143 lines
26 KiB
Plaintext
143 lines
26 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",
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"# Finding the minimum of a smooth function\n",
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"\n",
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"Demos various methods to find the minimum of a 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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"outputs_hidden": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[<matplotlib.lines.Line2D at 0x10f014710>]"
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]
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},
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"\n",
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"def f(x):\n",
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" return x**2 + 10 * np.sin(x)\n",
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"\n",
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"\n",
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"x = np.arange(-5, 5, 0.1)\n",
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"plt.plot(x, f(x))"
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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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"Now find the minimum with a few methods\n",
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"\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": 2,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" message: Optimization terminated successfully.\n",
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" success: True\n",
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" status: 0\n",
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" fun: -7.945823375615215\n",
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" x: [-1.306e+00]\n",
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" nit: 5\n",
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" jac: [-1.192e-06]\n",
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" hess_inv: [[ 8.589e-02]]\n",
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" nfev: 12\n",
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" njev: 6\n"
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]
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}
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],
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"source": [
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"import scipy as sp\n",
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"\n",
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"# The default (Nelder Mead)\n",
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"print(sp.optimize.minimize(f, x0=0))"
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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": 4,
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"metadata": {
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"collapsed": false,
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"jupyter": {
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"outputs_hidden": false
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}
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},
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"outputs": [],
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"source": [
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"plt.show()"
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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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"outputs": [],
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"source": []
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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 (ipykernel)",
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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": 4
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}
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