0_Simple_1D_fit.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "0_Simple_1D_fit.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNLXkSOlZReMNcOe0XFbTBL",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/rhiju/codon_riboswitch/blob/master/0_Simple_1D_fit.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eYnFXyXeN0sx"
      },
      "source": [
        "Fitting exponent of a polynomial; very simple 1D fit.\n",
        "Adapted from\n",
        " https://towardsdatascience.com/pytorch-vs-tensorflow-spotting-the-difference-25c75777377b"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vuLXaO3q2_Bo",
        "outputId": "28ba0c23-bbbe-463f-a0fd-611e1cfd683c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "\n",
        "\n",
        "import torch\n",
        "from torch.autograd import Variable\n",
        "import numpy as np\n",
        "\n",
        "def rmse(y, y_hat):\n",
        "    \"\"\"Compute root mean squared error\"\"\"\n",
        "    return torch.sqrt(torch.mean((y - y_hat).pow(2)))\n",
        "\n",
        "def forward(x, e):\n",
        "    \"\"\"Forward pass for our fuction\"\"\"\n",
        "    return x.pow(e.repeat(x.size(0)))\n",
        "\n",
        "# Let's define some settings\n",
        "n = 100 # number of examples\n",
        "learning_rate = 5e-7\n",
        "\n",
        "# Model parameters\n",
        "exp = Variable(torch.FloatTensor([2.0]), requires_grad=False)\n",
        "exp_hat = Variable(torch.FloatTensor([4]), requires_grad=True)\n",
        "\n",
        "# Model definition\n",
        "x = Variable(torch.rand(n) * 10, requires_grad=False)\n",
        "y = forward(x, exp)\n",
        "y += 10.0* torch.randn(n)\n",
        "\n",
        "# Optimizer (NEW)\n",
        "opt = torch.optim.SGD([exp_hat], lr=learning_rate, momentum=0.9)\n",
        "\n",
        "loss_history = []\n",
        "exp_history = []\n",
        "\n",
        "# Training loop\n",
        "for i in range(0, 2000):\n",
        "    opt.zero_grad()\n",
        "    \n",
        "    # Compute current estimate\n",
        "    y_hat = forward(x, exp_hat)\n",
        "    \n",
        "    # Calculate loss function\n",
        "    loss = rmse(y, y_hat)\n",
        "    \n",
        "    # Do some recordings for plots\n",
        "    loss_history.append(loss.item())\n",
        "    exp_history.append(exp_hat.item())\n",
        "    \n",
        "    # Update model parameters\n",
        "    loss.backward()\n",
        "    opt.step()\n",
        "    if (i%100 == 0):\n",
        "      print(\"Iteration %d\" % i)\n",
        "      print(\"loss = %s\" % loss.item())\n",
        "      print(\"exp = %s\" % exp_hat.item())\n"
      ],
      "execution_count": 280,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration 0\n",
            "loss = 3415.465576171875\n",
            "exp = 3.9962024688720703\n",
            "Iteration 100\n",
            "loss = 284.4277648925781\n",
            "exp = 2.918306589126587\n",
            "Iteration 200\n",
            "loss = 135.58291625976562\n",
            "exp = 2.64265513420105\n",
            "Iteration 300\n",
            "loss = 80.78827667236328\n",
            "exp = 2.475632429122925\n",
            "Iteration 400\n",
            "loss = 52.114959716796875\n",
            "exp = 2.3549914360046387\n",
            "Iteration 500\n",
            "loss = 34.69593811035156\n",
            "exp = 2.261051654815674\n",
            "Iteration 600\n",
            "loss = 23.411561965942383\n",
            "exp = 2.1854686737060547\n",
            "Iteration 700\n",
            "loss = 16.193899154663086\n",
            "exp = 2.1249895095825195\n",
            "Iteration 800\n",
            "loss = 12.12636661529541\n",
            "exp = 2.0795297622680664\n",
            "Iteration 900\n",
            "loss = 10.340106964111328\n",
            "exp = 2.049384832382202\n",
            "Iteration 1000\n",
            "loss = 9.72301959991455\n",
            "exp = 2.0316667556762695\n",
            "Iteration 1100\n",
            "loss = 9.530664443969727\n",
            "exp = 2.0217740535736084\n",
            "Iteration 1200\n",
            "loss = 9.471109390258789\n",
            "exp = 2.016268730163574\n",
            "Iteration 1300\n",
            "loss = 9.45233154296875\n",
            "exp = 2.0131773948669434\n",
            "Iteration 1400\n",
            "loss = 9.446304321289062\n",
            "exp = 2.0114259719848633\n",
            "Iteration 1500\n",
            "loss = 9.44434642791748\n",
            "exp = 2.010427474975586\n",
            "Iteration 1600\n",
            "loss = 9.443704605102539\n",
            "exp = 2.0098562240600586\n",
            "Iteration 1700\n",
            "loss = 9.44349479675293\n",
            "exp = 2.009528398513794\n",
            "Iteration 1800\n",
            "loss = 9.443424224853516\n",
            "exp = 2.009340763092041\n",
            "Iteration 1900\n",
            "loss = 9.443401336669922\n",
            "exp = 2.00923228263855\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n0Rgg4PB3hiI",
        "outputId": "6b823a14-23bc-4ab4-a305-e802e48325e1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        }
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.subplot(2,1,1)\n",
        "plt.plot(exp_history)\n",
        "plt.ylim(0, 10)\n",
        "plt.show()\n",
        "plt.subplot(2,1,2)\n",
        "plt.plot(loss_history)"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f85e603dcc0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TB85kojcN9C0"
      },
      "source": [
        "Fit should look good!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "42eny09x5q_y",
        "outputId": "0f8d6ea4-23c2-4144-9b01-b4c8d042c710",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "\n",
        "plt.scatter( x, y)\n",
        "x_fine = Variable(torch.linspace(0,10,50), requires_grad=False)\n",
        "y_fine = forward( x_fine, exp_hat )\n",
        "print( exp_hat )\n",
        "plt.plot(x_fine,y_fine.detach().numpy())\n",
        "plt.show()\n"
      ],
      "execution_count": 197,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([1.9961], requires_grad=True)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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rxdWMGdyb8sO17KqsiekGkYmba3cmBXkRaSWewPvwW5sYd+crzHt/B7265bBl7yGq6xuPek5bN4h4qnUkfgryItJKrIH3npfX8L8vrKKuITS2V1ldT0V1fcTXRrtx+HFtnSBRkBeRVtoLvI2Njl8vWMcD/9wQ8zmj3TimTyzg7svGkZ+Xe+RYt1yFJq9oPXkRaaWtMsmKqjpue/p9Xlsd+yT2WHrmNc1SPPsP1yVt96pMoyAvIhFFWhd+1Y4DfOXhxew5WAuEUgGNEV7bt3su3bvkxFz33tZAr4J8YhTkRSQmc5duZ+azy4/k3yFygM/LzeZHl4yJKzirwiZ5FORFpE3VdQ3c+fxKnlyyjS7ZWURaUDbbjEbnOjxbtbN3r8okCvIiEtXGsoPc+Pgy1uys5MZPnchvX4880NroHJtmfa7D14l1SQWJn4K8iET0wvIdzJy7gpxs44/Xn875owby3Ps7ktLjTsbuVRKiIC8iR6mpb+CnL65mzrtbmDg0n1//66kUhIN4Mnvc8WwALrFTkBeRI7buPcxNTyxj+fYKvn7OcL47bRRdcj6uWU+kx62VJlNDQV5EAPjbBzu449kVZBn8/trTmDrm2IjP60iPu+VKk03r2TSdT5JH08pEMlxVbQMz5y7n5ieKOXlQT1665dyoAb6jtNJk6qgnL5LB1u6s5KY/L2N92UEuPGUgq3Yc4Nx7FrabTok39aI6+NRRT14kAznn+PPirXz+12+x/3Ad3zrvRN5ev5cdFdXtLg/clHopKa+Kea15rTSZOgryIhmm/HAtNz6+jO//dQWThvfj5VvO5fkPdsScTulI6kUrTaaOgrxIBnln/R6m/fJNXlu9izsuGsWcr05iQK+uUdMmJeVVrXZ26kjqpWmlyYL8PAwoyM/T9n6dRDl5kQxQW9/Iz19dy+w3NjK8fw8evG4yYwv6HHk82rIC0LoSpqNLEKgOPjXUkxcJuA1lB7n8gXf4/T83ctXpQ3nh5nOOCvAQOZ3SXPN0jFIv6UU9eZGAcs7xxHvb+PELq+iam8XvrjmNaWOj175DKN8erUfflI7REgTpRUFeJIB2H6jme3OXs3BtGeec1J+fXzGeQb27tfmapnTK5FkL2k3HKPWSPjwL8maWDRQBJc65i81sOPAkcAywFLjWOVfr1fVE/CDWevHOnNL/8opSvv/XFRyubeDOS0bzlbOGkZVlMb9eK0IGi5c9+VuA1UDv8Pf3APc55540s98BNwAPeHg9kZSKdaq+F1P6Y7lJHKiu487nVvJscQnjCvpw35XjOWlgr7jfl9IxwWLOtd4AIO6TmA0B5gA/Af4DuAQoA451ztWb2VnAnc65qW2dp7Cw0BUVFSXcHpHOEC2tUZCfx9szp8T9vGha3iQg1LNuXoL4zvo9/OdfPmBXZQ3fPv8kbp5yErnZqqvIFGa21DlXGOkxr3ryvwS+CzR1G44Byp1z9eHvtwMRuwFmNgOYATB06FCPmiOSfLHWiyc6pb+tyUefHj2Ie/6+hkff3cLw/j145ltnMXFo35jOK5kh4Vu9mV0M7HbOLe3I651zs51zhc65wgEDBiTaHJFOE60uPMvsqMlDiU7pb2ui0rT73+BPi7bw1cnDeOk75yrASytefJ6bDHzezDYTGmidAtwP5JtZ0yeFIUD0hS1E0lC02vIG545ayyXRuvK2bgZZZjw14yx+dMkY8rpEr3OXzJVwkHfO3eGcG+KcGwZcBSxwzl0NLAS+GH7adcBziV5LxE+apupnW+vKleaThxKd0h/tZnLeiP68fMu5TBreL6H3IcGWzDr57wFPmtldQDHwUBKvJZIS0ycWcOtT70d8rHmaJZG68ukTC6iua+DHL6ziUG0D2VnGv/3LifynSholBp4Geefc68Dr4a83ApO8PL+IH3V0LZdY/fTF1Tz01iYanKNHl2z+++LRXDlJRQoSG9VYiW/MKy5h8qwFDJ/5YquVD/0sUjrFgPNHJVZIsO9QLV984B1mv7mRhnCp86HaBu7826q0+dlI6inIiy90ZCMKv5g+sYDLTyugeWbeAXOXlrRqfyw3Muccf/tgB5/+xT8p2rK/1ePaNk/ioSAvvpDue4AuXFNGy2mFLdsfy41s277DfO2RJdz8RDFD+kZP92jbPImVgrz4QrrvARpL+9u6kdU1NDL7jQ185r43WLxpHz/83CnM/bezKdC2eZIgrUIpvhDr4GVnLvQVi6b2RFscpHn725rU9Plfv83q0gNceMpA/ufSsUeCuxYLk0SpJy++EMuEIb/l7Zu3J5KW7W+r973/UC2/u+Y0/vCVwqN679o2TxKlnrz4QiwrH7aV7khF0IvUniYFEdofqVcOoUlNv7n6VHp1y414Lq3dLolQkBffaC+Y+S1vH+26BhFXl5w+sYDSiirue3UdtQ2N5GYbN08ZwXcuGJHklkomU5CXtJHsSUfxitaeLDOGz3zxqE8jB2vq+dX8dTz81iZ6dsvhzqljuOr04+PazKMz+G3MQxKnIC9pw2+DkOePGsBji7a2Ot40camkvIqZc5ezbOt+/rFyFzsPVHPV6cfz3Wmj6NejS2c3t11ebG4i/qMgL2nDbzsWLVxT1u5zqusbefTdLYw5rje/veZUTvXxUsB+G/MQbyjIiy9FSxv4YRCyqW3Rqmoief6mc8j2WWqmJb+NeYg3FOTFd/ycNoi0FV97CvLzfB/gwX9jHuIN1cmL7/h5iYO2yiYjSaeJS4lubiL+pJ68+I6f0waxtCGL0AJlnTFm4GU1jN/GPMQbCvLiO35OG0RrW5O83OxOm5GajLSWH8Y8xFtK14jv+Dlt8J0LTiInSn49niUHvFg7389pLfEP9eTFd/yYNqhraOTJJdu4/7V11Dc6uuVmUV3XGHH5gvZ41QP3c1pL/ENBXnzJL2kD5xwvrdjJz/6xlk17DnH6sL78/tpTOe2Ejm+e7VU9up/TWuIfCvIiUbyzYQ/3vLyGD7ZXcPKgnjx0XSFTRg3ELLFySK964H6bASz+pCAv0kLx1v38/B8f8db6PQzu0417v/hJLjt1iGe17l71wP2Y1hL/UZAXCVu5o4L7Xv2I11bvpl+PLvzgs6dw7Vkn0K3FIHCivOyB+yWtJf6lIC9pL9Fa8fW7K7nvtXW8uLyU3t1yuH3qSK47exg9uybnz0M9cOlMCvKS1uKtVGl+QxjQqytD+3Vn2db95OVmc/OUk/j6uZ+gT17kzTu8pB64dJaEg7yZHQ88CgwiNNFvtnPufjPrBzwFDAM2A1c45/Ynej2R5uKpVGl5Q9hdWcPuyhrOHzmAn31pPMf07Npp7RbpLF705OuB25xzy8ysF7DUzF4FrgfmO+dmmdlMYCbwPQ+ul5a0GUOI1z+HeCpVfvrS6ojrzny066ACvARWwkHeOVcKlIa/rjSz1UABcCnwqfDT5gCvk6FB3s+rKnqtrSAe688hnhtBLJUqy7eX89uFG9hdWRPxHJo8JEHm6bIGZjYMmAgsBgaFbwAAOwmlcyK9ZoaZFZlZUVlZ+5swpKNMmX7eFMRLyqtwfBzEm6bsx/JzaO8cLUVbAuE/P3Myb6/fw9UPLuLzv36btzfsoVeUgdRYSxe9WIpApLN5FuTNrCcwF/h359yB5o855xyhfH0rzrnZzrlC51zhgAEDvGqOr2TK9PP2gngsP4d4b4jTJxZw92XjKMjPw4Dj+nTjy5OO55F3t3D1g4v5aNdBZl40indmTuHH08d2eE2c9m4+ugGIX3lSXWNmuYQC/OPOuWfDh3eZ2WDnXKmZDQZ2e3GtdJQp08/bC+Kx/Bw6ckOcPrGAaWOPZV5xCQ++tYmH397M0H7d+ckXxnL5qUOO1LknUrrY3s0nU9Jxkn68qK4x4CFgtXPuF80eeh64DpgV/ve5RK+VrjJl+nl7QTyWn0O8N8R9h2p5bNEWHn13M3sO1jJ6cG/uv2oCnxs3mJzs1h9UW5YuNvXA2wv6bd18tDeq+JkXPfnJwLXACjN7P3zs+4SC+9NmdgOwBbjCg2ulpUyZ/NJeEI/l5xDrDXHTnkM89NZGnlm6neq6Rs4fOYBvnPsJzjrxmJjXlolnQLytm0+mpOMkPVkoXe4PhYWFrqioKNXNSHvJKteM5bxeXDvaOZxzvLluD4+8s5mFa3eTm5XFFyYW8PVzhzNiUK+438/kWQsiBu6C/DzenjmlVZtu/8sH1DV+/PeSm2VcOel4nli8jYYIf0eRziOSDGa21DlXGOkxzXgNmGSVa8Z6Xi9mcrY8x8Gaeh59dzNz3tnMhrJD9O/ZlZunjOCaM4cysFe3Dl8n7h54iw8IjcBT70UO8EFMx0l6UpBPglROfEpWfjgVeeeNZQd5bNFW/lK0jcqaenKzQ1G2S7bxif49EgrwEF/+/95X1lLXcHQwb2h0RNrSO9us07YAFGmPgrzHUj3xKVn54c7KO9fWN/Lqql08vngL72zYS06WMX5IPh+WVFDT0Bi6ZkW1Jz/TeAbE43mfjc4pwItvBDrIp6JHnepKi2SVaya7DPThtzZx36sfUVlTD0Df7rncPnUkXyocwhd+886RAN/Ei59pPAPi7W3g3fK5In4R2CCfqh51qistklWumYzz1tQ3MH/1bn41fx1rdlYe9VhVbQMF+XkM7NUtqT/TWMcQIr3/3GwDx1GDscrFi98ENsinqkedqolPzT+19MnLpVtuFuWH6zz7BONlGejanZU8tWQbfy3ezv7DdWRHKHmsrm888rvyw2SyaO8/0jGlasRPAhvkU9Wj9qLH2zLNdP6oASxcUxY1kLT81FJeVUdebjb3XTnB04CTSOVM+eFa/ra8lGeKtvHB9gpys41Pjx7EFYXHc/0fl0R8TdPvyi+TyaK9fwV18bPABvlU9f4S7fFGSjM9tmjrkccjpZ1SPQ4QTU19AwvXlPHssu0sXLubugbHyEG9+K+LR/OFiQX069EFCNWTt/W78uJThJZ6lkwV2CCfyt5fIj3eSAG7pZYBPNXjAM01NjqWbd3PX4tLeGF5KRVVdfTv2ZWvnDWML0wsYMxxvVvNSI3ld5XIzzTVFU8iqRTYIJ+uSwnEGpibPy/VOWvnHCtKKvjbBzt4cXkpOyqq6ZabxdQxx/KFiQWcc1L/iOvINEn27+p//rbSl590RDpDYIM8pOc+mrGW6jUP4Kn41OKcY3VpJS8s38ELy0vZuu8wudnGeSMGcPu0kXx69LFxbYSdrN/VvOIS9h+ui/iY1paRTBDoIJ+OIgXsliKlMiD5n1oaGx3vby/nlQ938veVO9my9zDZWcbZJx7DTeefxNQxx9Kne/I3wY5HWxuz5PusrSLJoCAf5peBuUgBu73qmqbXJaO9dQ2NvLdpH6+s3MkrK3ey60ANOVnG2Sf1Z8Z5n2DamGN9vT9qW731g9X1zCsuSbtPeyLxUJDH+4G5RG8YqU4z7TtUy+trdzN/zW7e+KiMyup6uuVm8amTBzJt7LGcP2ogffLSoxfcVvqrrtEpLy+BpyCPtyWI6VjJ0ZRff/2j3cxfvZvirftpdNC/Z1c+O3YwU04ZyHkjBpDXJbv9k/lMe+kv5eUl6BTk8bYE0a816y2VVdbw1voy3vxoD2+s28OegzUAjC3ozU1TRnDhKQMZe1wfsrJi24AD/JPyaq7p+rc9/UHEJYG1zowEnYI83pYg+qlmvbmDNfUs2byPRRv28ua6PawqDe213rd7LueMGMB5I/pz3skDGNS7Y8v3+vkTTNP1/TBrVqSzKcjjbQliqmvWm1TVNlC0ZR/vbtjLuxv3snx7BQ2NjtxsY+LQvtw+dSTnjugfd289Gr9/gknXeRMiiVKQx9sAkKqZtmWVNSzdso8lm/dTtGU/K0sqqG90ZGcZnxzSh2+eF9r/9LQT+tK9i/e/dr9+gmku1QPaIqmgIB/mVQDw8oYRLcddU9/AmtJKlm8vp3hbOUu37GfL3sMAdMnJYsKQfL5x3ic4Y3g/Cof1azUpKRm5c798ghGRo2kjb5/64bwVPL5oK81/O9lZRkF+HjsrqqkNb6LRv2cXTh3al8JhfTnthH6MLehN15zsqIG8Ze4cQp804t2uLtJKmXOXliR8XhGJnzbyTgPziku45+9rKK2oJi83i6q6xlbPaWh07G6z4t8AAAnuSURBVKyo5quThzH++Hw+OaQPBfl5rRb8amsQtL3ceSy9/Ejnn7u0hMtPK2h30paIdC4F+TYkqySw/HAt63cfZN3ug6zbdZC31+9h7a6Pd0aKFOCb1DU0csdnT2nz/G0F8rZy57FWyEQ7/8I1Zbw9c0qbbRORzhXIIO9FcE6kJNA5x56DtZSUV7Fl7yE27TnE5j2H2LT3MJv3HKKi6uMFs/Jys6lvjB7UW4olx91WIG8rdx5rhYxXg6x+rKsXCZqkB3kzmwbcD2QDDzrnZiXzel7Va0cLeP/39zWcd/IAdh2oZndlTejfA9WUlFexfX8VJfurKCmvoqb+48BtBsf1yWNY/+5c/MnBDDumB58Y0IOTB/WiID+PE7//UkxtMoipSqetQN5W9c+tT70f8Xwtg7cXg6x+rqsXCZKkBnkzywZ+A3wa2A4sMbPnnXOrknXNWHuj9Q2NHKptoLK6joM19Rysrqcy/G9FVV3U9U52VFRz6o9fbXX8mB5dGNI3j1GDe3HBKQMpyM+joG93TjimO0P7dadbbvQlAWJZXtiAq88c2uFNp5sC+fSJBRRt2ccTi7fR4BzZZlx+Wqiy6N5X1sYUvL0oE/V7Xb1IUCS7Jz8JWO+c2whgZk8ClwKeBvl3Nuzhl6+to7HRRQ2WJeVVnPbjV6mua6C6vpGGxo5VFfXsmsNtnzmZQb27MbBXVwb26sbA3l3bDOLtiRQ0c7ONHl1yqKiKfzPutso45xWXMHdpyZEp/g3OMXdpCYUn9Is5eHtRJpoOdfWxUtpJ/CzZQb4A2Nbs++3AGc2fYGYzgBkAQ4cO7dBFDMMI1Yh3zck6KlXSpHuXbD47bjBdc7LolptN15wsunfNoVfXHHp1y6Fntxx6hr/u3S2XNz4q47+eW9kq4N01faznf8DJmI0Zre4/Wg/6tqc/4OdXjOfuy8bF1I5E5xUEpa5eaSfxu6TWyZvZF4Fpzrmvh7+/FjjDOXdTpOd7USf/w3krjtr4usk1Zw7lrunjWh1vqxcWxB7a8JkvEu033pl17V7V66fa5FkLIt6sCvLzVGkknSaVdfIlwPHNvh8SPpY0C9eUxXy8vV5YEKfBt5X/78yceFDWkglS2kmCKdlBfgkwwsyGEwruVwH/mswLxvNHl4mDf35aXz0IN9GgpJ0kuLKSeXLnXD1wE/AKsBp42jm3MpnXjPbHlWXGvOKjP0RkYi9s+sQC7r5sHNkWeeVJBaf43D51JHktBt21hLH4SVKDPIBz7iXn3MnOuROdcz9J9vUi/dFBqIrkjmdXHBXoowW0oAe66RML+PkV4xWcPNB00yzIz8MI5eLTbVxBgi1wM17b2gmoZSomVcsC+0FQcuJ+EIS0kwRX4II8hP7oYpm9memBTsFJJPgCGeQh9gExBToRCbKk5+RTRQNiIiIB7smnUyomiJOuRMQfAhvkIT1SMZoWLyLJFNh0Tbpoa0KWiEiiAt2Tj0WqUyWZOCErGVL9exTxq4wO8n5IlWhafOL88HsU8auMTtf4IVWiKqDE+eH3KOJXGd2T90OqJJ2qgPzKD79HEb/K6CDvl1RJOlQB+Zlffo8ifpQR6Zp5xSVMnrWA4TNfZPKsBUcWKVOqJBj0exSJLvA9+VgG5ZQqSW/6PYpEl9Tt/+LlxfZ/LWl7NhEJura2/wt8ukaDciKSyQIf5DN1YxAREciAIK9BORHJZIEfeNWgnIhkssAHeVAduohkrsCna0REMpmCvIhIgCnIi4gEmIK8iEiAJRTkzexeM1tjZsvN7K9mlt/ssTvMbL2ZrTWzqYk3VURE4pVoT/5VYKxz7pPAR8AdAGY2GrgKGANMA35rZtlRz+Jz0RY4ExHxu4SCvHPuH865+vC3i4Ah4a8vBZ50ztU45zYB64FJiVwrVZoWOCspr8Lx8QJnCvQikg68zMl/DXg5/HUBsK3ZY9vDx1oxsxlmVmRmRWVlZR42xxvadUhE0lm7k6HM7DXg2AgP/cA591z4OT8A6oHH422Ac242MBtCq1DG+/pk0wJnIpLO2g3yzrkL23rczK4HLgYucB+vW1wCHN/saUPCx9KOdh0SkXSWaHXNNOC7wOedc4ebPfQ8cJWZdTWz4cAI4L1ErpUqWuBMRNJZomvX/BroCrxqZgCLnHPfcs6tNLOngVWE0jjfds41tHEe39ICZyKSzgK/M5SISNBl9M5QIiKZTEFeRCTAFORFRAJMQV5EJMAU5EVEAsxX1TVmVgZs6eDL+wN7PGxOOtB7zgx6z5khkfd8gnNuQKQHfBXkE2FmRdFKiIJK7zkz6D1nhmS9Z6VrREQCTEFeRCTAghTkZ6e6ASmg95wZ9J4zQ1Lec2By8iIi0lqQevIiItKCgryISIAFIsib2TQzW2tm681sZqrbk2xmdryZLTSzVWa20sxuSXWbOoOZZZtZsZm9kOq2dBYzyzezZ8xsjZmtNrOzUt2mZDKzW8P/T39oZk+YWbdUtykZzOxhM9ttZh82O9bPzF41s3Xhf/t6ca20D/Jmlg38BrgIGA182cxGp7ZVSVcP3OacGw2cCXw7A94zwC3A6lQ3opPdD/zdOTcKGE+A37+ZFQDfAQqdc2OBbOCq1LYqaR4BprU4NhOY75wbAcwPf5+wtA/ywCRgvXNuo3OuFngSuDTFbUoq51ypc25Z+OtKQn/4gd7FxMyGAJ8DHkx1WzqLmfUBzgMeAnDO1TrnylPbqqTLAfLMLAfoDuxIcXuSwjn3BrCvxeFLgTnhr+cA0724VhCCfAGwrdn32wl4wGvOzIYBE4HFqW1J0v2S0FaTjaluSCcaDpQBfwynqR40sx6pblSyOOdKgJ8BW4FSoMI594/UtqpTDXLOlYa/3gkM8uKkQQjyGcvMegJzgX93zh1IdXuSxcwuBnY755amui2dLAc4FXjAOTcROIRHH+H9KJyDvpTQze04oIeZXZPaVqWGC9W2e1LfHoQgXwIc3+z7IeFjgWZmuYQC/OPOuWdT3Z4kmwx83sw2E0rHTTGzx1LbpE6xHdjunGv6lPYMoaAfVBcCm5xzZc65OuBZ4OwUt6kz7TKzwQDhf3d7cdIgBPklwAgzG25mXQgN1Dyf4jYllYV2TX8IWO2c+0Wq25Nszrk7nHNDnHPDCP1+FzjnAt/Dc87tBLaZ2cjwoQuAVSlsUrJtBc40s+7h/8cvIMADzRE8D1wX/vo64DkvTprjxUlSyTlXb2Y3Aa8QGo1/2Dm3MsXNSrbJwLXACjN7P3zs+865l1LYJkmOm4HHwx2YjcBXU9yepHHOLTazZ4BlhCrIigno8gZm9gTwKaC/mW0HfgTMAp42sxsILbl+hSfX0rIGIiLBFYR0jYiIRKEgLyISYAryIiIBpiAvIhJgCvIiIgGmIC8iEmAK8iIiAfb/Af6+ei+tAbeXAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k8L-tcPfOAJb"
