Come_CATTIN_Projet.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "28eb4369",
   "metadata": {},
   "source": [
    "# Modélisation d'un système de Lennard-Jones en deux dimensions, calcul de diagramme de phase"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a0d3cd4",
   "metadata": {},
   "source": [
    "Côme Cattin, M1 SdM ENS Lyon, 2022"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0406838f",
   "metadata": {},
   "source": [
    "Code diponible sur GitHub : https://github.com/sequoia-dev/Phase_Diagram_LJ"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d780fd7c",
   "metadata": {},
   "source": [
    "## Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd28ea8e",
   "metadata": {},
   "source": [
    "Le but de ce projet est de modeliser un système de Lennard-Jones en deux dimensions à différentes températures et densités afin d'obtenir son diagramme de phase. Nous nous sommes basés principalement sur les routines déjà existantes et fournies en cours ansi qu'en TD"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea0fb95b",
   "metadata": {},
   "source": [
    "## Le système"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e385f42",
   "metadata": {},
   "source": [
    "Le système que nous allons modélisé est un système de Lennard-Jones : les particules le composant sont régies par le potentiel de Lennard-Jones :"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bda7d5ab",
   "metadata": {},
   "source": [
    "\\begin{equation}\n",
    "U_{LJ}(r) = 4\\epsilon \\left(\\left(\\frac\\sigma{r}\\right)^{12} - \\left(\\frac\\sigma{r}\\right)^6 \\right)\n",
    "\\end{equation}\n",
    "\n",
    "où $\\epsilon = 1$, $\\sigma = 1$ et $r$ est la distance entre deux particules du système."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3c49a2f",
   "metadata": {},
   "source": [
    "Nos modelisations porteront, sauf mention contraire, sur un système à 16 particules, en deux dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0f5b9f6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Dimension\n",
    "d=2\n",
    "#Number of particles\n",
    "NParticles=16\n",
    "\n",
    "# Lennard-Jones\n",
    "sigma = 1\n",
    "epsilon = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10595b1c",
   "metadata": {},
   "source": [
    "Aussi notre étude est restreinte à une zone particulière du diagramme de phase :\n",
    "\n",
    "\\begin{equation}\n",
    "kT \\in [0.3;1]\\\\\n",
    "\\rho \\in [0.05;0.8]\n",
    "\\end{equation}\n",
    "\n",
    "avec $k$ la constante de Boltzmann, $T$ la température et $\\rho$ la densité."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46489fc0",
   "metadata": {},
   "source": [
    "## Implémentation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "054a8f1a",
   "metadata": {},
   "source": [
    "Un certains nombre de bibliothèques sont nécessaire à notre étude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3f1ac00d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import standard libraries\n",
    "import numpy as np\n",
    "from scipy.special import gamma\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation, cm, colors, rc\n",
    "import random\n",
    "import time\n",
    "from imp import reload\n",
    "rc('animation', html='html5')\n",
    "\n",
    "# Import library of our own functions\n",
    "import MPCMolecularDynamics as MD\n",
    "reload(MD)\n",
    "\n",
    "#Include plots into notebook instead of plotting them in extra window\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "132abb32",
   "metadata": {},
   "source": [
    "Afin d'établir quantitativement la phase du système, nous avons tout d'abbord décidé de mesurer la compressibilité du système pour chaque zone du diagramme de phase. Nous utilisons pour cela la fonction `Generate_LJ_NVT_MolecularDynamics_Trajectory`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "661d9b45",
   "metadata": {},
   "source": [
    "**L'entièreté des codes suivants est diponible dans les fichiers `multi_processing.py`et `projet.py`**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79122482",
   "metadata": {},
   "source": [
    "## Compressibilité"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61022213",
   "metadata": {},
   "source": [
    "### Première version, non optimisée"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "901ae264",
   "metadata": {},
   "source": [
    "Une première approche, non pas la plus efficace, est d'estimer la compressibilité à chaque paramètre du système et cela tour à tour, avec  ainsi deux boucles `for`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "ff5378ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "def phase_diagram_compressibility(d,NParticles,sigma,epsilon,kT,rho):\n",
    "    \"\"\"\n",
    "    'Naive' version of the phase diagram computation.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    d : int\n",
    "        System dimension.\n",
    "    NParticles : int\n",
    "        Number of particles in the system.\n",
