{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<h1>Test Tri-Diagonal Matrix Algorithm on Fourier's Equation using Crank-Nicolson</h1></br><div id=\"toc\"></div>\n",
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     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "from IPython.display import HTML \n",
    "s=\"\"\"<h1>Test Tri-Diagonal Matrix Algorithm on Fourier's Equation using Crank-Nicolson</h1></br><div id=\"toc\"></div>\n",
    "<script src=\"https://kmahelona.github.io/ipython_notebook_goodies/ipython_notebook_toc.js\" defer></script>\"\"\";\n",
    "h=HTML(s); h"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check With Jacobi Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def laplace_equation_numerical_3(error_target, niter, nx, ny, xmax, ymax):\n",
    "\n",
    "    \"\"\"\n",
    "    Returns the velocity field and distance for 2D linear convection\n",
    "    \"\"\"\n",
    "    # Increments:\n",
    "    dx = xmax/(nx-1)\n",
    "    dy = ymax/(ny-1)\n",
    "\n",
    "    # Initialise data structures:\n",
    "    import numpy as np\n",
    "    p = np.zeros(((nx,ny,niter)))\n",
    "    x = np.zeros(nx)\n",
    "    y = np.zeros(ny)\n",
    "    jpos = np.zeros(ny)\n",
    "    jneg = np.zeros(ny)\n",
    "\n",
    "    # X Loop\n",
    "    for i in range(0,nx):\n",
    "      x[i] = i*dx\n",
    "\n",
    "    # Y Loop\n",
    "    for j in range(0,ny):\n",
    "      y[j] = j*dy\n",
    "\n",
    "    # Initial conditions\n",
    "    p[:,:,0] = 0\n",
    "\n",
    "    # Dirichlet Boundary Conditions:\n",
    "\n",
    "    # p boundary, left:\n",
    "    p[0,:,:] = 0\n",
    "\n",
    "    # p boundary, right:\n",
    "    for j in range(0,ny):\n",
    "      p[nx-1,j,:] = y[j] \n",
    "\n",
    "    # von Neumann Boundary Conditions:\n",
    "\n",
    "    # Values for correction at boundaries:\n",
    "    for j in range(0,ny):\n",
    "        jpos[j] = j + 1\n",
    "        jneg[j] = j - 1\n",
    "\n",
    "    # Set Reflection: \n",
    "    jpos[ny-1] = ny-2 \n",
    "    jneg[0] = 1 \n",
    "\n",
    "    while True: \n",
    "      for n in range(0,niter-1):\n",
    "        for i in range(1,nx-1):\n",
    "          for j in range(0,ny): \n",
    "            p[i,j,n+1] = 0.25*( p[i+1,j,n]+p[i-1,j,n]+p[i,jpos[j],n]+p[i,jneg[j],n] )\n",
    "            \n",
    "        error = (np.sum(np.abs(p[i,j,n+1])-np.abs(p[i,j,n]) ) / \n",
    "                    np.sum(np.abs(p[i,j,n+1]) ))\n",
    "        \n",
    "        if(error < error_target):\n",
    "          print \"n = \" + str(n) + \" completed\"\n",
    "          break\n",
    "      break\n",
    "            \n",
    "    return p, x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 3129 completed\n"
     ]
    }
   ],
   "source": [
    "p4, x4, y4 = laplace_equation_numerical_3(1.0e-6, 5000, 51, 26, 2.0, 1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def laplace_equation_numerical_4(error_target, niter, nx, ny, xmax, ymax):\n",
    "\n",
    "    \"\"\"\n",
    "    Returns the velocity field and distance for 2D linear convection\n",
    "    \"\"\"\n",
    "    # Increments:\n",
    "    dx = xmax/(nx-1)\n",
    "    dy = ymax/(ny-1)\n",
    "\n",
    "    # Initialise data structures:\n",
    "    import numpy as np\n",
    "    p = np.zeros(((nx,ny,niter)))\n",
    "    x = np.zeros(nx)\n",
    "    y = np.zeros(ny)\n",
    "    jpos = np.zeros(ny, dtype=np.int)\n",
    "    jneg = np.zeros(ny, dtype=np.int)\n",
