saccadic · January 23, 2021 13:17
diff --git a/opencv_solver.ipynb b/opencv_solver.ipynb
 {
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "opencv_solver",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPZukTZBkAo9clkILBcfbDO",
      "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/gist/saccadic/da5b95e72df0dc2c8f22c4a900e232c6/opencv_solver.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NpUDfIVXMz0N"
      },
      "source": [
        "import cv2\r\n",
        "import numpy as np\r\n",
        "import pandas as pd\r\n",
        "import matplotlib.pyplot as plt\r\n",
        "from sklearn.preprocessing import PolynomialFeatures"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4jkrz3_qNKGN"
      },
      "source": [
        "def model(x, hyperparameter):\r\n",
        "    data = []\r\n",
        "    for i in range(len(x)):\r\n",
        "        y = hyperparameter[0]\r\n",
        "        for k in range(1,len(hyperparameter)):\r\n",
        "            y = y + hyperparameter[k] * np.power(x[i],k)\r\n",
        "        data.append(y)\r\n",
        "    return np.array(data)"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KozaDRbYM8iV",
        "outputId": "373a1cc4-6a9b-4137-deb8-c9c2922f398c"
      },
      "source": [
        "pt = np.array([\r\n",
        "    [0.0,0.0],\r\n",
        "    [0.1230469,0.2],\r\n",
        "    [0.2480469,0.4],\r\n",
        "    [0.3730469,0.5],\r\n",
        "    [0.4980469,0.6],\r\n",
        "    [0.6231689,0.7],\r\n",
        "    [0.7481689,0.8],\r\n",
        "    [0.8731689,0.9],\r\n",
        "    [1.0,1.0],\r\n",
        "],dtype=np.double)\r\n",
        "\r\n",
        "x = pt.T[0]\r\n",
        "y = pt.T[1]\r\n",
        "\r\n",
        "data = pd.DataFrame.from_dict({'x': x})\r\n",
        "\r\n",
        "print(data)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "       x\n",
            "0   0.00\n",
            "1   0.10\n",
            "2   0.20\n",
            "3   0.30\n",
            "4   0.40\n",
            "5   0.41\n",
            "6   0.42\n",
            "7   0.46\n",
            "8   0.50\n",
            "9   0.51\n",
            "10  0.52\n",
            "11  0.53\n",
            "12  0.60\n",
            "13  0.70\n",
            "14  0.80\n",
            "15  0.90\n",
            "16  1.00\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UjKQlB2vM-cY",
