Simple_Pendulum.ipynb

{
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      "metadata": {
        "id": "nuyWScKsox7D"
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      "source": [
        ""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5ah0pf9_7Tnp"
      },
      "source": [
        "## Learning Stabilizable Bilinear Model for Simple Pendulum"
      ]
    },
    {
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      "execution_count": null,
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        "id": "2ucX9WtR7Tnv",
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            "\u001b[1mdpkg:\u001b[0m dependency problems prevent configuration of dreal:\n",
            " dreal depends on coinor-libclp-dev; however:\n",
            "  Package coinor-libclp-dev is not installed.\n",
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            "Processing triggers for libc-bin (2.27-3ubuntu1.3) ...\n",
            "/sbin/ldconfig.real: /usr/local/lib/python3.7/dist-packages/ideep4py/lib/libmkldnn.so.0 is not a symbolic link\n",
            "\n",
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            "+ rm dreal_4.21.06.2_amd64.deb\n",
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            "  Downloading dreal-4.21.6.2-cp37-none-manylinux1_x86_64.whl (1.2 MB)\n",
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            "\u001b[?25hInstalling collected packages: dreal\n",
            "Successfully installed dreal-4.21.6.2\n"
          ]
        }
      ],
      "source": [
        "#Installing and importing required packages\n",
        "import pkgutil\n",
        "if not pkgutil.find_loader(\"dreal\"):\n",
        "  !curl https://raw.githubusercontent.com/dreal/dreal4/master/setup/ubuntu/18.04/install.sh | bash\n",
        "  !pip install dreal --upgrade\n",
        "from dreal import *\n",
        "import torch \n",
        "import torch.nn.functional as F\n",
        "import numpy as np\n",
        "import timeit \n",
        "import matplotlib.pyplot as plt\n",
        "from IPython import display\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "x3Hv4bk88qgN"
      },
      "outputs": [],
      "source": [
        "def CheckLyapunovKoopman(x, f, V, ball_lb, ball_ub, config, epsilon,K,z):        \n",
        "    ball= Expression(0)\n",
        "    lie_derivative_of_V = Expression(0)\n",
        "    \n",
        "    for i in range(len(z)):\n",
        "        ball = x[0]*x[0]+x[1]*x[1]+x[2]*x[2]\n",
        "        lie_derivative_of_V += f[i]*V.Differentiate(x[0])/z[i].Differentiate(x[0])\n",
        "    ball_in_bound = logical_and(ball_lb <= ball, ball <= ball_ub,ball_lb<=x[0],ball_lb<=x[1],x[0]<=ball_ub,x[1]<=ball_ub,x[2]<=ball_ub,\\\n",
        "                                ball_lb<=x[2])\n",
        "\n",
        "    condition = logical_and(logical_imply(ball_in_bound, V >= 0),\n",
        "                           logical_imply(ball_in_bound, lie_derivative_of_V <= epsilon))\n",
        "\n",
        "    return CheckSatisfiability(logical_not(condition),config)\n",
        "\n",
        "def AddCounterexamples(x,CE,N): \n",
        "    c = []\n",
        "    nearby= []\n",
        "    for i in range(CE.size()):\n",
        "        c.append(CE[i].mid())\n",
        "        lb = CE[i].lb()\n",
        "        ub = CE[i].ub()\n",
        "        nearby_ = np.random.uniform(lb,ub,N)\n",
        "        nearby.append(nearby_)\n",
        "    for i in range(N):\n",
        "        n_pt = []\n",
        "        for j in range(x.shape[1]):\n",
        "            n_pt.append(nearby[j][i])             \n",
        "        x = torch.cat((x, torch.tensor([n_pt])), 0)\n",
        "    return x\n",
        "  \n",
        "def dtanh(s):\n",
        "    # Derivative of activation\n",
        "    return 1.0 - s**2\n",
        "\n",
        "def Tune(x):\n",
        "    # Circle function values\n",
        "    y = []\n",
        "    for r in range(0,len(x)):\n",
        "        v = 0 \n",
        "        for j in range(x.shape[1]):\n",
        "            v += x[r][j]**2\n",
        "        f = [torch.sqrt(v)]\n",
        "        y.append(f)\n",
        "    y = torch.tensor(y)\n",
        "    return y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N03W0zfx7Tnx"
      },
      "source": [
        "## Neural network model for Control Lyapunov function (CLF), Encoder and the Decoder\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GbEqR0-Z7Tny"
      },
      "outputs": [],
      "source": [
        "# Control Lyapunov function (CLF)\n",
        "class CLF(torch.nn.Module):\n",
        "    \n",
        "    def __init__(self,n_input,n_hidden,n_output):\n",
        "        super(CLF, self).__init__()\n",
        "        self.layer1 = torch.nn.Linear(n_input, n_hidden)\n",
        "        self.layer2 = torch.nn.Linear(n_hidden,n_output)\n",
        "\n",
        "\n",
        "    def forward(self,x):\n",
        "        sigmoid = torch.nn.Tanh()\n",
        "        h_1 = sigmoid(self.layer1(x))\n",
        "        out = sigmoid(self.layer2(h_1)).float()\n",
        "        return out\n",
        "\n",
        "# Encoder/ observables\n",
        "class Encoder(torch.nn.Module):\n",
        "    \n",
        "    def __init__(self,n_input,n_hidden,n_output):\n",
        "        super(Encoder, self).__init__()\n",
        "        self.layer1 = torch.nn.Linear(n_input, n_hidden)\n",
        "        self.layer2 = torch.nn.Linear(n_hidden,n_output)\n",
        "        self.control = torch.nn.Linear(n_input,1,bias=False)\n",
        "\n",
        "    def forward(self,x):\n",
        "        sigmoid = torch.nn.Tanh()\n",
        "        h_1 = sigmoid(self.layer1(x))\n",
        "        out = sigmoid(self.layer2(h_1)).float()\n",
        "        return out\n",
        "\n",
        "\n",
        "#Decoder\n",
        "class Decoder(torch.nn.Module):    \n",
        "    def __init__(self, N_INPUT, N_OUTPUT, N_HIDDEN, N_LAYERS):\n",
        "        super().__init__()\n",
        "        activation = torch.nn.Tanh\n",
        "        self.fcs = torch.nn.Sequential(*[\n",
        "                        torch.nn.Linear(N_INPUT, N_HIDDEN),\n",
        "                        activation()])\n",
        "        self.fch = torch.nn.Sequential(*[\n",
        "                        torch.nn.Sequential(*[\n",
        "                            torch.nn.Linear(N_HIDDEN, N_HIDDEN),\n",
        "                            activation(),\n",
        "                            ]) for _ in range(N_LAYERS-1)])\n",
        "        self.fce = torch.nn.Linear(N_HIDDEN, N_OUTPUT)\n",
        "        \n",
        "    def forward(self, x):\n",
        "        y=x\n",
        "        x = self.fcs(x)\n",
        "        x = self.fch(x)\n",
        "        x = self.fce(x)\n",
        "        return x"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2uWk7spS7Tnz"
      },
      "source": [
        "## Dynamical system"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PpXj0i_i7Tn0"
      },
      "outputs": [],
      "source": [
        "def f_next(x,u):\n",
        "    #Dynamics\n",
        "    y = []\n",
        "    G = 9.81  # gravity\n",
        "    L = 2   # length \n",
        "    m = 0.15  # ball mass\n",
        "    T=0.005\n",
        "    f1=[]\n",
        "    fdyn = [ x[0][1], \n",
        "              (-m*G*L*np.sin(x[0][0])) / (m*L**2)+u[0,:]]\n",
        "    y=torch.tensor(y)\n",
        "    # Euler discretization is used here. However Runga Kutta can also be used for discretization of nonlinear dynamics\n",
        "    y=x+torch.tensor(fdyn)*T\n",
        "    return y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BECmGVb27Tn1"
      },
      "source": [
        "## Options"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Gz6Xkrpa7Tn2"
      },
      "outputs": [],
      "source": [
        "\n",
        "#For learning \n",
        "\n",
        "N = 500             # sample size\n",
        "nx = 2            # input dimension\n",
        "nz=6              #dimension of lifted state space\n",
        "H1 = 6             # hidden dimension\n",
        "V_out = 1           # output dimension of CLF\n",
        "torch.manual_seed(10)  \n",
        "x = torch.Tensor(N, nx).uniform_(-6, 6)           \n",
        "x_0 = torch.zeros([1, nx])\n",
        "\n",
        "\n",
        "# For verifying \n",
        "\n",
        "# dReal variables\n",
        "x1 = Variable(\"x1\") \n",
        "x2 = Variable(\"x2\")\n",
        "ucontrol = Variable(\"ucontrol\")\n",
        "vars_ = [x1,x2]\n",
        "varsx_ = [x1,x2,ucontrol]\n",
        "config = Config()\n",
        "config.use_polytope_in_forall = True\n",
        "config.use_local_optimization = True\n",
        "config.precision = 5e-3\n",
        "epsilon = 0\n",
        "\n",
        "# Checking candidate V within a ball around the origin (ball_lb ≤ sqrt(∑xᵢ²) ≤ ball_ub)\n",
        "ball_lb = 0.8\n",
        "ball_ub = 2 "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cJU8-YXq7Tn3"
      },
      "source": [
        "## Learning and Falsification"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "80Zk0ZmS7Tn3",
        "outputId": "f6fd320d-d467-4233-f175-de62c012f975"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/torch/nn/modules/loss.py:520: UserWarning: Using a target size (torch.Size([])) that is different to the input size (torch.Size([3999])). This will likely lead to incorrect results due to broadcasting. Please ensure they have the same size.\n",
            "  return F.mse_loss(input, target, reduction=self.reduction)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0 Total loss= 76.701416015625\n",
            "1 Total loss= 75.83071899414062\n",
            "2 Total loss= 74.96640014648438\n",
            "3 Total loss= 74.10867309570312\n",
            "4 Total loss= 73.2578125\n",
            "5 Total loss= 72.41323852539062\n",
            "6 Total loss= 71.5748291015625\n",
            "7 Total loss= 70.74237060546875\n",
            "8 Total loss= 69.91571807861328\n",
            "9 Total loss= 69.09510040283203\n",
            "10 Total loss= 68.28044891357422\n",
            "11 Total loss= 67.47169494628906\n",
            "12 Total loss= 66.66888427734375\n",
            "13 Total loss= 65.87242889404297\n",
            "14 Total loss= 65.08194732666016\n",
            "15 Total loss= 64.29759979248047\n",
            "16 Total loss= 63.519378662109375\n",
            "17 Total loss= 62.74723434448242\n",
            "18 Total loss= 61.98136901855469\n",
