kenjisato/2015-04-20.ipynb

## 2015-04-20.ipynb
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   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Python 速習 (その2)\n",
    "\n",
    "### 経済動学 講義資料\n",
    "\n",
    "\n",
    "\n",
    "神戸大学 佐藤健治\n",
    "\n",
    "2015-4-17"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "このノートではPythonを使って\n",
    "\n",
    "離散時間力学系を可視化する方法を学ぶ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "入門的な段階で大きな問題になることは少ないけれども大切なこと: \n",
    "\n",
    "1. 解析学 &mdash; **無限**や**極限**の概念が中心\n",
    "1. コンピュータ &mdash; **有限**しか扱えない\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**有限** の意味するところは\n",
    "\n",
    "1. $0$と$1$の有限個の連なりで表現できる対象に対する\n",
    "1. 有限回の計算\n",
    "\n",
    "のみが可能ということ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "離散時間力学系は写像 $F: X \\to X$ のことだったので、この有限制約の中で、\n",
    "\n",
    "1. $X$\n",
    "1. $F$\n",
    "1. 軌道の収束・発散\n",
    "\n",
    "をどのように表現するか？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# $X$ をどのように表現するか？\n",
    "\n",
    " $X = \\mathbb{R}^n$ &mdash; 有限次元ベクトル空間\n",
    "\n",
    " $X \\ni x = [x_1 \\ \\dots x_n]$ \n",
    "\n",
    " 各$x_i$ は**実数**\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    " 実数は有限の概念ではない\n",
    " \n",
    " $\\sqrt{2} = 1.41421356\\dots $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    " \n",
    " **実は、$0.1$ など「普通の」小数でさえ有限の概念ではないので近似はまぬがれない**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# そもそも数はどのように表現されるか？\n",
    "\n",
    "## 整数\n",
    "\n",
    "\n",
    "$2 = \\color{red}{1} \\times 2^1 + \\color{red}{0} \\times 2^0 = (10)$\n",
    "\n",
    "$3 = \\color{red}{1} \\times 2^1 + \\color{red}{1} \\times 2^0 = (11)$\n",
    "\n",
    "$10 = \\color{red}{1}\\times 2^3 + \\color{red}{0} \\times 2^2 + \\color{red}{1} \\times 2^1 + \\color{red}{0} \\times 2^0 = (1010)$\n",
    "\n",
    "\n",
    "もっと大きな数字の場合も\n",
    "\n",
    "$N = a_n \\times 2^n + a_{n-1} \\times 2^{n-1} + \\dots + a_0 \\times 2^0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1010011001011100101010110011011010000000101100110010100110010101001111111010111110010011'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "format(201119302093024920940294035, 'b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "原理的に有限の01の列で表現できるので\n",
    "\n",
    "整数が問題になることはまずない"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 小数 \n",
    "\n",
    "\n",
    "$0.5 = \\color{red}{1} \\times 2^{-1} = (0.1)$\n",
    "\n",
    "$0.75 = \\color{red}{1} \\times 2^{-1} + \\color{red}{1} \\times 2^{-2} = (0.11)$\n",
    "\n",
    "つまり小数点以下は\n",
    "\n",
    "\\begin{align*}\n",
    "& a_{1} \\times 2^{-1} + \\dots + a_{n} \\times 2^{-n} \\\\\n",
    "&= [a_{1} \\times 2^{n-1} + \\dots a_{n} \\times 2^0] \\div 2^n \\\\\n",
    "&= \\text{Integer} / 2 ^n\n",
    "\\end{align*}\n",
    "\n",
    "と表されている (10進小数は, $\\text{Integer}/10^n$ と書ける数である)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 疑問\n",
    "\n",
    " $\\text{Integer} / 2 ^n$ で一般の小数、例えば $0.1$ を表現できる？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.1 == 3602879701896397 / 2 ** 55"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.001100110011001100110011001100110011001100110011001101'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'0.' + '0' * (55 - 53) + format(3602879701896397, 'b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "これが `0.1` の2進数表現\n",
    "\n",
    "これは正確な表現か？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 簡単な実験"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1.0 == 0.25 + 0.25 + 0.25 + 0.25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "OK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1.0 == sum(0.1 for _ in range(10)) # 0.1 を10回足す"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "何かがおかしい？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 確認\n",
    "\n",
    "任意の精度まで正確に10進表現してくれる`Decimal`を使って確認してみる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import decimal\n",
    "n = decimal.Decimal('0.1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Decimal('5.5511151231E-18')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decimal.Decimal('3602879701896397') / 2 ** 55 - decimal.Decimal('0.1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Decimal('-5.2041704279E-19')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decimal.Decimal('115292150460684697') / 2 ** 60 - decimal.Decimal('0.1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "`0.1` は2進数表現では有限長の小数にならない → 近似精度をいくらでも増やせる\n",
