exmaple.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from spectralCollocationSolver import SpectralCollocationSolver\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the barycentricInterpolation module can not be found (\"ModuleNotFoundError: No module named 'barycentricInterpolation'\"), probably you just forgot to install it. The package is provided in my github repository with the same name (https://github.com/lubo92/barycentricLagrangeInterpolation/). Download or clone the repository and then run the setup.py installation utility. For details see the readme in the repository."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Define the Function to Be Solved"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To some people the following coding approach may appear a little bit strange. I'm not sure if this is a good concept or not - but it works!\n",
    "In the provided python package (`spectralCollocationSolver`) a class `SepctralCollocationSolver` exists. This class contains all functionality to solve differential equations - with one exception: The traget function is not contained.\n",
    "In order to define the function to be solved, follow the provided exmaple:\n",
    "* First you need to create a child class of the `SpectralCollocationSolver`. In the example below it's the `HarmonicOscillator` class.\n",
    "* Copy the `__init__` method from the exmaple to your function.\n",
    "* Create the `residuals` function. In this function you define your differential equation to be solved. You have to return the residual of the interpolating function solving your differential equation at every node as well as the residuals for all boundary conditions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "**CAVEAT:**\n",
    "\n",
    "Since we are using a barycentric Langrange Interpolation to solve the differential equation, the target function is only defined on the intervall [-1,1]. If your differential equation is defined on an other domain you have to transform your coordinates, e.g. with a tangent.\n",
    "\n",
    "Be cautious: If you transform your coordinates, you need also transform your derivatives/ differential equations. For details see my repository on the Blasius equation, where I apply this Python package.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How to define the differential equation:**\n",
    "* `values` is the array containing the values of the interpolating function at all nodes\n",
    "* `self.f.derivative(values,self.D1)` returns the (values of the) first derivative of the function defined by '`values`' at the nodes\n",
    "* `self.f.derivative(values,self.D2)` returns the (values of the) second derivative of the function defined by '`values`' at the nodes\n",
    "* `self.f.evaluateFunction(-1,values,self.weights,self.nodes)` gives you the function at the point -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class HarmonicOscillator(SpectralCollocationSolver):\n",
    "    def __init__(self):\n",
    "        SpectralCollocationSolver.__init__(self)\n",
    "        \n",
    "    def residuals(self,values,args):\n",
    "        \"\"\"This function calculates some residuals:\n",
    "        - the residuals of the harmonic oscillator equation at every node\n",
    "        - the residuals of every boundary condition\n",
    "        \n",
    "        Parameters:\n",
    "        values(ndarray[nNodes]): values of the function to calculate residuals for - given at every sampling point\n",
    "        args(tuple): (omega^2,f(0),f'(0))\n",
    "\n",
    "        Returns:\n",
    "        ndarray[nNodes+2] : residuals at every node as well as residuals of the two boundary conditions\n",
    "        \"\"\"\n",
    "        omega2 = args[0]\n",
    "        boundary1 = args[1]\n",
    "        boundary2 = args[2]\n",
    "        \n",
    "        \n",
    "        #residuals at the sampling points\n",
    "        residuals1 = omega2*values + self.f.derivative(values,self.D2)\n",
    "        \n",
    "        #residuals for boundary conditions\n",
    "        residuals2 = self.f.evaluateFunction(-1,values,self.weights,self.nodes)-boundary1\n",
    "        residuals3 = self.f.evaluateFunction(-1,self.f.derivative(values,self.D1),self.weights,self.nodes)-boundary2\n",
    "        temp2 = np.reshape(residuals2,1)\n",
    "        temp3 = np.reshape(residuals3,1)\n",
    "        return np.concatenate((residuals1, temp2, temp3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initialize Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initializing spectral collocation solver class\n"
     ]
    }
   ],
   "source": [
    "solver = HarmonicOscillator()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Set up Solver\n",
    "'nNodes' is the number of nodes, at which the differential equation is solved. A low number of nodes gives very quick results and is in most cases nummerically stable, but it might not be possible approximate the target function well with only very few nodes. A high number of nodes may take longer to calculate and get's at some point nummerically unstable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initializing interpolating function class\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/wolfgang/anaconda3/envs/pa/lib/python3.7/site-packages/barycentricLagrangeInterpolation-1.0.0-py3.7.egg/barycentricLagrangeInterpolation/barycentricLagrangeInterpolation.py:66: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  np.repeat(np.reshape(nodes,[len(nodes),1]),len(s),axis=1)),axis=0)\n",
      "/home/wolfgang/anaconda3/envs/pa/lib/python3.7/site-packages/barycentricLagrangeInterpolation-1.0.0-py3.7.egg/barycentricLagrangeInterpolation/barycentricLagrangeInterpolation.py:69: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  temp1 = weights[j]/(s-nodes[j])\n",
      "/home/wolfgang/anaconda3/envs/pa/lib/python3.7/site-packages/barycentricLagrangeInterpolation-1.0.0-py3.7.egg/barycentricLagrangeInterpolation/barycentricLagrangeInterpolation.py:70: RuntimeWarning: invalid value encountered in multiply\n",
      "  l[j,:]=temp1*temp2\n",
      "/home/wolfgang/anaconda3/envs/pa/lib/python3.7/site-packages/barycentricLagrangeInterpolation-1.0.0-py3.7.egg/barycentricLagrangeInterpolation/barycentricLagrangeInterpolation.py:160: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  temp5=tempW/tempS\n",
      "/home/wolfgang/anaconda3/envs/pa/lib/python3.7/site-packages/barycentricLagrangeInterpolation-1.0.0-py3.7.egg/barycentricLagrangeInterpolation/barycentricLagrangeInterpolation.py:171: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  temp5 = np.nan_to_num(i/tempS*(tempW*temp7-temp5))\n",
      "/home/wolfgang/anaconda3/envs/pa/lib/python3.7/site-packages/barycentricLagrangeInterpolation-1.0.0-py3.7.egg/barycentricLagrangeInterpolation/barycentricLagrangeInterpolation.py:171: RuntimeWarning: invalid value encountered in multiply\n",
      "  temp5 = np.nan_to_num(i/tempS*(tempW*temp7-temp5))\n"
     ]
    }
   ],
   "source": [
    "solver.setupUtilities(nNodes = 70)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solve Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1440x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "omegaSquare = 30\n",
    "x0 = 1\n",
    "v0 = 0\n",
    "init = np.random.normal(size=solver.nNodes)\n",
    "solution = solver.solve(init,(omegaSquare,x0,v0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Check Result\n",
    "In order to check the result, we evalute the function at the point `t = 2*pi/omega` and subtract the initial vaule `x0=1`. We expect an result close to zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-7.083222897108499e-14"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solver.f.evaluateFunction(-1+2*np.pi/np.sqrt(omegaSquare),solution.x,solver.weights,solver.nodes)-1"
   ]
  }
 ],
 "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}