02 - Integrators and sampling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Integrators and sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Preliminary imports\n",
    "from simtk import openmm, unit\n",
    "from simtk.openmm import app\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To explore the integrators available for sampling in OpenMM, we'll use the alanine dipeptide in vacuum test system imported from [`openmmtools`](http://openmmtools.readthedocs.io):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create an alanine dipeptide in vacuum\n",
    "from openmmtools import testsystems\n",
    "t = testsystems.AlanineDipeptideVacuum()\n",
    "system, positions, topology = t.system, t.positions, t.topology"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integrators available for use\n",
    "\n",
    "There are several ways to specify which integrators to use for sampling:\n",
    "* Use one of the [built-in OpenMM integrators](http://docs.openmm.org/7.1.0/api-python/library.html#integrators)\n",
    "* Use the powerful [`CustomIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.CustomIntegrator.html#simtk.openmm.openmm.CustomIntegrator) facility to define your own integrator in terms of basic algebraic operations on positions and velocities\n",
    "* Use one of the high-quality integrators from [`openmmtools.integrators`](http://openmmtools.readthedocs.io/en/latest/integrators.html)\n",
    "* Write your own integrator plugin using C++ (and CUDA or OpenCL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Built-in OpenMM integrators\n",
    "\n",
    "OpenMM provides a number of built-in [`Integrators`](http://docs.openmm.org/7.1.0/userguide/application.html#integrators) that may be useful for your intended application, but also provides a very flexible way to efficiently define new integrators that can still be executed very efficiently on the GPU.\n",
    "\n",
    "All OpenMM integrators are derived from the [`Integrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.Integrator.html#simtk.openmm.openmm.Integrator) base class that provides some baseline functionality such that all integrators work the same way. \n",
    "\n",
    "OpenMM provides a [large number of integrators you can use directly](http://docs.openmm.org/7.1.0/api-python/library.html#integrators). Here are just a few of them:\n",
    "* [`VerletIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.VerletIntegrator.html#simtk.openmm.openmm.VerletIntegrator): A leapfrog Verlet integrator where the positions and velocities are half a timestep out of sync. This is useful in many situations, but care must be taken regarding the half timestep lag.\n",
    "* [`LangevinIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.LangevinIntegrator.html#simtk.openmm.openmm.LangevinIntegrator): A [leapfrog Langevin](https://github.com/pandegroup/openmm/issues/1766#issuecomment-289615072) / [VVVR](http://dx.doi.org/10.1103/PhysRevX.3.011007) / [Bussi-Parrinello](10.1103/PhysRevE.75.056707) Langevin integrator where the velocity is shifted from the positions by half a timestep.\n",
    "* [`MTSIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.mtsintegrator.MTSIntegrator.html#simtk.openmm.mtsintegrator.MTSIntegrator): A multiple-timestep integrator following [rRESPA from Tuckerman and Berne](http://dx.doi.org/10.1063/1.463137).\n",
    "* [`AMDIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.amd.AMDIntegrator.html#simtk.openmm.amd.AMDIntegrator): An integrator that implements the [accelerated MD algorithm of McCammon](https://doi.org/10.1063/1.2789432), though care must be taken in noting the potential energy reported is not actually modified.\n",
    "* Experimental variable-timestep integrators [`VariableVerletIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.VariableVerletIntegrator.html#simtk.openmm.openmm.VariableVerletIntegrator) and [`VariableLangevinIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.VariableLangevinIntegrator.html#simtk.openmm.openmm.VariableLangevinIntegrator) that should be used cautiously since they are no longer sympletic, but may be useful when forces are very large."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### OpenMM's `LangevinIntegrator`\n",
