{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "_pn-VhfqZjo6" }, "source": [ "Goals:\n", "- Understand the nature of the root finding problem.\n", "- Use standard tools for rootfinding of polynomials\n", "- Understand bracketting root finding methods\n", "- Understand open root finding methods" ] }, { "cell_type": "markdown", "metadata": { "id": "qFHNYFbOThzq" }, "source": [ "# Root finding" ] }, { "cell_type": "markdown", "metadata": { "id": "Tp3d-5v9af0t" }, "source": [ "The roots (*aka zeros*) of a function are values of function arguments forwhich the function is zero:\n", "\n", "Find $x$ such that:\n", "\n", "$$ f(x) = 0 $$\n", "\n", "It can become complicated when we consider vector $\\vec{x}$ and even $\\vec{f}$, which may seem complicated at first, but consider a special case of finding the roots of $\\vec{f}(\\vec{x})$ is our familiar linear system, $A \\vec{x} -\\vec{b} = \\vec{0}$. This topic is mearly the generalization to nonlinear functions.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "2VTiTpIodfvI" }, "source": [ "## Roots of some nonlinear functions" ] }, { "cell_type": "markdown", "metadata": { "id": "uwXnhF5ElHMA" }, "source": [ "Let's build some intuition by exploring some type of roots in 1D functions using the *graphical method*: Plot the function and examine where it crosses the x-axis.\n", "\n", "NB: Note the structure of the code below - Since we don't know *a priori* where the roots will be, we have to take a series of initial guesses and cross our finger.... and even then we may fail to find them all!" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "id": "FhifkcrmdkOJ" }, "outputs": [], "source": [ "# prompt: Define a function that takes a function, plots it with xrange -10 to 10 and y range -10 to 10 with a line, solves for the roots using fsolve if the roots were found, plot them with dots\n", "# NB: Modified from original output\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import root\n", "\n", "def plot_and_find_roots(func):\n", " \"\"\"Plots a function and finds its roots using fsolve.\n", "\n", " Args:\n", " func: The function to plot and find roots for.\n", " \"\"\"\n", "\n", " x = np.linspace(-10, 10, 400)\n", " y = func(x)\n", "\n", " plt.figure(figsize=(8, 6))\n", " plt.plot(x, y, label='f(x)')\n", " plt.axhline(y=0, color='black', linestyle='--') # Plot the x-axis\n", " plt.xlabel('x')\n", " plt.ylabel('f(x)')\n", " plt.title('Plot of f(x) and its Roots')\n", " plt.xlim([-10, 10])\n", " plt.ylim([-10, 10])\n", "\n", " x0s = np.arange(-10,10,1)\n", " for x0 in x0s:\n", " r = root(func, x0=x0)\n", " if r.success:\n", " plt.plot(r.x, r.fun, 'ro', markersize=8) # Plot root with a red dot\n", " plt.legend(['f(x)', 'Roots'])\n", "\n", " plt.grid(True)\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "8of0fQ2ReEKW" }, "source": [ "#### Example 1: Real roots - $x^2-4$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 564 }, "id": "6VKwATUteJYW", "outputId": "527745fd-8c46-4d80-f541-1521a11de378" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_and_find_roots(lambda x: x**2-4)" ] }, { "cell_type": "markdown", "metadata": { "id": "rSmMFWeYePtv" }, "source": [ "#### Example 2: No roots - $1/x$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 599 }, "id": "rfqRukYweTs8", "outputId": "3c02392c-3763-4ef6-8602-5953cebd69f9" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ ":1: RuntimeWarning: divide by zero encountered in divide\n", " plot_and_find_roots(lambda x: 1/x)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_and_find_roots(lambda x: 1/x)" ] }, { "cell_type": "markdown", "metadata": { "id": "Gp_xyKJxlpWj" }, "source": [ "Noting that the vertical line is a plotting artifact." ] }, { "cell_type": "markdown", "metadata": { "id": "i3LmXuQ1dVWi" }, "source": [ "#### Example 3: Infinite roots $sin(x^2)$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 564 }, "id": "FOMdaagOgxyA", "outputId": "9d81330d-e570-4ca8-9d25-9e6d3e88b305" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_and_find_roots(lambda x: np.sin(x**2))" ] }, { "cell_type": "markdown", "metadata": { "id": "rJRxUOG6lwPz" }, "source": [ "Only the roots closest to the initial guesses are found!" ] }, { "cell_type": "markdown", "metadata": { "id": "D4AEOI8kgMbc" }, "source": [ "## Complex roots - $x^2+1$" ] }, { "cell_type": "markdown", "metadata": { "id": "TGXfiiQfhWDZ" }, "source": [ "Even the graphical method is not completely reliable due to the existence of *complex roots*" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 564 }, "id": "Jfg1w5qEnnUa", "outputId": "78c0698b-b5b0-4968-fa95-9049f65fb602" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def fun(x):\n", " return x**2 + 1\n", "\n", "# Wrong!\n", "plot_and_find_roots(fun)" ] }, { "cell_type": "markdown", "metadata": { "id": "bbvcQSdsn8l8" }, "source": [ "**But this is wrong!** The quadratic has 2 roots but we need to use a different method:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "da3dkBMygO_z" }, "outputs": [], "source": [ "root(lambda x: x**2+1, x0 = [1+1j, 1-1j], method = \"krylov\")" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 564 }, "id": "ccpDG2mRoEUW", "outputId": "f2139e52-7b60-4061-b716-ed12d7114356" }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# prompt: Do a complex plot of x**2+1 and add points at the roots\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import root\n", "\n", "def complex_plot(func):\n", " \"\"\"Plots a complex function and finds its roots using root.\n", "\n", " Args:\n", " func: The function to plot and find roots for.\n", " \"\"\"\n", "\n", " real_range = np.linspace(-3, 3, 100)\n", " imag_range = np.linspace(-3, 3, 100)\n", "\n", " real_part = np.empty((len(real_range), len(imag_range)))\n", " imag_part = np.empty((len(real_range), len(imag_range)))\n", "\n", " for i, real in enumerate(real_range):\n", " for j, imag in enumerate(imag_range):\n", " z = complex(real, imag)\n", " result = func(z)\n", " real_part[i, j] = result.real\n", " imag_part[i, j] = result.imag\n", "\n", " plt.figure(figsize=(8, 6))\n", " plt.contourf(real_range, imag_range, real_part, cmap='viridis')\n", " plt.colorbar(label='Real Part')\n", " plt.xlabel('Real')\n", " plt.ylabel('Imaginary')\n", " plt.title('Complex Plot of f(z)')\n", " plt.grid(True)\n", "\n", " # Find roots and plot them\n", " r = root(lambda x: x**2 + 1, x0=[1 + 1j, 1 - 1j], method=\"krylov\")\n", " if r.success:\n", " for root_val in r.x:\n", " plt.plot(root_val.real, root_val.imag, 'ro', markersize=8) # Plot root with a red dot\n", "\n", " plt.show()\n", "\n", "\n", "# Use the function to plot x**2 + 1\n", "complex_plot(lambda z: z**2 + 1)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "67447ON1ojJI" }, "source": [ "DON'T WORRY - We won't be dealing with complex numbers in general in this course :-)" ] } ], "metadata": { "colab": { "authorship_tag": "ABX9TyOcuJ3HnrjQR3bjztA7+1FP", "include_colab_link": true, "provenance": [], "toc_visible": true }, "kernelspec": { "display_name": "Python 3", "name": "python3" }, "language_info": { "name": "python" } }, "nbformat": 4, "nbformat_minor": 0 }