{
 "metadata": {
  "name": ""
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "import numpy as np\n",
      "import matplotlib.pylab as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The demos for this week look at the Euler integration method of solving Ordinary Differential Equations. "
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Lecture 5.7 and 5.8 demo_eulerIntegration_reversion2Mean: Integration of ODE with reversion to the mean"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def eulerIntegration(t0, f0, a, T, N):\n",
      "    \"\"\"\n",
      "    Integration of an ODE with the Euler scheme\n",
      "\n",
      "    INPUT:\n",
      "        t0 : Initial time\n",
      "        f0 : Initial value of the function f(t0) = f0; \n",
      "        a  : Handle of the function a(t,f), which gives the value\n",
      "             of the derivative \n",
      "        T  : Length of integration interval [t0, t0+T]\n",
      "        N  : Number of time steps\n",
      "\n",
      "    OUTPUT:\n",
      "        t  : Times at which the trajectory is monitored\n",
      "        f  : Values of the trajectory that starts from f(t0) = f0\n",
      "    \"\"\"\n",
      "    # size of the integration step\n",
      "    deltaT = T/N;              \n",
      "    \n",
      "    # monitoring times\n",
      "    t = np.linspace(t0, t0+T, N+1)\n",
      "    # initialize trajectory\n",
      "    f = np.zeros((N+1,))\n",
      "    \n",
      "    ### Euler integration method\n",
      "    # initial condition\n",
      "    f[0] = f0\n",
      "    \n",
      "    # sum over steps to approximate the solution\n",
      "    for n in range(N):\n",
      "        f[n+1] = f[n] + a(t[n], f[n]) * deltaT\n",
      "    # Note that for-loops over large arrays can be a source of poor performance.\n",
      "    # It can be optimized in a number of ways, e.g. through packages\n",
      "    # such as Cython, PyPy, f2py (fortran) or Numba (to name but a few)\n",
      "        \n",
      "    return t, f"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Example: reversion to the mean. This process is described by the following ODE:\n",
      "$d\\sigma(t) = - \\alpha (\\sigma(t) - \\sigma_\\infty) dt  $"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def meanReversion(sigma_0):\n",
      "    sigma_infty, alpha = .2, .5\n",
      "    \n",
      "    def a(t, sigma):\n",
      "        return -alpha * (sigma - sigma_infty)\n",
      "    \n",
      "    t0, T, N = (0, 20, 100)\n",
      "    \n",
      "    t, sigma = eulerIntegration(t0, sigma_0, a, T, N)\n",
      "    fig = plt.figure()\n",
      "    ax = fig.add_subplot(111)\n",
      "    ax.plot(t, sigma, label='$\\sigma(t)$')\n",
      "    ax.plot([t[0], t[-1]], [sigma_infty, sigma_infty], 'k:', label='$\\sigma_{\\infty}$')\n",
      "    ax.set_ybound(0,.6)\n",
      "    ax.set_xlabel('t', fontsize=15)\n",
      "    ax.set_ylabel('f(t)', fontsize=15)\n",
      "    ax.legend(fontsize=15)\n",
      "    plt.show()\n",
      "    \n",
      "\n",
      "meanReversion(.5)\n",
