MID_controle_object_V2.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Tutoriel MID Contrôle\n",
    "\n",
    "On traite le quasipolynôme suivant :\n",
    "$$\n",
    "Q(s) = s^n+a_{n-1}s^{n-1}+...+a_0 + \\left[\\alpha_ms^m+...+\\alpha_0\\right]e^{-s\\tau}\n",
    "$$\n",
    "\n",
    "Cette fois-ci, on considère que l'on connait les paramètres du systèmes $a_i$ ainsi que l'un des hyperparamètres $s_0$ ou $\\tau$. Ainsi, nous allons utiliser la MID pour trouver les $\\alpha_j$ et l'hyperparamètre manquant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Packages nécessaires\n",
    "\n",
    "On utilise numpy pour les opérations mathématiques numériques telles que les opérations matricielles (produit matriciel par exemple).\n",
    "\n",
    "Sympy permet de réaliser des calculs en symbolique sur Python et donc de travailler avec des expressions mathématiques et en numérique."
   ]
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  {
   "cell_type": "code",
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   "source": [
    "# pip install sympy si nécessaire (module not found), pareil avec cxroots\n",
    "%matplotlib notebook\n",
    "import numpy as np\n",
    "import sympy as sp\n",
    "import cxroots as cx\n",
    "import matplotlib.pyplot as plt\n",
    "import traceback\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Paramètres\n",
    "$n$ est le degré du polynôme non retardé, $m$ est celui du polynôme retardé (celui multiplié par l'exponentielle).\n",
    "\n",
    "$s_0$ est le taux de décroissance exponentiel. Il s'agit de la racine dominante que l'on souhaite assigner (celle la plus à droite lorsqu'on plot les racines). Celui-ci doit être négatif pour que le système soit stable. Un $s_0$ positif signifie donc que le système est instable.\n",
    "\n",
    "$\\tau$ est le retard considéré."
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
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   "source": [
    "n = 2\n",
    "m = 1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Création de symboles\n",
    "\n",
    "Les variables s, tau, a et alpha vont désormais correspondre à des symboles et non des variables numériques.\n",
    "\n",
    "On considère dans nos cas concrets que les $a_i$ correspondent aux paramètres du système (de son équation) et les $\\alpha_j$ correspondent aux gains de la loi de commande retardée."
   ]
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  {
   "cell_type": "code",
   "execution_count": 3,
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   "outputs": [],
   "source": [
    "s = sp.symbols('s')  # define variable s for our problem to be solved\n",
    "tau = sp.symbols('tau')  # define variable tau : delay\n",
    "\n",
    "a = sp.symbols([\"a{:d}\".format(i) for i in range(n)], real=True)\n",
    "alpha = sp.symbols([\"alpha{:d}\".format(i) for i in range(m + 1)], real=True)\n",
    "avalue = [2, 1]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Création du quasipolynome"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{0} + a_{1} s + s^{2} + \\left(\\alpha_{0} + \\alpha_{1} s\\right) e^{- s \\tau}$"
      ],
      "text/plain": [
       "a0 + a1*s + s**2 + (alpha0 + alpha1*s)*exp(-s*tau)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Polynomial = s**n + np.array(a).dot([s**i for i in range(n)]) # Revient à faire s^n + a_{n-1}^{n-1}...\n",
    "Delayed = np.array(alpha).dot([s**i for i in range(m+1)])*sp.exp(-s*tau) # Revient à faire \n",
    "#b^m*s^m + b_{m-1}^{m-1}...\n",
    "Q = Polynomial + Delayed \n",
    "Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Créer le système à résoudre\n",
    "\n",
    "Dans ce cadre de MID orientée contrôle, on a $m+2$ inconnues qui sont les $\\alpha_j$ ($m+1$ variables de $0$ à $m$ inclus) et l'hyperparamètre manquant\n",
    "\n",
    "On parle donc de multiplicité de $m+2$ et on souhaite donc avoir $m+2$ équations. Pour l'instant nous avons une première équation qui correspond à notre quasipolynôme (=0). \n",
    "\n",
    "Il y a deux possibilités :\n",
    "\n",
    "- $s_0$ est donné\n",
    "- $\\tau$ est donné\n",
    "\n",
    "Dans ces deux cas, il faudra procéder en deux étapes en considérant d'abord les $m+1$ premières équations (toutes sauf la dernière) que l'on résoudra facilement en $\\alpha_j$ (système linéaire en $\\alpha$) et on remplacera ensuite les $\\alpha_j$ dans la dernière équation avec les expressions trouvées ce qui nous fera une équation permettant de trouver l'hyperparamètre manquant.\n",
    "\n",
    "Il faut donc calculer les $m+1$ dérivées suivantes ce qui se fait très simplement avec Sympy en utilisant la méthode <i>diff</i> en spécifiant en argument la variable de différenciation."
