examples/hoomd-blue/umbrella_integration/Umbrella_Integration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "T-Qkg9C9n7Cc"
   },
   "source": [
    "# Setting up the environment\n",
    "\n",
    "First, we set up our environment. We will be using a pre-compiled and packaged installation of HOOMD-blue and the hoomd-dlext plugin.\n",
    "It will be downloaded from Google Drive and made accessible to the Python process running in this Colab instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f730dbd3",
   "metadata": {
    "id": "3eTbKklCnyd_"
   },
   "outputs": [],
   "source": [
    "%%bash\n",
    "\n",
    "BASE_URL=\"https://drive.usercontent.google.com/download?id=1hsKkKtdxZTVfHKgqVF6qV2e-4SShmhr7\"\n",
    "COOKIES=\"/tmp/cookies.txt\"\n",
    "CONFIRMATION=\"$(wget -q --save-cookies $COOKIES --keep-session-cookies --no-check-certificate $BASE_URL -O- | sed -rn 's/.*confirm=(\\w+).*/\\1\\n/p')\"\n",
    "\n",
    "wget -q --load-cookies $COOKIES \"$BASE_URL&confirm=$CONFIRMATION\" -O pysages-env.zip\n",
    "rm -rf $COOKIES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "KRPmkpd9n_NG",
    "outputId": "b757f2aa-38cc-4726-c4ab-5197810b9d77"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "env: PYSAGES_ENV=/env/pysages\n"
     ]
    }
   ],
   "source": [
    "%env PYSAGES_ENV=/env/pysages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "J7OY5K9VoBBh"
   },
   "outputs": [],
   "source": [
    "%%bash\n",
    "\n",
    "mkdir -p $PYSAGES_ENV .\n",
    "unzip -qquo pysages-env.zip -d $PYSAGES_ENV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "EMAWp8VloIk4"
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import sys\n",
    "\n",
    "ver = sys.version_info\n",
    "sys.path.append(os.environ[\"PYSAGES_ENV\"] + \"/lib/python\" + str(ver.major) + \".\" + str(ver.minor) + \"/site-packages/\")\n",
    "\n",
    "os.environ[\"LD_LIBRARY_PATH\"] = \"/usr/lib/x86_64-linux-gnu:\" + os.environ[\"LD_LIBRARY_PATH\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Wy-75Pt7Bqs1"
   },
   "source": [
    "We'll also need some additional python dependencies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "LpBucu3V81xm"
   },
   "outputs": [],
   "source": [
    "!pip install -qq \"numpy<2\" gsd > /dev/null"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "we_mTkFioS6R"
   },
   "source": [
    "## PySAGES\n",
    "\n",
    "Next, we install PySAGES. The latest version is retrieved from GitHub and installed (along with its dependencies) using `pip`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "B-HB9CzioV5j"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2.27\n",
      "0.1.75\n"
     ]
    }
   ],
   "source": [
    "!pip install -qq git+https://github.com/SSAGESLabs/PySAGES.git > /dev/null"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LjPjqVjSOzTL"
   },
   "source": [
    "# Umbrella integration\n",
    "\n",
    "In [this tutorial](https://github.com/SSAGESLabs/PySAGES/blob/main/examples/hoomd-blue/harmonic_bias/Harmonic_Bias.md), we demonstrated how PySAGES can be used to run a single simulation with a biasing potential.\n",
    "However, if we want to look into the free-energy landscape a single simulation is not enough. Instead, we have to perform a series of simulations along a path in the space of the collective variables (CVs). From the histograms of the biasing, we can deduce the differences in free energy. For a more detailed explanation look at the literature, for example [J. Kaestner 2009](https://doi.org/10.1063/1.3175798).\n",
    "\n",
    "The first step here is also to generate a simulation snapshot that can be used as an initial condition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "QOrufad1RaMF",
    "outputId": "02f68f5a-54cc-435c-e3df-78f4826dc374"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting gsd\n",
      "  Downloading gsd-2.5.1-cp37-cp37m-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_12_x86_64.manylinux2010_x86_64.whl (335 kB)\n",
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      "     |████████████████████████████████| 335 kB 7.6 MB/s            \n",
      "\u001b[?25hRequirement already satisfied: numpy<2,>=1.9.3 in /usr/local/lib/python3.7/dist-packages (from gsd) (1.19.5)\n",
      "Installing collected packages: gsd\n",
      "Successfully installed gsd-2.5.1\n",
      "\u001b[33mWARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "import gsd\n",
    "import gsd.hoomd\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "class System:\n",
    "    def __init__(self):\n",
    "        self.L = 5\n",
    "        self.N = 200\n",
    "\n",
    "\n",
    "def post_process_pos(snapshot):\n",
    "    box_size = snapshot.configuration.box[:3]\n",
    "    snapshot.particles.image = np.rint(snapshot.particles.position / box_size)\n",
    "    snapshot.particles.position -= snapshot.particles.image * box_size\n",
    "    return snapshot\n",
    "\n",
    "\n",
    "def get_snap(system):\n",