    "\n",
    "    # X Loop\n",
    "    for i in range(0,nx):\n",
    "      x[i] = i*dx\n",
    "\n",
    "    # Y Loop\n",
    "    for j in range(0,ny):\n",
    "      y[j] = j*dy\n",
    "\n",
    "    # Initial conditions\n",
    "    p[:,:,0] = 0\n",
    "\n",
    "    # Dirichlet Boundary Conditions:\n",
    "\n",
    "    # p boundary, left:\n",
    "    p[0,:,:] = 0\n",
    "\n",
    "    # p boundary, right:\n",
    "    for j in range(0,ny):\n",
    "      p[nx-1,j,:] = y[j] \n",
    "\n",
    "    # von Neumann Boundary Conditions:\n",
    "\n",
    "    # Values for correction at boundaries:\n",
    "    for j in range(0,ny):\n",
    "        jpos[j] = int(j + 1)\n",
    "        jneg[j] = int(j - 1)\n",
    "\n",
    "    # Set Reflection: \n",
    "    jpos[ny-1] = int(ny-2)\n",
    "    jneg[0] = int(1)\n",
    "    i=1\n",
    "    j=0\n",
    "    while True: \n",
    "      for n in range(0,niter-1):\n",
    "        p[i:nx-1,j:ny,n+1] = 0.25*( p[i+1:nx,j:ny,n]+p[i-1:nx-2,j:ny,n]+\n",
    "                                    p[i:nx-1,jpos[j:ny],n]+p[i:nx-1,jneg[j:ny],n] )       \n",
    "        \n",
    "        error = (np.sum(np.abs(p[i:nx-1,j:ny,n+1])-np.abs(p[i:nx-1,j:ny,n]) ) / \n",
    "                    np.sum(np.abs(p[i:nx-1,j:ny,n+1]) ))\n",
    "        \n",
    "        if(error < error_target):\n",
    "          print \"n = \" + str(n) + \" completed\"\n",
    "          break\n",
    "      break\n",
    "            \n",
    "    return p, x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 6793 completed\n"
     ]
    }
   ],
   "source": [
    "p5, x5, y5 = laplace_equation_numerical_4(1.0e-6, 8000, 51, 26, 2.0, 1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def laplace_equation_analytical(INFINITY, NX, NY, XMAX, YMAX):\n",
    "    \n",
    "    from math import pi as PI\n",
    "    import math as ma\n",
    "    import numpy as np\n",
    "    \n",
    "    # Initialise data structures\n",
    "    p_coefficient = np.zeros((NX, NY))\n",
    "    p_analytical = np.zeros((NX, NY))\n",
    "    x = np.zeros(NX)\n",
    "    y = np.zeros(NY)\n",
    "    \n",
    "    # Constants\n",
    "    DX = XMAX/(NX-1)\n",
    "    DY = YMAX/(NY-1)\n",
    "    \n",
    "    # X Loop\n",
    "    for i in range(0,NX):\n",
    "        x[i] = i*DX\n",
    "\n",
    "    # Y Loop\n",
    "    for j in range(0,NY):\n",
    "        y[j] = j*DY\n",
    "    \n",
    "    # Analytical solution\n",
    "    for i in range(0, NX):\n",
    "        for j in range(0, NY):\n",
    "            p_coefficient[i,j] = ( (ma.sinh(1.0*PI*x[i]) * ma.cos(1.0*PI*y[j]) )\n",
    "                         / ( ((1.0*PI)**2.0) * ma.sinh(2.0*PI*1.0) ) )\n",
    "\n",
    "    for m in range(3, INFINITY, 2):\n",
    "        for i in range(0, NX):\n",
    "            for j in range(0, NY):\n",
    "               p_coefficient[i,j] += ( (ma.sinh(m*PI*x[i]) * ma.cos(m*PI*y[j]) )\n",
    "                         / ( ((m*PI)**2.0) * ma.sinh(2.0*PI*m) ) )\n",
    "  \n",
    "    for i in range (0, NX):\n",
    "        for j in range(0, NY):\n",
    "            p_analytical[i,j]= (x[i] / 4.0) - (4.0 * p_coefficient[i,j])\n",
    "        \n",
    "    return p_analytical, x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p3, x3, y3 = laplace_equation_analytical(100, 51, 26, 2.0, 1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_diffusion(p4,p3,x4,NY,TIME,TITLE):\n",
    "   \"\"\"\n",
