{
 "metadata": {
  "name": "development-benchmark-expect"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Test and benchmarks of expectation value calculation in QuTiP\n",
      "\n",
      "\n",
      "Copyright (C) 2011 and later, Paul D. Nation & Robert J. Johansson"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip.cyQ.spmatfuncs import cy_expect"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 50"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "op = rand_herm(N)\n",
      "ket = rand_ket(N)\n",
      "rho = ket2dm(ket)\n",
      "\n",
      "ket_data = ket.full()\n",
      "op_data = op.data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sop = spre(op)\n",
      "sop_data = sop.data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rho_vec = operator_to_vector(rho)\n",
      "rho_vec_data = rho_vec.full()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Test for consistent results\n",
      "\n",
      "Test various ways, from high level to low level, of calculating expectation values in qutip."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expect(op, ket)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "-7.758978511084069"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expect(op, rho)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "-7.75897851108407"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cy_expect(op_data.data, op_data.indices, op_data.indptr, ket_data, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "-7.758978511084069"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expect_psi(op_data, ket_data, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "-7.758978511084069"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expect_rho_vec(sop_data, rho_vec_data, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "-7.75897851108407"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Benchmarks"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### wavefunction"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "\n",
      "expect(op, ket)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 688 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "\n",
      "cy_expect(op_data.data, op_data.indices, op_data.indptr, ket_data, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 34 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "\n",
      "expect_psi(op_data, ket_data, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 30.2 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### density matrix"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "\n",
      "expect(op, rho)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 802 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "\n",
      "expect_rho_vec(sop_data, rho_vec_data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 640 \u00b5s per loop\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Software versions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from qutip.ipynbtools import version_table\n",
      "\n",
      "version_table()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>matplotlib</td><td>1.4.x</td></tr><tr><td>Numpy</td><td>1.8.0.dev-75cdf3d</td></tr><tr><td>Python</td><td>3.3.1 (default, Apr 17 2013, 22:30:32) \n",
        "[GCC 4.7.3]</td></tr><tr><td>IPython</td><td>1.0.dev</td></tr><tr><td>OS</td><td>posix [linux]</td></tr><tr><td>SciPy</td><td>0.13.0.dev-d74fd00</td></tr><tr><td>QuTiP</td><td>2.3.0.dev-7f0ed30</td></tr><tr><td>Cython</td><td>0.19.1</td></tr><tr><td colspan='2'>Thu Jul 04 15:50:58 2013 JST</td></tr></table>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "<IPython.core.display.HTML at 0x7f59a0de9fd0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}