            "19 Total loss= 61.22136306762695\n",
            "20 Total loss= 60.46753692626953\n",
            "21 Total loss= 59.71981430053711\n",
            "22 Total loss= 58.978519439697266\n",
            "23 Total loss= 58.24308776855469\n",
            "24 Total loss= 57.51393508911133\n",
            "25 Total loss= 56.79049301147461\n",
            "26 Total loss= 56.07314682006836\n",
            "27 Total loss= 55.361289978027344\n",
            "28 Total loss= 54.65534591674805\n",
            "29 Total loss= 53.95497131347656\n",
            "30 Total loss= 53.26018142700195\n",
            "31 Total loss= 52.57053756713867\n",
            "32 Total loss= 51.886497497558594\n",
            "33 Total loss= 51.20753479003906\n",
            "34 Total loss= 50.53377151489258\n",
            "35 Total loss= 49.86506271362305\n",
            "36 Total loss= 49.20126724243164\n",
            "37 Total loss= 48.54206085205078\n",
            "38 Total loss= 47.887939453125\n",
            "39 Total loss= 47.238319396972656\n",
            "40 Total loss= 46.593196868896484\n",
            "41 Total loss= 45.9528923034668\n",
            "42 Total loss= 45.31689453125\n",
            "43 Total loss= 44.68526077270508\n",
            "44 Total loss= 44.05836868286133\n",
            "45 Total loss= 43.436004638671875\n",
            "46 Total loss= 42.81819534301758\n",
            "47 Total loss= 42.205413818359375\n",
            "48 Total loss= 41.59740447998047\n",
            "49 Total loss= 40.994144439697266\n",
            "50 Total loss= 40.39500427246094\n",
            "51 Total loss= 39.800559997558594\n",
            "52 Total loss= 39.21052551269531\n",
            "53 Total loss= 38.62471008300781\n",
            "54 Total loss= 38.04356384277344\n",
            "55 Total loss= 37.46656799316406\n",
            "56 Total loss= 36.89419174194336\n",
            "57 Total loss= 36.32619857788086\n",
            "58 Total loss= 35.76279067993164\n",
            "59 Total loss= 35.204132080078125\n",
            "60 Total loss= 34.65016174316406\n",
            "61 Total loss= 34.10095977783203\n",
            "62 Total loss= 33.55668258666992\n",
            "63 Total loss= 33.01726150512695\n",
            "64 Total loss= 32.48292922973633\n",
            "65 Total loss= 31.953561782836914\n",
            "66 Total loss= 31.429622650146484\n",
            "67 Total loss= 30.91092300415039\n",
            "68 Total loss= 30.3975887298584\n",
            "69 Total loss= 29.889867782592773\n",
            "70 Total loss= 29.387680053710938\n",
            "71 Total loss= 28.891164779663086\n",
            "72 Total loss= 28.400571823120117\n",
            "73 Total loss= 27.915897369384766\n",
            "74 Total loss= 27.437231063842773\n",
            "75 Total loss= 26.96466827392578\n",
            "76 Total loss= 26.498266220092773\n",
            "77 Total loss= 26.038328170776367\n",
            "78 Total loss= 25.584644317626953\n",
            "79 Total loss= 25.137588500976562\n",
            "80 Total loss= 24.6968994140625\n",
            "81 Total loss= 24.26314353942871\n",
            "82 Total loss= 23.836084365844727\n",
            "83 Total loss= 23.415735244750977\n",
            "84 Total loss= 23.00242042541504\n",
            "85 Total loss= 22.596012115478516\n",
            "86 Total loss= 22.19636344909668\n",
            "87 Total loss= 21.804109573364258\n",
            "88 Total loss= 21.418752670288086\n",
            "89 Total loss= 21.04058837890625\n",
            "90 Total loss= 20.66956329345703\n",
            "91 Total loss= 20.305830001831055\n",
            "92 Total loss= 19.949371337890625\n",
            "93 Total loss= 19.59984588623047\n",
            "94 Total loss= 19.257911682128906\n",
            "95 Total loss= 18.923063278198242\n",
            "96 Total loss= 18.595413208007812\n",
            "97 Total loss= 18.274930953979492\n",
            "98 Total loss= 17.961776733398438\n",
            "99 Total loss= 17.65577507019043\n",
            "100 Total loss= 17.35680389404297\n",
            "101 Total loss= 17.06483268737793\n",
            "102 Total loss= 16.78007698059082\n",
            "103 Total loss= 16.502262115478516\n",
            "104 Total loss= 16.231327056884766\n",
            "105 Total loss= 15.967406272888184\n",
            "106 Total loss= 15.710299491882324\n",
            "107 Total loss= 15.459686279296875\n",
            "108 Total loss= 15.215845108032227\n",
            "109 Total loss= 14.978588104248047\n",
            "110 Total loss= 14.747599601745605\n",
            "111 Total loss= 14.523186683654785\n",
            "112 Total loss= 14.304937362670898\n",
            "113 Total loss= 14.092952728271484\n",
            "114 Total loss= 13.88683032989502\n",
            "115 Total loss= 13.686898231506348\n",
            "116 Total loss= 13.49258041381836\n",
            "117 Total loss= 13.304107666015625\n",
            "118 Total loss= 13.12143325805664\n",
            "119 Total loss= 12.944010734558105\n",
            "120 Total loss= 12.771991729736328\n",
            "121 Total loss= 12.605402946472168\n",
            "122 Total loss= 12.44377326965332\n",
            "123 Total loss= 12.287371635437012\n",
            "124 Total loss= 12.135720252990723\n",
            "125 Total loss= 11.9888916015625\n",
            "126 Total loss= 11.846723556518555\n",
            "127 Total loss= 11.709084510803223\n",
            "128 Total loss= 11.575826644897461\n",
            "129 Total loss= 11.446812629699707\n",
            "130 Total loss= 11.322083473205566\n",
            "131 Total loss= 11.201680183410645\n",
            "132 Total loss= 11.084616661071777\n",
            "133 Total loss= 10.97186279296875\n",
            "134 Total loss= 10.862256050109863\n",
            "135 Total loss= 10.757079124450684\n",
            "136 Total loss= 10.654946327209473\n",
            "137 Total loss= 10.556074142456055\n",
            "138 Total loss= 10.4608736038208\n",
            "139 Total loss= 10.368598937988281\n",
            "140 Total loss= 10.279338836669922\n",
            "141 Total loss= 10.193391799926758\n",
            "142 Total loss= 10.110066413879395\n",
            "143 Total loss= 10.029420852661133\n",
            "144 Total loss= 9.9518461227417\n",
            "145 Total loss= 9.876506805419922\n",
            "146 Total loss= 9.803990364074707\n",
            "147 Total loss= 9.733436584472656\n",
            "148 Total loss= 9.66631031036377\n",
            "149 Total loss= 9.600539207458496\n",
            "150 Total loss= 9.53707504272461\n",
            "151 Total loss= 9.47637939453125\n",
            "152 Total loss= 9.416866302490234\n",
            "153 Total loss= 9.359820365905762\n",
            "154 Total loss= 9.304356575012207\n",
            "155 Total loss= 9.250641822814941\n",
            "156 Total loss= 9.19935131072998\n",
            "157 Total loss= 9.149304389953613\n",
            "158 Total loss= 9.100607872009277\n",
            "159 Total loss= 9.054219245910645\n",
            "160 Total loss= 9.009060859680176\n",
            "161 Total loss= 8.965418815612793\n",
            "162 Total loss= 8.92331600189209\n",
            "163 Total loss= 8.882396697998047\n",
            "164 Total loss= 8.842978477478027\n",
            "165 Total loss= 8.805142402648926\n",
            "166 Total loss= 8.767498016357422\n",
            "167 Total loss= 8.7318754196167\n",
            "168 Total loss= 8.697076797485352\n",
            "169 Total loss= 8.663985252380371\n",
            "170 Total loss= 8.631612777709961\n",
            "171 Total loss= 8.600104331970215\n",
            "172 Total loss= 8.569515228271484\n",
            "173 Total loss= 8.54022216796875\n",
            "174 Total loss= 8.511676788330078\n",
            "175 Total loss= 8.48416519165039\n",
            "176 Total loss= 8.457162857055664\n",
            "177 Total loss= 8.43149185180664\n",
            "178 Total loss= 8.406500816345215\n",
            "179 Total loss= 8.382317543029785\n",
            "180 Total loss= 8.358142852783203\n",
            "181 Total loss= 8.335305213928223\n",
            "182 Total loss= 8.31363296508789\n",
            "183 Total loss= 8.291654586791992\n",
            "184 Total loss= 8.271136283874512\n",
            "185 Total loss= 8.250699043273926\n",
            "186 Total loss= 8.230448722839355\n",
            "187 Total loss= 8.212067604064941\n",
            "188 Total loss= 8.193370819091797\n",
            "189 Total loss= 8.17566967010498\n",
            "190 Total loss= 8.158440589904785\n",
            "191 Total loss= 8.140727996826172\n",
            "192 Total loss= 8.124828338623047\n",
            "193 Total loss= 8.108683586120605\n",
            "194 Total loss= 8.09298324584961\n",
            "195 Total loss= 8.077795028686523\n",
            "196 Total loss= 8.063547134399414\n",
            "197 Total loss= 8.048847198486328\n",
            "198 Total loss= 8.035172462463379\n",
            "199 Total loss= 8.021685600280762\n",
            "200 Total loss= 8.008230209350586\n",
            "201 Total loss= 7.995701789855957\n",
            "202 Total loss= 7.983636856079102\n",
            "203 Total loss= 7.97112512588501\n",
            "204 Total loss= 7.958994388580322\n",
            "205 Total loss= 7.9476752281188965\n",
            "206 Total loss= 7.9361796379089355\n",
            "207 Total loss= 7.925576686859131\n",
            "208 Total loss= 7.914863109588623\n",
            "209 Total loss= 7.904520511627197\n",
            "210 Total loss= 7.894618511199951\n",
            "211 Total loss= 7.884438514709473\n",
            "212 Total loss= 7.874909400939941\n",
            "213 Total loss= 7.865482330322266\n",
            "214 Total loss= 7.8563995361328125\n",
            "215 Total loss= 7.8471760749816895\n",
            "216 Total loss= 7.838756561279297\n",
            "217 Total loss= 7.830071449279785\n",
            "218 Total loss= 7.821576118469238\n",
            "219 Total loss= 7.813546657562256\n",
            "220 Total loss= 7.805759906768799\n",
            "221 Total loss= 7.797898769378662\n",
            "222 Total loss= 7.789910793304443\n",
            "223 Total loss= 7.7824554443359375\n",
            "224 Total loss= 7.77518892288208\n",
            "225 Total loss= 7.7682294845581055\n",
            "226 Total loss= 7.760781764984131\n",
            "227 Total loss= 7.753923416137695\n",
            "228 Total loss= 7.747429370880127\n",
            "229 Total loss= 7.740535259246826\n",