        "outputId": "ac1f453f-4303-4d9c-96d7-012415f1115e"
      },
      "source": [
        "order = 4\r\n",
        "pf = PolynomialFeatures(degree=order, include_bias=True)\r\n",
        "weights = pf.fit_transform(data)\r\n",
        "weight_values = pd.DataFrame(weights, columns=pf.get_feature_names(data.columns))\r\n",
        "print(weight_values)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "      1     x     x^2       x^3       x^4\n",
            "0   1.0  0.00  0.0000  0.000000  0.000000\n",
            "1   1.0  0.10  0.0100  0.001000  0.000100\n",
            "2   1.0  0.20  0.0400  0.008000  0.001600\n",
            "3   1.0  0.30  0.0900  0.027000  0.008100\n",
            "4   1.0  0.40  0.1600  0.064000  0.025600\n",
            "5   1.0  0.41  0.1681  0.068921  0.028258\n",
            "6   1.0  0.42  0.1764  0.074088  0.031117\n",
            "7   1.0  0.46  0.2116  0.097336  0.044775\n",
            "8   1.0  0.50  0.2500  0.125000  0.062500\n",
            "9   1.0  0.51  0.2601  0.132651  0.067652\n",
            "10  1.0  0.52  0.2704  0.140608  0.073116\n",
            "11  1.0  0.53  0.2809  0.148877  0.078905\n",
            "12  1.0  0.60  0.3600  0.216000  0.129600\n",
            "13  1.0  0.70  0.4900  0.343000  0.240100\n",
            "14  1.0  0.80  0.6400  0.512000  0.409600\n",
            "15  1.0  0.90  0.8100  0.729000  0.656100\n",
            "16  1.0  1.00  1.0000  1.000000  1.000000\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8_1fIg89Slib",
        "outputId": "3877b390-47af-4a06-90ff-2dda52de941a"
      },
      "source": [
        "retval, dst = cv2.solve(np.array(weights),np.array(y),flags=cv2.DECOMP_SVD)\r\n",
        "hyperparameter = dst.T[0]\r\n",
        "hyperparameter_values = pd.DataFrame([hyperparameter], columns=list(weight_values.columns))\r\n",
        "print(hyperparameter_values)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "          1         x       x^2       x^3       x^4\n",
            "0 -0.000567  2.060142  0.280604 -3.302395  1.960334\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "H3777KzLUIbU",
        "outputId": "0f4605ca-c7f3-4fb6-f9ee-29580ea58103"
      },
      "source": [
        "new_data = pd.DataFrame.from_dict({\r\n",
        "    'x': x,\r\n",
        "    'y1': y,\r\n",
        "    'y2': model(x, hyperparameter),\r\n",
        "})\r\n",
        "\r\n",
        "print(new_data)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "       x    y1        y2\n",