    "    L = system.L\n",
    "    snapshot = gsd.hoomd.Frame()\n",
    "    snapshot.configuration.box = [L, L, L, 0, 0, 0]\n",
    "\n",
    "    snapshot.particles.N = N = system.N\n",
    "    snapshot.particles.types = [\"A\", \"B\"]\n",
    "    snapshot.particles.position = np.zeros((N, 3))\n",
    "    snapshot.particles.velocity = np.random.standard_normal((N, 3))\n",
    "    snapshot.particles.image = np.zeros((N, 3), dtype=int)\n",
    "    snapshot.particles.typeid = np.zeros(N, dtype=int)\n",
    "    snapshot.particles.typeid += 1\n",
    "    snapshot.particles.typeid[0] = 0\n",
    "\n",
    "    rng = np.random.default_rng()\n",
    "    for particle in range(N):\n",
    "        snapshot.particles.position[particle, 0] = rng.random() * L - L / 2\n",
    "        snapshot.particles.position[particle, 1] = rng.random() * L - L / 2\n",
    "        snapshot.particles.position[particle, 2] = rng.random() * L - L / 2\n",
    "\n",
    "    snapshot.particles.position[0, 0] = -np.pi\n",
    "    snapshot.particles.position[0, 1] = -np.pi\n",
    "    snapshot.particles.position[0, 1] = -np.pi\n",
    "\n",
    "    return snapshot\n",
    "\n",
    "\n",
    "system = System()\n",
    "snap = get_snap(system)\n",
    "snap = post_process_pos(snap)\n",
    "snap.particles.validate()\n",
    "\n",
    "with gsd.hoomd.open(\"start.gsd\", \"w\") as f:\n",
    "    f.append(snap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AgFXHafmVUAi"
   },
   "source": [
    "For this simulation, we are using the PySAGES method `UmbrellaIntegration` so we start with importing this.\n",
    "\n",
    "In the next step, we write a function that generates the simulation context. We need to make sure that the context can depend on the replica of the simulation along the path. PySAGES sets variable `replica_num` in the keyword arguments of the function.\n",
    "We also set some general parameters for all replicas.\n",
    "\n",
    "In contrast to the single harmonic bias simulation, the simulation now contains an external potential `hoomd.md.external.field.Periodic` which changes the expected density of particles. See hoomd-blue's [documentation](https://hoomd-blue.readthedocs.io/en/stable/module-md-external-field.html) for details on the potential. For this example, the potential generates the free-energy landscape we are exploring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "tG6JhN7SNpSj",
    "outputId": "979d5793-f459-4202-ac4e-74f2aaabc1f3"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
     ]
    }
   ],
   "source": [
    "import hoomd\n",
    "\n",
    "import pysages\n",
    "from pysages.colvars import Component\n",
    "from pysages.methods import UmbrellaIntegration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "RsZhjfm2U5ps"
   },
   "outputs": [],
   "source": [
    "dpd_params = dict(\n",
    "    AA = dict(A = 5, gamma = 1),\n",
    "    AB = dict(A = 5, gamma = 1),\n",
    "    BB = dict(A = 5, gamma = 1),\n",
    ")\n",
    "periodic_params = dict(\n",
    "    A = dict(A = 0.5, i = 0, w = 0.2, p = 2),\n",
    "    B = dict(A = 0.0, i = 0, w = 0.02, p = 1),\n",
    ")\n",
    "\n",
    "def generate_simulation(\n",
    "    kT=1, dt=0.01, r_cut=1, dpd_params=dpd_params, periodic_params=periodic_params,\n",
    "    device=hoomd.device.auto_select(), seed=42,\n",
    "    **kwargs\n",
    "):\n",
    "    \"\"\"\n",
    "    Generates a simulation context to which will attatch our sampling method.\n",
    "    \"\"\"\n",
    "    print(f\"Operating replica {kwargs.get('replica_num')}\")\n",
    "\n",
    "    simulation = hoomd.Simulation(device=device, seed=seed)\n",
    "    simulation.create_state_from_gsd(\"start.gsd\")\n",
    "    simulation.run(0)\n",
    "\n",
    "    nlist = hoomd.md.nlist.Cell(buffer=0.4)\n",
    "    dpd = hoomd.md.pair.DPD(nlist=nlist, kT=kT, default_r_cut=r_cut)\n",
    "    dpd.params[(\"A\", \"A\")] = dpd_params[\"AA\"]\n",
    "    dpd.params[(\"A\", \"B\")] = dpd_params[\"AB\"]\n",
    "    dpd.params[(\"B\", \"B\")] = dpd_params[\"BB\"]\n",
    "\n",
    "    periodic = hoomd.md.external.field.Periodic()\n",
    "    periodic.params[\"A\"] = periodic_params[\"A\"]\n",
    "    periodic.params[\"B\"] = periodic_params[\"B\"]\n",
    "\n",
    "    nve = hoomd.md.methods.ConstantVolume(filter=hoomd.filter.All())\n",
    "\n",
    "    integrator = hoomd.md.Integrator(dt=dt)\n",
    "    integrator.forces.append(dpd)\n",
    "    integrator.methods.append(nve)\n",
    "    simulation.operations.integrator = integrator\n",
    "\n",
    "    return simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YRPnU0CJY31J"
   },
   "source": [
    "With the ability to generate the simulation context, we start to set up the umbrella integration method - starting with the CV that describes the single A-particle along the varying axis of the external potential."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "_o7puY5Sao5h"
   },
   "outputs": [],
   "source": [
