lammps/lib/colvars/colvarbias_abf.cpp

// -*- c++ -*-

// This file is part of the Collective Variables module (Colvars).
// The original version of Colvars and its updates are located at:
// https://github.com/Colvars/colvars
// Please update all Colvars source files before making any changes.
// If you wish to distribute your changes, please submit them to the
// Colvars repository at GitHub.

#include "colvarmodule.h"
#include "colvar.h"
#include "colvarbias_abf.h"


colvarbias_abf::colvarbias_abf(char const *key)
  : colvarbias(key),
    b_UI_estimator(false),
    b_CZAR_estimator(false),
    pabf_freq(0),
    system_force(NULL),
    gradients(NULL),
    samples(NULL),
    pmf(NULL),
    z_gradients(NULL),
    z_samples(NULL),
    czar_gradients(NULL),
    czar_pmf(NULL),
    last_gradients(NULL),
    last_samples(NULL)
{
  colvarproxy *proxy = cvm::main()->proxy;
  if (!proxy->total_forces_same_step()) {
    // Samples at step zero can not be collected
    feature_states[f_cvb_step_zero_data].available = false;
  }
}


int colvarbias_abf::init(std::string const &conf)
{
  colvarbias::init(conf);
  cvm::main()->cite_feature("ABF colvar bias implementation");

  colvarproxy *proxy = cvm::main()->proxy;

  enable(f_cvb_scalar_variables);
  enable(f_cvb_calc_pmf);

  // TODO relax this in case of VMD plugin
  if (cvm::temperature() == 0.0)
    cvm::log("WARNING: ABF should not be run without a thermostat or at 0 Kelvin!\n");

  // ************* parsing general ABF options ***********************

  get_keyval_feature((colvarparse *)this, conf, "applyBias",  f_cvb_apply_force, true);
  if (!is_enabled(f_cvb_apply_force)){
    cvm::log("WARNING: ABF biases will *not* be applied!\n");
  }

  get_keyval(conf, "updateBias",  update_bias, true);
  if (update_bias) {
    enable(f_cvb_history_dependent);
  } else {
    cvm::log("WARNING: ABF biases will *not* be updated!\n");
  }

  get_keyval(conf, "hideJacobian", hide_Jacobian, false);
  if (hide_Jacobian) {
    cvm::log("Jacobian (geometric) forces will be handled internally.\n");
  } else {
    cvm::log("Jacobian (geometric) forces will be included in reported free energy gradients.\n");
  }

  get_keyval(conf, "fullSamples", full_samples, 200);
  if ( full_samples <= 1 ) full_samples = 1;
  min_samples = full_samples / 2;
  // full_samples - min_samples >= 1 is guaranteed

  get_keyval(conf, "inputPrefix",  input_prefix, std::vector<std::string>());

  get_keyval(conf, "historyFreq", history_freq, 0);
  if (history_freq != 0) {
    if (output_freq == 0) {
      cvm::error("Error: historyFreq must be a multiple of outputFreq.\n",
                 COLVARS_INPUT_ERROR);
    } else {
      if ((history_freq % output_freq) != 0) {
        cvm::error("Error: historyFreq must be a multiple of outputFreq.\n",
                   COLVARS_INPUT_ERROR);
      }
    }
  }
  b_history_files = (history_freq > 0);

  // shared ABF
  get_keyval(conf, "shared", shared_on, false);
  if (shared_on) {
    cvm::main()->cite_feature("Multiple-walker ABF implementation");
    if ((proxy->replica_enabled() != COLVARS_OK) ||
        (proxy->num_replicas() <= 1)) {
      return cvm::error("Error: shared ABF requires more than one replica.",
                        COLVARS_INPUT_ERROR);
    }
    cvm::log("shared ABF will be applied among "+
             cvm::to_str(proxy->num_replicas()) + " replicas.\n");
    if (cvm::proxy->smp_enabled() == COLVARS_OK) {
      cvm::error("Error: shared ABF is currently not available with SMP parallelism; "
                 "please set \"SMP off\" at the top of the Colvars configuration file.\n",
                 COLVARS_NOT_IMPLEMENTED);
      return COLVARS_NOT_IMPLEMENTED;
    }

