diff --git a/assets/Notebooks/Line_search.ipynb b/assets/Notebooks/Line_search.ipynb index 78c11ff7..009d1666 100644 --- a/assets/Notebooks/Line_search.ipynb +++ b/assets/Notebooks/Line_search.ipynb @@ -1,23 +1,10 @@ { - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "name": "Line search.ipynb", - "provenance": [], - "include_colab_link": true - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - } - }, "cells": [ { "cell_type": "markdown", "metadata": { - "id": "view-in-github", - "colab_type": "text" + "colab_type": "text", + "id": "view-in-github" }, "source": [ "\"Open" @@ -44,14 +31,38 @@ }, { "cell_type": "code", + "execution_count": 2, "metadata": { - "id": "6mX5U4M6q12j", "colab": { "base_uri": "https://localhost:8080/", "height": 332 }, + "id": "6mX5U4M6q12j", "outputId": "e8ccbad8-9056-4186-bfd8-790893f7c5e1" }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "🤓 We'll compare ['random search', 'binary search', 'golden search', 'parabolic search'] on the Inverse Maxwell function on the [0, 6] interval\n", + "🤓 Random search: 80 function calls. 40 iterations. f = 0.71\n", + "🤓 Binary search: 23 function calls. 13 iterations. f = 0.71\n", + "🤓 Golden search: 20 function calls. 19 iterations. f = 0.71\n", + "🤓 Parabolic search: 17 function calls. 14 iterations. f = 0.71\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "#@title Line search for unimodal functions. Optimizers comparison { run: \"auto\" }\n", "# Need to implement brent method, but in scipy\n", @@ -253,7 +264,7 @@ " return -np.sqrt(2/math.pi) * x**2*np.exp(-x**2/(2*(a)**2))/(a)**3\n", "f_2 = lambda x: inverse_maxwell(x, 2) + 1 \n", "\n", - "# \"(x - 2) * x * (x + 2)**2\"\n", + "# \"(x - 2) * x * (x + 2)**2 + 10\"\n", "f_3 = lambda x: (x - 2) * x * (x + 2)**2 + 10 \n", "\n", "def callback(xk, f, funs, xs):\n", @@ -274,7 +285,7 @@ "if Parabolic_search:\n", " optimizers.append('parabolic search')\n", "\n", - "Function = 'Inverse Maxwell' #@param ['Inverse Maxwell', \"sin(sin(sin(sqrt(x/2))))\", \"(x - 2) * x * (x + 2)**2\"] \n", + "Function = 'Inverse Maxwell' #@param ['Inverse Maxwell', \"sin(sin(sin(sqrt(x/2))))\", \"(x - 2) * x * (x + 2)**2 + 10\"] \n", "a = 0 #@param {type:\"slider\", min:-5, max:5, step:1}\n", "b = 6 #@param {type:\"slider\", min:0, max:10, step:1}\n", "tolerance = 1e-3\n", @@ -286,7 +297,7 @@ " func = f_2\n", "elif Function == 'sin(sin(sin(sqrt(x/2))))':\n", " func = f_1\n", - "elif Function == '(x - 2) * x * (x + 2)**2':\n", + "elif Function == '(x - 2) * x * (x + 2)**2 + 10':\n", " func = f_3\n", "\n", "x = np.linspace(a,b)\n", @@ -361,33 +372,40 @@ "\n", "fig.tight_layout()\n", "plt.show()\n" - ], - "execution_count": 16, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "🤓 We'll compare ['random search', 'binary search', 'golden search', 'parabolic search'] on the Inverse Maxwell function on the [0, 6] interval\n", - "🤓 Random search: 78 function calls. 39 iterations. f = 0.71\n", - "🤓 Binary search: 23 function calls. 13 iterations. f = 0.71\n", - "🤓 Golden search: 20 function calls. 19 iterations. f = 0.71\n", - "🤓 Parabolic search: 17 function calls. 14 iterations. f = 0.71\n" - ] - }, - { - "output_type": "display_data", - "data": { - "image/png": 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\n", 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