      },
      "source": [
        "More of a challenge -- can we fit a (jittered) Gaussian?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EYFBSfqN7Ewz",
        "outputId": "71a9f486-209c-4f95-fe54-894ea142e403",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        }
      },
      "source": [
        "def forward_gaussian(x, params):\n",
        "    \"\"\"Forward pass for our fuction\"\"\"\n",
        "    return params[2] * torch.exp( -(1/2)*((x - params[0])/params[1])**2 )\n",
        "\n",
        "# Let's define some settings\n",
        "n = 100 # number of examples\n",
        "\n",
        "\n",
        "# Model definition\n",
        "p = torch.Tensor( [5,1,1] )\n",
        "x = Variable(torch.rand(n) * 10, requires_grad=False)\n",
        "y = forward_gaussian(x, p)\n",
        "y += 0.1* torch.randn(n)\n",
        "\n",
        "plt.scatter(x,y)\n",
        "\n",
        "# fit?\n",
        "p_init = Variable(torch.Tensor( 10.0 * torch.rand(3) ), requires_grad=True)\n",
        "print(p_init)\n",
        "y_hat = forward_gaussian(x, p_init)\n",
        "plt.scatter(x,y_hat.detach().numpy())"
      ],
      "execution_count": 323,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([6.3402, 3.0526, 3.9059], requires_grad=True)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f85d7be5048>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 323
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CFaBdY_B-MSw",
        "outputId": "0a6fa1c9-2988-454f-cff2-d71ea760562c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 808
        }
      },
      "source": [
        "p_hat = Variable(p_init.clone(), requires_grad=True)\n",
        "\n",
        "# Optimizer (NEW)\n",
        "learning_rate = 5e-2\n",
        "\n",
        "opt = torch.optim.SGD([p_hat], lr=learning_rate, momentum=0.5)\n",
        "#opt = torch.optim.Adagrad([p_hat], lr=learning_rate)\n",
        "\n",
        "loss_history = []\n",
        "p_history = []\n",
        "\n",
        "# Training loop\n",
        "for i in range(0, 10000):\n",
        "    opt.zero_grad()\n",
        "    \n",
        "    # Compute current estimate\n",
        "    y_hat = forward_gaussian(x, p_hat)\n",
        "    \n",
        "    # Calculate loss function\n",
        "    loss = rmse(y, y_hat)\n",
        "    \n",
        "    # Do some recordings for plots\n",
        "    loss_history.append(loss.item())\n",
        "    p_history.append(p_hat.detach().numpy().copy())\n",
        "    \n",
        "    # Update model parameters\n",
        "    loss.backward()\n",
        "    opt.step()\n",
        "    if (i%1000 == 0):\n",
        "      print(\"Iteration %d\" % i)\n",
        "      print(\"loss = %s\" % loss.item())\n",
        "      print(p_hat)\n",
        "\n",
        "plt.subplot(2,1,1)\n",
        "plt.plot(p_history)\n",
        "plt.ylim(0, 10)\n",
        "plt.show()\n",
        "plt.subplot(2,1,2)\n",
        "plt.plot(loss_history)"
      ],
      "execution_count": 324,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration 0\n",
            "loss = 2.568636178970337\n",
            "tensor([6.3361, 3.0319, 3.8703], requires_grad=True)\n",
            "Iteration 1000\n",
            "loss = 0.10196183621883392\n",
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n",
            "Iteration 2000\n",
            "loss = 0.10196183621883392\n",
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n",
            "Iteration 3000\n",
            "loss = 0.10196183621883392\n",
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n",
            "Iteration 4000\n",
            "loss = 0.10196183621883392\n",
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n",
            "Iteration 5000\n",
            "loss = 0.10196183621883392\n",
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n",
            "Iteration 6000\n",
            "loss = 0.10196183621883392\n",
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n",
            "Iteration 7000\n",
            "loss = 0.10196183621883392\n",
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n",
            "Iteration 8000\n",
            "loss = 0.10196183621883392\n",
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n",
            "Iteration 9000\n",
            "loss = 0.10196183621883392\n",
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NHFegOz1/rwIrqfpAv9bD34w1M8tcLqduzMxsCA56M7PMOejNzDLnoDczy5yD3swscw56M7PMOejNzDLnoDczy9z/A8cLZEqBxxwjAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f85d7b32a58>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 324
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aCMiNo1GOIO3"
      },
      "source": [
        "Answer: yes -- but have to tweak learning rates and have a good initial guess!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0t5jqKDfAaov",
        "outputId": "a89fd7c9-b1a1-4007-f610-f1b36c33610c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "plt.scatter( x, y)\n",
        "x_fine = Variable(torch.linspace(0,10,200), requires_grad=False)\n",
        "y_fine = forward_gaussian( x_fine, p_hat )\n",
        "print( p_hat )\n",
        "plt.plot(x_fine,y_fine.detach().numpy())\n",
        "plt.show()\n"
      ],
      "execution_count": 325,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([4.9856, 0.9835, 1.0263], requires_grad=True)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s9H3iAZXBReR",
        "outputId": "4fe91020-447f-4514-ed61-ac7100c321d7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "for i in range(5):\n",
        "  print( p_history[i] )\n",
        "print( len( p_history) )"
      ],
      "execution_count": 326,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[6.3402123 3.0526388 3.905934 ]\n",
            "[6.3360744 3.0318668 3.8703191]\n",
            "[6.3297563 3.0006866 3.8170116]\n",
            "[6.322183  2.9642708 3.755033 ]\n",
            "[6.3137903 2.9252021 3.6889277]\n",
            "10000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pCzA5HkPOP2T"
      },
      "source": [
        "Following two code blocks give some practice in making a movie in matplotlib"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jmpe2J8UCnyQ",
        "outputId": "a6a4894d-945f-4a8f-9ebc-40644b17face",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 561
        }
      },
      "source": [
        "from matplotlib import animation, rc\n",
        "from IPython.display import HTML\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "plt.scatter( x, y)\n",
        "ax.set_xlim(( 0, 10))\n",
        "ax.set_ylim((0, 2))\n",
        "\n",
        "line, = ax.plot([], [], lw=2)\n",
        "\n",
        "def init():\n",
        "    line.set_data([], [])\n",
        "    return (line,)\n",
        "\n",
        "def animate(i):\n",
        "    x_fine = Variable(torch.linspace(0,10,200), requires_grad=False)\n",
        "    y_fine = forward_gaussian( x_fine, p_history[20*i] )\n",
        "    line.set_data(x_fine.numpy(), y_fine.numpy())\n",
        "    return (line,)\n",
        "\n",
        "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
        "                               frames=500, interval=20, \n",
        "                               blit=True)\n",
        "\n",
        "HTML(anim.to_html5_video())"
      ],