    "\n",
    "`0.1 == 3602879701896397 / 2 ** 55` が `True` と評価される理由は **左辺は長い小数を見栄え良くするために丸めて表示されているが実は右辺の内部表現を持っている** から \n",
    "\n",
    "実用上多くの場合には問題にならない。ただし、問題が起こることもあるので、数表現自体に誤差があることに注意が必要です。いずれにせよこのように表現される「(倍精度)浮動小数点数」が実数や有理数の表現として使われます。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 数の表現\n",
    "\n",
    "よく使う3つの数表現を挙げておきましょう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "整数 (`int`型)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 10\n",
    "type(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "浮動小数点数 (float型)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "float"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = - 0.3\n",
    "type(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "複素数 (complex型)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "complex"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = 1.0 - 2.0j\n",
    "type(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# ベクトルの表現\n",
    "\n",
    "数の表現が確定したところで、ベクトルを表現する方法に入りましょう。外部ライブラリを使わずに表現しようとすると、**リスト** と呼ばれるものを使うことができます。ただし、足し算やスカラー倍などの基本演算でさえ定義されていないので、ベクトルの表現としては実用的ではありません。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 2.0, 3]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = [1.0 , 2.0 ,3]\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3, 4]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = [2, 3, 4]\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 2.0, 3, 2, 3, 4]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v + w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 2.0, 3, 1.0, 2.0, 3, 1.0, 2.0, 3]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v * 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Numpy \n",
    "\n",
    "数ベクトルの表現には、通常 `Numpy` の `ndarray` という型を使います。便利かつ高速だからです。これを$X$の表現とします。\n",
    "\n",
    "使う前にインポートします。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## ベクトルの定義"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$x = [1.0, 2.1, 3.0]$\n",
    "\n",
    "$y = [-1.0, 1.0, 8.9]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "x = np.array([1.0, 2.1, 3.0])\n",
    "y = np.array([-1.0, 1.0, 8.9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## ベクトルの和"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$x + y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0. ,   3.1,  11.9])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 線形結合"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$3x - 2y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5. ,  4.3, -8.8])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 * x - 2 * y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# $F$ をどのように表現するか?\n",
    "\n",
    "ベクトルの表現が定まったところで、次に写像を作ります。\n",
    "\n",
    "Pythonの関数が基本です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def f(a):\n",
    "    # do something\n",
    "    return 2 * a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2. ,  4.2,  6. ])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 線形写像\n",
    "\n",
    "線形写像は行列積で表現されます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.48,  0.52,  3.6 ])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([\n",
    "        [1.2, -0.8, 0],\n",
    "        [0.1, 0.2,  0], \n",
    "        [0,   0,    1.2]\n",
    "    ])\n",
    "\n",
    "np.dot(A, x) # 行列 × ベクトル"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "したがって、線形力学系\n",
    "\n",
    "$x_t \\mapsto Ax_t$\n",
    "\n",
    "を表現する基本のコードは次の関数のようになります"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def fa(x):\n",
    "    return np.dot(A, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 写像の族の表現\n",
    "\n",
    "われわれはこれから「力学系というもの」「線形力学系というもの」に対して実行可能な可視化のコードを書こうとしているわけです。\n",
    "\n",
    "上記では写像 $A$ を決め打ちしてしまいましたが、「力学系というもの」という一段抽象度の高い概念をコードにしてしまう方がコードをクリーンに保てることがよくあります。\n",
    "\n",
    "我々がいま採用している力学系の定義に絶対に必要なものは、「前向きに進めるための写像」と「$X$の次元」だけですから、これを備えているものを力学系であると、Pythonコードで表現しておきましょう。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## クラス\n",
    "\n",
