UMF_1.ipynb

{
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  {
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   "source": [
    "# Решение краевой задачи для волнового уравнения\n",
    "## Выполнил студент группы МП-30 Буканов Никита"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Задача:\n",
    "Струна конечной длины. Правый конец струны закреплен, левый движется по закону:\n",
    "$\\large a\\big [\\frac{(t-t_0)^2}{\\tau^2}+1\\big ]^{-1}-a\\big [\\frac{t_0^2}{\\tau^2}+1\\big ]^{-1}$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": false
   },
   "source": [
    "## Параметры:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   },
   "outputs": [
    {
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      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>VBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "VBox(children=(HBox(children=(Label(value='$\\\\large p_l$ -линейная плотность'), BoundedFloatText(value=1.0, step=0.01))), HBox(children=(Label(value='$\\\\large T$ -сила натяжения струны'), BoundedFloatText(value=1.0, step=0.01))), HBox(children=(Label(value='$\\\\large l$ -длина струны'), BoundedFloatText(value=1.0, step=0.01))), HBox(children=(Label(value='$\\\\large a$ -амплитуда импульса'), BoundedFloatText(value=1.0, step=0.01))), HBox(children=(Label(value='$\\\\large t_0$ -время подачи импульса'), BoundedFloatText(value=1.0, step=0.01))), HBox(children=(Label(value='$\\\\large t$ -характерное время нарастания/спадания импульса'), BoundedFloatText(value=1.0, step=0.01)))))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import *\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "import scipy.integrate as integrate\n",
    "%matplotlib inline \n",
    "\n",
    "default_value = 1;\n",
    "label0=Label(\"$\\large p_l$ -линейная плотность\")\n",
    "label1=Label(\"$\\large T$ -сила натяжения струны\")\n",
    "label2=Label(\"$\\large l$ -длина струны\")\n",
    "label3=Label(\"$\\large a$ -амплитуда импульса\")\n",
    "label4=Label(\"$\\large t_0$ -время подачи импульса\")\n",
    "label5=Label(\"$\\large t$ -характерное время нарастания/спадания импульса\")\n",
    "field0=widgets.BoundedFloatText(value=default_value,min=0,max=100.0,step=0.01,readout=True,readout_format='.2f')\n",
    "field1=widgets.BoundedFloatText(value=default_value,min=0,max=100.0,step=0.01,readout=True,readout_format='.2f')\n",
    "field2=widgets.BoundedFloatText(value=default_value,min=0,max=100.0,step=0.01,readout=True,readout_format='.2f')\n",
    "field3=widgets.BoundedFloatText(value=default_value,min=0,max=100.0,step=0.01,readout=True,readout_format='.2f')\n",
    "field4=widgets.BoundedFloatText(value=default_value,min=0,max=100.0,step=0.01,readout=True,readout_format='.2f')\n",
    "field5=widgets.BoundedFloatText(value=default_value,min=0,max=100.0,step=0.01,readout=True,readout_format='.2f')\n",
    "field6=widgets.BoundedIntText(value=100,min=50,max=1000,step=100,continuous_update=False,readout=True)\n",
    "field7=widgets.BoundedIntText(value=100,min=50,max=1000,step=100,continuous_update=False,readout=True)\n",
    "field8=widgets.BoundedFloatText(value=0.01,min=0,max=0.1,step=0.001,readout=True,readout_format='.2f')\n",
    "field9=widgets.BoundedFloatText(value=default_value,min=0,max=100,step=0.01,readout=True,readout_format='.2f')\n",
    "field10=widgets.BoundedFloatText(value=3/8,min=1/4,max=1/2,step=0.01,readout=True,readout_format='.2f')\n",
    "\n",
    "VBox([HBox([label0,field0]),HBox([label1,field1]),HBox([label2,field2]),HBox([label3,field3]),HBox([label4,field4]),HBox([label5,field5])])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": false
   },
   "source": [
    "## Режим работы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": [],
    "hideCode": false,
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   "outputs": [
    {