      "execution_count": 327,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<video width=\"432\" height=\"288\" controls autoplay loop>\n",
              "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAAB19W1kYXQAAAKuBgX//6rcRem9\n",
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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 327
        },
        {
          "output_type": "display_data",
          "data": {
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0a1WqiyMBpAAgrV6kfD31peuk7D8bO5gMg6fnrGdNyd5UF0cCRgFAWr1YVTvpPin7MT068Y1T+1BV7fzmDQ0Ok5aVNpPCizRWr655Eat/0qnRN5YfnzeIqfOLeWXRJiasL2Von66pLpIEhJ4ApNW7+fxjyaiXoSFdq3wi6dklj++OGgDAPa8t1+AwaTGJzgk81sxWmNlqM5sUYf39ZjY/9LXSzErD1lWFrZuWzMKLAHTrkEO1Q22annSu8onm+rMH0rldFu+v2c47q7alujgSEHGrgMwsE3gUOA/YAHxoZtPcfWntNu7+32Hb/wgYHnaIMncflrwii3ymutrrErFNGnscPzh7YIpLlLip84qZPH0FG0vL6NU1jy8cW8A/F27i/pkrOWtQvuYQlmaXyBPACGC1u69x93LgGeCSGNtfATydjMKJxDNj2RaWbNzNkZ1zGX9G/1QXJ2GRppqcuXQLHXIzmfdpKf9aWZLqIkoAJBIAegPrw15vCC07jJn1AwYAs8IWtzOzIjP7wMzGRXsTM5sQ2q6opEQffonP3XnozZr+8z8cfQztIuTtT1eRuq4eqKyuSzf9wMxVaguQZpfsRuDLgefcPfyT3S80PPlK4AEzi/iM7u5T3L3Q3QsLCgqSXCxpi95ctpUlG3fTo1Mul32+T6qL0yDRuq7uPlDJER1ymL++lNl6CpBmlkgAKAbCz66jQ8siuZx61T/uXhz6vgaYzaHtAyKN4u51o2d/cPbAVnX3D9FHJffumscPzv4cAA/MWBn1KaA29UWi01KKRJJIAPgQGGRmA8wsh5qL/GG9eczsOKAb8H7Ysm5mlhv6OR8YBSytv69IQ81eWcLCDbvI75jDlSP6pro4DRYrrfRVp/Ujv2MOCzbsYvaKw58CIrUfJCvbqQRL3ADg7pXAjcB0YBnwrLsvMbM7zezisE0vB57xQ29ZjgeKzGwB8BZwT3jvIZHGcHcenFlz9z/hC58jL6d13f1D7LTS7XOyuC7Um+n+mYc/BURqP0h0WkqRcAmNBHb3V4FX6y27td7r2yPs9x5wUhPKJ3KYd1ZtY/76Urp3yOGq0/qlujiNNm5476hjFb41sh9/+NcaFm7YxazlW/ni8UfWrYvWfpBO2U6lddBIYGlV3J0HQz1/vn/W52if0zazmeTlZHJdbVtAvR5BTZ2WUqSWAoC0Ku9/vJ2563bStX023z699d79J+Kq0/pR0CmXRcW7eDNs6shkTEspAkoGJ2mu/mjZdtk19yzXnjmAjrlt++PbLjuT684eyF3/XMpDs1bxxeN7YGZ11Ubhf5eJYwa3qtQXkh7a9hkkrVptb5faBs/ajJ952ZmtatRvU1w5oi+/n72ahRt28a+VJYwe3AOI3X4gkigFAElb0SZ6yco0OrXLTkGJWkb9p54zBuYzbcFGHnxzFWcfW6AcQZI0CgCStqL1aok2529bEOmpZ/veg3U5gt5dvZ0zB+WnuJTSVqgRWNJWrNGybVW8HEEPvhl9dLBIQykASNqK1NulXVZGm+7tEitHUNf22Xy4dicfrNnRwqWStkoBQNJW7WjZ3Kyaj6lRczc8efqKNpv2INZTzzWhWcNqM6CKNJUCgKS1AfkdOFhZDUBtxUdbzn0Tq4//+FH96RSaNWzOJ3oKkKZTAJC09vCsyHe7bTX3TawcQZ3bZfO90FNAtL+LSEOoF5CkrcXFu5gZNgK2vraa+yZWH//vjRrAn//9Ce+s2sbcdTs5tV+3Fi6dtCV6ApC0VVvXHW3EbxBz33Rpn83VoUFwegqQplIAkLRQf4KTR2et5o2lW8jNyuBnyn1ziGvOHED7nExmryhh4YbSVBdHWjEFAEm5SBOc/GZGTf3+lSP78p0z+ketFw+ibh1y6hLhPfTm6hSXRloztQFIykUa/FQd6vJzfWhiFOW+OdT3z/ocj7+3lpnLtrC4eBcn9u6S6iJJK6QnAEm5WI25PTq3a8GStB75HXO5amTNU8Ajs/QUII2jACApF60x9yhd/GOa8IXPkZuVwetLNrN88+5UF0daoYQCgJmNNbMVZrbazCZFWH+1mZWY2fzQ17Vh68ab2arQ1/hkFl7ahkiDnzIzjEkXHJeiErUOPTq344oRfQF4WE8B0ghxA4CZZQKPAhcAQ4ArzGxIhE3/n7sPC339KbRvd+A2YCQwArjNzNRxWQ5RO/ipR6fcumW3XjREdf4JuO7sgeRkZvDqok2s2rIn1cWRViaRJ4ARwGp3X+Pu5cAzwCUJHn8MMMPdd7j7TmAGMLZxRZW2bNzw3nWDmr47qn9gJnxpqqO6tOOyz/fBHR55S08B0jCJBIDewPqw1xtCy+r7upktNLPnzKxPA/fFzCaYWZGZFZWUlCRQLGlLlm/ezWuLN5OblVHX80cSc93ogWRnGi8v2MjHJXtTXRxpRZLVCPwy0N/dT6bmLv/xhh7A3ae4e6G7FxYUFCSpWNJa1I76vXJkX/X8aaDeXfO49NQ+VDs8rEyh0gCJjAMoBvqEvT46tKyOu28Pe/kn4L6wfUfX23d2QwspbU/4tIcFnXLZuueg7v6b4IZzBvLc3PW8tGAj148+hsFHdUp1kaQVSOQJ4ENgkJkNMLMc4HJgWvgGZtYz7OXFwLLQz9OB882sW6jx9/zQMgmw+iN/t+45CMDIAd11999IR3drz5Uj+uIOv3mj7WVJleYR9wnA3SvN7EZqLtyZwGPuvsTM7gSK3H0a8F9mdjFQCewArg7tu8PM7qImiADc6e5KZB5w0SZ7X7lF9dcN9T9TF/H0f9ZT5U4GNd1n31i6hQXrSxnap2uqiydpztJxftHCwkIvKipKdTGkmQyY9AqRPnUGfHLPhS1dnFbrf6Yu4skPPo247qxB+fztmpEtXCJJJTOb6+6FDdlHI4GlxUUb+RvE9M5N8fR/1kdd986qbfxnzfao60VAAUBSYOKYwbTLOvSjF+T0zo1VFefp/b7pK0jHJ3xJHwoA0uLGDe/NiAHd615nAF8/Vdk+GyrTLOLyDKB7hxzmrtvJG0u3tGyhpFVRAJAW91zRet5Zta3udTXw/NziNjnJe3O6YmSfiMuvPK0vN31xEAD3vraciqrqliyWtCIKANLi7npl2WGNwG11kvfm9KtxJ3HVaX3rngQyzbjqtL78atxJXDmyLwPyO7Bm2z6emRO5oVhEAUBa1K79Fewqq4i4rq1O8t6cfjXuJD6++8s8cNkwjurSjqc++JRR98zilYWb+PnYmjaVB2auYs+BisOm3dQTlygASIt65K3oqQrUC6hxIk2pecsLiygrr+LUft3Yvq+cnzy7IOI2CgLBpgAgLebT7ft5/L11GJCrXkBJE2lgXVlFFb9+YyW/+HLNnAozl26JuI2q3YJNAUBazL2vL6e8qpqvntKbe79+siZ5T5JoVWcbS8s4tV93vnzSUREH3sXaV4JBk8JLswhP9tarax7jhvXilUWbaJedwcQxg+nZJU8X/CTp1TWP4ggX8toqtV98+XheW7Q5YhBIpNqt/v9y4pjB+t+1EXoCkKSLVCf9u9kfA3DjOcfQs4vq+pMp0pSa4VVqR3drz9gTjzpsv0Sq3aK1L6jtoG1QAJCki1Qn7dQkKvv+Fz6XmkK1YbVTasaqUrv/smEc0SGn7nWi1W7R2hfUdtA2qApIki5avXJVtZOblRlxnTTNuOGxR1K3y87knq+fzPefKKJTbhZTbxhFQdgczNHEal+Q1k9PANIgifQlj1av3FvdPFPqS8f34OxjC9hzsJK7X10WfweUuK+tUwCQhCVaHzxxzGCyMw/NU5OVgbp5ppiZcfvFJ5CblcEL84qZvWJr3H3itS+0JA1kSz4FAElYQ+qDvfrQPidG5MRl0rIG5Hfgv887FoBfvriYZ+Z8GvOimkj7QktQY3TzUBuAJCzR+uDJ01dQWa/PYUW1M3n6CnUfTAPXnjmAfy7cyOLi3fxy6mKqQsG69qIKHPJ/ite+0BJi3XykumytmZ4AJGGJ1gdH6pMOajhMF1mZGdz79ZMB6i7+tdK1h48ao5tHQgHAzMaa2QozW21mkyKs/4mZLTWzhWb2ppn1C1tXZWbzQ1/T6u8rrUci9cH7DlaSmRG5ukcNh+njhF5doq5Lx4uqGqObR9wAYGaZwKPABcAQ4AozG1Jvs3lAobufDDwH3Be2rszdh4W+Lk5SuSUFEqkPvvu1ZVRV+2E1/sr1k356dWkXeXkaXlTTqTG6LUmkDWAEsNrd1wCY2TPAJcDS2g3c/a2w7T8ArkpmISV9xKoPfn3xZp784FOyM42bvjiIp+esV/qANPazscfx8+cXcrDyswlj0vWiWvvZUUqK5EokAPQGwmef3gCMjLH9NcBrYa/bmVkRUAnc4+5TG1xKSXvFpWX8/PmFAEy64HiuOXMAN547KMWlklhqL563vbSEXQcqyDCYdMFxaXtRTYfG6FRprnxMSW0ENrOrgEJgctjifu5eCFwJPGBmA6PsO8HMisysqKSkJJnFkmZWWVXNTU/PY1dZBV88rgffG9U/1UWSBI0b3pt5t57HWYPyqXZ4Y+lmqqs1kXw6ac4usIkEgGIgfPLRo0PLDmFmXwJ+CVzs7gdrl7t7cej7GmA2MDzSm7j7FHcvdPfCgoKChH8BSb0H31xF0bqdHNk5l8nfGIpFmaxc0lNGhvGbbw7liA45vLt6Ow/Nij5pj7S85szHlEgA+BAYZGYDzCwHuBw4pDePmQ0H/i81F/+tYcu7mVlu6Od8YBRhbQfS+s1YuoVH3lqNGTxw2XC6hyUck9ajR6d2/PayYTX/x5mreGPJ5lQXSUKaswts3ADg7pXAjcB0YBnwrLsvMbM7zay2V89koCPwj3rdPY8HisxsAfAWNW0ACgBtxPLNu/nxM/Nwh5vPH8zpA49IdZGkkabOK+YXLyzCQ7U/P3p6Hqu27EltoQRo3i6w5p5+9X2FhYVeVFSU6mK0es05kcf2vQe55NF32bCzjIuH9uLBy4ep6qeVqq1jrl/NUNAxl5k/PZsuedkpKplA5P9PXnbmYV2wzWxuqL01YUoFkWTpMntS/Q9NtGH+jVFeWc31T37Ehp1lDD26C/dderIu/q1YpDpmgJK9B/nGH97j5R+dGZg03uly/oZrzi6wegJIokQjdbLfM9IHY9Q9syKmZOjdNY93J53b6PcpLi0jLzuTsooqjuycy7Qbz+TIzpEHFEnrMGDSK1HnDAYY1qcrz19/RtQR3m1FKs7fZGrME4ByASVRS8+eFKt7WDIbjsLfB6j7Ha8a2U8X/zYgXl3y/PWl3PrSYtLxZjGSxqaNDuLsZwoASdTSCauifWB/+uyCqPW2jWk4ilZF8MyH6yNsLa3NOccVxE3W/dR/PuW3M1a2SHlqNeZC3pQ+80FMOBeYANASk0m0dMKqaFk3q9zZV15Jdr1H9sYO81d2z7Zr6rxinp9bHLMKqHuHHDIMHp61mntfX94iTwKNuZBPnVfMT59d0Oi7+CAmnAtEAGipySRaMmHV1HnFMe/aKqqcju2ymjyRR1W10z4ncgNgWz4xgiLa012tvOxMbr1oCPdfNozMDOP3sz/m1peWNOto4cZcyGvP8aoowSn8ZiXazWAQE84FohdQvMkkktXy35IJqyZPXxHzrg2gdH8F8249v9HvcbCyih8/M5/95YdfINr6iREUsZ7ietf7/LbPyeKGv3/E3z5Yx96Dldx36clkZyb3HrIhF/Jw8QJZ7c1KIr3j0q0XUHMKRACIVbeX7O6SLZWwKpHql6bcoe/cV84Pn/qI99dsp1O7LK4+oz8vfFQcmBMjKHp1zUu4t9h5Q47kL1d/nu8/UcSL84rZvOsAj37rlKSO/k70Ql5frPMh/GYl3s1g0BLOBaIKKFbdXqpb/hvbNhHv4t6UO/SFG0q56OF/8/6a7RR0yuXZH5zOT88fzLuTzuWTey7k3UnnBuokacsaWu0x6ph8nrp2JPkdc3l/zXa+8vC/WbJxV9LKE+tCbtTcoEU6T6KdD5lmh1R9BrGhN5ZABIBYH/JUfiCa0jYR6XeqbRNoysTdz8z5lEt//z7FpWUM7dOVl24YxfE9Ozf4ONI6NGbS9+F9u/Hyj0Yx9OguFJeW8fXfv8cLH21ISuNwrBub2qNHOkgLwt4AAAsnSURBVE+ineO/+ebQQ36XaMc3I5ATzAdmIFhLDZhqiKa+dzJHLW7be5Dbpi3hlYWbALjqtL78r4uG8NqizYGqE5XEHaio4pcvLub5jzYAcMGJR/GrcSdyRMfcRh8z0mAsg4jtXfXPk0TOh6nzipn43AIqqg4/YnamMfnSoa32892YgWCBCQDRTJ1XzMR/LKAirFdDdoYx+RvN/0GINgLTgE/uubBZ37uWu/PS/I3c8fISdu6voH1OJnddciJfP/XoVj8yUpqfu/Ns0XrufHkp+8qrOKJDDv/7qycy5oSj6tKDhF+Yu7bPxh12lVXEvEiHX8ijdUNu7Hky7I43KC2riLiuJW78motyATVW/f6ULTTiPdqHu6W6Vy7fvJv/8+py3l5ZMwFPblYG+8ur+O2MlWRmWNwGMxEz47LP9+WMgfn87LmFvL9mO9c9+RFnDcrnlxcez/JNew65idi5/7MLb7QOF/UbYqM9KTf2PNkV5eIP6dUW0BJ5iQLRBhDL5OkrDnscrKjyFmkETlW/442lZdz8jwVc8OA7vL2yhHbZGWRnWt3csLUnpgaASaL6dG/PU9eO5M5LTqBzuyzeWbWNLz/4Dr948fAso+ES6XCR7PMkVuBIl7EttTUT4e2DE/+xIOntFIEPAKlsBG5MA1xTrNyyh58/t5DRv57Nc3M3kJVhXH1Gf7rm5RwWBMsqqsiMkuEzXU4SSS8ZGcZ3Tu/P7InnMP70fphZxDEk9cU71xI9TxLtUTdxzODDRslDTRtAuoxtuX3akkOqpQEqqp3bpy1J6vsEvgoo1dUwzd3v+GBlFW8tL+Hvcz6tq+oxg4tO7snEMYPpd0QHHn9vbcR9q9zrMn/W0gAwiad7hxzuuOREvn16P77y8LsxnwAg+rnWkCqQSON5Jv5jAXe8vITS/Ye2N9Qe4/ZpS+raArq1z+a2r5yQ8LnY3NUz0doooi1vrFYdAOr/E845roC3lpc06J8ycczgiA2d6XCRa+yHrKKqmqK1O3l54Uamziuuuwszavpx3zXuRAbkd6jbPtZgoIljBqsXkDTKMT06cffXTuLnzy+sq16sLyczg5+cd+xhyxs6QDNSe1VFtde1OdTfvyk3Xs0110b4+d5SWm0voGizGIVLtMdKOk4C0ZAeOO7O2u37+fCTHcxeuZV3Vm5jz8HKiMeNdAz19pHmdOhcEhkcrKwmvHajU7ssRg/uwZnHHMGIAUcw/9Od3PyPhRHTQUTrpRNvToN4+yf6O2wsLSPDLGqqivrpMxpy/HjXM6h5UomW3iVQvYDiDRmHxHuspOPw72g9cO57fTmn9uvG8s17WL5pNwuLd/HRup1s31d+yLZZGUZmhh125xXpbxLEHCjScuqfX+7Oko27+efCTby5bAurtu7l5QUbeXnBxrjHinZ3HKu7aCL7x1L/4hzt4g+NfxpI5HqWnWnc9pUTEj5mIhIKAGY2FngQyAT+5O731FufCzwBnApsBy5z97WhdbcA1wBVwH+5+/RkFDzRf2Sqe6w05Omiqtop3V/Ojn3l0Xvg7DrAWfe9ddjyjrlZ7C+vrLuzqqx2KqNkbIz0N0nHIChtk5lxYu8unNi7C5MuOI612/bx1oqtzPlkB9OXbCZWotHcrAzueHkJfbu3p0endhR0yiW/Yw43nnMMd7y8hANRqppqJXM+jGga01U6XgqM5ropixsAzCwTeBQ4D9gAfGhm09x9adhm1wA73f0YM7scuBe4zMyGAJcDJwC9gJlmdqy7x/xrlpVXMX99KUDd8HIHPgu8zhEdc9i2tzzi/uGO6JDDex9vq93tsGN5aKEfss7DNw/bzz/bLvS92msutBVV1VRUOZVV1VRU13yf92kpry7aVHchLi4t46fPLuCJ99fSvUMO+8ur2F9exe4DFezcV07p/oqEHmPzO+ZwfM/ODD6yE8f37Myp/bpx5R8/YG+Uap/61ItHWlqsG6H++R34bv4AvjtqAP0nvRLzOAcqq/nLu2sjrsvKMDIMqh0yQ9/Dz6fMDGPwUZ347YyV5GZlkJOZQU5W6Cszg8wMIyN0jEwzzGp+TuTJor7i0jKK1u7g8I50hy6oXZ/fMZeSvQcPO05Bx1z+OP6zWp0Foeti/f0bK24bgJmdDtzu7mNCr28BcPe7w7aZHtrmfTPLAjYDBcCk8G3Dt4v1nrk9B3nP8Q80+pdqq3KzMrj9Kydwxci+h61LtA5UdfvS0hrSxhRt0FcG8NPzB7Nt30H+9v66Q55uDcjOyqA8zt1/W7fu3ouSnwrCzC4Fxrr7taHX3wZGuvuNYdssDm2zIfT6Y2AkcDvwgbs/GVr+Z+A1d38uwvtMACaEXp4ILI5X+Iy8zt0zO3bvbZlZOV5VWV5dXrYrIyevS+3rqr07iqvLdu+Id5xkqV8ey8yKmie3fPPqueGvswv6nxRp+6r9u8hs34V4v0+0/b26uhKvrk7V3ySJ8oFtqS5EmmhVf4uon82qyvKKkrWLwpdl5HXuntW5oB9mn41Rcq+u3F2yrrps9476xwo/P+ofK1kilqm2aNXVlWaWWZf3ol55G/o+4dePRpyrg929U0PeM20agd19CjAFwMyKGhrJ2iozK6rctTXwfwt9Jj6jv8VndH58xswanEAtkZHAxUCfsNdHh5ZF3CZUBdSFmsbgRPYVEZEUSCQAfAgMMrMBZpZDTaPutHrbTAPGh36+FJjlNXVL04DLzSzXzAYAg4A5ySm6iIg0RdwqIHevNLMbgenUdAN9zN2XmNmdQJG7TwP+DPzNzFYDO6gJEoS2exZYClQCN8TrARQypXG/Tpukv0UN/R0+o7/FZ/S3+EyD/xZpORJYRESaX+CzgYqIBJUCgIhIQKVVADCzsWa2wsxWm9mkVJcnVcysj5m9ZWZLzWyJmd2U6jKlmpllmtk8M/tnqsuSSmbW1cyeM7PlZrYsNFAzkMzsv0Pnx2Ize9rM2qW6TC3FzB4zs62hMVi1y7qb2QwzWxX63i3ecdImAISlnLgAGAJcEUolEUSVwE/dfQhwGnBDgP8WtW4ClqW6EGngQeB1dz8OGEpA/yZm1hv4L6DQ3U+kpoPK5aktVYv6KzC23rJJwJvuPgh4M/Q6prQJAMAIYLW7r3H3cuAZ4JIUlykl3H2Tu38U+nkPNSd5YHM3mNnRwIXAn1JdllQysy7AF6jpdYe7l7t7aey92rQsIC809qg9ED+daBvh7m9T0+My3CXA46GfHwfGxTtOOgWA3sD6sNcbCPBFr5aZ9QeGA/9JbUlS6gHgZ0Cwk73AAKAE+EuoOuxPZtYh3k5tkbsXA78GPgU2Abvc/Y3UlirljnT3TaGfNwNHxtshnQKA1GNmHYHngR+7++5UlycVzOwiYKu7z427cduXBZwC/N7dhwP7SOAxvy0K1W9fQk1Q7AV0MLOrUluq9BEaiBu3j386BQCljQhjZtnUXPyfcvcXUl2eFBoFXGxma6mpFjzXzJ5MbZFSZgOwwd1rnwafoyYgBNGXgE/cvcTdK4AXgDNSXKZU22JmPQFC37fG2yGdAkAiKScCwWoyC/4ZWObuv011eVLJ3W9x96PdvT81n4lZ7h7IOz133wysN7PaCau/SM0o+yD6FDjNzNqHzpcvEtAG8TDhKXnGAy/F2yGdsoFGTDmR4mKlyijg28AiM5sfWvYLd381hWWS9PAj4KnQTdIa4LspLk9KuPt/zOw54CNqes3NI0BpIczsaWA0kG9mG4DbgHuAZ83sGmAd8M24x1EqCBGRYEqnKiAREWlBCgAiIgGlACAiElAKACIiAaUAICISUAoAIiIBpQAgIhJQ/x9MritsYI+OQAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D5XfGJ5wOcYC"
      },
      "source": [
        "How about fitting a deep Relu-based neural network? \n",
        "\n",
        "Following based partially on https://medium.com/@benjamin.phillips22/simple-regression-with-neural-networks-in-pytorch-313f06910379"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VG_E5EbHMIli"
      },
      "source": [
        "\n",
        "def train_model(x,y,net,opt,niter=10000):\n",
        "  x_fit = torch.unsqueeze(x,dim=1)\n",
        "  y_target = torch.unsqueeze(y,dim=1)\n",
        "  loss_history = []\n",
        "\n",
        "  # Training loop\n",
        "  for i in range(niter):\n",
        "    opt.zero_grad()\n",
        "    \n",
        "    # Compute current estimate\n",
        "    prediction = net(x_fit)\n",
        "    loss = rmse(prediction, y_target)   \n",
        "     \n",
        "    # Do some recordings for plots\n",
        "    loss_history.append(loss.item())\n",
        "    #p_history.append(p_hat.detach().numpy().copy())\n",
        "    \n",
        "    # Update model parameters\n",
        "    loss.backward()\n",
        "    opt.step()\n",
        "    if (i%1000 == 0):\n",
        "      print(\"Iteration %d\" % i,)\n",
        "      print(\"loss = %s\" % loss.item())\n",
        "\n",
        "  plt.subplot(2,1,1)\n",
        "  plt.plot(loss_history)\n",
        "\n",
        "  plt.subplot(2,1,2)\n",
        "  plt.scatter(x,y.detach().numpy())\n",
        "  x_fine = Variable(torch.linspace(0,10,200), requires_grad=False)\n",
        "  x_fine = torch.unsqueeze( x_fine,dim=1) \n",
        "  y_fine = net( x_fine )\n",
        "  plt.plot(x_fine,y_fine.detach())\n",
        "  print( net.parameters() )"
      ],
      "execution_count": 328,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RgIbulGbaSYk",
        "outputId": "c1ddcebc-d13e-4272-e928-c11a7213994a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 622
        }
      },
      "source": [
        "import torch.nn.functional as F\n",
        "\n",
        "class Net(torch.nn.Module):\n",
        "    def __init__(self, n_feature, n_hidden, n_output):\n",
        "        super(Net, self).__init__()\n",
        "        self.hidden = torch.nn.Linear(n_feature, n_hidden)   # hidden layer\n",
        "        self.predict = torch.nn.Linear(n_hidden, n_output)   # output layer\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = F.relu(self.hidden(x))      # activation function for hidden layer\n",
        "        x = self.predict(x)             # linear output\n",
        "        x = torch.exp(x)\n",
        "        return x\n",
        "\n",
        "#loss_func = torch.nn.MSELoss()  # this is for regression mean squared loss\n",
        "\n",
        "net = Net(n_feature=1, n_hidden=20, n_output=1)     # define the network\n",
        "\n",
        "learning_rate = 5e-2\n",
        "#opt = torch.optim.SGD(net.parameters(), lr=learning_rate, momentum=0.5)\n",
        "opt = torch.optim.Adagrad(net.parameters(), lr=learning_rate)\n",
        "\n",
        "train_model(x,y,net,opt)\n"
      ],
      "execution_count": 329,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration 0\n",
            "loss = 0.6506519317626953\n",
            "Iteration 1000\n",
            "loss = 0.10605815798044205\n",
            "Iteration 2000\n",
            "loss = 0.10471247136592865\n",
            "Iteration 3000\n",
            "loss = 0.10419288277626038\n",
            "Iteration 4000\n",
            "loss = 0.10386976599693298\n",
            "Iteration 5000\n",
            "loss = 0.10233356058597565\n",
            "Iteration 6000\n",
            "loss = 0.10129152983427048\n",
            "Iteration 7000\n",
            "loss = 0.10092367231845856\n",
            "Iteration 8000\n",
            "loss = 0.10063023865222931\n",
            "Iteration 9000\n",
            "loss = 0.10039833933115005\n",
            "<generator object Module.parameters at 0x7f85d9b12d58>\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rGA6XO3cYrj3"
      },
      "source": [
        "Let's create a data set that is more challenging -- multiple Gaussian peaks."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vylWfQqjQ6Gp",
        "outputId": "cb8f42af-cbbc-4614-b2bc-00768bd71e7e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        }
      },
      "source": [
        "y2 = forward_gaussian(x, torch.tensor([2,0.1,2]) )+ forward_gaussian(x,[5,1,1])\n",
        "y2 += 0.1* torch.randn(n)\n",
        "plt.scatter(x,y2)"
      ],
      "execution_count": 330,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f85d8428978>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 330
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tFEXLuR6Y1WO",
        "outputId": "c7735c94-652b-457f-8e25-2601d7314785",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 622
        }
      },
      "source": [
        "net = torch.nn.Sequential(\n",
        "        torch.nn.Linear(1, 20),\n",
        "        torch.nn.ReLU(),\n",
        "        torch.nn.Linear(20, 1),\n",
