parabola2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'pandas'",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-3ae3419af99a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_line_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'matplotlib'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'inline'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mpandas\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mcodecs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'pandas'"
     ]
    }
   ],
   "source": [
    "import matplotlib\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline  \n",
    "\n",
    "import pandas as pd\n",
    "import codecs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parabola"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "output_type": "display_data",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "xmin, xmax= -1, 3\n",
    "a, b, c = -1, 1, -1\n",
    "\n",
    "x = np.linspace(xmin, xmax)\n",
    "y = a* x**2 + b*x + c\n",
    "ymin, ymax = np.min(y), np.max([1,np.max(y)])\n",
    "\n",
    "xticks = np.arange(int(xmin), int(xmax)+1)\n",
    "yticks = np.arange(int(ymin), int(ymax)+1)\n",
    "\n",
    "fig = plt.figure(figsize=(8,4))\n",
    "ax = fig.gca()\n",
    "\n",
    "for xt in xticks:\n",
    "    ax.axvline(x=xt, ymin=ymin, ymax=ymax, lw=1, ls='-.' if xt != 0 else '-', color='k'  if xt == 0 else 'lightgrey')\n",
    "\n",
    "for yt in yticks:\n",
    "    ax.axhline(y=yt, lw=1, ls='-.' if yt != 0 else '-', color='k' if yt == 0 else 'lightgrey')\n",
    "\n",
    "    \n",
    "\n",
    "\n",
    "ax.plot(x, y, c='g', lw=2, label=f\"$y={a}x^2+{b}x+{c}$\")\n",
    "\n",
    "# plt.scatter(dots, dots**2, c='r', s=7)\n",
    "\n",
    "\n",
    "ax.legend()\n",
    "plt.savefig('./pics/parabola4.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$y=x^2$\n",
    "\n",
    "$y = -x$\n",
    "\n",
    "$y = x^2 - x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'pd' is not defined",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-3-e6bd7e685b4f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mDataFrame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m{\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m11\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'$f(x)=x^2$'\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m11\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_index\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'pd' is not defined"
     ]
    }
   ],
   "source": [
    "t = pd.DataFrame({'x': np.linspace(0,1,11), '$f(x)=x^2$': np.linspace(0,1,11)**2})\n",
    "t = t.set_index('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 't' is not defined",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-34fc7a11cb38>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mt\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 't' is not defined"
     ]
    }
   ],
   "source": [
    "t\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "'\\\\begin{tabular}{lr} \\\\toprule {} &  \\\\$f(x)=x\\\\textasciicircum 2\\\\$ \\\\  x   &             \\\\  \\\\midrule 0.0 &        0.00 \\\\  0.1 &        0.01 \\\\  0.2 &        0.04 \\\\  0.3 &        0.09 \\\\  0.4 &        0.16 \\\\  0.5 &        0.25 \\\\  0.6 &        0.36 \\\\  0.7 &        0.49 \\\\  0.8 &        0.64 \\\\  0.9 &        0.81 \\\\  1.0 &        1.00 \\\\  \\\\bottomrule \\\\end{tabular} '"
      ]
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "st = t.to_latex().replace('\\n', ' ').replace('\\\\\\\\', r\"\\ \")\n",
    "st"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\\\begin{tabular}{lrr}\\n\\\\toprule\\n{} &    x &  \\\\$f(x)=x\\\\textasciicircum 2\\\\$ \\\\\\\\\\n\\\\midrule\\n0  &  0.0 &        0.00 \\\\\\\\\\n1  &  0.1 &        0.01 \\\\\\\\\\n2  &  0.2 &        0.04 \\\\\\\\\\n3  &  0.3 &        0.09 \\\\\\\\\\n4  &  0.4 &        0.16 \\\\\\\\\\n5  &  0.5 &        0.25 \\\\\\\\\\n6  &  0.6 &        0.36 \\\\\\\\\\n7  &  0.7 &        0.49 \\\\\\\\\\n8  &  0.8 &        0.64 \\\\\\\\\\n9  &  0.9 &        0.81 \\\\\\\\\\n10 &  1.0 &        1.00 \\\\\\\\\\n\\\\bottomrule\\n\\\\end{tabular}\\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "LookupError",
     "evalue": "unknown encoding: unicode",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mLookupError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-7-605f258093ca>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mcodecs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdecode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mst\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'unicode'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mLookupError\u001b[0m: unknown encoding: unicode"
     ]
    }
   ],
   "source": [
    "codecs.decode(st, 'unicode')"
   ]
  },
  {
   "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
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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