    "    sigma : float\n",
    "        Sigma parameter in the LJ system.\n",
    "    epsilon : float\n",
    "        Epsilon parameter in the LJ system.\n",
    "    kT : iterable of float\n",
    "        Temperatures at which the system is to be computed.\n",
    "    rho : iterable of float\n",
    "        Density at which the system is to be computed.\n",
    "    \n",
    "    Returns\n",
    "    ----------\n",
    "    compressibility : array\n",
    "        Compressibility of the system for every couple of rho and kT.\n",
    "    \"\"\"\n",
    "    \n",
    "    #Mass of particles in the system\n",
    "    m = np.ones(NParticles)\n",
    "    \n",
    "    #unit of time \n",
    "    tau = sigma*np.sqrt(m[0]/epsilon)    \n",
    "\n",
    "    # define the length of the trajectory\n",
    "    run_time = 100. * tau\n",
    "    \n",
    "    #Box size\n",
    "    LBox = np.power(NParticles/rho,1./d)\n",
    "    \n",
    "    #Initialization of the compressibility\n",
    "    compressibility = np.zeros((kT.shape[0],LBox.shape[0]))\n",
    "\n",
    "    #For every box length\n",
    "    for i, LBox_i in enumerate(LBox):\n",
    "        #For every temperature\n",
    "        for j, kT_j in enumerate(kT):\n",
    "            \n",
    "            #Get particles trajectories via the routine \n",
    "            ( t_tr, x_tr, y_tr, \n",
    "             vx_tr, vy_tr, \n",
    "             uPot_tr, uKin_tr, \n",
    "             pPot_tr, pKin_tr, \n",
    "             pHyper_tr, \n",
    "             [t,x,y,vx,vy]) = MD.Generate_LJ_NVT_MolecularDynamics_Trajectory(d,m,\n",
    "                                                                              LBox_i,\n",
    "                                                                              kT_j,\n",
    "                                                                              run_time,\n",
    "                                                                              number_of_time_steps_between_stored_configurations=1)\n",
    "            #Compute the compressibility via the routine and store it in an array\n",
    "            compressibility[i,j] = MD.Compressibility_from_pressure_fluctuations_in_NVT(d,m,\n",
    "                                                                                        NParticles,\n",
    "                                                                                        LBox_i,\n",
    "                                                                                        kT_j,\n",
    "                                                                                        pPot_tr, \n",
    "                                                                                        pHyper_tr, \n",
    "                                                                                        pKin_tr)\n",
    "\n",
    "    #Plot\n",
    "    plt.imshow(compressibility,extent=(0.8,0.05,0.3,5),aspect='auto')\n",
    "    cbar = plt.colorbar()\n",
    "    cbar.set_label('Compressibility')\n",
    "    plt.xlabel('$rho$')\n",
    "    plt.ylabel('$kT$')\n",
    "    plt.title('Phase diagram')\n",
    "    #plt.savefig('phase_diagramm.png')\n",
    "    \n",
    "    return compressibility\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49089333",
   "metadata": {},
   "source": [
    "Ce programme étant assez peu efficace, nous réduisons la taille du nombre de calcul effectués."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3ad1a196",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Calcul sur un diagramme de taille (5x5)\n",
    "kT = np.linspace(0.3,1,5)\n",
    "rho  = np.linspace(0.05,0.8,5)/sigma**d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "58f52788",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time to execute :  277.42178160000003\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": [
    "init_time = time.perf_counter()\n",
    "compressibility = phase_diagram_compressibility(d,NParticles,sigma,epsilon,kT,rho)\n",
    "\n",
    "print('Time to execute : ',time.perf_counter()-init_time)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99922e74",
   "metadata": {},
   "source": [
    "Nous observons deux choses dans ces résulats :\n",
    "- Déjà le temps de calcul est très long (~4min30sec sur ma machine) pour un diagramme de phase avec seulement une résolution 5x5, un temps laissé à la simulation de `100*tau` et 16 particules. Dans l'optique de réaliser un ensemble de simulations identiques afin d'obtenir une estimation de l'erreur commise nous devons optimiser notre fonction.\n",
    "- Le résultat physique n'est pas convainquant. En effet, des compressibilités négatives sont obtenues. Ensuite, pour certains couple $(rho,kT)$ les valeurs absolues de la compressibilité obtenues sont largement au dessus des autres, \"noyant\" ainsi les résultats.\n",
    "\n",
    "Peut-être ne nous laissons pas suffisement de temps à la simulation et ainsi mesurons nous avant l'état d'équilibre ?\n",
    "\n",