            "0   0.00  0.00 -0.000567\n",
            "1   0.10  0.20  0.205147\n",
            "2   0.20  0.40  0.399403\n",
            "3   0.30  0.60  0.569444\n",
            "4   0.40  0.70  0.707218\n",
            "5   0.41  0.71  0.719051\n",
            "6   0.42  0.72  0.730523\n",
            "7   0.46  0.73  0.772806\n",
            "8   0.50  0.80  0.809377\n",
            "9   0.51  0.82  0.817646\n",
            "10  0.52  0.83  0.825572\n",
            "11  0.53  0.87  0.833159\n",
            "12  0.60  0.90  0.877278\n",
            "13  0.70  0.91  0.916983\n",
            "14  0.80  0.93  0.939260\n",
            "15  0.90  0.96  0.959580\n",
            "16  1.00  1.00  0.998118\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "-eBumcbrUr3O",
        "outputId": "0a6fad6d-c05c-4fd6-a10b-b18dd21b61a5"
      },
      "source": [
        "x = np.array(range(1000)) / 1000\r\n",
        "y = model(x, hyperparameter)\r\n",
        "\r\n",
        "plt.clf()\r\n",
        "plt.plot(new_data[\"x\"],new_data[\"y1\"], c=\"k\")\r\n",
        "plt.plot(x,y, c=\"r\")\r\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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88YXvtP39++H552HoUMi5gNaBAwdITExk8+bNp/13z549AMyYMYNbzjh0USTYqNCl6MvOhqefhlGjyK5Vi4TnnmNVZiab77+fxMREEhMTSUn55UoTJUuWpH79+rRt25YGDRrQqlUr2rRp4+EGiBQOFboUbT/84Dtlf9Ei/tumDTcnJbF5yBAAypUrR4MGDejSpQv169enQYMGNGjQgJo1a+pwRAlJKnQpupYvhx49cAcP8kqLFgxcsoT69esT99JLxMTEULVqVV2zXCQXDWOk6HEOJk3CtW3LEee4qWRJBick8Nhjj/HNN9/QuXNnqlWrpjIXOYNG6FK0nDgBgwfD66+TcMkltP/+e+o1bcpXr7xC48aNvU4nUqRphC5Fx65duFatcG+8wVORkbRJTeUfY8eycuVKlblIPmiELkXDJ5+Q1bMnx48epadzHG/RgnXTphEdHe11MpGAoRG6eMs5sseNIzs2ls2HDtE6MpKukyfz2WefqcxFzpNG6OKd9HR+uusuKs6ezRzgrQ4d+Ojll6lRo4bXyUQCkgpdPJG+bx//bdWK2rt3M/6ii6g6bRqz+/TRkSsiF0CFLoVuw3vvUa5vX6qlp/Niy5b0/c9/qFKlitexRAKe5tCl0Bw/fpypd9xBzTvv5KLMTNY88wxDvvxSZS7iJxqhS6H4/PPP+eTOOxmdksL3FStS9vPPueGqq7yOJRJUNEKXAnXo0CH+Z9Agltx0E0+lpHCoeXNq7N5NWZW5iN+p0KXAzJ07l8b169Ny2jT+CWT260elL76AMmW8jiYSlFTo4ncpKSn06dOHPl268PaRI/QHePxxwl99FSIivA0nEsQ0hy5+45xj5syZDBs2jJKHDrG9alUuSUmB6dPhnnu8jicS9DRCF79ITk6mc+fO3HXXXdxcvTpJVapQ9ehR7KOPVOYihUSFLhckOzubKVOm0LBhQxYvXsxbf/kLM/fupXh2NixZArGxXkcUCRkqdPndtm/fTrt27Rg8eDDNmzdn+7Rp9Jk2DStTxnf/zyZNvI4oElI0hy7nLTMzk/HjxzNq1CgiIyOZPn06f65UCevZE+rVg4ULoXp1r2OKhByN0OW8rF+/npYtW/K3v/2N2NhYEhMTuSc8HOveHa6+2jfNojIX8US+Ct3MYs1sq5klmdnD51jnTjNLNLNNZva2f2OK19LS0hg1ahRNmzblu+++Y9asWcyZM4dLZ8+Gu++Gtm0hPh4qVfI6qkjIynPKxcyKAZOA9sAeYI2ZxTnnEnOtEw08AlzvnDtoZhcXVGApfCtWrGDAgAFs3ryZfv36MW7cOCpVrAhPPAH//Cf88Y8wcyZERnodVSSk5WeE3hxIcs7tdM6lA+8AXc9Y515gknPuIIBzbr9/Y4oXMjMzeeihh7j++us5duwYH3/8Ma+99pqvzEeO9JV5//4wa5bKXKQIyE+hVweScz3fk7Mst8uBy81suZmtNLOzHqtmZoPMLMHMElJSUn5fYik0jz32GOPHj2fw4MFs3LiR2NhYcA5GjIB//xv+5398Jw2Fa9+6SFHgr9/EcCAaaAvUAJaa2VXOudTcKznnpgJTAWJiYpyfPlsKQFxcHE8//TSDBg3ixRdf9C10Dh58EF54AR54ACZMAN2QQqTIyM8IfS9QM9fzGjnLctsDxDnnMpxzu4Bt+ApeAtCOHTvo168fTZo0YcKECb6F2dkwZIivzB96SGUuUgTlp9DXANFmFmVmxYFeQNwZ63yIb3SOmVXGNwWz0485pZCcOHGCO+64g7CwMGbPnk2JEiUgKwvuvRcmT4aHH4Znn1WZixRBeU65OOcyzWwosBAoBrzinNtkZqOBBOdcXM5rt5hZIpAFjHDOHSjI4FIwHnjgAdauXctHH31EVFSUr8z//Gd44w0YNQoef1xlLlJE5WsO3Tk3H5h/xrJRuR474KGcLwlQM2bMYPr06Tz66KPceuutvjK/+2546y3fIYr/+IfXEUXkN+jwBAFg7dq1DBkyhHbt2jF69GjfnPnAgb4yf+opeOQRryOKSB506r+QmppK9+7dqVixIjNnzqSYGQweDK++6ptiUZmLBASN0EOcc47+/fvz3XffsWTJEi6uUsV3SOK0afDoo755cxEJCCr0EDd27Fj+85//MH78eFq1bAnDh8OkSfDXv8K//qUdoCIBRFMuIWzJkiU88sgj9OjRgweHDfNNrYwfD8OGwTPPqMxFAowKPUTt27ePnj17Uq9ePV5++WXs//0/GDPGN3f+3HMqc5EApCmXEJSRkUHPnj05cuQIn376KWVffBFGj/bd+3PSJJW5SIBSoYegRx99lGXLlvHmm2/SaNky31RLnz4wdSqE6R9tIoFKv70h5oMPPuDZZ5/lvvvu466wMLj/fujc2XeIYrFiXscTkQugEXoI2b59O/3796dZs2ZMuOUW6NEDbrwR3n0XIiK8jiciF0gj9BBx/Phx7rjjDsLDw4kbPpyI3r199wCNi4OLLvI6noj4gUboIcA5x5AhQ9iwYQPLnnuOqvfeC7Vrw4IFULas1/FExE80Qg8BL7/8Mq+99hoT7ruP6594AipWhEWLoHJlr6OJiB+p0IPc119/zQMPPEDf1q0ZGhfn2/G5aBHUqOF1NBHxM025BLGDBw/SvXt3oitWZMa+fdiRI7BkCUTrZlIiwUgj9CCVnZ1Nv379+GnPHr6sVInw5GTfDtCrr/Y6mogUEI3Qg9SYMWP4+KOP2NaoEWU2bYLZs32HKIpI0FKhB6H4+Hj+MXIkC+vWpc7GjTBxItx+u9exRKSAacolyOzdu5fevXvzXKVK3Lxjh++0/vvv9zqWiBQCjdCDyKmLbvU4dIgH0tN99wN98kmvY4lIIVGhB5G///3vlF++nBfCwiA21nfXIV05USRkqNCDxOzZs/ly/HiWhocTds018N57uj6LSIhRoQeBrVu3Mvruu1kSHk5ErVowbx6ULu11LBEpZNopGuCOHTvGPV27MictjbJlymALFsDFF3sdS0Q8oEIPYM45ht57L09t3UqdsDCKzZ0L9ep5HUtEPKIplwA2ZfJk2s2cSRuA116D66/3OpKIeEgj9ACVkJBAytCh/AnIfuIJ6N3b60gi4jGN0APQgQMHeDs2lnHZ2Zzs04cSI0d6HUlEigCN0ANMdnY2z3TqxNMHDnA4JoYSM2boWHMRAVToAWfy//4vD69ezdGqVSm7aBEUL+51JBEpIjTlEkA+f+89Yl94gbASJSi7fDmUL+91JBEpQvI1QjezWDPbamZJZvbwb6zX3cycmcX4L6IAJCclUbJPHy41o/jHH2N16ngdSUSKmDwL3cyKAZOAjkADoLeZNTjLemWAB4FV/g4Z6tLT0tjQsiXNMzM5MH48F7Vt63UkESmC8jNCbw4kOed2OufSgXeArmdZ7wlgDHDSj/kEmP+HP9Dpxx/Z1KMH1R980Os4IlJE5afQqwPJuZ7vyVn2MzNrAtR0zs37rTcys0FmlmBmCSkpKecdNhQt/dvf6LJ8OWujo2n4zjtexxGRIuyCj3IxszBgHDA8r3Wdc1OdczHOuZgqVapc6EcHvZ1xcVw7dizbSpWi4Zo1EKaDkkTk3PLTEHuBmrme18hZdkoZoBHwuZntBloAcdoxemGO7t5NxB13cCwsjHKLFxNRrpzXkUSkiMtPoa8Bos0sysyKA72AuFMvOucOOecqO+dqO+dqAyuBLs65hAJJHAJcWhrJzZtTJSOD5Oefp1qzZl5HEpEAkGehO+cygaHAQmAzMMs5t8nMRptZl4IOGHKcI7FdO+qnpLDgzjtppvuBikg+5evEIufcfGD+GctGnWPdthceK3TtHj6chl9+yax69bhj5kyv44hIANFetiLk0KxZ1Bw/noUlS9J+5UrCtBNURM6DGqOIyEpMpNhdd7HJjIsXLKBCpUpeRxKRAKNCLwoOH+anNm04kZnJxief5NrWrb1OJCIBSIXutexsfujQgQo//sj0Dh3o/fA5L5UjIvKbVOgeSx0+nEtWruT/Lr2UYXPmYLq2uYj8Tip0D2W8/z7ln3uOtyIiuH3xYkqWLOl1JBEJYLoeule2bCGzd2/WAqVef53oyy/3OpGIBDiN0L1w6BCH27XjcEYGC+69l269enmdSESCgEbohS07myNdu3LRvn2MbNyYcZMmeZ1IRIKECr2QpT36KGWWLOHRMmV4dMECIiIivI4kIkFCUy6FyH3wAZFjxjADuOU//6FatWpeRxKRIKJCLyyJiWT07s0q4MATT9D2ppu8TiQiQUZTLoUhNZUTsbEcTktjSvv2TB850utEIhKEVOgFLTubtJ49CU9OZli1akyZNUsnD4lIgVChF7Dsp54i8pNPeCg8nEfmz6d8+fJeRxKRIKU59IL06acwahRvA40mT+aaa67xOpGIBDEVekFJTiate3cSnWPZn/7EPQMGeJ1IRIKcplwKQloaaZ07k374MCOvvJJ3pkzxOpGIhAAVegHIHDaMyHXrGFiyJOM++oiLLrrI60giEgI05eJvb7xB+NSpPAP0mDmTunXrep1IREKERuj+tH49mQMHsgxIHTGCLl26eJ1IREKICt1fUlNJu+02DqSn80KrVsx66imvE4lIiFGh+0N2Nhl9+hCWnMzgSpWY+v77hIfrj1ZECpdaxw/c008T8fHH/K8ZIz74gKpVq3odSURCkAr9QsXH4/7xD2YCNZ95htatW3udSERClAr9QiQnk9G9O9ucY16XLrw5fLjXiUQkhKnQf6/0dNK7dSPt8GH+ctllvPf667roloh4SoX+O2WPGEHxr7+mf/HiPDt3LuXKlfM6koiEOJ1Y9Ht8+CFhzz/PBCB22jQaN27sdSIRERX6edu1i/S+fVkDbBswgH79+nmdSEQEyGehm1msmW01syQze/gsrz9kZolmtt7M4s2slv+jFgHp6Zzs1o0Tx47xRMOG/N/EiV4nEhH5WZ6FbmbFgElAR6AB0NvMGpyx2jdAjHOuMTAbeMbfQYuCzOHDKbF+PQ+UKsWEuXMpUaKE15FERH6WnxF6cyDJObfTOZcOvAN0zb2Cc26xc+54ztOVQA3/xiwCPvyQ8IkTmQD0fPddoqKivE4kInKa/BR6dSA51/M9OcvOZQDw8dleMLNBZpZgZgkpKSn5T+m1XbtI69OH1cBPDz/Mrbfe6nUiEZFf8ethi2bWF4gB2pztdefcVGAqQExMjPPnZxeY9HSOde5MxokTPN+qFa/9619eJxIROav8FPpeoGau5zVylp3GzG4GRgJtnHNp/onnvbQHH6TUpk0MrFiRcR98QLFixbyOJCJyVvmZclkDRJtZlJkVB3oBcblXMLNrgSlAF+fcfv/H9IabM4fIyZN53ox75s7l4osv9jqSiMg55VnozrlMYCiwENgMzHLObTKz0WZ26g4OY4HSwHtmttbM4s7xdoFj1y7S7rqL1YCNHUurVq28TiQi8pvyNYfunJsPzD9j2ahcj2/2cy5vpadzuFMnsk6e5PVOnXjhoYe8TiQikiddy+Usjg0ZQtktW7j/0kt5+p13dNEtEQkIOvX/DFnvvUep6dOZGB7OkE8+oUyZMl5HEhHJF43Qc9u5k/Q//YkNQKWXX6Zhw4ZeJxIRyTeN0E9JS+PgLbdwMi2Nj/r2pffdd3udSETkvGiEnuPgoEFU2LGDEdHR/Ovll72OIyJy3jRCB9JmzqTC66/zUmQkQxctIjIy0utIIiLnLeQL3e3YQdbdd7MKqPPee9SqFZxX/hWR4BfahZ6Wxo9/+ANpGRl8OWwYHTp39jqRiMjvFtKFvv/uu6ny7bdMuOYaho0b53UcEZELErKFfvS117j43XeZVro0Qxct0kW3RCTghWShZyclYQMHstqMqz/+mMqVK3sdSUTkgoVeoael8UPbtqRnZrL5n/+k+Q03eJ1IRMQvQq7Qk3v1otrevUxv3Zp+o0bl/Q0iIgEipAr9wJQp1PzwQ16tWJHB8+frolsiElRCptAztmwh8v77WR0WxnWffUbp0qW9jiQi4lehUehpaXzfpg0ZWVn8MGEC9a++