{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "zReeXVyPfjR-" }, "source": [ "
\"Logo
\n", "# Polynomial regression with NumPy and Matplotlib\n", "\n", "This tutorial provides a comprehensive, step-by-step example of polynomial regression using NumPy, with Matplotlib for visualizing the results." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-10-13T21:47:50.879029Z", "iopub.status.busy": "2024-10-13T21:47:50.878463Z", "iopub.status.idle": "2024-10-13T21:47:51.578391Z", "shell.execute_reply": "2024-10-13T21:47:51.577563Z" }, "id": "RvLYGsnGfjSA" }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": { "id": "lI5rHD3lfjSA" }, "source": [ "Set a random seed" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-10-13T21:47:51.581277Z", "iopub.status.busy": "2024-10-13T21:47:51.580762Z", "iopub.status.idle": "2024-10-13T21:47:51.584014Z", "shell.execute_reply": "2024-10-13T21:47:51.583492Z" }, "id": "EYS_y6wmfjSB" }, "outputs": [], "source": [ "np.random.seed(12)" ] }, { "cell_type": "markdown", "metadata": { "id": "qbbG3wlPfjSB" }, "source": [ "Set the number of data points `N` and the degree `D` of the polynomial that is going to fit to the data.\n", "\n", "**Note:** for `D = 1` this is _linear regression_." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-10-13T21:47:51.586244Z", "iopub.status.busy": "2024-10-13T21:47:51.585848Z", "iopub.status.idle": "2024-10-13T21:47:51.588642Z", "shell.execute_reply": "2024-10-13T21:47:51.588115Z" }, "id": "kVDeLm0AfjSB" }, "outputs": [], "source": [ "N = 100 # number of points\n", "D = 2 # degree of polynomial" ] }, { "cell_type": "markdown", "metadata": { "id": "pG4yUYOmfjSB" }, "source": [ "### Generate some random data\n", "\n", "To generate some random data that is suitable for polynomial regression we're going to use the following functions:\n", "- [`np.random.uniform`](https://docs.scipy.org/doc/numpy-1.16.0/reference/generated/numpy.random.uniform.html) draws samples from a uniform distribution\n", "- [`np.random.sample`](https://docs.scipy.org/doc/numpy-1.16.0/reference/generated/numpy.random.sample.html) returns random floats in the half-open interval $[0.0, 1.0)$.\n", "- [`np.random.normal`](https://docs.scipy.org/doc/numpy-1.16.0/reference/generated/numpy.random.normal.html) draws random samples from a normal (Gaussian) distribution.\n", "- [`np.polyval`](https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyval.html) evaluates a polynomial (defined by its coefficients) at the given points" ] }, { "cell_type": "markdown", "metadata": { "id": "Ti-Egk5VfjSC" }, "source": [ "We are first going to generate a set of $x$ values taken at random in a given range ($[-N, N[$).\n", "\n", "The array `c` is used to store the coefficients of a random polynomial. To generate a random polynomial of degree $D$ we're going to generate $D$ random coefficients and set the coefficient of the leading term to $1$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 430 }, "execution": { "iopub.execute_input": "2024-10-13T21:47:51.590848Z", "iopub.status.busy": "2024-10-13T21:47:51.590468Z", "iopub.status.idle": "2024-10-13T21:47:51.758073Z", "shell.execute_reply": "2024-10-13T21:47:51.757344Z" }, "id": "ZujnBWOEfjSC", "outputId": "8ae083fb-90a9-412f-c44c-f2be4fe52d1d" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.random.uniform(-N , N, N) # x values are uniformly distributed between -100 and +100\n", "c = 200*np.random.sample((D,))-100 # random polynomial coefficients drawn from the interval [-100, 100)\n", "c = np.insert(c, 0, 1) # first coeff. of the random poly is 1\n", "y = np.polyval([1] + c, x)\n", "noise = np.random.normal(-0.5*np.std(y), 0.5*np.std(y), N) # some normally distributed noise\n", "y += noise # add noise to values\n", "plt.scatter(x, y)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 430 }, "execution": { "iopub.execute_input": "2024-10-13T21:47:51.790603Z", "iopub.status.busy": "2024-10-13T21:47:51.790119Z", "iopub.status.idle": "2024-10-13T21:47:51.941328Z", "shell.execute_reply": "2024-10-13T21:47:51.940612Z" }, "id": "4H9jY9c2fjSD", "outputId": "7deadd42-4bfb-49f0-a2a6-ad9645d57718" }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t = np.linspace(-N, N, num=N)\n", "p = np.poly1d(np.polyfit(x, y, D))\n", "plt.plot(x, y, 'o', t, p(t), '-')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "mY9Gw04ofjSD" }, "source": [ "### How well did we approximate?\n", "\n", "Show the coefficients of the approximating polynomial `p`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "execution": { "iopub.execute_input": "2024-10-13T21:47:51.943720Z", "iopub.status.busy": "2024-10-13T21:47:51.943327Z", "iopub.status.idle": "2024-10-13T21:47:51.947330Z", "shell.execute_reply": "2024-10-13T21:47:51.946794Z" }, "id": "2HejhTSIfjSD", "outputId": "c920c816-9583-4c4b-c410-0b54d094b067" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Coefficients of p: [ 1.782148 -21.511448 -3135.140655]\n", "Original coefficients: [ 1.000000 -22.956604 19.148379]\n" ] } ], "source": [ "np.set_printoptions(formatter={'float': '{: 12.6f}'.format})\n", "print(\"Coefficients of p: {}\".format(p.c))\n", "print(\"Original coefficients: {}\".format(c))" ] }, { "cell_type": "markdown", "metadata": { "id": "iv2QcMmzfjSD" }, "source": [ "Visualize the original polynomial `p_orig` and its approximation `p` obtained with polynomial regression." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 430 }, "execution": { "iopub.execute_input": "2024-10-13T21:47:51.949616Z", "iopub.status.busy": "2024-10-13T21:47:51.949204Z", "iopub.status.idle": "2024-10-13T21:47:52.071360Z", "shell.execute_reply": "2024-10-13T21:47:52.070593Z" }, "id": "bOKjV-N6fjSD", "outputId": "84050c32-edd0-4e8b-c83d-04b9abac6b3b" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p_orig = np.poly1d(c)\n", "plt.plot(x, y, 'o', t, p(t), '-', t, p_orig(t), '-')\n", "plt.show()" ] } ], "metadata": { "colab": { "include_colab_link": true, "provenance": [] }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.18" } }, "nbformat": 4, "nbformat_minor": 0 }