            "230 Total loss= 7.7339043617248535\n",
            "231 Total loss= 7.727664947509766\n",
            "232 Total loss= 7.721497058868408\n",
            "233 Total loss= 7.715142726898193\n",
            "234 Total loss= 7.7093305587768555\n",
            "235 Total loss= 7.703495502471924\n",
            "236 Total loss= 7.697502613067627\n",
            "237 Total loss= 7.6916327476501465\n",
            "238 Total loss= 7.686166286468506\n",
            "239 Total loss= 7.680662155151367\n",
            "240 Total loss= 7.675211429595947\n",
            "241 Total loss= 7.669735431671143\n",
            "242 Total loss= 7.664379596710205\n",
            "243 Total loss= 7.658899784088135\n",
            "244 Total loss= 7.654105186462402\n",
            "245 Total loss= 7.649059772491455\n",
            "246 Total loss= 7.643612861633301\n",
            "247 Total loss= 7.639071941375732\n",
            "248 Total loss= 7.6340789794921875\n",
            "249 Total loss= 7.629415035247803\n",
            "250 Total loss= 7.624241352081299\n",
            "251 Total loss= 7.619773864746094\n",
            "252 Total loss= 7.614917278289795\n",
            "253 Total loss= 7.610273361206055\n",
            "254 Total loss= 7.606143474578857\n",
            "255 Total loss= 7.601066589355469\n",
            "256 Total loss= 7.596867561340332\n",
            "257 Total loss= 7.592337608337402\n",
            "258 Total loss= 7.588122367858887\n",
            "259 Total loss= 7.583508491516113\n",
            "260 Total loss= 7.579073905944824\n",
            "261 Total loss= 7.574825286865234\n",
            "262 Total loss= 7.570742130279541\n",
            "263 Total loss= 7.566454887390137\n",
            "264 Total loss= 7.562313079833984\n",
            "265 Total loss= 7.5580339431762695\n",
            "266 Total loss= 7.553761959075928\n",
            "267 Total loss= 7.549872875213623\n",
            "268 Total loss= 7.545544624328613\n",
            "269 Total loss= 7.541543960571289\n",
            "270 Total loss= 7.5372114181518555\n",
            "271 Total loss= 7.533433437347412\n",
            "272 Total loss= 7.529248237609863\n",
            "273 Total loss= 7.525236129760742\n",
            "274 Total loss= 7.5212578773498535\n",
            "275 Total loss= 7.517269134521484\n",
            "276 Total loss= 7.513181686401367\n",
            "277 Total loss= 7.509171009063721\n",
            "278 Total loss= 7.505218505859375\n",
            "279 Total loss= 7.501264572143555\n",
            "280 Total loss= 7.497134208679199\n",
            "281 Total loss= 7.493320941925049\n",
            "282 Total loss= 7.489175319671631\n",
            "283 Total loss= 7.485435485839844\n",
            "284 Total loss= 7.481276512145996\n",
            "285 Total loss= 7.47715950012207\n",
            "286 Total loss= 7.473398685455322\n",
            "287 Total loss= 7.469276428222656\n",
            "288 Total loss= 7.465296745300293\n",
            "289 Total loss= 7.461158752441406\n",
            "290 Total loss= 7.457027435302734\n",
            "291 Total loss= 7.453122138977051\n",
            "292 Total loss= 7.4491071701049805\n",
            "293 Total loss= 7.445042610168457\n",
            "294 Total loss= 7.440901279449463\n",
            "295 Total loss= 7.436732769012451\n",
            "296 Total loss= 7.432491779327393\n",
            "297 Total loss= 7.42850923538208\n",
            "298 Total loss= 7.424320220947266\n",
            "299 Total loss= 7.420342445373535\n",
            "300 Total loss= 7.416110038757324\n",
            "301 Total loss= 7.411742210388184\n",
            "302 Total loss= 7.407595157623291\n",
            "303 Total loss= 7.403352737426758\n",
            "304 Total loss= 7.3990888595581055\n",
            "305 Total loss= 7.394870281219482\n",
            "306 Total loss= 7.390610694885254\n",
            "307 Total loss= 7.386031627655029\n",
            "308 Total loss= 7.381696701049805\n",
            "309 Total loss= 7.377520561218262\n",
            "310 Total loss= 7.372807025909424\n",
            "311 Total loss= 7.368436813354492\n",
            "312 Total loss= 7.36381721496582\n",
            "313 Total loss= 7.359328269958496\n",
            "314 Total loss= 7.354796409606934\n",
            "315 Total loss= 7.350176811218262\n",
            "316 Total loss= 7.345645904541016\n",
            "317 Total loss= 7.340823650360107\n",
            "318 Total loss= 7.336145401000977\n",
            "319 Total loss= 7.331536769866943\n",
            "320 Total loss= 7.326566696166992\n",
            "321 Total loss= 7.321812152862549\n",
            "322 Total loss= 7.3170084953308105\n",
            "323 Total loss= 7.3122100830078125\n",
            "324 Total loss= 7.3070549964904785\n",
            "325 Total loss= 7.302206993103027\n",
            "326 Total loss= 7.297277450561523\n",
            "327 Total loss= 7.292078495025635\n",
            "328 Total loss= 7.2870259284973145\n",
            "329 Total loss= 7.281824588775635\n",
            "330 Total loss= 7.276740550994873\n",
            "331 Total loss= 7.2713704109191895\n",
            "332 Total loss= 7.266132831573486\n",
            "333 Total loss= 7.260718822479248\n",
            "334 Total loss= 7.2554545402526855\n",
            "335 Total loss= 7.2499775886535645\n",
            "336 Total loss= 7.244429111480713\n",
            "337 Total loss= 7.238961219787598\n",
            "338 Total loss= 7.233346939086914\n",
            "339 Total loss= 7.227627754211426\n",
            "340 Total loss= 7.222090244293213\n",
            "341 Total loss= 7.216346740722656\n",
            "342 Total loss= 7.210594654083252\n",
            "343 Total loss= 7.204766750335693\n",
            "344 Total loss= 7.198845386505127\n",
            "345 Total loss= 7.192824363708496\n",
            "346 Total loss= 7.18691349029541\n",
            "347 Total loss= 7.180904865264893\n",
            "348 Total loss= 7.174714088439941\n",
            "349 Total loss= 7.168643474578857\n",
            "350 Total loss= 7.162317752838135\n",
            "351 Total loss= 7.155989170074463\n",
            "352 Total loss= 7.149631023406982\n",
            "353 Total loss= 7.1432929039001465\n",
            "354 Total loss= 7.1368327140808105\n",
            "355 Total loss= 7.1302642822265625\n",
            "356 Total loss= 7.123681545257568\n",
            "357 Total loss= 7.1169939041137695\n",
            "358 Total loss= 7.110412120819092\n",
            "359 Total loss= 7.103631496429443\n",
            "360 Total loss= 7.096712112426758\n",
            "361 Total loss= 7.089951038360596\n",
            "362 Total loss= 7.082921504974365\n",
            "363 Total loss= 7.07593297958374\n",
            "364 Total loss= 7.0688090324401855\n",
            "365 Total loss= 7.06170654296875\n",
            "366 Total loss= 7.054567813873291\n",
            "367 Total loss= 7.047221660614014\n",
            "368 Total loss= 7.039950370788574\n",
            "369 Total loss= 7.0325164794921875\n",
            "370 Total loss= 7.025177955627441\n",
            "371 Total loss= 7.017518520355225\n",
            "372 Total loss= 7.009994029998779\n",
            "373 Total loss= 7.002331256866455\n",
            "374 Total loss= 6.994670867919922\n",
            "375 Total loss= 6.986921310424805\n",
            "376 Total loss= 6.97906494140625\n",
            "377 Total loss= 6.9712677001953125\n",
            "378 Total loss= 6.963289260864258\n",
            "379 Total loss= 6.955286502838135\n",
            "380 Total loss= 6.947073936462402\n",
            "381 Total loss= 6.939036846160889\n",
            "382 Total loss= 6.93078088760376\n",
            "383 Total loss= 6.922534465789795\n",
            "384 Total loss= 6.914111137390137\n",
            "385 Total loss= 6.905785083770752\n",
            "386 Total loss= 6.897271633148193\n",
            "387 Total loss= 6.888737201690674\n",
            "388 Total loss= 6.880096912384033\n",
            "389 Total loss= 6.871459484100342\n",
            "390 Total loss= 6.862797737121582\n",
            "391 Total loss= 6.853978633880615\n",
            "392 Total loss= 6.845096111297607\n",
            "393 Total loss= 6.836230278015137\n",
            "394 Total loss= 6.827215671539307\n",
            "395 Total loss= 6.818143367767334\n",
            "396 Total loss= 6.809041976928711\n",
            "397 Total loss= 6.799914836883545\n",
            "398 Total loss= 6.79071044921875\n",
            "399 Total loss= 6.7813334465026855\n",
            "400 Total loss= 6.771960735321045\n",
            "401 Total loss= 6.762538433074951\n",
            "402 Total loss= 6.7530341148376465\n",
            "403 Total loss= 6.743460655212402\n",
            "404 Total loss= 6.733870029449463\n",
            "405 Total loss= 6.724114894866943\n",
            "406 Total loss= 6.71433162689209\n",
            "407 Total loss= 6.704505443572998\n",
            "408 Total loss= 6.694583415985107\n",
            "409 Total loss= 6.684569835662842\n",
            "410 Total loss= 6.674430847167969\n",
            "411 Total loss= 6.66428804397583\n",
            "412 Total loss= 6.654087543487549\n",
            "413 Total loss= 6.643817901611328\n",
            "414 Total loss= 6.6334004402160645\n",
            "415 Total loss= 6.62295389175415\n",
            "416 Total loss= 6.612486362457275\n",
            "417 Total loss= 6.601875305175781\n",
            "418 Total loss= 6.591163158416748\n",
            "419 Total loss= 6.580349445343018\n",
            "420 Total loss= 6.5696187019348145\n",
            "421 Total loss= 6.5586442947387695\n",
            "422 Total loss= 6.547600746154785\n",
            "423 Total loss= 6.5364990234375\n",
            "424 Total loss= 6.525282382965088\n",
            "425 Total loss= 6.514083385467529\n",
            "426 Total loss= 6.502744674682617\n",
            "427 Total loss= 6.491289138793945\n",
            "428 Total loss= 6.479785919189453\n",
            "429 Total loss= 6.468195915222168\n",
            "430 Total loss= 6.456501483917236\n",
            "431 Total loss= 6.444658279418945\n",
            "432 Total loss= 6.432804107666016\n",
            "433 Total loss= 6.420904159545898\n",
            "434 Total loss= 6.408810138702393\n",
            "435 Total loss= 6.3966898918151855\n",
            "436 Total loss= 6.384493350982666\n",
            "437 Total loss= 6.37213659286499\n",
            "438 Total loss= 6.359747409820557\n",