    "   Plots the 1D velocity field\n",
    "   \"\"\"\n",
    "   import numpy as np\n",
    "   import matplotlib.pyplot as plt\n",
    "   import matplotlib.cm as cm\n",
    "   plt.figure()\n",
    "   ax=plt.subplot(111)\n",
    "   colour=iter(cm.rainbow(np.linspace(0,5,NY)))\n",
    "   for j in range(0,NY,5):\n",
    "      c=next(colour)\n",
    "      ax.plot(x4,p4[:,j,TIME],'ko', markerfacecolor='none', alpha=0.5, label='j='+str(j)+' numerical')\n",
    "      ax.plot(x4,p3[:,j],linestyle='-',c=c,label='j='+str(j)+' analytical')\n",
    "   box=ax.get_position()\n",
    "   ax.set_position([box.x0, box.y0, box.width*1.5,box.height*1.5])\n",
    "   ax.legend( bbox_to_anchor=(1.02,1), loc=2)\n",
    "   plt.xlabel('x (m)')\n",
    "   plt.ylabel('p (Pa)')\n",
    "   #plt.ylim([0,8.0])\n",
    "   #plt.xlim([0,2.0*PI])\n",
    "   plt.title(TITLE)\n",
    "   plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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8pD0S10ZIuk3SDZIWxVSL/0lc/62kGfHaK5Kqs9zjakmXppXdK+mXkm4ENgcmxJSGMyT1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\npZT6J0SkN9DXTvBE4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdd0019cd90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_diffusion(p5,p3,x5,26,6793,'Analytical vs Numerical')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Crank-Nicolson Numerical Scheme\n",
    "\n",
    "Given:\n",
    "\n",
    "$$ r = {\\Delta t \\over {\\Delta x^2}} $$\n",
    "\n",
    "$$ \\left( -{r \\over 2} \\right) u_{i-1}^{n+1} + \\left( {1+r} \\right) u_i^{n+1} + \\left(-{r \\over 2} \\right) u_{i+1}^{n+1} = \\left( {r \\over 2} \\right) u_{i-1}^n + \\left( {1-r} \\right) u_i^n + \\left( {r \\over 2} \\right) u_{i+1}^n $$\n",
    "\n",
    "## Identify Coefficients\n",
    "\n",
    "$$ a_i = -{r \\over 2} $$\n",
    "\n",
    "$$ b_i = {1+r} $$\n",
    "\n",
    "$$ c_i = -{r \\over 2} $$\n",
    "\n",
    "$$ d_i =  \\left( {r \\over 2} \\right) u_{i-1}^n + \\left( {1-r} \\right) u_i^n + \\left( {r \\over 2} \\right) u_{i+1}^n $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "try:\n",
    "    import numpypy as np # for compatibility with numpy in pypy\n",
    "except:\n",
    "    import numpy as np # if using numpy in cpython\n",
    " \n",
    "## Tri Diagonal Matrix Algorithm(a.k.a Thomas algorithm) solver\n",
    "def TDMAsolver(a, b, c, d):\n",
    "    '''\n",
    "    TDMA solver, a b c d can be NumPy array type or Python list type.\n",
    "    refer to http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm\n",
    "    '''\n",
    "    nf = len(a) # number of equations\n",
    "    ac, bc, cc, dc = map(np.array, (a, b, c, d)) # copy the array\n",
    "    for it in xrange(1, nf):\n",
    "        mc = ac[it]/bc[it-1]\n",
    "        bc[it] = bc[it] - mc*cc[it-1]\n",
    "        dc[it] = dc[it] - mc*dc[it-1]\n",
    "\n",
    "    xc = ac\n",
    "    xc[-1] = dc[-1]/bc[-1]\n",
    "\n",
    "    for il in xrange(nf-2, -1, -1):\n",
    "        xc[il] = (dc[il]-cc[il]*xc[il+1])/bc[il]\n",
    "\n",
    "    del bc, cc, dc # delete variables from memory\n",
    "\n",
    "    return xc "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def crank_nicholson(tmax, nx, xmax, sigma):\n",
    "    \n",
    "    from scipy import linalg\n",
    "    \"\"\"\n",
    "    Returns the velocity field and distance for 2D linear convection\n",
    "    \"\"\"\n",
    "    # Increments:\n",
    "    dx = xmax/(nx-1)\n",
    "    dt = sigma * dx**2\n",
