3-Arrays.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#Arrays\" data-toc-modified-id=\"Arrays-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Arrays</a></div><div class=\"lev1 toc-item\"><a href=\"#多次元配列\" data-toc-modified-id=\"多次元配列-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>多次元配列</a></div><div class=\"lev1 toc-item\"><a href=\"#配列の初期化\" data-toc-modified-id=\"配列の初期化-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>配列の初期化</a></div><div class=\"lev1 toc-item\"><a href=\"#配列の情報を取るための関数\" data-toc-modified-id=\"配列の情報を取るための関数-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>配列の情報を取るための関数</a></div><div class=\"lev1 toc-item\"><a href=\"#配列の操作\" data-toc-modified-id=\"配列の操作-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>配列の操作</a></div><div class=\"lev1 toc-item\"><a href=\"#配列上の演算\" data-toc-modified-id=\"配列上の演算-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>配列上の演算</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:23.347000Z",
     "start_time": "2018-01-31T03:30:21.993Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{String,1}:\n",
       " \"Apple\" \n",
       " \"Orange\"\n",
       " \"Banana\""
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# まずは普通に配列を定義。\n",
    "# この指定の仕方はPythonとも同じ。\n",
    "fruits = [\"Apple\", \"Orange\", \"Banana\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:24.725000Z",
     "start_time": "2018-01-31T03:30:24.034Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5-element Array{Any,1}:\n",
       "  \"Apple\" \n",
       " 1        \n",
       "  \"Orange\"\n",
       " 2        \n",
       "  \"Banana\""
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 数字が混ざっていても大丈夫\n",
    "fruits_num = [\"Apple\", 1, \"Orange\", 2, \"Banana\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:25.073000Z",
     "start_time": "2018-01-31T03:30:24.719Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Apple\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 要素の取得\n",
    "# indexはPythonとは違って1始まりなので、注意。\n",
    "fruits[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:26.256000Z",
     "start_time": "2018-01-31T03:30:25.704Z"
    }
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "\u001b[91mBoundsError: attempt to access 3-element Array{String,1} at index [0]\u001b[39m",
     "output_type": "error",
     "traceback": [
      "\u001b[91mBoundsError: attempt to access 3-element Array{String,1} at index [0]\u001b[39m",
      "",
      "Stacktrace:",
      " [1] \u001b[1mgetindex\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{String,1}, ::Int64\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m.\\array.jl:520\u001b[22m\u001b[22m"
     ]
    }
   ],
   "source": [
    "# 0を指定するとエラーになる\n",
    "fruits[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:27.917000Z",
     "start_time": "2018-01-31T03:30:27.224Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "String[\"Apple\", \"Orange\", \"Banana\", \"Peach\"]\n",
      "String[\"Apple\", \"Orange\", \"Banana\"]\n"
     ]
    }
   ],
   "source": [
    "# pushとpopもできる\n",
    "push!(fruits, \"Peach\")\n",
    "println(fruits)\n",
    "pop!(fruits)\n",
    "println(fruits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:28.629000Z",
     "start_time": "2018-01-31T03:30:28.625Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{String,1}:\n",
       " \"Apple2\"\n",
       " \"Orange\"\n",
       " \"Banana\""
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 要素にアクセスして情報も更新できる\n",
    "fruits[1] = \"Apple2\"\n",
    "fruits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 多次元配列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:33.312000Z",
     "start_time": "2018-01-31T03:30:32.648Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Array{String,1},1}:\n",
       " String[\"Apple\", \"Orange\", \"Banana\"]         \n",
       " String[\"Apple\", \"Orange\", \"Banana\", \"Peach\"]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# もちろん、これも普通にできる\n",
    "fruits_2d = [[\"Apple\", \"Orange\", \"Banana\"], [\"Apple\", \"Orange\", \"Banana\", \"Peach\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:34.618000Z",
     "start_time": "2018-01-31T03:30:33.873Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×3 Array{Float64,2}:\n",
       " 0.445258  0.587788  0.996786  \n",
       " 0.522811  0.743046  0.00644533\n",
       " 0.99362   0.325897  0.536397  \n",
       " 0.831977  0.433696  0.300295  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 乱数で生成とかも。モジュールのインポートとかしなくていいのが、Pythonとの違いだなと笑\n",
    "rand(4,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 配列の初期化\n",