            "439 Total loss= 6.347269058227539\n",
            "440 Total loss= 6.3346123695373535\n",
            "441 Total loss= 6.321969032287598\n",
            "442 Total loss= 6.309236526489258\n",
            "443 Total loss= 6.296354293823242\n",
            "444 Total loss= 6.2834343910217285\n",
            "445 Total loss= 6.270374298095703\n",
            "446 Total loss= 6.257205009460449\n",
            "447 Total loss= 6.244067668914795\n",
            "448 Total loss= 6.230746269226074\n",
            "449 Total loss= 6.2173991203308105\n",
            "450 Total loss= 6.203864097595215\n",
            "451 Total loss= 6.190270900726318\n",
            "452 Total loss= 6.176691055297852\n",
            "453 Total loss= 6.162909984588623\n",
            "454 Total loss= 6.1490983963012695\n",
            "455 Total loss= 6.135165214538574\n",
            "456 Total loss= 6.12116813659668\n",
            "457 Total loss= 6.107051372528076\n",
            "458 Total loss= 6.09290075302124\n",
            "459 Total loss= 6.078638076782227\n",
            "460 Total loss= 6.064237594604492\n",
            "461 Total loss= 6.049870491027832\n",
            "462 Total loss= 6.035306930541992\n",
            "463 Total loss= 6.020705223083496\n",
            "464 Total loss= 6.006067752838135\n",
            "465 Total loss= 5.991278171539307\n",
            "466 Total loss= 5.97648811340332\n",
            "467 Total loss= 5.961572170257568\n",
            "468 Total loss= 5.94658088684082\n",
            "469 Total loss= 5.931431770324707\n",
            "470 Total loss= 5.916262626647949\n",
            "471 Total loss= 5.901027202606201\n",
            "472 Total loss= 5.885724067687988\n",
            "473 Total loss= 5.870345592498779\n",
            "474 Total loss= 5.854861736297607\n",
            "475 Total loss= 5.839345455169678\n",
            "476 Total loss= 5.823770523071289\n",
            "477 Total loss= 5.80804443359375\n",
            "478 Total loss= 5.792356967926025\n",
            "479 Total loss= 5.776463508605957\n",
            "480 Total loss= 5.760609149932861\n",
            "481 Total loss= 5.744653224945068\n",
            "482 Total loss= 5.728618621826172\n",
            "483 Total loss= 5.712522983551025\n",
            "484 Total loss= 5.69644021987915\n",
            "485 Total loss= 5.680144309997559\n",
            "486 Total loss= 5.663849353790283\n",
            "487 Total loss= 5.647462844848633\n",
            "488 Total loss= 5.631120204925537\n",
            "489 Total loss= 5.614593029022217\n",
            "490 Total loss= 5.598043441772461\n",
            "491 Total loss= 5.581468105316162\n",
            "492 Total loss= 5.564764976501465\n",
            "493 Total loss= 5.548079013824463\n",
            "494 Total loss= 5.531259536743164\n",
            "495 Total loss= 5.514406204223633\n",
            "496 Total loss= 5.497544288635254\n",
            "497 Total loss= 5.480562210083008\n",
            "498 Total loss= 5.4635186195373535\n",
            "499 Total loss= 5.44643497467041\n",
            "500 Total loss= 5.429344654083252\n",
            "501 Total loss= 5.412099361419678\n",
            "502 Total loss= 5.3948187828063965\n",
            "503 Total loss= 5.377537727355957\n",
            "504 Total loss= 5.360179901123047\n",
            "505 Total loss= 5.34280252456665\n",
            "506 Total loss= 5.3253068923950195\n",
            "507 Total loss= 5.307744979858398\n",
            "508 Total loss= 5.290150165557861\n",
            "509 Total loss= 5.272432327270508\n",
            "510 Total loss= 5.254693031311035\n",
            "511 Total loss= 5.236934661865234\n",
            "512 Total loss= 5.219076156616211\n",
            "513 Total loss= 5.201114654541016\n",
            "514 Total loss= 5.1830620765686035\n",
            "515 Total loss= 5.164979934692383\n",
            "516 Total loss= 5.146841049194336\n",
            "517 Total loss= 5.128653049468994\n",
            "518 Total loss= 5.1102190017700195\n",
            "519 Total loss= 5.091782569885254\n",
            "520 Total loss= 5.073266506195068\n",
            "521 Total loss= 5.054645538330078\n",
            "522 Total loss= 5.035976409912109\n",
            "523 Total loss= 5.017177581787109\n",
            "524 Total loss= 4.998252868652344\n",
            "525 Total loss= 4.979207992553711\n",
            "526 Total loss= 4.959996223449707\n",
            "527 Total loss= 4.940652370452881\n",
            "528 Total loss= 4.921199321746826\n",
            "529 Total loss= 4.901569843292236\n",
            "530 Total loss= 4.881739139556885\n",
            "531 Total loss= 4.861828327178955\n",
            "532 Total loss= 4.84162712097168\n",
            "533 Total loss= 4.821218490600586\n",
            "534 Total loss= 4.800544261932373\n",
            "535 Total loss= 4.779654502868652\n",
            "536 Total loss= 4.75848388671875\n",
            "537 Total loss= 4.7369465827941895\n",
            "538 Total loss= 4.715160369873047\n",
            "539 Total loss= 4.692972183227539\n",
            "540 Total loss= 4.670351982116699\n",
            "541 Total loss= 4.647388458251953\n",
            "542 Total loss= 4.623933792114258\n",
            "543 Total loss= 4.600033760070801\n",
            "544 Total loss= 4.575634002685547\n",
            "545 Total loss= 4.550774574279785\n",
            "546 Total loss= 4.52556848526001\n",
            "547 Total loss= 4.49990177154541\n",
            "548 Total loss= 4.474085330963135\n",
            "549 Total loss= 4.44819450378418\n",
            "550 Total loss= 4.422385215759277\n",
            "551 Total loss= 4.396823883056641\n",
            "552 Total loss= 4.371941089630127\n",
            "553 Total loss= 4.347789764404297\n",
            "554 Total loss= 4.324460983276367\n",
            "555 Total loss= 4.302008628845215\n",
            "556 Total loss= 4.280426025390625\n",
            "557 Total loss= 4.25955867767334\n",
            "558 Total loss= 4.2393388748168945\n",
            "559 Total loss= 4.219698429107666\n",
            "560 Total loss= 4.200587272644043\n",
            "561 Total loss= 4.181849479675293\n",
            "562 Total loss= 4.163371562957764\n",
            "563 Total loss= 4.1451897621154785\n",
            "564 Total loss= 4.127071380615234\n",
            "565 Total loss= 4.109009265899658\n",
            "566 Total loss= 4.0909881591796875\n",
            "567 Total loss= 4.072990894317627\n",
            "568 Total loss= 4.055043697357178\n",
            "569 Total loss= 4.03706169128418\n",
            "570 Total loss= 4.019090175628662\n",
            "571 Total loss= 4.00120210647583\n",
            "572 Total loss= 3.9832797050476074\n",
            "573 Total loss= 3.9654653072357178\n",
            "574 Total loss= 3.947728157043457\n",
            "575 Total loss= 3.9302213191986084\n",
            "576 Total loss= 3.9127066135406494\n",
            "577 Total loss= 3.8954458236694336\n",
            "578 Total loss= 3.8783156871795654\n",
            "579 Total loss= 3.8613626956939697\n",
            "580 Total loss= 3.84447979927063\n",
            "581 Total loss= 3.8277127742767334\n",
            "582 Total loss= 3.811034679412842\n",
            "583 Total loss= 3.794471502304077\n",
            "584 Total loss= 3.7780673503875732\n",
            "585 Total loss= 3.7617714405059814\n",
            "586 Total loss= 3.7456488609313965\n",
            "587 Total loss= 3.729585886001587\n",
            "588 Total loss= 3.7136456966400146\n",
            "589 Total loss= 3.69779634475708\n",
            "590 Total loss= 3.682107448577881\n",
            "591 Total loss= 3.666473865509033\n",
            "592 Total loss= 3.6509780883789062\n",
            "593 Total loss= 3.635526180267334\n",
            "594 Total loss= 3.620239734649658\n",
            "595 Total loss= 3.6050117015838623\n",
            "596 Total loss= 3.5899617671966553\n",
            "597 Total loss= 3.574976682662964\n",
            "598 Total loss= 3.560016632080078\n",
            "599 Total loss= 3.545232057571411\n",
            "600 Total loss= 3.530562400817871\n",
            "601 Total loss= 3.5159084796905518\n",
            "602 Total loss= 3.501377582550049\n",
            "603 Total loss= 3.4869558811187744\n",
            "604 Total loss= 3.472583055496216\n",
            "605 Total loss= 3.458355188369751\n",
            "606 Total loss= 3.444126605987549\n",
            "607 Total loss= 3.4300248622894287\n",
            "608 Total loss= 3.415964365005493\n",
            "609 Total loss= 3.4020092487335205\n",
            "610 Total loss= 3.3881661891937256\n",
            "611 Total loss= 3.374375581741333\n",
            "612 Total loss= 3.3606364727020264\n",
            "613 Total loss= 3.347055673599243\n",
            "614 Total loss= 3.333491086959839\n",
            "615 Total loss= 3.3200066089630127\n",
            "616 Total loss= 3.306631088256836\n",
            "617 Total loss= 3.293330192565918\n",
            "618 Total loss= 3.2801265716552734\n",
            "619 Total loss= 3.266979694366455\n",
            "620 Total loss= 3.253976345062256\n",
            "621 Total loss= 3.241013765335083\n",
            "622 Total loss= 3.2281570434570312\n",
            "623 Total loss= 3.2153537273406982\n",
            "624 Total loss= 3.2026329040527344\n",
            "625 Total loss= 3.190042734146118\n",
            "626 Total loss= 3.177539587020874\n",
            "627 Total loss= 3.165125608444214\n",
            "628 Total loss= 3.152740716934204\n",
            "629 Total loss= 3.1404972076416016\n",
            "630 Total loss= 3.1283342838287354\n",
            "631 Total loss= 3.116258382797241\n",
            "632 Total loss= 3.1042802333831787\n",
            "633 Total loss= 3.0923454761505127\n",
            "634 Total loss= 3.0805675983428955\n",
            "635 Total loss= 3.068819761276245\n",
            "636 Total loss= 3.057178020477295\n",
            "637 Total loss= 3.0456814765930176\n",
            "638 Total loss= 3.0342140197753906\n",
            "639 Total loss= 3.022892475128174\n",
            "640 Total loss= 3.011582374572754\n",
            "641 Total loss= 3.000434160232544\n",
            "642 Total loss= 2.989347219467163\n",
            "643 Total loss= 2.9784066677093506\n",
            "644 Total loss= 2.9674770832061768\n",
            "645 Total loss= 2.9566469192504883\n",
            "646 Total loss= 2.9459164142608643\n",
            "647 Total loss= 2.9352614879608154\n",
            "648 Total loss= 2.924701690673828\n",