    "cvs = [Component([0], 0),]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jhs3vpglaux4"
   },
   "source": [
    "Next, we define the path along the CV space. In this case, we start at position $-1.5$ and end the path at the position $1.5$. We are using linear interpolation with $25$ replicas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "Uvkeedv4atn3"
   },
   "outputs": [],
   "source": [
    "centers = list(np.linspace(-1.5, 1.5, 25))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "q37sUT-tbOMS"
   },
   "source": [
    "The next parameters we need to define and run the method are the harmonic biasing spring constant,\n",
    "(which we set to to $100$), the log frequency for the histogram ($50$), the number of steps we discard\n",
    "as equilibration before logging ($10^3$), and the number of time steps per replica ($10^4$).\n",
    "\n",
    "Since this runs multiple simulations, we expect the next cell to execute for a while."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "wIrPB2N0bFIl",
    "outputId": "2f018685-a115-4c66-a21a-eef1d515bd02"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Operating replica 0\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1549.37 | ETA 00:00:00\n",
      "Average TPS: 1549.08\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1751 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 25 / n_neigh_avg: 8.815\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 13 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 1\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1536.93 | ETA 00:00:00\n",
      "Average TPS: 1536.51\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1738 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 27 / n_neigh_avg: 8.79\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 3 / n_max: 11 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 2\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1574.37 | ETA 00:00:00\n",
      "Average TPS: 1574.01\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1714 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 24 / n_neigh_avg: 8.9\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 5 / n_max: 13 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 3\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1533.22 | ETA 00:00:00\n",
      "Average TPS: 1532.81\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1714 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 23 / n_neigh_avg: 9.045\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 12 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 4\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1514.8 | ETA 00:00:00\n",
      "Average TPS: 1513.9\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1760 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 23 / n_neigh_avg: 9\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 2 / n_max: 12 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 5\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1555.03 | ETA 00:00:00\n",
      "Average TPS: 1554.75\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1753 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 23 / n_neigh_avg: 8.91\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 3 / n_max: 11 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 6\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1530.93 | ETA 00:00:00\n",
      "Average TPS: 1530.63\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1785 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 25 / n_neigh_avg: 9.035\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 11 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 7\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1513.95 | ETA 00:00:00\n",
      "Average TPS: 1513.61\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1776 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 23 / n_neigh_avg: 8.905\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 3 / n_max: 12 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 8\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1517.25 | ETA 00:00:00\n",
      "Average TPS: 1516.84\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1785 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 23 / n_neigh_avg: 8.99\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 3 / n_max: 12 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 9\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1525.71 | ETA 00:00:00\n",
      "Average TPS: 1524.94\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1816 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 22 / n_neigh_avg: 8.9\n",
      "shortest rebuild period: 2\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 5 / n_max: 11 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 10\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1526.83 | ETA 00:00:00\n",
