53818.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "53818.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "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/bmreiniger/datascience.stackexchange/blob/master/53818.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D18EJpsKit3U",
        "colab_type": "text"
      },
      "source": [
        "As in the OP, except try to use better precision:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QrBTfvD6P550",
        "colab_type": "code",
        "outputId": "7f178b42-04de-4be5-94cc-5e94680e9104",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def pol(x):\n",
        "    return x * np.cos(x)\n",
        "\n",
        "x = np.linspace(0, 12, 100)\n",
        "rng = np.random.RandomState(1234)\n",
        "rng.shuffle(x)\n",
        "x = np.sort(x[:25])\n",
        "y = pol(np.longdouble(x)) + np.random.randn(25)*2\n",
        "\n",
        "plt.scatter(x, y, color='green', s=50, marker='.')\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9r4r3a2vg93365baIiO+lG/b3ZeYXmq5nAO8BPhARJ+m22n42Iv6y2ZIGcgo4lZmv/eJ6\nkO4XQFtdB3wzM1cz83+ALwA/1XBNVfh2RFwK0Pt7uuF6BhYRvwK8H/jFrGj9fFsD/yngqoi4MiKm\n6O50erjhmvYsIoJuj3glM3+v6XoGkZl3ZOblmTlL9//L32Zma2eQmfkK8GJEXN176ADds8C21beA\nd0XE63ufuwO0eCf0WR4GbundvgUY+OJMTYqIG+i2RT+Qmf9V1fu2MvB7OzNuAx6j+2H9fO+UzG31\nHuAjdGfD/9j75+eaLkpn/DpwX0R8DXgHcKjhevas90vlQeCrwD/RzYBWHaUaEfcDXwaujohTEXEr\ncBfw3oh4lu6vmLuarHE3ttmePwLeADzey4M/qWQsj7SVpDK0coYvSdo9A1+SCmHgS1IhDHxJKoSB\nL0mFMPAlqRAGviQVwsCXpEL8H0K0cBC0OjFDAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kNk4n_JGiWsl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "af3852ae-758a-4783-db3e-8ff8ba2294d0"
      },
      "source": [
        "type(y[0])"
      ],
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.float128"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UEBYFFS-P7_C",
        "colab_type": "code",
        "outputId": "5f6645d1-55dc-4be1-be89-7b58c3c4bcc6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 532
        }
      },
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "\n",
        "for p in range(1,30):\n",
        "    plot_range = [i/10 for i in range(0,120)]\n",
        "    poly = PolynomialFeatures(p)\n",
        "    X_fin = poly.fit_transform([[samp] for samp in x])\n",
        "    X_fin_plot = poly.fit_transform([[samp] for samp in plot_range])\n",
        "    reg = LinearRegression().fit(X_fin, y)\n",
        "\n",
        "    from sklearn.metrics import mean_squared_error, r2_score\n",
        "    print(p,r2_score(y, reg.predict(X_fin)))"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1 0.011428827986298185\n",
            "2 0.049824884417237536\n",
            "3 0.18510530303518846\n",
            "4 0.7524959057278297\n",
            "5 0.7849414255228335\n",
            "6 0.883372862306162\n",
            "7 0.9045044030836533\n",
            "8 0.9394157666425363\n",
            "9 0.9518632304961523\n",
            "10 0.951992420205271\n",
            "11 0.9535095748926792\n",
            "12 0.9521059512715203\n",
            "13 0.9495410592268169\n",
            "14 0.9458024870565721\n",
            "15 0.9418520107231447\n",
            "16 0.9405653534483068\n",
            "17 0.9337912337760239\n",
            "18 0.923540608174988\n",
            "19 0.9150580889315411\n",
            "20 0.9098877179697926\n",
            "21 0.9087915968482445\n",
            "22 0.9037422497047429\n",
            "23 0.8945135026074984\n",
            "24 0.8819064591003116\n",
            "25 0.8669722586908764\n",
            "26 0.850671481614115\n",
            "27 0.8337637689381888\n",
            "28 0.7261217111510339\n",
            "29 0.7126553231722585\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bndq1u1sibU9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "8cd32270-6085-4f34-e551-14138dd2a078"
      },
      "source": [
        "type(X_fin[0,0])"
      ],
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XgVwcjkei1SV",