    // If shared_freq is not set, we default to output_freq
    get_keyval(conf, "sharedFreq", shared_freq, output_freq);
  }

  // ************* checking the associated colvars *******************

  if (num_variables() == 0) {
    cvm::error("Error: no collective variables specified for the ABF bias.\n");
    return COLVARS_ERROR;
  }

  if (update_bias) {
    // Request calculation of total force
    if(enable(f_cvb_get_total_force)) return cvm::get_error();
  }

  bool b_extended = false;
  size_t i;
  for (i = 0; i < num_variables(); i++) {

    if (colvars[i]->value().type() != colvarvalue::type_scalar) {
      cvm::error("Error: ABF bias can only use scalar-type variables.\n");
    }
    colvars[i]->enable(f_cv_grid); // Could be a child dependency of a f_cvb_use_grids feature
    if (hide_Jacobian) {
      colvars[i]->enable(f_cv_hide_Jacobian);
    }

    // If any colvar is extended-system (restrained style, not external with constraint), we are running eABF
    if (colvars[i]->is_enabled(f_cv_extended_Lagrangian)
        && !colvars[i]->is_enabled(f_cv_external)) {
      b_extended = true;
    }

    // Cannot mix and match coarse time steps with ABF because it gives
    // wrong total force averages - total force needs to be averaged over
    // every time step
    if (colvars[i]->get_time_step_factor() != time_step_factor) {
      cvm::error("Error: " + colvars[i]->description + " has a value of timeStepFactor ("
        + cvm::to_str(colvars[i]->get_time_step_factor()) + ") different from that of "
        + description + " (" + cvm::to_str(time_step_factor) + ").\n");
      return COLVARS_ERROR;
    }

    // Here we could check for orthogonality of the Cartesian coordinates
    // and make it just a warning if some parameter is set?
  }

  if (b_extended) {
    cvm::main()->cite_feature("eABF implementation");
  } else {
    cvm::main()->cite_feature("Internal-forces free energy estimator");
  }

  if (get_keyval(conf, "maxForce", max_force)) {
    if (max_force.size() != num_variables()) {
      cvm::error("Error: Number of parameters to maxForce does not match number of colvars.");
    }
    for (i = 0; i < num_variables(); i++) {
      if (max_force[i] < 0.0) {
        cvm::error("Error: maxForce should be non-negative.");
        return COLVARS_ERROR;
      }
    }
    cap_force = true;
  } else {
    cap_force = false;
  }

  bin.assign(num_variables(), 0);
  force_bin.assign(num_variables(), 0);
  system_force = new cvm::real [num_variables()];

  // Construct empty grids based on the colvars
  if (cvm::debug()) {
    cvm::log("Allocating count and free energy gradient grids.\n");
  }

  samples   = new colvar_grid_count(colvars);
  gradients = new colvar_grid_gradient(colvars);
  gradients->samples = samples;
  samples->has_parent_data = true;

  // Data for eAB F z-based estimator
  if ( b_extended ) {
    get_keyval(conf, "CZARestimator", b_CZAR_estimator, true);
    if ( b_CZAR_estimator ) {
      cvm::main()->cite_feature("CZAR eABF estimator");
    }
    // CZAR output files for stratified eABF
    get_keyval(conf, "writeCZARwindowFile", b_czar_window_file, false,
               colvarparse::parse_silent);

    z_bin.assign(num_variables(), 0);
    z_samples   = new colvar_grid_count(colvars);
    z_samples->request_actual_value();
    z_gradients = new colvar_grid_gradient(colvars);
    z_gradients->request_actual_value();
    z_gradients->samples = z_samples;
    z_samples->has_parent_data = true;
    czar_gradients = new colvar_grid_gradient(colvars);
  }

