{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Find frequencies that make only $(\\hat{a}^2\\hat{b}^2\\hat{e}^{2}+\\hat{a}\\hat{b}\\hat{d}\\hat{e}^{\\dagger3})\\hat{c}^\\dagger +h.c.$ resonant in the 7th order expansion of $\\sin(\\hat{a}+\\hat{b}+\\hat{c}+\\hat{d}-\\hat{e}+h.c.)+\\sin(\\hat{a}+\\hat{b}+\\hat{c}-\\hat{d}+\\hat{e}+h.c.)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Proceed as in the 5th order example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import hamnonlineng as hnle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "letters = 'abcde'\n",
    "resonant = [hnle.Monomial(1, 'aabbeeC'), hnle.Monomial(1,'abdEEEC')]\n",
    "abc_sum = hnle.operator_sum('abc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "abc_pd_me = abc_sum + hnle.Monomial(1,'d') - hnle.Monomial(1,'e')\n",
    "abc_md_pe = abc_sum - hnle.Monomial(1,'d') + hnle.Monomial(1,'e')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of off-resonant constraints: 3182\n"
     ]
    }
   ],
   "source": [
    "sine_exp = (\n",
    "            hnle.sin_terms(abc_pd_me, 3)\n",
    "           +hnle.sin_terms(abc_pd_me, 5)\n",
    "           +hnle.sin_terms(abc_pd_me, 7)\n",
    "           +hnle.sin_terms(abc_md_pe, 3)\n",
    "           +hnle.sin_terms(abc_md_pe, 5)\n",
    "           +hnle.sin_terms(abc_md_pe, 7)\n",
    "           )\n",
    "off_resonant = hnle.drop_single_mode(\n",
    "                 hnle.drop_definitely_offresonant(\n",
    "                   hnle.drop_matching(sine_exp.m, resonant)))\n",
    "off_resonant = list(off_resonant)\n",
    "print('Number of off-resonant constraints: %d'%len(off_resonant))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try to solve (takes around a minute):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 16, 44, 42, 5]\n",
      "[16, 1, 44, 42, 5]\n",
      "2 solutions.\n"
     ]
    }
   ],
   "source": [
    "res = hnle.head_and_count(\n",
    "        hnle.solve_constraints_gecode(resonant, off_resonant, letters, maxfreq=44))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve it again, but now with linear programming methods and continuous values for the frequencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding resonant constraints...\n",
      "Adding off-resonant constraints...\n",
      "Adding distinct constraints...\n",
      "Dumping LP file...\n",
      "Solving...\n",
      "Status: 1 - Optimal\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[1.0, 16.0, 44.0, 42.0, 5.0]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hnle.solve_linearprog_pulp(resonant, off_resonant, letters, maxfreq=50, detune=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the detuning of all off-resonant terms and plot a histogram (x: detuning, y: number of terms with that detuning)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dets = hnle.detuning_of_monomial(res[0], off_resonant, letters)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vZ4z7tXlb3zS3NW/rm+a2Zn1909zWvK1vOKkaaGD9wgWTS4B/Bn4d+A/gm8D7quqxsbRM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\njTPIJalx/w/kD+7HoFbweAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f79913046d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(dets, bins=50, range=(0,50));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pmNUI+2X9j3rVq/74Jeueeup/J16MNNtGTfOc7EVfalsmfbRP8tvA7qq6pHu+E3i+qj4y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7990a3f690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(dets, bins=50, range=(0,400));"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}