traffic_flow.ipynb

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    "# This is a cell to hide code snippets from displaying\n",
    "# This must be at first cell!\n",
    "\n",
    "from IPython.display import HTML\n",
    "\n",
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   "source": [
    "# Traffic flow\n",
    "Numerical simulation of traffic flow using Godunov schemes\n",
    "\n",
    "### Use\n",
    "To execute this notebook, please go to the top menu and click on ``Cell -> Run all``\n",
    "\n",
    "----\n",
    "\n",
    "In case of **error** or **warning** messages, please go to the top menu and click on ``Cell -> Run all``"
   ],
   "cell_type": "markdown",
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   "source": [
    "hide_me\n",
    "import numpy as np\n",
    "import scipy.io as sio\n",
    "import matplotlib.pyplot as plt\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import display, clear_output\n",
    "from godunov import *\n",
    "from godunov_mod import *\n",
    "\n",
    "def traffic_compute(N,T,cfl,rhom,um,jam,filename): \n",
    "    # Variables para facelas chamadas:\n",
    "    #N=100 # INPUT\n",
    "    #T=0.2 #min# INPUT\n",
    "    #cfl=0.95# INPUT\n",
    "    #rhom=750 #coches/km # INPUT\n",
    "    #um=50 #  km/h\n",
    "    #jam =0 # jam or not\n",
    "    #filename='initial_condition_jam_horreo.mat'\n",
    "\n",
    "    # Load rho0 and define w0 from filename\n",
    "    content = sio.loadmat(filename)\n",
    "    rho0 = content['rho0'][0]\n",
    "    a = content['a'][0][0]\n",
    "    b = content['b'][0][0]\n",
    "    if(np.size(rho0)==1):\n",
    "        w0=lambda x: rho0*np.ones(np.size(x))\n",
    "    else:\n",
    "        w0=lambda x: rho0\n",
    "\n",
    "    # Parámetros para a representación:\n",
    "    extrax=(b-a)/10.\n",
    "    extray=rhom/10.\n",
    "    liminf=0.\n",
    "    limsup=rhom+extray\n",
    "\n",
    "    # Solución aproximada\n",
    "    if jam == 0:\n",
    "        x,t,rho_aprox=godunov(a,b,N,T*60,cfl,w0,um*1000/3600,rhom/1000)\n",
    "    else:\n",
    "        x,t,rho_aprox=godunov_mod(a,b,N,T*60,cfl,w0,um*1000/3600,rhom/1000)\n",
    "\n",
    "    Mt=np.size(t)-1\n",
    "    dt=t[1]-t[0]\n",
    "    rho_aprox[0,:]=np.nan\n",
    "    rho_aprox[-1,:]=np.nan\n",
    "    return a,b,x,rho_aprox,extrax,extray,liminf,limsup,Mt,dt,t\n"
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      "text/plain": "VBox(children=(Output(), BoundedFloatText(value=0.0, description='Maximum density [vehicles/km]:', max=10000.0…",
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    "hide_me\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import ipywidgets as widgets\n",
    "from IPython.display import display, clear_output\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "# To prevent automatic figure display when execution of the cell ends\n",
    "%config InlineBackend.close_figures=False \n",
    "\n",
    "plt.ioff()\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_title('t = 0 min')\n",
    "ax.set_xlabel('$x$ [m]')\n",
    "ax.set_ylabel(r'$\\rho$ [vehicles/km]')\n",
    "line, = ax.plot([], [], lw=2)\n",
    "out=widgets.Output()\n",
    "style = {'description_width': 'initial'}\n",
    "\n",
    "rhom=widgets.BoundedFloatText(\n",
    "    min=0,\n",
    "    max=10000.0,\n",
    "    step=1.,\n",
    "    description='Maximum density [vehicles/km]:',\n",
    "    disabled=False, style=style\n",
    ")\n",
    "\n",
    "um=widgets.BoundedFloatText(\n",
    "    min=0,\n",
    "    max=100.0,\n",
    "    step=1.,\n",
    "    description='Maximum velocity [km/h]:',\n",
    "    disabled=False, style=style\n",
    ")\n",
    "\n",
    "T=widgets.BoundedFloatText(\n",
    "    min=0,\n",
    "    max=5.0,\n",
    "    step=0.1,\n",
    "    description='Final time [min]:',\n",
    "    disabled=False, style=style\n",
    ")\n",
    "\n",
    "filename = widgets.Dropdown(\n",
    "    options=[('Jam at Horreo', 'initial_condition_jam_horreo.mat'), ('Jam at Ronda', 'initial_condition_jam_ronda.mat'), \\\n",
    "             ('100 vehicles at Ronda', 'initial_condition_uniform_100vechicles_ronda.mat'), ('140 vehicles at Horreo', \\\n",
    "              'initial_condition_uniform_140vechicles_horreo.mat')],\n",
    "    value='initial_condition_jam_horreo.mat',\n",
    "    description='Initial condition:', style=style\n",
    ")\n",
    "\n",
    "jam=widgets.RadioButtons(\n",
    "    options=[('No',0), ('Yes',1)],\n",
    "    description='Traffic interruption at x=0:',\n",
    "    disabled=False, style=style\n",
    ")\n",
    "\n",
    "N=widgets.BoundedIntText(\n",
    "    min=0,\n",
    "    max=1000.,\n",
    "    step=1,\n",
    "    description='Number of cells:',\n",
    "    disabled=False, style=style\n",
    ")\n",
    "\n",
    "cfl=widgets.BoundedFloatText(\n",
    "    min=0,\n",
    "    max=10.,\n",
    "    step=0.01,\n",
    "    description='CFL number:',\n",
    "    disabled=False, style=style\n",
    ")\n",
    "\n",
    "button=widgets.Button(\n",
    "    description='Run',\n",
    "    disabled=False,\n",
    "    button_style='',\n",
    "    tooltip='Run',\n",
    "    icon='check'\n",
    ")\n",
    "\n",
    "vbox=widgets.VBox(children=(out,rhom,um,T,filename,jam,N,cfl,button))\n",
    "display(vbox)\n",
    "\n",
    "def on_button_clicked(b):\n",
    "    a,b,x,rho_aprox,extrax,extray,liminf,limsup,Mt,dt,t = \\\n",
    "      traffic_compute(N.value,T.value,cfl.value,rhom.value,um.value,jam.value,filename.value)\n",
    "    def init():\n",
    "        ax.set_xlim(a-extrax,b+extrax)\n",
    "        ax.set_ylim(liminf,limsup)\n",
    "        line.set_data([], [])\n",
    "        return (line,)\n",
    "    \n",
    "    def animate(i):\n",
    "        # update the data\n",
    "        ax.set_title('t = '+'%.3f' % ((t[i]+dt)/60)+' min')\n",
    "        line.set_data(x, 1000.*rho_aprox[:,i])\n",
    "        return (line,)\n",
    "    \n",
    "    anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=Mt, interval=100, \n",
    "                               blit=True)\n",
    "    with out:\n",
    "        clear_output(wait=True)\n",
    "        display(HTML(anim.to_jshtml()))\n",
    "    \n",
    "button.on_click(on_button_clicked)\n"
   ]
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