Additional documentation for QuTiP issue report "extra dims and mul".

gistfile1.txt

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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import qutip as qt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = qt.sigmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X.dims[0].append(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2, 1], [2]], shape = [2, 2], type = other\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0\\\\1.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2, 1], [2]], shape = [2, 2], type = other\n",
       "Qobj data =\n",
       "[[ 0.  1.]\n",
       " [ 1.  0.]]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rho = qt.ket2dm(qt.basis(2, 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following line should work, as it is a multiplication of dims ``[[2, 1], [2]]`` with ``[[2], [2]]`` and ``[[2], [2, 1]]``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "list index out of range",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-6-12905920855a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mX\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mrho\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdag\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mC:\\Anaconda\\lib\\site-packages\\qutip\\qobj.pyc\u001b[0m in \u001b[0;36m__mul__\u001b[1;34m(self, other)\u001b[0m\n\u001b[0;32m    400\u001b[0m                         not isinstance(dims[1][0], list)):\n\u001b[0;32m    401\u001b[0m                     \u001b[0mr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdims\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 402\u001b[1;33m                     \u001b[0mmask\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mdims\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mdims\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m1\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mr\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    403\u001b[0m                     out.dims = [max([1], [dims[0][n]\n\u001b[0;32m    404\u001b[0m                                           for n in r if not mask[n]]),\n",
      "\u001b[1;31mIndexError\u001b[0m: list index out of range"
     ]
    }
   ],
   "source": [
    "X * rho * X.dag()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multiplying on the right does not result in an exception, but produces the wrong ``dims``, namely ``[[2], [2]]``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0\\\\0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[ 0.  1.]\n",
       " [ 0.  0.]]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho * X.dag()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Meanwhile, the exception is caused by left-multiplication."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "list index out of range",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-8-bc6677a05cab>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mX\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mrho\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mC:\\Anaconda\\lib\\site-packages\\qutip\\qobj.pyc\u001b[0m in \u001b[0;36m__mul__\u001b[1;34m(self, other)\u001b[0m\n\u001b[0;32m    400\u001b[0m                         not isinstance(dims[1][0], list)):\n\u001b[0;32m    401\u001b[0m                     \u001b[0mr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdims\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 402\u001b[1;33m                     \u001b[0mmask\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mdims\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mdims\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m1\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mr\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    403\u001b[0m                     out.dims = [max([1], [dims[0][n]\n\u001b[0;32m    404\u001b[0m                                           for n in r if not mask[n]]),\n",
      "\u001b[1;31mIndexError\u001b[0m: list index out of range"
     ]
    }
   ],
   "source": [
    "X * rho"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Cython</td><td>0.22</td></tr><tr><td>SciPy</td><td>0.15.1</td></tr><tr><td>QuTiP</td><td>3.2.0.dev-58e6a6a</td></tr><tr><td>Python</td><td>2.7.8 |Anaconda 2.2.0 (64-bit)| (default, Jul  2 2014, 15:12:11) [MSC v.1500 64 bit (AMD64)]</td></tr><tr><td>IPython</td><td>3.1.0</td></tr><tr><td>OS</td><td>nt [win32]</td></tr><tr><td>Numpy</td><td>1.9.2</td></tr><tr><td>matplotlib</td><td>1.4.3</td></tr><tr><td colspan='2'>Mon Apr 13 14:35:20 2015 AUS Eastern Standard Time</td></tr></table>"
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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qutip.ipynbtools import version_table\n",
    "version_table()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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