{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization of a state-to-state transfer in a lambda system with RWA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.751470Z",
     "start_time": "2019-02-12T04:40:52.635450Z"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "matplotlib.pylab 1.15.4\n",
      "matplotlib       3.0.2\n",
      "scipy            1.2.0\n",
      "krotov           0.1.0.post1+dev\n",
      "qutip            4.3.1\n",
      "numpy            1.15.4\n",
      "CPython 3.6.8\n",
      "IPython 7.2.0\n"
     ]
    }
   ],
   "source": [
    "# NBVAL_IGNORE_OUTPUT\n",
    "%load_ext watermark\n",
    "import numpy as np\n",
    "import scipy\n",
    "import matplotlib\n",
    "import matplotlib.pylab as plt\n",
    "import krotov\n",
    "import qutip\n",
    "from qutip import Qobj\n",
    "%watermark -v --iversions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\newcommand{tr}[0]{\\operatorname{tr}}\n",
    "\\newcommand{diag}[0]{\\operatorname{diag}}\n",
    "\\newcommand{abs}[0]{\\operatorname{abs}}\n",
    "\\newcommand{pop}[0]{\\operatorname{pop}}\n",
    "\\newcommand{aux}[0]{\\text{aux}}\n",
    "\\newcommand{opt}[0]{\\text{opt}}\n",
    "\\newcommand{tgt}[0]{\\text{tgt}}\n",
    "\\newcommand{init}[0]{\\text{init}}\n",
    "\\newcommand{lab}[0]{\\text{lab}}\n",
    "\\newcommand{rwa}[0]{\\text{rwa}}\n",
    "\\newcommand{bra}[1]{\\langle#1\\vert}\n",
    "\\newcommand{ket}[1]{\\vert#1\\rangle}\n",
    "\\newcommand{Bra}[1]{\\left\\langle#1\\right\\vert}\n",
    "\\newcommand{Ket}[1]{\\left\\vert#1\\right\\rangle}\n",
    "\\newcommand{Braket}[2]{\\left\\langle #1\\vphantom{#2} \\mid\n",
    "#2\\vphantom{#1}\\right\\rangle}\n",
    "\\newcommand{Ketbra}[2]{\\left\\vert#1\\vphantom{#2}\n",
    "\\right\\rangle \\hspace{-0.2em} \\left\\langle #2\\vphantom{#1}\\right\\vert}\n",
    "\\newcommand{op}[1]{\\hat{#1}}\n",
    "\\newcommand{Op}[1]{\\hat{#1}}\n",
    "\\newcommand{dd}[0]{\\,\\text{d}}\n",
    "\\newcommand{Liouville}[0]{\\mathcal{L}}\n",
    "\\newcommand{DynMap}[0]{\\mathcal{E}}\n",
    "\\newcommand{identity}[0]{\\mathbf{1}}\n",
    "\\newcommand{Norm}[1]{\\lVert#1\\rVert}\n",
    "\\newcommand{Abs}[1]{\\left\\vert#1\\right\\vert}\n",
    "\\newcommand{avg}[1]{\\langle#1\\rangle}\n",
    "\\newcommand{Avg}[1]{\\left\\langle#1\\right\\rangle}\n",
    "\\newcommand{AbsSq}[1]{\\left\\vert#1\\right\\vert^2}\n",
    "\\newcommand{Re}[0]{\\operatorname{Re}}\n",
    "\\newcommand{Im}[0]{\\operatorname{Im}}\n",
    "\\newcommand{toP}[0]{\\omega_{12}}\n",
    "\\newcommand{toS}[0]{\\omega_{23}}\n",
    "\\newcommand{oft}[0]{\\left(t\\right)}$\n",
    "\n",
    "The purpose of this example is to illustrate and test the use of complex control\n",
    "fields.\n",
    "Essentially, this is accomplished by rewriting the Hamiltonian as the\n",
    "sum of two independent controls (real and imaginary parts).\n",
    "\n",
    "## Define the Hamiltonian\n",
    "\n",
    "The system consists of three levels $\\Ket{1}$,\n",
    "$\\Ket{2}$ and $\\Ket{3}$ with energy levels $E_{1}, E_{2}$ and $E_{3}$ which\n",
    "interact with a pair of pulses,\n",
    "with time-dependent frequencies of\n",
    "$\\omega_{P}=\\omega_{P}\\oft$ (pump laser) and \n",
    "$\\omega_{S} = \\omega_{S}\\oft$\n",
    "(stokes laser) respectively.\n",
    "The pulses each have time-dependent envelopes\n",
    "$\\varepsilon_{P}\\oft$ and $\\varepsilon_{S}\\oft$.\n",
    "Furthermore, it is assumed that\n",
    "the frequencies are tuned\n",
    "such that $\\omega_{P}=\\omega_{P}\\oft$ selectively\n",
    "addresses\n",
    "the $\\Ket{1} \\leftrightarrow \\Ket{2}$ and \n",
    "$\\omega_{S}=\\omega_{S}\\oft$\n",
    "addresses the $\\Ket{2} \\leftrightarrow \\Ket{3}$ transition.\n",
    "\n",
    "We transform into\n",
    "the interaction picture using the operator\n",
    "\n",
    "$$\\op{U}_{0} = \\Ketbra{1}{1}\n",
    "e^{-i\\left(E_{2} - \\omega_{P} \\right)t} + \\Ketbra{2}{2} e^{-iE_{2}t} +\n",
    "\\Ketbra{3}{3} e^{-i\\left(E_{2}-\\omega_{S}\\right)t}\\,\\,,$$\n",
    "\n",
    "where $\\toP$ and\n",
    "$\\toS$, the splittings between the first and second and between the second and\n",
    "third energy levels, are close to the central frequencies of $\\omega_{S}\\oft$\n",
    "and $\\omega_{P}\\oft$.\n",
    "\n",
    "In the rotating wave approximation, the fast rotating\n",
    "terms\n",
    "$e^{\\pm i\\left(\\toP + \\omega_{P}\\oft \\right)t}$ and \n",
    "$e^{\\pm i\\left(\\toS +\n",
    "\\omega_{S}\\oft \\right)t}$ can be neglegted.\n",
    " \n",
    "Consequently,\n",
    "\n",
    "$$ \\op{H}_{0} =\n",
    "\\Delta_{P} \\Ketbra{1}{1}  +\\Delta_{S} \\Ketbra{3}{3}$$\n",
    "\n",
    "describes the drift\n",
    "Hamiltonian of a system with the respective detunings $\\Delta_{P}=E_{1} +\n",
    "\\omega_{P} - E_{2}$ and $\\Delta_{S} = E_{3} + \\omega_{S} -E_{2}$.\n",
    "\n",
    "The control\n",
    "Hamiltonian is given by \n",
    "\n",
    "$$    \\op{H}_{1}\\oft = \\op{H}_{1,P}\\oft +\n",
    "\\op{H}_{1,S}\\oft = \\Omega_{P}\\oft \\Ketbra{1}{2} + \\Omega_{S}\\oft\\Ketbra{2}{3} +\n",
