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Last active October 27, 2020 18:48
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Exeample 1.7
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{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "[Launch in Binder](https://mybinder.org/v2/gh/fedxa/PHYS30471_env/main?urlpath=git-pull?repo=https://gist.github.com/3b89fa213d7e6794ea267a2280328142.git%26urlpath=tree/3b89fa213d7e6794ea267a2280328142.git/ex1_7.ipynb)"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "# Exercise 1.7"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "import matplotlib.pyplot as plt\nimport math",
"execution_count": 13,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Iteartion step"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def iteration(l, x):\n f = x*x-l\n fprime = 2*x\n return x-f/fprime",
"execution_count": 9,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Make `nstep` iterations and return the list of values"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def make_iterations(l, x0, nsteps):\n x = x0\n xl = [x]\n for i in range(nsteps):\n x = iteration(l, x)\n xl.append(x)\n return xl",
"execution_count": 10,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "make_iterations(0.5, 0.1, 10)",
"execution_count": 11,
"outputs": [
{
"data": {
"text/plain": "[0.1,\n 2.55,\n 1.3730392156862743,\n 0.8685974371897991,\n 0.722119047433116,\n 0.7072628275743689,\n 0.7071067984011347,\n 0.7071067811865477,\n 0.7071067811865476,\n 0.7071067811865475,\n 0.7071067811865476]"
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Positive $\\lambda$"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Plot several results fo rpositive $\\lambda$. Converges to $\\pm\\sqrt{\\lambda}$ depending on the sign of $x_0$. Otherwise precise value of $x_0$ does not matter after several steps."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "n = 10\nirange = range(0, n+1)\n\nl = 0.5\nplt.title('$\\lambda = %g$'%(l))\nplt.plot(irange, make_iterations(l, 1, n), 'o-')\nplt.plot(irange, make_iterations(l, 0.1, n), 'v-')\nplt.plot(irange, make_iterations(l, -1, n), '^-')\nplt.plot(irange, make_iterations(l, -2, n), '>-')",
"execution_count": 33,
"outputs": [
{
"data": {
"text/plain": "[<matplotlib.lines.Line2D at 0x7f8cf3cc8e80>]"
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "n = 10\nirange = range(0, n+1)\n\nl = 1\nplt.title('$\\lambda = %g$'%(l))\nplt.plot(irange, make_iterations(l, 1, n), 'o-')\nplt.plot(irange, make_iterations(l, 0.1, n), 'v-')\nplt.plot(irange, make_iterations(l, -1, n), '^-')\nplt.plot(irange, make_iterations(l, -2, n), '>-')",
"execution_count": 34,
"outputs": [
{
"data": {
"text/plain": "[<matplotlib.lines.Line2D at 0x7f8cf3c23e50>]"
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "n = 10\nirange = range(0, n+1)\n\nl = 2\nplt.title('$\\lambda = %g$'%(l))\nplt.plot(irange, make_iterations(l, 1, n), 'o-')\nplt.plot(irange, make_iterations(l, 0.1, n), 'v-')\nplt.plot(irange, make_iterations(l, -1, n), '^-')\nplt.plot(irange, make_iterations(l, -2, n), '>-')",
"execution_count": 35,
"outputs": [
{
"data": {
"text/plain": "[<matplotlib.lines.Line2D at 0x7f8cf3c03eb0>]"
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "n = 10\nirange = range(0, n+1)\n\nl = 5\nplt.title('$\\lambda = %g$'%(l))\nplt.plot(irange, make_iterations(l, 1, n), 'o-')\nplt.plot(irange, make_iterations(l, 0.1, n), 'v-')\nplt.plot(irange, make_iterations(l, -1, n), '^-')\nplt.plot(irange, make_iterations(l, -2, n), '>-')",
"execution_count": 36,
"outputs": [
{
"data": {
"text/plain": "[<matplotlib.lines.Line2D at 0x7f8cf3b6aa60>]"
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Negative $\\lambda$"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "n = 1000\nirange = range(0, n+1)\n\nl = -1\nplt.title('$\\lambda = %g$'%(l))\nplt.plot(irange, make_iterations(l, 0.1, n), '-', label='x0=0.1')\nplt.plot(irange, make_iterations(l, 0.10001, n), '-', label='x0=0.10001')\nplt.legend()",
"execution_count": 39,
"outputs": [
{
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x7f8cf3addd00>"
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Quite chaotic, and really strongly depends on initial conditions!"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "",
"execution_count": null,
"outputs": []
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"name": "python",
"version": "3.8.6",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"toc": {
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"base_numbering": 1,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
},
"gist": {
"id": "3b89fa213d7e6794ea267a2280328142",
"data": {
"description": "Exeample 1.7",
"public": true
}
},
"_draft": {
"nbviewer_url": "https://gist.github.com/3b89fa213d7e6794ea267a2280328142"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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