A IJulia notebook showing Taylor's method integration of the pendulum

PendulumIntegration.ipynb

{
 "metadata": {
  "language": "Julia",
  "name": "",
  "signature": "sha256:444e00256b512fb645b06d0f13b58e2ab82a13140f7179683fe36c231b1aa41a"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "using TaylorSeries"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Par\u00e1metros para el integrador de Taylor\n",
      "const ordenTaylor = 28\n",
      "const epsAbs = 1.0e-20\n",
      "\n",
      "println(\" Taylor order = $ordenTaylor\\n Eps = $epsAbs\\n\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " Taylor order = 28\n",
        " Eps = 1.0e-20\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function taylorStepper{T<:Real}( jetEqs::Function, vec0::Array{T,1}, order::Int64, epsilon::T)\n",
      "    n = length( vec0 )\n",
      "    vec0T = [ Taylor([vec0[i]], order) for i=1:n ]\n",
      "    vec1T = jetEqs( vec0T )\n",
      "    \n",
      "    # Step-size\n",
      "    hh = Inf\n",
      "    for i=1:n\n",
      "        h1 = stepsize( vec1T[i], epsilon )\n",
      "        hh = min( hh, h1 )\n",
      "    end\n",
      "    #hh = hh*0.125\n",
      "    \n",
      "    # Values at t0+h\n",
      "    for i=1:n\n",
      "        vec0[i] = evalTaylor( vec1T[i], hh )\n",
      "    end\n",
      "    \n",
      "    return hh, vec0\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "taylorStepper (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function stepsize{T<:Real}(x::Taylor{T}, epsilon::Float64)\n",
      "    ord = x.order\n",
      "    h = Inf\n",
      "    for k in [ord-1, ord]\n",
      "        kinv = 1.0/k\n",
      "        aux = abs( x.coeffs[k+1] )\n",
      "        h = min(h, (epsilon/aux)^kinv)\n",
      "    end\n",
      "    return h\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "stepsize (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "energy{T<:Real}( x::T, vx::T ) = 0.5*vx^2 - cos(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "energy (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function jetPendulum{T<:Real}( vec::Array{Taylor{T},1} )\n",
      "    xT = vec[1]\n",
      "    vxT = vec[2]\n",
      "    ord = xT.order\n",
      "    # Now the implementation\n",
      "    for k = 0:ord-1\n",
      "        knext = k+1\n",
      "        # Taylor expansions up to order k <--- This part makes it somewhat slower\n",
      "        xTt = Taylor( xT.coeffs[1:k+1], k)\n",
      "        vxTt = Taylor( vxT.coeffs[1:k+1], k)\n",
      "        # Eqs of motion <--- This is quite straight :-)\n",
      "        xDot = vxTt\n",
      "        vxDot = -sin(xTt)\n",
      "        # The equations of motion define the recurrencies\n",
      "        xT.coeffs[knext+1]  = xDot.coeffs[knext] / knext\n",
      "        vxT.coeffs[knext+1] = vxDot.coeffs[knext] / knext\n",
      "    end    \n",
      "    return [ Taylor(xT, ord), Taylor(vxT, ord) ]\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "jetPendulum (generic function with 1 method)"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x0 = pi-0.001\n",
      "vx0 = 0.0\n",
      "\n",
      "energy(x0,vx0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "0.9999995000000417"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "taylorStepper( jetPendulum, [x0, vx0], ordenTaylor, epsAbs )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(1.6634940262677569,[3.13886,-0.00254412])"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "function pendulumIntegration( x0::Float64, vx0::Float64, time_max::Float64, jetEqs::Function, \n",
      "                            orden::Int64=ordenTaylor, epsilon::Float64=epsAbs )\n",
      "    # Initial conditions and energy\n",
      "    t0 = 0.0\n",
      "    ene0 = energy(x0, vx0)\n",
      "    \n",
      "    # Change, measured in the local `eps` of the change of energy\n",
      "    eps_ene = eps(ene0); dEne = zero(Int64)\n",
      "    \n",
      "    # Vectors to plot the orbit with PyPlot\n",
      "    tV, xV, vxV = Float64[], Float64[], Float64[]\n",
      "    DeneV = Int64[]\n",
      "    push!(tV, t0)\n",
      "    push!(xV, x0)\n",
      "    push!(vxV, vx0)\n",
      "    push!(DeneV, zero(Int64))\n",
      "    \n",
      "    # This is the main loop; we include a minimum step size for security\n",
      "    dt = 1.0\n",
      "    while t0 < time_max && dt>1.0e-8\n",
      "        # Here we integrate\n",
      "        dt, (x1, vx1) = taylorStepper( jetEqs, [x0, vx0], orden, epsilon );\n",
      "        t0 += dt\n",
      "        push!(tV,t0)\n",
      "        push!(xV,x1)\n",
      "        push!(vxV, vx1)\n",
      "        eneEnd = energy(x1, vx1)\n",
      "        dEne = itrunc( (eneEnd-ene0)/eps_ene )\n",
      "        push!(DeneV, dEne)\n",
      "        x0, vx0 = x1, vx1\n",
      "    end\n",
      "\n",
      "    return tV, xV, vxV, DeneV\n",
      "end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "pendulumIntegration (generic function with 3 methods)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tV, xV, vxV, DeneV = pendulumIntegration( x0, vx0, 2pi, jetPendulum);\n",
      "@time tV, xV, vxV, DeneV = pendulumIntegration( x0, vx0, 73.0, jetPendulum);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "elapsed time: 0."
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "008199471 seconds (8622688 bytes allocated)\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "minimum([tV[i+1]-tV[i] for i=1:length(tV)-1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "0.27844305590169327"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "using PyPlot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "INFO: Loading help data...\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(tV, xV, \"-\", tV, vxV, \"-\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x118d1a910>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "2-element Array{Any,1}:\n",
        " PyObject <matplotlib.lines.Line2D object at 0x11c0a5f10>\n",
        " PyObject <matplotlib.lines.Line2D object at 0x11c0a91d0>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(tV, DeneV, \"-\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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",
       "text": [
        "Figure(PyObject <matplotlib.figure.Figure object at 0x11c090ed0>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "1-element Array{Any,1}:\n",
        " PyObject <matplotlib.lines.Line2D object at 0x117508b10>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    }
   ],
   "metadata": {}
  }
 ]
}