{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QobjEvo usage example\n",
    "Features of QobjEvo for the users.  \n",
    "Made by Eric Giguere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qutip import *\n",
    "import time\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition of time-dependant Qobj\n",
    "\n",
    "QobjEvo are definied from list of Qobj:  \n",
    "[Qobj0, [Qobj1, coeff1], [Qobj2, coeff2]]  \n",
    "coeff can be one of: \n",
    "- function\n",
    "- string\n",
    "- np.array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definition of base Qobj and \n",
    "N = 4\n",
    "\n",
    "def sin_w(t, args):\n",
    "    return np.cos(args[\"w\"]*t)\n",
    "\n",
    "def cos_w(t, args):\n",
    "    return np.cos(args[\"w\"]*t)\n",
    "\n",
    "tlist = np.linspace(0,10,10000)\n",
    "tlistlog = np.logspace(-3,1,10000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.414 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.732\\\\0.0 & 0.0 & 0.0 & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[0.         1.         0.         0.        ]\n",
       " [0.         0.         1.41421356 0.        ]\n",
       " [0.         0.         0.         1.73205081]\n",
       " [0.         0.         0.         0.        ]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# constant QobjEvo\n",
    "cte_QobjEvo = QobjEvo(destroy(N))\n",
    "cte_QobjEvo(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}-0.416 & 1.0 & 0.0 & 0.0\\\\0.0 & -0.416 & 1.414 & 0.0\\\\0.0 & 0.0 & -0.416 & 1.732\\\\0.0 & 0.0 & 0.0 & -0.416\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[-0.41614684  1.          0.          0.        ]\n",
       " [ 0.         -0.41614684  1.41421356  0.        ]\n",
       " [ 0.          0.         -0.41614684  1.73205081]\n",
       " [ 0.          0.          0.         -0.41614684]]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# QobjEvo with function based coeff\n",
    "func_QobjEvo = QobjEvo([destroy(N),[qeye(N),cos_w]],args={\"w\":2})\n",
    "func_QobjEvo(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}-0.416 & 1.0 & 0.0 & 0.0\\\\0.0 & -0.416 & 1.414 & 0.0\\\\0.0 & 0.0 & -0.416 & 1.732\\\\0.0 & 0.0 & 0.0 & -0.416\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[-0.41614684  1.          0.          0.        ]\n",
       " [ 0.         -0.41614684  1.41421356  0.        ]\n",
       " [ 0.          0.         -0.41614684  1.73205081]\n",
       " [ 0.          0.          0.         -0.41614684]]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# QobjEvo with sting based coeff\n",
    "str_QobjEvo = QobjEvo([destroy(N),[qeye(N),\"cos(w*t)\"]],args={\"w\":2})\n",
    "str_QobjEvo(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}-0.416 & 1.0 & 0.0 & 0.0\\\\0.0 & -0.416 & 1.414 & 0.0\\\\0.0 & 0.0 & -0.416 & 1.732\\\\0.0 & 0.0 & 0.0 & -0.416\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[-0.41614684  1.          0.          0.        ]\n",
       " [ 0.         -0.41614684  1.41421356  0.        ]\n",
       " [ 0.          0.         -0.41614684  1.73205081]\n",
       " [ 0.          0.          0.         -0.41614684]]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# QobjEvo with array based coeff\n",
    "array_QobjEvo = QobjEvo([destroy(N),[qeye(N),np.cos(2*tlist)]],tlist=tlist)\n",
    "array_QobjEvo(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}-0.416 & 1.0 & 0.0 & 0.0\\\\0.0 & -0.416 & 1.414 & 0.0\\\\0.0 & 0.0 & -0.416 & 1.732\\\\0.0 & 0.0 & 0.0 & -0.416\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[-0.41614684  1.          0.          0.        ]\n",
       " [ 0.         -0.41614684  1.41421356  0.        ]\n",
       " [ 0.          0.         -0.41614684  1.73205081]\n",
       " [ 0.          0.          0.         -0.41614684]]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# QobjEvo with array based coeff, log timescale\n",
    "Log_array_QobjEvo = QobjEvo([destroy(N),[qeye(N),np.cos(2*tlistlog)]],tlist=tlistlog)\n",
    "Log_array_QobjEvo(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\\begin{equation*}\\left(\\begin{array}{*{11}c}-0.416 & 1.0 & 0.0 & 0.0\\\\0.0 & -0.416 & 1.414 & 0.0\\\\0.0 & 0.0 & -0.416 & 1.732\\\\0.0 & 0.0 & 0.0 & -0.416\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = False\n",
       "Qobj data =\n",
       "[[-0.41614684  1.          0.          0.        ]\n",
       " [ 0.         -0.41614684  1.41421356  0.        ]\n",
       " [ 0.          0.         -0.41614684  1.73205081]\n",
       " [ 0.          0.          0.         -0.41614684]]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reference\n",
    "destroy(N) + qeye(N) * np.cos(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mathematic\n",