    "Pour le vérifier, nous devons augmenter le temps de simulation, ainsi le temps de calcul. Nous devons alors optimiser de notre fonction."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73c55321",
   "metadata": {},
   "source": [
    "### Parallelisation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd7c58bf",
   "metadata": {},
   "source": [
    "Notre fonction étant principalement composée de deux boucles `for` imbriquées et chaque résultat de cette boucle étant indépendant des autres, une parallelisation de notre code semble être une bonne solution pour résoudre ce problème de temps de calcul. Pour distribuer sur plusieurs coeurs notre routine, nous utiliserons la bibliothèque `multiprocessing` de Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "544c07c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import multiprocessing as mp\n",
    "#Nous avons également besoin de la bibliothèque itertools\n",
    "#afin d'obtenir l'ensemble des couples de kT et rho possibles\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcb5d22f",
   "metadata": {},
   "source": [
    "De cette bibliothèque, nous utiliserons l'objet `Pool` pour distribuer nos calculs. De cette objet, par soucis de lisibilité de notre code nous utiliserons sa fonction `map`. Pour être plus précis, comme notre fonction principale `Generate_LJ_NVT_MolecularDynamics_Trajectory` recquiert plusieurs paramètres, nous utiliserons la fonction `starmap`. Enfin, comme nous souhaitons concatener tous nos résultats dans un tableau, donc dans l'ordre, nous utiliserons cette fonction en version synchrone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2469bb8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Nous modifions quelque peu la fonction routine afin que cette dernière soit compatible avec le multiprocessing.\n",
    "\n",
    "def Generate_LJ_NVT_MolecularDynamics_Trajectory(d,m,system,run_time,\n",
    "                                                 starting_configuration=[],\n",
    "                                                 time_step = 0.01,\n",
    "                                                 number_of_time_steps_between_stored_configurations=100,\n",
    "                                                 number_of_time_steps_between_velocity_resets=100,\n",
    "                                                 start_from_stable_grid = False,\n",
    "                                                 debug=False):\n",
    "    \"\"\"\n",
    "    \n",
    "    MODIFIED FUNCTION FOR MULTIPROSSESSING\n",
    "    \n",
    "    \n",
    "    generates a NVT MD simulations of a LJ system with sigma=epsilon=1  \n",
    "        - where the particle masses are specified in the array m\n",
    "        - so that NParticles = m.size\n",
    "        - in a volume V=(LBox,LBox) at a specified temperature kT\n",
    "        - with a time step of time_step tau \n",
    "          where the LJ unit of time is calculated as a function of m[-1], i.e. the mass of the LAST particle\n",
    "        - runs are either started from \n",
    "                a specified starting configuration [t,x,y,vx,vy] or\n",
    "                initialized with zero velocities and particles placed on a square grid\n",
    "        - the simulations are thermostated by redrawing random velocities from the \n",
    "          Maxwell-Boltzmann distribution number_of_time_steps_between_velocity_resets time steps\n",
    "        - the function returns \n",
    "                trajectory lists t_tr, x_tr, y_tr, vx_tr, vy_tr, uPot_tr, uKin_tr, pPot_tr, pKin_tr, pHyper_tr \n",
    "                     of sampling times and sampled coordinates, velocities and energies and pressures\n",
    "                a final configuration [t,x,y,vx,vy] from which the run can be restarted\n",
    "                while the energies and pressures are recorded at every time step, configurations \n",
    "                     and velocities are stored at a time interval of time_between_stored_configurations\n",
    "                    \n",
    "    \"\"\"\n",
    "    #Added this line to make multiprossessing easier\n",
    "    LBox, kT = system\n",
    "    \n",
    "    NParticles = m.size\n",
    "    sigma = 1\n",
    "    epsilon = 1\n",
    "    #unit of time\n",
    "    #tau = sigma*np.sqrt(m[-1]/epsilon)      \n",
    "\n",
    "    # define the length of the trajectory\n",
    "    number_of_timesteps = int(np.round(run_time/time_step))\n",
    "\n",
    "    #starting configuration\n",
    "    if starting_configuration!=[]:\n",
    "        [t,x,y,vx,vy] = starting_configuration\n",
    "    else:\n",
    "        # default initial state\n",
    "        if start_from_stable_grid:\n",
    "            x,y = MD.StableGridPositionsIn2d(LBox,LBox,NParticles)\n",
    "        else:\n",
    "            x,y = MD.GridPositionsIn2d(LBox,LBox,NParticles)\n",
    "        vx = MD.RandomVelocities(m,kT)\n",
    "        vy = MD.RandomVelocities(m,kT)\n",
    "        t = 0\n",
    "        if debug:\n",
