Test qutip.propagator with Odeoptions.rhs_reuse

qutip-example-propagator-resue-rhs.ipynb

{
 "metadata": {
  "name": "test-propagator-resue-rhs"
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Test qutip.propagator with Odeoptions.rhs_reuse\n",
      "\n",
      "Code based on problem report by wmwitzel: https://github.com/qutip/qutip/issues/18 "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import qutip as qtp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S = qtp.jmat(1/2.)\n",
      "I = qtp.qeye(2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "H0 = qtp.tensor(S[2], I) + 0.1*qtp.tensor(I, S[2])\n",
      "\n",
      "H0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation}\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = True}\\\\[1em]\\begin{pmatrix}0.550 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.450 & 0.0 & 0.0\\\\0.0 & 0.0 & -0.450 & 0.0\\\\0.0 & 0.0 & 0.0 & -0.550\\\\\\end{pmatrix}\\end{equation}"
       ],
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.55  0.    0.    0.  ]\n",
        " [ 0.    0.45  0.    0.  ]\n",
        " [ 0.    0.   -0.45  0.  ]\n",
        " [ 0.    0.    0.   -0.55]]"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Hint = 0.1*sum([qtp.tensor(S[i], S[i]) for i in xrange(3)])\n",
      "\n",
      "Hint"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation}\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = True}\\\\[1em]\\begin{pmatrix}0.025 & 0.0 & 0.0 & 0.0\\\\0.0 & -0.025 & 0.050 & 0.0\\\\0.0 & 0.050 & -0.025 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.025\\\\\\end{pmatrix}\\end{equation}"
       ],
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = True\n",
        "Qobj data =\n",
        "[[ 0.025  0.     0.     0.   ]\n",
        " [ 0.    -0.025  0.05   0.   ]\n",
        " [ 0.     0.05  -0.025  0.   ]\n",
        " [ 0.     0.     0.     0.025]]"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Turning interaction on linearly:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "qtp.propagator([H0, [Hint, 'w*t']], 5, [], {'w':1/5.})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation}\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = False}\\\\[1em]\\begin{pmatrix}(-0.946-0.323j) & 0.0 & 0.0 & 0.0\\\\0.0 & (-0.581-0.811j) & (0.057-0.040j) & 0.0\\\\0.0 & (-0.051-0.046j) & (-0.677+0.732j) & 0.0\\\\0.0 & 0.0 & 0.0 & (-0.899+0.439j)\\\\\\end{pmatrix}\\end{equation}"
       ],
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[-0.94633811-0.32318029j  0.00000000+0.j          0.00000000+0.j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j         -0.58073735-0.81115709j  0.05656517-0.03959453j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j         -0.05118736-0.04633785j -0.67733746+0.73242498j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j          0.00000000+0.j          0.00000000+0.j\n",
        "  -0.89865955+0.43864333j]]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Turning interaction off linearly with rhs_reuse (bug?):\n",
      "\n",
      "#### -> more like unexpected behavior, because RHS function from previous call to propator is reused"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "odeOpts = qtp.Odeoptions(1e-10, 1e-8)\n",
      "odeOpts.rhs_reuse = True\n",
      "#qtp.rhs_clear()  # this fixes the problem\n",
      "\n",
      "qtp.propagator([H0, [Hint, '1-w*t']], 5, [], {'w':1/5.}, options=odeOpts)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/local/lib/python2.7/dist-packages/qutip/propagator.py:76: UserWarning: propagator is using previously defined rhs function (options.rhs_reuse = True)\n",
        "  warnings.warn(\"propagator is using previously defined rhs function (options.rhs_reuse = True)\")\n"
       ]
      },
      {
       "latex": [
        "\\begin{equation}\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = False}\\\\[1em]\\begin{pmatrix}(-0.946-0.323j) & 0.0 & 0.0 & 0.0\\\\0.0 & (-0.581-0.811j) & (0.057-0.040j) & 0.0\\\\0.0 & (-0.051-0.046j) & (-0.677+0.732j) & 0.0\\\\0.0 & 0.0 & 0.0 & (-0.899+0.439j)\\\\\\end{pmatrix}\\end{equation}"
       ],
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[-0.94633580-0.32318436j  0.00000000+0.j          0.00000000+0.j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j         -0.58073723-0.81115776j  0.05656514-0.03959461j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j         -0.05118735-0.04633793j -0.67733701+0.73242557j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j          0.00000000+0.j          0.00000000+0.j\n",
        "  -0.89865924+0.43864704j]]"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Turning interaction off linearly with rhs_reuse:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "qtp.propagator([H0, [Hint, '1-w*t']], 5, [], {'w':1/5.})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation}\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = False}\\\\[1em]\\begin{pmatrix}(-0.946-0.323j) & 0.0 & 0.0 & 0.0\\\\0.0 & (-0.581-0.811j) & (-0.051-0.046j) & 0.0\\\\0.0 & (0.057-0.040j) & (-0.677+0.732j) & 0.0\\\\0.0 & 0.0 & 0.0 & (-0.899+0.439j)\\\\\\end{pmatrix}\\end{equation}"
       ],