  get_keyval(conf, "integrate", b_integrate, num_variables() <= 3); // Integrate for output if d<=3
  if (b_integrate) {
    // For now, we integrate on-the-fly iff the grid is < 3D
    if ( num_variables() > 3 ) {
      cvm::error("Error: cannot integrate free energy in dimension > 3.\n");
      return COLVARS_ERROR;
    }
    pmf = new integrate_potential(colvars, gradients);
    if ( b_CZAR_estimator ) {
      czar_pmf = new integrate_potential(colvars, czar_gradients);
    }
    // Parameters for integrating initial (and final) gradient data
    get_keyval(conf, "integrateMaxIterations", integrate_iterations, 10000, colvarparse::parse_silent);
    get_keyval(conf, "integrateTol", integrate_tol, 1e-6, colvarparse::parse_silent);
    // Projected ABF, updating the integrated PMF on the fly
    get_keyval(conf, "pABFintegrateFreq", pabf_freq, 0, colvarparse::parse_silent);
    get_keyval(conf, "pABFintegrateMaxIterations", pabf_integrate_iterations, 100, colvarparse::parse_silent);
    get_keyval(conf, "pABFintegrateTol", pabf_integrate_tol, 1e-4, colvarparse::parse_silent);
  }

  // For shared ABF, we store a second set of grids.
  // This used to be only if "shared" was defined,
  // but now we allow calling share externally (e.g. from Tcl).
  last_samples   = new colvar_grid_count(colvars);
  last_gradients = new colvar_grid_gradient(colvars);
  last_gradients->samples = last_samples;
  last_samples->has_parent_data = true;
  shared_last_step = -1;

  // If custom grids are provided, read them
  if ( input_prefix.size() > 0 ) {
    read_gradients_samples();
    // Update divergence to account for input data
    pmf->set_div();
  }

  // if extendedLangrangian is on, then call UI estimator
  if (b_extended) {
    get_keyval(conf, "UIestimator", b_UI_estimator, false);

    if (b_UI_estimator) {

      cvm::main()->cite_feature("Umbrella-integration eABF estimator");
      std::vector<double> UI_lowerboundary;
      std::vector<double> UI_upperboundary;
      std::vector<double> UI_width;
      std::vector<double> UI_krestr;

      bool UI_restart = (input_prefix.size() > 0);

      for (i = 0; i < num_variables(); i++) {
        UI_lowerboundary.push_back(colvars[i]->lower_boundary);
        UI_upperboundary.push_back(colvars[i]->upper_boundary);
        UI_width.push_back(colvars[i]->width);
        UI_krestr.push_back(colvars[i]->force_constant());
      }
      eabf_UI = UIestimator::UIestimator(UI_lowerboundary,
                                         UI_upperboundary,
                                         UI_width,
                                         UI_krestr,                // force constant in eABF
                                         output_prefix,              // the prefix of output files
                                         cvm::restart_out_freq,
                                         UI_restart,                    // whether restart from a .count and a .grad file
                                         input_prefix,   // the prefixes of input files
                                         cvm::temperature());
    }
  }

  cvm::log("Finished ABF setup.\n");
  return COLVARS_OK;
}

/// Destructor
colvarbias_abf::~colvarbias_abf()
{
  if (samples) {
    delete samples;
    samples = NULL;
  }

  if (gradients) {
    delete gradients;
    gradients = NULL;
  }

  if (pmf) {
    delete pmf;
    pmf = NULL;
  }

  if (z_samples) {
    delete z_samples;
    z_samples = NULL;
  }

  if (z_gradients) {
    delete z_gradients;
    z_gradients = NULL;
  }

  if (czar_gradients) {
    delete czar_gradients;
    czar_gradients = NULL;
  }

  if (czar_pmf) {
    delete czar_pmf;
    czar_pmf = NULL;
  }

  // shared ABF
  // We used to only do this if "shared" was defined,
  // but now we can call shared externally
  if (last_samples) {
    delete last_samples;
    last_samples = NULL;
  }