    "            print(\"No starting configuration\")\n",
    "\n",
    "    #initialize Trajectory\n",
    "    t_tr = []\n",
    "    x_tr = []\n",
    "    vx_tr = []\n",
    "    y_tr = []\n",
    "    vy_tr = []\n",
    "\n",
    "    fx,fy = MD.LJ_forces_as_a_function_of_positions(d,epsilon,sigma,LBox,(x,y))\n",
    "    # force for initial configuration needed for first time step\n",
    "\n",
    "    for timestep in range(number_of_timesteps):\n",
    "        (x,y),(vx,vy) = MD.VelocityVerletTimeStepPartOne(m,(x,y),(vx,vy),(fx,fy),time_step)\n",
    "        fx,fy = MD.LJ_forces_as_a_function_of_positions(2,epsilon,sigma,LBox,(x,y))\n",
    "        (x,y),(vx,vy) = MD.VelocityVerletTimeStepPartTwo(m,(x,y),(vx,vy),(fx,fy),time_step)\n",
    "        t += time_step\n",
    "        \n",
    "        t_tr.append(t)\n",
    "        x_tr.append(x)\n",
    "        vx_tr.append(vx)\n",
    "        y_tr.append(y)\n",
    "        vy_tr.append(vy)\n",
    "    \n",
    "        # thermostat: reinitialise velocities to control temperature\n",
    "#        if np.mod( timestep*time_step, time_between_velocity_resets ) == 0.0 and timestep>1:\n",
    "        if timestep%number_of_time_steps_between_velocity_resets == 0 and timestep>1:\n",
    "            vx = MD.RandomVelocities(m,kT)\n",
    "            vy = MD.RandomVelocities(m,kT)\n",
    "\n",
    "    # convert trajectory lists to arrays to simplify the data analysis\n",
    "    t_tr = np.array(t_tr)\n",
    "    x_tr = np.array(x_tr)\n",
    "    vx_tr = np.array(vx_tr)\n",
    "    y_tr = np.array(y_tr)\n",
    "    vy_tr = np.array(vy_tr)\n",
    "\n",
    "    # analyse results \n",
    "    uPot_tr = MD.LJ_energy_as_a_function_of_positions(d,epsilon,sigma,LBox,(x_tr,y_tr))\n",
    "    uKin_tr = MD.TotalKineticEnergy(m,vx_tr) + MD.TotalKineticEnergy(m,vy_tr)\n",
    "    pPot_tr = MD.LJ_virial_pressure_as_a_function_of_positions(d,epsilon,sigma,LBox,(x_tr,y_tr)) \n",
    "    pKin_tr = MD.KineticPressure_as_a_function_of_velocities(d,LBox,m,(vx_tr,vy_tr))\n",
    "    pHyper_tr = MD.LJ_hyper_virial_as_a_function_of_positions(d,epsilon,sigma,LBox,(x_tr,y_tr)) \n",
    "    \n",
    "    # reduce the number of stored configurations and velocities\n",
    "#    skip = int(time_between_stored_configurations / delta_t)\n",
    "    skip = number_of_time_steps_between_stored_configurations\n",
    "    x_tr = x_tr[::skip]\n",
    "    y_tr = y_tr[::skip]\n",
    "    vx_tr = vx_tr[::skip]\n",
    "    vy_tr = vy_tr[::skip]    \n",
    "    # note that t_tr is not compressed as it contains the times corresponding to the stored energies and pressures\n",
    "    # as a consequence a corresponding skipping operation needs to be performed, when configurations are plotted \n",
    "    # as a function of time\n",
    "    \n",
    "    return t_tr, x_tr, y_tr, vx_tr, vy_tr, uPot_tr, uKin_tr, pPot_tr, pKin_tr, pHyper_tr, [t,x,y,vx,vy]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53c9e2ca",
   "metadata": {},
   "source": [
    "Nous définissons une fonction qui va, à chaque nouvelle itération, calculer les résultats que nous souhaitons et concatener ces derniers dans un tableau."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "0f8d3c35",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_results(d,m,system,run_time,method,ensemble=False,NTrajectories=10):\n",
    "    \"\"\"\n",
    "    The routine that will be executed in each iteration into multiprocessing.\n",
    "    First generate the trajectory via MD LJ, then calculate the compressibility\n",
    "    of the system.\n",
    "    \n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    d : int\n",
    "        Dimension of the LJ system.\n",
    "    m : array ; size = number of particles\n",
    "        Array of the mass of each particles\n",
    "    system: iterrable\n",
    "         iterrable containnig LBox (length of the box, iterable) \n",
    "         and kT (temperature, iterable) of the system.\n",
    "    run_time : int\n",
    "        How long the simulation will be.\n",
    "    method : str\n",
    "        Method to use\n",
    "    ensemble : bool\n",
    "        True to calculate an ensemble of trajectory; to get the uncertanty on this quantity.\n",
    "    NTrajectories : int\n",
    "        Number of independant trajectories to calculate.\n",
    "        \n",
    "        \n",
    "    Returns\n",
    "    -------\n",
    "    result : Array\n",
    "        Compressibility, MSD, Pressure of the system for every couple of LBox and kT given in\n",
    "        system, depending on the method selected.\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    #Extract data\n",
    "    LBox, kT = system\n",
    "    \n",
    "    \n",
    "    if ensemble :\n",
    "        #Calulate independant trajectories\n",
    "        (t_tr_ens, \n",
    "         x_tr_ens, \n",
    "         y_tr_ens, \n",
    "         vx_tr_ens, \n",
    "         vy_tr_ens, \n",
    "         uPot_tr_ens, \n",
    "         uKin_tr_ens, \n",