    "\n",
    "Let's create a [`LangevinIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.LangevinIntegrator.html#simtk.openmm.openmm.LangevinIntegrator), which uses a version of [velocity Verlet with velocity randomization (VVVR)](http://dx.doi.org/10.1103/PhysRevX.3.011007), also known as the [Bussi-Parrinello Langevin integrator](10.1103/PhysRevE.75.056707), where the velocity is shifted from the positions by half a timestep.\n",
    "\n",
    "We first have to create a [`LangevinIntegrator`](http://docs.openmm.org/7.1.0/api-python/library.html#integrators) and bind it to a [`Context`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.Context.html#simtk.openmm.openmm.Context). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create a new integrator since the previously-created integrator was irrevocably bound to the previous Context\n",
    "temperature = 298.0 * unit.kelvin\n",
    "collision_rate = 91.0 / unit.picosecond\n",
    "timestep = 2.0 * unit.femtoseconds\n",
    "integrator = openmm.LangevinIntegrator(temperature, collision_rate, timestep)\n",
    "# Create a Context for this integrator\n",
    "context = openmm.Context(system, integrator)\n",
    "# Set the positions\n",
    "context.setPositions(positions)\n",
    "# Minimize the potential energy\n",
    "openmm.LocalEnergyMinimizer.minimize(context)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial velocities are, by default, zero, but we can select initial velocities from the Maxwell distribution with [`context.setVelocitiesToTemperature()`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.Context.html#simtk.openmm.openmm.Context.setVelocitiesToTemperature):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Set velocities from Maxwell-Boltzmann distribution\n",
    "context.setVelocitiesToTemperature(temperature)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To integrate a trajectory, we call [`integrator.step`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.Integrator.html#simtk.openmm.openmm.Integrator.step):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Integrate some dynamics\n",
    "nsteps = 100 # number of integrator steps\n",
    "integrator.step(nsteps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can write a little loop to report some information every few timesteps:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0.400 ps : potential   -61.905959 kJ/mol\n",
      "   0.600 ps : potential   -68.611887 kJ/mol\n",
      "   0.800 ps : potential   -56.856249 kJ/mol\n",
      "   1.000 ps : potential   -53.224507 kJ/mol\n",
      "   1.200 ps : potential   -46.608933 kJ/mol\n",
      "   1.400 ps : potential   -44.661197 kJ/mol\n",
      "   1.600 ps : potential   -79.666820 kJ/mol\n",
      "   1.800 ps : potential   -55.995149 kJ/mol\n",
      "   2.000 ps : potential   -41.718949 kJ/mol\n",
      "   2.200 ps : potential   -14.412992 kJ/mol\n"
     ]
    }
   ],
   "source": [
    "# Run a few iterations of a few steps each, reporting potential energy\n",
    "for iteration in range(10):\n",
    "    integrator.step(100)\n",
    "    state = context.getState(getEnergy=True)\n",
    "    print('%8.3f ps : potential %12.6f kJ/mol' % (state.getTime() / unit.picoseconds, state.getPotentialEnergy() / unit.kilojoules_per_mole))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## The `Simulation` convenience class\n",
    "\n",
    "While we could write our own wrapper to run a simulation and write data to disk, OpenMM's [`app` layer](http://docs.openmm.org/7.1.0/api-python/app.html) provides the [`Simulation` class](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.app.simulation.Simulation.html#simtk.openmm.app.simulation.Simulation) to help you do this using a modular Python-based plugin architecture to specify which and how data should be stored. The [user guide](http://docs.openmm.org/7.1.0/userguide/application.html#a-first-example) provides a nice overview of this.\n",
    "\n",
    "### Running a `Simulation` that writes data to the terminal\n",