  if (last_gradients) {
    delete last_gradients;
    last_gradients = NULL;
  }

  if (system_force) {
    delete [] system_force;
    system_force = NULL;
  }
}


/// Update the FE gradient, compute and apply biasing force
/// also output data to disk if needed

int colvarbias_abf::update()
{
  if (cvm::debug()) cvm::log("Updating ABF bias " + this->name);

  size_t i;
  for (i = 0; i < num_variables(); i++) {
    bin[i] = samples->current_bin_scalar(i);
  }
  if (cvm::proxy->total_forces_same_step()) {
    // e.g. in LAMMPS, total forces are current
    force_bin = bin;
  }

  if (cvm::step_relative() > 0 || is_enabled(f_cvb_step_zero_data)) {

    if (update_bias) {
//       if (b_adiabatic_reweighting) {
//         // Update gradients non-locally based on conditional distribution of
//         // fictitious variable TODO
//
//       } else
      if (samples->index_ok(force_bin)) {
        // Only if requested and within bounds of the grid...

        for (i = 0; i < num_variables(); i++) {
          // get total forces (lagging by 1 timestep) from colvars
          // and subtract previous ABF force if necessary
          update_system_force(i);
        }
          gradients->acc_force(force_bin, system_force);
          if ( b_integrate ) {
            pmf->update_div_neighbors(force_bin);
          }
      }
    }

    if ( z_gradients && update_bias ) {
      for (i = 0; i < num_variables(); i++) {
        z_bin[i] = z_samples->current_bin_scalar(i);
      }
      if ( z_samples->index_ok(z_bin) ) {
        for (i = 0; i < num_variables(); i++) {
          // If we are outside the range of xi, the force has not been obtained above
          // the function is just an accessor, so cheap to call again anyway
          update_system_force(i);
        }
        z_gradients->acc_force(z_bin, system_force);
      }
    }

    if ( b_integrate ) {
      if ( pabf_freq && cvm::step_relative() % pabf_freq == 0 ) {
        cvm::real err;
        int iter = pmf->integrate(pabf_integrate_iterations, pabf_integrate_tol, err);
        if ( iter == pabf_integrate_iterations ) {
          cvm::log("Warning: PMF integration did not converge to " + cvm::to_str(pabf_integrate_tol)
            + " in " + cvm::to_str(pabf_integrate_iterations)
            + " steps. Residual error: " +  cvm::to_str(err));
        }
        pmf->set_zero_minimum(); // TODO: do this only when necessary
      }
    }
  }

  if (!cvm::proxy->total_forces_same_step()) {
    // e.g. in NAMD, total forces will be available for next timestep
    // hence we store the current colvar bin
    force_bin = bin;
  }

  // Reset biasing forces from previous timestep
  for (i = 0; i < num_variables(); i++) {
    colvar_forces[i].reset();
  }

  // Compute and apply the new bias, if applicable
  if (is_enabled(f_cvb_apply_force) && samples->index_ok(bin)) {

    cvm::real count = cvm::real(samples->value(bin));
    cvm::real fact = 1.0;

    // Factor that ensures smooth introduction of the force
    if ( count < full_samples ) {
      fact = (count < min_samples) ? 0.0 :
        (cvm::real(count - min_samples)) / (cvm::real(full_samples - min_samples));
    }

    std::vector<cvm::real>  grad(num_variables());

    if ( pabf_freq ) {
      // In projected ABF, the force is the PMF gradient estimate
      pmf->vector_gradient_finite_diff(bin, grad);
    } else {
      // Normal ABF
      gradients->vector_value(bin, grad);
    }