            "649 Total loss= 2.914276599884033\n",
            "650 Total loss= 2.903909206390381\n",
            "651 Total loss= 2.8935976028442383\n",
            "652 Total loss= 2.883437156677246\n",
            "653 Total loss= 2.873338222503662\n",
            "654 Total loss= 2.8633339405059814\n",
            "655 Total loss= 2.853415012359619\n",
            "656 Total loss= 2.8435540199279785\n",
            "657 Total loss= 2.8338329792022705\n",
            "658 Total loss= 2.8241870403289795\n",
            "659 Total loss= 2.8145620822906494\n",
            "660 Total loss= 2.805142879486084\n",
            "661 Total loss= 2.7957324981689453\n",
            "662 Total loss= 2.786416530609131\n",
            "663 Total loss= 2.777214527130127\n",
            "664 Total loss= 2.7680580615997314\n",
            "665 Total loss= 2.7590243816375732\n",
            "666 Total loss= 2.75004506111145\n",
            "667 Total loss= 2.7411623001098633\n",
            "668 Total loss= 2.7323782444000244\n",
            "669 Total loss= 2.723673105239868\n",
            "670 Total loss= 2.715104103088379\n",
            "671 Total loss= 2.7065200805664062\n",
            "672 Total loss= 2.698042154312134\n",
            "673 Total loss= 2.6896770000457764\n",
            "674 Total loss= 2.6813952922821045\n",
            "675 Total loss= 2.6731531620025635\n",
            "676 Total loss= 2.665048599243164\n",
            "677 Total loss= 2.6569607257843018\n",
            "678 Total loss= 2.6489949226379395\n",
            "679 Total loss= 2.64107346534729\n",
            "680 Total loss= 2.6332430839538574\n",
            "681 Total loss= 2.625474452972412\n",
            "682 Total loss= 2.6177990436553955\n",
            "683 Total loss= 2.6101980209350586\n",
            "684 Total loss= 2.6026651859283447\n",
            "685 Total loss= 2.5952038764953613\n",
            "686 Total loss= 2.58781099319458\n",
            "687 Total loss= 2.580519676208496\n",
            "688 Total loss= 2.5732955932617188\n",
            "689 Total loss= 2.566086769104004\n",
            "690 Total loss= 2.559011220932007\n",
            "691 Total loss= 2.551957607269287\n",
            "692 Total loss= 2.5449893474578857\n",
            "693 Total loss= 2.5381040573120117\n",
            "694 Total loss= 2.5312349796295166\n",
            "695 Total loss= 2.5244863033294678\n",
            "696 Total loss= 2.5178329944610596\n",
            "697 Total loss= 2.5111937522888184\n",
            "698 Total loss= 2.504627227783203\n",
            "699 Total loss= 2.498135805130005\n",
            "700 Total loss= 2.491670846939087\n",
            "701 Total loss= 2.4852936267852783\n",
            "702 Total loss= 2.478951930999756\n",
            "703 Total loss= 2.4727210998535156\n",
            "704 Total loss= 2.466503620147705\n",
            "705 Total loss= 2.460374116897583\n",
            "706 Total loss= 2.45428466796875\n",
            "707 Total loss= 2.448263168334961\n",
            "708 Total loss= 2.4422895908355713\n",
            "709 Total loss= 2.436373710632324\n",
            "710 Total loss= 2.430544853210449\n",
            "711 Total loss= 2.4247446060180664\n",
            "712 Total loss= 2.4190192222595215\n",
            "713 Total loss= 2.413320541381836\n",
            "714 Total loss= 2.407681941986084\n",
            "715 Total loss= 2.4020869731903076\n",
            "716 Total loss= 2.3965604305267334\n",
            "717 Total loss= 2.3910727500915527\n",
            "718 Total loss= 2.3856406211853027\n",
            "719 Total loss= 2.3802549839019775\n",
            "720 Total loss= 2.3749172687530518\n",
            "721 Total loss= 2.369652509689331\n",
            "722 Total loss= 2.3644001483917236\n",
            "723 Total loss= 2.3592140674591064\n",
            "724 Total loss= 2.354067087173462\n",
            "725 Total loss= 2.349001884460449\n",
            "726 Total loss= 2.343935489654541\n",
            "727 Total loss= 2.3389334678649902\n",
            "728 Total loss= 2.3339760303497314\n",
            "729 Total loss= 2.3290226459503174\n",
            "730 Total loss= 2.3241658210754395\n",
            "731 Total loss= 2.3193447589874268\n",
            "732 Total loss= 2.314556360244751\n",
            "733 Total loss= 2.309838056564331\n",
            "734 Total loss= 2.305114507675171\n",
            "735 Total loss= 2.30043625831604\n",
            "736 Total loss= 2.2958269119262695\n",
            "737 Total loss= 2.2912356853485107\n",
            "738 Total loss= 2.286689043045044\n",
            "739 Total loss= 2.282191038131714\n",
            "740 Total loss= 2.277719259262085\n",
            "741 Total loss= 2.273293972015381\n",
            "742 Total loss= 2.2688732147216797\n",
            "743 Total loss= 2.264522075653076\n",
            "744 Total loss= 2.260207176208496\n",
            "745 Total loss= 2.25590181350708\n",
            "746 Total loss= 2.251652956008911\n",
            "747 Total loss= 2.2474253177642822\n",
            "748 Total loss= 2.243234634399414\n",
            "749 Total loss= 2.2391161918640137\n",
            "750 Total loss= 2.234973907470703\n",
            "751 Total loss= 2.230884313583374\n",
            "752 Total loss= 2.226827621459961\n",
            "753 Total loss= 2.2227940559387207\n",
            "754 Total loss= 2.2188456058502197\n",
            "755 Total loss= 2.214890241622925\n",
            "756 Total loss= 2.2109484672546387\n",
            "757 Total loss= 2.207030773162842\n",
            "758 Total loss= 2.203153133392334\n",
            "759 Total loss= 2.1993441581726074\n",
            "760 Total loss= 2.1955196857452393\n",
            "761 Total loss= 2.191732883453369\n",
            "762 Total loss= 2.1879684925079346\n",
            "763 Total loss= 2.184251308441162\n",
            "764 Total loss= 2.180574655532837\n",
            "765 Total loss= 2.176891565322876\n",
            "766 Total loss= 2.1732640266418457\n",
            "767 Total loss= 2.169639825820923\n",
            "768 Total loss= 2.1660306453704834\n",
            "769 Total loss= 2.1624832153320312\n",
            "770 Total loss= 2.1589431762695312\n",
            "771 Total loss= 2.1554088592529297\n",
            "772 Total loss= 2.1519453525543213\n",
            "773 Total loss= 2.148446559906006\n",
            "774 Total loss= 2.145014762878418\n",
            "775 Total loss= 2.1416115760803223\n",
            "776 Total loss= 2.138230323791504\n",
            "777 Total loss= 2.1348767280578613\n",
            "778 Total loss= 2.131516456604004\n",
            "779 Total loss= 2.128209352493286\n",
            "780 Total loss= 2.12489652633667\n",
            "781 Total loss= 2.1216530799865723\n",
            "782 Total loss= 2.118403196334839\n",
            "783 Total loss= 2.1151466369628906\n",
            "784 Total loss= 2.1119344234466553\n",
            "785 Total loss= 2.1087729930877686\n",
            "786 Total loss= 2.105618476867676\n",
            "787 Total loss= 2.1024625301361084\n",
            "788 Total loss= 2.0993216037750244\n",
            "789 Total loss= 2.0962700843811035\n",
            "790 Total loss= 2.093165397644043\n",
            "791 Total loss= 2.0901010036468506\n",
            "792 Total loss= 2.0870749950408936\n",
            "793 Total loss= 2.0840604305267334\n",
            "794 Total loss= 2.0810658931732178\n",
            "795 Total loss= 2.0780844688415527\n",
            "796 Total loss= 2.0751397609710693\n",
            "797 Total loss= 2.0721828937530518\n",
            "798 Total loss= 2.069295644760132\n",
            "799 Total loss= 2.066382646560669\n",
            "800 Total loss= 2.0634734630584717\n",
            "801 Total loss= 2.0606579780578613\n",
            "802 Total loss= 2.0577945709228516\n",
            "803 Total loss= 2.054975986480713\n",
            "804 Total loss= 2.0521633625030518\n",
            "805 Total loss= 2.0493550300598145\n",
            "806 Total loss= 2.0465774536132812\n",
            "807 Total loss= 2.0438363552093506\n",
            "808 Total loss= 2.0410988330841064\n",
            "809 Total loss= 2.038376569747925\n",
            "810 Total loss= 2.035661220550537\n",
            "811 Total loss= 2.0330049991607666\n",
            "812 Total loss= 2.030301094055176\n",
            "813 Total loss= 2.0276501178741455\n",
            "814 Total loss= 2.0250048637390137\n",
            "815 Total loss= 2.022374153137207\n",
            "816 Total loss= 2.0197839736938477\n",
            "817 Total loss= 2.0171959400177\n",
            "818 Total loss= 2.0146448612213135\n",
            "819 Total loss= 2.012066602706909\n",
            "820 Total loss= 2.009518623352051\n",
            "821 Total loss= 2.0069875717163086\n",
            "822 Total loss= 2.0044689178466797\n",
            "823 Total loss= 2.001966953277588\n",
            "824 Total loss= 1.9994956254959106\n",
            "825 Total loss= 1.9970448017120361\n",
            "826 Total loss= 1.9945639371871948\n",
            "827 Total loss= 1.9921367168426514\n",
            "828 Total loss= 1.9896790981292725\n",
            "829 Total loss= 1.9872708320617676\n",
            "830 Total loss= 1.9848663806915283\n",
            "831 Total loss= 1.9824994802474976\n",
            "832 Total loss= 1.9801582098007202\n",
            "833 Total loss= 1.9777765274047852\n",
            "834 Total loss= 1.975425124168396\n",
            "835 Total loss= 1.9731332063674927\n",
            "836 Total loss= 1.9707967042922974\n",
            "837 Total loss= 1.9685161113739014\n",
            "838 Total loss= 1.9661846160888672\n",
            "839 Total loss= 1.9639477729797363\n",
            "840 Total loss= 1.9616483449935913\n",
            "841 Total loss= 1.9594579935073853\n",
            "842 Total loss= 1.9571689367294312\n",
            "843 Total loss= 1.9549461603164673\n",
            "844 Total loss= 1.952682375907898\n",
            "845 Total loss= 1.9505276679992676\n",
            "846 Total loss= 1.9483332633972168\n",
            "847 Total loss= 1.9461760520935059\n",
            "848 Total loss= 1.9440146684646606\n",
            "849 Total loss= 1.9418410062789917\n",
            "850 Total loss= 1.939732313156128\n",
            "851 Total loss= 1.9375799894332886\n",
            "852 Total loss= 1.9354687929153442\n",
            "853 Total loss= 1.9333627223968506\n",
            "854 Total loss= 1.931252360343933\n",
            "855 Total loss= 1.929177165031433\n",