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      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>VBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "VBox(children=(HBox(children=(Label(value='Режим работы:'), ToggleButtons(options=('Расчёт заданного числа шагов', 'Расчёт с заданной точностью'), value='Расчёт заданного числа шагов'))), HBox(children=(Label(value='Количество шагов по $x$:'), BoundedIntText(value=100, max=1000, min=50, step=100))), HBox(children=(Label(value='Количество шагов по $t$:'), BoundedIntText(value=100, max=1000, min=50, step=100))), HBox(children=(Label(value='Точность:'), BoundedFloatText(value=0.01, max=0.1, step=0.001))), HBox(children=(Label(value='Время симуляции:'), BoundedFloatText(value=1.0, step=0.01))), HBox(children=(Label(value='Параметр $\\\\sigma$ неявной схемы:'), BoundedFloatText(value=0.375, max=0.5, min=0.25, step=0.01)))))"
      ]
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   ],
   "source": [
    "toogle = widgets.ToggleButtons(options=['Расчёт заданного числа шагов','Расчёт с заданной точностью'],disabled=False,button_style='')\n",
    "global mode\n",
    "mode = 0\n",
    "def changed(changed):\n",
    "    global mode\n",
    "    if mode == 0:\n",
    "        mode = 1\n",
    "    else:\n",
    "        mode = 0\n",
    "toogle.observe(changed,'value')\n",
    "VBox([HBox([Label('Режим работы:'),toogle]),\n",
    "HBox([Label('Количество шагов по $x$:'),field6]),HBox([Label('Количество шагов по $t$:'),field7]),HBox([Label('Точность:'),field8]),HBox([Label('Время симуляции:'),field9]),\n",
    "     HBox([Label('Параметр $\\sigma$ неявной схемы:'),field10])])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "pl=field0.value\n",
    "T=field1.value\n",
    "l=field2.value\n",
    "amp=field3.value\n",
    "inp_time_0=field4.value\n",
    "print(inp_time_0)\n",
    "inp_time=field5.value\n",
    "x_count = field6.value\n",
    "t_count = field7.value\n",
    "requared_acc = field8.value\n",
    "max_time = field9.value\n",
    "a=np.sqrt(T/pl)\n",
    "h=l/x_count\n",
    "tau=max_time/t_count\n",
    "cur_acc = 1\n",
    "iteration = 0\n",
    "MAX_ITER=8\n",
    "sigma = field10.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": false
   },
   "source": [
    "## Начальные и гарничные условия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": false
   },
   "source": [
    "## U(t,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "code_folding": [],
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "amp=field3.value\n",
    "inp_time_0=field4.value\n",
    "inp_time=field5.value\n",
    "def psi1(t):\n",
    "    return amp*(1/(1+(t-inp_time_0)**2/inp_time**2)-1/((inp_time_0/inp_time)**2+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": false
   },
   "source": [
    "## U(t,l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "code_folding": [],
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "def psi2(t):\n",
    "    return 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": false
   },
   "source": [
    "## U(0,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "code_folding": [],
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "l=field2.value\n",
    "def f1(x):\n",
    "    return 0 #psi1(0)*(1-x/l)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": false
   },
   "source": [
    "## U'(0,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "def f2(x):\n",
    "    return 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": false
   },
   "source": [
    "## F(t,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hidePrompt": false
   },
   "outputs": [],
   "source": [
    "def F(t,x):\n",
    "    return 0\n",
    "def F1(t,x):\n",
    "    return integrate.quad(F,0,t,args=(x))[0]+f2(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": false
   },
   "source": [
    "## Решение с использованием неявной девятиточечной схемы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "code_folding": [],