    "\n",
    "For example, to run a simulation that prints data to the terminal, we can use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#\"Step\",\"Potential Energy (kJ/mole)\",\"Temperature (K)\"\n",
      "100,-62.9054570957087,286.01895827090476\n",
      "200,-64.33437593944836,347.42175703278053\n",
      "300,-67.72941304871347,304.51604091122385\n",
      "400,-64.22377510619117,390.58958557742034\n",
      "500,-61.07334367545991,264.6725483897139\n",
      "600,-64.18695589900017,263.4275585831681\n",
      "700,-63.81141036003828,302.9999995436537\n",
      "800,-55.093099682591856,269.23174668004293\n",
      "900,-50.787087897304446,483.4972334970732\n",
      "1000,-66.6517731687054,407.2612586386403\n"
     ]
    }
   ],
   "source": [
    "from sys import stdout\n",
    "integrator = openmm.LangevinIntegrator(temperature, collision_rate, timestep)\n",
    "simulation = app.Simulation(topology, system, integrator)\n",
    "simulation.context.setPositions(positions)\n",
    "simulation.minimizeEnergy()\n",
    "simulation.reporters.append(app.StateDataReporter(stdout, 100, step=True, potentialEnergy=True, temperature=True))\n",
    "simulation.step(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Running a `Simulation` that writes a trajectory to disk\n",
    "\n",
    "For example, to run a simulation that writes data in the extensible MDTraj HDF5 format, Amber NetCDF format, or CHARMM DCD format, we can use the [MDTraj Reporters](http://mdtraj.org/1.6.2/api/reporters.html):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/choderaj/miniconda3/lib/python3.5/site-packages/mdtraj/utils/validation.py:116: TypeCastPerformanceWarning: Casting xyz dtype=float64 to <class 'numpy.float32'> \n",
      "  TypeCastPerformanceWarning)\n"
     ]
    }
   ],
   "source": [
    "import mdtraj\n",
    "integrator = openmm.LangevinIntegrator(temperature, collision_rate, timestep)\n",
    "simulation = app.Simulation(topology, system, integrator)\n",
    "simulation.context.setPositions(positions)\n",
    "simulation.minimizeEnergy()\n",
    "reportInterval = 100\n",
    "simulation.reporters.append(mdtraj.reporters.HDF5Reporter('output.h5', reportInterval, coordinates=True, time=True, cell=True, potentialEnergy=True, temperature=True))\n",
    "simulation.reporters.append(mdtraj.reporters.DCDReporter('output.dcd', reportInterval))\n",
    "simulation.reporters.append(mdtraj.reporters.NetCDFReporter('output.nc', reportInterval))\n",
    "simulation.step(2000)\n",
    "del simulation # Make sure to close all files"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We can easily view a trajectory in MDTraj."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b19596ffcd2d4bb5bfc4e0822f771229"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "traj = mdtraj.load('output.h5', 'r')\n",
    "import nglview\n",
    "view = nglview.show_mdtraj(traj)\n",
    "view.add_ball_and_stick('all')\n",
    "view.center_view(zoom=True)\n",
    "view"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Using multiple integrators with `CompoundIntegrator`\n",
    "\n",
    "Sometimes, it's useful to switch between multiple integrators without incurring the overhead of tearing down and setting up a new [`Context`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.Context.html#simtk.openmm.openmm.Context). We can do this with [`CompoundIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.CompoundIntegrator.html#simtk.openmm.openmm.CompoundIntegrator`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#\"Step\",\"Potential Energy (kJ/mole)\",\"Temperature (K)\"\n",
      "100,-60.64755020593293,239.18009122786273\n",
      "200,-61.795576034113765,362.03493769001295\n",
      "300,-72.56706993073203,213.3772931139509\n",
      "400,-54.83631915599108,234.63283247451068\n",
      "500,-77.72501386667136,302.5295557999244\n",
      "600,-57.91668747761287,195.10468882675625\n",
      "700,-54.702352833002806,256.0834849750133\n",
      "800,-74.0872640889138,335.15020829593345\n",
      "900,-52.89097060263157,271.1203304521301\n",
      "1000,-72.65809746505693,327.0748051910193\n"
