apsidal_precession.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from gravipy.tensorial import *\n",
    "from sympy import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Schwarzschild計量のChristoffel記号を計算する。\n",
    "[gravipy](https://github.com/wojciechczaja/GraviPy)を使う。\n",
    "\n",
    "レポジトリのdocsディレクトリにあるチュートリアル用ipnbファイルを参考にした。\n",
    "以下$(−,+,+,+)$型の計量を採用する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "t, r, theta, phi, M = symbols('t, r, theta, phi, M')\n",
    "chi = Coordinates('\\chi', [t, r, theta, phi])\n",
    "Metric = diag(-(1-2*M/r), 1/(1-2*M/r), r**2, r**2*sin(theta)**2)  #Schwarzschild計量\n",
    "g = MetricTensor('g', chi, Metric)\n",
    "Ga = Christoffel('Ga', g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{2 M}{r} - 1 & 0 & 0 & 0\\\\0 & \\frac{1}{- \\frac{2 M}{r} + 1} & 0 & 0\\\\0 & 0 & r^{2} & 0\\\\0 & 0 & 0 & r^{2} \\sin^{2}{\\left(\\theta \\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[2*M/r - 1,              0,    0,                  0],\n",
       "[        0, 1/(-2*M/r + 1),    0,                  0],\n",
       "[        0,              0, r**2,                  0],\n",
       "[        0,              0,    0, r**2*sin(theta)**2]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#計量テンソル\n",
    "g(All, All)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}0 & - \\frac{M}{r \\left(2 M - r\\right)} & 0 & 0\\\\- \\frac{M}{r \\left(2 M - r\\right)} & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right] & \\left[\\begin{matrix}\\frac{M \\left(- 2 M + r\\right)}{r^{3}} & 0 & 0 & 0\\\\0 & - \\frac{M \\left(- 2 M + r\\right)}{r \\left(2 M - r\\right)^{2}} & 0 & 0\\\\0 & 0 & 2 M - r & 0\\\\0 & 0 & 0 & - \\left(- 2 M + r\\right) \\sin^{2}{\\left(\\theta \\right)}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & \\frac{1}{r} & 0\\\\0 & \\frac{1}{r} & 0 & 0\\\\0 & 0 & 0 & - \\frac{\\sin{\\left(2 \\theta \\right)}}{2}\\end{matrix}\\right] & \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & \\frac{1}{r}\\\\0 & 0 & 0 & \\frac{\\sin{\\left(2 \\theta \\right)}}{2 \\sin^{2}{\\left(\\theta \\right)}}\\\\0 & \\frac{1}{r} & \\frac{\\sin{\\left(2 \\theta \\right)}}{2 \\sin^{2}{\\left(\\theta \\right)}} & 0\\end{matrix}\\right]\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[Matrix([\n",
       "[               0, -M/(r*(2*M - r)), 0, 0],\n",
       "[-M/(r*(2*M - r)),                0, 0, 0],\n",
       "[               0,                0, 0, 0],\n",
       "[               0,                0, 0, 0]]), Matrix([\n",
       "[M*(-2*M + r)/r**3,                              0,       0,                         0],\n",
       "[                0, -M*(-2*M + r)/(r*(2*M - r)**2),       0,                         0],\n",
       "[                0,                              0, 2*M - r,                         0],\n",
       "[                0,                              0,       0, -(-2*M + r)*sin(theta)**2]]), Matrix([\n",
       "[0,   0,   0,               0],\n",
       "[0,   0, 1/r,               0],\n",
       "[0, 1/r,   0,               0],\n",
       "[0,   0,   0, -sin(2*theta)/2]]), Matrix([\n",
       "[0,   0,                              0,                              0],\n",
       "[0,   0,                              0,                            1/r],\n",
       "[0,   0,                              0, sin(2*theta)/(2*sin(theta)**2)],\n",
       "[0, 1/r, sin(2*theta)/(2*sin(theta)**2),                              0]])]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Christoffel記号\n",
    "Ga(-All, All, All) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "次に測地線方程式による四元加速度\n",
    "$$\n",
    "a^{\\alpha}  = \\frac{d^2x^{\\alpha}}{d\\lambda^2}= -\\Gamma^{\\alpha}_{\\mu \\nu} \\frac{dx^{\\mu}}{d\\lambda} \\frac{dx^{\\nu}}{d\\lambda} =  -\\Gamma^{\\alpha}_{\\mu \\nu} v^{\\mu}v^{\\nu}\n",
    "$$\n",
    "を計算する。ここで$\\lambda$は何らかのパラメータである(固有時ではない)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "var(\"v_0, v_1, v_2, v_3\")\n",