    "\\text{h.c.}\\,\\,,$$\n",
    "\n",
    "where $\\Omega_{P} = \\Omega_{P}\\oft = \\frac{\\mu_{21}\n",
    "\\varepsilon_{P}\\oft}{2} e^{-i\\Phi_{S}\\oft t}$ and\n",
    "$\\Omega_{S} = \\Omega_{S}\\oft =\n",
    "\\frac{\\mu_{23} \\varepsilon_{S}\\oft}{2} e^{-i\\Phi_{P}\\oft t}$\n",
    "with the phases\n",
    "$\\Phi_{P}\\oft = \\toP - \\omega_{P}\\oft$ and $\\Phi_{S}\\oft = \\toS -\n",
    "\\omega_{S}\\oft$\n",
    "and $\\mu_{ij}$ the $ij^{\\text{th}}$ dipole-transition moment.\n",
    "In order to optimize, we rewrite $\\Omega_{P}\\oft = \\Omega_{P}^\\text{Re}\\oft +\n",
    "i\\Omega_{P}^\\text{Im}\\oft$\n",
    "and $\\Omega_{S}\\oft = \\Omega_{S}^\\text{Re}\\oft +\n",
    "i\\Omega_{S}^\\text{Im}\\oft$, such that optimization of the pulses involves only\n",
    "real functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.781057Z",
     "start_time": "2019-02-12T04:40:55.755916Z"
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   "source": [
    "def ham_and_states():\n",
    "    \"\"\"Lambda-system Hamiltonian\"\"\"\n",
    "    E1 = 0.\n",
    "    E2 = 10.\n",
    "    E3 = 5.\n",
    "    ω_P = 9.5\n",
    "    ω_S = 4.5\n",
    "    Ω_init = 5.\n",
    "    H0 =  Qobj([[E1+ω_P-E2, 0., 0.], \\\n",
    "                [0., 0., 0.],        \\\n",
    "                [0., 0., E3+ω_S-E2]])\n",
    "    \n",
    "        \n",
    "    H1P_re = Qobj([[0.,-1.,0.], [-1.,0.,0.],[0.,0.,0.]])    \n",
    "    H1P_im = Qobj([[0.,-1.j,0.],[1.j,0.,0.],[0.,0.,0.]])\n",
    "    ΩP_re = lambda t, args: Ω_init\n",
    "    ΩP_im = lambda t, args: Ω_init\n",
    "    \n",
    "    H1S_re = Qobj([[0.,0.,0.],[0.,0.,1.],[0.,1.,0.]])\n",
    "    H1S_im = Qobj([[0.,0.,0.],[0.,0.,1.j],[0.,-1.j,0.]])\n",
    "    ΩS_re = lambda t, args: Ω_init    \n",
    "    ΩS_im = lambda t, args: Ω_init\n",
    "    \n",
    "    \"\"\"Initial and target states\"\"\"\n",
    "    psi0 = qutip.Qobj(np.array([1.,0.,0.]))\n",
    "    psi1 = qutip.Qobj(np.array([0.,0.,1.]))    \n",
    "    \n",
    "    return ([H0, \\\n",
    "            [H1P_re, ΩP_re], [H1P_im, ΩP_im], \\\n",
    "            [H1S_re, ΩS_re], [H1S_im, ΩS_im]], \\\n",
    "            psi0, psi1)\n",
    "\n",
    "H, psi0, psi1 = ham_and_states()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We introduce projectors for each of the three energy levels\n",
    "$\\op{P}_{i} =\n",
    "\\Ketbra{i}{i}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.798666Z",
     "start_time": "2019-02-12T04:40:55.787265Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "3"
    }
   },
   "outputs": [],
   "source": [
    "proj1 = Qobj([[1.,0.,0.],[0.,0.,0.],[0.,0.,0.]])\n",
    "proj2 = Qobj([[0.,0.,0.],[0.,1.,0.],[0.,0.,0.]])\n",
    "proj3 = Qobj([[0.,0.,0.],[0.,0.,0.],[0.,0.,1.]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the optimization target\n",
    "\n",
    "In the following we consider dynamics acting\n",
    "over a duration of $\\Delta_{t} = 5$, beginning at\n",
    "$t_{0} = 0$ and ending at $T =\n",
    "\\Delta_{t}$. \n",
    "The time grid is divided into $n_{t} = 500$ equidistant time\n",
    "steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.809020Z",
     "start_time": "2019-02-12T04:40:55.802160Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "4"
    }
   },
   "outputs": [],
   "source": [
    "tlist = np.linspace(0.,5.,500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the objective of this example is a state to state transfer from the\n",
    "initial state\n",
    "$\\Ket{\\Psi_{\\init}} = \\Ket{1}$ into the final state\n",
    "$\\Ket{\\Psi_{\\tgt}} = \\Ket{3}$ at the\n",
    "final time $t_{1}$, the optimization\n",
    "objective is set as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.816607Z",
     "start_time": "2019-02-12T04:40:55.813293Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "5"
    }
   },
   "outputs": [],
   "source": [
    "objective = krotov.Objective(initial_state=psi0, target=psi1, H=H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial guess shapes\n",
    "\"stimulated Raman adiabatic passage\" (STIRAP) is a\n",
    "process in which population in $\\Ket{1}$ is transferred into\n",
    "$\\Ket{3}$ without\n",
    "having to pass through $\\Ket{2}$ (which could for instance be a rapidly decaying\n",
    "level).\n",
    "In order for this process to occur, a temporally finite Stokes pulse of\n",
    "sufficient amplitude driving the $\\Ket{2} \\leftrightarrow \\Ket{3}$ transition is\n",
    "applied first, whilst second pump pulse of similar intensity follows some time\n",
    "later such that the pulses still have a partial temporal overlap.\n",
    "\n",
    "In order to\n",
    "demonstrate the Krotov's optimization method however, we choose an initial guess\n",
    "consisting of two low intensity and real Blackman pulses which are temporally\n",
    "disjoint.\n",
    "\n",
    "For the real components of the matrix elements, we supply our guess\n",
    "pulses shaped as Blackman window functions `S(t,offset)`, with an offset\n",
    "ensuring that the two pulses don't overlap.\n",