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[-0.94633582-0.32318044j  0.00000000+0.j          0.00000000+0.j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j         -0.58073805-0.81115714j -0.05118751-0.04633791j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j          0.05656517-0.03959451j -0.67733759+0.73242409j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j          0.00000000+0.j          0.00000000+0.j\n",
        "  -0.89866198+0.43864341j]]"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Turning interaction off linearly without rhs_reuse (more like it):"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "odeOpts = qtp.Odeoptions(1e-10, 1e-8)\n",
      "odeOpts.rhs_reuse = False\n",
      "\n",
      "qtp.propagator([H0, [Hint, '1-w*t']], 5, [], {'w':1/5.}) #, options=odeOpts)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation}\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = False}\\\\[1em]\\begin{pmatrix}(-0.946-0.323j) & 0.0 & 0.0 & 0.0\\\\0.0 & (-0.581-0.811j) & (-0.051-0.046j) & 0.0\\\\0.0 & (0.057-0.040j) & (-0.677+0.732j) & 0.0\\\\0.0 & 0.0 & 0.0 & (-0.899+0.439j)\\\\\\end{pmatrix}\\end{equation}"
       ],
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[-0.94633582-0.32318044j  0.00000000+0.j          0.00000000+0.j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j         -0.58073805-0.81115714j -0.05118751-0.04633791j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j          0.05656517-0.03959451j -0.67733759+0.73242409j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j          0.00000000+0.j          0.00000000+0.j\n",
        "  -0.89866198+0.43864341j]]"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Turning interaction on linearly 'a+b*t': A solution is to keep the time function the same but change the arguments."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "odeOpts = qtp.Odeoptions(1e-10, 1e-8)\n",
      "\n",
      "# odeOpts.rhs_reuse = False  # this works but give worse performance\n",
      "\n",
      "odeOpts.rhs_reuse = True  # this make sure that both calls to propagator below use the same RHS function\n",
      "qtp.rhs_clear()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "qtp.propagator([H0, [Hint, 'a+b*t']], 5, [], {'a':0, 'b':1/5.}, options=odeOpts)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation}\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = False}\\\\[1em]\\begin{pmatrix}(-0.946-0.323j) & 0.0 & 0.0 & 0.0\\\\0.0 & (-0.581-0.811j) & (0.057-0.040j) & 0.0\\\\0.0 & (-0.051-0.046j) & (-0.677+0.732j) & 0.0\\\\0.0 & 0.0 & 0.0 & (-0.899+0.439j)\\\\\\end{pmatrix}\\end{equation}"
       ],
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[-0.94633580-0.32318436j  0.00000000+0.j          0.00000000+0.j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j         -0.58073723-0.81115776j  0.05656514-0.03959461j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j         -0.05118735-0.04633793j -0.67733701+0.73242557j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j          0.00000000+0.j          0.00000000+0.j\n",
        "  -0.89865924+0.43864704j]]"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Turning interaction off linearly with rhs_reuse but same 'a+b*t':"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "qtp.propagator([H0, [Hint, 'a+b*t']], 5, [], {'a':1, 'b':-1/5.}, options=odeOpts)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "\\begin{equation}\\text{Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = False}\\\\[1em]\\begin{pmatrix}(-0.946-0.323j) & 0.0 & 0.0 & 0.0\\\\0.0 & (-0.581-0.811j) & (-0.051-0.046j) & 0.0\\\\0.0 & (0.057-0.040j) & (-0.677+0.732j) & 0.0\\\\0.0 & 0.0 & 0.0 & (-0.899+0.439j)\\\\\\end{pmatrix}\\end{equation}"
       ],
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isherm = False\n",
        "Qobj data =\n",
        "[[-0.94633579-0.32318446j  0.00000000+0.j          0.00000000+0.j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j         -0.58073724-0.81115775j -0.05118735-0.04633793j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j          0.05656514-0.03959461j -0.67733700+0.73242558j\n",
        "   0.00000000+0.j        ]\n",
        " [ 0.00000000+0.j          0.00000000+0.j          0.00000000+0.j\n",
        "  -0.89865926+0.43864693j]]"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Software versions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip.ipynbtools import version_table; version_table()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Cython</td><td>0.17.4</td></tr><tr><td>SciPy</td><td>0.11.0</td></tr><tr><td>QuTiP</td><td>2.3.0.dev-374c4b6</td></tr><tr><td>Python</td><td>2.7.4 (default, Apr 19 2013, 18:28:01) \n",
        "[GCC 4.7.3]</td></tr><tr><td>IPython</td><td>1.0.dev</td></tr><tr><td>OS</td><td>posix [linux2]</td></tr><tr><td>Numpy</td><td>1.7.1</td></tr><tr><td>matplotlib</td><td>1.3.x</td></tr><tr><td colspan='2'>Tue Apr 30 16:27:55 2013 JST</td></tr></table>"
       ],
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "<IPython.core.display.HTML at 0x573a950>"
       ]
      }
     ],
     "prompt_number": 12
    }
   ],
   "metadata": {}
  }
 ]
}