    "クラスという仕組みを使います。これは「考察の対象」とその対象がもつ「動作」を組み合わせて表現するための方法です。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "class System:\n",
    "    \"\"\"Dynamical System\"\"\"\n",
    "    def __init__(self, dim):\n",
    "        self.dim = dim\n",
    "\n",
    "    def forward(self, x):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 線形写像のクラス\n",
    "\n",
    "線形写像のクラスを作ります。上で定義した `System`クラスの `dim` と `forward` を引き継ぎ、線形システム特有の事情にあわせて調整します。メソッド(動作を表す関数のこと)も具体的に定義しておきます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "class LinearSystem0(System):\n",
    "\n",
    "    def __init__(self, A):\n",
    "        self.A = A\n",
    "        super().__init__(A.shape[0])\n",
    "\n",
    "    def forward(self, x):\n",
    "        return np.dot(self.A, x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## インスタンス化"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "「システムというもの」から特定のシステムを作ることを**インスタンス化**といいます。\n",
    "\n",
    "次のコードがインスタンス化のためのコードです。オブジェクトが生成され、その直後に `__init__()` メソッドが呼び出されます。その際に仮引数 `A` は `M` で置き換えられます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "theta = np.pi / 7.0\n",
    "M = 0.9 * np.array([[np.cos(theta), -np.sin(theta)], \n",
    "                      [np.sin(theta), np.cos(theta)]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rot = LinearSystem0(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 使ってみる"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.6156243 ,  0.79593136])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = np.array([1.0, 0.5])\n",
    "x1 = rot.forward(x0)\n",
    "x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.18838499,  0.88579687])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2 = rot.forward(x1)\n",
    "x2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# シミュレーション\n",
    "\n",
    "`for`を使って繰り返し写像を適用します。これがシミュレーションの基本コードです"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.   0.5]\n",
      "[ 0.6156243   0.79593136]\n",
      "[ 0.18838499  0.88579687]\n",
      "[-0.19314346  0.79183133]\n",
      "[-0.46582109  0.56665221]\n"
     ]
    }
   ],
   "source": [
    "T = 5\n",
    "x0 = np.array([1.0, 0.5])\n",
    "for i in range(T):\n",
    "    x = x0\n",
    "    print(x)\n",
    "    x0 = rot.forward(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 汎用的なシミュレーションコード\n",
    "\n",
    "次のようにシミュレーションのコードを書きます。引数として、`system`を取りますが、`LinearSystem0`のインスタンスでなくとも `forward`メソッドさえ実装されていれば動きます。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def run0(system, x0, time):\n",
    "\n",
    "    path = np.empty((time, len(x0)))\n",
    "\n",
    "    path_iter = iter(path)\n",
    "    tick = system.forward\n",
    "\n",
    "    prev_state = next(path_iter)\n",
    "    prev_state[:] = x0\n",
    "    for state in path_iter:\n",
    "        state[:] = tick(prev_state)\n",
    "        prev_state = state\n",
    "    return path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  3.19365135e-05,  -3.88494564e-05],\n",
       "       [  4.10669567e-05,  -1.90308752e-05],\n",
       "       [  4.07315131e-05,   6.04852781e-07],\n",
       "       [  3.27918505e-05,   1.63959252e-05],\n",
       "       [  2.01874599e-05,   2.61000620e-05],\n",
       "       [  6.17749240e-06,   2.90469185e-05],\n",
       "       [ -6.33353156e-06,   2.59656145e-05],\n",
       "       [ -1.52751354e-05,   1.85815746e-05],\n",
       "       [ -1.96421981e-05,   9.10240860e-06],\n",
       "       [ -1.94817564e-05,  -2.89299210e-07]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path = run0(rot, x0, 100)\n",
    "path[-10:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "数字だけを見ていても力学系の動作が掴みづらいので可視化してみましょう"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 可視化\n",
    "\n",
    "matplotlib というライブラリを使います。使う前にインポートする必要があります。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tTnW4xHrAxPrtceoSSbW38Et5tiw+H7iK6uCKi2z/okDslkm6g2qrpjtKZ4n+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\nSZIkdWJwlCRJUif/D4tPP5NRlqDGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1079895f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(11,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(path[:,0], path[:,1], color='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "動きを表現するために矢線をつけてみます"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tYKyv7EX6YgqwIIPnPralFxLH/zKwF6OZWa86i7SCushfigecA9Rqz60MXBMR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\nwdHMzMzMCvl/qS4ZT8zH8FEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107bc6400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(11,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.quiver(path[:-1, 0], path[:-1, 1], path[1:, 0]-path[:-1, 0], \n",
    "          path[1:, 1]-path[:-1, 1],\n",
    "          scale_units='xy', angles='xy', scale=1, width=0.005)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "先ほどの軌道はゼロに収束しているように見えますが、\n",
    "\n",
    "- シミュレーションが有限時間しか実行できないことと\n",
    "- 浮動小数点数には必ず誤差がある\n",
    "\n",
    "という理由から、シミュレーションでは収束性を確実には判定できません。しかし、力学系の振る舞いの特徴をつかむ上では役に立つでしょう。収束性の判定条件 \n",
    "\n",
    "$\\| x_t - x^* \\| < \\epsilon$ \n",
    "\n",
    "が部分的にでも成り立っているかを見るために、ノルムを計算してこれをプロットしてみましょう。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x107f965f8>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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cAlwL7AO8uKq+3HFJkiRpyNkyOUKq6gfAu9rN/5nE/5aSJGnB2TI5xJLsS9M6\neTBwSlWd13FJkiRpiNkyOWKq6n7gD9rNdybZo8t6JEnS6DFMDr8PAFcDhwOnd1uKJEkaNXZzLwJJ\nTqCZe/Ju4Ceq6s6OS5IkSUPIbu7R9RngC8Ay4P/uuBZJkjRCbJlcJJI8B7gU2A48vaqu67gkSZI0\nZGyZHGFVdTnwIWA34E87LkeSJI0IWyYXkSSHAZtpJjI/oao+03FJkiRpiNgyOeKq6kZgXbv5l0n2\n6rAcSZI0AgyTi897gG8DTwXe3nEtkiRpkbObexFK8tPAV4FtwDOr6jsdlyRJkoaA3dwCoKq+BryP\nZjDOXyUxrEuSpHlhy+QileRA4DvAgcCvVtVHOi5JkiQNOFsm9YiqugP43Xbzz5Ms67IeSZK0OBkm\nF7cPAl8DDgL+R7elSJKkxchu7kUuyTOBy2j+4fCCqrq445IkSdKAsptbj1JVVwF/DgQ4O8mSjkuS\nJEmLiGFyNPw/wFbgGOC3Oq5FkiQtInZzj4gkrwTOB+4FjqqqmzsuSZIkDRi7uTWVTwMXAPsD5zj3\npCRJmguGyRFRTRP0G4F7gBOBX++0IEmStCgYJkdIVd0InN5uvifJU7qsR5IkDT/D5Oj5MM29k/sB\nH0ji74AkSeqbQWLEtN3dvwncDrwEeFO3FUmSpGHmaO4RleQXgE8CDwHPqarvdlySJEnqmKO5NWNV\ndT7wIWAv4G+TLO24JEmSNIQMk6PtzcBNwAuAt3VciyRJGkJ2c4+4JC8HLgK2Ac+vqis6LkmSJHVk\n3rq5k6xJsjnJtUnOmOScM9vjVyRZ2e5bnuRfklyd5NtJ3jyb4jT/quqzwNnAbjTd3Xt0XJIkSRoi\n04bJJEuAs4A1wNHAKUmOGnfOWuDIqloBnEoTTqBp7XprVT0DWAW8afx7NRB+F/ge8CzgDzuuRZIk\nDZGZtEweC2ypquurahtwHnDyuHNOAs4FqKqNwLIkB1XVLVV1ebv/fmAT8KQ5q15zov1v8+tAAb+X\n5CXdViRJkobFTMLkocDWnu0b233TnXNY7wlJDgdWAhtnW6TmX1V9Ffhjmt+JjyY5uOOSJEnSEJhJ\nmJzpCJ3xN2s+8r4k+wIfB97StoJpMK0DNgAH0QTKJZ1WI0mSBt5M5ha8CVjes72cpuVxqnMOa/eR\nZDfgE8DfVdWnJvqCJOt6NjdU1YYZ1KU5VlXbk5wCXA6spgmXf9BlTZIkaf4kWU3zd37/nzHd1EDt\nZNbfAV6c7FmsAAASy0lEQVQK3Ax8Ezilqjb1nLMWOL2q1iZZBby7qlYlCc29lHdU1Vsn+XynBhow\n7T2Tn6dpuT6hqj7TcUmSJGkBzMvUQFW1HTidZi7Ca4CPVdWmJKclOa0950LguiRbgHOAN7Zv/2ng\nNcBLklzWLmtmU6AWXlX9CztHdf9dkuVTnS9JkkaXk5ZrQkkeA1wI/BzwdWB1O5pfkiQtUj6bW3Om\nqnbQtCrfBLwQeGe3FUmSpEFky6SmlOSFwJdoBmu9sqo+3XFJkiRpntgyqTlXVV8Hfq/dPDfJU7us\nR5IkDRZbJjWtdlT++TRPProCOM75QiVJWnxsmdS8qOZfHK8HrgWeDXzYCc0lSRIYJjVDVXUXcCJw\nF82z2B2QI0mSDJOauar6LvDLwHbgbUn+a8clSZKkjhkmNStV9UXgt9rN97aPYZIkSSPKMKlZq6q/\nAf6cZrqgTyRZ0XFJkiSpI47mVl/aATiformP8rvAqva+SkmSNKQcza0FU1UPA/8FuBJ4GvDxJLt1\nW5UkSVpohkn1raruA14B3Ar8LHBWOyelJEkaEYZJ7ZKquoFmMvMfAaey82k5kiRpBBgmtcuqaiPw\na0ABf5zkt6Z5iyRJWiQMk5oTVfUP7Jwy6C+T/Jcu65EkSQvDMKk5U1Xn0HRzB/jbJK/ouCRJkjTP\nDJOaU1X1J8D/BywB/sFJzSVJWtwMk5oPvw+8F9gDuCDJ8zuuR5IkzRPDpOZcNTPhnw58FNgX+EyS\no7utSpIkzQfDpOZFO6n564B/Ag4APpfkiG6rkiRJc80wqXlTVduA/wx8GXgS8PkkT+m2KkmSNJcM\nk5pXVfUQzVNyLgGeCnw5yZHdViVJkuaKYVLzrqruBV4G/CvwZJpAeVS3VUmSpLlgmNSCqKq7gZcD\nG4BDgC8leXanRUmSpF1mmNSCqar7gZ8HLgKeAGxIcmy3VUmSpF1hmNSCqqoHgZOBTwPLaAblHNdt\nVZIkqV+GSS24qvoRzSjvjwH7ARclOb7bqiRJUj8Mk+pEO23QrwIfBPYG/tFneUuSNHwMk+pMO7H5\nfwXOpnn04qeSvLHbqiRJ0mwYJtWpqtoBvAn4f2l+H/8yybuS+LspSdIQSPMY5Q4LSKqq0mkRGghJ\nfh34a2Ap8Ang19pJzyVJ0gLoJ5cZJjVQkrwU+CSwP/AN4OSquq3bqiRJGg395DK7EjVQquoLwAuB\nG4BVwDeSPL3bqiRJ0mQMkxo4VXU18AKa53kfAXw9yYu7rUqSJE3EMKmBVFW3AKuB9cDjgM8l+Y1O\ni5IkSY9imNTAqqoHgF8E3gPsBvx1kvcl2avbyiRJ0hgH4GgoJHkd8F5gT+BS4Jeq6vpOi5IkaZFx\nAI4Wrao6F/gp4DrgucC3kqzptipJkmSY1NCoqsuB5wH/CBwAXJjkD53gXJKk7viXsIZKVd0FnAz8\nQbvrj4ALkhzQXVWSJI0u75nU0ErycuAjwIHA9TRPzPlqp0VJkjTE5u2eySRrkmxOcm2SMyY558z2\n+BVJVvbsf3+SW5NcNZvCpOlU1WeBY4CLgcOBLyX5H0l277QwSZJGyLRhMskS4CxgDXA0cEqSo8ad\nsxY4sqpWAKcCZ/cc/kD7XmnOVdX3geOAP253/T7NJOc+NUeSpAUwk5bJY4EtVXV9VW0DzqO5Z63X\nScC5AFW1EViW5OB2+yvAXXNXsvTjquo/qur/Al5M0919DHBpkjcl8RYKSZLm0UzC5KHA1p7tG9t9\nsz1nZpJy2+1+tqvqq/c03d0fBPYCzloDO5IcMgj1ue2222677fbQbM/CTMLkTD98fAvQjItKsm5s\n2TDTN0kT2B+oqtcDvwzc+Zlm91VJ/rOtlJIk/bgkq5OsW9e8XtfXZ0w3mjvJKmBdVa1pt98O7Kiq\nP+k5573Ahqo6r93eDLy4qm5ttw8HLqiqZ07w+Y7m1rxI8iSae3Zf3u66AHhTVW2d/F2SJI2u+RrN\nfQmwIsnh7SjZVwHrx52zHnhtW8Qq4O6xICl1papuBk4Afgu4F3gFsCnJW9qBZZIkaRdNGyarajtw\nOnARcA3wsaralOS0JKe151wIXJdkC3AO8Max9yf5KPB14GlJtiZ5/Tz8HNKEqmpHVb0XOAr4OLAP\n8G7gG0me02lxkiQtAk5arpGS5BXAXwLLgYeBPwf+qKoe6LQwSZIGwLxNWi4tFlV1AfAM4D00v/9v\nA76d5JUO0JEkafZsmdTISvJ84K+BZ7e7NgBvrarLOytKkqQO2TIpzUJVXQw8j+ae4DuB1TSTnf/N\n2KT7kiRparZMSkCSxwF/APw3YClwP/BO4C+q6qEua5MkaaH0k8sMk1KPJE8D3kXziFCA7wNvp5nF\nYEdnhUmStADs5pZ2UVV9t6pOBo4HrgSeAnwEuMxBOpIkPZphUppAVX0BeC7wBppnzT8LOB+4OMla\nQ6UkSQ27uaVpJNmTJlT+PjA2MOcbwB8Cn6+u/xBJkjRHvGdSmkdJ9qJ5NOPvAU9od38F+CPgi4ZK\nSdKwM0xKCyDJvsCbgN8FDmh3Xwr8KfCJ9hGkkiQNHcOktICS7E8zR+VbgCe2u/+N5hGNH/ARjZKk\nYWOYlDrQ3lP5WuD/BFa0u+8AzgL+sqpu76o2SZJmwzApdSjJEuBkmu7vF7S7fwh8GPirqrq0q9ok\nSZoJw6Q0ANppg46jCZUn9hzaCPwV8PdV9cMuapMkaSqGSWnAtE/U+U3g9cCydvedwPuB91bV97qq\nTZKk8QyT0oBKsjfwappR4M/tOXQR8EHg0z4DXJLUNcOkNODaLvDnA2+kCZd7tIfuAT5GEyy/4ZyV\nkqQuGCalIZLkQOAU4HXA83oOXQucC3yoqm7oojZJ0mgyTEpDKskzaELla4BD2t0FfAn4e+CTVXVr\nR+VJkkaEYVIackmWAi+jCZavZGc3+A5+PFje1k2FkqTFzDApLSJJHgu8AvgVYA2wW3toB7CBJliu\nr6ofdFKgJGnRMUxKi1SSZcBJNMHy5ewMlgAXAxcA64ErHbwjSeqXYVIaAUkeRxMsfxk4Htiz5/BW\ndgbLDVX1o4WvUJI0rAyT0ohp5698KU24PBE4uOfwgzTd4Z8DPgtsstVSkjQVw6Q0wpI8BjiG5j7L\nk4BnjzvlJnYGy89X1e0LW6EkadAZJiU9IsmTaLrBX9YuB4075UrgyzSjxL/i1EOSJMOkpAm1T955\nJk2ofDnwM/z4vZYAm9kZLr9cVTcuaJGSpM4ZJiXNSJI9gWNpQuWLgRcCe487bSvwDeBf2/VlVfXD\nhaxTkrSwDJOS+pJkd+C5NMHyZ4DjgP3HnfYfwGU0wXIj8C1gS1XtWMBSJUnzyDApaU60g3mOAlb1\nLM8Axv9ZvZcmYF5KEy6/BVxbVQ8vXLWSpLlimJQ0b9on8jwf+Kl2fQzwpAlOfQC4AriKZpDPlcBV\nVXXPApUqSeqTYVLSgkpyME33+DE96+WTnH4DTcC8Crga2ARsrqoHFqBUSdIMGCYldS7JE4Bntcsz\n2/UzePTo8TE30ATLsWUzcC1wi5OsS9LCMkxKGkhJlgBHsjNgHtUuT+PHnzPe635gC02w7F2+B9xq\n0JSkuWeYlDRUkiwFnsrOcHkU8JPACuCAKd76EHA9cB3wb+0y9vr7wD2GTUmaPcOkpEUjyQE0oXL8\n8lSmDpoA99HMk3nDuGUrzWMlb6qqB+enckkaXoZJSSMhyf7AETTB8oie5anAk4F9ZvAxd9MEy5vb\n9djrW4AftOtbquqhua5fkgaVYVLSyGsfHbmMJlSOX5YDh9JMabT7DD/yXnaGy9t6ltsn2L7bSdwl\nDTPDpCTNQBs4H08TLMfC5aHAIcDB7TL2erIBQhPZAdzRLv/eLnf0rO8C7uxZj71+wHs8JQ0Cw6Qk\nzaE2dD6OneHyCcATJ1jG9o9/BOVMbaPpdp9suadd7m2X8a/vA35oIJW0qwyTktSh9hnnBwAH0rR8\njq0f3+5/XLse/3qvOfj6h2lC5dhy/7jX99M8nWj8emx5sGfd+/ohQ6o0OuYlTCZZA7wbWAL8TVX9\nyQTnnAmcQPM/nl+vqstm8V7D5CwlWV1VG7quY5h4zWbPazY7u3K9kuwJPJbmXs/Jlv3HLY/tWe8H\n7LFrP8GUHupZHpzg9Q971j+cYN+Peo71vj4K+Ga7r3f5j57X27wPdSf/XM6O12v2+sllS6f5wCXA\nWcDxNCMdL06yvqo29ZyzFjiyqlYkeQFwNrBqJu9V31YDGzquYdisxms2W6vxms3Gavq8XlU1Fq5u\n7ffLk+xGEyonWvZpl33bZZ9x673bZZ8J1nvQtJzORetpX5JspwmYky3bxq3HXm8Dtve8nmjZPsV6\nuuXhKV4/3LPv4ZkuM2gFXo1/LmdjNV6veTdlmASOBbZU1fUASc4DTqZ55NmYk4BzAapqY5Jl7fN6\nj5jBeyVJc6CqtrFzUM+caRsG9qQJk3uzM1j2vt6zZ73nuH17tK/Hr/ekmTf01nbf2LL7uNe70/xd\ntbT9zkWtuU33xwLmjnHbeyU5td2/o+ec8a93dakptmuK9VSvZ3Ns/DLVsd6FcdsvTPI7Uxwfvz3d\nOdO9nu2+2awnez3Tfb2vr6mq7zFHpguTh9JM8jvmRuAFMzhnbHTkdO+VJA2wqnqYnfdVzqkk66pq\n3TTnhObvqrGQuXvP693aZfee9e492+OXpZNsL51g3xJ2htjdxr1eMu547+ulPcd7z+t9/ZgJzlnS\n7qdnezIzmUdVO72s6wIG0NuA/zlXHzZdmJzpTde7dM9jEm/unqUk7+i6hmHjNZs9r9nseL1mz2sm\ndeJdSd41Vx82XZi8iWaS3zHLaVoYpzrnsPac3WbwXhx8I0mSNLweM83xS4AVSQ5vp7x4FbB+3Dnr\ngdcCJFlF8wSIW2f4XkmSJA2xKVsmq2p7ktOBi2ju33hfVW1Kclp7/JyqujDJ2iRbaO6pef1U753P\nH0aSJEkLq/NJyyVJkjS8puvmnldJ1iTZnOTaJGd0WcugSvL+JLcmuapn3wFJPpfku0k+m2RZlzUO\nkiTLk/xLkquTfDvJm9v9XrNJJNkzycYklye5Jsk72/1esykkWZLksiQXtNterykkuT7Jle01+2a7\nz2s2hXaqvY8n2dT+2XyB12xySX6y/f0aW+5J8mav2eSSvL39+/KqJB9Jskc/16uzMNkzqfka4Gjg\nlCRHdVXPAPsAzTXq9XvA56rqacAX2m01tgFvrapnAKuAN7W/V16zSbQTZr+kqp4DPAt4SZLj8JpN\n5y3ANeyc9cLrNbUCVlfVyqo6tt3nNZvae4ALq+oomj+bm/GaTaqqvtP+fq0EjqF5QtP5eM0mlORw\n4A3Ac6vqmTS3JL6aPq5Xly2Tj0yI3k62OzapuXpU1VeAu8btfmSi+Hb9ygUtaoBV1S1VdXn7+n6a\nSfIPxWs2pap6sH25O83/UO7CazapJIcBa4G/YefUaF6v6Y2fvcNrNokkjwVeVFXvh2YcQlXdg9ds\npo6nyRhb8ZpN5l6aBpi9k4w9FOBm+rheXYbJySY71/QOakfMQ/P0iIO6LGZQtf/qWglsxGs2pSSP\nSXI5zbX5l6q6Gq/ZVP6CZtLf3mdGe72mVsDnk1yS5A3tPq/Z5I4Abk/ygSSXJvnrJPvgNZupVwMf\nbV97zSZQVXcCfwbcQBMi766qz9HH9eoyTDryZw60z3H1Wo6TZF/gE8Bbquq+3mNes0erqh1tN/dh\nwM8kecm4416zVpITgduq6jImeWCD12tCP912P55Ac/vJi3oPes0eZSnwXOCvquq5NLOl/Fh3o9ds\nYu10hK8A/mH8Ma/ZTkl+Avht4HCapxbum+Q1vefM9Hp1GSZnMiG6JnZrmuefk+QQ4LaO6xkoSXaj\nCZIfqqpPtbu9ZjPQdqP9E839Rl6zib0QOCnJv9G0fPxskg/h9ZpSVf2gXd9Ocx/bsXjNpnIjcGNV\nXdxuf5wmXN7iNZvWCcC32t818PdsMs8Dvl5Vd1TVduCTwE/Rx+9Yl2HSSc37tx54Xfv6dcCnpjh3\npCQJ8D6ah9i/u+eQ12wSSR4/NlovyV40z7G9DK/ZhKrq96tqeVUdQdOV9sWq+jW8XpNKsneS/drX\n+wAvB67CazapqroF2Jrkae2u44GrgQvwmk3nFHZ2cYO/Z5PZDKxKslf7d+fxNIMKZ/071uk8k0lO\nAN7NzknN39lZMQMqyUeBFwOPp7l34Q+BTwN/DzwZuB74laq6u6saB0k7CvnLwJXsbJp/O/BNvGYT\nSvJMmpusH9MuH6qqdyU5AK/ZlJK8GPidqjrJ6zW5JEfQtEZC03374ap6p9dsakmeTTPIa3fgezQP\nBVmC12xS7T9Wvg8cMXaLk79nk0vyuzSBcQdwKfAbwH7M8no5abkkSZL61umk5ZIkSRpuhklJkiT1\nzTApSZKkvhkmJUmS1DfDpCRJkvpmmJQkSVLfDJOSJEnq2/8GHY9DtGmQhLMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107d9bdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "epsilon = 1e-2\n",