    "The imaginary components are coupled\n",
    "to pulses that are zero at all times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.829336Z",
     "start_time": "2019-02-12T04:40:55.819110Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "6"
    }
   },
   "outputs": [],
   "source": [
    "def S(t,offset):\n",
    "    \"\"\"Shape envelope function for the field update\"\"\"\n",
    "    return krotov.shapes.blackman(t,1.+offset,4.+offset)\n",
    "\n",
    "def shape_field_real(eps,offset):\n",
    "    \"\"\"Applies the total pulse shape to the real part of a guess pulse\"\"\"\n",
    "    field_shaped = lambda t, args: eps(t, args)*S(t,offset)\n",
    "    return field_shaped\n",
    "\n",
    "def shape_field_imag(eps,offset):\n",
    "    \"\"\"Initializes the imaginary parts of the guess pulses to zero\"\"\"\n",
    "    field_shaped = lambda t, args: eps(t, args)*0.\n",
    "    return field_shaped\n",
    "\n",
    "H[1][1] = shape_field_real(H[1][1],1.) # Re[Ωₚ]\n",
    "H[2][1] = shape_field_imag(H[2][1],1.) # Im[Ωₚ]\n",
    "H[3][1] = shape_field_real(H[3][1],-1.) # Re[Ωₛ]\n",
    "H[4][1] = shape_field_imag(H[4][1],-1.) # Im[Ωₛ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We choose an appropriate update factor $\\lambda_{a}$ for the problem at hand and\n",
    "make sure Krotov considers pulses which start and end with zero amplitude."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.839565Z",
     "start_time": "2019-02-12T04:40:55.833234Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "7"
    }
   },
   "outputs": [],
   "source": [
    "def update_shape(t):\n",
    "    \"\"\"Scales the Krotov methods update of the pulse value at the time t\"\"\"\n",
    "    return krotov.shapes.flattop(t,0.,5.,0.3,func='sinsq')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.851044Z",
     "start_time": "2019-02-12T04:40:55.842793Z"
    }
   },
   "outputs": [],
   "source": [
    "opt_lambda = 2.\n",
    "pulse_options = { \n",
    "    H[1][1]: dict(lambda_a=opt_lambda, shape=update_shape),\n",
    "    H[2][1]: dict(lambda_a=opt_lambda, shape=update_shape),\n",
    "    H[3][1]: dict(lambda_a=opt_lambda, shape=update_shape),\n",
    "    H[4][1]: dict(lambda_a=opt_lambda, shape=update_shape)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate dynamics of the guess field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:55.858312Z",
     "start_time": "2019-02-12T04:40:55.853316Z"
    },
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     "n": "10"
    }
   },
   "outputs": [],
   "source": [
    "def plot_pulse(pulse, tlist, label):\n",
    "    fig, ax = plt.subplots()\n",
    "    if callable(pulse):\n",
    "        pulse = np.array([pulse(t, args=None) for t in tlist])\n",
    "    ax.plot(tlist, pulse)\n",
    "    ax.set_xlabel('time')\n",
    "    ax.set_ylabel('%s pulse amplitude' % label)\n",
    "    plt.show(fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:56.293915Z",
     "start_time": "2019-02-12T04:40:55.860421Z"
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   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pulse(H[1][1], tlist, 'Ωₚ')\n",
    "plot_pulse(H[3][1], tlist, 'Ωₛ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The imaginary parts are zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:56.300681Z",
     "start_time": "2019-02-12T04:40:56.295922Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "12"
    }
   },
   "outputs": [],
   "source": [
    "assert np.all([H[2][1](t, None) == 0 for t in tlist])\n",
    "assert np.all([H[4][1](t, None) == 0 for t in tlist])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After assuring ourselves that our guess pulses appear as expected, we propagate\n",
    "the system using our guess. Since the pulses are temporally disjoint, we expect\n",
    "the first pulse to have no effect, whilst the second merely transfers population\n",
    "out of $\\Ket{1}$ into $\\Ket{2}$ and back again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:57.224259Z",
     "start_time": "2019-02-12T04:40:56.304263Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "13"
    }
   },
   "outputs": [],
   "source": [
    "guess_dynamics = objective.mesolve(tlist, e_ops=[proj1,proj2,proj3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:57.232092Z",
     "start_time": "2019-02-12T04:40:57.226227Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "14"
    }
   },
   "outputs": [],
   "source": [
    "def plot_population(result):\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(result.times, result.expect[0], label='1')\n",
    "    ax.plot(result.times, result.expect[1], label='2')\n",
    "    ax.plot(result.times, result.expect[2], label='3')\n",
    "    ax.legend()\n",
    "    ax.set_xlabel('time')\n",
    "    ax.set_ylabel('population')\n",
    "    plt.show(fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:40:57.443794Z",
     "start_time": "2019-02-12T04:40:57.236490Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "15"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_population(guess_dynamics)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimize\n",