    "hidePrompt": false
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   "outputs": [],
   "source": [
    "def Progonka(M,V):\n",
    "    A=np.zeros(M.shape[0])\n",
    "    B=np.zeros(M.shape[0])\n",
    "    R=np.zeros((M.shape[0],1))\n",
    "    A[0]=-1*M[0,1]/M[0,0]\n",
    "    B[0]=V[0]/M[0,0]\n",
    "    for i in range(1,M.shape[0]-1):\n",
    "        A[i]=-M[i,i+1]/[M[i,i]+M[i,i-1]*A[i-1]]\n",
    "        B[i]=(V[i]-M[i,i-1]*B[i-1])/[M[i,i]+M[i,i-1]*A[i-1]]\n",
    "    i = M.shape[0]-1\n",
    "    R[i]=(V[i]-M[i,i-1]*B[i-1])/[M[i,i]+M[i,i-1]*A[i-1]]\n",
    "    for i in range(M.shape[0]-2,-1,-1):\n",
    "        R[i]=A[i]*R[i+1]+B[i]\n",
    "    return R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hidePrompt": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Итерация  1 запушена \n",
      "Количество шагов сетки: \n",
      "   По времени: 100   \n",
      "   По координате: 100\n",
      "Итерация 1 завершилась \n",
      "\n",
      "\n",
      "Достигнута nочность: 1\n",
      "Итерация  2 запушена \n",
      "Количество шагов сетки: \n",
      "   По времени: 200   \n",
      "   По координате: 200\n",
      "Итерация 2 завершилась\n",
      "\n",
      "Достигнута nочность: 0.00470943629164\n"
     ]
    }
   ],
   "source": [
    "pl=field0.value\n",
    "T=field1.value\n",
    "l=field2.value\n",
    "amp=field3.value\n",
    "inp_time_0=field4.value\n",
    "inp_time=field5.value\n",
    "x_count = field6.value\n",
    "t_count = field7.value\n",
    "requared_acc = field8.value\n",
    "max_time = field9.value\n",
    "a=np.sqrt(T/pl)\n",
    "h=l/x_count\n",
    "tau=max_time/t_count\n",
    "cur_acc = 1\n",
    "iteration = 0\n",
    "MAX_ITER=8\n",
    "sigma = field10.value\n",
    "if psi1(0)==f1(0) and psi2(0)==f1(l):\n",
    "    while (requared_acc<cur_acc or iteration<2) and iteration <MAX_ITER:\n",
    "        x = np.linspace(0,l,x_count,dtype=np.longdouble)\n",
    "        timeline = np.linspace(0,max_time,t_count,dtype=np.longdouble)\n",
    "        U = np.zeros((t_count,x_count))\n",
    "        M = np.zeros((x_count-2,x_count-2),dtype=np.float32)\n",
    "        A = np.zeros((x_count-3),dtype=np.longdouble)\n",
    "        B = np.zeros((x_count-3),dtype=np.longdouble)\n",
    "        print(\"Итерация \",iteration+1,'запушена',\"\\nКоличество шагов сетки:\",\n",
    "              \"\\n   По времени:\",t_count,\" \",\"\\n   По координате:\",x_count)\n",
    "        V = np.zeros((x_count-2),dtype=np.float32)\n",
    "        h2 = h*h\n",
    "        tau2 = tau*tau\n",
    "        const1 = (a/h)**2\n",
    "        for i in range (t_count):#Задаём граничные условия\n",
    "            U[i][0]=psi1(timeline[i])\n",
    "            U[i][x_count-1]=psi2(timeline[i])\n",
    "        for i in range (1,x_count-1):#Задаём начальные условия\n",
    "            U[0][i]=f1(x[i])\n",
    "            U[1][i]=U[0][i]+tau*f2(x[i])+tau**2/2*(a**2*(f1(x[i-1])-2*f1(x[i])+f1(x[i+1]))/h**2+F(0,x[i]))\n",
    "        for i in range(1,t_count-1):\n",
    "            for j in range(1,x_count-1):\n",
    "                M[j-1][j-1]=1/tau2+2*sigma*const1\n",
    "                V[j-1]=(F(timeline[i],x[j])\n",
    "                +(2*U[i][j]-U[i-1][j])/tau2\n",
    "                +sigma*const1*(U[i-1][j+1]-2*U[i-1][j]+U[i-1][j-1])\n",
    "                +(1-2*sigma)*const1*(U[i][j+1]-2*U[i][j]+U[i][j-1]))\n",
    "            for j in range(1,x_count-2):\n",
    "                M[j-1][j]=-1*sigma*const1\n",
    "                M[j][j-1]=-1*sigma*const1\n",
    "            V[0]=V[0]+sigma*const1*U[i+1][0]\n",
    "            V[x_count-3]=V[x_count-3]+sigma*const1*U[i+1][x_count-1]\n",
    "            C=Progonka(M,V)\n",
    "            for i1 in range(1,x_count-1):\n",
    "                U[i+1][i1]=C[i1-1]\n",
    "        if iteration>0:\n",
    "            for i in range(0,prev_t_count):\n",