    "var(\"a_0, a_1, a_2, a_3\")\n",
    "a_list = [a_0, a_1, a_2, a_3]\n",
    "v_list = [v_0, v_1, v_2, v_3]\n",
    "for i in range(4):\n",
    "    a_list[i] = 0\n",
    "\n",
    "#縮約を取る\n",
    "for i, j, k in product(range(4), repeat=3):\n",
    "    a_list[i] -= Ga( -i-1, j + 1, k + 1)*v_list[j]*v_list[k]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 M v_{0} v_{1}}{r \\left(2 M - r\\right)}$"
      ],
      "text/plain": [
       "2*M*v_0*v_1/(r*(2*M - r))"
      ]
     },
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     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{M v_{1}^{2} \\left(- 2 M + r\\right)}{r \\left(2 M - r\\right)^{2}} - \\frac{M v_{0}^{2} \\left(- 2 M + r\\right)}{r^{3}} - v_{2}^{2} \\left(2 M - r\\right) + v_{3}^{2} \\left(- 2 M + r\\right) \\sin^{2}{\\left(\\theta \\right)}$"
      ],
      "text/plain": [
       "M*v_1**2*(-2*M + r)/(r*(2*M - r)**2) - M*v_0**2*(-2*M + r)/r**3 - v_2**2*(2*M - r) + v_3**2*(-2*M + r)*sin(theta)**2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{v_{3}^{2} \\sin{\\left(2 \\theta \\right)}}{2} - \\frac{2 v_{1} v_{2}}{r}$"
      ],
      "text/plain": [
       "v_3**2*sin(2*theta)/2 - 2*v_1*v_2/r"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{v_{2} v_{3} \\sin{\\left(2 \\theta \\right)}}{\\sin^{2}{\\left(\\theta \\right)}} - \\frac{2 v_{1} v_{3}}{r}$"
      ],
      "text/plain": [
       "-v_2*v_3*sin(2*theta)/sin(theta)**2 - 2*v_1*v_3/r"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    display(a_list[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "実行速度の観点からsympy数式から関数へ変換する。\n",
    "\n",
    "参考:https://docs.sympy.org/latest/modules/utilities/lambdify.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.utilities.lambdify import lambdify\n",
    "a_func = lambdify((t, r, theta, phi, M, v_0, v_1, v_2, v_3), a_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "位置と速度の四元ベクトル$x^\\mu, v^\\mu$を入力すると四元加速度$a^\\mu$を返す関数を定義する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "a = lambda x, v: np.array(a_func(x[0], x[1], x[2], x[3], 1, v[0], v[1], v[2], v[3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "時間発展はRunge–Kutta法([wikipedia](https://ja.wikipedia.org/wiki/%E3%83%AB%E3%83%B3%E3%82%B2%EF%BC%9D%E3%82%AF%E3%83%83%E3%82%BF%E6%B3%95))で計算する。\n",
    "\n",
    "ニュートン運動方程式のRunge–Kutta法によるシュミレーションを参考にした。\n",
    "\n",
    "https://www.compadre.org/PICUP/resources/Numerical-Integration/\n",
    "\n",
    "\n",
    "今解きたい問題は、\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "&\\frac{dv^\\mu}{d\\lambda} = a^\\mu(x^\\mu, v^\\mu)\\\\\n",
    "&\\frac{dx^\\mu}{d\\lambda} = v^\\mu\n",
    "\\end{align}\n",
    "$$\n",
    "であるので、\n",
    "$$\n",
    "\\begin{align}\n",
    "&k^\\mu_{1v} = a^\\mu(x^\\mu, v^\\mu)d\\lambda \\\\\n",
    "&k^\\mu_{1x} = v^\\mu d\\lambda \\\\\n",
    "&k^\\mu_{2v} = a^\\mu(x^\\mu + \\frac{k^\\mu_{1x}}{2}, v^\\mu+ \\frac{k^\\mu_{1v}}{2})d\\lambda\\\\\n",
    "&k^\\mu_{2x} = ( v^\\mu+ \\frac{k^\\mu_{1v}}{2})d\\lambda \\\\\n",
    "&k^\\mu_{3v} = a^\\mu(x^\\mu + \\frac{k^\\mu_{2x}}{2}, v^\\mu+ \\frac{k^\\mu_{2v}}{2})d\\lambda\\\\\n",
    "&k^\\mu_{3x} = ( v^\\mu+ \\frac{k^\\mu_{2v}}{2})d\\lambda\\\\\n",
    "&k^\\mu_{4v} = a^\\mu(x^\\mu + k^\\mu_{3x}, v^\\mu + k^\\mu_{3v})d\\lambda\\\\\n",
    "&k^\\mu_{4x} = (v^\\mu + k^\\mu_{3v})d\\lambda\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "を計算して、$x^\\mu$, $v^\\mu$を\n",
    "$$\n",
    "\\begin{align}\n",
    "x^\\mu_{\\mathrm{next}} = x^\\mu + \\frac{1}{6}(k^\\mu_{1x} + 2k^\\mu_{2x} + 2k^\\mu_{3x} + k^\\mu_{4x}) \\\\\n",
    "v^\\mu_{\\mathrm{next}} = v^\\mu + \\frac{1}{6}(k^\\mu_{1v} + 2k^\\mu_{2v} + 2k^\\mu_{3v} + k^\\mu_{4v})\n",
    "\\end{align}\n",
    "$$\n",
    "と更新していけば良い。ニュートン運動方程式で$t$に相当するのがパラメータ$\\lambda$であることに注意。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10**5 #計算ステップ数\n",
    "\n",
    "x = np.array([0.0, 17.32050808,  0.95531662, -0.78539816]) #初期位置\n",
    "# theta成分(x[2])を0にしてしまうと0/0計算が発生するので適当な値を持たせておく\n",
    "v = np.array([1, -0.02886728, -0.00824957,  0.01750001]) #初期速度\n",
    "#t=0付近で\\lambda=tと選ぶとdt/d\\lambda = 1なので時間成分の速さは1にする\n",
    "#空間成分の速度は楕円軌道を描くように選ぶ\n",
    "\n",
    "dlam = 0.1 #1ステップごとに進む\\lambda幅\n",
    "R = [] \n",
    "Theta = []\n",
    "Phi = []\n",
    "T = []\n",
    "for _ in range(N):\n",
    "    T.append(x[0])\n",
    "    R.append(x[1])\n",
    "    Theta.append(x[2])\n",
    "    Phi.append(x[3])\n",
    "    k1v = a(x, v)*dlam\n",
    "    k1x = v*dlam\n",
    "    k2v = a(x+k1x/2, v+k1v/2)*dlam\n",
    "    k2x = (v+k1v/2)*dlam\n",
    "    k3v = a(x+k2x/2, v+k2v/2)*dlam\n",
    "    k3x = (v+k2v/2)*dlam\n",
    "    k4v = a(x+k3x, v+k3v)*dlam\n",
    "    k4x = (v+k3v)*dlam\n",
    "    v = v + (1/6)*(k1v+2*k2v+2*k3v+k4v)\n",
    "    x = x + (1/6)*(k1x+2*k2x+2*k3x+k4x)\n",
    "X = R*np.cos(Phi)*np.sin(Theta)\n",
    "Y = R*np.sin(Phi)*np.sin(Theta)\n",
    "Z = R*np.cos(Theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "今、謎のパラメータ$\\lambda$で$x$, $y$, $z$がパラメーター付けされているので、$t$によるパラメータ付けに変えたい。時系列データの補間を行う。\n",
    "\n",
    "参考：\n",
    "https://qiita.com/kenichi-hamaguchi/items/3c5e63e195e06a21d1da"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 10 #時間幅\n",
    "T_new = np.arange(0, T[-1], dt)\n",
    "X_new = np.interp(T_new, T, X)\n",
    "Y_new = np.interp(T_new, T, Y)\n",
    "Z_new = np.interp(T_new, T, Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "アニメーションを実装する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.9999861283738\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib nbagg\n",
    "import matplotlib.pyplot as plt \n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import matplotlib.animation as animation\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection=\"3d\")\n",
    "L = 50 #描画空間のサイズ\n",
    "def update(i):\n",
    "    ax.clear()\n",
    "    ax.scatter(0, 0, 0, marker=\"o\", c=\"orange\", s=100)\n",
    "    ax.plot(X_new[:i], Y_new[:i], Z_new[:i], c=\"black\", alpha = 0.4)\n",
    "    ax.scatter(X_new[i], Y_new[i], Z_new[i], marker=\"o\", c=\"blue\", s=10)\n",
    "    ax.set_title(r\"$t=$\"+str(int(T_new[i])))\n",
    "    ax.view_init(elev=30, azim=225)\n",
    "    ax.set_xlim(-L, L)\n",
    "    ax.set_ylim(-L, L)\n",
    "    ax.set_zlim(-L, L)\n",
    "\n",
    "ani = animation.FuncAnimation(fig, update, frames=len(T_new), interval=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 固有時の計算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "var(\"ds2, dx_0, dx_1, dx_2, dx_3\")\n",
    "dx_list = [dx_0, dx_1, dx_2, dx_3]\n",
    "ds2 = 0\n",
    "for i, j in product(range(4), repeat=2):\n",
    "    ds2 += g(i+1,j+1)*dx_list[i]*dx_list[j]\n",
    "ds2_func = lambdify((t, r, theta, phi, M, dx_0, dx_1, dx_2, dx_3), ds2)\n",
    "dtau = lambda x, dx: np.sqrt(-ds2_func(x[0], x[1], x[2], x[3], 1, dx[0], dx[1], dx[2], dx[3]) + 0j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10**5\n",
    "x = np.array([0.0, 17.32050808,  0.95531662, -0.78539816])\n",
    "v = np.array([1, -0.02886728, -0.00824957,  0.01750001])\n",
    "dlam = 0.1\n",
    "R = [] \n",
    "Theta = []\n",
    "Phi = []\n",
    "T = []\n",
    "tau = 0  #固有時\n",
    "Tau = []\n",
    "\n",
    "for _ in range(N):\n",
    "    Tau.append(tau)\n",
    "    T.append(x[0])\n",
    "    R.append(x[1])\n",
    "    Theta.append(x[2])\n",
    "    Phi.append(x[3])\n",
    "    k1v = a(x, v)*dlam\n",
    "    k1x = v*dlam\n",
    "    k2v = a(x+k1x/2, v+k1v/2)*dlam\n",
    "    k2x = (v+k1v/2)*dlam\n",
    "    k3v = a(x+k2x/2, v+k2v/2)*dlam\n",
    "    k3x = (v+k2v/2)*dlam\n",
    "    k4v = a(x+k3x, v+k3v)*dlam\n",
    "    k4x = (v+k3v)*dlam\n",
    "    v = v + (1/6)*(k1v+2*k2v+2*k3v+k4v)\n",
    "    x = x + (1/6)*(k1x+2*k2x+2*k3x+k4x)\n",
    "    tau = tau + dtau(x, (1/6)*(k1x+2*k2x+2*k3x+k4x))\n",