        "    )\n",
        "learning_rate = 5e-2\n",
        "#opt = torch.optim.SGD(net.parameters(), lr=learning_rate, momentum=0.5)\n",
        "opt = torch.optim.Adagrad(net.parameters(), lr=learning_rate)\n",
        "train_model(x,y2,net,opt)"
      ],
      "execution_count": 331,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration 0\n",
            "loss = 0.8984338045120239\n",
            "Iteration 1000\n",
            "loss = 0.3373429477214813\n",
            "Iteration 2000\n",
            "loss = 0.3371569514274597\n",
            "Iteration 3000\n",
            "loss = 0.3371359407901764\n",
            "Iteration 4000\n",
            "loss = 0.3371322453022003\n",
            "Iteration 5000\n",
            "loss = 0.33713123202323914\n",
            "Iteration 6000\n",
            "loss = 0.3371293246746063\n",
            "Iteration 7000\n",
            "loss = 0.33713024854660034\n",
            "Iteration 8000\n",
            "loss = 0.33712896704673767\n",
            "Iteration 9000\n",
            "loss = 0.337127685546875\n",
            "<generator object Module.parameters at 0x7f85d9ca02b0>\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7iDkXNbtZeEs",
        "outputId": "e3297943-cbbd-4084-cffc-da097bf1522b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 962
        }
      },
      "source": [
        "net = torch.nn.Sequential(\n",
        "        torch.nn.Linear(1, 20),\n",
        "        torch.nn.LeakyReLU(),\n",
        "        torch.nn.Linear(20, 10),\n",
        "        torch.nn.LeakyReLU(),\n",
        "        torch.nn.Linear(10, 1),\n",
        "    )\n",
        "learning_rate = 5e-2\n",
        "#opt = torch.optim.SGD(net.parameters(), lr=learning_rate, momentum=0.5)\n",
        "opt = torch.optim.Adagrad(net.parameters(), lr=learning_rate)\n",
        "train_model(x,y2,net,opt,20000)"
      ],
      "execution_count": 332,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration 0\n",
            "loss = 0.5471477508544922\n",
            "Iteration 1000\n",
            "loss = 0.2512850761413574\n",
            "Iteration 2000\n",
            "loss = 0.22438602149486542\n",
            "Iteration 3000\n",
            "loss = 0.20600242912769318\n",
            "Iteration 4000\n",
            "loss = 0.19369515776634216\n",
            "Iteration 5000\n",
            "loss = 0.1825144737958908\n",
            "Iteration 6000\n",
            "loss = 0.17274044454097748\n",
            "Iteration 7000\n",
            "loss = 0.16503643989562988\n",
            "Iteration 8000\n",
            "loss = 0.15767067670822144\n",
            "Iteration 9000\n",
            "loss = 0.15269309282302856\n",
            "Iteration 10000\n",
            "loss = 0.14784452319145203\n",
            "Iteration 11000\n",
            "loss = 0.14386367797851562\n",
            "Iteration 12000\n",
            "loss = 0.14025616645812988\n",
            "Iteration 13000\n",
            "loss = 0.1374252587556839\n",
            "Iteration 14000\n",
            "loss = 0.1351102739572525\n",
            "Iteration 15000\n",
            "loss = 0.1326572299003601\n",
            "Iteration 16000\n",
            "loss = 0.1306663453578949\n",
            "Iteration 17000\n",
            "loss = 0.12873081862926483\n",
            "Iteration 18000\n",
            "loss = 0.12697412073612213\n",
            "Iteration 19000\n",
            "loss = 0.12497102469205856\n",
            "<generator object Module.parameters at 0x7f85d9ca04c0>\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ZjN3+Iq6x/62LbA+rbvAVYAvw31EfumBNDvGhHffcqG19GauBaCtRCXYYsVVilaRqo9bl/XhhXR7vAQJY9X03Z/P4AHOBtfZrfo59p2+GcW3FqreMfMfut597jf35rgbeA65Mtn+n95hhXFn73Ozv7Dv2e30KKM00Lnv9I8BXY56bz+PllBsK+h3T282VUsoFiqXOWimlVAKarJVSygU0WSullAtkbVqvaOPHjzeNjY252LRSSo1IK1euPGCMmeD0eE6SdWNjIytWrMjFpkecJauaWPzSJprbuqmvK2fBvOnMn5O3mzeVUkVCRBIN35CbZK1Ss2RVE9999gO6AyEAmtq6+e6zHwBowlZKDaJ11gW0+KVN/Yk6ojsQYvFLmwoUkVKqWGmyLqDmtu601iulRi9N1gVUX1ee1nql1OilybqAFsybTrnfO2hdud/LgnnTCxSRUqpYaQNjAUUaEbU3iFIqGU3WBTZ/ToMmZ6VUUloNopRSLqDJWimlXECTtVJKuYAma6WUcgFN1kop5QLaGyTPdOAmpVQmNFnnkQ7cpJTKlFaD5JEO3KSUypQm6zzSgZuUUpnSZJ1HOnCTUipTmqzzSAduUkplShsY8yh24Kajasr4zmUnaeOiUiopTdZ5Fhm46a0PD/CFh95hZn1NoUNSSrmAVoMUyPJtBwmFDa9vOVDoUJRSLqDJukDWNbcD8M721gJHopRyA03WBbK++TAA72w/iDGmwNEopYqdJusCONTZR/PhHk6YWMWhrgBbWo4UOiSlVJHTZF0AkSqQL503DYDl2w8WMhyllAtosi6AdXYVyGWzjuKomjLe0WSdF0tWNXHeoleZtvB5zlv0KktWNRU6JKVSpl33CmBdczv1tWWMqSxhzjF1fLC7rdAhjXg6iJZyOy1ZF8CmvR2cPNnqXz2roZYdrV209wQKHNXIpoNoKbfTZF0Ae9t7aBhjjQcyw74pZoNdj61yo8lhsCyn9UoVG60GybOeQIjD3QEmVpcC9N/BuLa5nbOOHVfI0FwnnYkcvCKE4nSR9IrkOkylskKTdZ7t7+gFYGJ1Wf//E6tL+xsdVWrSqYNesqopbqIGHNcrVWy0GiTPWuxkPcEuWYNVul6v1SBpSbUOOpLUnTTo8LTKJZKWrEXkYeDTQIsxZlbuQxrZ9sdJ1rMaanl9ywF6AiHKYoZQVfGlOpFDvKQekenwtDqPpiqEVKpBHgF+Djya21BGh/0dPQD9ddZglaxDYcOmvR2cdnRdoUJzlfq68riNg7ETOSSahecnV5/Sn2Q7e4O8sfUAW1uO4BXh18t2xk3G2gVQFUrSZG2MeV1EGnMfyujQ0tGLR2BcVXSyrgVgbfNhTdYpWjBv+qCkCfFLyk5JvaGunNOPGcN/vLmdVze2sHzbQfpC4SHPi03GiapfNFmrXMpanbWI3CoiK0Rkxf79+7O12RFnf0cv46pK8XoGeiFMGVNOTZmv/zZ0ldz8OQ385OpTaKgrR7CSb3RJOSLe7Dw+jxAIhblg8Wvc/Yf1NLV1c9O5U/ntLWdxVE3ZkH1F14XrPJqqULLWG8QY8wDwAMDcuXO1id1BS0cvE6JK1QAiwsz6WtY1aY+QdEQmckjkghMnMOeYOt7+sJXIlzIYNrR09FJb7ue2i47nlguO7X/+vvaeuNuJJONUq1+UyjbtupdnLR09TKwpHbJ+VkMNj769k2AojM+rnXQi0m3MM8awfk87r21s4dWNLaz6qA2nksPh7gD3vLiRCdWl/dt0SsaTa60Sd6rVL0plmybrPNvf0cuMyUOn8ppZX0tvMMyH+zuZflR1ASIrDtHJua7Cz5GeIIGwlW6dGvO6+0K8ufUAr2xs4U+bWthz2CodnzallqoyHx09Qcf9BcKGu55b17+9eMkYrDtNjTFD5tHU3iAqX1Lpuvc4cCEwXkR2A3caYx7KdWAjUShsOHCkb1C3vYj+OxmbDo/aZB3b0+JQ19DxUiL1x2dMHcNrm6zS81sfttIXDFNZ4uX8EybwzU9O5MLpE5hYXca0hc8n3W9b98B+YpPx5Noypo6r5L83tPCvr27lG5eckFL1i1LZlkpvkBvyEchocLCzj1DY9N+9GO3YCVWU+T2sa27nmjMKEFwRSNQnOlpTWzfn3/MaAI3jKrjxrKlcfNJEzpw2lhLf4Cokp2qNRGKTcThsuO6Bt7l36WbuXbqZBi1NqwLQapA8aonTxzrC6xFOnlzD2lF823mqPSr8HuE7l53ExSdN5NgJVQmf61StEW1MhT/hNp5b08wHuwc+F+1brQpBW7LyKN7di9Fm1tewobmdcHh0dqZJpUeF3yv84zWn8pXzj02aqGFwFz+n7d155cyE21j80iZ6goP7YDvd2q6TG6hc0WSdR5FuYZPi9OUFmFVfS0dvkF2HuvIZVtGI1yc6elC8SdWlLL72NK4+Y0pa250/p4E3F17MjkVX8LPrZg/qm7342tOSlo6dSvzR1SuR+vamtm4MA6VvTdgqW7QaJI92tnbh80h/N7BY/XcyNrUzdVxlPkMrCtGNe01t3Xg9Qjhs+PpFx3HHJ07En4UujZk0Diaq937+/T1ccepkvbNR5ZyWrPNoZ2sXR4+tcOxHfeJRVfg8MuKHS01UXfCZ0+r54jlT8XuFidWl/PaWs1kw76SsJOpMxSvxl/k8TBtfye1PrGLp+n16Z6PKOS1Z59GO1k6OGVvh+Hipz8sJk6pZO4JvO080ENI5x43jb3+3mje3tnLpzKNYdM0p1FWUFDJcYGh3vkjf6ktOnsiNDy7n64+9x9jKElo7+4a8Vu9sVNmiyTpPjDHsbO1i7tQxCZ83s76G1za2YIxBRtgsJktWNfGt360ZMuB/dyDED/+4HmMMPYEwi64+hes+dnRRvX+n6pNHv3wWN/xyGVtaOijxegYNBqV3Nqps0mqQPDnY2ceR3mDSuuhZ9TW0dvaxr703T5HlR6RE7TQzy8HOPurryvnD33yc6888pqgSdSK1FX5+ffOZNI6rBIHxVSUJB5ZSKlNass6THa1WD4/G8c7VIAAzG6xGxnXNhznKoSHSjZLd8FJV6uPZr51Lqc99ky+MqyrlsVvO4rp/X8aBjl5+f9t5nDpFh7pV2aUl6zzZ2doJkLRkffLkGkQYccOlJmpoK/F6+PH8Wa5M1BETq8t47CtnUVvh5wsPvaPTtKms02SdJztau/CINXZ1IlWlPqaNq2TtCBsu1amhzQPcc+2pI6K6oL6unMdvOZuKEi9feGg5W/Z1xH2e3jyjMqHJOk92tnZSX1eeUulxRn3NiCtZL5g3nZKY7ndlPg/3Xjd7RCTqiKPHVvDYV87C4xE+/+BydhzoHPS43jyjMqXJOk92tHZZjVApmNVQS1NbN4fidAVzo95giA+aDtMXCuOzZ8hpqCtn0TUjo0Qd69gJVTz2lbMIhg1/+ctl7DrY1V+avuPJ1SnNyq5ULG1gzANjDNv2H+Gq2fUpPT8yXOr6Pe2cd/z4XIaWNbHjUBtjDe4/oboUn1dobuvhpnOm8t3LTx4VM7ifOKmaX998Jjc8sIz5v3iTzt7gkPFFounNMyoZLVnnwe5D3XT0BDk5zqQD8Qzcdu6OeuvYS/tDXQHaugMYrGnMmtt6uOX8adx91axRkagjZtbX8uubz+JgZ1/CRA1684xKTpN1HkTqnyNJOJmxlSXU15a5pt46lXGoX/hgb56iKS6nHV3nOK1YtItOmpDzWJS7aTVIHqxvPowI/PVvVrL3cE9KU0HNqK8tujFCnOZDTOUSfjRf5jekMAHCaxv35yka5VZass6DVza2gIE9h3tS7gEwq6GGbQc66ex1nj8wm5J1J0vUiyGVS/jRfJkfbyCoWOnOZqNGH03WebBxT8eQS+FkPQBm1tdiDGzcm/uqkFS6kyUaAvSvzm0k0d3ho32MjGQTIAAIaPc9lZAm6xw72NnnOB5GoqqBWQ2RCXRzn6wTJeKIRAPw/+y/N1Pu9zK2whoXY0yFn7pyv46RESUyAcLPrpsd93ED2n1PJaR11jmW6LbjRFUDR9WUMbayJGf11tH1z04NYNEJOtEA/LMaavnpdbNHdVVHqubPaeCOJ1fHfWw01+ur5LRknWORZFsWM+t2sqoBEWFmju5kjK32cBKdfJ3qXa84ZTK/veVsTdRpcKoO0WOoEtFknWPrmtupry1j0TWnDpr7L