    "                for j in range(0,prev_x_count):\n",
    "                    U2[i][j]=U[2*i][2*j]\n",
    "            C = abs(Pr_U-U2)\n",
    "            v=-1\n",
    "            for t in C:\n",
    "                v = max(max(t),v)\n",
    "            cur_acc=v;\n",
    "            print(\"Итерация\",iteration+1,\"завершилась\")\n",
    "            if mode == 0:\n",
    "                break\n",
    "        Pr_U = np.copy(U)\n",
    "        U2 = np.zeros((t_count,x_count))\n",
    "        prev_t_count = t_count\n",
    "        prev_x_count = x_count\n",
    "        x_count*=2\n",
    "        t_count*=2\n",
    "        h=l/x_count\n",
    "        tau=max_time/t_count\n",
    "        iteration+=1\n",
    "        print(\"Итерация\",iteration,\"завершилась\",'\\n')\n",
    "        print(\"\\nДостигнута nочность:\",cur_acc)\n",
    "else:\n",
    "    print(\"Ошибка. Граничные и начальные условия не согласованы!!!!\")\n",
    "print(\"\\nДостигнута nочность:\",cur_acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
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    "hideCode": false,
    "hidePrompt": false,
    "scrolled": true
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       "<p>Failed to display Jupyter Widget of type <code>VBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "VBox(children=(Label(value='Длительность анимации'), FloatSlider(value=3.0, max=20.0, min=0.1, readout_format='f')))"
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     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "anim_speed=widgets.FloatSlider(\n",
    "    value=3,\n",
    "    min=0.1,\n",
    "    max=20,\n",
    "    step=0.1,\n",
    "    disabled=False,\n",
    "    continuous_update=True,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='f'\n",
    ")\n",
    "VBox([Label('Длительность анимации'),anim_speed])"
   ]
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   "execution_count": 12,
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x19461095da0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1945094da58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "maxv=-1e10\n",
    "minv=1e10\n",
    "minv = [min(minv,min(t)) for t in U]\n",
    "minv=min(minv)\n",
    "maxv = [max(maxv,max(t)) for t in U]\n",
    "maxv=max(maxv)\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlim(0,l)\n",
    "ax.set_ylim(minv-1,maxv+1)\n",
    "ax.grid(True)\n",
    "line, = ax.plot([], [], lw=2)\n",
    "# initialization function: plot the background of each frame\n",
    "def init():\n",
    "    line.set_data([], [])\n",
    "    return (line,)\n",
    "# animation function. This is called sequentially\n",
    "def animate(i):\n",
    "    x = np.linspace(0,l,U.shape[1],dtype=np.longdouble)\n",
    "    line.set_data(x, U[i])\n",
    "    return (line,)\n",
    "# call the animator. blit=True means only re-draw the parts that have changed.\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=U.shape[0], interval=1000/U.shape[0]*anim_speed.value, blit=True)\n",
    "# equivalent to rcParams['animation.html'] = 'html5'\n",
    "\n",
    "rc('animation', html='html5')\n",
    "anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hideCode": false,
    "hidePrompt": false,
    "scrolled": false
   },
   "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, fig.canvas.height);\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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\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 overriden (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=\"720\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e0af8635122543e48f67ed06e4377960",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>VBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "VBox(children=(HBox(children=(IntSlider(value=0, description='Step:', max=199), Label(value=''))), HBox(children=(BoundedFloatText(value=0.0, continuous_update=True, description='Time:', max=1.0, step=0.1), Label(value='')))))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "%matplotlib notebook\n",