            "856 Total loss= 1.9271187782287598\n",
            "857 Total loss= 1.9250307083129883\n",
            "858 Total loss= 1.922997236251831\n",
            "859 Total loss= 1.9209532737731934\n",
            "860 Total loss= 1.918920636177063\n",
            "861 Total loss= 1.9169046878814697\n",
            "862 Total loss= 1.91492760181427\n",
            "863 Total loss= 1.9129009246826172\n",
            "864 Total loss= 1.9108613729476929\n",
            "865 Total loss= 1.908931851387024\n",
            "866 Total loss= 1.9069758653640747\n",
            "867 Total loss= 1.904992699623108\n",
            "868 Total loss= 1.9031040668487549\n",
            "869 Total loss= 1.9011133909225464\n",
            "870 Total loss= 1.8992286920547485\n",
            "871 Total loss= 1.8972769975662231\n",
            "872 Total loss= 1.8953443765640259\n",
            "873 Total loss= 1.8934693336486816\n",
            "874 Total loss= 1.8915787935256958\n",
            "875 Total loss= 1.8897038698196411\n",
            "876 Total loss= 1.8878536224365234\n",
            "877 Total loss= 1.8859868049621582\n",
            "878 Total loss= 1.8840962648391724\n",
            "879 Total loss= 1.882289171218872\n",
            "880 Total loss= 1.8804672956466675\n",
            "881 Total loss= 1.878610610961914\n",
            "882 Total loss= 1.876818299293518\n",
            "883 Total loss= 1.8750404119491577\n",
            "884 Total loss= 1.8732285499572754\n",
            "885 Total loss= 1.871504545211792\n",
            "886 Total loss= 1.8696887493133545\n",
            "887 Total loss= 1.8679414987564087\n",
            "888 Total loss= 1.8661633729934692\n",
            "889 Total loss= 1.8644213676452637\n",
            "890 Total loss= 1.8626748323440552\n",
            "891 Total loss= 1.8609859943389893\n",
            "892 Total loss= 1.8592387437820435\n",
            "893 Total loss= 1.8575055599212646\n",
            "894 Total loss= 1.8557860851287842\n",
            "895 Total loss= 1.8541349172592163\n",
            "896 Total loss= 1.8524141311645508\n",
            "897 Total loss= 1.8507194519042969\n",
            "898 Total loss= 1.8490506410598755\n",
            "899 Total loss= 1.8474302291870117\n",
            "900 Total loss= 1.8457345962524414\n",
            "901 Total loss= 1.8440806865692139\n",
            "902 Total loss= 1.8424572944641113\n",
            "903 Total loss= 1.8408253192901611\n",
            "904 Total loss= 1.8391791582107544\n",
            "905 Total loss= 1.837541937828064\n",
            "906 Total loss= 1.8359555006027222\n",
            "907 Total loss= 1.8343329429626465\n",
            "908 Total loss= 1.8327631950378418\n",
            "909 Total loss= 1.8311443328857422\n",
            "910 Total loss= 1.8295626640319824\n",
            "===========Verifying==========\n",
            "Not a Control Lyapunov function (CLF). Found counterexample: \n",
            "x1 : [0.80713750736159939, 0.8080305079735558]\n",
            "x2 : [0.81381812300244161, 0.81479461461526292]\n",
            "ucontrol : [0.82742901822698334, 0.82834381886161101]\n",
            "==============================\n",
            "911 Total loss= 1.8245986700057983\n",
            "912 Total loss= 1.8224979639053345\n",
            "913 Total loss= 1.8201736211776733\n",
            "914 Total loss= 1.8179157972335815\n",
            "915 Total loss= 1.8158146142959595\n",
            "916 Total loss= 1.813920021057129\n",
            "917 Total loss= 1.8122093677520752\n",
            "918 Total loss= 1.8106050491333008\n",
            "919 Total loss= 1.8088829517364502\n",
            "920 Total loss= 1.8071027994155884\n",
            "===========Verifying==========\n",
            "Not a Control Lyapunov function (CLF). Found counterexample: \n",
            "x1 : [0.80027688840860955, 0.80029428323029739]\n",
            "x2 : [0.83594000772381172, 0.83595203237778892]\n",
            "ucontrol : [0.81248901349928615, 0.81287219497639851]\n",
            "==============================\n",
            "921 Total loss= 1.7940961122512817\n",
            "922 Total loss= 1.7918423414230347\n",
            "923 Total loss= 1.7896100282669067\n",
            "924 Total loss= 1.7873815298080444\n",
            "925 Total loss= 1.7851958274841309\n",
            "926 Total loss= 1.7829409837722778\n",
            "927 Total loss= 1.7808502912521362\n",
            "928 Total loss= 1.7789578437805176\n",
            "929 Total loss= 1.7771103382110596\n",
            "930 Total loss= 1.7752785682678223\n",
            "===========Verifying==========\n",
            "Satisfy conditions!!\n",
            "tanh((-0.063711367547512054 - 0.16911858320236206 * tanh((-0.52538853883743286 + 0.25131899118423462 * tanh((0.015193558298051357 + 0.02894548699259758 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) + 0.15944404900074005 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.2158597856760025 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.13618244230747223 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) + 0.044943384826183319 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) + 0.3597559928894043 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.23946775496006012 * tanh((0.15631702542304993 - 0.15780241787433624 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) + 0.048089355230331421 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.25035038590431213 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) + 0.11122904717922211 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.02903197705745697 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.28498479723930359 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.20773886144161224 * tanh((0.38947579264640808 + 0.61237508058547974 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.57135260105133057 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.18181151151657104 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.31363782286643982 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.85250216722488403 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.48041239380836487 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.36777022480964661 * tanh((0.45586979389190674 + 0.21744748950004578 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.079708859324455261 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.43432712554931641 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.31430131196975708 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) + 0.0071628745645284653 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.74219298362731934 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.083998948335647583 * tanh((0.48714867234230042 + 0.25509932637214661 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.54438036680221558 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.099790938198566437 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.39482107758522034 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.51046067476272583 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.57432448863983154 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.35072365403175354 * tanh((0.63841402530670166 + 0.43609163165092468 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.060976069420576096 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.05473664402961731 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.025618413463234901 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.32936123013496399 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.22740285098552704 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))))) - 0.60842025279998779 * tanh((-0.2797456681728363 + 0.092845827341079712 * tanh((0.015193558298051357 + 0.02894548699259758 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) + 0.15944404900074005 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.2158597856760025 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.13618244230747223 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) + 0.044943384826183319 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) + 0.3597559928894043 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) + 0.11317264288663864 * tanh((0.15631702542304993 - 0.15780241787433624 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) + 0.048089355230331421 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.25035038590431213 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) + 0.11122904717922211 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.02903197705745697 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.28498479723930359 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.22867313027381897 * tanh((0.38947579264640808 + 0.61237508058547974 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.57135260105133057 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.18181151151657104 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.31363782286643982 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.85250216722488403 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.48041239380836487 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.39446547627449036 * tanh((0.45586979389190674 + 0.21744748950004578 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.079708859324455261 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.43432712554931641 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.31430131196975708 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) + 0.0071628745645284653 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.74219298362731934 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.52428847551345825 * tanh((0.48714867234230042 + 0.25509932637214661 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.54438036680221558 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.099790938198566437 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 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0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.51046067476272583 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.57432448863983154 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.014891669154167175 * tanh((0.63841402530670166 + 0.43609163165092468 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.060976069420576096 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.05473664402961731 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.025618413463234901 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.32936123013496399 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.22740285098552704 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2))))))))  is a Control Lyapunov function (CLF).\n",