     ]
    }
   ],
   "source": [
    "# Define a CompoundIntegrator with high- and low-friction integrators\n",
    "integrator = openmm.CompoundIntegrator()\n",
    "integrator.addIntegrator(openmm.LangevinIntegrator(temperature, 91/unit.picosecond, timestep)) # high friction\n",
    "integrator.addIntegrator(openmm.LangevinIntegrator(temperature, 1/unit.picosecond, timestep)) # low friction\n",
    "simulation = app.Simulation(topology, system, integrator)\n",
    "simulation.reporters.append(app.StateDataReporter(stdout, 100, step=True, potentialEnergy=True, temperature=True))\n",
    "simulation.context.setPositions(positions)\n",
    "simulation.minimizeEnergy()\n",
    "# Simulate with high friction\n",
    "integrator.setCurrentIntegrator(0)\n",
    "simulation.step(500)\n",
    "# Simulate with low friction\n",
    "integrator.setCurrentIntegrator(1)\n",
    "simulation.step(500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Writing your own integrator with `CustomIntegrator`\n",
    "\n",
    "OpenMM provides an enormously flexible way of creating your own integrators to implement most discrete timestep integrator schemes using [`CustomIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.Integrator.html#simtk.openmm.openmm.Integrator). By simply defining the algebraic update equations for each step of the integrator, OpenMM will automatically build custom CUDA or OpenCL kernels for you that implement your integrator on the GPU without the need to move positions or forces back and forth across the bus, which enables you to achieve native GPU performance with a fully custom integrator."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Velocity Verlet as a `CustomIntegrator`\n",
    "\n",
    "As an example, let's implement velocity Verlet as a [`CustomIntegrator`](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.CustomIntegrator.html#simtk.openmm.openmm.CustomIntegrator).\n",
    "\n",
    "For velocity Verlet without constraints, the update equations are\n",
    "```\n",
    "v_{t+1/2} = v_t + 0.5 * dt * f/m\n",
    "x_t+1     = x_t + dt * v_t\n",
    "v_{t+1}   = v_{t+1/2} + 0.5 * dt * f/m\n",
    "```\n",
    "The implementation (which could be as an integrator or a subclass) follows the equations very closely:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Implement velocity Verlet (without constraints) as a CustomIntegrator\n",
    "integrator = openmm.CustomIntegrator(1.0 * unit.femtoseconds)\n",
    "integrator.addUpdateContextState() # allow barostat and other updates\n",
    "integrator.addComputePerDof(\"v\", \"v+0.5*dt*f/m\")\n",
    "integrator.addComputePerDof(\"x\", \"x+dt*v\")\n",
    "integrator.addComputePerDof(\"v\", \"v+0.5*dt*f/m\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Implement velocity Verlet (without constraints) as a subclass of CustomIntegrator\n",
    "class UnconstrainedVelocityVerlet(openmm.CustomIntegrator):\n",
    "    def __init__(self, timestep):\n",
    "        super(UnconstrainedVelocityVerlet, self).__init__(timestep)\n",
    "        self.addUpdateContextState()\n",
    "        self.addComputePerDof(\"v\", \"v+0.5*dt*f/m\")\n",
    "        self.addComputePerDof(\"x\", \"x+dt*v\")\n",
    "        self.addComputePerDof(\"v\", \"v+0.5*dt*f/m\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#\"Step\",\"Potential Energy (kJ/mole)\",\"Temperature (K)\"\n",
      "100,-127.77282452094369,286.3273670076637\n",
      "200,-131.89038940146565,308.01981723569605\n",
      "300,-33.780074902810156,633.1154202537523\n",
      "400,-26.982670115902692,606.0901425212013\n",
      "500,-27.576255827210844,608.600851442005\n",
      "600,-9.853612564504147,525.2376649715369\n",
      "700,-24.56833182182163,593.1140681896692\n",
      "800,-24.22325546797947,592.141947546782\n",
      "900,-29.777317664120346,618.4986696833976\n",
      "1000,-15.503658221103251,553.173709813896\n"
     ]
    }
   ],
   "source": [
    "# Now use this subclass in a simulation!\n",
    "integrator = UnconstrainedVelocityVerlet(1.0 * unit.femtoseconds)\n",
    "simulation = app.Simulation(topology, system, integrator)\n",
    "simulation.context.setPositions(positions)\n",
    "simulation.minimizeEnergy()\n",
    "simulation.context.setVelocitiesToTemperature(temperature)\n",
    "reportInterval = 100\n",
    "simulation.reporters.append(app.StateDataReporter(stdout, 100, step=True, potentialEnergy=True, temperature=True))\n",
    "simulation.step(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What else can you do with `CustomIntegrator`?\n",
    "\n",
    "You can also implement integrators with a variety of other features:\n",
    "* SHAKE/RATTLE constraints\n",
    "* stochastic integrators that make use of Gaussian or uniform noise kernels\n",
    "* (hybrid) Monte Carlo schemes that accept/reject proposed configurations\n",
    "* control flow inside integrators\n",
    "* nonequilibrium integrators that change the potential (via [global Context variables]()) during integration\n",
    "\n",
    "See the [`CustomIntegrator` documentation](http://docs.openmm.org/7.1.0/api-python/generated/simtk.openmm.openmm.CustomIntegrator.html#simtk.openmm.openmm.CustomIntegrator) for more information. There are also plenty of examples that do all of these things in [`openmmtools.integrators`](http://openmmtools.readthedocs.io/en/latest/integrators.html) that you can examine the source for! (Remember you can do that in Jupyter with the `??` command.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integrators available in `openmmtools.integrators`\n",
    "\n",
    "The [`openmmtools.integrators`](http://openmmtools.readthedocs.io/en/latest/integrators.html) module provides a wide variety of high-quality integrators you can use. This includes:\n",
    "\n",
    "* A fully general [`LangevinIntegrator`](http://openmmtools.readthedocs.io/en/latest/api/generated/openmmtools.integrators.LangevinIntegrator.html#openmmtools.integrators.LangevinIntegrator) that will automatically construct any Trotter splittings of the Langevin propagator you desire, and can Metropolize them if needed\n",
    "* Popular Langevin integrators like [`VVVRIntegrator`](http://openmmtools.readthedocs.io/en/latest/api/generated/openmmtools.integrators.VVVRIntegrator.html#openmmtools.integrators.VVVRIntegrator) and [`BAOABIntegrator`](http://openmmtools.readthedocs.io/en/latest/api/generated/openmmtools.integrators.BAOABIntegrator.html#openmmtools.integrators.BAOABIntegrator)\n",
    "* Metropolized integrators like those that use velocity Verlet ([`HMCIntegrator`](http://openmmtools.readthedocs.io/en/latest/api/generated/openmmtools.integrators.HMCIntegrator.html#openmmtools.integrators.HMCIntegrator)) or Langevin ([`GHMCIntegrator`](http://openmmtools.readthedocs.io/en/latest/api/generated/openmmtools.integrators.GHMCIntegrator.html#openmmtools.integrators.GHMCIntegrator)) cores\n",
    "* Metropolis Monte Carlo integrators, like [`MetropolisMonteCarloIntegrator`](http://openmmtools.readthedocs.io/en/latest/api/generated/openmmtools.integrators.MetropolisMonteCarloIntegrator.html#openmmtools.integrators.MetropolisMonteCarloIntegrator)\n",
    "* Nonequilibrium integrators that correctly track protocol work, shadow work, and heat, and either change Context variables on the fly ([`AlchemicalNonequilibriumLangevinIntegrator`](http://openmmtools.readthedocs.io/en/latest/api/generated/openmmtools.integrators.AlchemicalNonequilibriumLangevinIntegrator.html#openmmtools.integrators.AlchemicalNonequilibriumLangevinIntegrator)) or allow you to make the perturbations yourself by calling `updateParametersInContext` for individual `Force` objects ([`ExternalPerturbationLangevinIntegrator`](`http://openmmtools.readthedocs.io/en/latest/api/generated/openmmtools.integrators.ExternalPerturbationLangevinIntegrator.html#openmmtools.integrators.ExternalPerturbationLangevinIntegrator))\n"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### OpenMMTools general `LangevinIntegrator` provides access to a whole family of integrators\n",
    "\n",
    "Langevin dynamics is described by equations of motion that cannot be integrated exactly, but for which exact solutions exist for integration distinct pieces of the equations of motion called `R`, `V`, and `O`:\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "High-quality Langevin integrators are based on symmetric Trotter splittings of the Langevin operator. \n",