    "matplotlib.rcParams['figure.figsize'] = [10.0, 10.0]\n",
    "import matplotlib.pyplot as plt\n",
    "w=widgets.IntSlider(\n",
    "    value=0,\n",
    "    min=0,\n",
    "    max=U.shape[0]-1,\n",
    "    step=1,\n",
    "    description='Step:',\n",
    "    disabled=False,\n",
    "    continuous_update=True,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='d'\n",
    ")\n",
    "w1 = widgets.BoundedFloatText(\n",
    "    value=0,\n",
    "    min=0,\n",
    "    max=max_time,\n",
    "    step=0.1,\n",
    "    continuous_update=True,\n",
    "    description='Time:',\n",
    "    disabled=False\n",
    ")\n",
    "global z \n",
    "z = Label()\n",
    "global z1 \n",
    "z1 = Label()\n",
    "def pltsin(i):\n",
    "    global ax1\n",
    "    global fig1\n",
    "    global z\n",
    "    x = np.linspace(0,l,U.shape[1],dtype=np.longdouble)\n",
    "    timeline=np.linspace(0,max_time,U.shape[0],dtype=np.longdouble)\n",
    "    if ax1.lines:\n",
    "        for line in ax1.lines:\n",
    "            line.set_xdata(x)\n",
    "            y = U[i['new']]\n",
    "            line.set_ydata(y)\n",
    "    else:\n",
    "        y = U[0]\n",
    "        ax1.plot(x, y)\n",
    "    z.value=\"Time:\"+str(timeline[i['new']])\n",
    "    w.value=i['new']\n",
    "    fig1.canvas.draw()\n",
    "def pltsin1(t):\n",
    "    global ax1\n",
    "    global fig1\n",
    "    global z\n",
    "    x = np.linspace(0,l,U.shape[1],dtype=np.longdouble)\n",
    "    timeline=np.linspace(0,max_time,U.shape[0],dtype=np.longdouble)\n",
    "    t = t['new']\n",
    "    minv = 1000000\n",
    "    mini=0\n",
    "    p=abs(timeline-t)\n",
    "    for i in range(len(p)):\n",
    "        if p[i]<minv:\n",
    "            minv = p[i]\n",
    "            mini = i\n",
    "    pltsin({'new': mini})\n",
    "\n",
    "%matplotlib notebook\n",
    "global ax1\n",
    "global fig1\n",
    "maxv=-1e10\n",
    "minv=1e10\n",
    "minv = [min(minv,min(t)) for t in U]\n",
    "minv=min(minv)\n",
    "maxv = [max(maxv,max(t)) for t in U]\n",
    "maxv=max(maxv)\n",
    "w.observe(pltsin,'value')\n",
    "w1.observe(pltsin1,'value')\n",
    "fig1,ax1 = plt.subplots(1,1)\n",
    "ax1.set_xlabel('X')\n",
    "ax1.set_ylabel('Y')\n",
    "ax1.set_xlim(( 0, l))\n",
    "ax1.set_ylim((minv-1,maxv+1))\n",
    "x = np.linspace(0,l,U.shape[1],dtype=np.longdouble)\n",
    "ax1.plot(x,U[0])\n",
    "ax1.grid(True)\n",
    "VBox([HBox([w,z]),HBox([w1,z1])])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidePrompt": true
   },
   "source": [
    "## Явная схема"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hidePrompt": true,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Итерация  1 запушена \n",
      "Количество шагов сетки: \n",
      "   По времени: 100   \n",
      "   По координате: 100\n",
      "Итерация 1  завершена \n",
      "\n",
      "Итерация  2 запушена \n",
      "Количество шагов сетки: \n",
      "   По времени: 200   \n",
      "   По координате: 200\n",
      "\n",
      "Достигнута точность: 0.00249594706893\n"
     ]
    }
   ],
   "source": [
    "pl=field0.value\n",
    "T= field1.value\n",
    "l=field2.value\n",
    "amp=field3.value\n",
    "Inp_time_0=field4.value\n",
    "Inp_time=field5.value\n",
    "x_count = field6.value\n",
    "t_count = field7.value\n",
    "requared_acc = field8.value\n",
    "max_time = field9.value\n",
    "a=np.sqrt(T/pl)\n",
    "h=l/x_count\n",
    "tau=max_time/t_count\n",
    "cur_acc = 1\n",
    "iteration = 0\n",
    "if a*tau/h<=1:\n",
    "    while (requared_acc<cur_acc or iteration<2) and iteration <8:\n",
    "        x = np.linspace(0,l,x_count,dtype=np.longdouble)\n",