      "meanReversion(.015)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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ERCSJIUFERJIYEkREJIkhQUREkhgSREQkiSFBRESSGBJERCRJ9pAwGo2IjIxE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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7dee978>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7dee4e0>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "demo_eulerIntegration_exponential: Integration of ODE for the exponential; \n",
      "demo_eulerIntegration_bankAccount: demo Euler integration scheme for exponential"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Example: growth of deposited money $M$ on a bank account with interest $r$. The ODE describing the deposit as a function of time is given by:\n",
      "$dM_t = r M_t dt$. We approximate the solution using the Euler Integration Method and compare this to the true solution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def bankAccount(N, T):\n",
      "   \n",
      "    t0 = 0\n",
      "    M0, r = (100, .05)\n",
      "    \n",
      "    def growth(t, M):\n",
      "        return r * M\n",
      "\n",
      "    t, M_euler = eulerIntegration(t0, M0, growth, T, N)\n",
      "    M = M0 * np.exp(r * t)\n",
      "    \n",
      "    fig = plt.figure()\n",
      "    ax = fig.add_subplot(111)\n",
      "    ax.plot(t, M, 'k', label = '$M(t)$')\n",
      "    ax.plot(t, M_euler, 'b', label = '$M_{euler}(t)$')\n",
      "    ax.plot(t, M_euler, 'bo', linewidth=2)\n",
      "    ax.set_xlabel('t', fontsize=15)\n",
      "    ax.set_ylabel('M(t)', fontsize=15)\n",
      "    ax.legend(fontsize=15, loc='upper left')\n",
      "    plt.show()\n",
      "    \n",
      "\n",
      "bankAccount(N=5, T=20)\n",
      "# Increasing N or decreasing T will decrease the error between M and the approximation M_euler.\n",
      "bankAccount(N=20, T=20)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZsoUnnngCAF9fX9asWcMjjzxCYGAggwYNKvkkZD0MIaq8rKwsxo4dS926dVm/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\nFwkMIYQQ5fJ/QoH6l0BavcEAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7e14668>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xkCsMIYTBHT16lPbt21O7dm2d+RUnTkjhQGMiCUMIYVCrVq2iZ8+ezJw5ky+/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\nc/7eF4w0AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7df32e8>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Lecture 5.9 -- eulerIntegrationVariableGrid.m"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "At each step the Euler integration method makes use of the interval size of consecutive time stamps $\\Delta T = t_n - t_{n-1}$. So far we have assumed that these time stamps are equally seperated, i.e. $\\Delta T$ is constant. But this is not a requirement for the Euler integration method.\n",
      "\n",
      "We can implement a new Euler integration scheme which makes use of a variable grid size of time stamps."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def eulerIntegrationVariableGrid(f0, a, t):\n",
      "    \"\"\"\n",
      "    eulerIntegrationVariableGrid: Integration of an ODE with the Euler scheme\n",
      "    \n",
      "    INPUT:\n",
      "        f0   : Initial value of the function\n",
      "        a    : Handle of the function a(t,f), which gives the value\n",