    "         pPot_tr_ens, \n",
    "         pKin_tr_ens, \n",
    "         pHyper_tr_ens, \n",
    "         local_list_of_starting_configurations) = Generate_Ensemble_of_LJ_NVT_MolecularDynamics_Trajectories(\n",
    "             d,m,system,NTrajectories,run_time,\n",
    "             number_of_time_steps_between_stored_configurations=1)\n",
    "             \n",
    "    \n",
    "    else :\n",
    "        #Generate trajectories\n",
    "        ( t_tr, x_tr, y_tr, \n",
    "         vx_tr, vy_tr, \n",
    "         uPot_tr, uKin_tr, \n",
    "         pPot_tr, pKin_tr, \n",
    "         pHyper_tr, \n",
    "         [t,x,y,vx,vy]) = Generate_LJ_NVT_MolecularDynamics_Trajectory(d,m,\n",
    "                                                                       system,\n",
    "                                                                       run_time,\n",
    "                                                                       number_of_time_steps_between_stored_configurations=1)\n",
    "    \n",
    "    \n",
    "    if method == 'Compressibility':\n",
    "        #Compute the compressibility\n",
    "        compressibility = MD.Compressibility_from_pressure_fluctuations_in_NVT(d,m,\n",
    "                                                                                    NParticles,\n",
    "                                                                                    LBox,\n",
    "                                                                                    kT,\n",
    "                                                                                    pPot_tr, \n",
    "                                                                                    pHyper_tr, \n",
    "                                                                                    pKin_tr)\n",
    "        \n",
    "        return compressibility\n",
    "    \n",
    "    if method == 'MSD':\n",
    "        \n",
    "        #Compute the Mean Square Displacement of independant trajectories\n",
    "        if ensemble:\n",
    "            msd_x_ens = []\n",
    "            msd_y_ens = []\n",
    "            \n",
    "            for i in x_tr_ens:\n",
    "                delta_t , msd_x = MD.MeanSquareDisplacements(t_tr_ens[0,:],i)\n",
    "                msd_x_ens.append(msd_x)\n",
    "                \n",
    "            for i in y_tr_ens:\n",
    "                delta_t , msd_y = MD.MeanSquareDisplacements(t_tr_ens[0,:],i)\n",
    "                msd_y_ens.append(msd_y)\n",
    "                \n",
    "            msd_x_ens= np.array(msd_x_ens)\n",
    "            msd_y_ens = np.array(msd_y_ens)\n",
    "            \n",
    "            msd_tot_ens = (msd_x_ens + msd_y_ens)/2\n",
    "            #Get only when the system is equilibrated\n",
    "            msd_tot_ens = msd_tot_ens[:,:100]\n",
    "            #Do the mean\n",
    "            msd_mean = np.mean(msd_tot_ens)\n",
    "            #Get the standard deviation\n",
    "            msd_std = np.std(msd_tot_ens)\n",
    "            \n",
    "            \n",
    "            return msd_mean , msd_std\n",
    "            \n",
    "        else :\n",
    "            #Compute the mean square displacement\n",
    "            delta_t , msd_x = MD.MeanSquareDisplacements(t_tr, x_tr)\n",
    "            delta_t , msd_y = MD.MeanSquareDisplacements(t_tr, y_tr)\n",
    "        \n",
    "            msd_tot = (msd_x+msd_y)/2\n",
    "        \n",
    "            #Take only when equilibrated\n",
    "            msd_tot = msd_tot[:100]\n",
    "            msd = np.mean(msd_tot)\n",
    "        \n",
    "        \n",
    "            return msd\n",
    "    \n",
    "    if method == 'Pressure':\n",
    "        #Compute the pressure\n",
    "        P = pPot_tr + pKin_tr\n",
    "        \n",
    "        #Take only when equilibrated\n",
    "        P = P[:100]\n",
    "        P = np.mean(P)\n",
    "        \n",
    "        \n",
    "        return P"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1028b386",
   "metadata": {},
   "source": [
    "Nous définissons finalement une fonction `main` qui va nous permettre de lancer l'ensemble des fonctions définies plus haut de façon paralleles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "69db97d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def main(d,NParticles,sigma,epsilon,kT,rho,method,ensemble=False,NTrajectories=10):\n",
    "    \"\"\"\n",
    "    \n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    d : int\n",
    "        Dimension of the LJ system.\n",
    "    NParticles : int\n",
    "        Number of particles in the system\n",
    "    sigma : float\n",
    "        Sigma parameter in the LJ system.\n",
    "    epsilon : float\n",
    "        Epsilon parameter in the LJ system.\n",
    "    kT : iterable of float\n",
    "        Temperatures at which the system is to be computed\n",
    "    rho : iterable of float\n",
    "        Density at which the system is to be computed\n",