    "norms = np.sqrt(np.sum(path ** 2, axis=1))\n",
    "\n",
    "fig = plt.figure(figsize=(11,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(norms[-80:], color='black', linewidth=2)\n",
    "ax.hlines(epsilon, *ax.get_xlim(), color='red', linestyle='dotted', linewidth=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 非線形システムの例\n",
    "\n",
    "## Tinkerbell Map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "class Tinkerbell(System):\n",
    "    \"\"\"\n",
    "    Tinkerbell map [http://en.wikipedia.org/wiki/Tinkerbell_map]\n",
    "    \"\"\"\n",
    "    def __init__(self, a=0.9, b=-0.6013, c=2.0, d=0.5):\n",
    "        self.a = a\n",
    "        self.b = b\n",
    "        self.c = c\n",
    "        self.d = d\n",
    "        super().__init__(dim=2)\n",
    "\n",
    "    def forward(self, x):\n",
    "        return np.array([\n",
    "            x[0] * x[0] - x[1] * x[1] + self.a * x[0] + self.b * x[1],\n",
    "            2 * x[0] * x[1] + self.c * x[0] + self.d * x[1]\n",
    "        ])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Henon Map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Henon(System):\n",
    "    \"\"\"\n",
    "    Henon map [http://en.wikipedia.org/wiki/Hénon_map]\n",
    "    \"\"\"\n",
    "    def __init__(self, a=1.4, b=0.3):\n",
    "        self.a = a\n",
    "        self.b = b\n",
    "        super().__init__(2)\n",
    "\n",
    "    def forward(self, x):\n",
    "        return np.array([\n",
    "            1 - self.a * x[0] * x[0] + x[1],\n",
    "            self.b * x[0]\n",
    "        ])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "シミュレーションのコードが繰り返しでてくるので、これもクラスにしておきましょう"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Simulation:\n",
    "    def __init__(self, system, x0, duration):\n",
    "        self.system = system\n",
    "        self.x0 = x0\n",
    "        self.duration = duration\n",
    "    \n",
    "    def run(self, x0=None, duration=None):\n",
    "        system = self.system\n",
    "        x0 = self.x0[:] if x0 is None else x0\n",
    "        duration = self.duration if duration is None else duration\n",
    "        \n",
    "        path = np.empty((duration, len(x0)))\n",
    "        path_iter = iter(path)\n",
    "        tick = system.forward\n",
    "\n",
    "        prev_state = next(path_iter)\n",
    "        prev_state[:] = x0\n",
    "        for state in path_iter:\n",
    "            state[:] = tick(prev_state)\n",
    "            prev_state = state\n",
    "        return path\n",
    "    \n",
    "    def plot(self, fig_options={}, plot_options={}):\n",
    "        path = self.run()\n",
    "        \n",
    "        fig = plt.figure(**fig_options)\n",
    "        ax = fig.add_subplot(111)\n",
    "        ax.plot(path[:,0], path[:,1], **plot_options)\n",
    "        plt.show()\n",
    "    \n",
    "    def __iter__(self):\n",
    "        self.counter = 0\n",
    "        self.x = self.x0\n",
    "        return self\n",
    "        \n",
    "    def __next__(self):\n",
    "        while self.counter < self.duration:\n",
    "            self.counter += 1\n",
    "            x = self.x[:]\n",
    "            self.x = self.system.forward(x)\n",
    "            return x\n",
    "        raise StopIteration\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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X0GMoBC4LgZXAXAo9KEFD3ou8Uo7Vy8PfZt1tBYXAcmUdw2dZxmQyMBN4FDgJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107fbcb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tkb = Tinkerbell()\n",
    "sim_tkb = Simulation(tkb,  [0.0, 0.1], duration=3000)\n",
    "sim_tkb.plot(fig_options=dict(figsize=(11,8)),\n",