    "X = R*np.cos(Phi)*np.sin(Theta)\n",
    "Y = R*np.sin(Phi)*np.sin(Theta)\n",
    "Z = R*np.cos(Theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 10 #時間幅\n",
    "T_new = np.arange(0, T[-1], dt)\n",
    "X_new = np.interp(T_new, T, X)\n",
    "Y_new = np.interp(T_new, T, Y)\n",
    "Z_new = np.interp(T_new, T, Z)\n",
    "R_new = np.interp(T_new, T, R)\n",
    "Tau_new = np.interp(T_new, T, Tau)\n",
    "Dtau_new = np.diff(Tau_new) #dtごとのd\\tau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f21bcb9ba90>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax2 = ax1.twinx()\n",
    "ax1.plot(T_new[:-1], Dtau_new.real, label=r\"$d\\tau$\")\n",
    "ax2.plot(T_new[:-1], R_new[:-1], c=\"orange\", label=r\"$r$\")\n",
    "ax1.set_xlabel(r\"$t$\")\n",
    "ax1.set_ylabel(r\"$d\\tau$\")\n",
    "ax2.set_ylabel(r\"$r$\")\n",
    "handler1, label1 = ax1.get_legend_handles_labels()\n",
    "handler2, label2 = ax2.get_legend_handles_labels()\n",
    "ax1.legend(handler1 + handler2, label1 + label2, loc=2, borderaxespad=0.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "重力源に近づいたときに固有時がゆっくり進み、遠ざかると早く進むことがわかる。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 事象の地平線に衝突する場合\n",
    "\n",
    "$r=2M$付近では$d\\lambda$を小さくして慎重に計算する必要がある。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10**5\n",
    "x = np.array([0, 4,  np.pi/2, 0]) \n",
    "# theta成分を0にしてしまうと0/0計算が\n",
    "#発生するので適当な値を持たせておく\n",
    "v = np.array([1, 0, 0, 0.11]) \n",
    "\n",
    "R = [] \n",
    "Theta = []\n",
    "Phi = []\n",
    "T = []\n",
    "tau = 0  #固有時\n",
    "Tau = []\n",
    "\n",
    "np.seterr(all=\"raise\") #エラーが起こったら計算を止める\n",
    "for _ in range(N):\n",
    "    try:\n",
    "        #事象の地平線に近づいたらd\\lambdaを小さくする\n",
    "        dlam = 0.01*(np.abs(x[1] - 2))\n",
    "        Tau.append(tau)\n",
    "        T.append(x[0])\n",
    "        R.append(x[1])\n",
    "        Theta.append(x[2])\n",
    "        Phi.append(x[3])\n",
    "        k1v = a(x, v)*dlam\n",
    "        k1x = v*dlam\n",
    "        k2v = a(x+k1x/2, v+k1v/2)*dlam\n",
    "        k2x = (v+k1v/2)*dlam\n",
    "        k3v = a(x+k2x/2, v+k2v/2)*dlam\n",
    "        k3x = (v+k2v/2)*dlam\n",
    "        k4v = a(x+k3x, v+k3v)*dlam\n",
    "        k4x = (v+k3v)*dlam\n",
    "        v = v + (1/6)*(k1v+2*k2v+2*k3v+k4v)\n",
    "        x = x + (1/6)*(k1x+2*k2x+2*k3x+k4x)\n",
    "        tau = tau + dtau(x, (1/6)*(k1x+2*k2x+2*k3x+k4x))\n",
    "    except FloatingPointError:\n",
    "        break\n",
    "X = R*np.cos(Phi)*np.sin(Theta)\n",
    "Y = R*np.sin(Phi)*np.sin(Theta)\n",
    "Z = R*np.cos(Theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 1 #時間幅\n",
    "T_new = np.arange(0, T[-1], dt)\n",
    "X_new = np.interp(T_new, T, X)\n",
    "Y_new = np.interp(T_new, T, Y)\n",
    "Z_new = np.interp(T_new, T, Z)\n",
    "R_new = np.interp(T_new, T, R)\n",
    "Tau_new = np.interp(T_new, T, Tau)\n",
    "Dtau_new = np.diff(Tau_new) #dtごとのds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"639.9999861283738\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib nbagg\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "circle_phi = np.linspace(0, 2*np.pi, 100)\n",
    "circle_x = 2*np.cos(circle_phi)\n",
    "circle_y = 2*np.sin(circle_phi)\n",
    "L = 6 #描画する空間のサイズ\n",
    "def update(i):\n",
    "    ax.clear()\n",
    "    ax.plot(circle_x, circle_y, c=\"black\")\n",
    "    ax.plot(X_new[:i], Y_new[:i], c=\"black\", alpha=0.6)\n",
    "    ax.scatter(X_new[i], Y_new[i], marker=\"o\", c=\"blue\", s=10)\n",
    "    ax.set_title(r\"$t=$\"+str(int(T_new[i]))+\"\\t\"+r\"$\\tau=$\"+str(round(Tau_new[i].real,2)))\n",
    "    ax.set_xlim(-L, L)\n",
    "    ax.set_ylim(-L, L)\n",
    "    ax.set_aspect('equal')\n",
    "\n",