    "- addition (QobjEvo, Qobj)\n",
    "- substraction (QobjEvo, Qobj)\n",
    "- product (QobjEvo, Qobj, scalar)\n",
    "- division (scalar)\n",
    "\n",
    "The examples are done with function type coefficients only, but work for any type of coefficient.  \n",
    "Mixing coefficients type is possible, however this support would be removed if QobjEvo * QobjEvo is to be implemented."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build objects\n",
    "o1 = QobjEvo([qeye(N),[destroy(N),sin_w]],args={\"w\":2})\n",
    "o2 = QobjEvo([qeye(N),[create(N),cos_w]],args={\"w\":2})\n",
    "t = np.random.random()*10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# addition and subtraction \n",
    "o3 = o1 + o2\n",
    "print(o3(t) == o1(t) + o2(t))\n",
    "o3 = o1 - o2\n",
    "print(o3(t) == o1(t) - o2(t))\n",
    "o3 = o1 + destroy(N)\n",
    "print(o3(t) == o1(t) + destroy(N))\n",
    "o3 = o1 - destroy(N)\n",
    "print(o3(t) == o1(t) - destroy(N))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# product\n",
    "oc = QobjEvo([qeye(N)])\n",
    "o3 = o1 * destroy(N)\n",
    "print(o3(t) == o1(t) * destroy(N))\n",
    "o3 = o1 * (0.5+0.5j)\n",
    "print(o3(t) == o1(t) * (0.5+0.5j))\n",
    "o3 = o1 / (0.5+0.5j)\n",
    "print(o3(t) == o1(t) / (0.5+0.5j))\n",
    "o3 = o1 * oc\n",
    "print(o3(t) == o1(t) * oc(t))\n",
    "o3 = oc * o1\n",
    "print(o3(t) == oc(t) * o1(t))\n",
    "o3 = o1 * o2\n",
    "print(o3(t) == o1(t) * o2(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "o1 = QobjEvo([qeye(N),[destroy(N),sin_w]],args={\"w\":2})\n",
    "o2 = QobjEvo([qeye(N),[create(N),cos_w]],args={\"w\":2})\n",
    "o1 += o2\n",
    "print(o1(t) == (qeye(N)*2 + destroy(N)*sin_w(t,args={\"w\":2}) + create(N)*cos_w(t,args={\"w\":2})))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "o1 = QobjEvo([qeye(N),[destroy(N),sin_w]],args={\"w\":2})\n",
    "o2 = QobjEvo([qeye(N),[create(N),cos_w]],args={\"w\":2})\n",
    "o1 -= o2\n",
    "print(o1(t) == (destroy(N)*sin_w(t,args={\"w\":2}) - create(N)*cos_w(t,args={\"w\":2})))\n",
    "\n",
    "o1 = QobjEvo([qeye(N),[destroy(N),sin_w]],args={\"w\":2})\n",
    "o2 = QobjEvo([qeye(N),[create(N),cos_w]],args={\"w\":2})\n",
    "o1 += -o2\n",
    "print(o1(t) == (destroy(N)*sin_w(t,args={\"w\":2}) - create(N)*cos_w(t,args={\"w\":2})))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "o1 = QobjEvo([qeye(N),[destroy(N),sin_w]],args={\"w\":2})\n",
    "o1 *= destroy(N)\n",
    "print(o1(t) == (destroy(N) + destroy(N)*destroy(N)*sin_w(t,args={\"w\":2})))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unitary operations: \n",
    "- conj\n",
    "- dag \n",
    "- trans \n",
    "- _cdc: QobjEvo.dag * QobjEvo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "o_real = QobjEvo([qeye(N),[destroy(N), sin_w]], args={\"w\":2})\n",
    "o_cplx = QobjEvo([qeye(N),[create(N), cos_w]], args={\"w\":-1j})\n",
    "\n",
    "print(o_real(t).trans() == o_real.trans()(t))\n",
    "print(o_real(t).conj() == o_real.conj()(t))\n",
    "print(o_real(t).dag() == o_real.dag()(t))\n",
    "\n",
    "print(o_cplx(t).trans() == o_cplx.trans()(t))\n",
    "print(o_cplx(t).conj() == o_cplx.conj()(t))\n",
    "print(o_cplx(t).dag() == o_cplx.dag()(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# the operator norm correspond to c.dag * c.\n",
    "td_cplx_f0 = qobjevo.QobjEvo([qeye(N)])\n",
    "td_cplx_f1 = qobjevo.QobjEvo([qeye(N),[destroy(N)*create(N),sin_w]], args={'w':2.+0.001j})\n",
    "td_cplx_f2 = qobjevo.QobjEvo([qeye(N),[destroy(N),cos_w]], args={'w':2.+0.001j})\n",
    "td_cplx_f3 = qobjevo.QobjEvo([qeye(N),[create(N),1j*np.sin(tlist)]], tlist=tlist)\n",
    "\n",
    "print(td_cplx_f0(t).dag()*td_cplx_f0(t) == td_cplx_f0._cdc()(t))\n",
    "print(td_cplx_f1(t).dag()*td_cplx_f1(t) == td_cplx_f1._cdc()(t))\n",
    "print(td_cplx_f2(t).dag()*td_cplx_f2(t) == td_cplx_f2._cdc()(t))\n",
    "print(td_cplx_f3(t).dag()*td_cplx_f3(t) == td_cplx_f3._cdc()(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Liouvillian and lindblad dissipator, to use in solver\n",
    "\n",
    "Functions in qutip.superoperator can be used for QobjEvo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "td_L = liouvillian(H=func_QobjEvo)\n",
    "L = liouvillian(H=func_QobjEvo(t))\n",
    "td_L(t) == L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "td_cplx_f0 = qobjevo.QobjEvo([qeye(N)])\n",
    "td_cplx_f1 = qobjevo.QobjEvo([[destroy(N)*create(N),sin_w]], args={'w':2.})\n",
    "\n",
    "td_L = liouvillian(H=func_QobjEvo,c_ops=[td_cplx_f0,td_cplx_f1])\n",
    "L = liouvillian(H=func_QobjEvo(t),c_ops=[td_cplx_f0(t),td_cplx_f1(t)])\n",