      "Average TPS: 1526.47\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1839 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 24 / n_neigh_avg: 8.935\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 13 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 11\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1446.93 | ETA 00:00:00\n",
      "Average TPS: 1446.66\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1835 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 24 / n_neigh_avg: 8.945\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 2 / n_max: 12 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 12\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1512.16 | ETA 00:00:00\n",
      "Average TPS: 1511.88\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1853 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 21 / n_neigh_avg: 8.81\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 12 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 13\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1508.2 | ETA 00:00:00\n",
      "Average TPS: 1507.81\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1876 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 21 / n_neigh_avg: 8.87\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 12 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 14\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1500.12 | ETA 00:00:00\n",
      "Average TPS: 1499.76\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1902 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 22 / n_neigh_avg: 8.595\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 10 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 15\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1497.22 | ETA 00:00:00\n",
      "Average TPS: 1496.43\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1952 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 22 / n_neigh_avg: 8.97\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 13 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 16\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1497.51 | ETA 00:00:00\n",
      "Average TPS: 1497.24\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1876 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 24 / n_neigh_avg: 8.74\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 11 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 17\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1531.08 | ETA 00:00:00\n",
      "Average TPS: 1530.71\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1934 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 21 / n_neigh_avg: 8.695\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 3 / n_max: 12 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 18\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1435.61 | ETA 00:00:00\n",
      "Average TPS: 1435.28\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1922 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 22 / n_neigh_avg: 8.83\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 5 / n_max: 11 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 19\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1484.94 | ETA 00:00:00\n",
      "Average TPS: 1484.59\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1974 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 23 / n_neigh_avg: 8.67\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 3 / n_max: 11 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 20\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1491.34 | ETA 00:00:00\n",
      "Average TPS: 1491.02\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1975 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 23 / n_neigh_avg: 8.975\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 3 / n_max: 13 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 21\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1467.32 | ETA 00:00:00\n",
      "Average TPS: 1466.88\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "2001 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 24 / n_neigh_avg: 8.815\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 11 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 22\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1451.02 | ETA 00:00:00\n",
      "Average TPS: 1450.67\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1993 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 24 / n_neigh_avg: 8.785\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 4 / n_max: 13 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 23\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1482.95 | ETA 00:00:00\n",
      "Average TPS: 1482.68\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "2037 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 22 / n_neigh_avg: 8.89\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 5 / n_max: 13 / n_avg: 7.40741\n",
      "** run complete **\n",
      "Operating replica 24\n",
      "notice(2): Group \"all\" created containing 200 particles\n",