    "\n",
    "ここでは、Arrayを作成するときに使う関数をまとめます。痒いところに手が届く関数が多くて素晴らしい…。\n",
    "\n",
    "【参考】\n",
    "- [Multi-dimensional Arrays](https://docs.julialang.org/en/stable/manual/arrays/)\n",
    "- [Arrays](https://docs.julialang.org/en/stable/stdlib/arrays/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:38.286000Z",
     "start_time": "2018-01-31T03:30:37.081Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0, 0.0, 0.0, 0.0, 0.0]\n",
      "[0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0]\n",
      "Int8[0 0 0 0; 0 0 0 0]\n",
      "[0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0]\n"
     ]
    }
   ],
   "source": [
    "# numpyとかで配列を初期化するときによく使うzeros\n",
    "# 普通の1d-array\n",
    "println(zeros(5))\n",
    "\n",
    "# 多次元配列も可能\n",
    "println(zeros(2,4))\n",
    "\n",
    "# 型の指定もできる\n",
    "println(zeros(Int8, 2,4))\n",
    "\n",
    "# 型の変換もできるみたい\n",
    "# 出力が、「0 => 0.0」 となっているのに注目\n",
    "zeros_array = zeros(Int8, 2,4)\n",
    "println(zeros(zeros_array, Float64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:39.083000Z",
     "start_time": "2018-01-31T03:30:39.048Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 1.0, 1.0, 1.0, 1.0]\n",
      "[1.0 1.0 1.0 1.0; 1.0 1.0 1.0 1.0]\n",
      "Int8[1 1 1 1; 1 1 1 1]\n",
      "[1.0 1.0 1.0 1.0; 1.0 1.0 1.0 1.0]\n"
     ]
    }
   ],
   "source": [
    "# onesもある。似たような感じで使える。\n",
    "# 普通の1d-array\n",
    "println(ones(5))\n",
    "\n",
    "# 多次元配列も可能\n",
    "println(ones(2,4))\n",
    "\n",
    "# 型の指定もできる\n",
    "println(ones(Int8, 2,4))\n",
    "\n",
    "# 型の変換もできる\n",
    "ones_array = ones(Int8, 2,4)\n",
    "println(ones(ones_array, Float64))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上の関数以外にも似たものとして、`trues` とか `falses` とかがあるっぽく、似たような感じで使える"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:42.128000Z",
     "start_time": "2018-01-31T03:30:41.496Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×2 Array{Int64,2}:\n",
       " 10  10\n",
       " 10  10\n",
       " 10  10"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 0や1, trueやfalse以外の値を入れたい場合は、fill関数を使うと良いっぽい。\n",
    "fill(10, (3,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 配列の情報を取るための関数\n",
    "\n",
    "配列の長さとかサイズとかを配列を操作するときには見ると思うのですが、そのあたりの関数をまとめます。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:44.452000Z",
     "start_time": "2018-01-31T03:30:44.448Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×3 Array{Float64,2}:\n",
       " 1.0  1.0  1.0\n",
       " 1.0  1.0  1.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ここではこの配列を例にします\n",
    "ones_2d = ones(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:44.747000Z",
     "start_time": "2018-01-31T03:30:44.608Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 配列のdimentionを取得\n",
    "ndims(ones_2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:45.027000Z",
     "start_time": "2018-01-31T03:30:44.776Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Base.OneTo(2), Base.OneTo(3))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# indexを取得する関数\n",
    "indices(ones_2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:45.029000Z",
     "start_time": "2018-01-31T03:30:44.947Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 長さ、、、ではなくて、要素の数を取得する関数であることに注意。\n",
    "# Pythonのlenとは違う\n",
    "length(ones_2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:46.806000Z",
     "start_time": "2018-01-31T03:30:46.655Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Base.OneTo(6)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 要素へのインデックスをiterableな形で取得してくれる方法がある\n",
    "# それが以下。\n",
    "eachindex(ones_2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:46.921000Z",
     "start_time": "2018-01-31T03:30:46.808Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1=>1.0\n",
      "2=>1.0\n",
      "3=>1.0\n",
      "4=>1.0\n",
      "5=>1.0\n",
      "6=>1.0\n"
     ]
    }
   ],
   "source": [
    "# こんな感じで呼び出せる。以下は、for文の例。\n",
    "# ドキュメントを斜め読みした感じでは、早いらしい。\n",
    "for iter in eachindex(ones_2d)\n",
    "    println(iter, \"=>\", ones_2d[iter])\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:49.313000Z",
     "start_time": "2018-01-31T03:30:49.288Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# non-zeroな要素の数を返してくれる関数。\n",
    "# 以下だと、6と返ってくる\n",
    "countnz(ones_2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 配列の操作\n",
    "\n",
    "reshapeや配列の結合など、配列に加える操作周りの方法。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:51.008000Z",
     "start_time": "2018-01-31T03:30:50.993Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Array{Float64,2}:\n",