    "print(td_L(t) == L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "td_P = spre(td_cplx_f1)\n",
    "P = spre(td_cplx_f1(t))\n",
    "print(td_P(t) == P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting the list back for the object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Quantum object: dims = [[[4], [4]], [[4], [4]]], shape = (16, 16), type = super, isherm = False\n",
      "Qobj data =\n",
      "[[0.+0.j         0.-1.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.-1.41421356j 0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.-1.73205081j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+1.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.-1.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+1.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.-1.41421356j 0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+1.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.-1.73205081j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+1.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+1.41421356j 0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.-1.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+1.41421356j 0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.-1.41421356j 0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+1.41421356j 0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.-1.73205081j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+1.41421356j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+1.73205081j 0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.-1.j         0.+0.j         0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+1.73205081j 0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.-1.41421356j 0.+0.j        ]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+1.73205081j 0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.-1.73205081j]\n",
      " [0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+1.73205081j\n",
      "  0.+0.j         0.+0.j         0.+0.j         0.+0.j        ]], [Quantum object: dims = [[[4], [4]], [[4], [4]]], shape = (16, 16), type = super, isherm = True\n",
      "Qobj data =\n",
      "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]], <function cos_w at 0x7f11bb38eae8>], [Quantum object: dims = [[[4], [4]], [[4], [4]]], shape = (16, 16), type = super, isherm = True\n",
      "Qobj data =\n",
      "[[1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 2. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 3. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 2. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 4. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 6. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 3. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 6. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 9. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]], <qutip.qobjevo._Prod object at 0x7f11bb34ac50>], [Quantum object: dims = [[[4], [4]], [[4], [4]]], shape = (16, 16), type = super, isherm = True\n",
      "Qobj data =\n",
      "[[-0.5  0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.  -2.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.  -4.5  0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.  -0.5  0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.  -2.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.  -4.5  0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.  -0.5  0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.  -2.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.  -4.5  0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.  -0.5  0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.  -2.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "  -4.5  0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]], <qutip.qobjevo._Prod object at 0x7f11bb34a128>], [Quantum object: dims = [[[4], [4]], [[4], [4]]], shape = (16, 16), type = super, isherm = True\n",
      "Qobj data =\n",
      "[[-0.5  0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.  -0.5  0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.  -0.5  0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.  -0.5  0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.  -2.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.  -2.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.  -2.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.  -2.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.  -4.5  0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.  -4.5  0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.  -4.5  0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.  -4.5  0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]\n",