      "-----\n",
      "You are using DPD. Please cite the following:\n",
      "* C L Phillips, J A Anderson, and S C Glotzer. \"Pseudo-random number generation\n",
      "  for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU\n",
      "  devices\", Journal of Computational Physics 230 (2011) 7191--7201\n",
      "-----\n",
      "notice(2): -- Neighborlist exclusion statistics -- :\n",
      "notice(2): Particles with 0 exclusions             : 200\n",
      "notice(2): Neighbors included by diameter          : no\n",
      "notice(2): Neighbors excluded when in the same body: no\n",
      "** starting run **\n",
      "Time 00:00:06 | Step 10000 / 10000 | TPS 1517.48 | ETA 00:00:00\n",
      "Average TPS: 1517.18\n",
      "---------\n",
      "-- Neighborlist stats:\n",
      "1948 normal updates / 100 forced updates / 0 dangerous updates\n",
      "n_neigh_min: 0 / n_neigh_max: 25 / n_neigh_avg: 8.85\n",
      "shortest rebuild period: 1\n",
      "-- Cell list stats:\n",
      "Dimension: 3, 3, 3\n",
      "n_min    : 3 / n_max: 11 / n_avg: 7.40741\n",
      "** run complete **\n"
     ]
    }
   ],
   "source": [
    "method = UmbrellaIntegration(cvs, 100.0, centers, 50, int(1e3))\n",
    "raw_result = pysages.run(method, generate_simulation, int(1e4))\n",
    "result = pysages.analyze(raw_result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_xFSKCpKb6XF"
   },
   "source": [
    "What is left after the run is evaluating the resulting histograms for each of the replicas. For a better visualization, we group the histogram into 4 separate plots. This also helps to demonstrate that the histograms overlap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "id": "OOpagwvlb3_d",
    "outputId": "62b507a1-d404-4924-ec1b-00b9d3f39085"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "bins = 50\n",
    "\n",
    "fig, ax = plt.subplots(2, 2)\n",
    "\n",
    "counter = 0\n",
    "hist_per = len(result[\"centers\"]) // 4 + 1\n",
    "\n",
    "for x in range(2):\n",
    "    for y in range(2):\n",
    "        for i in range(hist_per):\n",
    "            if counter+i < len(result[\"centers\"]):\n",
    "                center = np.asarray(result[\"centers\"][counter+i])\n",
    "                histo, edges = result[\"histograms\"][counter+i].get_histograms(bins=bins)\n",
    "                edges = np.asarray(edges)[0]\n",
    "                edges = (edges[1:] + edges[:-1]) / 2\n",
    "                ax[x, y].plot(edges, histo, label=f\"center {center}\")\n",
    "                ax[x, y].legend(loc=\"best\", fontsize=\"xx-small\")\n",
    "                ax[x, y].set_yscale(\"log\")\n",
    "        counter += hist_per\n",
    "\n",
    "while counter < len(result[\"centers\"]):\n",
    "    center = np.asarray(result[\"centers\"][counter])\n",
    "    histo, edges = result[\"histograms\"][counter].get_histograms(bins=bins)\n",
    "    edges = np.asarray(edges)[0]\n",
    "    edges = (edges[1:] + edges[:-1]) / 2\n",
    "    ax[1,1].plot(edges, histo, label=f\"center {center}\")\n",
    "    counter += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5YZYZPUqdG7S"
   },
   "source": [
    "And finally, as the last step, we can visualize the estimated free-energy path from the histograms and compare it with the analytical shape of the input external potential."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "_UKh6FyLcN9y",
    "outputId": "cba839f6-78e8-43c3-f540-5567c5c4b00e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d418b8b50>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "def external_field(r, A, p, w, **kwargs):\n",
    "    return A * np.tanh(1 / (2 * np.pi * p * w) * np.cos(p * r))\n",
    "\n",
    "x = np.linspace(-2, 2, 100)\n",
    "data = external_field(x, **periodic_params[\"A\"])\n",
    "\n",
    "centers = np.asarray(result[\"centers\"])\n",
    "free_energy = np.asarray(result[\"free_energy\"])\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_xlabel(\"CV\")\n",
    "ax.set_ylabel(\"Free energy $[\\epsilon]$\")\n",
    "ax.plot(x, data - np.min(data), label=\"test\")\n",
    "ax.plot(centers, free_energy - np.min(free_energy), color=\"teal\")\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd6fc3f6",
   "metadata": {
    "id": "IXryBllMNiKM"
   },
   "source": [
    "We can see, that the particle positions are indeed centered around the constraint values we set up earlier. Also, we see the shape of the histograms is very similar to the expected analytical prediction. We expect this since a liquid of soft particles is not that much different from an ideal gas."
   ]
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "collapsed_sections": [],
   "name": "Umbrella-Integration-PySAGES-HOOMD.ipynb",
   "provenance": [],
   "toc_visible": true
  },
  "jupytext": {
   "formats": "ipynb,md",
   "main_language": "python"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "name": "python3"
  },
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}