            "==============================\n"
          ]
        }
      ],
      "source": [
        "#For reproducibility\n",
        "torch.manual_seed(123)\n",
        "\n",
        "T=0.005\n",
        "out_iters = 0\n",
        "valid = False\n",
        "modelde = Decoder(nx,nz,20,2)\n",
        "\n",
        "#Decoder\n",
        "modelde = Decoder(nz,nx,20,2)\n",
        "\n",
        "\n",
        "lossx=torch.nn.MSELoss()\n",
        "x_init=2*torch.Tensor(1, nx).uniform_(-1, 1) \n",
        "Nd=4000\n",
        "xnew=torch.zeros((Nd,nx))\n",
        "ynew1=torch.zeros((Nd,nx))\n",
        "u1=torch.tensor([])\n",
        "U=[]\n",
        "for k in range(0,Nd):\n",
        "    xnew[k,:]=x_init\n",
        "    unew=0.005*torch.Tensor(1, 1).uniform_(-1, 1) \n",
        "    U.append([1,unew])\n",
        "    u1=torch.cat((u1,unew),1)\n",
        "    ynew1[k,:]=f_next(x_init,unew)\n",
        "    ynew=f_next(x_init,unew)\n",
        "    x_init=ynew\n",
        "u1=torch.cat((torch.ones(1,Nd),u1),0).t()[0:Nd-1,:]\n",
        "U=torch.tensor(U)\n",
        "\n",
        "#Encoder\n",
        "modelen = Encoder(nx,H1, nz)\n",
        "\n",
        "while out_iters < 2 and not valid: \n",
        "    start = timeit.default_timer()\n",
        "\n",
        "    # Candidate control Lyapunov function (CLF)\n",
        "    model = CLF(nz,H1, V_out)\n",
        "\n",
        "    L = []\n",
        "    i = 0  \n",
        "    t = 0\n",
        "    max_iters = 2000\n",
        "    learning_rate = 0.001\n",
        "    optimizer = torch.optim.Adam(list(modelen.parameters()) + list(modelde.parameters())+ list(model.parameters()), lr=learning_rate)\n",
        "\n",
        "    while i < max_iters and not valid: \n",
        "\n",
        "        V_candidate= (model(modelen(x.float())))\n",
        "        X0 = model(modelen(x_0))\n",
        "        x_data=xnew[0:Nd-1,:]\n",
        "        y_data=xnew[1:Nd,:]\n",
        "        Circle_Tuning = Tune(x)\n",
        "        V_candidate=V_candidate\n",
        "        Phi=modelen(x_data.float())\n",
        "        mt=[]\n",
        "        mt=torch.zeros((2*nz,1))\n",
        "        mat=[]\n",
        "        mat=torch.zeros((2*nz,Nd-1))\n",
        "        for b in range(Nd-1):\n",
        "          mt=torch.kron(u1[b,:].t(),Phi[b,:].t())\n",
        "          mat[:,b]=mt\n",
        "        mat=mat\n",
        "        matrix=torch.matmul(torch.transpose(modelen(y_data.float()),0,1),torch.pinverse(mat))\n",
        "        K=matrix[0:nz,0:nz]\n",
        "        B1=matrix[0:nz,nz:2*nz]\n",
        "        uc=u1.t()\n",
        "        phy_loss=[]\n",
        "        for k in range(Nd-1):\n",
        "              temp=torch.norm(modelde(modelen(y_data[k:k+1,:].float()))-f_next(modelde(modelen(x_data[k:k+1,:].float()).detach()).detach(),U[k:k+1,1:2]))\n",
        "              phy_loss.append(temp)\n",
        "        phy_loss=torch.tensor(phy_loss)\n",
        "\n",
        "\n",
        "        #Koopman based bilinear system\n",
        "        fk=torch.matmul(((K-torch.eye(nz))/T),modelen(x_data.float()).t())+torch.mul(torch.matmul(B1/T,modelen(x_data.float()).t()),uc[1,:])\n",
        "        \n",
        "        # Reconstruction Loass\n",
        "        loss_reconstruction=lossx(x_data.float(),modelde(modelen(x_data.float())))\n",
        "\n",
        "        #Dynamics Loss\n",
        "        loss_dyn=lossx((torch.transpose(torch.matmul(K,torch.transpose(modelen(x_data.float()),0,1)),0,1))+torch.transpose(torch.mul(torch.matmul(B1,torch.transpose(modelen(x_data.float()),0,1)),uc[1,:]),0,1),modelen(y_data.float()))\n",
        "        \n",
        "        #Physics informed loss\n",
        "        loss_phy_inf=lossx(phy_loss,torch.tensor(0))\n",
        "\n",
        "        # Compute lie derivative of candidate CLF V : L_V = ∂V/∂z*[Kd-I]z/T+∂V/∂z∑Bᵢzuᵢ/T\n",
        "        L_V = torch.diagonal(torch.mm(torch.mm(torch.mm(dtanh(V_candidate),model.layer2.weight)*dtanh(torch.tanh(torch.mm(modelen(x.float()),model.layer1.weight.t())+model.layer1.bias)),model.layer1.weight),fk.float()),0)\n",
        "\n",
        "        #Control Lyapunov loss + ROA loss\n",
        "        Lyapunov_risk = (F.relu(-V_candidate)+ 1.5*F.relu(L_V+0.5)).mean()\\\n",
        "                    +2.2*((Circle_Tuning-6*V_candidate).pow(2)).mean()+(X0).pow(2) \n",
        "       \n",
        "        Total_loss=Lyapunov_risk+2*loss_dyn+0.001*loss_reconstruction+0.001*loss_phy_inf\n",
        "\n",
        "        print(i, \"Total loss=\",Total_loss.item()) \n",
        "        L.append(Total_loss.item())\n",
        "        optimizer.zero_grad()\n",
        "\n",
        "        Total_loss.backward(retain_graph=True)\n",
        "        optimizer.step() \n",
        "        \n",
        "        w1 = model.layer1.weight.data.numpy()\n",
        "        w2 = model.layer2.weight.data.numpy()\n",
        "        b1 = model.layer1.bias.data.numpy()\n",
        "        b2 = model.layer2.bias.data.numpy()\n",
        "        \n",
        "        #z_learn\n",
        "        w1k = modelen.layer1.weight.data.numpy()\n",
        "        w2k = modelen.layer2.weight.data.numpy()\n",
        "        b1k = modelen.layer1.bias.data.numpy()\n",
        "        b2k = modelen.layer2.bias.data.numpy()\n",
        "\n",
        "        # Falsification\n",
        "        # Train for atleast 900 epochs before falsification\n",
        "        if i % 10 == 0 and i>900:\n",
        "\n",
        "            #Extracting govering K and B1 of the the Koopman based bilinear system\n",
        "            koop=((K-torch.eye(nz))/T).detach().numpy().astype(float)\n",
        "            B1koop=B1.detach().numpy().astype(float)/T\n",
        "\n",
        "\n",
        "            #z_learn expression ###########\n",
        "            z1k = np.dot(vars_,w1k.T)+b1k\n",
        "            a1k = []\n",
        "            for j in range(0,len(z1k)):\n",
        "                a1k.append(tanh(z1k[j]))\n",
        "            z2k = np.dot(a1k,w2k.T)+b2k\n",
        "            zz1=tanh(z2k.item(0))\n",
        "            zz2=tanh(z2k.item(1))\n",
        "            zz3=tanh(z2k.item(2))\n",
        "            zz4=tanh(z2k.item(3))\n",
        "            zz5=tanh(z2k.item(4))\n",
        "            zz6=tanh(z2k.item(5))\n",
        "            varsz_=[tanh(z2k.item(0)),tanh(z2k.item(1)),tanh(z2k.item(2)),tanh(z2k.item(3)),tanh(z2k.item(4)),tanh(z2k.item(5))]\n",
        "            z1 = np.dot(varsz_,w1.T)+b1\n",
        "            a1 = []\n",
        "            for j in range(0,len(z1)):\n",
        "                a1.append(tanh(z1[j]))\n",
        "            z2 = np.dot(a1,w2.T)+b2\n",
        "            V_learn = tanh(z2.item(0))\n",
        "    \n",
        "            # Koopman based bilinear system of Variable dReal\n",
        "            f_koop=[koop[0,0]*zz1+koop[0,1]*zz2+koop[0,2]*zz3+koop[0,3]*zz4+koop[0,4]*zz5+koop[0,5]*zz6,\n",
        "                    koop[1,0]*zz1+koop[1,1]*zz2+koop[1,2]*zz3+koop[1,3]*zz4+koop[1,4]*zz5+koop[1,5]*zz6,\n",
        "                    koop[2,0]*zz1+koop[2,1]*zz2+koop[2,2]*zz3+koop[2,3]*zz4+koop[2,4]*zz5+koop[2,5]*zz6,\n",
        "                    koop[3,0]*zz1+koop[3,1]*zz2+koop[3,2]*zz3+koop[3,3]*zz4+koop[3,4]*zz5+koop[3,5]*zz6,\n",
        "                    koop[4,0]*zz1+koop[4,1]*zz2+koop[4,2]*zz3+koop[4,3]*zz4+koop[4,4]*zz5+koop[4,5]*zz6,\n",
        "                    koop[5,0]*zz1+koop[5,1]*zz2+koop[5,2]*zz3+koop[5,3]*zz4+koop[5,4]*zz5+koop[5,5]*zz6]+\\\n",
        "                    [B1koop[0,0]*zz1*ucontrol+B1koop[0,1]*zz2*ucontrol+B1koop[0,2]*zz3*ucontrol+B1koop[0,3]*zz4*ucontrol+B1koop[0,4]*zz5*ucontrol+B1koop[0,5]*zz6*ucontrol,\n",
        "                    B1koop[1,0]*zz1*ucontrol+B1koop[1,1]*zz2*ucontrol+B1koop[1,2]*zz3*ucontrol+B1koop[1,3]*zz4*ucontrol+B1koop[1,4]*zz5*ucontrol+B1koop[1,5]*zz6*ucontrol,\n",
        "                    B1koop[2,0]*zz1*ucontrol+B1koop[2,1]*zz2*ucontrol+B1koop[2,2]*zz3*ucontrol+B1koop[2,3]*zz4*ucontrol+B1koop[2,4]*zz5*ucontrol+B1koop[2,5]*zz6*ucontrol,\n",
        "                    B1koop[3,0]*zz1*ucontrol+B1koop[3,1]*zz2*ucontrol+B1koop[3,2]*zz3*ucontrol+B1koop[3,3]*zz4*ucontrol+B1koop[3,4]*zz5*ucontrol+B1koop[3,5]*zz6*ucontrol,\n",
        "                    B1koop[4,0]*zz1*ucontrol+B1koop[4,1]*zz2*ucontrol+B1koop[4,2]*zz3*ucontrol+B1koop[4,3]*zz4*ucontrol+B1koop[4,4]*zz5*ucontrol+B1koop[4,5]*zz6*ucontrol,\n",
        "                     B1koop[5,0]*zz1*ucontrol+B1koop[5,1]*zz2*ucontrol+B1koop[5,2]*zz3*ucontrol+B1koop[5,3]*zz4*ucontrol+B1koop[5,4]*zz5*ucontrol+B1koop[5,5]*zz6*ucontrol]\n",
        "            \n",
        "            print('===========Verifying==========')        \n",
        "            start_ = timeit.default_timer() \n",
        "            result= CheckLyapunovKoopman(varsx_, f_koop, V_learn, ball_lb, ball_ub, config,epsilon,K,varsz_)\n",
        "\n",
        "            stop_ = timeit.default_timer() \n",
        "\n",
        "            if (result): \n",
        "                print(\"Not a Control Lyapunov function (CLF). Found counterexample: \")\n",
        "                print(result)\n",
        "                x = AddCounterexamples(x,result,10)\n",
        "            else:  \n",
        "                valid = True\n",
        "                print(\"Satisfy conditions!!\")\n",
        "                print(V_learn, \" is a Control Lyapunov function (CLF).\")\n",
        "            t += (stop_ - start_)\n",
        "            print('==============================') \n",
        "        i += 1\n",
        "\n",
        "    stop = timeit.default_timer()\n",
        "    out_iters+=1\n",
        "\n",
        "    "
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Plots as in paper"
      ],
      "metadata": {
        "id": "jjbN3iUpKsJN"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1y9lK4XL1y6u",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "575a5408-373b-4b1d-e5c9-fd02b0b0b558"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# For reproducibility\n",
        "torch.manual_seed(3407)\n",
        "\n",
        "# 10 different initial conditions\n",
        "for k in range(10):  \n",
        "  x_init=1*torch.Tensor(1, nx).uniform_(-1, 1)\n",
        "  NT=3000\n",
        "  times=torch.linspace(0,NT*T,NT)\n",
        "  xnew=torch.zeros((NT,nx))\n",
        "  unew=torch.zeros((1,1))\n",
