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@hannorein
Last active September 22, 2023 22:09
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Sqrt7 IAS15
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "40a79c53",
"metadata": {
"ExecuteTime": {
"end_time": "2023-09-22T21:56:12.064141Z",
"start_time": "2023-09-22T21:56:11.660035Z"
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "1283edb7",
"metadata": {
"ExecuteTime": {
"end_time": "2023-09-22T22:08:25.851441Z",
"start_time": "2023-09-22T22:08:25.841389Z"
}
},
"outputs": [],
"source": [
"def old(a):\n",
" x = 1.\n",
" for k in range(20):\n",
" x6 = x*x*x*x*x*x\n",
" x += (a/x6-x)/7.\n",
" return x\n",
"def new(a):\n",
" scale = 1.\n",
" if a<1e-7:\n",
" scale = 0.1\n",
" a *= 1e7 \n",
" if a>1e2:\n",
" scale = 10\n",
" a *= 1e-7\n",
" x = 1.\n",
" for k in range(20):\n",
" x6 = x*x*x*x*x*x\n",
" x += (a/x6-x)/7.\n",
" return x*scale \n",
"def rahil(a):\n",
" i = 0\n",
" x = 1\n",
" while 1:\n",
" x6 = x*x*x*x*x*x\n",
" xnew = (a/x6-x)/7.\n",
" if np.abs(xnew)<1.0e-14 or i>100:\n",
" break\n",
" x += xnew\n",
" i += 1\n",
" return x"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "a0e2ac72",
"metadata": {
"ExecuteTime": {
"end_time": "2023-09-22T22:08:26.571491Z",
"start_time": "2023-09-22T22:08:26.492025Z"
}
},
"outputs": [],
"source": [
"_a = np.logspace(-15, 10,1000)\n",
"_old = np.zeros(len(_a))\n",
"_new = np.zeros(len(_a))\n",
"_rahil = np.zeros(len(_a))\n",
"for i in range(len(_a)):\n",
" _old[i] = old(_a[i])\n",
" _new[i] = new(_a[i]) \n",
" _rahil[i] = rahil(_a[i]) "
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "7a248b35",
"metadata": {
"ExecuteTime": {
"end_time": "2023-09-22T22:08:35.934980Z",
"start_time": "2023-09-22T22:08:35.659954Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x13c0ea1f0>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.set_xscale(\"log\")\n",
"ax.set_yscale(\"log\")\n",
"ax.set_ylabel(\"absolute error\")\n",
"ax.plot(_a, np.abs(_old-np.power(_a,1./7.)), label=\"old\")\n",
"ax.plot(_a, np.abs(_new-np.power(_a,1./7.)), label=\"new\")\n",
"ax.plot(_a, np.abs(_rahil-np.power(_a,1./7.)), label=\"rahil\")\n",
"ax.legend()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "40cc5218",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.6"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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