    "Different splittings of the Langevin propagator result in inequivalent update equations:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "We can use [`openmmtools.integrators.LangevinIntegrator`](http://openmmtools.readthedocs.io/en/latest/api/generated/openmmtools.integrators.LangevinIntegrator.html#openmmtools.integrators.LangevinIntegrator) to automatically construct integrators that appropriately respect constraints."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, the OVRVO splitting would result in the following equations: \n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generate an integrator with the  `VRORV` (BAOAB) splitting championed by [Leimkuhler and Matthews](http://dx.doi.org/10.1063/1.4802990), which has minimal configurational error even close to the stability limit, we simply specify this in the `splitting` string:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#\"Step\",\"Potential Energy (kJ/mole)\",\"Temperature (K)\"\n",
      "100,-67.16098641697317,331.39432585096176\n",
      "200,-56.77709147334099,330.5416736713131\n",
      "300,-68.85795614868402,293.40220303789624\n",
      "400,-67.32519708503969,359.62986949438505\n",
      "500,-75.15428447266459,352.7438799988138\n",
      "600,-69.15727468896512,313.61209281851245\n",
      "700,-51.05764958751388,292.25541374423835\n",
      "800,-62.27562237903476,298.58983317820787\n",
      "900,-69.62062949687243,273.3599649350594\n",
      "1000,-62.73300904035568,356.77270203019003\n"
     ]
    }
   ],
   "source": [
    "# Construct an integrator with the VRORV (BAOAB) splitting\n",
    "from openmmtools import integrators\n",
    "integrator = integrators.LangevinIntegrator(temperature=temperature, collision_rate=collision_rate, timestep=timestep,\n",
    "                                           splitting='V R O R V')\n",
    "simulation = app.Simulation(topology, system, integrator)\n",
    "simulation.context.setPositions(positions)\n",
    "simulation.minimizeEnergy()\n",
    "simulation.context.setVelocitiesToTemperature(temperature)\n",
    "reportInterval = 100\n",
    "simulation.reporters.append(app.StateDataReporter(stdout, 100, step=True, potentialEnergy=True, temperature=True))\n",
    "simulation.step(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also Metropolize the integrator by inserting `{` and `}` characters where we want to Metropolize away any shadow work. For GHMC with a velocity Verlet (`V R V`) core, we can use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create GHMC integrator based on OVRVO with inner velocity Verlet step Metropolized\n",
    "integrator = integrators.LangevinIntegrator(temperature=temperature, collision_rate=collision_rate, timestep=timestep,\n",
    "                                           splitting='O { V R V } O')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#\"Step\",\"Potential Energy (kJ/mole)\",\"Temperature (K)\"\n",
      "100,-50.94500440172851,316.5890885907146\n",
      "200,-70.86862775118789,425.7851351833933\n",
      "300,-74.25950151728466,453.4474461101337\n",
      "400,-64.15730081126094,307.977283584025\n",
      "500,-56.92715934396256,322.7432617799971\n",
      "600,-50.704172395169735,228.08857827861158\n",
      "700,-69.33136096945964,361.78764266595925\n",
      "800,-76.94631380029023,327.69454587616735\n",
      "900,-61.15952996502165,241.43007497285038\n",
      "1000,-50.48465806245804,391.5968234677794\n"
     ]
    }
   ],
   "source": [
    "simulation = app.Simulation(topology, system, integrator)\n",
    "simulation.context.setPositions(positions)\n",
    "simulation.minimizeEnergy()\n",
    "simulation.context.setVelocitiesToTemperature(temperature)\n",
    "reportInterval = 100\n",
    "simulation.reporters.append(app.StateDataReporter(stdout, 100, step=True, potentialEnergy=True, temperature=True))\n",
    "simulation.step(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step      0 : allow forces to update the context state\n",
