# Source code for propertyestimator.protocols.utils

    """
    A set of utilities for setting up property estimation workflows.
    """
    import copy
    from collections import namedtuple

    from propertyestimator import unit
    from propertyestimator.protocols import analysis, forcefield, gradients, groups, reweighting, coordinates, simulation, \
        storage
    from propertyestimator.thermodynamics import Ensemble
    from propertyestimator.utils.statistics import ObservableType
    from propertyestimator.workflow import WorkflowOptions
    from propertyestimator.workflow.plugins import available_protocols
    from propertyestimator.workflow.schemas import ProtocolReplicator, WorkflowSimulationDataToStore
    from propertyestimator.workflow.utils import ProtocolPath, ReplicatorValue

    BaseReweightingProtocols = namedtuple('BaseReweightingProtocols', 'unpack_stored_data '
                                                                      'analysis_protocol '
                                                                      'decorrelate_statistics '
                                                                      'decorrelate_trajectory '
                                                                      'concatenate_trajectories '
                                                                      'concatenate_statistics '
                                                                      'build_reference_system '
                                                                      'reduced_reference_potential '
                                                                      'build_target_system '
                                                                      'reduced_target_potential '
                                                                      'mbar_protocol ')

    BaseSimulationProtocols = namedtuple('BaseSimulationProtocols', 'build_coordinates '
                                                                    'assign_parameters '
                                                                    'energy_minimisation '
                                                                    'equilibration_simulation '
                                                                    'production_simulation '
                                                                    'analysis_protocol '
                                                                    'converge_uncertainty '
                                                                    'extract_uncorrelated_trajectory '
                                                                    'extract_uncorrelated_statistics ')

    def generate_base_reweighting_protocols(analysis_protocol, mbar_protocol, workflow_options,
                                            replicator_id='data_repl', id_suffix=''):
        """Constructs a set of protocols which, when combined in a workflow schema,
        may be executed to reweight a set of existing data to estimate a particular
        property. The reweighted observable of interest will be calculated by
        following the passed in `analysis_protocol`.

        Parameters
        ----------
        analysis_protocol: AveragePropertyProtocol
            The protocol which will take input from the stored data,
            and generate a set of observables to reweight.
        mbar_protocol: BaseReweightingProtocol
            A template mbar reweighting protocol, which has it's reference
            observables already set. This method will automatically set the
            reduced potentials on this object.
        workflow_options: WorkflowOptions
            The options being used to generate a workflow.
        replicator_id: str
            The id to use for the data replicator.
        id_suffix: str
            A string suffix to append to each of the protocol ids.

        Returns
        -------
        BaseReweightingProtocols:
            A named tuple of the protocol which should form the bulk of
            a property estimation workflow.
        ProtocolReplicator:
            A replicator which will clone the workflow for each piece of
            stored data.
        """

        assert isinstance(analysis_protocol, analysis.AveragePropertyProtocol)

        assert f'$({replicator_id})' in analysis_protocol.id
        assert f'$({replicator_id})' not in mbar_protocol.id

        replicator_suffix = '_$({}){}'.format(replicator_id, id_suffix)

        # Unpack all the of the stored data.
        unpack_stored_data = storage.UnpackStoredSimulationData('unpack_data{}'.format(replicator_suffix))
        unpack_stored_data.simulation_data_path = ReplicatorValue(replicator_id)

        # The autocorrelation time of each of the stored files will be calculated for this property
        # using the passed in analysis protocol.
        if isinstance(analysis_protocol, analysis.ExtractAverageStatistic):

            analysis_protocol.statistics_path = ProtocolPath('statistics_file_path', unpack_stored_data.id)

        elif isinstance(analysis_protocol, analysis.AverageTrajectoryProperty):

            analysis_protocol.input_coordinate_file = ProtocolPath('coordinate_file_path', unpack_stored_data.id)
            analysis_protocol.trajectory_path = ProtocolPath('trajectory_file_path', unpack_stored_data.id)