2utEIiJ+FxKFntStGzX37+e9W2+l89ChXscRESkQQV/oeydMoN6CBbxdrRr958zxOo6ISIEJ6kI/vk2K67IAAAZDSURBVGEDZR96iDXh4dy4fDnFixf3OpKISIEJ2kJ3J07wQ9u2ZGRnc3LGDGpERXkdSUSkQAVtoW/q2JGon37ikz59aN23r9dxREQKXFAWetK//02jJUt4PyqKO994w+s4IiKFIugK/eCaNVwyciRfFy9O2y+/JCws6DZRROSsgqrtso8f58DNN5PhHOGzZ1OpalWvI4mIFJqgKvSvbrqJeocPs+q++2ism1WISIgJmkJf99hjNFu9mnn16xM7aZLXcURECl1QFPq+Zcuo8+STrL3oItp++aUuuiUiISngCz398GEOx8aS6Rxl5s2jVPnyXkcSEfFEwBf6qhtu4Irjx0n8+9+pe9NNXscREfFMQBf68gcfpPWGDSxu2pTrn37a6zgiIp4K2EJPWrCAq55/ng1lynDD0qVexxER8Vy+Ct3MYs1sq5klmdnDZ3k90szezXl9lZnV9nfQ3I7++CPp3bqRaUaVTz8lomTJgvw4EZGAkGehm1kxYBLQEWgA9DazBmesNgA46JyrB4wHxvg76CnOOVa0bEmDtDSSn3iCqs2bF9RHiYgElPyM0JsDSc65nc65dOAdoOsZ63QFXst5PBv4gxXQsYOfDBhA+6QkVrZuzdUjRxbER4iIBKT8FHp1IDnX8z05y866jnMuEzgEVDrzjcxskJklmFlCSkrK7woc3aIF6+rUofmiRb/r+0VEglWh7hR1zk11zsU452KqVKnyu96jzqBBXL1jB2GRkX5OJyIS2PJT6HuBmrme18hZdtZ1zCwcKAcc8EdAERHJn/wU+hog2syizKw40AuIO2OdOODunMd3AJ8555z/YoqISF7C81rBOZdpZkOBhUAx4BXn3CYzGw0kOOfigOnAG2aWBPyEr/RFRKQQ5VnoAM65+cD8M5aNyvX4JNDDv9FEROR8BOyZoiIicjoVuohIkFChi4gECRW6iEiQMK+OLjSzFODb3/ntlYEf/RgnEGibQ4O2OTRcyDbXcs6d9cxMzwr9QphZgnMuxuschUnbHBq0zaGhoLZZUy4iIkFChS4iEiQCtdCneh3AA9rm0KBtDg0Fss0BOYcuIiK/FqgjdBEROYMKXUQkSBTpQi9qN6cuDPnY5ofMLNHM1ptZvJnV8iKnP+W1zbnW625mzswC/hC3/Gyzmd2Z87PeZGZvF3ZGf8vH3+3LzGyxmX2T8/e7kxc5/cXMXjGz/Wa28Ryvm5k9n/Pnsd7MmlzwhzrniuQXvkv17gDqAMWBdUCDM9YZAkzOedwLeNfr3IWwzTcBJXMe3xcK25yzXhlgKbASiPE6dyH8nKOBb4AKOc8v9jp3IWzzVOC+nMcNgN1e577Abb4RaAJsPMfrnYCPAQNaAKsu9DOL8gi9SN2cupDkuc3OucXOueM5T1fiu4NUIMvPzxngCWAMcLIwwxWQ/GzzvcAk59xBAOfc/kLO6G/52WYHlM15XA74byHm8zvn3FJ894c4l67A685nJVDezKpdyGcW5UL3282pA0h+tjm3Afj+Dx/I8tzmnH+K1nTOzSvMYAUoPz/ny4HLzWy5ma00s9hCS1cw8rPNjwN9zWwPvvsvPFA40Txzvr/vecrXDS6k6DGzvkAM0MbrLAXJzMKAcUB/j6MUtnB80y5t8f0rbKmZXeWcS/U0VcHqDbzqnPs/M2uJ7y5ojZxz2V4HCxRFeYQeijenzs82Y2Y3AyOBLs65tELKVlDy2uYyQCPgczPbjW+uMS7Ad4zm5+e8B4hzzmU453YB2/AVfKDKzzYPAGYBOOdWACXwXcQqWOXr9/18FOVCD8WbU+e5zWZ2LTAFX5kH+rwq5LHNzrlDzrnKzrnazrna+PYbdHHOJXgT1y/y83f7Q3yjc8ysMr4pmJ2FGdLP8rPN3wF/ADCz+vgKPaVQUxauOKBfztEuLYBDzrl9F/SOXu8JzmMvcSd8I5MdwMicZaPx/UKD7wf+HpAErAbqeJ25ELb5U+AHYG3OV5zXmQt6m89Y93MC/CiXfP6cDd9UUyKwAejldeZC2OYGwHJ8R8CsBW7xOvMFbu9MYB+Qge9fXAOAwcDgXD/jSTl/Hhv88fdap/6LiASJojzlIiIi50GFLiISJFToIiJBQoUuIhIkVOgiIkFChS4iEiRU6CIiQeL/A4kAv7zOhJsXAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
 }
	{
	"nbformat": 4,
	"nbformat_minor": 0,
	"metadata": {
	"colab": {
	"name": "opencv_solver",
	"provenance": [],
	"collapsed_sections": [],