        "colab_type": "text"
      },
      "source": [
        "Unfortunately, sklearn automatically has cast us back down to float64's..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q5gluMHSXJnJ",
        "colab_type": "code",
        "outputId": "a9d3fa33-611f-4adf-a6e6-8809fec51ce9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 158
        }
      },
      "source": [
        "reg.coef_"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-2.15699472e-20,  6.34191867e-23,  4.13697839e-26, -6.22013603e-28,\n",
              "        3.17236397e-30,  4.44991496e-30,  3.26377017e-29,  2.34378115e-28,\n",
              "        1.65497898e-27,  1.14923786e-26,  7.83956463e-26,  5.24266815e-25,\n",
              "        3.42715053e-24,  2.18162169e-23,  1.34573681e-22,  7.99329235e-22,\n",
              "        4.53392541e-21,  2.42867004e-20,  1.20970456e-19,  5.47759538e-19,\n",
              "        2.17662418e-18,  7.14175946e-18,  1.70684073e-17,  2.01684452e-17,\n",
              "       -1.54401693e-17,  4.02804514e-18, -5.35084232e-19,  3.91929698e-20,\n",
              "       -1.51369279e-21,  2.41719937e-23])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Oo0lE9_3XkVV",
        "colab_type": "code",
        "outputId": "6d73663c-c824-47af-bf17-70ea220e8142",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 517
        }
      },
      "source": [
        "from scipy.linalg import lstsq\n",
        "out = lstsq(X_fin, y)\n",
        "print(out)\n",
        "p = out[0]\n",
        "plot_range = [i/10 for i in range(0,120)]\n",
        "plt.scatter(x, y, color='green', s=50, marker='.')\n",
        "plt.plot(plot_range,X_fin_plot@p)\n",
        "plt.show()"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(array([-7.27124977e-23,  5.99552863e-22,  2.70965459e-24, -2.16792885e-25,\n",
            "       -8.29400054e-27, -9.62830430e-28, -7.09742585e-29,  2.94945943e-28,\n",
            "        2.13806856e-27,  1.46393021e-26,  9.86750839e-26,  6.53365710e-25,\n",
            "        4.23524894e-24,  2.67647692e-23,  1.64048101e-22,  9.68894100e-22,\n",
            "        5.46791476e-21,  2.91560519e-20,  1.44622986e-19,  6.52389796e-19,\n",
            "        2.58347489e-18,  8.45016406e-18,  2.01390571e-17,  2.37470049e-17,\n",
            "       -1.80729927e-17,  4.69331028e-18, -6.20988156e-19,  4.53256536e-20,\n",
            "       -1.74505214e-21,  2.77876142e-23]), array([], dtype=float64), 7, array([1.74673168e+31, 2.03479963e+28, 6.75579705e+25, 2.47150857e+23,\n",
            "       1.79426999e+21, 1.68006616e+19, 1.54723519e+17, 2.20703707e+15,\n",
            "       3.46213112e+13, 2.76068048e+13, 6.53615022e+11, 1.01563184e+11,\n",
            "       1.49208430e+10, 7.10031989e+08, 4.14658000e+08, 1.41208183e+07,\n",
            "       2.51036395e+06, 7.39040636e+05, 3.13389577e+04, 2.29231274e+04,\n",
            "       4.06070145e+03, 1.08387721e+03, 1.04227465e+02, 6.97471996e+00,\n",
            "       1.00742442e+00]))\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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i5qRRPLamgU9fWpu0cZ7b1My0cSXMnDiaH01SU8BgaIYvIgnz4XnVvLW3jbdb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\nLyKSI5TwRURyhBK+iEiOUMIXEckR/x84ZBCahpvCkQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pq7Wq71ii9i9",
        "colab_type": "text"
      },
      "source": [
        "# Rescale things, so that the 24th powers don't diverge quite so much:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dS6ZrZKsbKKU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x_sc = (10+np.longdouble(x))/24\n",
        "plot_range_sc = np.longdouble((10+np.array(plot_range))/24)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jld3JsZGQBzp",
        "colab_type": "code",
        "outputId": "cd5d7911-4f97-4753-bf03-043d73cfb6a0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 532
        }
      },
      "source": [
        "for p in range(1,30):\n",