      "step      1 : if(has_kT_changed = 1):\n",
      "step      2 :    sigma <- sqrt(kT/m)\n",
      "step      3 :    has_kT_changed <- 0\n",
      "step      4 : end\n",
      "step      5 : v <- (a * v) + (b * sigma * gaussian)\n",
      "step      6 : constrain velocities\n",
      "step      7 : xold <- x\n",
      "step      8 : vold <- v\n",
      "step      9 : old_ke <- sum(0.5 * m * v * v)\n",
      "step     10 : v <- v + (dt / 2) * f / m\n",
      "step     11 : constrain velocities\n",
      "step     12 : new_ke <- sum(0.5 * m * v * v)\n",
      "step     13 : shadow_work <- shadow_work + (new_ke - old_ke)\n",
      "step     14 : old_pe <- energy\n",
      "step     15 : old_ke <- sum(0.5 * m * v * v)\n",
      "step     16 : x <- x + ((dt / 1) * v)\n",
      "step     17 : x1 <- x\n",
      "step     18 : constrain positions\n",
      "step     19 : v <- v + ((x - x1) / (dt / 1))\n",
      "step     20 : constrain velocities\n",
      "step     21 : new_pe <- energy\n",
      "step     22 : new_ke <- sum(0.5 * m * v * v)\n",
      "step     23 : shadow_work <- shadow_work + (new_ke + new_pe) - (old_ke + old_pe)\n",
      "step     24 : old_ke <- sum(0.5 * m * v * v)\n",
      "step     25 : v <- v + (dt / 2) * f / m\n",
      "step     26 : constrain velocities\n",
      "step     27 : new_ke <- sum(0.5 * m * v * v)\n",
      "step     28 : shadow_work <- shadow_work + (new_ke - old_ke)\n",
      "step     29 : accept <- step(exp(-(shadow_work)/kT) - uniform)\n",
      "step     30 : ntrials <- ntrials + 1\n",
      "step     31 : if(accept != 1):\n",
      "step     32 :    x <- xold\n",
      "step     33 :    v <- -vold\n",
      "step     34 :    nreject <- nreject + 1\n",
      "step     35 : end\n",
      "step     36 : naccept <- ntrials - nreject\n",
      "step     37 : shadow_work <- 0\n",
      "step     38 : v <- (a * v) + (b * sigma * gaussian)\n",
      "step     39 : constrain velocities\n"
     ]
    }
   ],
   "source": [
    "# We can even pretty-print LangevinIntegrator to inspect what it does\n",
    "integrator.pretty_print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can introduce multiple-timestepping by using [force groups](http://docs.openmm.org/7.1.0/userguide/theory.html#force-groups). For example, let's move the `NonbondedForce` to force group 1 and leave all other valence forces in force group 0:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for force in system.getForces():\n",
    "    if force.__class__.__name__ in ['NonbondedForce']:\n",
    "        force.setForceGroup(1)\n",
    "    else:\n",
    "        force.setForceGroup(0)\n",
    "        \n",
    "# Create multiple-timestep integrator version of OVRVO\n",
    "integrator = integrators.LangevinIntegrator(temperature=temperature, collision_rate=collision_rate, timestep=timestep,\n",
    "                                           splitting='O V1 V0 V0 R V0 V0 V1 O')        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#\"Step\",\"Potential Energy (kJ/mole)\",\"Temperature (K)\"\n",
      "100,-71.78612236864865,287.89150426416455\n",
      "200,-28.55955516709946,304.3825782817174\n",
      "300,-32.27793036978983,293.5305956514006\n",
      "400,-54.082260109484196,282.3200457012227\n",
      "500,-41.46222233248409,232.26141018645774\n",
      "600,-79.86386944167316,244.18488459256298\n",
      "700,-56.59906441566909,349.993730368857\n",
      "800,-69.21101092477329,352.3312100179651\n",
      "900,-63.39392724260688,326.8612533450796\n",
      "1000,-56.1127566841169,326.8732721603572\n"
     ]
    }
   ],
   "source": [
    "simulation = app.Simulation(topology, system, integrator)\n",
    "simulation.context.setPositions(positions)\n",
    "simulation.minimizeEnergy()\n",
    "simulation.context.setVelocitiesToTemperature(temperature)\n",
    "reportInterval = 100\n",
    "simulation.reporters.append(app.StateDataReporter(stdout, 100, step=True, potentialEnergy=True, temperature=True))\n",
    "simulation.step(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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