    "    method : str\n",
    "        Method used, propertiy to compute\n",
    "    ensemble : bool\n",
    "        True to calculate an ensemble of trajectory; to get the uncertanty on this quantity.\n",
    "    NTrajectories : int\n",
    "        Number of independant trajectories to calculate.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    result : Array\n",
    "        Compressibility, MSD, Pressure of the system for every couple of LBox and kT given in\n",
    "        system, depending on the method selected.\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    #the System\n",
    "    m = np.ones(NParticles)\n",
    "    LBox = np.power(NParticles/rho,1./d)\n",
    "    \n",
    "    #Unit of time\n",
    "    tau = sigma*np.sqrt(m[0]/epsilon)\n",
    "    \n",
    "    # define the length of the trajectory\n",
    "    run_time = 100. * tau\n",
    "    \n",
    "    \n",
    "    #Multiprocessing\n",
    "    #Get the number of cpu\n",
    "    pool = mp.Pool(mp.cpu_count())\n",
    "    #Every possible couple of rho and kT\n",
    "    couple = list(itertools.product(LBox,kT))\n",
    "\n",
    "\n",
    "    if method == 'Compressibility':\n",
    "        #Compute the compressibility\n",
    "        compressibility = pool.starmap(\n",
    "            get_results,\n",
    "            [(d, m, (LBox_i, kT_j), run_time,method,ensemble,NTrajectories) for LBox_i, kT_j in couple]\n",
    "            )\n",
    "    \n",
    "        #End of multiprocessing\n",
    "        pool.close()\n",
    "        \n",
    "        #Convert to np.array for better data analysis\n",
    "        compressibility = np.array(compressibility)\n",
    "        #Reshape to have a square matrix\n",
    "        compressibility = compressibility.reshape((len(rho),len(kT)))\n",
    "        result = compressibility\n",
    "        plot = result\n",
    "    \n",
    "    if method == 'MSD':\n",
    "        #Compute the mean square displacement\n",
    "        msd = pool.starmap(\n",
    "            get_results,\n",
    "            [(d, m, (LBox_i, kT_j), run_time,method,ensemble,NTrajectories) for LBox_i, kT_j in couple]\n",
    "            )\n",
    "        \n",
    "        #End of multiprocessing\n",
    "        pool.close()\n",
    "        \n",
    "        msd = np.array(msd)\n",
    "        \n",
    "        if ensemble:\n",
    "            #Ensemble of independant trajectories\n",
    "            \n",
    "            #The mean\n",
    "            msd_mean = msd[:,0]\n",
    "            #The std\n",
    "            msd_std = msd[:,1]\n",
    "            #Convert to square matrix\n",
    "            msd_mean = msd_mean.reshape((len(rho),len(kT)))\n",
    "            msd_std = msd_std.reshape((len(rho),len(kT)))\n",
    "            \n",
    "            result = (msd_mean,np.sqrt(msd_std))\n",
    "            plot = msd_mean\n",
    "        \n",
    "        \n",
    "        else:\n",
    "            #Only one trajectory\n",
    "            msd = msd.reshape((len(rho),len(kT)))\n",
    "            result = msd\n",
    "            plot = result\n",
    "        \n",
    "    if method == 'Pressure':\n",
    "        #Compute the pressure\n",
    "        P = pool.starmap(\n",
    "            get_results,\n",
    "            [(d, m, (LBox_i, kT_j), run_time,method,ensemble,NTrajectories) for LBox_i, kT_j in couple]\n",
    "            )\n",
    "        \n",
    "        #End of multiprocessing\n",
    "        pool.close()\n",
    "        \n",
    "        P = np.array(P)\n",
    "        #Get a square matrix\n",
    "        P = P.reshape((len(rho),len(kT)))\n",
    "        result = P\n",
    "        plot = result\n",
    "        \n",
    "    \n",
    "    #Plot\n",
    "    \n",
    "    plt.imshow(plot,extent=(0.8,0.05,0.3,5),aspect='auto')\n",
    "    cbar = plt.colorbar()\n",
    "    cbar.set_label(method)\n",
    "    plt.xlabel('rho')\n",
    "    plt.ylabel('kT')\n",
    "    plt.title('Phase diagram')\n",
    "    plt.savefig('phase_diagramm.png')\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "8454c765",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time to execute :  137.45388387399998\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": [
    "#Test of the speed-up\n",
    "init_time = time.perf_counter()\n",
    "\n",
    "compressibility = main(\n",
    "    d,NParticles,sigma,epsilon,kT,rho,method='Compressibility')\n",
    "#Save it to a .npy file\n",
    "#np.save('compressibility.npy',compressibility)\n",
    "\n",
    "print('Time to execute : ',time.perf_counter()-init_time)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55d2c795",
   "metadata": {},
   "source": [
    "Avec la parallelisation, nous gagnons un facteur deux en temps de calcul (sur ma machine). Cela va nous permettre d'une part d'effectuer de plus longues simulations afin de tester l'influence du retour à l'état d'équilibre du système. D'autre part, cette optimisation nous permet d'obtenir des diagrammes de phase plus résolu que (5x5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "1efaa18f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#To change the length of the calculus please change the line 42 in main() : run_time = 100. * tau"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72f89482",