    "            plot_options=dict(linestyle='', marker='.', alpha=0.3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FDgNORWFzGdPvLB9G+0sL4Dt4PqaZWdu1o1I5gBp1jgT+AvyUDRt1dgH+WBRFEULYB/hc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10915a7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "henon = Henon()\n",
    "sim_henon = Simulation(henon,  [0.0, 0.1], duration=60000)\n",
    "sim_henon.plot(fig_options=dict(figsize=(11,8)),\n",
    "               plot_options=dict(linestyle='', marker='.', alpha=0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "`__iter__` と `__next__` というメソッドを定義したことで `for` でループを回すことができるようになります [イテレータクラス](https://docs.python.org/3.3/tutorial/classes.html#iterators)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(                     x,                      y)\n",
      "--------------------------------------------------\n",
      "(                   0.0,                    0.1)\n",
      "(              -0.07013,                   0.05)\n",
      "(  -0.09076378310000001,   -0.12227299999999999)\n",
      "( -0.014877272096376182,    -0.2204681460980274)\n",
      "(   0.07079308114313376,   -0.13342868804559813)\n",
      "(   0.13115288869480732,   0.055980162384200643)\n",
      "(   0.09844402981613778,     0.3049797785942996)\n",
      "(  -0.17810615237921568,      0.409424825763938)\n",
      "(   -0.5423895713096526,    -0.2973420526871539)\n",
      "(  -0.10358468712864322,    -0.9108997119842471)\n"
     ]
    }
   ],
   "source": [
    "print(\"({:>22}, {:>22})\".format(\"x\", \"y\"))\n",
    "print(\"-\" * 50)\n",
    "for x,y in Simulation(tkb,  [0.0, 0.1], duration=10):\n",
    "    print(\"({:>22}, {:>22})\".format(x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 関数型プログラミング\n",
    "\n",
    "システムを表現するクラスとそのサブクラス, シミュレーションを表すクラスを作りました。オブジェクト指向と言われるパラダイムを使っています\n",
    "\n",
    "Pythonは関数型プログラミングというプログラミング手法も利用できます。関数を引数に取る関数を書くことができるので、クラスを作ることは必ずしも必要ではありません。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def linearsys(mat):\n",
    "    def f(x):\n",
    "        return np.dot(mat, x)\n",
    "    return f\n",
    "\n",
    "def quiver_plot(func, x0, duration, axis=None, quiver_options={}):\n",
    "    if axis is None:\n",
    "        fig = plt.figure(figsize=(11,8))\n",
    "        ax = fig.add_subplot(111)\n",
    "    else:\n",
    "        ax = axis\n",
    "    \n",
    "    path = np.empty((duration, len(x0)))\n",
    "    path[0, :] = x0[:]\n",
    "    for i in range(1, duration):\n",
    "        path[i, :] = func(path[i-1, :])\n",
    "        \n",
    "    ax.quiver(path[:-1, 0], path[:-1, 1], path[1:, 0]-path[:-1, 0], \n",
    "              path[1:, 1]-path[:-1, 1],\n",
    "              scale_units='xy', angles='xy', scale=1, width=0.005,\n",
    "              **quiver_options)\n",
    "    \n",
    "    return path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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c+KhamDQPMIaeJZR+S+o37DppZjn1X2LoI1KJoUP9oa/9FU02fg78GCjnA9cB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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1091e8b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(11,8))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "f = linearsys(M)\n",
    "x0, x1 = np.array([100, 5]), np.array([80, -30])\n",
    "\n",
    "quiver_plot(f, x0, duration=40, axis=ax)\n",
    "quiver_plot(f, x1, duration=40, axis=ax, quiver_options=dict(color='red'))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 線形写像の固有値, 固有ベクトル\n",
    "\n",
    "\n",
    "線形写像の固有値・固有ベクトルと力学系の挙動との関係を可視化してみましょう。固有値計算のために、必要なライブラリをインポートします。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy.linalg as la"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\\begin{align}\n",
    "    A = \\begin{bmatrix}\n",
    "            1 & 3 \\\\\n",
    "            2 & 4 \n",
    "        \\end{bmatrix}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "A = np.array([\n",
    "        [0.4, 1.0],\n",
    "        [0.01, 1.2]\n",
    "    ])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 固有値と固有ベクトルの計算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "s, v = la.eig(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.38768944  1.21231056]\n"
