Loop over replicas when computing well-tempered metadynamics scaling factor

[giacomofiorin]

Fixes #819

[giacomofiorin]

Still working on this (including test, documentation update).

When finished, I want to use it as a test for a CI job that cherry-picks bugfixes into release branches (e.g. namd-3.0, gromacs-2025).

[giacomofiorin]

@HanatoK I didn't understand this comment before, and forgot to ask you about it

[HanatoK]

As I understand, without keepHills, the code only accumulates the hills that are off-grid. However, in theory, those Gaussian hills that have been projected onto the histogram are truncated, which means they do not affect the bias energy of an off-grid position.

With keepHills I think it would be better to compute the bias energy from all hills, no matter whether they are in the histogram.

[HanatoK]

In my opinion, the logic of computing bias energy should be the same as colvarbias_meta::calc_energy without adding the new hills:

  bool index_ok = false;
  std::vector<int> curr_bin;

  if (use_grids) {

    curr_bin = values ?
      hills_energy->get_colvars_index(*values) :
      hills_energy->get_colvars_index();

    index_ok = hills_energy->index_ok(curr_bin);

  }

  if ( index_ok ) {
    // index is within the grid: get the energy from there
    for (ir = 0; ir < replicas.size(); ir++) {

      bias_energy += replicas[ir]->hills_energy->value(curr_bin);
      if (cvm::debug()) {
        cvm::log("Metadynamics bias \""+this->name+"\""+
                 ((comm != single_replica) ? ", replica \""+replica_id+"\"" : "")+
                 ": current coordinates on the grid: "+
                 cvm::to_str(curr_bin)+".\n");
        cvm::log("Grid energy = "+cvm::to_str(bias_energy)+".\n");
      }
    }
  } else {
    // off the grid: compute analytically only the hills at the grid's edges
    for (ir = 0; ir < replicas.size(); ir++) {
      calc_hills(replicas[ir]->hills_off_grid.begin(),
                 replicas[ir]->hills_off_grid.end(),
                 bias_energy,
                 values);
    }
  }

[HanatoK]

Is it possible to move the checking out of the for loop, just like colvarbias_meta::calc_energy?

[HanatoK]

Now I feel the old code summing the hills starting from new_hills_begin is incorrect, and this fixes it. Is that right?