	"authorship_tag": "ABX9TyPZukTZBkAo9clkILBcfbDO",
	"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/gist/saccadic/da5b95e72df0dc2c8f22c4a900e232c6/opencv_solver.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "NpUDfIVXMz0N"
	},
	"source": [
	"import cv2\r\n",
	"import numpy as np\r\n",
	"import pandas as pd\r\n",
	"import matplotlib.pyplot as plt\r\n",
	"from sklearn.preprocessing import PolynomialFeatures"
	],
	"execution_count": 1,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "4jkrz3_qNKGN"
	},
	"source": [
	"def model(x, hyperparameter):\r\n",
	" data = []\r\n",
	" for i in range(len(x)):\r\n",
	" y = hyperparameter[0]\r\n",
	" for k in range(1,len(hyperparameter)):\r\n",
	" y = y + hyperparameter[k] * np.power(x[i],k)\r\n",
	" data.append(y)\r\n",
	" return np.array(data)"
	],
	"execution_count": 2,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "KozaDRbYM8iV",
	"outputId": "373a1cc4-6a9b-4137-deb8-c9c2922f398c"
	},
	"source": [
	"pt = np.array([\r\n",
	" [0.0,0.0],\r\n",
	" [0.1230469,0.2],\r\n",
	" [0.2480469,0.4],\r\n",
	" [0.3730469,0.5],\r\n",
	" [0.4980469,0.6],\r\n",
	" [0.6231689,0.7],\r\n",
	" [0.7481689,0.8],\r\n",
	" [0.8731689,0.9],\r\n",
	" [1.0,1.0],\r\n",
	"],dtype=np.double)\r\n",
	"\r\n",
	"x = pt.T[0]\r\n",
	"y = pt.T[1]\r\n",
	"\r\n",
	"data = pd.DataFrame.from_dict({'x': x})\r\n",
	"\r\n",
	"print(data)"
	],
	"execution_count": 3,
	"outputs": [
	{
	"output_type": "stream",
	"text": [
	" x\n",
	"0 0.00\n",
	"1 0.10\n",
	"2 0.20\n",
	"3 0.30\n",
	"4 0.40\n",
	"5 0.41\n",
	"6 0.42\n",
	"7 0.46\n",
	"8 0.50\n",
	"9 0.51\n",
	"10 0.52\n",
	"11 0.53\n",
	"12 0.60\n",
	"13 0.70\n",
	"14 0.80\n",
	"15 0.90\n",
	"16 1.00\n"
	],
	"name": "stdout"
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "UjKQlB2vM-cY",
	"outputId": "ac1f453f-4303-4d9c-96d7-012415f1115e"
	},
	"source": [
	"order = 4\r\n",
	"pf = PolynomialFeatures(degree=order, include_bias=True)\r\n",
	"weights = pf.fit_transform(data)\r\n",
	"weight_values = pd.DataFrame(weights, columns=pf.get_feature_names(data.columns))\r\n",
	"print(weight_values)"
	],
	"execution_count": 4,
	"outputs": [
	{
	"output_type": "stream",
	"text": [
	" 1 x x^2 x^3 x^4\n",
	"0 1.0 0.00 0.0000 0.000000 0.000000\n",
	"1 1.0 0.10 0.0100 0.001000 0.000100\n",
	"2 1.0 0.20 0.0400 0.008000 0.001600\n",
	"3 1.0 0.30 0.0900 0.027000 0.008100\n",
	"4 1.0 0.40 0.1600 0.064000 0.025600\n",
	"5 1.0 0.41 0.1681 0.068921 0.028258\n",