     ]
    }
   ],
   "source": [
    "print(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.99992423 -0.77618596]\n",
      " [ 0.01230963 -0.63050405]]\n"
     ]
    }
   ],
   "source": [
    "print(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 固有値・固有ベクトルであることの確認\n",
    "\n",
    "\\begin{align}\n",
    "Av_i = s_i v_i\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(np.dot(A, v[:, 0]), np.dot(s[0], v[:, 0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(np.dot(A, v[:, 0]), np.dot(s[0], v[:, 0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## 可視化\n",
    "\n",
    "固有空間の可視化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x109c996a0>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ykYZYkrsD11XV91pnkSSNvrn0MsuhJEnShHDOoSRJkubFcigNiSR7tM4gSZLl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\nLIeSJEma8v8Bd6BX1Q0VmM8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1096ec208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v0_line = 6 *  np.array([v[:, 0], -v[:, 0]])\n",
    "v1_line = 6 * np.array([v[:, 1], -v[:, 1]])\n",
    "\n",
    "fig = plt.figure(figsize=(11,8))\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.plot(v0_line[:, 0], v0_line[:, 1], color='black', linestyle='dashed')\n",
    "ax.plot(v1_line[:, 0], v1_line[:, 1], color='black', linestyle='dashed')\n",
    "\n",
    "ax.text(3 * v[0,0], 3 * v[1,0] + 0.3, '$s_0$', fontsize=30)\n",
    "ax.text(3 * v[0,1], 3 * v[1,1] - 0.2, '$s_1$', fontsize=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZmsCdwEPAyR1OrlFM1jYE/gkMBC4nE79bzvLVO3XCEhHpxdJOVcfh93jzO1Xdjzcz358k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\nJljNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109590e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v0_line = 6 *  np.array([v[:, 0], -v[:, 0]])\n",
    "v1_line = 6 * np.array([v[:, 1], -v[:, 1]])\n",
    "\n",
    "fig = plt.figure(figsize=(11,8))\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.plot(v0_line[:, 0], v0_line[:, 1], color='black', linestyle='dashed')\n",
    "ax.plot(v1_line[:, 0], v1_line[:, 1], color='black', linestyle='dashed')\n",
    "\n",
    "xlim = ax.get_xlim()\n",
    "\n",
    "\n",
    "f = linearsys(A)\n",
    "# Upper Left\n",
    "quiver_plot(f, np.array([- 5.0, 0.5]), duration=7, \n",
    "            axis=ax, quiver_options=dict(color='gray'))\n",
    "quiver_plot(f, np.array([- 5.0, 1.0]), duration=6, \n",
    "            axis=ax, quiver_options=dict(color='gray'))\n",
    "quiver_plot(f, np.array([- 5.0, 2.0]), duration=6, \n",
    "            axis=ax, quiver_options=dict(color='gray'))\n",
    "\n",
    "# Upper Right\n",
    "quiver_plot(f, np.array([6.0, 0.5]), duration=7, \n",
    "            axis=ax, quiver_options=dict(color='orange'))\n",
    "quiver_plot(f, np.array([6.0, 1.0]), duration=6, \n",
    "            axis=ax, quiver_options=dict(color='orange'))\n",
    "quiver_plot(f, np.array([6.0, 2.0]), duration=6, \n",
    "            axis=ax, quiver_options=dict(color='orange'))\n",
    "\n",
    "# Lower Right\n",
    "quiver_plot(f, np.array([6.0, -0.5]), duration=7, \n",
    "            axis=ax, quiver_options=dict(color='blue'))\n",
    "quiver_plot(f, np.array([6.0, -1.0]), duration=6, \n",
    "            axis=ax, quiver_options=dict(color='blue'))\n",
    "quiver_plot(f, np.array([6.0, -2.0]), duration=6, \n",
    "            axis=ax, quiver_options=dict(color='blue'))\n",
    "\n",
    "# Lower Left\n",
    "quiver_plot(f, np.array([-6.0, -0.5]), duration=7, \n",
    "            axis=ax, quiver_options=dict(color='green'))\n",
    "quiver_plot(f, np.array([-6.0, -1.0]), duration=6, \n",
    "            axis=ax, quiver_options=dict(color='green'))\n",
    "quiver_plot(f, np.array([-6.0, -2.0]), duration=6, \n",
    "            axis=ax, quiver_options=dict(color='green'))\n",
    "\n",
    "# Stable Manifold\n",
    "\n",
    "quiver_plot(f, v0_line[0], duration=10, \n",
    "            axis=ax, quiver_options=dict(color='red'))\n",
    "quiver_plot(f, v0_line[1], duration=10, \n",
    "            axis=ax, quiver_options=dict(color='red'))\n",
    "\n",
    "ax.set_xlim(xlim)\n",
    "ax.set_ylim(xlim)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}