102_InterpolationSciPy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'scipy'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-5-f2287e87e857>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minterpolate\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0minterp1d\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'scipy'"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (1.20.1)\n",
      "\u001b[33mWARNING: You are using pip version 20.2.4; however, version 21.0.1 is available.\n",
      "You should consider upgrading via the '/usr/local/Cellar/jupyterlab/2.2.9_1/libexec/bin/python -m pip install --upgrade pip' command.\u001b[0m\n",
      "Requirement already satisfied: matplotlib in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (3.3.4)\n",
      "Requirement already satisfied: numpy>=1.15 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (1.20.1)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (1.3.1)\n",
      "Requirement already satisfied: pillow>=6.2.0 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (8.1.0)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.3 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (2.4.7)\n",
      "Requirement already satisfied: cycler>=0.10 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (0.10.0)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from matplotlib) (2.8.1)\n",
      "Requirement already satisfied: six in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from cycler>=0.10->matplotlib) (1.15.0)\n",
      "\u001b[33mWARNING: You are using pip version 20.2.4; however, version 21.0.1 is available.\n",
      "You should consider upgrading via the '/usr/local/Cellar/jupyterlab/2.2.9_1/libexec/bin/python -m pip install --upgrade pip' command.\u001b[0m\n",
      "Collecting scipy\n",
      "  Using cached scipy-1.6.1-cp39-cp39-macosx_10_9_x86_64.whl (30.9 MB)\n",
      "Requirement already satisfied: numpy>=1.16.5 in /usr/local/Cellar/jupyterlab/2.2.9_1/libexec/lib/python3.9/site-packages (from scipy) (1.20.1)\n",
      "Installing collected packages: scipy\n",
      "Successfully installed scipy-1.6.1\n",
      "\u001b[33mWARNING: You are using pip version 20.2.4; however, version 21.0.1 is available.\n",
      "You should consider upgrading via the '/usr/local/Cellar/jupyterlab/2.2.9_1/libexec/bin/python -m pip install --upgrade pip' command.\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "!{sys.executable} -m pip install numpy\n",
    "!{sys.executable} -m pip install matplotlib\n",
    "!{sys.executable} -m pip install scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy import interpolate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.linspace(0,10,num=11)\n",
    "y=np.array([1,1,1,1,1,2,2,2,2,2,2])\n",
    "f=interp1d(x,y)\n",
    "f2=interp1d(x,y,kind='cubic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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": [
    "xnew=np.linspace(0,10,num=41)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(x,y,'o')\n",
    "plt.plot(xnew,f(xnew),'-')\n",
    "plt.plot(xnew,f2(xnew),'--')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cubic-spline interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "tck=interpolate.splrep(x,y)\n",
    "xnew=np.arange(0,3*np.pi,np.pi/50)\n",
    "ynew=interpolate.splev(xnew,tck)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": [
    "plt.plot(x,y,'o')\n",
    "plt.plot(xnew,ynew,'-')\n",
    "plt.grid()"
   ]
  },
  {
   "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": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}