5WqgZn1tWze10Ffkj666Uqlq13syWT+nAZ+PH8W1aXWxZjXI9zxiRP4xedPx+txx3CmxSLeic8rwrc+eWKBIlJuoNUgObZ+Tzsz6mszmvtvZn0NgZBh874OZjWk1kc7FYkutwXidi3cdbCLn7+6lQ67d8rE6tKUb59Xg8XOPFNd5qO9J8jb21qZP6cBj8PJz6nrpBodNFnnUHdfiG37j3D5KZMzev2sqLGts5msneqfG+rKeXPhxUPWP7emmW8/vYaewEAJf8/hnv7puDRhpC/25P3TpZu575UtlPo9/OiqWUMmX0g0HZoe/9FBk3UObdjbTtgMjPWRrqljK6gq9WW93nrBvOmDfvgQvw79SG+QO3+/jmfe2z1kxDwYPHu3lvqG545PnEBvMMz9f/6QUp+XH1xxMr9f3dx/TD0icadD09nTRw9N1jm0vv8288yStccjnDy5OutjhDhNABv9o1+9q43bn1jFroNd3H7JCdz3ypa422pu69ZSXxaICN+5dDo9gRAPvbGdj1q7eGPrgf5j6tT9M/oKSU+YI5sm6xxa19xObbk/4c0Qycysr+XJd3cRCpusNuQ51aGHwoZ/f/1D7n15M5Nqynjy/57DxxrH8vTK3XGrTurryhP209ZkkToR4c4rZ9AbDPP4Ox+l9hoGbqbRE+bIpr1Bcmh982FmTK4Z1uSvM+tr6A6E2B4ziH0qlqxqYvbdL9O48HkaFz7PnB++nPAuuT2Hu7nxweXc8+Im5s06ihduP5+PNY4F4vdgiFSdODVYar/h9IkI/zB/VsrPj9xMk8qNTcrdNFnnSDAUZuPeDmZkWAUCA5e1AJ+9/620bkdesqqJBU+toa070L/uUFeABU+vibudF9fu5bL7/oc1u9tYfO2p/PyGOdSW+/sfj75lOrb7oVP/YO03nBmPR6hPY7Lk5rZuPWEWUL6madNqkBzZdqCT3mA44/rq2HrgQ12BtC5rF7+0iUB4aD1nIGQGVU909QX50R838Pg7H3HqlFruu34O08bH75LnVHWSaoOlSt23Lz2Jhc+8P2gcbIG4NzFFTopO1VQqd/LZXqMl6xyJ3LmY6hjWsYZ7WZuoRBV5bF3zYa781zd44t2P+OsLj+Ppr57rmKgTSVTqVpmZP6eBRdecOqiEfc5x4xyrohJVU+XbaJoQOJ/VT1qyzrJI1UWklLO26TDTj6pOezvDvaxNNJbH5NoyHvyfbdzz4ibGVPp57OazOHeY04dlctOPSixyTHsCIb78yLss29bKF89pZOn6fY49PgrVGyT6ex99BTDSGzrzWf00KpN1tro4xW7nopMm8MzKpkFn2h8sWYvXI2lv3ynZpnpZu2DedBY8tWZIVYjPA9Xlfn78/AY+OWMSf3HiBBY8/b529ypiZX4vD940ly8+9A6/WbaT+288g0/MmDTkefk4Ycb77cDgnihOwwGPxO/VcH+n6RDj0H9zOObOnWtWrFiR0Wuz2Vc0lS8WWJeL6V62x9ZVgXOdotOdgcm2v+DpNQRCA1v0euCfPzs75TiXrGrirufW9TcyVpV6ASEYDvP/Pj2DCr+X7/3n2mEfC5UfHT0BbnxwORv2dPDgTXO54MTcTAXm9BuM950v93sp83s41BVIsEXrt7F90RUJt5+NGPPN6Zhk8hsSkZXGmLmOjxdTss7mG0/3i5VuQj1v0aspz+4R/UVNVaQ3R3TJ2APce13qyTqiJxBi0X9t5JG3dnDy5Br+9YbZHD+x2vE9ZHJyUfnR1tXHDb9czvYDR7j549NYsqo5qwkr0W8wunovXV4RwsZQW+6nsy84qBAS+xtPloizmSeyIVsnjmTJuqiqQbJ5c4XTtpxGm0u3jimd52dySRSvN0cYuPsP69I6Fpv2dvCNx1exaV8HN398Gt++dDqlPqshSrt7uU9dRQm/uflMrviXN/jFaw4NNWkAAAusSURBVB/2rx9u3XBsW0u0yG9wON+LyB2Y0V1JY7cfr/Qe730NN09ku1Ser/aaokrWiWYjWbKqKeUzb6JtOUk3oSZqwIuWaYu8U/yHugKDjoUTYwyPvr2Tf3hhAzVlfh750se4cPrEQc/JZ32byp7/2XKAlvaeIeu7AyG+/fT7vL55P1PHVdI4voLGcZU0jquktsIfZ0uWeFdxsSK/tXRL1t44Y5o4bR9SS8TDKWS4eWiEokrWk2rK2BvnSwiw4Ok1/cupHGynL1ZduZ/eYHjYfYLj9S2Ot6+7PjMzoy9Boh/GHU+uZvFLmxxLBK1Hevn20+/zysYWLpo+gcWfPY3xVaUpvQftH13cIsnGaYTzvlCYZdtaeTamu1xdhZ+p4yqZNq6iP5FPtRP5nb9fmzBRw8Cwucm+8xF+r7D42tP4psOsOLHq7JNJKonY6bfhEWHawucTlpZTORkUS314rJSStYhcCtwHeIEHjTGLsh2IMYbDcS6RIgIhw91/WEdFiS+lSyCnRHTXZ2YC2eniVOrzJPziVpb6Mv6QF8yb7jj9EzifpF7fvJ9vPbWGw90B7rpyBjed2+h4u3sqAzqp4pJs4ohIe0NPIMSug11sP9DJztYudrRa/6/YeYjfr2kmnaaqyAk88r2IbrR2Ern5KtXS+JGeIEtWNVFX4Y/bphQ7a1G8k0akBJ+otJzsZBCv5L3gqTXc/Yd1tHUFCvobSdrAKCJeYDPwSWA38C5wgzFmvdNrMmlgDITC/Hb5R7zwwR6Wbz+Y1mshfiNers6Q8Ro4Uo0pHbPvfjnpjyLy4+wNhlj84iYefGM7J06q4l9umMNJR2V+q7sqTtMWPu84FVuqjWy9wRC7Dnazs7WTHa1d/OiPjj9lBKvU2xOwrkbLfB56Q+GUkr0AP71udsql8TEVfo70BIeU8iOl9NhGxuh69FR7YSVrVE+n40Ak5juvzOzqOdawe4OIyDnAXcaYefbf3wUwxvzE6TXD6boH0Ljw+bRfE+k2N66yhBvPnsqnZk6i3O+lvMRLhd9HWYmHEq9nWIMqRaT6gQ63V0WqJwWwvtCBkOGL50zle5efTFmc+RKV+zl997wi/PPnTssoacz54ctxS7Plfg9zG8fy5tYDJKkliavM5+Ezs+s5cKSPVze2pL8BW125n9V3firuY0tWNSW8Am2I6rIb76YdGHySS3QydBLvZJKJbPQGaQB2Rf29Gzgrzo5uBW4FOOaYY9IMc7C6cn/cEmVtmY+vXXQ8//TypkFdf2Dg4Ld29nHfK1vijr/sEfoTeNhY/VYDIUNduZ+vnD+Nr/7FcfjiDLIfK5WGjGzU/UZXUyQ7OQRChhKvh9OPGaOJegRzqt4bTre1O6+cOaRPv98r/OTqU1n80qaMErVHYExlCX/evD9pH+xk2roDnPGjpbR29jGpupRvXHIC15wxBYB7XtyY8LVNbd383VOrwUDQfh+GgcJdQ8wVdyaNqLHj7eRKKiXra4FLjTFfsf/+AnCWMeY2p9cMt2Qdr3Xa7xEWf/a0IbOSCMRtbBlbUcLfXznD6q7XZ3XZ67GX1+9pZ/m2g0Naqf1e4bQpdcysr6GuogSPCL3BEL3BMD0B6//eYJil6/cOmuIq1uSaMr5z2UlZ/fB+sOQDfrMs+RjH2kd65MtF9Z7TNtMpaUb6UsfGZIzhdyt28f1nP+hPmPFeKwLBTM4MwyBiJW5rWTDGZHRyAqgq9TG+qoQ/Lbgow1iGX7JuAo6O+nuKvS5nkjV8RfdrnOZQZXKoq2/IFzhRX1KAEp8HEXj2vab+iWF9HqHU56HM76XU56HU72VMRQl723sG1duVej0suuYU/s/pU4b13uNZsqqJZ1amdsi1j/TIl4t+vU7bTLWkGV2YiiUilPq8VJUNXDFXlnjxez0c7h5otIOhdxc7qSnz8dULj+P+P31Ie08w6fOd3HbR8QAYAwbD5r1HeGXjvrQTdmWpl8/NPZrK0txd1aaSrN8FThCRaVhJ+nrgL3MWkS3VL2SqfYVTqf/t6g3x1FfPBawZU4wxjtUi+ezek6wHQDTtI62yKV61i98jlPg8dPZZ65J1Uf3Bkg94bNlHg0roYYPja6J/V04nio6eIF+78Hjqa8v55pOr065nBusq9FufGlxVed6iV9NO1H6v8A/zc3/3ZNJkbYwJishtwEtYXfceNsasy2lUaUi1r3AqCS860VlTaDk3RuZzlLl0SsvaR1pl03C7dy5Z1TQkUUPyvs0/tYdVcGpQNViJdcG86Xz+7GPi7iPC7xUwDKpWdWpTSvZbq/B7MEC3XQ2azd4gyaTUz9oY8wLwQo5jyUiqX6ZkH0Ix3wyS6qXomAq/9pFWWZdOwSQ26Xb2Bh2TaKK+zZF+0oluxIk87ydXn8LcqWP791tX4ccYhlSxpHLCSfZbM0jBxiApqoGccilRd7vYFuFU5asqJFn3JNDR8lThpdPVFJL3bY48nqytKZuN6qm8h1w14idrYBw1M8U4zaTxs+tm8+bCizMe1a+prRvDwFk+F7NizJ/TQLnf+aPSmVlUMUinbUUYqLJLdlfh/DkNvLnwYsdKyWw2qkfPeuSkUI34oyZZZ3vqqXzPJu3UVVAgo5ONUtmWahIT4PNnHzOob3M8sevzNTFz5OTglLAL1Yg/apI1DHwI2xddMewEl+/hRXUGcVXsnL6LYyr8gwpJP71uNj+ef0r/46nOH5nveSaLaV5LKLJR99wk38OL6gh5qtg5fUeT9ZZItZNAvgceK7aBzkZNA2O2FWK2imIdulGpCP2OZs5V03q5jX4xlVLZ4qppvdwmnzfGKKVGt5yUrEVkP7Azw5ePBw5kMRw30Pc88o229wv6ntM11RjjOGV9TpL1cIjIikSXAiORvueRb7S9X9D3nG2jquueUkq5lSZrpZRygWJM1g8UOoAC0Pc88o229wv6nrOq6OqslVJKDVWMJWullFIxNFkrpZQLFE2yFpFLRWSTiGwVkYWFjifXRORoEXlNRNaLyDoRub3QMeWLiHhFZJWI/LHQseSDiNSJyNMislFENojIOYWOKddE5Jv293qtiDwuImWFjinbRORhEWkRkbVR68aKyFIR2WL/PyZb+yuKZC0iXuAXwGXADOAGEZlR2KhyLgh8yxgzAzgb+PooeM8RtwMbCh1EHt0HvGiMOQk4jRH+3kWkAfgGMNcYMwtrOsDrCxtVTjwCXBqzbiHwijHmBOAV+++sKIpkDZwJbDXGbDPG9AFPAFcVOKacMsbsMca8Zy93YP2AR/y96yIyBbgCeLDQseSDiNQCFwAPARhj+owxbYWNKi98QLmI+IAKoLnA8WSdMeZ14GDM6quAX9nLvwLmZ2t/xZKsG4BdUX/vZhQkrggRaQTmAMsLG0le/Az4NhB/NoWRZxqwH/gPu+rnQRGpLHRQuWSMaQL+CfgI2AMcNsa8XNio8maSMWaPvbwXmJStDRdLsh61RKQKeAa4wxjTXuh4cklEPg20GGNWFjqWPPIBpwP/ZoyZA3SSxUvjYmTX016FdaKqBypF5MbCRpV/xuoXnbW+0cWSrJuAo6P+nmKvG9FExI+VqB8zxjxb6Hjy4DzgMyKyA6uq62IR+U1hQ8q53cBuY0zkqulprOQ9kn0C2G6M2W+MCQDPAucWOKZ82ScikwHs/1uyteFiSdbvAieIyDQRKcFqjHiuwDHllIgIVj3mBmPMvYWOJx+MMd81xkwxxjRifcavGmNGdInLGLMX2CUikSl9LgHWFzCkfPgIOFtEKuzv+SWM8EbVKM8BN9nLNwG/z9aGi2I8a2NMUERuA17Cajl+2BizrsBh5dp5wBeAD0Rktb3ue8aYFwoYk8qNvwEeswsi24AvFTienDLGLBeRp4H3sHo9rWIE3nouIo8DFwLjRWQ3cCewCPidiNyMNUz057K2P73dXCmlil+xVIMopZRKQJO1Ukq5gCZrpZRyAU3WSinlApqslVLKBTRZK6WUC2iyVkopF/hfEsFGPNOaAiwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hxw3uDAQbL__"
      },
      "source": [
        "Even harder -- 4 Gaussians"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HGKwAMUNZvZn",
        "outputId": "b88f0752-cb3f-4eea-c1ea-3a7538c10a56",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "y3 = forward_gaussian(x, torch.tensor([2,0.1,2]) )+ forward_gaussian(x,[5,2,1]) + forward_gaussian(x, torch.tensor([4,0.1,5]))+forward_gaussian(x, torch.tensor([9,0.2,3]) )\n",
        "y3 += 0.1* torch.randn(n)\n",
        "plt.scatter(x,y3)"
      ],
      "execution_count": 343,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f85d7a9eda0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 343
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xhbba-45cMgl"
      },
      "source": [
        "This fitting problem is impossible for single layer NN"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2NjCSaz4bSuc",
        "outputId": "9830f309-bc61-4d7f-a31c-6334c750a53e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 622
        }
      },
      "source": [
        "net = torch.nn.Sequential(\n",
        "        torch.nn.Linear(1, 100),\n",
        "        torch.nn.ReLU(),\n",
        "        torch.nn.Linear(100, 1),\n",
        "    )\n",
        "learning_rate = 5e-2\n",
        "#opt = torch.optim.SGD(net.parameters(), lr=learning_rate, momentum=0.5)\n",
        "opt = torch.optim.Adagrad(net.parameters(), lr=learning_rate)\n",
        "train_model(x,y3,net,opt)"
      ],
      "execution_count": 345,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration 0\n",
            "loss = 2.3479881286621094\n",
            "Iteration 1000\n",
            "loss = 0.8736760020256042\n",
            "Iteration 2000\n",
            "loss = 0.8651277422904968\n",
            "Iteration 3000\n",