        # Decorrelate the frames of the stored trajectory and statistics arrays.
        decorrelate_statistics = analysis.ExtractUncorrelatedStatisticsData('decorrelate_stats{}'.format(replicator_suffix))
        decorrelate_statistics.statistical_inefficiency = ProtocolPath('statistical_inefficiency', analysis_protocol.id)
        decorrelate_statistics.equilibration_index = ProtocolPath('equilibration_index', analysis_protocol.id)
        decorrelate_statistics.input_statistics_path = ProtocolPath('statistics_file_path', unpack_stored_data.id)

        decorrelate_trajectory = analysis.ExtractUncorrelatedTrajectoryData('decorrelate_traj{}'.format(replicator_suffix))
        decorrelate_trajectory.statistical_inefficiency = ProtocolPath('statistical_inefficiency', analysis_protocol.id)
        decorrelate_trajectory.equilibration_index = ProtocolPath('equilibration_index', analysis_protocol.id)
        decorrelate_trajectory.input_coordinate_file = ProtocolPath('coordinate_file_path', unpack_stored_data.id)
        decorrelate_trajectory.input_trajectory_path = ProtocolPath('trajectory_file_path', unpack_stored_data.id)

        # Stitch together all of the trajectories
        join_trajectories = reweighting.ConcatenateTrajectories('concat_traj' + id_suffix)
        join_trajectories.input_coordinate_paths = ProtocolPath('coordinate_file_path', unpack_stored_data.id)
        join_trajectories.input_trajectory_paths = ProtocolPath('output_trajectory_path', decorrelate_trajectory.id)

        join_statistics = reweighting.ConcatenateStatistics('concat_stats' + id_suffix)
        join_statistics.input_statistics_paths = ProtocolPath('output_statistics_path', decorrelate_statistics.id)

        # Calculate the reduced potentials for each of the reference states.
        build_reference_system = forcefield.BuildSmirnoffSystem('build_system{}'.format(replicator_suffix))
        build_reference_system.force_field_path = ProtocolPath('force_field_path', unpack_stored_data.id)
        build_reference_system.substance = ProtocolPath('substance', unpack_stored_data.id)
        build_reference_system.coordinate_file_path = ProtocolPath('coordinate_file_path', unpack_stored_data.id)

        reduced_reference_potential = reweighting.CalculateReducedPotentialOpenMM('reduced_potential{}'.format(
                                                                                  replicator_suffix))
        reduced_reference_potential.system_path = ProtocolPath('system_path', build_reference_system.id)
        reduced_reference_potential.thermodynamic_state = ProtocolPath('thermodynamic_state', unpack_stored_data.id)
        reduced_reference_potential.coordinate_file_path = ProtocolPath('coordinate_file_path', unpack_stored_data.id)
        reduced_reference_potential.trajectory_file_path = ProtocolPath('output_trajectory_path', join_trajectories.id)
        reduced_reference_potential.kinetic_energies_path = ProtocolPath('output_statistics_path', join_statistics.id)

        # Calculate the reduced potential of the target state.
        build_target_system = forcefield.BuildSmirnoffSystem('build_system_target' + id_suffix)
        build_target_system.force_field_path = ProtocolPath('force_field_path', 'global')
        build_target_system.substance = ProtocolPath('substance', 'global')
        build_target_system.coordinate_file_path = ProtocolPath('output_coordinate_path', join_trajectories.id)

        reduced_target_potential = reweighting.CalculateReducedPotentialOpenMM('reduced_potential_target' + id_suffix)
        reduced_target_potential.thermodynamic_state = ProtocolPath('thermodynamic_state', 'global')
        reduced_target_potential.system_path = ProtocolPath('system_path', build_target_system.id)
        reduced_target_potential.coordinate_file_path = ProtocolPath('output_coordinate_path', join_trajectories.id)
        reduced_target_potential.trajectory_file_path = ProtocolPath('output_trajectory_path', join_trajectories.id)
        reduced_target_potential.kinetic_energies_path = ProtocolPath('output_statistics_path', join_statistics.id)

        # Finally, apply MBAR to get the reweighted value.
        mbar_protocol.reference_reduced_potentials = ProtocolPath('statistics_file_path', reduced_reference_potential.id)
        mbar_protocol.target_reduced_potentials = [ProtocolPath('statistics_file_path', reduced_target_potential.id)]

        if (isinstance(mbar_protocol, reweighting.ReweightStatistics) and
            mbar_protocol.statistics_type != ObservableType.PotentialEnergy and
            mbar_protocol.statistics_type != ObservableType.TotalEnergy and
            mbar_protocol.statistics_type != ObservableType.Enthalpy and
            mbar_protocol.statistics_type != ObservableType.ReducedPotential):

            mbar_protocol.statistics_paths = ProtocolPath('output_statistics_path', decorrelate_statistics.id)

        elif isinstance(mbar_protocol, reweighting.ReweightStatistics):

            mbar_protocol.statistics_paths = [ProtocolPath('statistics_file_path', reduced_target_potential.id)]
            mbar_protocol.frame_counts = ProtocolPath('number_of_uncorrelated_samples', decorrelate_statistics.id)