   ]
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   "cell_type": "code",
   "execution_count": 5,
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     "name": "stdout",
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     "text": [
      "a0 + a1*s + s**2 + (alpha0 + alpha1*s)*exp(-s*tau)\n",
      "a1 + alpha1*exp(-s*tau) + 2*s - tau*(alpha0 + alpha1*s)*exp(-s*tau)\n",
      "-2*alpha1*tau*exp(-s*tau) + tau**2*(alpha0 + alpha1*s)*exp(-s*tau) + 2\n"
     ]
    }
   ],
   "source": [
    "SysDerivatif = [Q]\n",
    "print(Q)\n",
    "for i in range(m+1):\n",
    "    DerniereDerivee = SysDerivatif[-1]\n",
    "    SysDerivatif.append(DerniereDerivee.diff(s)) # Dérivée par rapport à s\n",
    "    print(SysDerivatif[-1])"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Résolution du système\n",
    "\n",
    "Après avoir créé le système dérivatif, il suffit de le résoudre avec Sympy en spécifiant bien que l'on souhaite obtenir les expressions des $a_i$ et des $\\alpha_j$.\n",
    "\n",
    "Ici, on a bien $n+m+1 = 4$ ce qui nous retourne $a_0, a_1, \\alpha_0$ et $\\alpha_1$ en gardant bien à l'esprit que $a_2=1$.\n",
    "\n",
    "Le \".args[0]\" sert à extraire les solutions à partir du solveur qui retourne un set."
   ]
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  {
   "cell_type": "code",
   "execution_count": 6,
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    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left( \\left(a_{0} s \\tau - a_{0} + a_{1} s^{2} \\tau + s^{3} \\tau + s^{2}\\right) e^{s \\tau}, \\  - \\left(a_{0} \\tau + a_{1} s \\tau + a_{1} + s^{2} \\tau + 2 s\\right) e^{s \\tau}\\right)$"
      ],
      "text/plain": [
       "((a0*s*tau - a0 + a1*s**2*tau + s**3*tau + s**2)*exp(s*tau), -(a0*tau + a1*s*tau + a1 + s**2*tau + 2*s)*exp(s*tau))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = sp.linsolve(SysDerivatif[:-1], alpha).args[0] # Solveur selon les alpha et les a\n",
    "sol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\tau$ connu\n",
    "\n",
    "On cherche donc à trouver $s_0$ et on choisit le $s_0$ réel **négatif** qui est le **plus proche de $0$** s'il existe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_tau_connu(tau_val, acoef, Q):\n",
    "    sys = [Q]\n",
    "    for i in range(m+1):\n",
    "        DerniereDerivee = sys[-1]\n",
    "        sys.append(DerniereDerivee.diff(s)) # Dérivée par rapport à s\n",
    "    sol = sp.linsolve(SysDerivatif[:-1], alpha).args[0]\n",
    "    finaleq = SysDerivatif[-1].subs({alph : alphacoef for alph, alphacoef in zip(alpha, sol)}) \n",
    "    finaleq = finaleq.subs({asymb: aval for asymb, aval in zip(a, acoef)})\n",
    "    solS0 = finaleq.subs({tau : tau_val})\n",
    "    solS0 = sp.solve(solS0)\n",
    "    solS0eval = [i.evalf() for i in solS0]\n",
    "    try :\n",
    "        solution = max([i for i in solS0eval if i<0])\n",
    "    except Exception :\n",
    "        traceback.print_exc()\n",
    "    return solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tau**2*(-s*(s**2*tau + s*tau + 2*s + 2*tau + 1)*exp(s*tau) + (s**3*tau + s**2*tau + s**2 + 2*s*tau - 2)*exp(s*tau))*exp(-s*tau) + 2*tau*(s**2*tau + s*tau + 2*s + 2*tau + 1) + 2\n",
      "[-4.59643376575614, -1.82362043478586]\n"
     ]
    }
   ],
   "source": [
    "value_tau = 0.738\n",
    "\n",
    "finaleq = SysDerivatif[-1].subs({alph : alphacoef for alph, alphacoef in zip(alpha, sol)}) #remplace les coeffs\n",
    "finaleq = finaleq.subs({asymb: aval for asymb, aval in zip(a, avalue)})\n",
    "print(finaleq)\n",
    "solS0 = finaleq.subs({tau : value_tau})\n",
    "solS0 = sp.solve(solS0)\n",
    "print(solS0)\n",
    "solS0eval = [i.evalf() for i in solS0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -1.82362043478586$"
      ],
      "text/plain": [
       "-1.82362043478586"
      ]
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     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve_tau_connu(0.738, [2, 1], Q) # Safety check on function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.82362043478586\n",
      "[-0.881837285449719, 0.0163447037006065]\n"
     ]
    }
   ],
   "source": [
    "computedS0 = solS0[1]\n",
    "print(computedS0)\n",
    "alpha_num = sol.subs({asymb: aval for asymb, aval in zip(a, avalue)})\n",
    "alpha_num = alpha_num.subs({s : computedS0})\n",
    "alpha_num = alpha_num.subs({tau : value_tau})\n",
    "alpha_num_eval = [i.evalf() for i in alpha_num]\n",
    "alpha_num_eval\n",
    "print (alpha_num_eval)\n",
    "alpha_sens = alpha_num_eval"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $s_0$ connu\n",
    "\n",
    "On cherche donc à trouver $\\tau$ et on choisit le $\\tau$ réel **positif** qui est le **plus proche de $0$** s'il existe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.755813953488372 - 0.100700628347028*I, 0.755813953488372 + 0.100700628347028*I]\n"
     ]
    }
   ],
   "source": [
    "# value_s0 = -1.8236\n",
    "value_s0 = -1.8\n",
    "\n",
    "finaleq = SysDerivatif[-1].subs({alph : alphacoef for alph, alphacoef in zip(alpha, sol)}) #remplace les coeffs\n",
    "finaleq = finaleq.subs({asymb: aval for asymb, aval in zip(a, avalue)})\n",