    "We now supply Krotov with all the information it needs to optimize,\n",
    "consisting of the `objectives` (maximize population in $\\Ket{3}$ at $t_{1}$),\n",
    "`pulse_options` (the initial shapes of our pulses and how they may be changed)\n",
    "as well as the `propagator` to use, optimization functional (`chi_constructor`),\n",
    "`info_hook` (processing occuring inbetween iterations of optimization) and the\n",
    "maximum number of iterations to perform, `iter_stop`. We will stop the\n",
    "optimization when the error goes below $10^{-3}$ or the fidelity has converged\n",
    "to within 5 digits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:41:22.349155Z",
     "start_time": "2019-02-12T04:40:57.446355Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "16"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  iter.        J_T   g_a_int_1   g_a_int_2   g_a_int_3   g_a_int_4     g_a_int          J  Delta_J_T    Delta J  secs\n",
      "      0   1.02e+00    0.00e+00    0.00e+00    0.00e+00    0.00e+00    0.00e+00   1.02e+00        n/a        n/a     1\n",
      "      1   6.26e-01    2.25e-02    2.91e-02    2.13e-02    2.68e-02    9.98e-02   7.26e-01  -3.99e-01  -2.99e-01     2\n",
      "      2   3.30e-01    1.79e-02    2.31e-02    1.52e-02    1.79e-02    7.41e-02   4.04e-01  -2.96e-01  -2.22e-01     2\n",
      "      3   1.58e-01    1.09e-02    1.38e-02    8.81e-03    9.51e-03    4.30e-02   2.01e-01  -1.72e-01  -1.29e-01     2\n",
      "      4   7.17e-02    5.70e-03    6.87e-03    4.50e-03    4.45e-03    2.15e-02   9.32e-02  -8.60e-02  -6.45e-02     2\n",
      "      5   3.18e-02    2.74e-03    3.11e-03    2.16e-03    1.95e-03    9.96e-03   4.18e-02  -3.98e-02  -2.99e-02     2\n",
      "      6   1.40e-02    1.27e-03    1.35e-03    1.00e-03    8.31e-04    4.45e-03   1.85e-02  -1.78e-02  -1.34e-02     2\n",
      "      7   6.16e-03    5.84e-04    5.69e-04    4.62e-04    3.47e-04    1.96e-03   8.13e-03  -7.85e-03  -5.88e-03     2\n",
      "      8   2.72e-03    2.68e-04    2.37e-04    2.12e-04    1.43e-04    8.60e-04   3.58e-03  -3.44e-03  -2.58e-03     2\n",
      "      9   1.21e-03    1.24e-04    9.75e-05    9.79e-05    5.86e-05    3.78e-04   1.59e-03  -1.51e-03  -1.13e-03     2\n",
      "     10   5.44e-04    5.76e-05    3.98e-05    4.55e-05    2.37e-05    1.67e-04   7.11e-04  -6.66e-04  -5.00e-04     2\n"
     ]
    }
   ],
   "source": [
    "oct_result = krotov.optimize_pulses(\n",
    "    [objective],\n",
    "    pulse_options,\n",
    "    tlist,\n",
    "    propagator=krotov.propagators.expm,\n",
    "    chi_constructor=krotov.functionals.chis_re,\n",
    "    info_hook=krotov.info_hooks.print_table(\n",
    "        J_T=krotov.functionals.J_T_re,\n",
    "        show_g_a_int_per_pulse=True,\n",
    "        unicode=False,\n",
    "    ),\n",
    "    check_convergence=krotov.convergence.Or(\n",
    "        krotov.convergence.value_below(1e-3, name='J_T'),\n",
    "        krotov.convergence.delta_below(1e-5),\n",
    "        krotov.convergence.check_monotonic_error,\n",
    "    ),\n",
    "    iter_stop=15,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:41:22.361922Z",
     "start_time": "2019-02-12T04:41:22.354011Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "17"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Krotov Optimization Result\n",
       "--------------------------\n",
       "- Started at 2019-02-11 23:54:13\n",
       "- Number of objectives: 1\n",
       "- Number of iterations: 10\n",
       "- Reason for termination: Reached convergence: J_T < 0.001\n",
       "- Ended at 2019-02-11 23:54:39"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oct_result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We appear to have found pulse-shapes that fulfill our objective, but what do\n",
    "they look like?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:41:22.898498Z",
     "start_time": "2019-02-12T04:41:22.365141Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "18"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pump pulse amplitude and phase:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stokes pulse amplitude and phase:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_pulse_amplitude_and_phase(pulse_real, pulse_imaginary,tlist):\n",
    "    ax1 = plt.subplot(211)\n",
    "    ax2 = plt.subplot(212)\n",
    "    amplitudes = [np.sqrt(x*x + y*y) for x,y in zip(pulse_real,pulse_imaginary)]\n",
    "    phases = [np.arctan2(y,x)/np.pi for x,y in zip(pulse_real,pulse_imaginary)]\n",
    "    ax1.plot(tlist,amplitudes)\n",
    "    ax1.set_xlabel('time')\n",
    "    ax1.set_ylabel('pulse amplitude')\n",
    "    ax2.plot(tlist,phases)\n",
    "    ax2.set_xlabel('time')\n",
    "    ax2.set_ylabel('pulse phase (π)')    \n",
    "    plt.show()\n",
    "    \n",
    "print(\"pump pulse amplitude and phase:\")\n",
    "plot_pulse_amplitude_and_phase(\n",
    "    oct_result.optimized_controls[0], oct_result.optimized_controls[1], tlist)\n",
    "print(\"Stokes pulse amplitude and phase:\")\n",