//     if ( b_adiabatic_reweighting) {
//       // Average of force according to conditional distribution of fictitious variable
//       // need freshly integrated PMF, gradient TODO
//     } else
    if ( fact != 0.0 ) {
      if ( (num_variables() == 1) && colvars[0]->periodic_boundaries() ) {
        // Enforce a zero-mean bias on periodic, 1D coordinates
        // in other words: boundary condition is that the biasing potential is periodic
        // This is enforced naturally if using integrated PMF
        colvar_forces[0].real_value = fact * (grad[0] - gradients->average ());
      } else {
        for (i = 0; i < num_variables(); i++) {
          // subtracting the mean force (opposite of the FE gradient) means adding the gradient
          colvar_forces[i].real_value = fact * grad[i];
        }
      }
      if (cap_force) {
        for (i = 0; i < num_variables(); i++) {
          if ( colvar_forces[i].real_value * colvar_forces[i].real_value > max_force[i] * max_force[i] ) {
            colvar_forces[i].real_value = (colvar_forces[i].real_value > 0 ? max_force[i] : -1.0 * max_force[i]);
          }
        }
      }
    }
  }

  // update the output prefix; TODO: move later to setup_output() function
  if (cvm::main()->num_biases_feature(colvardeps::f_cvb_calc_pmf) == 1) {
    // This is the only bias computing PMFs
    output_prefix = cvm::output_prefix();
  } else {
    output_prefix = cvm::output_prefix() + "." + this->name;
  }

  if (shared_on && shared_last_step >= 0 && cvm::step_absolute() % shared_freq == 0) {
    // Share gradients and samples for shared ABF.
    replica_share();
  }

  // Prepare for the first sharing.
  if (shared_last_step < 0) {
    // Copy the current gradient and count values into last.
    last_gradients->copy_grid(*gradients);
    last_samples->copy_grid(*samples);
    shared_last_step = cvm::step_absolute();
    cvm::log("Prepared sample and gradient buffers at step "+cvm::to_str(cvm::step_absolute())+".\n");
  }

  // update UI estimator every step
  if (b_UI_estimator)
  {
    std::vector<double> x(num_variables(),0);
    std::vector<double> y(num_variables(),0);
    for (i = 0; i < num_variables(); i++)
    {
      x[i] = colvars[i]->actual_value();
      y[i] = colvars[i]->value();
    }
    eabf_UI.update_output_filename(output_prefix);
    eabf_UI.update(cvm::step_absolute(), x, y);
  }

  /// Compute the bias energy
  int error_code = calc_energy(NULL);

  return error_code;
}


int colvarbias_abf::replica_share() {

  colvarproxy *proxy = cvm::main()->proxy;

  if (proxy->replica_enabled() != COLVARS_OK) {
    cvm::error("Error: shared ABF: No replicas.\n");
    return COLVARS_ERROR;
  }
  // We must have stored the last_gradients and last_samples.
  if (shared_last_step < 0 ) {
    cvm::error("Error: shared ABF: Tried to apply shared ABF before any sampling had occurred.\n");
    return COLVARS_ERROR;
  }

  // Share gradients for shared ABF.
  cvm::log("shared ABF: Sharing gradient and samples among replicas at step "+cvm::to_str(cvm::step_absolute()) );

  // Count of data items.
  size_t data_n = gradients->raw_data_num();
  size_t samp_start = data_n*sizeof(cvm::real);
  size_t msg_total = data_n*sizeof(size_t) + samp_start;
  char* msg_data = new char[msg_total];

  if (proxy->replica_index() == 0) {
    int p;
    // Replica 0 collects the delta gradient and count from the others.
    for (p = 1; p < proxy->num_replicas(); p++) {
      // Receive the deltas.
      proxy->replica_comm_recv(msg_data, msg_total, p);

      // Map the deltas from the others into the grids.
      last_gradients->raw_data_in((cvm::real*)(&msg_data[0]));
      last_samples->raw_data_in((size_t*)(&msg_data[samp_start]));

      // Combine the delta gradient and count of the other replicas
      // with Replica 0's current state (including its delta).
      gradients->add_grid( *last_gradients );
      samples->add_grid( *last_samples );
    }

    // Now we must send the combined gradient to the other replicas.
    gradients->raw_data_out((cvm::real*)(&msg_data[0]));
    samples->raw_data_out((size_t*)(&msg_data[samp_start]));
    for (p = 1; p < proxy->num_replicas(); p++) {
      proxy->replica_comm_send(msg_data, msg_total, p);
    }