    "solTau = finaleq.subs({s : value_s0})\n",
    "solTau = sp.solve(solTau)\n",
    "print(solTau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.755813953488372 - 0.100700628347028*I\n",
      "computedTau apres transformation add  0.7558139535\n",
      "computedTau apres arrondissement float  0.7558\n",
      "[-0.882502510615450, 1.37794678445848e-5]\n"
     ]
    }
   ],
   "source": [
    "computedTau = solTau[0]\n",
    "print (computedTau)\n",
    "\n",
    "if type(computedTau).__name__ == \"Add\":\n",
    "\n",
    "    computedTau = computedTau.as_real_imag()[0].evalf(10)\n",
    "    print (\"computedTau apres transformation add \",computedTau)\n",
    "    \n",
    "elif type(computedTau).__name__ == \"Float\":\n",
    "    \n",
    "    computedTau = float(computedTau.evalf(10))\n",
    "    print (\"computedTau apres transformation float \",computedTau)\n",
    "    \n",
    "computedTau = round(computedTau,4)\n",
    "print (\"computedTau apres arrondissement \",computedTau)\n",
    "\n",
    "alpha_num = sol.subs({asymb: aval for asymb, aval in zip(a, avalue)})\n",
    "alpha_num = alpha_num.subs({tau : computedTau})\n",
    "alpha_num = alpha_num.subs({s : value_s0})\n",
    "alpha_num_eval = [i.evalf() for i in alpha_num]\n",
    "print (alpha_num_eval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On retrouve logiquement les même valeurs de gain lorsque nous avons le couple $s_0$ et $\\tau$ correspondant. Dans cet exemple on a soit fixé $\\tau$ à $0.738$ et calculé $s_0$ qui est environ égal à $-1.5$ selon nos critères soit, nous avons fixé $s_0$ à $-1.5$ et le $\\tau$ calculé est environ égal à $0.738$.\n",
    "\n",
    "Le choix de fixer $s_0$ ou $\\tau$ se fait selon si l'on connait le retard de commande ou si l'on souhaite fixer la vitesse de convergence $s_0$.\n",
    "\n",
    "Ces hyperparamètres ($s_0$ ou $\\tau$) dépend évidemment des coefficients du système $a_i$ et donc, selon les valeurs des coefficients, certaines valeurs d'hyperparamètres sont possibles ou non. Pour cela, on peut tracer le graphe d'admissibilité."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle s^{2} \\tau^{2} + s \\tau^{2} + 4 s \\tau + 2 \\tau^{2} + 2 \\tau + 2$"
      ],
      "text/plain": [
       "s**2*tau**2 + s*tau**2 + 4*s*tau + 2*tau**2 + 2*tau + 2"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polyAdm = SysDerivatif[-1].subs({alph : alphacoef for alph, alphacoef in zip(alpha, sol)})\n",
    "polyAdm = polyAdm.subs({asymb: aval for asymb, aval in zip(a, avalue)})\n",
    "sp.simplify(polyAdm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Admissibilité"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
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       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    var resizeObserver = new ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\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, 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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"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\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data']);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Plot Admissibilité')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s0range = np.arange(-10, 0, 0.01)\n",
    "taurange = np.arange(0, 10, 0.01)\n",
    "\n",
    "func = sp.lambdify([s, tau], polyAdm)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "X, Y = np.meshgrid(s0range, taurange)\n",
    "z = func(X, Y)\n",
    "CS = ax.contour(X, Y, z, [0])\n",
    "ax.grid()\n",
    "plt.xlabel(r\"$s_0$\")\n",
    "plt.ylabel(r\"$\\tau$\")\n",
    "plt.title(\"Plot Admissibilité\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sensibilité en $\\tau$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_nominal = value_tau\n",
    "step = 1e-2\n",
    "nbIt = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "values = [0] + [-step * i for i in range(1, nbIt + 1)] + [step * i for i in range(1, nbIt + 1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "values.sort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_sens = []\n",
    "s0_sens = []\n",
    "for value in values :\n",
    "    tau_sens.append(tau_nominal + value)\n",
    "    s0_sens.append(solve_tau_connu(tau_sens[-1], [2, 1], Q))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-1.85618056091116,\n",
       " -1.85062211334813,\n",
       " -1.84560644930057,\n",
       " -1.84111940350753,\n",
       " -1.83714828538220,\n",
       " -1.83368182726193,\n",
       " -1.83071014356143,\n",
       " -1.82822470069588,\n",
       " -1.82621829782361,\n",
       " -1.82468505865446,\n",
       " -1.82362043478586,\n",
       " -1.82302122127399,\n",
       " -1.82288558543080,\n",
       " -1.82321311017491,\n",
       " -1.82400485367054,\n",
       " -1.82526342748842,\n",
       " -1.82699309614456,\n",
       " -1.82919990165969,\n",
       " -1.83189181778737,\n",
       " -1.83507893986148,\n",
       " -1.83877371791975]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s0_sens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getRoots(m, Q, dominancy, delay, avalue, alphavalue, xwindow, ywindow):\n",