    "        timeline = np.linspace(0,max_time,t_count,dtype=np.longdouble)\n",
    "        U = np.zeros((t_count,x_count))\n",
    "        V = np.zeros((t_count,x_count))\n",
    "        h2 = h*h\n",
    "        tau2 = tau*tau\n",
    "        const1 = (a/h)**2\n",
    "        print(\"Итерация \",iteration+1,'запушена',\"\\nКоличество шагов сетки:\",\"\\n   По времени:\",t_count,\" \",\"\\n   По координате:\",x_count)\n",
    "        for i in range (t_count): #Задаём граничные условия\n",
    "            U[i][0]=psi1(timeline[i])\n",
    "            U[i][x_count-1]=psi2(timeline[i])\n",
    "        for i in range (0,x_count): #Задаём начальные условия\n",
    "            U[0][i]=f1(x[i])\n",
    "        for i in range(0,t_count-1):\n",
    "            for j in range(1,x_count-1):\n",
    "                U[i+1][j]=tau*(F1(timeline[i],x[j])+a**2*tau*(U[i][j+1]-2*U[i][j]+U[i][j-1])/2/(h**2)+a*(V[i][j+1]-V[i][j-1])/(2*h))+U[i][j]\n",
    "                V[i+1][j]=tau*(a**2*tau*(V[i][j+1]-2*V[i][j]+V[i][j-1])/(2*h**2)+a*(U[i][j+1]-U[i][j-1])/(2*h))+V[i][j]\n",
    "            V[i+1][0]=V[i][0]+a*tau*(U[i][1]-U[i][0])/h\n",
    "            V[i+1][x_count-1]=V[i][x_count-1]+a*tau*(U[i][x_count-1]-U[i][x_count-2])/h\n",
    "        if iteration>0:\n",
    "            for i in range(0,prev_t_count):\n",
    "                for j in range(0,prev_x_count):\n",
    "                    U2[i][j]=U[2*i][2*j]\n",
    "            C = abs(Pr_U-U2)\n",
    "            v=-1\n",
    "            for t in C:\n",
    "                v = max(max(t),v)\n",
    "            cur_acc=v;\n",
    "            if mode == 0:\n",
    "                break\n",
    "        Pr_U = np.copy(U)\n",
    "        U2 = np.zeros((t_count,x_count))\n",
    "        prev_t_count = t_count\n",
    "        prev_x_count = x_count\n",
    "        x_count*=2\n",
    "        t_count*=2\n",
    "        h=l/x_count\n",
    "        tau=max_time/t_count\n",
    "        iteration+=1\n",
    "        print(\"Итерация\",iteration,\" завершена\",'\\n')\n",
    "    print('\\nДостигнута точность:',cur_acc)\n",
    "else:\n",
    "    print('При заданных параметрах схема не устойчива')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "code_folding": [
     0
    ],
    "hideCode": false,
    "hidePrompt": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "19ca770c1187438fa119f9c9a4a86b35",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>VBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "VBox(children=(Label(value='Длительность анимации'), FloatSlider(value=3.0, max=20.0, min=0.1, readout_format='f')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "anim_speed=widgets.FloatSlider(\n",
    "    value=3,\n",
    "    min=0.1,\n",
    "    max=20,\n",
    "    step=0.1,\n",
    "    disabled=False,\n",
    "    continuous_update=True,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='f'\n",
    ")\n",
    "VBox([Label('Длительность анимации'),anim_speed])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "code_folding": [],
    "hideCode": false,
    "hidePrompt": true
   },
   "outputs": [
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x194610e7f28>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1946116ce10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "maxv=-1e10\n",
    "minv=1e10\n",
    "minv = [min(minv,min(t)) for t in U]\n",
    "minv=min(minv)\n",
    "maxv = [max(maxv,max(t)) for t in U]\n",
    "maxv=max(maxv)\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlim(0,l)\n",
    "ax.set_ylim(minv-1,maxv+1)\n",
    "ax.grid(True)\n",
    "line, = ax.plot([], [], lw=2)\n",
    "# initialization function: plot the background of each frame\n",
    "def init():\n",
    "    line.set_data([], [])\n",
    "    return (line,)\n",
    "# animation function. This is called sequentially\n",
    "def animate(i):\n",
    "    x = np.linspace(0,l,U.shape[1],dtype=np.longdouble)\n",