   "metadata": {},
   "source": [
    "**L'ensemble des résultats suivants ont été préalablement calculé sur les machines multi-coeur du Centre Blaise Pascal (192 coeurs) afin de réduire le temps de calcul.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "94d5c6d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Phase diagram')"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "#Compressibility calculated on a 5x5 grid during run_time = 10000 * tau\n",
    "compressibility = np.load('t10000_5x5/compressibility.npy')\n",
    "plt.imshow(compressibility,extent=(0.8,0.05,0.3,5),aspect='auto')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Compressibility')\n",
    "plt.xlabel('$rho$')\n",
    "plt.ylabel('$kT$')\n",
    "plt.title('Phase diagram')\n",
    "#plt.savefig('phase_diagramm.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b327c20e",
   "metadata": {},
   "source": [
    "Les résultats, bien que nous ayons augmenté d'un facteur 100 le temps laissé à la simulation et augmenté la résolution de notre diagramme de phase, ne sont pas physiquement satisfaisant. Nous continuons de trouver des points avec une compressibilité bien supérieure à leurs voisins.\n",
    "\n",
    "La compressibilité ne semble alors plus une grandeur de choix pour estimer la phase du système. Nous avons donc abandonné cette grandeur au profit du Déplacement Moyen Carré, *Mean Square Displacement, MSD*."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6db6d05c",
   "metadata": {},
   "source": [
    "## Mean Square Displacement, MSD"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54944639",
   "metadata": {},
   "source": [
    "### Trajectoire unique"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "244f3e31",
   "metadata": {},
   "source": [
    "Nous avons déjà implémenté, par simplicité, le calcul de MSD dans les fonctions de routine `main()` et `get_results()`. Nous effectuons de nouveaux nos calculs sur une grille (25x25) sur les ordinateurs multi-coeur du CBP avec `run_time = 500 * tau`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "ae462d29",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Uncomment this code to run it, otherwhise, results are given in the next cell\n",
    "\n",
    "\n",
    "##Get MSD\n",
    "#msd = main(\n",
    "#    d,NParticles,sigma,epsilon,kT,rho,method='MSD')\n",
    "##Save it to a .npy file\n",
    "#np.save('msd.npy',msd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "201d1195",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Phase diagram')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "msd = np.load('msd_t500_25x25/msd.npy')\n",
    "plt.imshow(msd,extent=(0.8,0.05,0.3,5),aspect='auto')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('MSD')\n",
    "plt.xlabel('$rho$')\n",
    "plt.ylabel('$kT$')\n",
    "plt.title('Phase diagram')\n",
    "#plt.savefig('phase_diagramm.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b8945f7",
   "metadata": {},
   "source": [
    "Ce résultats est obtenue en ~10 min sur la machine `platinum1` du CBP possédant 192 coeurs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb4718bf",
   "metadata": {},
   "source": [
    "Nous obtenons des résulats physiquement convainquants cette fois-ci. En effet, nous observons que le déplacement moyen carré augmente effectivement avec la température et diminue avec la densité. Les zones les plus claires sont ainsi les zones en phase liquide. Les zones les plus foncées sont donc les zones en phase solide du système. \n",
    "\n",
    "Afin de départager les phases solides de liquides,nous pouvons concidérer que le système est solide si il prossède un MSD <= 0.050. Effectivement avec un tel deplacement moyen carré, l'échelle de déplacement des particules est inférieure à leur propre taille, définissant ainsi un solide. On observe toujours des vibrations des particules dans le solide."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f10b988",
   "metadata": {},
   "source": [
    "### Estimation de l'erreur *via* un ensemble de trajectoires indépendantes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3afdd428",
   "metadata": {},
   "source": [
    "Afin de founir une estimation de l'erreur commise sur nos résultats, nous avons implémenté dans les fonctions de routine parallelisé la possibilité d'obtenir des résultats générés à partir d'un ensemble de trajectoires indépendantes. Pour cela nous utilisons les paramètres `ensemble` et `NTrajectories` des fonctions de routine.\n",
    "\n",
    "Les résultats présentés ont été obtenues sur un ensemble de 10 trajectoires indépendantes de 16 particules chacune, `run_time = 200 * tau` et sur un diagramme de phase de (10x10) points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "53efbee1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Uncomment this code to run it, otherwhise, results are given in the next cell\n",
