TaylorSeriesRelation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-09T21:53:31.334410Z",
     "start_time": "2018-11-09T21:53:29.413713Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from tqdm import tqdm_notebook as tqdm\n",
    "\n",
    "from sklearn.decomposition import TruncatedSVD\n",
    "import powerlaw\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "mus = [0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5]\n",
    "y = []\n",
    "ts = []\n",
    "for mu in mus:\n",
    "    exp =(4/mu)-1\n",
    "    y.append(1/exp)\n",
    "    ts.append(mu/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(mus,y, label=r\"$\\dfrac{1}{(4/\\mu)-1}$\")\n",
    "plt.scatter(mus,ts, label=r\"$\\dfrac{\\mu}{2}$\")\n",
    "\n",
    "\n",
    "plt.rcParams['figure.figsize'] = [8,8]\n",
    "matplotlib.rcParams.update({'font.size': 20})\n",
    "legend_prop={'size':18}\n",
    "marker_size = 75\n",
    "\n",
    "plt.xlabel(r\"$\\mu$\")\n",
    "plt.legend(prop=legend_prop)\n",
    "plt.title(r\"Taylor Series Relation for $\\mu$\")\n",
    "plt.savefig(\"img/taylor-series.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}