      "               of the derivative \n",
      "        t    : Times at which the trajectory is monitored\n",
      "\n",
      "    OUTPUT:\n",
      "        f    : Values of the trajectory that starts from \n",
      "               f(1) = f0 at t(1) = t0\n",
      "    \"\"\"\n",
      "    # length of the different time intervals\n",
      "    deltaT = np.diff(t)\n",
      "    \n",
      "    # reserve memory for the trajectory\n",
      "    f = np.zeros_like(t)\n",
      "    \n",
      "    #  initial value of trajectory\n",
      "    f[0] = f0\n",
      "    for n in range(deltaT.size):\n",
      "       f[n+1] = f[n] + a(t[n], f[n]) * deltaT[n]\n",
      "    return f\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We revisit the previous example, but consider a non-equally spaced time array `t`. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def eulerIntegrationBankAccountExample(t):\n",
      "    M0, r = (100, .05)\n",
      "    def a(t, M):\n",
      "        return r * M\n",
      "    M_euler = eulerIntegrationVariableGrid(M0,a,t)\n",
      "    nPlot = 1000\n",
      "    tPlot = np.linspace(t[0], t[-1], nPlot)\n",
      "    M = M0 * np.exp(r * (tPlot - t[0]))\n",
      "    \n",
      "    fig = plt.figure()\n",
      "    ax = fig.add_subplot(111)\n",
      "    ax.plot(tPlot, M, 'k', label = '$M(t)$')\n",
      "    ax.plot(t, M_euler, 'b', label = '$M_{euler}(t)$')\n",
      "    ax.plot(t, M_euler, 'bo', linewidth=2)\n",
      "    ax.set_xlabel('t', fontsize=15)\n",
      "    ax.set_ylabel('M(t)', fontsize=15)\n",
      "    ax.legend(fontsize=15, loc='upper left')\n",
      "    \n",
      "# Example 1\n",
      "eulerIntegrationBankAccountExample(t = np.array([1, 3, 7, 8, 10, 12, 15, 20]))\n",
      "# Example 2\n",
      "eulerIntegrationBankAccountExample(t = np.r_[[1, 7], np.linspace(10, 20, 30)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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du3LlCj179sTGxoZDhw5RsWJFje4PDo4gICCUjIyylCuXhZVVZ7ZscWHFCujW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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7eac860>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NBw8exIULF/Cvf/1L4mPQZDzpoIRBCJGZ169fY86cOXj69CliY2MFw+slkZ0N\n/PMPFbilgRIGIUQmMjIyMGHCBAwePBgBAQFQVVUVK+7TlWbT0y1ha2uJyEhaabahUQ2DECJ1ly9f\nxowZM7B+/XosWrRIomXJaaXZ+kNFb0KI3GKMYffu3XB3d8cff/yBkSNHShRPxe36RUVvQohcevv2\nLb7//nvcuHFDovkVH3v5korbskQJgxDS4B48eIDJkydDR0cHMTExUFdXrzXm05Vmzc0tER9PxW1Z\nooRBCGlQly5dwqxZs7Bq1So4OzuLVa8QVau4dMkV9vaauHaNituyQjUMQkiDYIzhxx9/xM6dO3Hs\n2DGJ6hU11SqcnCyouF1PqIZBCJG5169fw9HREQ8ePEBsbCy6d+8uUTytNCuf6NZ1hJB6lZqaikGD\nBqFt27aIiIiQOFkAwMuXVKuQRxKdYRQXF+Pp06cAgE6dOol1i0RCSNNx5swZLFiwAO7u7vjmm2/E\nivm4uK2qWoY2bSyRm2sJTU1X5OZSrUKe1FrDiI2Nxe+//47Lly8jNTVVaJuuri5GjRqFefPmyXTZ\ncaphECJb5eXl2LRpE37//XecOHECpqamYsWJKm6rqbniwAErtGlDE/EaWr1N3IuIiMDq1asRFxeH\nYcOGYfDgwejTpw86dOgAxhgKCgpw+/ZtxMTEIDo6GgMGDICXlxfMzKT/C6WEQYjsFBQUYNasWSgu\nLkZAQIBE60HRRDzZqrei97Rp0+Di4oJTp07V+gZ4/PgxDh06hGnTpuHRo0fi95YQotDi4uIwdepU\nTJ48GV5eXuByuRLFv3tHE/EUSbUJIyMjA2pqamIdRENDAz/88AMWL15cbx0jhMgvxhj27t0LNzc3\n7Nu3D7a2trXGfDoRb/58S9y7R8VtRVJtwvg4WURERMDExAStWrWqsl9RURFu3boFMzMzsRMMIURx\nFRUV4ZtvvsGdO3dw9epVaGtr1xojqlZx+bIrjIw0oa7uiowMKm4rArGG1Zqbm+POnTsit929e1fi\nBcQIIYopJSUFAwYMgLq6OmJiYsRKFgDg4xMilCwAoKzMHR07PoKPjxWsrNZjxAg3WFmth7f3WCpu\ny6nPnrj35s0bOrMgpAk4evQonJ2dsX37djg4OEgUSxPxGodqE0Z4eDjCw8MFFfQDBw4gODhYaJ+3\nb98iKCgIffv2FfsBHR0dERQUhM6dOyMpKQlA5dDdxYsX4/3791BRUYGvry8GDBgAAPD09ISfnx+U\nlZXh4+McyFRRAAAgAElEQVQDS0tLiZ8kIaTu3r17h2XLliE0NBShoaHo16+fxMd4/55qFY0Cq8a2\nbdtYhw4dWMeOHRmHw2Ft27ZlHTt2FPrp1q0bGzVqFLt582Z1h6kiIiKC3bp1ixkaGgraRowYwYKD\ngxljjJ07d46Zm5szxhhLTk5mRkZGrLS0lGVmZjItLS1WXl5e5Zg1PA1CyGfIyMhg/fv3Z1OmTGEv\nX74UO+7s2XBmaenKRozYyAwNXZma2h7WqdNaBjDBj5bWGnb2bHgD9p7URtLPzmrPMFauXImVK1cC\nAPh8Pk6fPg1jY+PPTlDDhw9HVlaWUFvXrl3x8uVLAEBhYSE0NTUBAIGBgbC3tweXywWfz4e2tjZi\nY2MxaNCgz+4HIaRmf//9NxYsWIC1a9diyZIln3VXvO7dXeHoqIlr19Z/NBGPahWKRqwaxqcf8PXN\ny8sLw4YNw4oVK1BRUYGYmBgAQF5enlBy4PF4yM3NbdC+ENLUlZaWwtXVFQEBATh9+jQGDx4sUbyo\nAnd2tjuuXaPJeIqu2oRx9OhRzJgxQ+xvFeXl5fjjjz8wa9YsiTsxf/58+Pj4YNKkSThx4gQcHR1x\n8eJFkftW1x83NzfBv83NzWFubi5xPwhp6jIzMzF9+nR07twZt27dQseOHSWKZwzIyqLJePIqLCwM\nYWFhdY6vdmmQfv364e3bt5g3bx6mTp0KXV1dkQdITk7GyZMncejQIbRs2RKJiYm1PmhWVhbGjx8v\nKHq3bt0ar169AlA5Iaht27Z4+fIlvLy8AACrV68GAIwdOxabNm2qsk4NLQ1CyOf7888/sXDhQqxZ\ns0aiGx19mIynrFyG8nJL3LgRgjdvaLkPRSDxZ2d1xY3y8nJ28OBBZmxszDgcDuvQoQMbNmwYs7Gx\nYePHj2eDBw9mbdu2ZRwOh/Xv358dPnyYVVRUiFU4yczMFCp6m5iYsLCwMMYYY5cuXWJffvklY+x/\nRe+SkhKWkZHBevXqJfIxangahJBavH37li1cuJD16tWLxcbGih139mw409ISLmS3arWWrVmzp0o7\nFbjlk6SfnWLdcS8xMRGXL19GQkKCYHnzzp07w8TEBKNHj4ahoaHYCcre3h7h4eF49uwZNDQ0sHnz\nZvTt2xfff/89SkpKoKamBl9fX5iYmAAAPDw84OfnBxUVFXh7e8PKyqrKMekMg5C6uXfvHqZNm4be\nvXtj//79aNOmjdixdFc8xVdvq9UqEkoYhEju8OHDcHFxwdatW/Htt9+KXa/8YOhQN1y96lalfcQI\nN4SFVW0n8qfeVqvdtGmTRG+gDRs2iL0vIUR2ioqKsHjxYly/fh2XL18Wa+LtpwsHjhhhiZs3aTJe\nU1PtGYaSkhKaN28OdXX1Gg/AGAOHwxFcqpIFOsMgRDz//PMPpk2bhkGDBmH37t21/n0DoudVKCu7\nYvp0TVy7livUrqW1ltaCUiD1doahpaWFBw8eoH///pg+fTpsbW3RunXreukkIUS62H+XI9+4cSN+\n+uknzJ49W+xYUfMqysvd8ezZenh7W2HXLpqM11RUmzDS0tIQFxcHf39/bNiwAQsXLoS1tTWmT5+O\n8ePH04KDhCiIp0+fYv78+cjLy0NUVBR69+4tUTwtHEg+qHF58wEDBmDHjh148OABLly4gC5dumDx\n4sXo1KkTZsyYgYiICGn1kxBSByEhITA2Noa+vj6uXr1aa7IICoqAldU6mJu7wcpqHY4fj6CbHJH/\nkXTcbklJCVu+fDlTVlZmkyZNkjS8QdThaRDSqL17944tW7aM8Xg8FhoaKlaMqHkVKipr2Zdf7mG9\netG8isZI0s9Ose+HERUVBX9/f5w8eRJFRUWYMmUKFi5c2HCZjBBSJykpKZgxYwZ69eqFhIQEdOjQ\nQay46m5y1KHDeri5Ua2C1LL44M2bN+Hv74/jx4/j8ePHGDt2LHbu3AkbGxuxRlcQQqSHMYZ9+/Zh\nw4YN8PDwwIIFCyQaGk+1ClKbahOGrq4usrKyMGrUKLi5ucHW1laiWaCEEOl59uwZ5s+fj5ycHLEL\n25/OrcjIKBC5H9UqyAdiz8P48E1F1O4cDgdPnjxpwG7WjOZhkKbs4sWLmDdvHmbOnImtW7dCVVW1\n1hjRcyvmo127Nnj27CdBG82raNzqbR6GJDO3JV1SgBDy+d69e4d169bB398fhw4dwujRo8WOFT23\n4ld0774A/ftTrYKIVm3C+Pj+EoQQ+ZKQkIDZs2dDV1cXiYmJYhe2PyguFv2n37o1D8HBbvXQQ9IY\niT1KihAie+Xl5di+fTt27tyJHTt2YNasWbWe4X9aq7CwoHWgSN1QwiBEQdy/fx9z5sxBs2bNcOPG\nDXzxxRe1xoiqVVy65IrJkzVx65ZrlXWgnJzGNkjfSeNQ40xvQojsMcawf/9+DBo0CFOnTsWlS5fE\nShaA6FpFRYU7Xr16BG9vK1hZrceIEW6wslpPxW1SKzrDIESOPXr0CAsWLEB+fj7Cw8NhYGAgUfy7\ndzS3gtQfShiEyKmTJ09i8eLF+Oabb7B+/fpah8t+WquwtbVEYiLVKkj9oYRBiJwpLCyEk5MTrl+/\njtOnT2PQoEG1xlRXq7C01ERaGtUqSP2ghEGIHLl06RIcHR0xfvx4xMfHi70ET3W1CsbonhWk/kg9\nYTg6OiIoKAidO3dGUlKSoH3Xrl3w9fWFsrIyxo0bh23btgEAPD094efnB2VlZfj4+MDS0lLaXSak\nwb1+/RorVqzA+fPn8csvv8DKykqieKpVEGmQesJwcHCAk5MT5syZI2i7cuUKzpw5g3/++QdcLldw\nu9eUlBQEBAQgJSUFubm5GDNmDFJTU6GkRIO7SONx6dIlLFiwAGPGjEFSUlKta7