fig.select(\"#img-ff04feb6-322\")\n",
       "   .click(Gadfly.zoomslider_zoomout_click)\n",
       ".mouseenter(Gadfly.zoomslider_button_mouseover)\n",
       ".mouseleave(Gadfly.zoomslider_button_mouseout)\n",
       ";\n",
       "    });\n",
       "]]> </script>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "Plot(...)"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Gadfly\n",
    "plot([f, f′], -3, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多変数関数の勾配を計算する"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import ReverseDiff  # https://github.com/JuliaDiff/ReverseDiff.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f′ (generic function with 1 method)"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x) = 2dot(x, x) + sum(x)\n",
    "f′(x) = ReverseDiff.gradient(f, x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 1.0\n",
       " 1.0\n",
       " 1.0"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f′(zeros(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Float64,1}:\n",
       " 5.0\n",
       " 5.0\n",
       " 5.0"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f′(ones(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 多変数関数の最小化を行う"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using Optim  # https://github.com/JuliaNLSolvers/Optim.jl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "f (generic function with 1 method)"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2変数のRosenbrock関数 https://en.wikipedia.org/wiki/Rosenbrock_function\n",
    "f(x) =  (1.0 - x[1])^2 + 100.0 * (x[2] - x[1]^2)^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Results of Optimization Algorithm\n",
       " * Algorithm: Nelder-Mead\n",
       " * Starting Point: [0.0,0.0]\n",
       " * Minimizer: [0.9999710322210338,0.9999438685860869]\n",
       " * Minimum: 1.164323e-09\n",
       " * Iterations: 74\n",
       " * Convergence: true\n",
       "   *  √(Σ(yᵢ-ȳ)²)/n < 1.0e-08: true\n",
       "   * Reached Maximum Number of Iterations: false\n",
       " * Objective Function Calls: 108"
      ]
     },
     "execution_count": 257,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize(f, zeros(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Results of Optimization Algorithm\n",
       " * Algorithm: BFGS\n",
       " * Starting Point: [0.0,0.0]\n",
       " * Minimizer: [0.9999999926033423,0.9999999852005353]\n",
       " * Minimum: 5.471433e-17\n",
       " * Iterations: 16\n",
       " * Convergence: true\n",
       "   * |x - x'| < 1.0e-32: false\n",
       "   * |f(x) - f(x')| / |f(x)| < 1.0e-32: false\n",
       "   * |g(x)| < 1.0e-08: true\n",
       "   * f(x) > f(x'): false\n",
       "   * Reached Maximum Number of Iterations: false\n",
       " * Objective Function Calls: 69\n",
       " * Gradient Calls: 69"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "optimize(f, zeros(2), BFGS())"
   ]
  }
 ],
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