    "ani = animation.FuncAnimation(fig, update, frames=len(T_new), interval=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f21bc91d2e8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7HwFeBG5MQpjvUrJKpsJeMPSDsPvJVqsCf79mH3kGH7xoSIqDE5EcUND0vGq4zI/faGb5ZrYKOESQfN5q4Rh/ZmZrzOxJM2uaCmIYsDuuzJ5wXdIoWSXbiNvh5D6oeuOsTe7Os2v2M31MKQN6aXglEUm4WNPzquHyvs5s7t7g7pOBcmCamV3UbP/fAaPcfRLB3dNjqQn7bEpWyTbsFsgrhD0Lztq0YX8N26vquGWSqgBFJDrufhRYSLOqPHevjusA9whwWfh+LxA/4V55uC5plKySrbB3MFbg3rOT1bNr9pOfZ9x40eDUxyUiOc3MBphZ3/B9d+A6YFOzMvHtE7fy3jOx/wtcb2b9wo4V14frkkbJKhWG3Qo1m6Bmy7urgirAfcwaW0b/kqIIgxORHDUEWGhma4BlBG1Wz5rZA2Z2a1jms2G39tUEs2X8OYC7Hwa+Fu63DHggXJc05h0cGTwKJSUlXldXF3UYnVf3DjwzCqZ8Gy78AgCrdx9l3g8W86+3TeKOqZq+XkQSz8xOuHtJ1HEkgu6sUqFkJPSd9L6qwN+v3U9hvnHDBFUBioici5JVqgy7NXg4+HQ17s5za/cze2wZfXoURh2ZiEjaU7JKlfJbwRtg3x9Yv6+GPUdO6tkqEZF2yrCJojJY/8ug+xDYu4Dn6y4nP8+4dsKgqKMSEckIurNKFcuDYR+Cfc/zx3XvcMXo/uoFKCLSTkpWqTT0FojV0u/Ecj6oZ6tERNpNySqVBl1NA4XM6b2CGyYqWYmItJeSVSoV9mRd/UXc2H81A3sXRx2NiEjGULJKoV3VJ3iu+hJG5VfAiX1RhyMikjGUrFLo+fX7ebU2HAdyf1KH0RIRySpKVin04oaD5PWbFHRhV7ISEWk3JasUqTp+muXvHOG6CYNhyA1w4AVobIg6LBGRjKBklSIvbzyEO1w/cRAMuRHqj8DhZVGHJSKSEZSsUuSFDQcY1rc7E4b0hsHXAgb7no86LBGRjKBklQIn6mO8vrWK6yYMwsygWymUToP9SlYiIu2hZJUCr22p4nSskevjxwIccn1QDVh/NLrARCRnmVmxmS01s9XhBItfbaHM35rZBjNbY2YvmdnIuG0NZrYqXM6eCj3BlKxS4MUNB+ldXMDlo/u/t3LQXPBGOPRqdIGJSC47DVzj7pcAk4EbzWx6szIrganuPgl4EvjXuG0n3X1yuNxKkilZJVmsoZGXNh3kmgsGUpgf9+cumw753eHAS9EFJyI5ywPHw4+F4eLNyix09xPhxzeB8hSG+D5KVkn29jtHOHriTNBlPV5+NxgwGw6+HE1gIpILCsxsedwyP36jmeWb2SrgEPCiu7/VxrHuAf4Q97k4POabZvYnSYj9fTSfVZK9tOkQhfnGB84vO3vj4Lmw6ktw8gB018C2IpJwMXef2tpGd28AJptZX+BpM7vI3dc1L2dmHwemAnPiVo90971mNgZ42czWuvu2RH+BJrqzSrI/bjzI9DGl9CpuYfr6QXODV91diUiE3P0osBC4sfk2M7sW+EfgVnc/HbfP3vB1O/AKMCWZMSpZJdGOqjq2V9ZxzQUDWy7QbwoU9lW7lYiknJkNCO+oMLPuwHXApmZlpgD/SZCoDsWt72dm3cL3ZcAsYEMy440kWZlZXzN70sw2mdlGM5sRRRzJ9tLGgwBce2Er09fn5cOgq+HgS+DechkRkeQYAiw0szXAMoI2q2fN7AEza+rd9y2gJ/A/zbqoXwgsN7PVBHdk33D3pCarqNqs/g143t1vM7MioEdEcSTVSxsPcf6gngzv38bXG3QN7Hkajm+HXuelLjgRyWnuvoYWqu7c/b6499e2su8S4OLkRXe2lN9ZmVkf4APATwDcvT6sL80qx06eYdnOw8xt7a6qyWC1W4mInEsU1YCjgUrgv8xspZk9YmYlzQuZ2fym7paxWCz1UXbRa1sqiTU6c1trr2rS+4JgyhC1W4mItCqKZFUAXAr8yN2nAHXAl5oXcveH3X2qu08tKMi8HvYvbTxI/5Iipozo13ZBMxh4VTCShdqtRERaFEWy2gPsiXv47EmC5JU1GhqdV7ZUctX4AeTn2bl3GDgHTh2A2q3JD05EJAOlPFm5+wFgt5mND1fNJcldHlNt5a5g1IpWu6w3NzB8zu7Qa8kLSkQkg0X1nNXfAL8Iu0xOBv4lojiSYuHmQ+TnGVeOG9C+HXqPh+KBGtRWRKQVkTQGufsqgqE7stLLmyq5bGQ/+nRvYdSKlpjBgA+8125l7ag6FBHJIRrBIsEOHDvFxv017a8CbDJwDpzYDXXvJCcwEZEMpmSVYAs3ByOSXD2+g8lqUFO7laoCRUSaU7JKsIWbDjGsb3fOH9SzYzv2mQhF/ZWsRERaoGSVQKdjDSyuqOKq8QOwjrY7WR4MvFI9AkVEWqBklUDLdhyhrr6h4+1VTQbOgePb4MTexAYmIpLhlKwSaOHmQxQV5DHjvNLOHWCg2q1ERFqiZJVACzcfYvqYUnoUdfKJgL6XQGFvOPR6YgMTEclwSlYJsvvwCbZX1nHV+e18ELgleflQNgOqFicuMBGRLKBklSCvhF3WrxrfhWQFUDYLjq6D+qybNUVEpNOUrBLk1S2VjOjfg9FlZ8120jEDZwMOVW8kJC4RkZaYWbGZLTWz1Wa23sy+2kKZbmb2hJlVmNlbZjYqbtuXw/WbzeyGZMerZJUAp2MNLNlWzZzzO9FlvbnSaWAFULkoMcGJiLTsNHCNu19CMEbrjWY2vVmZe4Aj7j4W+C7wTQAzmwDcCUwEbgR+aGb5yQz2nMnKzJYkM4BssGzHEU7UN3S9ChCgoAT6TVGyEpGk8sDx8GNhuDSfVG8e8Fj4/klgrgX/I58HPO7up919B1ABTGvtXGaWZ2Zf6Uq87bmzKm7hxFd25aTZ5tUthyjK70KX9eYGzIbqpdBQn5jjiUiuKmiacT1c5sdvNLN8M1sFHAJejJtnsMkwYDeAu8eAY0Bp/PrQnnBdi9y9EbilK1+kPclqvJk9bWb/v5ndaWZXA4925aTZ5pXNlVwxpn/nu6w3N3A2NJyCIysSczwRyVWxphnXw+Xh+I3u3uDuk4FyYJqZXZTEWNaY2f1m1qnmp/bstINgvqltwGXAXwJnNcTlqr1HT7L10HHmdKXLenNls4JXVQWKSAq4+1FgIUH7U7y9wHAAMysA+gDV8etD5eG6tvQnaOfaZ2bPmNnXzOz29sbYnluBendfBixr70FzyaubK4EEdFmP130Q9BwLlYvhwi8m7rgiIiEzGwCccfejZtYduI6wA0WcBcDdwBvAbcDL7u5mtgD4pZk9BAwFxgFL2zqfu98RnrcbQceMiwnauf6nPfG2J1nNac+BctWrW4JR1s8b0MFR1s9lwCzY95wmYxSRZBkCPBb24ssDfu3uz5rZA8Byd18A/AT4bzOrAA4T3Bnh7uvN7NfABiAGfNrdG9pzUnc/DawIl3Y7Z7Jy99qOHDCXnGloZElFNbdcMrTrXdabGzAbdjwGtVuCae9FRBLI3dcAU1pYf1/c+1NAi1V17v4g8GDSAmxGz1l1wcpdR6k9HWPO+WWJP/iApnYrPTkgIqJk1QWvbakkP8+YOTYJyar3eCjqp5EsRERQsuqS17ZWMmV4X3oXFyb+4JYHpdOhSndWIiJKVp10uK6etXuP8YFEdllvbsBMOLZBg9qKSM5Tsuqk17dW4k5yk1XZTIJBbZs/VC4ikluUrDrptS1V9O1RyMXD+iTvJKXTgupAVQWKSI5TsuoEd+e1rZXMHltGfl4Sn4Eq7Al9J6mThYjkPCWrTti4v5bK2tPJrQJsUjYDqt6ExnY9bycikpWUrDrh9a3BEEsfGJeKZDUTYrVQsyH55xIRSVNKVp3w+tYqxg/qxeA+Z82ekngDZgavejhYRHKYklUHnaxvYOnOw1w5LgkPArekZDQUD1S7lYjkNCWrDlq68zD1sUauTEV7FQSD2JbNVI9AEclpkSWrcIbKlWb2bFQxdMbrWyopKshj2qj+qTtp2Qyo3QqnKlN3ThGRNBLlndXngI0Rnr9TFlVUMW1Uf7oX5afupGUzgtdqPRwsIrkpkmRlZuXAzcAjUZy/sw7VnGLTgdrUtVc16T8VrEDtViKSs6K6s/oe8PdAY2sFzGy+mS03s+WxWCx1kbXh9a1VAFyZii7r8Qq6Q7/JSlYikrNSnqzM7BbgkLu/3VY5d3/Y3ae6+9SCgvZMaJx8r2+tpKxnNy4Y3Cv1Jy+bDtVLoTE9EreIZDYzG25mC81sg5mtN7PPtVDm78xsVbisM7MGM+sfbttpZmvDbcuTHW8Ud1azgFvNbCfwOHCNmf08gjg6pLHRWVRRxZXjyshL5hBLrSmbAbE6OLY+9ecWkWwUA77g7hOA6cCnzWxCfAF3/5a7T3b3ycCXgVfd/XBckavD7VOTHWzKk5W7f9ndy919FHAn8LK7fzzVcXTUxgM1VB2vZ3YyJlpsj6ZOFqoKFJEEcPf97r4ifF9L0OFtWBu7fBT4VSpia4mes2qnRWF71exUd65oUjIKigcpWYlIRxQ0tf2Hy/yWCpnZKGAK0GKXYzPrAdwI/CZutQMvmNnbrR03kSJtDHL3V4BXooyhvRZVVHH+oJ4M6p2CIZZaYha0WylZiUj7xc5VRWdmPQmS0L3uXtNKsQ8Bi5tVAc52971mNhB40cw2uftriQn7bLqzaodTZxpYuuMws8emuBdgc+8+HFwVbRwikhXMrJAgUf3C3Z9qo+idNKsCdPe94esh4GlgWrLiBCWrdlm+8winY42pf76qOT0cLCIJYmYG/ATY6O4PtVGuDzAHeCZuXYmZ9Wp6D1wPrEtmvOnRJzzNvV5RSWG+ccWYFA6x1JL+U8Hyg6rAYTdHG4uIZLpZwF3AWjNbFa77CjACwN1/HK77MPCCu9fF7TsIeDrIdxQAv3T355MZrJJVOyzaWsWlI/rRoyjiP1dBD+h7idqtRKTL3H0RcM7ncNz9UeDRZuu2A5ckJbBWqBrwHKqPn2b9vproqwCbDJgZPhysmYNFJHcoWZ3D4m3VAMxO9RBLrSmbAbHjcCyp1cMiImlFyeocFm2tpHdxARcP6xN1KIGycOZgzW8lIjlEyaoN7s6irVXMPK+M/CiGWGpJyUgoHqxp7kUkpyhZtWFHVR37jp1iVrq0V0HwcPCAmepkISI5RcmqDYsrwilBohoPsDVlM+D4Njh1KOpIRERSQsmqDYsqqijv152RpT2iDuX93m230t2ViOQGJatWNDQ6S7ZVM3tsGeGDb+mj/6WQV6h2KxHJGUpWrVi79xi1p2LMSrcqQID8Yuh3me6sRCRnKFm1oqm9auZ5pRFH0oqyGXB4GTTURx2JiEjSKVm1YtHWKiYM6U1pz25Rh9KyATOh4RQcXR11JCIiSadk1YKT9Q28/c6R6CZabI+mEdjVbiUiOUDJqgVLdx6mvqExPdurmvQYBj1GQNXiqCMREUk6JasWLK6ooig/j2mjIp4S5FwGzIbKxeAedSQiIkmlZNWCRVuruHRkX7oX5UcdStsGzoaT+6BuR9SRiIgklZJVM4fr6tmwv4bZ6VwF2GTAlcHrodejjUNEMo6ZDTezhWa2wczWm9nnWihzlZkdM7NV4XJf3LYbzWyzmVWY2ZeSHa8mX2xmybagy3pat1c16TMBCvtC5SIYc3fU0YhIZokBX3D3FeEU9W+b2YvuvqFZudfd/Zb4FWaWD/wAuA7YAywzswUt7JswurNqZnFFNb26pdGUIG2xPBgwCyp1ZyUiHePu+919Rfi+FtgIDGvn7tOACnff7u71wOPAvOREGlCyamZxRRXTzyulID9D/jQDr4SazXCqMupIRCT9FJjZ8rhlfkuFzGwUMAV4q4XNM8xstZn9wcwmhuuGAbvjyuyh/YmuU1QNGGf34RPsOnyCv5g1KupQ2m/A7OC1chEM/3C0sYhIuom5+9S2CphZT+A3wL3uXtNs8wpgpLsfN7ObgN8C45ITatsy5PYhNZqGWErrh4Gb6z8V8roFyUpEpAPMrJAgUf3C3Z9qvt3da9z9ePj+OaDQzMqAvcDwuKLl4bqkUbKKs3hbNQN7deO8AT2jDqX98rtB6TT1CBSRDrFgOomfABvd/aFWyoWwfVsAAA6DSURBVAwOy2Fm0whyRjWwDBhnZqPNrAi4E1iQzHhVDRhqbHSWVFQx5/wB6TclyLkMvBI2fBNidVBQEnU0IpIZZgF3AWvNbFW47ivACAB3/zFwG/DXZhYDTgJ3ursDMTP7DPC/QD7wU3dfn8xglaxCmw/WUl1Xz8xM6LLe3IDZ4P8CVW/C4LlRRyMiGcDdFwFt/s/c3b8PfL+Vbc8BzyUhtBapGjDU1F41a2yaTgnSlrKZQTf2Q69GHYmISFIoWYUWV1QxZkAJQ/p0jzqUjivqE0zGeOClqCMREUmKlCer9gzxkWpnGhpZuuMws87LwCrAJoPnQvVSOFMbdSQiIgkXxZ1V0xAfE4DpwKfNbEIEcbxr9e6j1NU3ZGYVYJPBc8Fj6hUoIlkp5cmqi0N8JMXiimrMYPqYDE5WZbOC560OqipQRLJPpL0B2xriIxwWZD5AUVFRUuNYvK2Ki4b2oW+P5J4nqQq6B1Pdq91KRLJQZB0szjHEB+7+sLtPdfepBQXJy6kn6mOs3HWEmZlcBdhk0Fw4ulrjBIpI1okkWZ1riI9UWrbzCGcaPLM7VzRpesbq0CuRhiEikmhR9AY85xAfqbQknML+8nSfwr49+k+Fwt6qChSRrBPFnVXTEB/XxM0+eVMEcQBBe9WUERkwhX175BXAwDlKViKSdVLewaI9Q3ykytET9azfV8Pnrz0/6lASZ9A1sPd3UPcOlIyMOhoRkYTI6REs3thWjXuGDrHUmiE3BK/7/hBtHCIiCZTTyWrxtipKivKZVN436lASp/cF0HMs7Hkm6khERBImp5PVkm3VTBvdn8JMmcK+PcygfB4cfFlDL4lI1siiX+mOOXDsFNsr65iViVOCnEv5rdBYD/tfiDoSEZGEyNlktWRbMCXIjPOyqL2qSdlMKOqvqkARyRo5m6wWV1TTr0chFw7uHXUoiZdXAENvhn2/h8ZY1NGISBpqzwwYZvYxM1tjZmvNbImZXRK3bWe4fpWZLU92vDmZrNydJduqmHFeKXl5adGLPvHK50H9YahaEnUkIpKe2jMDxg5gjrtfDHwNeLjZ9qvdfbK7T012sDmZrHZWn2D/sVPMzIYhlloz5HrIK4I9C6KORETSUHtmwHD3Je5+JPz4JlCe2ijfk5PJqmkK+5nZ2F7VpLBX8IDwnmfAPepoRCQaBWa2PG6Z31KhtmbAiHMPEP8ApwMvmNnbrR03kSKdIiQqb2yrZkifYkaXlUQdSnIN/1NYOh8OL4fSy6OORkRSL3auKrpzzYARlrmaIFnNjls92933mtlA4EUz2+TuryUq8OZy7s6qsTFor5p5XhnBmLpZbMQdkN8dtv006khEJA21ZwYMM5sEPALMc/fqpvXuvjd8PQQ8DUxLZqw5l6w2HajlyIkz2V0F2KSoDwz/M3jnVxA7GXU0IpJG2jMDhpmNAJ4C7nL3LXHrS8ysV9N74HpgXTLjzblk1fR8VVZMttge5/0FnDkGe56OOhIRSS8tzoBhZn9lZn8VlrkPKAV+2KyL+iBgkZmtBpYCv3f355MZrHkGNL6XlJR4XV1dQo71F48uY2dVHS9/8aqEHC/teSMsGAs9x8DcP0YdjYikkJmdcPesaJzPqTurMw2NvLW9OjtHrWiN5cGYT8LBl+D4zqijERHplJxKVmv2HKOuviE7xwNsy5i7AYPtj0YdiYhIp+RUsnojbK+aPiaH7qwASkbA4Otg28PqaCEiGSmnktXiimomDOlN/5KiqENJvYlfgZP7oeI/o45ERKTDciZZnTrTwNu7juRGl/WWDJoTjGix4esQS0xnFRGRVMmZZPX2O0eojzXmTpf1lkx6AE4dgq0/ijoSEZEOyZlktWRbFfl5xrTROZysBsyCITfAhm9qFmERySg5lKyquaS8Dz275eRwiO+5+AE4XQUbvxN1JCIi7ZYTyar21BnW7DmW3VOCtFfZNBh5J6x/EKqWRh2NiEi75ESyWrrjMA2NntvtVfEu/xF0HwpL/j9VB4pIRsiJZLVkWzVFBXlcOqJf1KGkh6K+MPMXULcDln066mhERM4pJ5LV4ooqpo7sR3FhftShpI+Bs2Hi/4Wd/w2bvht1NCIibcr6ZFV9/DSbDtTm3hBL7XHRP0H5h2HF38LaBzSjsIikraxPVm9uPwyQW4PXtldeAcz+NYy+G9beHyStxljUUYmInCXr+3Ev2VZFz24FTBrWJ+pQ0lNeAUz/adCOtfl7cOgVmPpDGDAj6shERN6V9XdWS7ZVM210fwrys/6rdp7lwaXfhdlPBs9gvTgTlnwi6NquqkERSQOR/IKb2Y1mttnMKszsS8k6z76jJ9lRVZe74wF2hBmM+DO4eSNc+Hew+0l44Qp4bhKsexAOLYKG01FHKSIJYmbDzWyhmW0ws/Vm9rkWypiZ/Xv4W73GzC6N23a3mW0Nl7uTHW/KqwHNLB/4AXAdsAdYZmYL3H1Dos/1xrZqAD0M3BGFPWHKv8LEf4RdT8C2n8Kafwq25XWDPhOg1/nQaxz0GAbFg6B4IBT2gcLeUNAT8rtDfnGQAEUkXcWAL7j7CjPrBbxtZi82+y3+IDAuXK4AfgRcYWb9gfuBqYCH+y5w9yPJCjaKNqtpQIW7bwcws8eBeUDCk9WSbdX061HIBYN7JfrQ2a+oD4ydHyynq6FyUbAcXQ+Hl8Pu/wFvbPsYeUWQVxi8Wj5YQfiaFyzYe69YmNysWZJrLeF1MhEqgUqmmfM76Dkm4Yd19/3A/vB9rZltBIbx/t/iecDP3N2BN82sr5kNAa4CXnT3wwBm9iJwI/CrhAcaiiJZDQN2x33eQ5Cx38fM5gPzAYqKOjf/1HkDSxjQawR5efqB6pJupVA+L1iaNJ6BU5Vw6mAwknusBs7UBCNiNJyChpPQeDoo11gP3hAsjTHAg0Tnje+9x8P38W1krbWXdbIdTe1vkonyunVl7wIzWx73+WF3f7h5ITMbBUwB3mq2qaXf62FtrE+atO0NGP5BHwYoKSnp1K/M/7lqbEJjkjh5hdBjaLCISLqKufvUtgqYWU/gN8C97l6TmrA6LooOFnuB4XGfy8N1IiKSQmZWSJCofuHuT7VQpLXf65T/jkeRrJYB48xstJkVAXcCCyKIQ0QkZ5mZAT8BNrr7Q60UWwB8IuwVOB04FrZ1/S9wvZn1M7N+wPXhuqRJeTWgu8fM7DMEXywf+Km7r091HCIiOW4WcBew1sxWheu+AowAcPcfA88BNwEVwAngk+G2w2b2NYKbD4AHmjpbJIt5BjQ6l5SUeF1dXdRhiIhkFDM74e4lUceRCBrWQURE0p6SlYiIpD0lKxERSXtKViIikvYyooOFmTUCJzu5ewHBGFjZSt8vs2Xz98vm7waZ8f26u3tW3JRkRLLqCjNbfq4nuDOZvl9my+bvl83fDbL/+6WbrMi4IiKS3ZSsREQk7eVCsjprhOEso++X2bL5+2Xzd4Ps/35pJevbrEREJPPlwp2ViIhkOCUrERFJe1mdrMzsRjPbbGYVZvalqOPpCjMbbmYLzWyDma03s8+F6/ub2YtmtjV87Rd1rF1hZvlmttLMng0/jzazt8Jr+EQ4rUxGCqcEf9LMNpnZRjObkU3Xz8w+H/7bXGdmvzKz4ky+fmb2UzM7ZGbr4ta1eL3CKTT+Pfyea8zs0ugiz05Zm6zMLB/4AfBBYALwUTObEG1UXRIDvuDuE4DpwKfD7/Ml4CV3Hwe8FH7OZJ8DNsZ9/ibwXXcfCxwB7okkqsT4N+B5d78AuITge2bF9TOzYcBnganufhHB9D93ktnX71HgxmbrWrteHwTGhct84EcpijFnZG2yAqYBFe6+3d3rgceBeRHH1Gnuvt/dV4Tvawl+6IYRfKfHwmKPAX8STYRdZ2blwM3AI+FnA64BngyLZOz3M7M+wAcIJrvD3evd/ShZdP0IRnTobmYFQA9gPxl8/dz9NaD5HE2tXa95wM888CbQ18yGpCbS3JDNyWoYsDvu855wXcYzs1HAFOAtYFA4cyfAAWBQRGElwveAvwcaw8+lwFF3bxrSJpOv4WigEvivsJrzETMrIUuun7vvBb4N7CJIUseAt8me69ekteuVtb836SKbk1VWMrOewG+Ae929Jn6bB88hZOSzCGZ2C3DI3d+OOpYkKQAuBX7k7lOAOppV+WX49etHcHcxGhgKlHB2FVpWyeTrlYmyOVntBYbHfS4P12UsMyskSFS/cPenwtUHm6obwtdDUcXXRbOAW81sJ0GV7TUEbTx9w2olyOxruAfY4+5vhZ+fJEhe2XL9rgV2uHulu58BniK4ptly/Zq0dr2y7vcm3WRzsloGjAt7IxURNPYuiDimTgvbb34CbHT3h+I2LQDuDt/fDTyT6tgSwd2/7O7l7j6K4Fq97O4fAxYCt4XFMvn7HQB2m9n4cNVcYANZcv0Iqv+mm1mP8N9q0/fLiusXp7XrtQD4RNgrcDpwLK66UBIgq0ewMLObCNpB8oGfuvuDEYfUaWY2G3gdWMt7bTpfIWi3+jUwAngHuMPdmzcKZxQzuwr4orvfYmZjCO60+gMrgY+7++ko4+ssM5tM0HmkCNgOfJLgP4xZcf3M7KvARwh6rq4E/pKg3SYjr5+Z/Qq4CigDDgL3A7+lhesVJujvE1R9ngA+6e7Lo4g7W2V1shIRkeyQzdWAIiKSJZSsREQk7SlZiYhI2lOyEhGRtKdkJSIiaU/JSkRE0p6SlYiIpD0lK5FOMrNyM/tI1HGI5AIlK5HOm0swvp+IJJlGsBDphHD4q2eAo0At8Kfuvj3aqESyl5KVSCeZ2fMEYxiuO2dhEekSVQOKdN54YFPUQYjkAiUrkU4wszKCaSBi5ywsIl2mZCXSOaOAfVEHIZIrlKxEOmcTUGZm68xsZtTBiGQ7dbAQEZG0pzsrERFJe0pWIiKS9pSsREQk7SlZiYhI2lOyEhGRtKdkJSIiaU/JSkRE0t7/A9v4L3nNTi97AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "fig = plt.figure()\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax2 = ax1.twinx()\n",
    "ax1.plot(T_new,Tau_new.real, label=r\"$\\tau$\")\n",
    "ax2.plot(T_new, R_new, c=\"orange\", label=r\"$r$\")\n",
    "ax1.set_xlabel(r\"$t$\")\n",
    "ax1.set_ylabel(r\"$\\tau$\")\n",
    "ax2.set_ylabel(r\"$r$\")\n",
    "handler1, label1 = ax1.get_legend_handles_labels()\n",
    "handler2, label2 = ax2.get_legend_handles_labels()\n",
    "ax1.legend(handler1 + handler2, label1 + label2, loc=2, borderaxespad=0.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kerr計量の場合"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "t, r, theta, phi, M, a, rhosq, Delta = symbols('t, r, theta, phi, M, a, rhosq, Delta')\n",