        "  y1=torch.zeros((1,nz))\n",
        "  U=torch.zeros((NT,1))\n",
        "  for i in range(NT):\n",
        "    xnew[i,:]=x_init\n",
        "\n",
        "    # Valid Control Lyapunov function (CLF)\n",
        "    V_clf= (model(modelen(x_init.float()).detach()))\n",
        "\n",
        "\n",
        "    #Sontag's formula\n",
        "    a=torch.diagonal(torch.mm(torch.mm(torch.mm(dtanh(V_clf),model.layer2.weight)*dtanh(torch.tanh(torch.mm(modelen(x_init.float()),model.layer1.weight.t())+model.layer1.bias)),model.layer1.weight),torch.matmul(((K-torch.eye(nz))/T),modelen(x_init.float()).t()).float()),0)\n",
        "    b=torch.diagonal(torch.mm(torch.mm(torch.mm(dtanh(V_clf),model.layer2.weight)*dtanh(torch.tanh(torch.mm(modelen(x_init.float()),model.layer1.weight.t())+model.layer1.bias)),model.layer1.weight),(torch.matmul(B1/T,modelen(x_init.float()).t())).float()),0)\n",
        "    unew=torch.div(-a-torch.pow((torch.pow(a,2)+torch.pow(b,4)),0.5),b)\n",
        "    if b==torch.zeros((1,1)):\n",
        "      unew=torch.zeros((1,1))\n",
        "\n",
        "    # Append unew to U\n",
        "    U[i,:]=unew\n",
        "    unew=1*torch.ones((1,1))*unew\n",
        "\n",
        "    #Propogate to the next state\n",
        "    y1=f_next(x_init,unew)\n",
        "    x_init=y1\n",
        "\n",
        "  # Ploting\n",
        "  plt.figure(1)\n",
        "  plt.plot(times.numpy(),(xnew[:,0]).numpy())\n",
        "  plt.xlabel('$t$',fontsize=18)\n",
        "  plt.ylabel('$x_1$',fontsize=18) \n",
        "  plt.title('$State$',fontsize=18)\n",
        "\n",
        "  plt.figure(2)\n",
        "  plt.plot(times.numpy(),xnew[:,1].numpy())\n",
        "  plt.xlabel('$t$',fontsize=18)\n",
        "  plt.ylabel('$x_2$',fontsize=18) \n",
        "  plt.title('$State$',fontsize=18)\n",
        "\n",
        "  plt.figure(3)\n",
        "  plt.plot(times.numpy(),U[:,0].detach().numpy())\n",
        "  plt.xlabel('$t$',fontsize=18)\n",
        "  plt.ylabel('$u$',fontsize=18) \n",
        "  plt.title('$Control$',fontsize=18)\n",
        "\n",
        "  plt.figure(4)\n",
        "  plt.plot(xnew[:,0].numpy(),xnew[:,1].numpy())\n",
        "  plt.xlabel('$x_1$',fontsize=18)\n",
        "  plt.ylabel('$x_2$',fontsize=18) \n",
        "plt.show()\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DbIeyG4f7Tn6"
      },
      "source": [
        "\n",
        "\n",
        "```\n",
        "# This is formatted as code\n",
        "```\n",
        "\n",
        "### Checking CLF for smaller epsilon"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mzZygLtU7Tn6",
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "95201743-738d-4fc9-fb13-0320a3caee2a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Satisfy conditions with epsilon=  -1e-05\n",
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0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.51046067476272583 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.57432448863983154 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) + 0.67006832361221313 * tanh((0.63841402530670166 + 0.43609163165092468 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.060976069420576096 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.05473664402961731 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.025618413463234901 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.32936123013496399 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.22740285098552704 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))))) + 0.58142769336700439 * tanh((0.1925053596496582 - 0.044996496289968491 * tanh((0.015193558298051357 + 0.02894548699259758 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) + 0.15944404900074005 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.2158597856760025 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.13618244230747223 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) + 0.044943384826183319 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) + 0.3597559928894043 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.14696323871612549 * tanh((0.15631702542304993 - 0.15780241787433624 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) + 0.048089355230331421 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.25035038590431213 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) + 0.11122904717922211 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.02903197705745697 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.28498479723930359 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) + 0.71858227252960205 * tanh((0.38947579264640808 + 0.61237508058547974 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.57135260105133057 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.18181151151657104 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.31363782286643982 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.85250216722488403 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.48041239380836487 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) + 0.0044294283725321293 * tanh((0.45586979389190674 + 0.21744748950004578 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.079708859324455261 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.43432712554931641 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.31430131196975708 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) + 0.0071628745645284653 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.74219298362731934 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) + 0.23549668490886688 * tanh((0.48714867234230042 + 0.25509932637214661 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.54438036680221558 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.099790938198566437 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.39482107758522034 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.51046067476272583 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.57432448863983154 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) + 0.38464561104774475 * tanh((0.63841402530670166 + 0.43609163165092468 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.060976069420576096 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.05473664402961731 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.025618413463234901 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.32936123013496399 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.22740285098552704 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))))) + 0.5407525897026062 * tanh((0.35486981272697449 + 0.11028695106506348 * tanh((0.015193558298051357 + 0.02894548699259758 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) + 0.15944404900074005 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.2158597856760025 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.13618244230747223 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) + 0.044943384826183319 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) + 0.3597559928894043 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.09610893577337265 * tanh((0.15631702542304993 - 0.15780241787433624 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) + 0.048089355230331421 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.25035038590431213 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) + 0.11122904717922211 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.02903197705745697 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.28498479723930359 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) + 0.13262985646724701 * tanh((0.38947579264640808 + 0.61237508058547974 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.57135260105133057 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.18181151151657104 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.31363782286643982 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.85250216722488403 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.48041239380836487 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.041511569172143936 * tanh((0.45586979389190674 + 0.21744748950004578 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.079708859324455261 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.43432712554931641 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.31430131196975708 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) + 0.0071628745645284653 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.74219298362731934 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) + 0.40222132205963135 * tanh((0.48714867234230042 + 0.25509932637214661 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.54438036680221558 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) + 0.099790938198566437 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.39482107758522034 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.51046067476272583 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.57432448863983154 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2)))) - 0.014891669154167175 * tanh((0.63841402530670166 + 0.43609163165092468 * tanh((-0.86864030361175537 + 0.36716684699058533 * x1 - 0.044786538928747177 * x2)) - 0.060976069420576096 * tanh((-0.82800012826919556 + 0.0048404335975646973 * x1 + 0.028053991496562958 * x2)) - 0.05473664402961731 * tanh((-0.20149464905261993 + 0.092372775077819824 * x1 + 0.42671284079551697 * x2)) - 0.025618413463234901 * tanh((0.11393880844116211 - 0.025842092931270599 * x1 + 0.20275238156318665 * x2)) - 0.32936123013496399 * tanh((0.29771235585212708 + 0.20115748047828674 * x1 + 0.046631194651126862 * x2)) - 0.22740285098552704 * tanh((1.1048214435577393 + 0.0040428987704217434 * x1 - 0.39066570997238159 * x2))))))))  is a Control Lyapunov function (CLF).\n"
          ]
        }
      ],
      "source": [
        "epsilon = -0.00001\n",
        "start_ = timeit.default_timer() \n",
        "result = CheckLyapunovKoopman(varsx_, f_koop, V_learn, ball_lb, ball_ub, config,epsilon,K,varsz_)\n",
        "stop_ = timeit.default_timer() \n",
        "\n",
        "if (result): \n",
        "    print(\"Not a Control Lyapunov function (CLF). Found counterexample: \")\n",
        "    print(result)\n",
        "else:  \n",
        "    print(\"Satisfy conditions with epsilon= \",epsilon)\n",
        "    print(V_learn, \" is a Control Lyapunov function (CLF).\")\n",
        "t += (stop_ - start_)"
      ]
    },
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        "   "
      ]
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      "name": "Simple_Pendulum.ipynb",
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