    "\n",
    "##Number of independant trajectories\n",
    "#NTajectories = 10\n",
    "\n",
    "##(10x10) phase diagram\n",
    "kT = np.linspace(0.3,1,10)\n",
    "rho  = np.linspace(0.05,0.8,10)/sigma**d\n",
    "\n",
    "#Get MSD\n",
    "#msd_mean , msd_std = main(\n",
    "#    d,NParticles,sigma,epsilon,kT,rho,method='MSD',ensemble=True,NTrajectories=NTrajectories)\n",
    "\n",
    "##Save it to a .npy file\n",
    "#np.save('msd_mean.npy',msd_mean)\n",
    "#np.save('msd_std.npy',msd_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "049a19da",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Phase diagram')"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "msd_mean = np.load('msd_ens_t200_10x10_ens10/msd_mean.npy')\n",
    "msd_std = np.load('msd_ens_t200_10x10_ens10/msd_std.npy')/np.sqrt(10)\n",
    "\n",
    "plt.imshow(msd_mean,extent=(0.8,0.05,0.3,5),aspect='auto')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('MSD')\n",
    "plt.xlabel('$rho$')\n",
    "plt.ylabel('$kT$')\n",
    "plt.title('Phase diagram')\n",
    "#plt.savefig('phase_diagramm.png')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "a3f2e8dc",
   "metadata": {},
   "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": [
    "for i , kT_i in enumerate(msd_mean):\n",
    "    plt.errorbar(rho,msd_mean[i,:],yerr=msd_std[i,:],label='kT = {:.2f}'.format(kT[i]))\n",
    "    \n",
    "plt.xlabel('$rho$')\n",
    "plt.ylabel('MSD')\n",
    "plt.title(\"Retour à l'équilibre ?\")\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f01175f0",
   "metadata": {},
   "source": [
    "Ce résultat a été obtenu en ~15min sur la machine `epyc3`, 256 coeurs, du CBP. Nous constatons que les barre d'erreur sont trop grandes pour être suffisement satisfaisantes. Nous lançons donc le même programme en augmentant le temps de simulation : `run_time = 500*tau` et en diminuant le nombre de trajectoires pour réduire le temps de calcul : `NTrajectories = 5`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "b36c4513",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Phase diagram')"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "msd_mean = np.load('msd_ens_t500_10x10_ens5/msd_mean.npy')\n",
    "msd_std = np.load('msd_ens_t500_10x10_ens5/msd_std.npy')/np.sqrt(5)\n",
    "\n",
    "plt.imshow(msd_mean,extent=(0.8,0.05,0.3,5),aspect='auto')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('MSD')\n",
    "plt.xlabel('$rho$')\n",
    "plt.ylabel('$kT$')\n",
    "plt.title('Phase diagram')\n",
    "#plt.savefig('phase_diagramm.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "52460253",
   "metadata": {},
   "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": [
    "for i , kT_i in enumerate(msd_mean):\n",
    "    plt.errorbar(rho,msd_mean[i,:],yerr=msd_std[i,:],label='kT = {:.2f}'.format(kT[i]))\n",
    "    \n",
    "plt.xlabel('$rho$')\n",
    "plt.ylabel('MSD')\n",
    "plt.title(\"Retour à l'équilibre ?\")\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6edf34bc",
   "metadata": {},
   "source": [
    "Ce résultat est obtenue en ~1h30 sur la même machine. Par manque de temps dans la réalisation de ce projet, nous n'avons pas pu lancer plus de calcul afin de réduire les barres d'erreur."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56b54614",
   "metadata": {},
   "source": [
    "## Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc009589",
   "metadata": {},
   "source": [
    "Nous avons ainsi optimisé l'automatisation de l'exploration du diagramme de phase du système de Lennard-Jones. Cette optimisation a été réalisé par la parallelisation des taches effectuées. \n",
    "\n",
    "Nos résultats, prométeurs, sont physiquement cohérents lorsque ces derniers reposent sur le MSD. Il reste cependant une erreur importante dans nos résultats. Ces erreurs peuvent être réduites en augmentant le temps de calcul et le nombre de trajectoires indépendantes générées; des temps de calculs plus long sont donc à prévoir pour un tel projet. Une méthode alternative pour estimer l'erreur associée à nos calculs serait d'explorer le diagramme de phase de différentes manière : en diminuant la température, en diminuant la densité... Cela peut-être aiséement mis en place dans nos fonctions de routine avec la méthode `np.flip`. Ces tests ont été effectués mais non présenté dans ce rapport car beaucoup d'entre eux n'ont pas eu le temps de connverger.\n",
    "\n",
    "Aussi, nous avons implémenté dans nos fonctions de routine la possibilité d'obtenir un diagramme de phase reposant non pas sur le MSD ou la compressibilité mais sur la pression. Au vu de peu de temps à notre disposition pour ce projet nous avons préféré ne pas détailler les calculs de cette grandeurs. Cette grandeur peux aussi être étudié dans l'optique d'une fortification de nos résulats."
   ]
  }
 ],
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