    "    line.set_data(x, U[i])\n",
    "    return (line,)\n",
    "# call the animator. blit=True means only re-draw the parts that have changed.\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=U.shape[0], interval=1000/U.shape[0]*anim_speed.value, blit=True)\n",
    "# equivalent to rcParams['animation.html'] = 'html5'\n",
    "\n",
    "rc('animation', html='html5')\n",
    "anim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hideCode": false,
    "hidePrompt": true,
    "scrolled": false
   },
   "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, fig.canvas.height);\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\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\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 overriden (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"
    },
    {
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\" width=\"720\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0bd91ef61a6e4891ad6ee379da0f0f87",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>VBox</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "VBox(children=(HBox(children=(IntSlider(value=0, description='Step:', max=199), Label(value=''))), HBox(children=(BoundedFloatText(value=0.0, continuous_update=True, description='Time:', max=1.0, step=0.1), Label(value='')))))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "%matplotlib notebook\n",
    "matplotlib.rcParams['figure.figsize'] = [10.0, 10.0]\n",
    "import matplotlib.pyplot as plt\n",
    "w=widgets.IntSlider(\n",
    "    value=0,\n",
    "    min=0,\n",
    "    max=U.shape[0]-1,\n",
    "    step=1,\n",
    "    description='Step:',\n",
    "    disabled=False,\n",
    "    continuous_update=True,\n",
    "    orientation='horizontal',\n",
    "    readout=True,\n",
    "    readout_format='d'\n",
    ")\n",
    "w1 = widgets.BoundedFloatText(\n",
    "    value=0,\n",
    "    min=0,\n",
    "    max=max_time,\n",
    "    step=0.1,\n",
    "    continuous_update=True,\n",
    "    description='Time:',\n",
    "    disabled=False\n",
    ")\n",
    "global z \n",
    "z = Label()\n",
    "global z1 \n",
    "z1 = Label()\n",
    "def pltsin(i):\n",
    "    global ax1\n",
    "    global fig1\n",
    "    global z\n",
    "    x = np.linspace(0,l,U.shape[1],dtype=np.longdouble)\n",
    "    timeline=np.linspace(0,max_time,U.shape[0],dtype=np.longdouble)\n",
    "    if ax1.lines:\n",
    "        for line in ax1.lines:\n",
    "            line.set_xdata(x)\n",
    "            y = U[i['new']]\n",
    "            line.set_ydata(y)\n",
    "    else:\n",
    "        y = U[0]\n",
    "        ax1.plot(x, y)\n",
    "    z.value=\"Time:\"+str(timeline[i['new']])\n",
    "    w.value=i['new']\n",
    "    fig1.canvas.draw()\n",
    "def pltsin1(t):\n",
    "    global ax1\n",
    "    global fig1\n",
    "    global z\n",
    "    x = np.linspace(0,l,U.shape[1],dtype=np.longdouble)\n",
    "    timeline=np.linspace(0,max_time,U.shape[0],dtype=np.longdouble)\n",
    "    t = t['new']\n",
    "    minv = 1000000\n",
    "    mini=0\n",
    "    p=abs(timeline-t)\n",
    "    for i in range(len(p)):\n",
    "        if p[i]<minv:\n",
    "            minv = p[i]\n",
    "            mini = i\n",
    "    pltsin({'new': mini})\n",
    "\n",
    "%matplotlib notebook\n",
    "global ax1\n",
    "global fig1\n",
    "maxv=-1e10\n",
    "minv=1e10\n",
    "minv = [min(minv,min(t)) for t in U]\n",
    "minv=min(minv)\n",
    "maxv = [max(maxv,max(t)) for t in U]\n",
    "maxv=max(maxv)\n",
    "w.observe(pltsin,'value')\n",
    "w1.observe(pltsin1,'value')\n",
    "fig1,ax1 = plt.subplots(1,1)\n",
    "ax1.set_xlabel('X')\n",
    "ax1.set_ylabel('Y')\n",
    "ax1.set_xlim(( 0, l))\n",
    "ax1.set_ylim((minv-1,maxv+1))\n",
    "x = np.linspace(0,l,U.shape[1],dtype=np.longdouble)\n",
    "ax1.plot(x,U[0])\n",
    "ax1.grid(True)\n",
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