        # TODO: Implement a cleaner way to handle this.
        if workflow_options.convergence_mode == WorkflowOptions.ConvergenceMode.NoChecks:
            mbar_protocol.required_effective_samples = -1

        base_protocols = BaseReweightingProtocols(unpack_stored_data,
                                                  analysis_protocol,
                                                  decorrelate_statistics,
                                                  decorrelate_trajectory,
                                                  join_trajectories,
                                                  join_statistics,
                                                  build_reference_system,
                                                  reduced_reference_potential,
                                                  build_target_system,
                                                  reduced_target_potential,
                                                  mbar_protocol)

        # Create the replicator object.
        component_replicator = ProtocolReplicator(replicator_id=replicator_id)
        component_replicator.template_values = ProtocolPath('full_system_data', 'global')

        return base_protocols, component_replicator

    def generate_base_simulation_protocols(analysis_protocol, workflow_options, id_suffix='',
                                           conditional_group=None):
        """Constructs a set of protocols which, when combined in a workflow schema,
        may be executed to run a single simulation to estimate a particular
        property. The observable of interest to extract from the simulation is determined
        by the passed in `analysis_protocol`.

        The protocols returned will:

            1) Build a set of liquid coordinates for the
               property substance using packmol.

            2) Assign a set of smirnoff force field parameters
               to the system.

            3) Perform an energy minimisation on the system.

            4) Run a short NPT equilibration simulation for 100000 steps
               using a timestep of 2fs.

            5) Within a conditional group (up to a maximum of 100 times):

                5a) Run a longer NPT production simulation for 1000000 steps using a timestep of 2fs

                5b) Extract the average value of an observable and it's uncertainty.

                5c) If a convergence mode is set by the options, check if the target uncertainty has been met.
                    If not, repeat steps 5a), 5b) and 5c).

            6) Extract uncorrelated configurations from a generated production
               simulation.

            7) Extract uncorrelated statistics from a generated production
               simulation.

        Parameters
        ----------
        analysis_protocol: AveragePropertyProtocol
            The protocol which will extract the observable of
            interest from the generated simulation data.
        workflow_options: WorkflowOptions
            The options being used to generate a workflow.
        id_suffix: str
            A string suffix to append to each of the protocol ids.
        conditional_group: ProtocolGroup, optional
            A custom group to wrap the main simulation / extraction
            protocols within. It is up to the caller of this method to
            manually add the convergence conditions to this group.
            If `None`, a default group with uncertainty convergence
            conditions is automatically constructed.

        Returns
        -------
        BaseSimulationProtocols
            A named tuple of the generated protocols.
        ProtocolPath
            A reference to the final value of the estimated observable
            and its uncertainty (an `EstimatedQuantity`).
        WorkflowSimulationDataToStore
            An object which describes the default data from a simulation to store,
            such as the uncorrelated statistics and configurations.
        """

        assert isinstance(analysis_protocol, analysis.AveragePropertyProtocol)

        build_coordinates = coordinates.BuildCoordinatesPackmol(f'build_coordinates{id_suffix}')
        build_coordinates.substance = ProtocolPath('substance', 'global')
        build_coordinates.max_molecules = 1000

        assign_parameters = forcefield.BuildSmirnoffSystem(f'assign_parameters{id_suffix}')
        assign_parameters.force_field_path = ProtocolPath('force_field_path', 'global')
        assign_parameters.coordinate_file_path = ProtocolPath('coordinate_file_path', build_coordinates.id)
        assign_parameters.substance = ProtocolPath('output_substance', build_coordinates.id)

        # Equilibration
        energy_minimisation = simulation.RunEnergyMinimisation(f'energy_minimisation{id_suffix}')
        energy_minimisation.input_coordinate_file = ProtocolPath('coordinate_file_path', build_coordinates.id)
        energy_minimisation.system_path = ProtocolPath('system_path', assign_parameters.id)

        equilibration_simulation = simulation.RunOpenMMSimulation(f'equilibration_simulation{id_suffix}')
        equilibration_simulation.ensemble = Ensemble.NPT
        equilibration_simulation.steps_per_iteration = 100000
        equilibration_simulation.output_frequency = 5000
        equilibration_simulation.timestep = 2.0 * unit.femtosecond
        equilibration_simulation.thermodynamic_state = ProtocolPath('thermodynamic_state', 'global')
        equilibration_simulation.input_coordinate_file = ProtocolPath('output_coordinate_file', energy_minimisation.id)
        equilibration_simulation.system_path = ProtocolPath('system_path', assign_parameters.id)