    "plot_pulse_amplitude_and_phase(\n",
    "    oct_result.optimized_controls[2], oct_result.optimized_controls[3], tlist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And how does the population end up in $\\Ket{3}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:41:23.628149Z",
     "start_time": "2019-02-12T04:41:22.905901Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "19"
    }
   },
   "outputs": [],
   "source": [
    "opt_dynamics = oct_result.optimized_objectives[0].mesolve(\n",
    "    tlist, e_ops=[proj1, proj2, proj3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-02-12T04:41:23.853468Z",
     "start_time": "2019-02-12T04:41:23.633866Z"
    },
    "attributes": {
     "classes": [],
     "id": "",
     "n": "20"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6re+OfEe1pZq50XPtHYrigFRSUBzKjWP7UFJlZvX+bHuH0ilZpIWvkr9iWMAw+nbva+9wFAekkoLiUGL7dCfU143lu443XVhptu1Z20kvTletBKVBKikoDkUIwdUjgtmWWsCx/HJ7h9PpfJX8Fd2cuzG1z1R7h6I4KJUUFIdz1fBghICvd2fYO5ROJac8h/XH1jM7cjbOemd7h6M4KJUUFIfTq5srEyL9+Hp3hprh3Ia+OfwNNbKGq/tebe9QFAemkoLikK4eEUxGYQXbjxbYO5ROwWwxszx5OeN6jSPEK8Te4SgOTCUFxSFNi+mBp7OB5bvUI6S2sCljEyfLTzK3r+pgVhqnkoLikFyd9MwY1JM1+7Mor1ZzFlrry+QvCXAN4ILeF9g7FMXBqaSgOKzZw4Moq67hpwMn7R1Kh3a8+DibMzczp+8cDDqb7quldAIqKSgOa1SoD0HdXPlmT6a9Q+nQliUtQy/0qoNZsYpKCorD0ukEs4cF8fvhXHKKK+0dTodUYa5gRcoKJodMJsAtwN7hKB2ASgqKQ5s9PAiLhO/jT9g7lA5pzdE1FFcXM6/fPHuHonQQKikoDi3C34Mhwd58s1s9QmouKSVLDi0hslsksYGx9g5H6SBUUlAc3uxhQSRmFXMou9jeoXQoCXkJHCw4yPx+89VGOorVVFJQHN6sIb0w6AQrVGuhWZYcWoKH0YOZ4TPtHYrSgaikoDg8Xw9nLujrz7d7M6lRy15YJac8h5/SfuLyiMvVRjpKs6ikoHQIs4cHcbK4iq1H8u0dSofwWeJn1Mgaboi5wd6hKB2MSgpKhzClfyCeLga+2aOWvWhKcXUxXyZ/ybQ+0+jt2dve4SgdjEoKSofgYtRz2aCerNmfrZa9aMKXSV9SZirj1oG32jsUpQNSSUHpMGYPC6K8uoa1B9RWnQ2pqqnis8TPGNtzLP19+9s7HKUDUklB6TBG1i17oUYhNei7lO/Ir8zn1kGqlaC0jEoKSodRt+zF5pQ8tezFeVSaK3kv/j2G+g9ldI/R9g5H6aCsXjJRCKEHAuufI6U8ZougFKUhs4cH8daGFL7be4LbJ4XbOxyHsixpGTkVObw46UU1Wc1GTCYTGRkZVFY67k2Ji4sLwcHBGI3GFp1vVVIQQtwHPA2cBCy1hyUwuInzpgOvA3rgQynli+cpMxd4pra+eCnlddYGr3Q9p5e92JOpkkI9ZaYyFu1bxNieYxnZY6S9w+m0MjIy8PT0JDQ01CETr5SS/Px8MjIyCAsLa1Ed1j4+egCIllIOkFIOqn01lRD0wNvApUAMMF8IEXNWmSjgCWC8lHIA8GCzfwOly7lqeDAHs4o5mKWWvajzQcIHFFYVcv/w++0dSqdWWVmJr6+vQyYEACEEvr6+rWrJWJsUjgNFzax7FJAipUyVUlYDS4ErzipzO/C2lLIQQEqZ08xrKF3Q6WUv1D4LAKQXp7M4cTGXR1zOQL+B9g6n03PUhFCntfFZmxRSgY1CiCeEEA/XvZo4JwgtmdTJqD1WX1+grxBisxBiW+3jpnMIIe4QQsQJIeJyc3OtDFnprHzcnbgw2p/v1LIXSCl5acdLOOudeWjEQ/YOR2kHt956KwEBAQwcaJsbAGuTwjFgHeAEeNZ7tZYBiAIuBOYDHwghup1dSEr5vpQyVkoZ6+/v3waXVTq62cOCOVlcxZYjefYOxa7WpK1hU+Ym7hpyF36ufvYOR2kHN998M2vWrLFZ/VZ1NEsp/wEghPCo/bnUitMygfpz7INrj9WXAWyXUpqAo0KIZLQksdOauJSu6+L+AXi5GFi68zgTo7rmjUJeRR7/2v4vBvkN4vr+19s7HKWdTJo0ibS0NJvVb1VLQQgxUAixBzgAHBBC7BJCDGjitJ1AlBAiTAjhBMwDvj+rzLdorQSEEH5oj5NSmxG/0kW5GPXMje3Nmv3ZZBc57vBAW5FS8syWZ6g0V/LchOcw6KweXa4ojbL2L+l94GEp5QYAIcSFwAfAuIZOkFKahRD3AmvRhqR+JKU8IIR4FoiTUn5f+940IUQiUAM8JqVUy2AqVrlpbCiLNh/l8+3pPDIt2t7htKsP933Irxm/8vioxwn3VkNz7eEfKw+QeKJtR8DF9PLi6VlN3W/blrVJwb0uIQBIKTcKIdybOklKuQpYddaxv9f7XgIP174UpVlCfN2YHB3Akh3HuHdyJM4Gvb1DahebMjbx5p43mRE2g+v6qWk9StuyNimkCiGeAj6t/fkG1GMexQEsGBfKTR/t4MeELK4aHmzvcGxub85eHvn1EaJ9onlm3DMOPzyyM7P3Hb2tWDv66FbAH/im9uVfe0xR7GpCpB/h/u58siUNreHZee3P28/dP99NgFsA71z8Dq4GV3uHpNjB/PnzGTt2LElJSQQHB7No0aI2rd/a0UeFgJoqqTgcnU5wy/gwnvp2P1tT8xkX0TmHZf5y7Bee2PQEPi4+fDjtQ/zduuaIKwWWLFli0/obbSkIIV6r/bpSCPH92S+bRqYoVrpmRDD+ns68vSHF3qG0uaqaKl7b9RoPbXiIyG6RfDbjM3q497B3WEon1lRLoa4P4T+2DkRRWsrFqOf2iWE8v+oQu48VMjyku71DajUpJb9m/Mqru14ltSiVq6Ku4olRT+BicLF3aEon12hSkFLuqv12qJTy9frvCSEeAH61VWCK0hzXj+7DOxuP8OYvh/n4llH2DqfF8ivyWZu2lhUpKzhUcIjenr3535T/MT5ovL1DU7oIa0cfLUBbAru+m89zTFHswt3ZwB2Twnl5TRLbU/MZHe5rs2tZpIWkgiR2ndxFcmEymaWZFFcXU1VTRY2lBjejG24GN9yN7ngYPfB08sTDSfvqadS+d9I7UV1TTVVNFVllWWSWZJKYn8iRoiMARHeP5tlxzzIrYpaamKa0q0b/2oQQ84HrgLCz+hA8gQJbBqYozXXr+DA+3ZrO86sO8u0949t8uGZJdQlLDy3lm8PfkFGaAYCfqx/BHsH0cOuBs8EZndBRYaqgzFxGXkUeacVplFaXUmIqwWwxn7degSDQPZCIbhHMjJjJxKCJRPt0rcl4iuNo6hZkC5AF+AH/rXe8BEiwVVCK0hIuRj0PT+3LY8sT+CEhi1lDerVJvVJKlh9ezlt73qKgsoCRPUZy55A7GdNzjNWdvlJKqmqqKDWVUlxdjKnGhJPeCWe9M/6u/hj1LdslS1HaWlN9CulAOjC2fcJRlNa5angwH21O418/HuTCaH88XVr3YVtmKuOpzU+xLn0dIwJH8O6Ud4nxjWn6xLMIIXAxuOBicFGrmSotdvz4cW666SZOnjyJEII77riDBx54oE2vYe2CeGOEEDuFEKVCiGohRI0QQm17pTgcvU7w/OyBnCyp5L8/JbeqrryKPG5YdQPrj63n0dhH+fiSj1uUEBSlrRgMBv773/+SmJjItm3bePvtt0lMTGzTa1g7o/kttP0ODgOuwG1oW20qisMZFtKdBWNDWbw1jV3phS2qo7CykIVrF5JZmsm7U95lwYAFakkJxe569uzJ8OHDAfD09KR///5kZrbtDoTWJgWklCmAXkpZI6X8GDjvLmmK4ggevSSaXt6uPLB0D0UVpmada6ox8dDGh8goyeDti99mbC/19FRxPGlpaezZs4fRo0e3ab3WjnUrr90TYa8Q4mW0zmerE4qitDcPZwNvXjeMuf/byp+Xx/O/G0ZYfaf/xp432HVyFy9MfIGRPUbaOFKlw1r9OGTva9s6ewyCS19sslhpaSlz5szhtddew8vLq01DsPaD/Ua0PRHuBcrQdlSb06aRKEobGx7Snccv7cfaAyd54xfrlsCIy45j8YHFXNP3GmaGz7RxhIrSfCaTiTlz5nD99ddz1VVXtXn91i6Il177bQXwjzaPQlFsZOGEMBKzinn152T8PZ25bnRIg2XLTeU8uflJgjyCeDT20XaMUumQrLijb2tSShYuXEj//v15+GHbbEPT1OS1fUCD6xFLKQe3eUSK0oaEELw0ZzAFZdU8+e0+LFJyw5g+5y378YGPySzN5JPpn+BmdGvnSBWlaZs3b+bTTz9l0KBBDB06FIDnn3+eGTNmtNk1mmopqPaz0uEZ9TrevX4E93yxmye/3c+JUxU8Mi0ave6PPoac8hwWH1jMJaGXMCJwhB2jVZSGTZgwweb7hlgzeU1ROjxXJz3v3ziCp77bzzsbj7DjaAGvzB1KiK/WInhn7zuYLCYeGN62E4EUpaOxqk9BCFHCH4+RnAAjUCalbNtub0WxIYNex/OzBzE6zJenvt3PlFd