fit_polynomials.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "time = np.array([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0])\n",
    "height = np.array([1.1, 2.2, 3.1, 4.0, 4.8, 5.5, 6.0, 6.4, 6.9, 7.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6.67272727,  1.04      ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "line = np.polyfit(x=time, y=height, deg=1)\n",
    "line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb030039978>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb030070160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.scatter(time, height)\n",
    "plt.plot(time, np.poly1d(line)(time))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/vince/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:1: RankWarning: Polyfit may be poorly conditioned\n",
      "  if __name__ == '__main__':\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([  5.35903504e+03,  -2.20342165e+04,   3.22968022e+04,\n",
       "        -1.24946605e+04,  -1.97891743e+04,   3.03477926e+04,\n",
       "        -1.92241427e+04,   6.74687107e+03,  -1.34570302e+03,\n",
       "         1.50051460e+02,  -5.55531337e+00])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "high_deg = np.polyfit(x=time, y=height, deg=len(time))\n",
    "high_deg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb0300111d0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+NN6QQ0QugIpbfGLtzqP8eOVW2kZF8NLsMVzav6vTkURChopbWpXbY/nNu5/x1Lq9DO8d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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb02ffe99b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.scatter(time, height)\n",
    "plt.plot(time, np.poly1d(high_deg)(time))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}