Z9WquYNs0SSUlU\nqyANT+oJY/jw4cjKyhJq27t3L9asWQMulwsA6NSpEwAgMDAQ9vb24HK54PP50NbWRmxsrFjXdAmR\nd69fv8bKlSsRFBSE/fv3Y+zY2usK1dUqzM018eAB1SpIw5KLr+ppaWmIiIjAoEGDYG5ujhs3bgAA\n8vLywOPxBPvxeDzk5ubKqpuE1JvLly+jX79+KC0tRVJSkljJAqi+VsHl0rwK0vDkouhdVlaGFy9e\n4Nq1a4iLi4OdnR0yMjJE7lvdMggfr31lbm4Oc3PzBugpIZ/nw1nF2bNnsX//flhbW0sUT7UK8jnC\nwsIQFhZW53i5SBg8Hg+2trYAKu8jrqSkhGfPnkFTUxPZ2dmC/XJycqCpqSnyGLRYIpF3ly9fxvz5\n8zFy5EgkJSWhbdu2tcZ8XK8oKytDQgLds4LU3adfpjdt2iRRvFxckpo4cSIuX74MAEhNTUVpaSk6\nduwIGxsb+Pv7o7S0FJmZmUhLS8PAgQNl3FtCJFNUVITvv/8ec+fOxZ49e+Dn5yd2sli69AJCQrYi\nPNwN0dFboaRUgi5dXIT2q6xVWDRU9wkRkPoZhr29PcLDw/H8+XN0794dmzdvhqOjIxwdHdG3b1+o\nqqri0KFDAAADAwPY2dnBwMAAKioq8PX1pXtvEIUSEhKC7777DiNGjBD7rOIDUfWK169/hbb2AhgZ\n0bwKIn3V3nFPkdAd94i8KSgogIuLC8LCwrBv375ai9qfDpX9v/+zhLPzZTx86FZl3xEj3BAWVrWd\nEEnV2x33CCGSY4zh5MmTWLp0KaZOnYrbt2+jZcuWNcaIGip75YorWrR4IXJ/qlcQWaGEQUg9yc3N\nxffff4/U1FT8+eefGDx4sFhxoi49vX/vjl69FuDVK5pbQeQHJQxCPlNFRQUOHDgAV1dXLFq0CAEB\nAWjWrJnY8SUl1d8udcuWUbQOFJEblDAI+QxpaWn45ptv8PbtW1y5cgWGhoY17v9prWLWLEvcvVv9\nsh40t4LIE0oYhNRBWVkZduzYgR9//BHr1q2Dk5MTlJWVa4ypblmPwYM1oa7uiowMuvRE5BslDEIk\nFB8fj/nz56Njx46Ii4tDz549xYqrblmPli3Xw8eHliAn8o8SBiFiKioqwoYNG3D06FFs27YNc+fO\nlWhe0Nu3tKwHUWyUMAgRQ2BgIJycnDBq1Cjcvn1bsKJydT6tVQwfbokbN2gJcqLYKGEQUoPs7Gw4\nOTnh7t27OHTokFiLWoqqVVy+7IopUzQRF0fDZInikou1pAiRN2VlZdi5cydMTEzwr3/9C4mJiWKv\ngCyqVlFW5o4XL2gJcqLY6AyDkE/ExcXhu+++Q7t27XD16lXo6uqKHVtRATx8SLUK0jjRGQYh//Xy\n5Us4OTnBxsYGLi4uuHTpkkTJ4tIlYMAAIC+PahWkcaKEQZq8D+s/9enTB+/evUNycjJmzZol9gio\nhATAygpYuBBYvRo4etQSWlquQvvQEuSkMaBLUqRJS0tLw5IlS/Dw4UP4+/tj2LBhYsdmZQHr1gGh\nocD69cA33wCVt6U3A4cDmldBGh1a3pw0ScXFxfD09MTevXuxZs0aLFmyBNzKT/taPXsGuLsDhw4B\nTk7A8uVAq1YN3GFCGoCkn510SYo0KYwxnD59Gn369EF6ejoSExOxfPlysZJFcTHg6Qno6QGlpUBK\nCuDmRsmCNB10SYo0Genp6ViyZAmysrLg5+eHkSNHihVXVgb8/ntlchgyBIiJAXR0GrSrhMglOsMg\njV5xcTE2bNiAQYMGYdSoUUhISBArWTAGnDkD9OsHHDkC/PUXcPw4JQvSdNEZBmm0GGM4c+YMnJ2d\nYWpqioSEBPB4PLFir14FVq0CCguBf/8bsLYG6HbypKmT+hmGo6MjNDQ00Ldv3yrbduzYASUlJRQU\nFAjaPD09oaOjAz09PYSEhEizq0SB3b9/H19//TVWr16NAwcOwN/fX6xkcfcuMGkSMH06MH9+5ZDZ\nr76iZEEIIIOE4eDggODg4Crt2dnZuHjxInr06CFoS0lJQUBAAFJSUhAcHIxFixahoqJCmt0lCubN\nmzdYv349TE1NYW5ujsTERIwePbrWuEePgO++A4YPr6xT3LsHzJsH1HKLC0KaFKknjOHDh6Ndu3ZV\n2l1cXLB9+3ahtsDAQNjb24PL5YLP50NbWxuxsbHS6ipRIIwxHDt2DHp6esjIyEBCQgJ++OEHqKqq\n1hj36lXlXApDQ6BNm8pE8cMPgJqalDpOiAKRixpGYGAgeDwe+vXrJ9Sel5eHQYMGCf7P4/GQm5sr\n7e4ROXfjxg0sXboUJSUl8Pf3x9ChQ2uNKS0F9u2rnE9hbQ3ExwNffCGFzhKiwGSeMIqLi+Hh4YGL\nFy8K2mqaSFLdcg1ubm6Cf5ubm4u9sihRXPn5+XB1dcW5c+fg7u6OefPmQUmp5pPmigogIABwdQX0\n9YGLFytHQRHSFISFhSEsLKzO8TJPGPfv30dWVhaMjIwAADk5Oejfvz+uX78OTU1NZGdnC/bNycmB\npqamyON8nDBI41ZaWgofHx94eXnBwcEB9+7dQ+vWrWuNu3SpcuSTsjLg5wfQdwrS1Hz6ZXrTpk0S\nxcs8YfTt2xePHz8W/L9nz564efMm2rdvDxsbG8yYMQMuLi7Izc1FWloaBg4cKMPeEllijCEoKAgu\nLi7Q1dUVe+nxhITKRJGRAXh4AFOm0KgnQupC6gnD3t4e4eHheP78Obp3747NmzfDwcFBsP3jS04G\nBgaws7ODgYEBVFRU4OvrK9E9lEnjcffuXSxbtgyZmZnw9vaGtbV1rTHVLw5ICKkLWnyQyLWCggJs\n3rwZR48exdq1a7F48eJa1316/ryymH3wIC0OSEhNaPFB0iiUlJTgp59+Qu/evVFaWork5GQsW7as\nxmTxYXHA3r2BkhIgOZkWBySkPsm8hkHIxxhj+PPPP7Fq1Sro6+sjIiIC+vr6NcbQ4oCESAclDCI3\nrl+/juXLl6OoqAj79++vdYY2Y8Dff1fe5a5z58rFAWlMBCENhxIGkbmsrCysWbMGkZGR2LJlC+bM\nmQPlWtbkoMUBCZE+qmEQmXn58iVWrVqF/v37Q09PD/fu3YODg0ONyeLuXcDWlhYHJEQWKGEQqXv/\n/j327NmD3r1749mzZ0hKSsLGjRuhrq5ebczHiwMOHkyLAxIiC3RJikjNh9ujrl27FjweDxcuXBDM\n8P8gKCgCPj4hKClRQbNmZZg/3xL//GOGvXsrzyju3QPat5fREyCkiaOEQaQiMjISK1euRHFxMX76\n6SeMHTu2yiTMoKAILF16AffvuwvaLl1yhbk5EB9vRosDEiJjdEmKNKjbt29j/PjxmD17Nr7//nvE\nx8fD2tpa5Ix9H58QoWQBABUV7uByL1KyIEQOUMIgDeLhw4eYN28eRo8ejdGjR+PevXuYNWtWtavJ\npqcDycmiT3jfvaNCBSHygBIGqVfPnz/HihUrYGJigu7duyM1NRXOzs5o1qxZlX3LyyvnUYwdWznh\njsstE3nM5s3LG7rbhBAxUMIg9aK4uBienp7o3bs33rx5g9u3b2PLli1o06ZNlX2fPgW8vAAtrco1\nn2bMAB4+BHbvtoSWlqvQvlpaa+HkZCGtp0EIqQEVvclnKSsrw2+//QY3NzcMGTKk2iXHGQNiY4E9\neyrPKiZNAv78E+jf/3/7jBtnBgDYtWs93r1TRvPm5XByGitoJ4TIFq1WS+qkoqICAQEB2LhxIzQ1\nNeHl5QVTU9Mq+xUXA/7+lYmisBBYtKhy/kSHDtLvMyFEmKSfnXSGQSTCGMOZM2ewfv16qKmpwdfX\nF6NHj64y6ik9Hdi7t3KJ8cGDga1bASsroJY7qBJC5BglDCIWxhguXryIdevWoaSkBFu3bsX48eOF\nEkV5OXDuXOXZxK1bgIMDEBcH9Owpw44TQuoNJQxSq6ioKLi6uiI/Px+bN2/G1KlThYbHPn0K/Por\nsG8f0KVL5WWn06eB5s1l2GlCSL2jhEGqdePGDaxfvx537tzBxo0bMXv2bKioVL5lGAOuXwd8fasv\nYhNCGhepX1F2dHSEhoYG+vbtK2j74YcfoK+vDyMjI9ja2uLly5eCbZ6entDR0YGenh5CQkKk3d0m\nKTk5Gba2tpgwYQLGjx+P1NRUODg4QEVFBcXFgJ8f8OWXwMyZgJFRZb3Cz4+SBSGNndQThoODA4KD\ng4XaLC0tkZycjMTEROjq6sLT0xMAkJKSgoCAAKSkpCA4OBiLFi1CRUWFtLvcZKSmpmLWrFkYNWoU\nhg4dirS0NCxatAiqqqpIT6+8N/YXXwCnTlUWsdPSKttoxBMhTYPUE8bw4cPRrl07oTYLCwvBNXFT\nU1Pk5OQAAAIDA2Fvbw8ulws+nw9tbW3ExsZKu8uN3r179zB79mwMHToUenp6SE9Px/Lly9GsWQuh\nmdgqKpVF7L//rrxhEY14IqRpkbs/eT8/P3z11VcAgLy8PPB4PME2Ho+H3NxcWXWt0fmQKIYNGwY9\nPT3cv38f69atw7t3rQQzsbdu/d9M7G3baMQTIU2ZXCUMd3d3qKqqYsaMGdXuI2qVUyKZDwsBfpwo\n1q51RUpKa8yZA+jqAqmpwMmTlYXtOXNoxBMhRI5GSf3+++84d+4cQkNDBW2amprIzs4W/D8nJwea\nmpoi493c3AT/Njc3h7m5eUN1VWHdvXsXW7duRUhICJydneHr6wsVldZVZmLv3El1CUIao7CwMISF\nhdX9AEwGMjMzmaGhoeD/58+fZwYGBuzp06dC+yUnJzMjIyNWUlLCMjIyWK9evVhFRUWV48noaSiM\nO3fusBkzZrBOnToxd3d39vLlS5aWxpiLC2MdOjD29deMnTvHWHm5rHtKCJEmST87pX5Jyt7eHkOG\nDMG9e/fQvXt3+Pn5wcnJCUVFRbCwsICJiQkWLVoEADAwMICdnR0MDAxgbW0NX19fuiQlgbt372Lm\nzJkwMzODoaEhUlPvo2/ftbCza01FbEKIxGjxwUYoMTERHh4euHLlCpYtW4bp050QENAS+/YBGhrA\n998DdnZUlyCkqZP0s5O+UzYiMTEx+Prrr2FtbY0BAwbC3z8Ld+6swb/+1ZKK2ISQz0ZnGAqOMYbL\nly/D3d0dGRkZWLbMFc2bz8P+/VxaTpwQUiNJPzspYSgoxhj+/vtveHh4oLCwEI6OHnj0aAIOH1bG\n4MGViYKWEyeE1IQSRiNXXl6OEydOwMPDA0pKXFhZeSMhYSji4zlwcAD+7/9och0hRDyUMBqp0tJS\nHDlyBF5eXmjbVgcGBjsQFtYbGhocKmITQuqE7rjXyBQVFeHXX3/Fv/+9A127TgSfH4G4OA0YGnJw\n8mTlqrGEECINlDDk1JMnT7Br1y7s3XsQfP5qqKvfwfPn6pg2DfjjDypiE0KkjxKGnElPT8eOHTtw\n9Oh19Oy5HeXlbujSRRnff09FbEKIbFHCkBNxcXHYtu3fCAlRQadOblBV1cLYsUpUxCaEyA1KGDLE\nGMOFCxewdet/cPu2KZSUfkHv3upwclKmIjYhRO7QKCkZeP/+Pfz9A7BpUzCeP5+G0lJLTJ3KxeLF\nSlTEJoRIDQ2rlWOvXr3C3r0HsX37Q5SWfoOWLXlYvlwNDg4cKmITQqSOhtXKoaysLGzefAx//NEG\nFRVzMWBABVxd21IRmxCiUOgMo4EwxhAVFYPVqyMQFzcAXK4p5sypwMqVramITQiRC3RJSsbKysrw\n229nsXlzLvLzJ0BTUwVr1rTB3LlqVMQmhMgVuiQlIy9eFGLDhiD4+amhpMQCI0YU4OTJrjA1VZZ1\n1wghpF7QGcZnun07A87O1xEWpg81ta5wdCzFhg3dqYhNCJF7dAMlKWCM4ejR69DROYN+/dogK8sE\nv/3Gw8uXGvD2pmRBCGmc6JKUBF69eoM1ayJx6FArvH2rh1GjuDh9Wg19+ujJumuEENLgpH6G4ejo\nCA0NDfTt21fQVlBQAAsLC+jq6sLS0hKFhYWCbZ6entDR0YGenh5CQkKk3V0AQFxcFoYPD0K7ds9x\n7FgvLFrUFq9ft0dIyL/Qp08LmfSJEEKkTeoJw8HBAcHBwUJtXl5esLCwQGpqKkaPHg0vLy8AQEpK\nCgICApCSkoLg4GAsWrQIFRUVUulnRQWDt/d18HhXYGraDoWFnfDXX8p48UIX27b1gZoaRyr9kIWw\nsDBZd6HRoNeyftHrKVtSTxjDhw9Hu3bthNrOnDmDuXPnAgDmzp2L06dPAwACAwNhb28PLpcLPp8P\nbW1txMbG1mt/goIiYGW1DubmbrCyWocjR4Ixc2YoWrRIwcqV3TB4sBoePOAiKWkgJkzQrNfHllf0\nR1l/6LWsX/R6ypZc1DAeP34MDQ0NAICGhgYeP34MAMjLy8OgQYME+/F4POTm5tbb4wYFRWDp0gu4\nf99d0BYSshpt2+pg8+bOWL6cB2Xl7vX2eIQQosjkbpQUh8MBh1P95Z6atknKxydEKFlU8oKpaRZW\nruwLZeXGe9mJEEIkJRdnGBoaGsjPz0eXLl3w6NEjdO7cGQCgqamJ7OxswX45OTnQ1Kx6WUhLS+sz\nEsmnCQO4cAHgcLbW8XiNw6ZNm2TdhUaDXsv6Ra9n/dHS0pJof7lIGDY2Njh48CBWrVqFgwcPYuLE\niYL2GTNmwMXFBbm5uUhLS8PAgQOrxKenp0u7y4QQ0uRIPWHY29sjPDwcz549Q/fu3bF582asXr0a\ndnZ2+PXXX8Hn83H8+HEAgIGBAezs7GBgYAAVFRX4+vrW6yUpQggh4msUS4MQQghpeHJX9JZEcHAw\n9PT0oKOjg23btsm6OwqPz+ejX79+MDExEXnpj9RM0kmppGaiXk83NzfweDyYmJjAxMSkypwuIlp2\ndjZGjhyJPn36wNDQED4+PgAkf38qbMIoLy/H4sWLERwcjJSUFPzxxx+4c+eOrLul0DgcDsLCwhAf\nH1/v812aAkkmpZLaiXo9ORwOXFxcEB8fj/j4eIwdO1ZGvVMsXC4XO3fuRHJyMq5du4Y9e/bgzp07\nEr8/FTZhxMbGQltbG3w+H1wuF9OnT0dgYKCsu6Xw6Apl3UkyKZXUTtTrCdB7tC66dOkCY2NjAEDL\nli2hr6+P3Nxcid+fCpswcnNz0b37/ybV1fekvqaIw+FgzJgx+PLLL/HLL7/IujuNQnWTUknd7dq1\nC0ZGRpg/fz5d4quDrKwsxMfHw9TUVOL3p8ImDBotVf+io6MRHx+P8+fPY8+ePYiMjJR1lxqV2ial\nktotXLgQmZmZSEhIQNeuXbF8+XJZd0mhFBUVYfLkyfD29karVq2Etonz/lTYhPHppL7s7GzweDwZ\n9kjxde3aFQDQqVMnTJo0ieoY9eDDpFQAQpNSSd107txZ8MG2YMECeo9K4P3795g8eTJmz54tmOsm\n6ftTYRPGl19+ibS0NGRlZaG0tBQBAQGwsbGRdbcUVnFxMV6/fg0AePPmDUJCQoRGp5C6+TApFYDQ\npFRSN48ePRL8+9SpU/QeFRNjDPPnz4eBgQGcnZ0F7RK/P5kCO3fuHNPV1WVaWlrMw8ND1t1RaBkZ\nGczIyIgZGRmxPn360OtZB9OnT2ddu3ZlXC6X8Xg85ufnx54/f85Gjx7NdHR0mIWFBXvx4oWsu6kw\nPn09f/31VzZ79mzWt29f1q9fPzZhwgSWn58v624qhMjISMbhcJiRkREzNjZmxsbG7Pz58xK/P2ni\nHiGEELEo7CUpQggh0kUJgxBCiFgoYRBCCBELJQxCCCFioYRBCCFELJQwCCGEiIUSBiEN5Pjx44JJ\nUYQ0BjQPg5AGMmXKFDx//hxXrlyRdVcIqRd0hkEIIUQslDAIaQDz5s3DX3/9hfDwcCgpKUFJSQmb\nN2+WdbcI+Swqsu4AIY3Rhg0bkJ2djZcvX8LX1xcAaDVlovAoYRDSAHr16oV27dqBMUb3RyeNBl2S\nIoQQIhZKGIQQQsRCCYMQQohYKGEQ0kBUVVXx9u1bWXeDkHpDCYOQBqKvr4+kpCQEBgbixo0bQrcX\nJUQRUcIgpIEsWrQIlpaWcHR0xMCBA/HLL7/IukuEfBZaGoQQQohY6AyDEEKIWChhEEIIEQslDEII\nISWgd4sAAAAvSURBVGKhhEEIIUQslDAIIYSIhRIGIYQQsVDCIIQQIhZKGIQQQsRCCYMQQohY/h/+\n8WXv0TBGRwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7eac748>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Lecture 5.10: eulerIntegrationVanDerPol.m"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Van Der Pol oscillator is an example of a non-linear, second order equation. We cannot apply Euler's method directly, since the system is second order. However, the system can be rewritten as a system of coupled first order equations, to which Euler's method can be applied in a consecutive fashion. This is done in `eulerIntegrationVanDerPol`"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def eulerIntegrationVanDerPol(t0, x0, p0, mu, T, N):\n",
      "    \"\"\"\n",
      "    Van Der Pol oscillator solved via Euler integration\n",
      "    INPUT:\n",
      "        t0 : Initial time\n",
      "        x0 : Initial position \n",
      "        p0 : Initial momentum \n",
      "        mu : damping strength\n",
      "        T  : Length of integration interval [t0, t0+T]\n",
      "        N  : Number of time steps\n",
      "\n",
      "    OUTPUT:\n",
      "        t  : Times at which the trajectory is monitored\n",
      "             t(n) = t0 + n Delta T\n",
      "        x  : Values of the position along the trajectory\n",
      "        p  : Values of the momentum along the trajectory\n",