  } else {
    // All other replicas send their delta gradient and count.
    // Calculate the delta gradient and count.
    last_gradients->delta_grid(*gradients);
    last_samples->delta_grid(*samples);

    // Cast the raw char data to the gradient and samples.
    last_gradients->raw_data_out((cvm::real*)(&msg_data[0]));
    last_samples->raw_data_out((size_t*)(&msg_data[samp_start]));
    proxy->replica_comm_send(msg_data, msg_total, 0);

    // We now receive the combined gradient from Replica 0.
    proxy->replica_comm_recv(msg_data, msg_total, 0);
    // We sync to the combined gradient computed by Replica 0.
    gradients->raw_data_in((cvm::real*)(&msg_data[0]));
    samples->raw_data_in((size_t*)(&msg_data[samp_start]));
  }

  // Without a barrier it's possible that one replica starts
  // share 2 when other replicas haven't finished share 1.
  proxy->replica_comm_barrier();
  // Done syncing the replicas.
  delete[] msg_data;

  // Copy the current gradient and count values into last.
  last_gradients->copy_grid(*gradients);
  last_samples->copy_grid(*samples);
  shared_last_step = cvm::step_absolute();

  if (b_integrate) {
    // Update divergence to account for newly shared gradients
    pmf->set_div();
  }
  return COLVARS_OK;
}


template <class T> int colvarbias_abf::write_grid_to_file(T const *grid,
                                                          std::string const &filename,
                                                          bool close) {
  std::ostream *os = cvm::proxy->output_stream(filename);
  if (!os) {
    return cvm::error("Error opening file " + filename + " for writing.\n", COLVARS_ERROR | COLVARS_FILE_ERROR);
  }
  grid->write_multicol(*os);
  if (close) {
    cvm::proxy->close_output_stream(filename);
  } else {
    // Insert empty line between frames in history files
    *os << std::endl;
    cvm::proxy->flush_output_stream(os);
  }

  // In dimension higher than 2, dx is easier to handle and visualize
  // but we cannot write multiple frames in a dx file now
  // (could be implemented as multiple dx files)
  if (num_variables() > 2 && close) {
    std::string  dx = filename + ".dx";
    std::ostream *dx_os = cvm::proxy->output_stream(dx);
    if (!dx_os)  {
      return cvm::error("Error opening file " + dx + " for writing.\n", COLVARS_ERROR | COLVARS_FILE_ERROR);
    }
    grid->write_opendx(*dx_os);
    // if (close) {
      cvm::proxy->close_output_stream(dx);
    // }
    // else {
    //   // TODO, decide convention for multiple datasets in dx file
    //   *dx_os << std::endl;
    //   dx_os->flush();
    // }
  }
  return COLVARS_OK;
}


void colvarbias_abf::write_gradients_samples(const std::string &prefix, bool close)
{
  write_grid_to_file<colvar_grid_count>(samples, prefix + ".count", close);
  write_grid_to_file<colvar_grid_gradient>(gradients, prefix + ".grad", close);

  if (b_integrate) {
    // Do numerical integration (to high precision) and output a PMF
    cvm::real err;
    pmf->integrate(integrate_iterations, integrate_tol, err);
    pmf->set_zero_minimum();
    write_grid_to_file<colvar_grid_scalar>(pmf, prefix + ".pmf", close);
  }

  if (b_CZAR_estimator) {
    // Write eABF CZAR-related quantities
    write_grid_to_file<colvar_grid_count>(z_samples, prefix + ".zcount", close);
    if (b_czar_window_file) {
      write_grid_to_file<colvar_grid_gradient>(z_gradients, prefix + ".zgrad", close);
    }

