polynomial fit.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# https://stackoverflow.com/questions/19165259/python-numpy-scipy-curve-fitting\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "points = np.array([(1, 1), (2, 4), (3, 1), (9, 3)])\n",
    "# get x and y vectors\n",
    "x = points[:,0]\n",
    "y = points[:,1]\n",
    "\n",
    "# calculate polynomial\n",
    "z = np.polyfit(x, y, 3)\n",
    "f = np.poly1d(z)\n",
    "\n",
    "# calculate new x's and y's\n",
    "x_new = np.linspace(x[0], x[-1], 50)\n",
    "y_new = f(x_new)\n",
    "\n",
    "plt.plot(x,y,'o', x_new, y_new)\n",
    "plt.xlim([x[0]-1, x[-1] + 1 ])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "points = np.array([(6, 42), (7, 56), (8, 72), (9, 90)])\n",
    "# get x and y vectors\n",
    "x = points[:,0]\n",
    "y = points[:,1]\n",
    "\n",
    "# calculate polynomial\n",
    "z = np.polyfit(x, y, 2)\n",
    "f = np.poly1d(z)\n",
    "\n",
    "# calculate new x's and y's\n",
    "x_new = np.linspace(0, x[-1], 50)\n",
    "y_new = f(x_new)\n",
    "\n",
    "# insert specifically x=3\n",
    "x = np.insert(x,0,3)\n",
    "y = np.insert(y,0,f([3])[0])\n",
    "\n",
    "plt.plot(x,y,'o', x_new, y_new)\n",
    "plt.xlim([-1, x[-1] + 1 ])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.000000000000165"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f([3])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.insert(x,0,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 12, 42, 56, 72, 90])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.insert(y,0,f([3])[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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