        # Production
        production_simulation = simulation.RunOpenMMSimulation(f'production_simulation{id_suffix}')
        production_simulation.ensemble = Ensemble.NPT
        production_simulation.steps_per_iteration = 1000000
        production_simulation.output_frequency = 3000
        production_simulation.timestep = 2.0 * unit.femtosecond
        production_simulation.thermodynamic_state = ProtocolPath('thermodynamic_state', 'global')
        production_simulation.input_coordinate_file = ProtocolPath('output_coordinate_file', equilibration_simulation.id)
        production_simulation.system_path = ProtocolPath('system_path', assign_parameters.id)

        # Set up a conditional group to ensure convergence of uncertainty
        if conditional_group is None:

            conditional_group = groups.ConditionalGroup(f'conditional_group{id_suffix}')
            conditional_group.max_iterations = 100

            if workflow_options.convergence_mode != WorkflowOptions.ConvergenceMode.NoChecks:

                condition = groups.ConditionalGroup.Condition()

                condition.left_hand_value = ProtocolPath('value.uncertainty',
                                                         conditional_group.id,
                                                         analysis_protocol.id)

                condition.right_hand_value = ProtocolPath('target_uncertainty', 'global')

                condition.condition_type = groups.ConditionalGroup.ConditionType.LessThan

                conditional_group.add_condition(condition)

                # Make sure the simulation gets extended after each iteration.
                production_simulation.total_number_of_iterations = ProtocolPath('current_iteration',
                                                                                conditional_group.id)

        conditional_group.add_protocols(production_simulation, analysis_protocol)

        # Point the analyse protocol to the correct data source
        if isinstance(analysis_protocol, analysis.AverageTrajectoryProperty):
            analysis_protocol.input_coordinate_file = ProtocolPath('coordinate_file_path', build_coordinates.id)
            analysis_protocol.trajectory_path = ProtocolPath('trajectory_file_path', production_simulation.id)

        elif isinstance(analysis_protocol, analysis.ExtractAverageStatistic):
            analysis_protocol.statistics_path = ProtocolPath('statistics_file_path', production_simulation.id)

        else:
            raise ValueError('The analysis protocol must inherit from either the '
                             'AverageTrajectoryProperty or ExtractAverageStatistic '
                             'protocols.')

        # Finally, extract uncorrelated data
        statistical_inefficiency = ProtocolPath('statistical_inefficiency', conditional_group.id, analysis_protocol.id)
        equilibration_index = ProtocolPath('equilibration_index', conditional_group.id, analysis_protocol.id)
        coordinate_file = ProtocolPath('output_coordinate_file', conditional_group.id, production_simulation.id)
        trajectory_path = ProtocolPath('trajectory_file_path', conditional_group.id, production_simulation.id)
        statistics_path = ProtocolPath('statistics_file_path', conditional_group.id, production_simulation.id)

        extract_uncorrelated_trajectory = analysis.ExtractUncorrelatedTrajectoryData(f'extract_traj{id_suffix}')
        extract_uncorrelated_trajectory.statistical_inefficiency = statistical_inefficiency
        extract_uncorrelated_trajectory.equilibration_index = equilibration_index
        extract_uncorrelated_trajectory.input_coordinate_file = coordinate_file
        extract_uncorrelated_trajectory.input_trajectory_path = trajectory_path

        extract_uncorrelated_statistics = analysis.ExtractUncorrelatedStatisticsData(f'extract_stats{id_suffix}')
        extract_uncorrelated_statistics.statistical_inefficiency = statistical_inefficiency
        extract_uncorrelated_statistics.equilibration_index = equilibration_index
        extract_uncorrelated_statistics.input_statistics_path = statistics_path

        # Build the object which defines which pieces of simulation data to store.
        output_to_store = WorkflowSimulationDataToStore()

        output_to_store.total_number_of_molecules = ProtocolPath('output_number_of_molecules', build_coordinates.id)
        output_to_store.substance = ProtocolPath('output_substance', build_coordinates.id)
        output_to_store.statistical_inefficiency = statistical_inefficiency
        output_to_store.statistics_file_path = ProtocolPath('output_statistics_path', extract_uncorrelated_statistics.id)
        output_to_store.trajectory_file_path = ProtocolPath('output_trajectory_path', extract_uncorrelated_trajectory.id)
        output_to_store.coordinate_file_path = coordinate_file