    // Calculate CZAR estimator of gradients
    for (std::vector<int> ix = czar_gradients->new_index();
          czar_gradients->index_ok(ix); czar_gradients->incr(ix)) {
      for (size_t n = 0; n < czar_gradients->multiplicity(); n++) {
        czar_gradients->set_value(ix, z_gradients->value_output(ix, n)
          - cvm::temperature() * cvm::boltzmann() * z_samples->log_gradient_finite_diff(ix, n), n);
      }
    }
    write_grid_to_file<colvar_grid_gradient>(czar_gradients, prefix + ".czar.grad", close);

    if (b_integrate) {
      // Do numerical integration (to high precision) and output a PMF
      cvm::real err;
      czar_pmf->set_div();
      czar_pmf->integrate(integrate_iterations, integrate_tol, err);
      czar_pmf->set_zero_minimum();
      write_grid_to_file<colvar_grid_scalar>(czar_pmf, prefix + ".czar.pmf", close);
    }
  }
  return;
}


// For Tcl implementation of selection rules.
/// Give the total number of bins for a given bias.
int colvarbias_abf::bin_num() {
  return samples->number_of_points(0);
}
/// Calculate the bin index for a given bias.
int colvarbias_abf::current_bin() {
  return samples->current_bin_scalar(0);
}
/// Give the count at a given bin index.
int colvarbias_abf::bin_count(int bin_index) {
  if (bin_index < 0 || bin_index >= bin_num()) {
    cvm::error("Error: Tried to get bin count from invalid bin index "+cvm::to_str(bin_index));
    return -1;
  }
  std::vector<int> ix(1,(int)bin_index);
  return samples->value(ix);
}


void colvarbias_abf::read_gradients_samples()
{
  std::string samples_in_name, gradients_in_name, z_samples_in_name, z_gradients_in_name;

  for ( size_t i = 0; i < input_prefix.size(); i++ ) {
    samples_in_name = input_prefix[i] + ".count";
    gradients_in_name = input_prefix[i] + ".grad";
    z_samples_in_name = input_prefix[i] + ".zcount";
    z_gradients_in_name = input_prefix[i] + ".zgrad";
    // For user-provided files, the per-bias naming scheme may not apply

    std::ifstream is;

    cvm::log("Reading sample count from " + samples_in_name + " and gradient from " + gradients_in_name);
    is.open(samples_in_name.c_str());
    if (!is.is_open()) cvm::error("Error opening ABF samples file " + samples_in_name + " for reading");
    samples->read_multicol(is, true);
    is.close();
    is.clear();

    is.open(gradients_in_name.c_str());
    if (!is.is_open()) {
      cvm::error("Error opening ABF gradient file " +
                 gradients_in_name + " for reading", COLVARS_INPUT_ERROR);
    } else {
      gradients->read_multicol(is, true);
      is.close();
    }

    if (b_CZAR_estimator) {
      // Read eABF z-averaged data for CZAR
      cvm::log("Reading z-histogram from " + z_samples_in_name + " and z-gradient from " + z_gradients_in_name);

      is.clear();
      is.open(z_samples_in_name.c_str());
      if (!is.is_open())  cvm::error("Error opening eABF z-histogram file " + z_samples_in_name + " for reading");
      z_samples->read_multicol(is, true);
      is.close();
      is.clear();

      is.open(z_gradients_in_name.c_str());
      if (!is.is_open())  cvm::error("Error opening eABF z-gradient file " + z_gradients_in_name + " for reading");
      z_gradients->read_multicol(is, true);
      is.close();
    }
  }
  return;
}


std::ostream & colvarbias_abf::write_state_data(std::ostream& os)
{
  std::ios::fmtflags flags(os.flags());

  os.setf(std::ios::fmtflags(0), std::ios::floatfield); // default floating-point format
  os << "\nsamples\n";
  samples->write_raw(os, 8);
  os.flags(flags);

  os << "\ngradient\n";
  gradients->write_raw(os, 8);

  if (b_CZAR_estimator) {
    os.setf(std::ios::fmtflags(0), std::ios::floatfield); // default floating-point format
    os << "\nz_samples\n";
    z_samples->write_raw(os, 8);
    os.flags(flags);
    os << "\nz_gradient\n";
    z_gradients->write_raw(os, 8);
  }