      "\n",
      "    \"\"\"\n",
      "    # Size of integration step\n",
      "    deltaT = T/N\n",
      "    \n",
      "    # initialize monitoring times\n",
      "    t = np.linspace(t0, t0 + T, N + 1)\n",
      "    \n",
      "    # intialize x and p\n",
      "    x = np.zeros_like(t)\n",
      "    p = np.zeros_like(t)\n",
      "    \n",
      "    ## Euler integration \n",
      "    # initial conditions\n",
      "    x[0] = x0\n",
      "    p[0] = p0\n",
      "    for n in np.arange(N):\n",
      "        x[n+1] = x[n] + p[n] * deltaT\n",
      "        p[n+1] = p[n] + (mu * (1 - x[n] * x[n]) * p[n] - x[n]) * deltaT\n",
      "\n",
      "    return t, x, p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We plot the time series of the position and momentum, and the corresponding phase space plots, for two values of the damping parameter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def vanDerPolExample(mu, x0, p0):\n",
      "    t0, T, N = 0, 20, 1e5\n",
      "    t, x, p = eulerIntegrationVanDerPol(t0, x0, p0, mu, T, N)\n",
      "    fig = plt.figure(figsize=(15, 7))\n",
      "    ax = fig.add_subplot(121)\n",
      "    ax.plot(t, x, label='x(t)')\n",
      "    ax.plot(t, p, label='p(t)')\n",
      "    ax.set_title('Time series of x(t) and p(t) ($\\mu$ = {})'.format(mu), fontsize=15)\n",
      "    ax.set_xlabel('t')\n",
      "    ax.legend(fontsize=15, loc='upper right')\n",
      "    ax2 = fig.add_subplot(122)\n",
      "    ax2.plot(x, p)\n",
      "    ax2.set_title('Phase space plot ($\\mu$ = {})'.format(mu), fontsize=15)\n",
      "    ax2.set_xlabel('x(t)')\n",
      "    ax2.set_ylabel('p(t)')\n",
      "    plt.show()\n",
      "\n",
      "# The behavior of the system is sensitive to the damping mu of the system\n",
      "vanDerPolExample(mu=.01, x0=0, p0=1)\n",
      "vanDerPolExample(mu=2, x0=0, p0=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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C0L9mZoC5ufyrQQOgUSP5V5MmgIsLYGWl7aNmTHN4DB1jjFWAr0s1x2PoVIfP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3MM+dE1NFAJ5vHHA++9J3d9DMN4juFhytAp/XNvvgmcey5d//vflKVnZgYLunFkWajk0unJppgZ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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa075080>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HDwPDhwN9+oiExdUtWSK2DRvKjYMsw8SMHIKu3g4mZmSK2r2ugBjKyF5XIiL3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orqCkHnqWV9kF4PjBoFPPvsjTLXxLLsdHaI9Y1FSn6KoPP8/NjC94ICGjEjhNgO0wvEnTsBFxeu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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x8576a20>"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, this can be turned into a fancy animation. Unfortunately I could not get it to work on my computer -- there is apparently a problem with the backend. But supposedly the following code works (you might need to run it directly from the command line)\n",
      "\n",
      "The file `van_der_pol_demo.py`  can be found in the github repository. Credit goes to chanGimeno for this implementation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%run van_der_pol_demo.py "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}