       " 1.0  1.0  1.0  1.0\n",
       " 1.0  1.0  1.0  1.0\n",
       " 1.0  1.0  1.0  1.0\n",
       " 1.0  1.0  1.0  1.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reshape\n",
    "ones_1d = ones(16)\n",
    "reshape(ones_1d, (4,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:51.275000Z",
     "start_time": "2018-01-31T03:30:51.172Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×8 Array{Float64,2}:\n",
       " 1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0\n",
       " 1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 片方の次元だけ指定するパターンも可能\n",
    "reshape(ones_1d, 2, :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:51.578000Z",
     "start_time": "2018-01-31T03:30:51.329Z"
    }
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "\u001b[91mDimensionMismatch(\"array size 16 must be divisible by the product of the new dimensions (3, Colon())\")\u001b[39m",
     "output_type": "error",
     "traceback": [
      "\u001b[91mDimensionMismatch(\"array size 16 must be divisible by the product of the new dimensions (3, Colon())\")\u001b[39m",
      "",
      "Stacktrace:",
      " [1] \u001b[1m_throw_reshape_colon_dimmismatch\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Float64,1}, ::Tuple{Int64,Colon}\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m.\\reshapedarray.jl:109\u001b[22m\u001b[22m",
      " [2] \u001b[1m_reshape_uncolon\u001b[22m\u001b[22m at \u001b[1m.\\reshapedarray.jl:104\u001b[22m\u001b[22m [inlined]",
      " [3] \u001b[1mreshape\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Float64,1}, ::Tuple{Int64,Colon}\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m.\\reshapedarray.jl:97\u001b[22m\u001b[22m",
      " [4] \u001b[1mreshape\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Float64,1}, ::Int64, ::Colon, ::Vararg{Colon,N} where N\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m.\\reshapedarray.jl:96\u001b[22m\u001b[22m"
     ]
    }
   ],
   "source": [
    "# でもちゃんとreshapeできないとだめ。\n",
    "# 例えば、3とか指定するとだめ。\n",
    "reshape(ones_1d, 3, :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:51.742000Z",
     "start_time": "2018-01-31T03:30:51.496Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3×5 Array{Int64,2}:\n",
       "  1   2   3   4   5\n",
       "  6   7   8   9  10\n",
       " 11  12  13  14  15"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# verticalな方向に結合する\n",
    "a = [1 2 3 4 5]\n",
    "b = [6 7 8 9 10; 11 12 13 14 15]\n",
    "vcat(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:53.414000Z",
     "start_time": "2018-01-31T03:30:53.312Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5×2 Array{Int64,2}:\n",
       " 1   6\n",
       " 2   7\n",
       " 3   8\n",
       " 4   9\n",
       " 5  10"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Horizontalな方向に結合する\n",
    "a = [1; 2; 3; 4; 5;]\n",
    "b = [6; 7; 8; 9; 10;]\n",
    "hcat(a, b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 配列上の演算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:55.686000Z",
     "start_time": "2018-01-31T03:30:55.128Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 4 5 6]\n",
      "[0 1 2 3 4]\n",
      "[2 4 6 8 10]\n",
      "[0.5 1.0 1.5 2.0 2.5]\n"
     ]
    }
   ],
   "source": [
    "# 全体に1足したいとかはこれでできる。\n",
    "a = [1 2 3 4 5]\n",
    "println(a + 1)\n",
    "println(a - 1)\n",
    "println(a * 2)\n",
    "println(a / 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:56.431000Z",
     "start_time": "2018-01-31T03:30:55.311Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 1\n",
       " 3\n",
       " 6"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 累積演算は以下のような感じ。\n",
    "accumulate(+, [1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:56.450000Z",
     "start_time": "2018-01-31T03:30:55.480Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       " 101\n",
       " 103\n",
       " 106"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 真ん中に値を挟むと、その値が最初の演算に使われる。\n",
    "# 以下の例であれば、100+1が最初に出てくる。\n",
    "accumulate(+, 100, [1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-01-31T12:30:57.212000Z",
     "start_time": "2018-01-31T03:30:57.184Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3-element Array{Int64,1}:\n",
       "  0\n",
       "  0\n",
       " -1"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accumulate(min, 0, [1,2,-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "他にもたくさんあるが、ここまでで。他の例は[こちら](https://docs.julialang.org/en/stable/stdlib/arrays/)見れる。"
   ]
  }
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