    "    nt = int((tmax / dt) - 1)\n",
    "    \n",
    "    # Initialise data structures:\n",
    "    import numpy as np\n",
    "    from math import pi as PI\n",
    "    \n",
    "    u = np.zeros((nx,nt))\n",
    "    x = np.zeros(nx)\n",
    "\n",
    "    # Coefficients\n",
    "    a = np.zeros(nx-2)\n",
    "    b = np.zeros(nx-2)\n",
    "    c = np.zeros(nx-2)\n",
    "    d = np.zeros(nx-2)\n",
    "    \n",
    "    #Constants\n",
    "    r = 0.5\n",
    "\n",
    "    # X Loop\n",
    "    for i in range(0,nx):\n",
    "      x[i] = i*dx\n",
    "\n",
    "    # Initial conditions\n",
    "    u[:,0] = np.sin(PI*x / xmax)\n",
    "\n",
    "    # Dirichlet Boundary Conditions:\n",
    "    # p boundary, left:\n",
    "    u[0,:] = 0.0\n",
    "    # p boundary, right:\n",
    "    u[nx-1,:] = 0.0 \n",
    "    \n",
    "    B1 = 0\n",
    "    B2 = 0\n",
    "    \n",
    "    m=0\n",
    "    i=1\n",
    "\n",
    "    for n in range(0,nt-1):\n",
    "        a[m:nx-2] = - r / 2.0\n",
    "        b[m:nx-2] = 1.0 + r\n",
    "        c[m:nx-2] = - r / 2.0\n",
    "        d[m:nx-2] = ( (r / 2.0) * u[i-1:nx-2, n] +\n",
    "                      (1 - r) * u[i:nx-1, n] +\n",
    "                      (r / 2.0) * u[i+1:nx, n] )\n",
    "\n",
    "        u[i:nx-1, n+1] = TDMAsolver(a, b, c, d)     \n",
    "            \n",
    "    return u, x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "uu, xx = crank_nicholson(0.1, 101, 1.0, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def fourier_equation_analytical(NX, XMAX, T):\n",
    "    \n",
    "    from math import pi as PI\n",
    "    import numpy as np\n",
    "    \n",
    "    # Initialise data structures\n",
    "    u_analytical = np.zeros(NX)\n",
    "    x = np.zeros(NX)\n",
    "\n",
    "    # Constants\n",
    "    DX = XMAX/(NX-1)\n",
    "\n",
    "    # X Loop\n",
    "    for i in range(0, NX):\n",
    "        x[i] = i*DX\n",
    "  \n",
    "    for i in range (0, NX):\n",
    "        u_analytical[i]= ( (np.sin(PI*x[i] / XMAX))*\n",
    "                            np.exp(-1.0*(PI**2)*T / XMAX**2) )\n",
    "        \n",
    "    return u_analytical, x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "uuu, xxx = fourier_equation_analytical(101, 1.0, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_fourier(u_num,u_ana,x4):\n",
    "   \"\"\"\n",
    "   Plots the 1D velocity field\n",
    "   \"\"\"\n",
    "\n",
    "   import matplotlib.pyplot as plt\n",
    "   import matplotlib.cm as cm\n",
    "   plt.figure()\n",
    "   ax=plt.subplot(111)\n",
    "   ax.plot(x4,u_num[:, -1],'ko', markerfacecolor='none', alpha=0.5, label='numerical')\n",
    "   ax.plot(x4,u_ana[:],linestyle='-',c='r',label='analytical')\n",
    "   box=ax.get_position()\n",
    "   ax.set_position([box.x0, box.y0, box.width*1.5,box.height*1.5])\n",
    "   ax.legend( bbox_to_anchor=(1.02,1), loc=2)\n",
    "   plt.xlabel('x (m)')\n",
    "   plt.ylabel('u (K)')\n",
    "   #plt.ylim([0,8.0])\n",
    "   #plt.xlim([0,2.0*PI])\n",
    "   #plt.title(TITLE)\n",
    "   plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hnohHIUnbhL/rheB2vVg8J9SqRSkd094k80CPcioXs9pzI6y/MOwNXI/0A3Da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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdcdbe5acd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_fourier(uu,uuu,xx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "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": 0
}