        # Define where the final values come from.
        final_value_source = ProtocolPath('value', conditional_group.id, analysis_protocol.id)

        base_protocols = BaseSimulationProtocols(build_coordinates,
                                                 assign_parameters,
                                                 energy_minimisation,
                                                 equilibration_simulation,
                                                 production_simulation,
                                                 analysis_protocol,
                                                 conditional_group,
                                                 extract_uncorrelated_trajectory,
                                                 extract_uncorrelated_statistics)

        return base_protocols, final_value_source, output_to_store

    def generate_gradient_protocol_group(template_reweighting_protocol,
                                         reference_force_field_paths,
                                         target_force_field_path,
                                         coordinate_file_path,
                                         trajectory_file_path,
                                         statistics_file_path='',
                                         replicator_id='repl',
                                         perturbation_scale=1.0e-4,
                                         substance_source=None,
                                         id_suffix='',
                                         enable_pbc=True,
                                         use_subset_of_force_field=True,
                                         effective_sample_indices=None):
        """Constructs a set of protocols which, when combined in a workflow schema,
        may be executed to reweight a set of existing data to estimate a particular
        property. The reweighted observable of interest will be calculated by
        following the passed in `analysis_protocol`.

        Parameters
        ----------
        template_reweighting_protocol: BaseMBARProtocol
            A template protocol which will be used to reweight the observable of
            interest to small perturbations to the parameter of interest. These
            will then be used to calculate the finite difference gradient. This
            utility takes care of setting the target and reference reduced potentials.

            In the case that the template is of type `ReweightStatistics` and the
            observable is an energy, the statistics path will automatically be pointed
            to the energies evaluated using the perturbed parameter as opposed to the
            energy measured during the reference simulation.
        reference_force_field_paths: ProtocolPath or list of ProtocolPath
            The paths to the force field parameters which were used to generate
            the trajectories from which the observables of interest were calculated.
        target_force_field_path: ProtocolPath
            The path to the force field parameters which the observables are being
             estimated at (this is mainly only useful when estimating the gradients
             of reweighted observables).
        coordinate_file_path: ProtocolPath
            A path to the initial coordinates of the simulation trajectory which
            was used to estimate the observable of interest.
        trajectory_file_path: ProtocolPath
            A path to the simulation trajectory which was used
            to estimate the observable of interest.
        statistics_file_path: ProtocolPath, optional
            A path to the statistics where were generated from
            the trajectory passed to the `trajectory_file_path`
            parameter. This is optional in cases where multiple
            reference force fields are passed to this method.
        replicator_id: str
            A unique id which will be used for the protocol replicator which will
            replicate this group for every parameter of interest.
        perturbation_scale: float
            The default amount to perturb parameters by.
        substance_source: PlaceholderInput, optional
            An optional protocol path to the substance whose gradient
            is being estimated. If None, the global property substance
            is used.
        id_suffix: str
            An optional string to append to the end of each of the
            protocol ids.
        enable_pbc: bool
            If true, periodic boundary conditions are employed when recalculating
            the reduced potentials.
        use_subset_of_force_field: bool
            If True, any reduced potentials will only be calculated from a subset
            of the force field which depends on the parameter of interest.
        effective_sample_indices: ProtocolPath, optional
            A placeholder variable which can be used to make the gradient protocols
            dependant on an MBAR protcol to ensure gradients aren't calcuated when
            the MBAR protocol failed due to insufficient samples.

        Returns
        -------
        ProtocolGroup
            The protocol group which will estimate the gradient of
            an observable with respect to one parameter.
        ProtocolReplicator
            The replicator which will copy the gradient group for
            every parameter of interest.
        ProtocolPath
            A protocol path which points to the final gradient value.
        """

        assert isinstance(template_reweighting_protocol, reweighting.BaseMBARProtocol)

        id_suffix = f'_$({replicator_id}){id_suffix}'

        # Set values of the optional parameters.
        substance_source = ProtocolPath('substance', 'global') if substance_source is None else substance_source
        effective_sample_indices = effective_sample_indices if effective_sample_indices is not None else []