        "    plot_range = [i/10 for i in range(0,120)]\n",
        "    poly = PolynomialFeatures(p)\n",
        "    X_fin = poly.fit_transform([[samp] for samp in x_sc])\n",
        "    X_fin_plot = poly.fit_transform([[samp] for samp in plot_range_sc])\n",
        "    reg = LinearRegression().fit(X_fin, y)\n",
        "\n",
        "    from sklearn.metrics import mean_squared_error, r2_score\n",
        "    print(p,r2_score(y, reg.predict(X_fin)))"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1 0.011428827986298185\n",
            "2 0.049824884417237536\n",
            "3 0.18510530303518602\n",
            "4 0.7524959057277869\n",
            "5 0.784941425522926\n",
            "6 0.8833728623085528\n",
            "7 0.9045044031029656\n",
            "8 0.9394157670063518\n",
            "9 0.9518632280982889\n",
            "10 0.951992411594822\n",
            "11 0.9535126179587199\n",
            "12 0.957145096885098\n",
            "13 0.9631896012324069\n",
            "14 0.9633918895274786\n",
            "15 0.9639783450857222\n",
            "16 0.9641071602726566\n",
            "17 0.9641954933818148\n",
            "18 0.9642842474103579\n",
            "19 0.9669955788906639\n",
            "20 0.9671503542187585\n",
            "21 0.9669799699290126\n",
            "22 0.9667149826472317\n",
            "23 0.9665419869408751\n",
            "24 0.9689217306108523\n",
            "25 0.9688833854305549\n",
            "26 0.9690891604031492\n",
            "27 0.9690520208381211\n",
            "28 0.9692332308303898\n",
            "29 0.9693984055707766\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nj8sFQMAjI-F",
        "colab_type": "text"
      },
      "source": [
        "Much better, though still not the perfect 24th-degree polynomial we theoretically have."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lfOL50kOXEmK",
        "colab_type": "code",
        "outputId": "fe406a55-7574-49ea-cbef-a1c3604cba34",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 500
        }
      },
      "source": [
        "poly = PolynomialFeatures(24)\n",
        "X_fin = poly.fit_transform([[samp] for samp in x_sc])\n",
        "X_fin_plot = poly.fit_transform([[samp] for samp in plot_range_sc])\n",
        "out = lstsq(X_fin, y)\n",
        "print(out)\n",
        "p = out[0]\n",
        "plt.scatter(x_sc, y, color='green', s=50, marker='.')\n",
        "plt.plot(plot_range_sc,X_fin_plot@p)\n",
        "plt.ylim((-15,15))\n",
        "plt.show()"
      ],
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(array([-9.70735879e+09,  1.62489216e+11, -1.18372780e+12,  4.84204523e+12,\n",
            "       -1.18061140e+13,  1.60671047e+13, -7.29622437e+12, -9.49103779e+12,\n",
            "        9.84862139e+12,  7.85291665e+12, -8.60879261e+12, -9.50738538e+12,\n",
            "        5.02663914e+12,  1.15028301e+13,  7.94717843e+11, -1.11151291e+13,\n",
            "       -7.19590952e+12,  7.32182678e+12,  1.16892285e+13, -1.95712566e+12,\n",
            "       -1.37963685e+13, -9.75089382e+11,  1.71893316e+13, -1.19358536e+13,\n",
            "        2.58071453e+12]), array([], dtype=float64), 16, array([7.71500877e+00, 2.17173309e+00, 5.52044287e-01, 1.39313172e-01,\n",
            "       3.00874756e-02, 4.69103972e-03, 7.91697434e-04, 1.23507580e-04,\n",
            "       1.52646534e-05, 1.29587522e-06, 8.77543799e-08, 5.65212329e-09,\n",
            "       3.47783420e-10, 1.60453592e-11, 7.88822085e-13, 2.59927120e-14,\n",
            "       8.51963151e-16, 2.74341805e-17, 2.14843389e-17, 1.95349324e-17,\n",
            "       7.30847754e-18, 5.80764785e-18, 5.03208411e-18, 3.04650858e-18,\n",
            "       9.12813935e-19]))\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pDMM9EMzw5u4KXB4v19i8nAM2TfihSsQWG+Dz+dEWRgxMICG29ytYOzcOf31n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\nRK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uPNVTLVpgsqL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}