+5caxfZg1wokVKSu4rt919Pbsbe8wFcWurO1o9qz7Xmjj+q4AxtgqKEWxFSEEVw4LYnS4D6+uS+bjzUf5POU7nLoL/Gqmc7ygnODurlYNX6001VBcYaKowkRxpfa1qMJEaaUZTxcjfh7OhPi40dvHuvoUxRE0e01eqT3Q+lYI8TTweNuHpCi219PblZevHsL14/xZsO7vUDaCf36XwT/JwMPZQG8fN7xcDHg4G7BISaXJQqW5htJK8+kP/yqzxapr+bg7MTHKjyuHBTEpyv+MvgxFcTTWPj6qPxhWB8QClTaJSFHa0bbcldRQzTfzH8dS1YMdaQUcySnleEE5JVVmsosr0QmBi1GHh7OBQE8XvF2NeLsZ8XY14uWqfa17ebkY8HAxUFJpJq+kipTcUnann+Lngyf5bu8JogI8ePSSaKbFBKrWg+KQrG0pzKr3vRlIQ3uEpCgdlsliYmnSUiYETSCqexQA0T08mzjLOgGeEOHvwehwX64f3Ydqs4W1B7J59edk7vx0F9NiAnlpzmC6uzu1yfUUpa1Y26dwi60DUZT2tjlzM3kVecztO9fm13Iy6Jg1pBeXDuzBR5uP8p+1yVz5zmY+vnkk4f4eNr++0jlUVlYyadIkqqqqMJvNXH311fzjH207n9japbPDhRArhRC5QogcIcR3QojwNo1EUdrZisMr8HXxZULwhHa7pkGv445JESy5YwyllWbmvreN1NzSdru+0rE5Ozuzfv164uPj2bt3L2vWrGHbtm1teg1r1z76AvgS6An0Ar4ClrRpJIrSjvIr8vkt4zdmRczCqGv/Xc9G9OnOsjvHApLrP9xOTonqolOaJoTAw0NrWZpMJkwmU5v3TVmbFNyklJ9KKc21r88AlzaNRFHa0Q+pP2CWZq6MvNJuMUQGeLD41lGcKjfxp093UW3laCala6upqWHo0KEEBAQwdepUuy2dvVoI8TiwFG0S27XAKiGED4CUsqBNo1IUG/sx9UcG+Q0ioluEXeMY0Mub/1wzhHu+2M0r65J5/NJ+do1Hsd5LO17iUMGhNq2zn08//jLqL42W0ev17N27l1OnTjF79mz279/PwIED2ywGa1sKc4E7gQ3ARuAuYB6wC4hrs2gUpR0cLznOwYKDXBJ6ib1DAeCywT2ZP6o37/12hLg0dX+lWKdbt25cdNFFrFmzpk3rtXb0UVhLKhdCTAdeR9uL4UMp5XnXmhVCzAGWAyOllCrJKDb1c/rPAEzpM8XOkfzhycti+C05j7+t2M8P90/AqFd7WDm6pu7obSE3Nxej0Ui3bt2oqKhg3bp1/OUvbRuHtaOPjEKI+4UQy2tf9wohGu2dE0Lo0fZxvhSIAeYLIc7Z9VwI4Qk8AGxvfviK0nzr0tcxwHcAQR5B9g7lNHdnA0/PiiHpZAmLt6TZOxzFQWVlZXHRRRcxePBgRo4cydSpU5k5s20Xs7a2T+FdtEXw3qn9+cbaY7c1cs4oIEVKmQoghFiKNuEt8axy/wReAh6zMhZFabETpSfYl7ePB4c/aO9QzjE1JpCJUX68vSGFeaNC8HBu9io0Sic3ePBg9uzZY9NrWNtGHSmlXCClXF/7ugVoavPaIOB4vZ8zao+dJoQYDvSWUv5odcSK0gp1j46m9plq50jOJYTg0WnRFJab+Pj3o/YOR+mirE0KNUKI08M0aieu1bTmwkIIHfAK8IgVZe8QQsQJIeJyc3Nbc1mli/st4zciu0US4tXwtpz2NKR3N6b0D+T9TakUlZvsHY7SBVmbFB4DNgghNgohNgLrafrDPBOovzh9cO2xOp7AQGCjECINbSnu74UQsWdXJKXATYezAAAgAElEQVR8X0oZK6WM9ff3tzJkRTlTmamMXTm7mBg80d6hNOrhqX0pqTTziepbUOzA2qSwGXgPsAAFtd9vbeKcnUCUECJMCOGENoT1+7o3pZRFUko/KWWolDIU2AZcrkYfKbayLWsbZouZiUGOnRRienlxQV9/Ptueria0OSBbb4fZWq2Nz9qk8H9AGFqn8JtAOPBpE4GZgXuBtcBB4Esp5QEhxLNCiMtbHrKitMymjE24G90ZGjDU3qE06ebxoeSWVLF6f5a9Q1HqcXFxIT8/32ETg5SS/Px8XFxavuCEtcMbBkop6w8n3SCEOHsU0TmklKuAVWcd+3sDZS+0MhZFaTYpJZsyNzGu1zi7rHXUXBdE+RPu587Hm9O4YqjjDJ3t6oKDg8nIyMCR+zZdXFwIDg5u8fnWJoXdQogxUsptAEKI0aiZzEoHcvjUYXLKc5gQ1H4roraGTidYMC6Up78/QPzxUwzp3c3eISmA0WgkLKxFc3k7DGsfH40Atggh0mo7hbcCI4UQ+4QQCTaLTlHayJbMLQCM7zXezpFY76rhQTgbdHy163jThRWljVjbUphu0ygUxcZ2ntxJqFcoge6B9g7Fap4uRi4Z0IOV8Vk8NTMGZ4Pe3iEpXYBVLQUpZXpjL1sHqSitYbaY2XVyFyN7NDXf0vHMGRFMUYWJ9Qdz7B2K0kWoVbeUTu9g/kHKTGWM6jHK3qE024RIPwI8nfl6d4a9Q1G6CJUUlE5vR/YOAGJ7nDMv0uHpdYLZw4LYmJRLQVm1vcNRugCVFJROb2f2TiK8I/Bz9bN3KC0ya0gvzBbJusRse4eidAEqKSidmsliYnfO7g7Zn1BnQC8vgru7snq/SgqK7amkoHRqB/IOUGGuYFTPjtefUEcIwaUDe7A5JY+iCrVInmJbKikondrp/oTAjtefUN/0gT0x1UjWHzpp71CUTk4lBcXxWSyw9wtYch18cycc32H1qTuzd9K3e1+6u3S3YYC2N6x3NwK9nFm9Tz1CUmxLJQXFsVks8M3t8O1dkJMIh3+CRdNgxwdNnlpjqSEhN4FhAcPaIVDb0ukElwzowW+Hc6k0tWorE0VplEoKimPb9jbsXw6Tn4T798CD+6DvdFj1GBz+udFTU06lUG4uZ4j/kHYK1rYm9wug0mRha2q+vUNROjGVFBTHlZsEvzwL/WbCxEdBCHD2gKsXQeBA+OY2KGv4AzI+Nx6Aof6Ov1S2NcaE++Ji1LHxkJrdrNiOSgqK4/r1JdA7wazXtYRQx8kd5nwAlcWw/p8Nnp6Qm0B35+4Ee7Z8GWFH4mLUMz7Cjw1JuQ67nr/S8amkoDim3GTY/w2Muh3czzPpLKA/jL4Tdn0CJ8+/tUdCXgJD/Icg6ieUDu6ifgEcKyjnSG6ZvUNROimVFBTHtP1/YHCGsfc2XGbSY2B0g99fOeetoqoijhYdZbD/YBsG2f4ujNb2KN+YpB4hKbahkoLieEwVsG85xFxx/lZCHTcfGHkr7P8a8o+c8da+vH0AnS4pBHd3o2+gBxtUUlBsRCUFxfEc/AGqimDYDU2XHXsfCD3s/PCMw/G58eiEjoF+A20UpP1MivJnZ1qhGpqq2IRKCorjif8CuoVAHyu2zvQMhJjLYe/nUF1++nBCbgKR3SJxN7rbMFD7GB/pR7XZwq70QnuHonRCKikojqWiEI7+BgNmg87KP8/YW6GyCA6sAMAiLezL3ddp5iecbVSYDwad4PeUPOtOKD4Bv/5bm9ux/2uwqBaG0jBrt+NUlPaRvBYsZuh/ufXn9BkPftEQ9xEMu56jRUcpMZV0uv6EOu7OBoaHdGezNUkh8Tv47j6oKgYnD9jxPoR+DPO+ABcv2werdDiqpaA4loMrwbMn9Bpu/TlCaK2FzDjI3kdCbgLQ+TqZ6xsX6cu+zCKKyhtZNTX5J/jqFvCLgvt2wePH4PI34dhWWH4rqLkOynmopKA4DnMVHFkP0TOsf3RUZ/Bc0BkhYRnxufF4OXkR6hVqkzAdwYRIP6SErakNtBYK02H5LRA4AG76FnwjtP+mw2+C6S9Cyjqt1aAoZ1FJQXEcx7eDqRwipzT/XDcfiJoG+5YTnxvPIP9B6ETn/fMe0rsb7k56NqecZ5kPKeH72vkd8z4HZ88z3x95G0RO1ZYQKbOyX0LpMjrv/zVKx3NkPegMEGrFqKPzGTyX0tJsjpw60mk7mesY9TpGh/uev19h/9daZ/3UZ7VRXGcTAi75l5aAN79m+2CVDkUlBcVxHNkAwSNb3gHadzr7PLojkQzx69xJAbShqal5ZWSeqvjjoLkKfvkHBA6CEbc0fLJ/NAyaqy1B3siigkrXo5KC4hjK8iErHiImt7wOowsJwdpktYHeEW0UmOMaF+ELwLYj9T7Udy2GU8dg2rNN98uMfwDMlbD3MxtGqXQ0KikojuHoRkBC+EWtqibezZ2I6mq80n5vk7AcWXSgJ93djH/sr1Bjgi1vQO8x1iXXwBhtOO/ORdpmRoqCSgqKoziyAVy8oVfLd0mTUpJQmsFgiwESvmzD4ByTTicYE+7L1rqWwv6voeg4THjI+kpGLoRT6ZC63jZBKh2OSgqKYzj6G4ROBH3L51MeKzlGUXURgwOHQcovUF7QhgE6prERvmSequB4fin8/hoExGijsKzVbyY4e2sLECoKNk4KQojpQogkIUSKEOLx87z/sBAiUQiRIIT4RQjRx5bxKA6qKFO7W+0zvlXV1O20NiRmHlhMcPD7tojOoY0N1/oVjm5bCbkHtX6C5szxMDhra0cdXKmtTqt0eTZLCkIIPfA2cCkQA8wXQsScVWwPECulHAwsB162VTyKAzu2VfvaZ1yrqknITcDd6E54xHTwjeoSd7+RAR74eTjT/eCn4O4PA65qfiWDroHqUkha3fYBKh2OLVsKo4AUKWWqlLIaWApcUb+AlHKDlLJuacttQOfYN1FpnvQt4OQJPQa1qpr43HgG+Q1CrzfAoKsh7XdtMbhOTAjBpb1NxJRuRQ67EQxOza8kdAK4B2itBaXLs2VSCAKO1/s5o/ZYQxYC571VEULcIYSIE0LE5ebmtmGIikNI3wIho0Gnb3EV5aZykguT/1jvaODVgDy9cmpnNle3HiElGeHXtqwCnR6ip0PKz2CubtvglA7HITqahRA3ALHAv8/3vpTyfSllrJQy1t/fv32DU2yrvEB7Ft7KR0cH8g9gkZY/ZjL7RULPobDvqzYI0oHVmOif9S0bLEPZlOvW8nqiZ2grqaZ3/qG8SuNsmRQygd71fg6uPXYGIcQU4G/A5VLKKhvGo9iQqcbE0aKjFFUVNe/Euv6EkNYlhbpO5sF+9VZGHXQ1nNhzzladncqhHzGU5/Cj86V/zFdoifALweAKh1a1VWRKB2XLpLATiBJChAkhnIB5wBnDQYQQw4D30BKC2nS2g/oq+SsmfzWZy7+9nAuWXcAzW56h3FTe9ImgPTrSO0NQM5bKPo+E3AT6ePWhm0u3Pw4OuAoQnbvDOe4j8A5BRlzM1iP5yJYuh2101Sa8Ja1WS2p3cTZLClJKM3AvsBY4CHwppTwghHhWCFG3g8q/AQ/gKyHEXiFE5x9D2IlIKXlt12s8u/VZortH868J/2Jev3msSFnB3b/cjammkbX+66Rv0dY7Mji3Ko6E3IRzF8HzDtKGue77qnN+0OWlwNFfYcQCxkQGkFdaxZHc0pbX128GFGdAdkLbxah0ODbdeU1KuQpYddaxv9f7vgVrJCuO4qvkr1i0fxHX9L2Gv43+G3qdnssjLmeg30Ce2PQEb+x5g0diH2m4gqoSbb2jiQ+3Ko7M0kzyK/PPfHRUZ9DV8MOD2gddz062SF7cR9qqssNvYmyVBwBbj+QTGeDZxIkNiLpE+5r8U+f7b6VYzSE6mpWOJ7kwmRd3vMj4XuN5csyT6OuNHJoZPpNro6/lkwOfsDdnb8OVHN8BsgZCxrYqlkZ3Wou5Qvvg7GyPkEwVsPdz6D8LPALo7eNKUDfX1vUrePhrO94d/qnt4lQ6HJUUlGaTUvKvbf/Cw+jBCxNfOO9mNg+PeBg/Vz9e2fVKw8+5j20FoYPeo1oVT3xuPK4GV6K6R537ppsPRFwM+7/pXIu+HVgBlacgdiGgzVcYE+7LttQCLJZWPCqLmgYZO9Vy2l2YSgpKs/2Q+gO7c3bzwPAH6O7S/bxl3Ixu3DXkLvbk7GFT5qbzV5S+FXoMPndnsGbam7uXQX6DMOgaeBo66BrtWfnxba26jkPZuQj8+p6xIdHYCF8KyqpJzilpeb1R0wCpbXikdEkqKSjNUm4q55VdrzDIbxCzo2Y3WvaqqKvo4d6DxQcWn/umuQoy41o9P6HcVE5SQVLjO61FX6oNt+wsj5BO7NX+28Uu1HZRqzUm3Afgj1VTW6LXMHDza/YjpEpTDaVV5pZfV3EYKikozbLk0BLyKvL4y6i/NLkHskFn4Lp+17EjeweHCg6d+eaJvdoGL63sTziQf4AaWcPQgKENF3L20BLDgRXangMdXdwiMLrBkHlnHA7u7kZvH9fWJQWdTtsjO+VnsNQ0WTyjsJzbFscx4Om1DHx6LTPf3MS21vRrKHankoJitXJTOZ8c+ITxQeOt3gN5Tt85uBpcWXJoyZlvHNuifW1lUqjryG4ynsFzoaKg43eiVpzSWjyDrgbXbue8PTbcl+1HW9uvMFX7b5W5u9Fi+zOLuPLtzWxPzee2CWE8Oq0vxRVm5r2/jf/92oknDHZyKikoVluatJRTVae4a8hdVp/j5eTFtD7TWJu2lgpzvaWZ07dqK5l6tG7Zkr25ewn3Dsfb2bvxgpFTwaOHtl1lRxa/FEzlpzuYzzY2wpeiChOJWcUtv0bEZG0AQCMJNLekioWLd+Js0LPinnE8MaM/906OYu2Dk5g1pBcvrj7ER78fbXkMit2opKBYpdxUzif7P2F8L+tbCXUuj7icMlMZG45t0A5YLFqnb5/WtRIs0kJ8bnzjj47q6A0w7HpIWaft39ARSak9OgoaAb3O/zuPDfcDaN0jHDcfCB7VYFKQUvLwl3spqjDxwU2xZ8yLcHXS8+rcIUwf0IPnfkxs3aMsxS5UUlCssixpGYVVhfxpyJ+afW5sj1h6uffi+yO1E9ZzEqGyqNXrHaUVp1FUVcRQfyuSAsCwG0FatPH9HVHaJshLhpG3NVikh7cLYX7urf8wjpoKWXuh5OQ5b63en82mw3k8cWl/Ynp5nfO+Qa/jP3OHEObnzgNL91BU0Qn6cboQlRSUJlWaK1l8YDFje4617q78LDqhY2bETLZmbSWnPKfepjqtaynE59TutGZty8UnDMIugN2fdsw5C9vfA9fuMKDxUV9jwn3ZcbQAc00rfse6LT1Tfj7jcKWphud+SCSmpxc3jGl4o0QPZwOvXjuUvNIqXlx9qMFyiuNRSUFp0oqUFeRX5nP74NtbXMflEZdjkRZWpa7S1jvy7AXdWrf76t7cvXg5eRHqHWr9ScNvgqJjcHRjq67d7vKPwKEftb4Eo2ujRcdG+FJSZebAiVb0K/QYpPXBnPUIadnO45woquTJy/qj14kGTtYMDu7GbRPDWbLjmBqR1IGopKA0ymQx8fH+jxnqP5TYwNgW19PHqw8DfAewOm211lLoM/aMMfYtsTdnL0P8hzQ5NPYM/WeBq482+asj2fYO6I0w6o4mi56er9CaD2IhtEdIRzacHsZbZa7h3Y1HGBXqw9gIX6uqeWhKX3r7uPLUt/tb13JR2o1KCkqjfkz9kayyLG4ffDuilR/il4ZdSmJ+IukVua0eilpQWUBqUSrDAoY170SDM8Teot11F6S2KoZ2U5YPez7XhtV6BjZZPMDThcgAjzboV5gGVUXaGlXAyvgssosruXdypNV/C65Oev42I4bDOaUs2Xm86RMUu1NJQWlQjaWGRfsW0c+nHxODJra6vktCtVU413i4aUtat8LO7J0AjOwxsvknj7xdWyRv+3utiqHdxC0CcwWMvdfqU8aG+7IzrQBTa+7Owy/U/jvVPkL6dFs6Ef7uTIzya1Y1lwwIZHSYD6+uS1adzh2ASgpKg34+9jNpxWncNui2VrcSAHq492C4zoM1nl4Q0L9Vde3M3omrwZUBfgOaf7JXTxh4Fez5TBsF5ciqy2HH+9pdezP+m42N8KW8uoaEjFb8fi5eWovu8Dr2ZRQRf/wUN47p0+y/BSEET82MobC8mnc2pLQ8HqVdqKSgnJeUkg8SPiDUK5QpIW207YXFwvRT+aQYdBw+1boPhx3ZOxgeOByjztiyCsbcDdWl2p4EjizuIyjLhQkPNeu0MeHaM/9Wd/BGTYOcA6z8bQeuRj1XjQhuUTUDg7yZMzyYjzencSzfyl35FLtQSUE5r43HN5JUmMTCQQvP2CuhVU7uZ2phLjoEa9LWtLia3PJcjhYdZVSPViy53WuotsbPljehqhW7ldlSdRn8/iqEX9TshQN93J3o18OzbfoVgMpDa7hyWC+8XFqYhIHHLonGoBc8v+pg62JSbEolBeUcNZYa3tjzBn28+jAzfGbbVZy6AT+LhVH+Q1lzdE2L9xOu609oVVIAuOBxKM+HnR+2rh5b2fEBlOfBRX9t0eljwn2JSy+gytz0wnYN8o+mxKUnE+SeRuclWCPQy4W7LohgzYFsthzJa1Vdiu2opKCcY9XRVaScSuHeofc2vEdBS6RuBP9+XBp1JcdKjpFYkNiianZk78DD6EE/n36ti6f3yNrWwhuO11ooL9BaCZFTW7wJ0YRIPypNFnYcLWhxGBJYbx7KRMMBBgS4tLieOrdPCie4uyvPrkxUQ1QdlEoKyhmqa6p5Z+879PPpx7TQaW1XsalSWwQv/CIuDrkYgzCw5mjzHyFJKdmWtY3YwNi2SVgXPqG1Fja/3vq62tKG56GqGKY+2+IqJkT54WrU89OBc5eqsNaWI/l8Vz4AV1mpTTpsJRejnr/N6M+h7BKWqiGqDkklBUX7wD6+Aw6u5P82PUNGaQYPDn+weZPCmnL0N21YZeTFeDt7My5oHGvS1mCRzbtbPFp0lMzSTCYGt36ILADBsdrObFvegML0tqmztXIOah3MsQshMKbF1bgY9VzQ1591iSdbvJT2p1vTOeg8BKl3hsPrWhxLfdMH9mBMuA///SmJonI1RNXRqKTQlWXEwVc3w4shsGgq2csX8P7R75hcVs74n1+CY9vb7lqHfgAnTwibBMD00Olkl2UTnxvfrGrqtvZsi3kTp035h7ZU9Lqn2q7OlrJY4MdHtS1KW9iXUN+0AYFkF1eSkNn8oanZRZWsO3iSy0dGIUIntNleFEIInp41gKIKE6+sS9JmTBcchZxD2mMzxa5UUuiKCo7C0uvhw4u15/wjFsC8L/j3yNlYDM48FjUfcpPgo2mw5gkwV7fuehYLJK+ByIu1GcXARb0vwlnvzOqjq5tV1W8ZvxHZLZKeHj1bF1N93kHakM/E7yCp5aOi2kTcIkj/Hab9U1vCupUm9wtArxP8dCC72ed+seMYFim5bnQI9J0O+YfhZMv6gc7Wv6cXjw8qZXTcQ9S8EAJvDIV3RsPLYfD6UPjlWW29J6XdqaTQlUipPZZ4dzyk/goXPQkP7ocZ/2a1s46fTu7g9sF3Ejz1Obh/N4y6U1tz54u52vDIlsqMg9KT0O+PkUweTh5MCp7E2rS1mC3W7e1bVFXE7pO7mRQ8qeWxNGT8AxA4EFbeb7+71cI0WPc0RFysLfPdBrq5OTE6zIe1B7KbNdqrylzDF9uPcVF0AH183bWVWYUeEpa2PqjKIvj2bu5IvoNx+oP8yCRMl70BV3+k9aH4Rmid7G+OgG/u0G5ilHajkkJXUZQJn82BHx7SRt3cvRUueAycPcguy+af2/7JYP/BLBxUu6OXkzvMeBmueAeO/gqfz9X6Hloi4UvQO0PfMzuup4dOp6CygLiTcVZVs/7YeszSzLQ+bdgBXsfgDLP/pyWEHx7SEmh7MlXCV7eATg+Xv9HqxQLrmzGoJ0dyy5q1auqqfVnklVaxYFyodsDDX1sgL+Erq/ZubtCp4/DhVG0HuYmPkDh3M/eX3sTz2bEwcI6WnG/4Gh5KhPH3a623t0fBxhfBXNXy6ypWU0mhs5MS4pfBO2O11Uln/AduWAHdegPaaKM///ZnzBYzL0x44dwRPcOuh9nvaY80VtzZ/H0IzNWw/2vodxm4nLll5sTgibgZ3KwehbQmbQ3BHsHE+La887VRPQZpz/ETv9UmtbWn1X+GE7u1xOTdslnDDZk1uBdOBh3Ld2VYfc4nW9IJ93dnYmS9dY4GXwslJ7SVU1si5xB8OAVKsuDGFXDx3xkX04ebx4Xy8eY0Vu3L+qOsV0+t1XD/Xm1l240vwLvjtAELik2ppNCZlWTD0utgxR3aKJY//Q6jbged9s8upeTpLU+zJ2cPz457lhCvkPPXM3guTP2