        # Define the protocol which will evaluate the reduced potentials of the
        # reference, forward and reverse states using only a subset of the full
        # force field.
        reduced_potentials = gradients.GradientReducedPotentials(f'gradient_reduced_potentials{id_suffix}')

        reduced_potentials.substance = substance_source
        reduced_potentials.thermodynamic_state = ProtocolPath('thermodynamic_state', 'global')
        reduced_potentials.reference_force_field_paths = reference_force_field_paths
        reduced_potentials.reference_statistics_path = statistics_file_path
        reduced_potentials.force_field_path = target_force_field_path
        reduced_potentials.trajectory_file_path = trajectory_file_path
        reduced_potentials.coordinate_file_path = coordinate_file_path
        reduced_potentials.parameter_key = ReplicatorValue(replicator_id)
        reduced_potentials.perturbation_scale = perturbation_scale
        reduced_potentials.use_subset_of_force_field = use_subset_of_force_field
        reduced_potentials.enable_pbc = enable_pbc
        reduced_potentials.effective_sample_indices = effective_sample_indices

        # Set up the protocols which will actually reweight the value of the
        # observable to the forward and reverse states.
        template_reweighting_protocol.bootstrap_iterations = 1
        template_reweighting_protocol.required_effective_samples = 0
        template_reweighting_protocol.reference_reduced_potentials = ProtocolPath('reference_potential_paths',
                                                                                  reduced_potentials.id)

        # We need to make sure we use the observable evaluated at the target state
        # if the observable depends on the parameter being reweighted.
        use_target_state_energies = (isinstance(template_reweighting_protocol, reweighting.ReweightStatistics) and
                                     (template_reweighting_protocol.statistics_type == ObservableType.PotentialEnergy or
                                      template_reweighting_protocol.statistics_type == ObservableType.ReducedPotential or
                                      template_reweighting_protocol.statistics_type == ObservableType.TotalEnergy or
                                      template_reweighting_protocol.statistics_type == ObservableType.Enthalpy))

        template_reweighting_schema = template_reweighting_protocol.schema

        # Create the reweighting protocols from the template schema.
        reverse_mbar_schema = copy.deepcopy(template_reweighting_schema)
        reverse_mbar_schema.id = f'reverse_reweight{id_suffix}'
        reverse_mbar = available_protocols[reverse_mbar_schema.type](reverse_mbar_schema.id)
        reverse_mbar.schema = reverse_mbar_schema
        reverse_mbar.target_reduced_potentials = [ProtocolPath('reverse_potentials_path', reduced_potentials.id)]

        forward_mbar_schema = copy.deepcopy(template_reweighting_schema)
        forward_mbar_schema.id = f'forward_reweight{id_suffix}'
        forward_mbar = available_protocols[forward_mbar_schema.type](forward_mbar_schema.id)
        forward_mbar.schema = forward_mbar_schema
        forward_mbar.target_reduced_potentials = [ProtocolPath('forward_potentials_path', reduced_potentials.id)]

        if use_target_state_energies:
            reverse_mbar.statistics_paths = [ProtocolPath('reverse_potentials_path', reduced_potentials.id)]
            forward_mbar.statistics_paths = [ProtocolPath('forward_potentials_path', reduced_potentials.id)]

        # Set up the protocol which will actually evaluate the parameter gradient
        # using the central difference method.
        central_difference = gradients.CentralDifferenceGradient(f'central_difference{id_suffix}')
        central_difference.parameter_key = ReplicatorValue(replicator_id)
        central_difference.reverse_observable_value = ProtocolPath('value', reverse_mbar.id)
        central_difference.forward_observable_value = ProtocolPath('value', forward_mbar.id)
        central_difference.reverse_parameter_value = ProtocolPath('reverse_parameter_value', reduced_potentials.id)
        central_difference.forward_parameter_value = ProtocolPath('forward_parameter_value', reduced_potentials.id)

        # Assemble all of the protocols into a convenient group wrapper.
        gradient_group = groups.ProtocolGroup(f'gradient_group{id_suffix}')
        gradient_group.add_protocols(reduced_potentials, reverse_mbar, forward_mbar, central_difference)

        # Create the replicator which will copy the group for each parameter gradient
        # which will be calculated.
        parameter_replicator = ProtocolReplicator(replicator_id=replicator_id)
        parameter_replicator.template_values = ProtocolPath('parameter_gradient_keys', 'global')

        return gradient_group, parameter_replicator, ProtocolPath('gradient', gradient_group.id, central_difference.id)