            "loss = 0.8542529344558716\n",
            "Iteration 4000\n",
            "loss = 0.8475580215454102\n",
            "Iteration 5000\n",
            "loss = 0.8427165150642395\n",
            "Iteration 6000\n",
            "loss = 0.8387426733970642\n",
            "Iteration 7000\n",
            "loss = 0.8352997899055481\n",
            "Iteration 8000\n",
            "loss = 0.8322075605392456\n",
            "Iteration 9000\n",
            "loss = 0.8293583989143372\n",
            "<generator object Module.parameters at 0x7f85d85650f8>\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q-TwAyRDcRch"
      },
      "source": [
        "But its within reach of a 2-layer NN"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2Jrq2MZzbr67",
        "outputId": "f4e9693b-9755-4425-fc5f-93ae116f7685",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 622
        }
      },
      "source": [
        "net = torch.nn.Sequential(\n",
        "        torch.nn.Linear(1, 20),\n",
        "        torch.nn.LeakyReLU(),\n",
        "        torch.nn.Linear(20, 10),\n",
        "        torch.nn.LeakyReLU(),\n",
        "        torch.nn.Linear(10, 1),\n",
        "    )\n",
        "learning_rate = 5e-2\n",
        "#opt = torch.optim.SGD(net.parameters(), lr=learning_rate, momentum=0.5)\n",
        "opt = torch.optim.Adagrad(net.parameters(), lr=learning_rate)\n",
        "train_model(x,y3,net,opt,10000)"
      ],
      "execution_count": 346,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration 0\n",
            "loss = 1.1564594507217407\n",
            "Iteration 1000\n",
            "loss = 0.872823178768158\n",
            "Iteration 2000\n",
            "loss = 0.8643032312393188\n",
            "Iteration 3000\n",
            "loss = 0.8434626460075378\n",
            "Iteration 4000\n",
            "loss = 0.8361644744873047\n",
            "Iteration 5000\n",
            "loss = 0.8336700797080994\n",
            "Iteration 6000\n",
            "loss = 0.8306252956390381\n",
            "Iteration 7000\n",
            "loss = 0.8291360139846802\n",
            "Iteration 8000\n",
            "loss = 0.828275740146637\n",
            "Iteration 9000\n",
            "loss = 0.8281446099281311\n",
            "<generator object Module.parameters at 0x7f85d8565308>\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4k7OR3-ScV1A"
      },
      "source": [
        "More channels in the 2 hidden-layer net -- works better!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xQ1n1wkhb3Py",
        "outputId": "8b976fd0-58df-4672-a938-544ff73e7f63",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 962
        }
      },
      "source": [
        "net = torch.nn.Sequential(\n",
        "        torch.nn.Linear(1, 200),\n",
        "        torch.nn.LeakyReLU(),\n",
        "        torch.nn.Linear(200, 100),\n",
        "        torch.nn.LeakyReLU(),\n",
        "        torch.nn.Linear(100, 1),\n",
        "    )\n",
        "learning_rate = 5e-2\n",
        "#opt = torch.optim.SGD(net.parameters(), lr=learning_rate, momentum=0.5)\n",
        "opt = torch.optim.Adagrad(net.parameters(), lr=learning_rate)\n",
        "train_model(x,y2,net,opt,20000)"
      ],
      "execution_count": 347,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration 0\n",
            "loss = 1.7383670806884766\n",
            "Iteration 1000\n",
            "loss = 0.799701988697052\n",
            "Iteration 2000\n",
            "loss = 0.7395354509353638\n",
            "Iteration 3000\n",
            "loss = 0.6609401106834412\n",
            "Iteration 4000\n",
            "loss = 0.5791382789611816\n",
            "Iteration 5000\n",
            "loss = 0.5247427225112915\n",
            "Iteration 6000\n",
            "loss = 0.47608333826065063\n",
            "Iteration 7000\n",
            "loss = 0.4298020899295807\n",
            "Iteration 8000\n",
            "loss = 0.39238160848617554\n",
            "Iteration 9000\n",
            "loss = 0.3617577850818634\n",
            "Iteration 10000\n",
            "loss = 0.33564528822898865\n",
            "Iteration 11000\n",
            "loss = 0.30997493863105774\n",
            "Iteration 12000\n",
            "loss = 0.292263388633728\n",
            "Iteration 13000\n",
            "loss = 0.27756762504577637\n",
            "Iteration 14000\n",
            "loss = 0.26488202810287476\n",
            "Iteration 15000\n",
            "loss = 0.25256916880607605\n",
            "Iteration 16000\n",
            "loss = 0.2410452961921692\n",
            "Iteration 17000\n",
            "loss = 0.23066698014736176\n",
            "Iteration 18000\n",
            "loss = 0.21990860998630524\n",
            "Iteration 19000\n",
            "loss = 0.20789529383182526\n",
            "<generator object Module.parameters at 0x7f85d8565308>\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_G9AmK3BcuYc"
      },
      "source": [
        "Three-layer net works even better!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kPI70Okub-Pu",
        "outputId": "97cb46cd-5b9c-44ba-b47d-a360357cb31a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 966
        }
      },
      "source": [
        "net = torch.nn.Sequential(\n",
        "        torch.nn.Linear(1, 20),\n",
        "        torch.nn.LeakyReLU(),\n",
        "        torch.nn.Linear(20, 10),\n",
        "        torch.nn.LeakyReLU(),\n",
        "        torch.nn.Linear(10, 10),\n",
        "        torch.nn.LeakyReLU(),\n",
        "        torch.nn.Linear(10, 1),\n",
        "    )\n",
        "learning_rate = 5e-2\n",
        "#opt = torch.optim.SGD(net.parameters(), lr=learning_rate, momentum=0.5)\n",
        "opt = torch.optim.Adagrad(net.parameters(), lr=learning_rate)\n",
        "train_model(x,y2,net,opt,20000)"
      ],
      "execution_count": 348,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration 0\n",
            "loss = 1.4351842403411865\n",
            "Iteration 1000\n",
            "loss = 0.5992989540100098\n",
            "Iteration 2000\n",
            "loss = 0.507056713104248\n",
            "Iteration 3000\n",
            "loss = 0.47102436423301697\n",
            "Iteration 4000\n",
            "loss = 0.3819512128829956\n",
            "Iteration 5000\n",
            "loss = 0.3294842839241028\n",
            "Iteration 6000\n",
            "loss = 0.3136163055896759\n",
            "Iteration 7000\n",
            "loss = 0.2691132724285126\n",
            "Iteration 8000\n",
            "loss = 0.23590272665023804\n",
            "Iteration 9000\n",
            "loss = 0.21257615089416504\n",
            "Iteration 10000\n",
            "loss = 0.19253303110599518\n",
            "Iteration 11000\n",
            "loss = 0.17630213499069214\n",
            "Iteration 12000\n",
            "loss = 0.1666833609342575\n",
            "Iteration 13000\n",
            "loss = 0.15983259677886963\n",
            "Iteration 14000\n",
            "loss = 0.1561565101146698\n",
            "Iteration 15000\n",
            "loss = 0.15059688687324524\n",
            "Iteration 16000\n",
            "loss = 0.145700603723526\n",
            "Iteration 17000\n",
            "loss = 0.14307595789432526\n",
            "Iteration 18000\n",
            "loss = 0.1400602012872696\n",
            "Iteration 19000\n",
            "loss = 0.13672463595867157\n",
            "<generator object Module.parameters at 0x7f85d8020990>\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a55xWmI7cxRL"
      },
      "source": [
        "Next up -- need to learn how to do batches.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e3xOalYXchT6"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}