    "chi = Coordinates('\\chi', [t, r, theta, phi])\n",
    "\n",
    "rhosq = r**2+(a**2)*cos(theta)**2\n",
    "Delta = r**2-2*M*r+a**2\n",
    "\n",
    "Metric_kerr = Matrix([[(1-(2*M*r)/rhosq),0,0,(2*a*M*r*sin(theta)**2)/rhosq], \\\n",
    "[0,-rhosq/Delta,0,0], [0,0,-rhosq,0], [(2*a*M*r*sin(theta)**2)/rhosq,0,0, \\\n",
    "-(sin(theta)**2)*((r**2+a**2)+(2*(a**2)*M*r*sin(theta)**2)/rhosq)]])\n",
    "\n",
    "# 結構時間かかる\n",
    "g_kerr = MetricTensor('g_kerr', chi, Metric_kerr)\n",
    "Ga_kerr = Christoffel('Ga_kerr', g)\n",
    "var(\"v_0, v_1, v_2, v_3\")\n",
    "var(\"a_0, a_1, a_2, a_3\")\n",
    "a_list = [a_0, a_1, a_2, a_3]\n",
    "v_list = [v_0, v_1, v_2, v_3]\n",
    "for i in range(4):\n",
    "    a_list[i] = 0\n",
    "#縮約を取る\n",
    "for i, j, k in product(range(4), repeat=3):\n",
    "    a_list[i] -= Ga_kerr( -i-1, j + 1, k + 1)*v_list[j]*v_list[k]\n",
    "\n",
    "a_kerr_func= lambdify((t, r, theta, phi, a, M, v_0, v_1, v_2, v_3), a_list)\n",
    "# a = 0.8, M = 1で計算\n",
    "a_kerr = lambda x, v: np.array(a_kerr_func(x[0], x[1], x[2], x[3], 0.8, 1, v[0], v[1], v[2], v[3]))\n",
    "\n",
    "var(\"ds2_kerr, dx_0, dx_1, dx_2, dx_3\")\n",
    "dx_list = [dx_0, dx_1, dx_2, dx_3]\n",
    "ds2_kerr = 0\n",
    "for i, j in product(range(4), repeat=2):\n",
    "    ds2_kerr += g_kerr(i+1,j+1)*dx_list[i]*dx_list[j]\n",
    "ds2_kerr_func = lambdify((t, r, theta, phi, a, M, dx_0, dx_1, dx_2, dx_3), ds2_kerr)\n",
    "dtau_kerr = lambda x, dx: np.sqrt(ds2_kerr_func(x[0], x[1], x[2], x[3], 0.8, 1, dx[0], dx[1], dx[2], dx[3]) + 0j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 10**4\n",
    "x = np.array([0.0, 17.32050808,  0.95531662, -0.78539816])\n",
    "v = np.array([1, -0.02886728, -0.00824957,  0.01750001])\n",
    "dlam = 0.5\n",
    "R = [] \n",
    "Theta = []\n",
    "Phi = []\n",
    "T = []\n",
    "tau = 0  #固有時\n",
    "Tau = []\n",
    "\n",
    "for _ in range(N):\n",
    "    Tau.append(tau)\n",
    "    T.append(x[0])\n",
    "    R.append(x[1])\n",
    "    Theta.append(x[2])\n",
    "    Phi.append(x[3])\n",
    "    k1v = a_kerr(x, v)*dlam\n",
    "    k1x = v*dlam\n",
    "    k2v = a_kerr(x+k1x/2, v+k1v/2)*dlam\n",
    "    k2x = (v+k1v/2)*dlam\n",
    "    k3v = a_kerr(x+k2x/2, v+k2v/2)*dlam\n",
    "    k3x = (v+k2v/2)*dlam\n",
    "    k4v = a_kerr(x+k3x, v+k3v)*dlam\n",
    "    k4x = (v+k3v)*dlam\n",
    "    v = v + (1/6)*(k1v+2*k2v+2*k3v+k4v)\n",
    "    x = x + (1/6)*(k1x+2*k2x+2*k3x+k4x)\n",
    "    tau = tau + dtau_kerr(x, (1/6)*(k1x+2*k2x+2*k3x+k4x))\n",
    "X = R*np.cos(Phi)*np.sin(Theta)\n",
    "Y = R*np.sin(Phi)*np.sin(Theta)\n",
    "Z = R*np.cos(Theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
    {
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\" width=\"639.9999861283738\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib nbagg\n",
    "dt = 10 #時間幅\n",
    "T_new = np.arange(0, T[-1], dt)\n",
    "X_new = np.interp(T_new, T, X)\n",
    "Y_new = np.interp(T_new, T, Y)\n",
    "Z_new = np.interp(T_new, T, Z)\n",
    "Tau_new = np.interp(T_new, T, Tau)\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection=\"3d\")\n",
    "L = 50 #描画する空間のサイズ\n",
    "def update(i):\n",
    "    ax.clear()\n",
    "    ax.scatter(0, 0, 0, marker=\"o\", c=\"orange\", s=100)\n",
    "    ax.plot(X_new[:i], Y_new[:i], Z_new[:i], c=\"black\", alpha = 0.4)\n",
    "    ax.scatter(X_new[i], Y_new[i], Z_new[i], marker=\"o\", c=\"blue\", s=10)\n",
    "    ax.set_title(r\"$t=$\"+str(int(T_new[i]))+\"\\t\"+r\"$\\tau=$\"+str(int(Tau_new[i].real)))\n",
    "    ax.view_init(elev=30, azim=225)\n",
    "    ax.set_xlim(-L, L)\n",
    "    ax.set_ylim(-L, L)\n",
    "    ax.set_zlim(-L, L)\n",
    "\n",
    "ani = animation.FuncAnimation(fig, update, frames=len(T_new), interval=1)"
   ]
  }
 ],
 "metadata": {
  "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}