      " [ 0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
      "   0.   0. ]], <qutip.qobjevo._Prod object at 0x7f11bb34a128>]]\n"
     ]
    }
   ],
   "source": [
    "print(td_L.to_list())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Arguments modification\n",
    "\n",
    "To change the args: qobjevo.arguments(new_args)\n",
    "\n",
    "Call with other arguments without changing them: qobjevo.with_args(t, new_args)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "def Args(t, args):\n",
    "    return args['w']\n",
    "td_args = qobjevo.QobjEvo([qeye(N), Args],args={'w':1.}) \n",
    "print(td_args(t) == qeye(N))\n",
    "td_args.arguments({'w':2.})\n",
    "print(td_args(t) == qeye(N)*2)\n",
    "print(td_args(t,args={'w':3.}) == qeye(N)*3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When summing QobjEvo that have an arguments in common, only one is kept."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "td_args_1 = qobjevo.QobjEvo([qeye(N), [destroy(N), Args]],args={'w':1.})\n",
    "td_args_2 = qobjevo.QobjEvo([qeye(N), [destroy(N), Args]],args={'w':2.})\n",
    "td_str_sum = td_args_1 + td_args_2\n",
    "\n",
    "# Only one value for args is kept\n",
    "print(td_str_sum(t) == td_args_1(t) + td_args_2(t)) \n",
    "print(td_str_sum(t) == 2*td_args_2(t)) \n",
    "\n",
    "# Updating args affect all part\n",
    "td_str_sum.arguments({'w':1.})\n",
    "print(td_str_sum(t) == 2*td_args_1(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Argument with different names are fine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "def Args2(t, args):\n",
    "    return args['x']\n",
    "td_args_1 = qobjevo.QobjEvo([qeye(N), [destroy(N), cos_w]],args={'w':1.})\n",
    "td_args_2 = qobjevo.QobjEvo([qeye(N), [destroy(N), Args2]],args={'x':2.})\n",
    "td_str_sum = td_args_1 + td_args_2\n",
    "\n",
    "# Only one value for args is kept\n",
    "print(td_str_sum(t) == td_args_1(t) + td_args_2(t))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4x4 sparse matrix of type '<class 'numpy.complex128'>'\n",
       "\twith 7 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Obtain the sparce matrix at a time t instead of a Qobj\n",
    "str_QobjEvo(1, data=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "# Test is the QobjEvo does depend on time\n",
    "print(cte_QobjEvo.const)\n",
    "print(str_QobjEvo.const)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4], [4]]\n",
      "(4, 4)\n",
      "True\n",
      "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "# Obtain the size, shape, oper flag etc:\n",
    "# The QobjEvo.cte always exist and contain the constant part of the QobjEvo\n",
    "# It can be used to get the shape, etc. since the QobjEvo do not directly have them.\n",
    "td_cplx_f1 = qobjevo.QobjEvo([[destroy(N)*create(N),sin_w]], args={'w':2.})\n",
    "print(td_cplx_f1.cte.dims)\n",
    "print(td_cplx_f1.cte.shape)\n",
    "print(td_cplx_f1.cte.isoper)\n",
    "print(td_cplx_f1.cte)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 1.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4], [4]], shape = (4, 4), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[1. 0. 0. 0.]\n",
       " [0. 1. 0. 0.]\n",
       " [0. 0. 1. 0.]\n",
       " [0. 0. 0. 1.]]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Creating a copy\n",
    "str_QobjEvo_2 = str_QobjEvo.copy()\n",
    "str_QobjEvo_2 += 1\n",
    "str_QobjEvo_2(1) -  str_QobjEvo(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "QuTiP: Quantum Toolbox in Python\n",
      "Copyright (c) 2011 and later.\n",
      "A. J. Pitchford, P. D. Nation, R. J. Johansson, A. Grimsmo, and C. Granade\n",
      "\n",
      "QuTiP Version:      4.4.0.dev0+8b414dd\n",
      "Numpy Version:      1.16.2\n",
      "Scipy Version:      1.2.1\n",
      "Cython Version:     0.29.6\n",
      "Matplotlib Version: 3.0.1\n",
      "Python Version:     3.7.0\n",
      "Number of CPUs:     4\n",
      "BLAS Info:          OPENBLAS\n",
      "OPENMP Installed:   False\n",
      "INTEL MKL Ext:      False\n",
      "Platform Info:      Linux (x86_64)\n",
      "Installation path:  /home/eric/anaconda3/lib/python3.7/site-packages/qutip-4.4.0.dev0+8b414dd-py3.7-linux-x86_64.egg/qutip\n",
      "==============================================================================\n",
      "Please cite QuTiP in your publication.\n",
      "==============================================================================\n",
      "For your convenience a bibtex reference can be easily generated using `qutip.cite()`\n"
     ]
    }
   ],
   "source": [
    "about()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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