  os.flags(flags);
  return os;
}


std::istream & colvarbias_abf::read_state_data(std::istream& is)
{
  if ( input_prefix.size() > 0 ) {
    cvm::error("ERROR: cannot provide both inputPrefix and a colvars state file.\n", COLVARS_INPUT_ERROR);
  }

  if (! read_state_data_key(is, "samples")) {
    return is;
  }
  if (! samples->read_raw(is)) {
    return is;
  }

  if (! read_state_data_key(is, "gradient")) {
    return is;
  }
  if (! gradients->read_raw(is)) {
    return is;
  }
  if (b_integrate) {
    // Update divergence to account for restart data
    pmf->set_div();
  }

  if (b_CZAR_estimator) {

    if (! read_state_data_key(is, "z_samples")) {
      return is;
    }
    if (! z_samples->read_raw(is)) {
      return is;
    }

    if (! read_state_data_key(is, "z_gradient")) {
      return is;
    }
    if (! z_gradients->read_raw(is)) {
      return is;
    }
  }

  return is;
}


int colvarbias_abf::write_output_files()
{
  if (cvm::debug()) {
    cvm::log("ABF bias trying to write gradients and samples to disk");
  }

  if (shared_on && cvm::main()->proxy->replica_index() > 0
    && ! (b_CZAR_estimator || b_UI_estimator) ) {
    // No need to report the same data as replica 0, let it do the I/O job
    // except if using an eABF FE estimator
    return COLVARS_OK;
  }

  write_gradients_samples(output_prefix);
  if (b_history_files) {
    if ((cvm::step_absolute() % history_freq) == 0) {
      write_gradients_samples(output_prefix + ".hist", false);
    }
  }

  if (b_UI_estimator) {
    eabf_UI.calc_pmf();
    eabf_UI.write_files();
  }

  return COLVARS_OK;
}


int colvarbias_abf::calc_energy(std::vector<colvarvalue> const *values)
{
  bias_energy = 0.0; // default value, overridden if a value can be calculated

  if (num_variables() > 1 || values != NULL) {
    // Use simple estimate: neglect effect of fullSamples,
    // return value at center of bin
    if (pmf != NULL) {
      std::vector<int> const curr_bin = values ?
        pmf->get_colvars_index(*values) :
        pmf->get_colvars_index();

      if (pmf->index_ok(curr_bin)) {
        bias_energy = pmf->value(curr_bin);
      }
    }
    return COLVARS_OK;
  }

  // Get the home bin.
  int home0 = gradients->current_bin_scalar(0);
  if (home0 < 0) return COLVARS_OK;
  int gradient_len = (int)(gradients->number_of_points(0));
  int home = (home0 < gradient_len) ? home0 : (gradient_len-1);

  // Integrate the gradient up to the home bin.
  cvm::real sum = 0.0;
  for (int i = 0; i < home; i++) {
    std::vector<int> ix(1,i);

    // Include the full_samples factor if necessary.
    unsigned int count = samples->value(ix);
    cvm::real fact = 1.0;
    if ( count < full_samples ) {
      fact = (count < min_samples) ? 0.0 :
        (cvm::real(count - min_samples)) / (cvm::real(full_samples - min_samples));
    }
    if (count > 0) sum += fact*gradients->value(ix)/count*gradients->widths[0];
  }

  // Integrate the gradient up to the current position in the home interval, a fractional portion of a bin.
  std::vector<int> ix(1,home);
  cvm::real frac = gradients->current_bin_scalar_fraction(0);
  unsigned int count = samples->value(ix);
  cvm::real fact = 1.0;
  if ( count < full_samples ) {
    fact = (count < min_samples) ? 0.0 :
      (cvm::real(count - min_samples)) / (cvm::real(full_samples - min_samples));
  }
  if (count > 0)
    sum += fact*gradients->value(ix)/count*gradients->widths[0]*frac;

  // The applied potential is the negative integral of force samples.
  bias_energy = -sum;
  return COLVARS_OK;
}