n9mHZ3M7YlHXaJvBD5p/zlqvBlYtCLuKntJ8oNzW+9EFBZQHbs7YzPWx6m6zD1KAJD0HMFfDz02022qZJW9+B3YthwsNa8mxj3m5GpsYE8u3eTKsmsu0+Vkj88VMsGBuKrv6eCf0uA/cA2NGChQQL0+HTKwEJt66B8AtOv/XXGf0Z2rsbf16eQEpOyZnnefXUHivd8DVYzLB4FnxzJ5TmNj8GxSoqKXRGda2Dt0fDkfUw7Tm4+UftWe3pIpL/xv2XH1J/4L5h9zE9bHrjdY67T1vLf+tbEPex9bHs+EDbrCVi8nnfvjb6WkpMJaw8srLRar5N+ZYaWcOMsBnWX7slhIAr34WAAfDlTZD2u22vt/tTWPuEdjc8+UmbXWZubG9OlZv4MSGrybJvr0/B29XInLPXOTI4w8iF2iik5nQCl+ZoCcFUrrUQAs9cxNDJoOOd64fjYtRx46IdZBSe5wYhcgrcvQ0mPaa1PN8aof0ddsQd9BycSgqdTVaCdje14g7wj9ZaB+Pu055V1zJbzDyz9RkWJy5mXvQ8bh9kxY5qQsAlL2gzbH98xLpHCFkJkLoBRt8J+vNPNBvqP5QBvgP4/NDnDc5ZqLHUsOzQMmIDY4nqHtX0dVvLyR1u/Aa8e8Pn12id8raw4wOtYzviYpiz6Ix/o7Y2KcqPvoEevP9baqMdzvsyivjlUA63TQjDw/k8/2YjbgG9E2x6xboLVxZpfVnFWXDdV+ckhDq9urnyf7eOpqzKzPUfbifzVMW5hYyuWuK8azP0GAw/PKiNkDu2zbpYFKuopNBZ5CbBij/Be5Pg5AG47L9wy2rwO/NDNLM0k4VrF/LN4W+4c/Cd/HX0X61/HKM3aE15/2j4coF2zcb8/go4eUDsrQ0WEUJwY8yNHC06yk9p5x8Hv/H4Rk6UnWB+v3MfQdmMRwAsWAndQuDT2bD9/bbrfDZXw+rHYdWj2lDPaz87PVTXVoQQ3D4xnEPZJWxIyjlvGSklL6w+iLerkQXjQ89fkWeg1mKM/0KbZNeY6nJYch3kJGq/Y8joRovH9PLik1tHUVBazRVv/c6u9MLzF/SP1v5tZr+nPZb66BIteWdYN2BBaZxNk4IQYroQIkkIkSKEePw87zsLIZbVvr9dCBFqy3g6HXM1JK2GJfO1ERoHvoWx92jDSUfedsadZ7mpnA/3fcjV319NcmEyL0x8gXuH3dv85/MuXnDdMjA4aUNVyxpYhTN1IxxYoS1R7dqt0Sqnh06nb/e+vLb7NaprzpwTYbKYeH3P6/Tx6sPkkPM/grIZz0BY+JO2Uujqx7S5HUWZraszex98MBm2vwuj79I+LJ3c2ibeJlwxNIhQXzee++HgefsWViZkseVIPo9eEt34aqgTH9EmIq56rOGRSKZKrT8rfbP24R1l3fLrw0O6s+Ke8Xg4G5j3/lb++1MSlabzXEMIGDIPHtgLFz8Nx7dr824+mAx7l0BVybnnKFYRLV2pssmKhdADycBUIAPYCcyXUibWK3M3MFhK+SchxDxgtpTy2sbqjY2NlXFxXfiOoOSkNgIjdYOWECoKwM1Pe9Y76g5w/2O0iEVaSCpI4sfUH1mZupKCygIuDL6Qv4z6C8GerRzhcnwnfHIZ9BioPRZwr7dnb8Up+OAi7c767q1NbjQPsCVzC3f+fCc3D7iZR2IfOX188YHF/CfuP7w5+U0u7H1h62JuKYtF60vZ8LyWaEfdriU7jwDr68hNhk3/hYRl4O6vDTuNvtR2MTdgY1ION3+8k/snR/LwtOjTx4/mlTH7nc2E+Lix4u7x6HVN3Czs+Qy+u0dbafaiJ858r7JIa0mmboQr34Gh1zU7zlPl1Ty7MpFv9mQS1M2VhRPCuCY2GM+GklVlMcQv0TYkyk/RhkBHTtGG0fYZr7WYbTlAoQMQQuySUja50botk8JY4Bkp5SW1Pz8BIKV8oV6ZtbVltgohDEA24C8bCarTJgVLjTZBrO5VngfFJ7The0WZkHsQsvdDWW3T36UbRF5M9cA5FAePoKSmglNVpzhecpz04nSOnDpC3Mk4iqqKMAgDF/S+gAUDFjR/T+PGHFoFy28Bzx7aUNfIKdoErK9vg6y9WhO/GfsAPLftOZYlLeOpMU9xTd9r+DXjVx7a+BDjeo3jrclv2XbUkTUKjsIv/9BaZDqDNkM7egYEj9Q+dPT1PrCqSiEvSeuoPrQKjm8Dg4uWuCc81CazlVvq4S/38s3uTJ6ZFcNNY0NJzSvltsVxFFWY+O6eCYT4WtFykVJ7XJmwVPt9LnwCdEY48gus/gucSodZb2hDmlthc0oer65LJi69ECe9jnGRvowO86V/T0+iAj3x83DC2VCvL8Zi0VoNid/Bwe+huLZl59od/Ptrj558I7W/WY9A7eXaDYxu2s2LTo+UEim1FWKllLVfQSJPP0Fs72ksdYx6gUHfsgc8jpAUrgamSylvq/35RmC0lPLeemX215bJqP35SG2ZBhdbb2lSWPHzY3xybC11v63kzN9b1sxWV8cAAAcuSURBVL5o8Ks8o+zZX88+dvZVGvpav/4GywqhzSYVOu2PVuhBp6e6pppqy7lLUOiEjmCPYIYFDGN0z9GM6zUOX1ffc8q1ieM7tPkLBalgdAdTmfb1qve0ETXNYKoxcc8v97A1ayteTl4UVxfT36c/H0z7AG9n76YraC95KbDrYy05FNcb++/qoyUGc+WZ23wGxGiPOobMb17rwkYqTTXc/flu1h/KwdPFQGmVGW9XI4sWxDKiTzOSVY1JG3Swe7H2by50UF0C3cO0FkIzNwZqzN7jp/gh/gS/HMrhaN6Zs+s9nQ24OOlx0usw6AV6ncBikdRYLPQ0n2Cw5QAxlsOEygwiOI43Dc/Or5RGKnDGhAELovalQ0px5s8IJO1/k5I97AEmzr6zRed2qqQghLgDuAMgJCRkRHp681ez3LD1P/xw5DtAnP6nrPtOaBf54/v6ZRo4fvpIvffFeY5R/2rirOueLqfTPkz0RoTeCDojwuACTu4IJ3cwuNQr+0cERp0RTyfP0y9vZ2+CPYIJ8gjCqG/5DlnNZq6G/cshK1678xp8rbaeUEuqsphZeWQl8bnxRHWPYk7UHFwMrV/H3yak1IZmZsZpHZ6lJ7Wx9Hon8OoFPuEQMka7K3UwFovkx31ZbEvNp4eXC/NGheDv2YLObim1Ge+HVoGsgd6jIeZKrc/JRorKTRzMLuZoXhl5JVXkl1VTZa6h2iwxWyyYLRK9EBh0Ap3urK+AuyzBu6YQT3MBnqY8XGpKMVoqcaqpwCCrMNZUoKcGIWVtGpDo5B8pQTtuj5QA+tgFhI5u3s1WHUdICurxkaIoioOwNinYcvTRTiBKCBEmhHAC5vH/7d1NiFVlAMbx/5NpxWS4SMIayRCJQCrLXGS0CAozKYlcRJ8gbcowosI2QUEQFNGmFpIu+iCpLDCTTHAgjMrSNBvtw0pICYzEUiTDfFqcw2ESuk3jnHuae54fDJ57verzIjPPPe89531hzQmvWQPcVR7fAmzsVAgREVGvUdxr8e9sH5O0BFgPjANW2h6U9ATwme01wArgZUm7gQMUxREREQ2prRQAbK8D1p3w3GNDjn8HFtWZISIihi93NEdERCWlEBERlZRCRERUUgoREVFJKURERKW2m9fqIuln4L/f0lw4G/jHJTR6VMbcDhlzO5zMmM+3PfnfXjTmSuFkSPpsOHf09ZKMuR0y5nboxpgzfRQREZWUQkREVNpWCsubDtCAjLkdMuZ2qH3MrfpMISIiOmvbmUJERHTQmlKQNE/S15J2S1rWdJ66SVopaX+5kVErSJoqaUDSTkmDkpY2nalukk6XtFnS9nLMjzedqRskjZP0uaS1TWfpBkl7JO2QtE1SrRvKtGL6SNI44BvgWmAvxV4Pt9re2WiwGkm6GjgMvGR7ZtN5ukHSFGCK7a2SJgJbgIU9/v8soM/2YUnjgU3AUtsfNxytVpIeBGYDZ9le0HSeuknaA8zutFXxaGnLmcIcYLft723/AawCbmo4U61sf0CxR0Vr2P7J9tby+BCwCxjZvqBjhAuHy4fjy6+efqcnqR+4AXix6Sy9qC2lcB7w45DHe+nxHxZtJ2kaMAv4pNkk9SunUrYB+4ENtnt9zM8BjwDHmw7SRQbel7Sl3LO+Nm0phWgRSWcCq4EHbP/WdJ662f7T9qVAPzBHUs9OF0paAOy3vaXpLF12le3LgOuB+8rp4Vq0pRT2AVOHPO4vn4seU86rrwZetf1W03m6yfZBYACY13SWGs0Fbizn2FcB10h6pdlI9bO9r/x1P/A2xZR4LdpSCp8CMyRdIGkCxV7QaxrOFKOs/NB1BbDL9rNN5+kGSZMlTSqPz6C4mOKrZlPVx/ajtvttT6P4Pt5o+/aGY9VKUl954QSS+oDrgNquKmxFKdg+BiwB1lN8+Pi67cFmU9VL0mvAR8CFkvZKWtx0pi6YC9xB8e5xW/k1v+lQNZsCDEj6guLNzwbbrbhMs0XOATZJ2g5sBt61/V5d/1grLkmNiIjhacWZQkREDE9KISIiKimFiIiopBQiIqKSUoiIiEpKIaIDSZMk3VsenyvpzaYzRdQpl6RGdFCuobS2LSvNRpzadICI/7mngOnlgnPfAhfZninpbmAh0AfMAJ4BJlDcPHcUmG/7gKTpwPPAZOAIcI/tnr3jOMa+TB9FdLYM+K5ccO7hE35vJnAzcAXwJHDE9iyKO8nvLF+zHLjf9uXAQ8ALXUkdMUI5U4gYuYFy34ZDkn4F3imf3wFcXK7WeiXwRrEsEwCndT9mxPClFCJG7uiQ4+NDHh+n+N46BThYnmVEjAmZPoro7BAwcSR/sNzL4QdJi6BYxVXSJaMZLmK0pRQiOrD9C/ChpC+Bp0fwV9wGLC5XuBykx7eBjbEvl6RGREQlZwoREVFJKURERCWlEBERlZRCRERUUgoREVFJKURERCWlEBERlZRCRERU/gI1nIkjDDcmJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_population(opt_dynamics)"
   ]
  }
 ],
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