	"6 1.0 0.42 0.1764 0.074088 0.031117\n",
	"7 1.0 0.46 0.2116 0.097336 0.044775\n",
	"8 1.0 0.50 0.2500 0.125000 0.062500\n",
	"9 1.0 0.51 0.2601 0.132651 0.067652\n",
	"10 1.0 0.52 0.2704 0.140608 0.073116\n",
	"11 1.0 0.53 0.2809 0.148877 0.078905\n",
	"12 1.0 0.60 0.3600 0.216000 0.129600\n",
	"13 1.0 0.70 0.4900 0.343000 0.240100\n",
	"14 1.0 0.80 0.6400 0.512000 0.409600\n",
	"15 1.0 0.90 0.8100 0.729000 0.656100\n",
	"16 1.0 1.00 1.0000 1.000000 1.000000\n"
	],
	"name": "stdout"
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "8_1fIg89Slib",
	"outputId": "3877b390-47af-4a06-90ff-2dda52de941a"
	},
	"source": [
	"retval, dst = cv2.solve(np.array(weights),np.array(y),flags=cv2.DECOMP_SVD)\r\n",
	"hyperparameter = dst.T[0]\r\n",
	"hyperparameter_values = pd.DataFrame([hyperparameter], columns=list(weight_values.columns))\r\n",
	"print(hyperparameter_values)"
	],
	"execution_count": 5,
	"outputs": [
	{
	"output_type": "stream",
	"text": [
	" 1 x x^2 x^3 x^4\n",
	"0 -0.000567 2.060142 0.280604 -3.302395 1.960334\n"
	],
	"name": "stdout"
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/"
	},
	"id": "H3777KzLUIbU",
	"outputId": "0f4605ca-c7f3-4fb6-f9ee-29580ea58103"
	},
	"source": [
	"new_data = pd.DataFrame.from_dict({\r\n",
	" 'x': x,\r\n",
	" 'y1': y,\r\n",
	" 'y2': model(x, hyperparameter),\r\n",
	"})\r\n",
	"\r\n",
	"print(new_data)"
	],
	"execution_count": 6,
	"outputs": [
	{
	"output_type": "stream",
	"text": [
	" x y1 y2\n",
	"0 0.00 0.00 -0.000567\n",
	"1 0.10 0.20 0.205147\n",
	"2 0.20 0.40 0.399403\n",
	"3 0.30 0.60 0.569444\n",
	"4 0.40 0.70 0.707218\n",
	"5 0.41 0.71 0.719051\n",
	"6 0.42 0.72 0.730523\n",
	"7 0.46 0.73 0.772806\n",
	"8 0.50 0.80 0.809377\n",
	"9 0.51 0.82 0.817646\n",
	"10 0.52 0.83 0.825572\n",
	"11 0.53 0.87 0.833159\n",
	"12 0.60 0.90 0.877278\n",
	"13 0.70 0.91 0.916983\n",
	"14 0.80 0.93 0.939260\n",
	"15 0.90 0.96 0.959580\n",
	"16 1.00 1.00 0.998118\n"
	],
	"name": "stdout"
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 265
	},
	"id": "-eBumcbrUr3O",
	"outputId": "0a6fad6d-c05c-4fd6-a10b-b18dd21b61a5"
	},
	"source": [
	"x = np.array(range(1000)) / 1000\r\n",
	"y = model(x, hyperparameter)\r\n",
	"\r\n",
	"plt.clf()\r\n",
	"plt.plot(new_data[\"x\"],new_data[\"y1\"], c=\"k\")\r\n",
	"plt.plot(x,y, c=\"r\")\r\n",
	"plt.show()"
	],
	"execution_count": 7,
	"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"
	}
	}
	]
	}
	]
	}