    "    derivees = [Q, Q.diff(s)]\n",
    "    for i in range(len(derivees)) :\n",
    "        derivees[i] = derivees[i].subs({ai: ai_num for ai, ai_num in zip(a, avalue)})\n",
    "        derivees[i] = derivees[i].subs({alphai: alphai_num for alphai, alphai_num in zip(alpha, alphavalue)})\n",
    "        derivees[i] = derivees[i].subs({tau : delay})\n",
    "    func = [sp.lambdify(s, i) for i in derivees]\n",
    "    rect = cx.Rectangle(xwindow, ywindow)\n",
    "    root_count = rect.count_roots(func[0])\n",
    "    roots = rect.roots(func[0], func[1], rootErrTol=1e-5, absTol=1e-5, M=m+2)\n",
    "    xroot, yroot = np.real(roots[0]), np.imag(roots[0])\n",
    "    return xroot, yroot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "sensIterations = len(tau_sens)\n",
    "bList = np.linspace(start=255, stop=0, num=sensIterations//2) #Blue to black\n",
    "rList = np.linspace(start=0, stop=255, num=sensIterations//2) #black to red\n",
    "if len(bList)+len(rList)==sensIterations-1 :\n",
    "    zerosToFill = [0] * (sensIterations//2 + 1)\n",
    "else :\n",
    "    zerosToFill = [0] * (sensIterations//2 )\n",
    "bList = [*bList, *zerosToFill]\n",
    "rList = [*zerosToFill, *rList]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "colorArray = []\n",
    "for i in range(len(tau_sens)):\n",
    "    colorArray.append([rList[i], 0, bList[i]])\n",
    "colorArray = np.array(colorArray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\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(\n",
       "            '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",
       "\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 = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(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 (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.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 = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    var resizeObserver = new ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\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 toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\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",
       "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",
       "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], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.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,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\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",
       "        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.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\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(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\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(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\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",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\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",
       "        }\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",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\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",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\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, 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\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"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\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data']);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\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;\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",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\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.innerHTML =\n",
       "        '<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 / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<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 () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\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",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('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",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\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",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\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(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Sensitivity plot, $\\\\tau \\\\in $[0.638, 0.838]')"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.cm as cm\n",
    "scaler = lambda x : [i / 255 for i in x]\n",
    "plt.figure()\n",
    "for i in range(len(tau_sens)):\n",
    "    xroot, yroot = getRoots(1, Q, s0_sens[i], tau_sens[i],\n",
    "                            avalue, alpha_sens, [-5, 5], [-5, 5])\n",
    "    plt.scatter(xroot, yroot, c=[scaler(colorArray[i])])\n",
    "plt.grid()\n",
    "plt.xlabel(r\"$Re(s)$\")\n",
    "plt.ylabel(r\"$Im(s)$\")\n",
    "tau_sens.sort()\n",
    "plt.title(r\"Sensitivity plot, $\\tau \\in $\"+f\"[{tau_sens[0]}, {tau_sens[-1]}]\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}