97 lines
3.3 KiB
Plaintext
97 lines
3.3 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# Optimization of a two-parameter function\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import numpy as np\n\n\n# Define the function that we are interested in\ndef sixhump(x):\n return (\n (4 - 2.1 * x[0] ** 2 + x[0] ** 4 / 3) * x[0] ** 2\n + x[0] * x[1]\n + (-4 + 4 * x[1] ** 2) * x[1] ** 2\n )\n\n\n# Make a grid to evaluate the function (for plotting)\nxlim = [-2, 2]\nylim = [-1, 1]\nx = np.linspace(*xlim) # type: ignore[call-overload]\ny = np.linspace(*ylim) # type: ignore[call-overload]\nxg, yg = np.meshgrid(x, y)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## A 2D image plot of the function\n Simple visualization in 2D\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n\nplt.figure()\nplt.imshow(sixhump([xg, yg]), extent=xlim + ylim, origin=\"lower\") # type: ignore[arg-type]\nplt.colorbar()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## A 3D surface plot of the function\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"from mpl_toolkits.mplot3d import Axes3D\n\nfig = plt.figure()\nax: Axes3D = fig.add_subplot(111, projection=\"3d\")\nsurf = ax.plot_surface(\n xg,\n yg,\n sixhump([xg, yg]),\n rstride=1,\n cstride=1,\n cmap=\"viridis\",\n linewidth=0,\n antialiased=False,\n)\n\nax.set_xlabel(\"x\")\nax.set_ylabel(\"y\")\nax.set_zlabel(\"f(x, y)\")\nax.set_title(\"Six-hump Camelback function\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Find minima\n\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import scipy as sp\n\n# local minimization\nres_local = sp.optimize.minimize(sixhump, x0=[0, 0])\n\n# global minimization\nres_global = sp.optimize.differential_evolution(sixhump, bounds=[xlim, ylim])\n\nplt.figure()\n# Show the function in 2D\nplt.imshow(sixhump([xg, yg]), extent=xlim + ylim, origin=\"lower\") # type: ignore[arg-type]\nplt.colorbar()\n# Mark the minima\nplt.scatter(res_local.x[0], res_local.x[1], label=\"local minimizer\")\nplt.scatter(res_global.x[0], res_global.x[1], label=\"global minimizer\")\nplt.legend()\nplt.show()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.11"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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