---

colvargrid.h

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// -*- 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.

#ifndef COLVARGRID_H
#define COLVARGRID_H

#include <iostream>
#include <iomanip>

#include "colvar.h"
#include "colvarmodule.h"
#include "colvarvalue.h"
#include "colvarparse.h"

template <class T> class colvar_grid : public colvarparse {

protected:

  size_t nd;

  std::vector<int> nx;

  std::vector<int> nxc;

  size_t mult;

  size_t nt;

  std::vector<T> data;

  std::vector<size_t> new_data;

  std::vector<colvar *> cv;

  std::vector<bool> use_actual_value;

  inline size_t address(std::vector<int> const &ix) const
  {
    size_t addr = 0;
    for (size_t i = 0; i < nd; i++) {
      addr += ix[i]*static_cast<size_t>(nxc[i]);
      if (cvm::debug()) {
        if (ix[i] >= nx[i]) {
          cvm::error("Error: exceeding bounds in colvar_grid.\n", COLVARS_BUG_ERROR);
          return 0;
        }
      }
    }
    return addr;
  }

public:

  std::vector<colvarvalue> lower_boundaries;

  std::vector<colvarvalue> upper_boundaries;

  std::vector<bool>        periodic;

  std::vector<bool>        hard_lower_boundaries;

  std::vector<bool>        hard_upper_boundaries;

  std::vector<cvm::real>   widths;

  bool has_parent_data;

  bool has_data;

  inline size_t num_variables() const
  {
    return nd;
  }

  inline std::vector<int> const &number_of_points_vec() const
  {
    return nx;
  }

  inline size_t number_of_points(int const icv = -1) const
  {
    if (icv < 0) {
      return nt;
    } else {
      return nx[icv];
    }
  }

  inline std::vector<int> const & sizes() const
  {
    return nx;
  }

  inline void set_sizes(std::vector<int> const &new_sizes)
  {
    nx = new_sizes;
  }

  inline size_t multiplicity() const
  {
    return mult;
  }

  inline void request_actual_value(bool b = true)
  {
    size_t i;
    for (i = 0; i < use_actual_value.size(); i++) {
      use_actual_value[i] = b;
    }
  }

  int setup(std::vector<int> const &nx_i,
            T const &t = T(),
            size_t const &mult_i = 1)
  {
    if (cvm::debug()) {
      cvm::log("Allocating grid: multiplicity = "+cvm::to_str(mult_i)+
               ", dimensions = "+cvm::to_str(nx_i)+".\n");
    }

    mult = mult_i;

    data.clear();

    nx = nx_i;
    nd = nx.size();

    nxc.resize(nd);

    // setup dimensions
    nt = mult;
    for (int i = nd-1; i >= 0; i--) {
      if (nx[i] <= 0) {
        cvm::error("Error: providing an invalid number of grid points, "+
                   cvm::to_str(nx[i])+".\n", COLVARS_BUG_ERROR);
        return COLVARS_ERROR;
      }
      nxc[i] = nt;
      nt *= nx[i];
    }

    if (cvm::debug()) {
      cvm::log("Total number of grid elements = "+cvm::to_str(nt)+".\n");
    }

    data.reserve(nt);
    data.assign(nt, t);

    return COLVARS_OK;
  }

  int setup()
  {
    return setup(this->nx, T(), this->mult);
  }

  void reset(T const &t = T())
  {
    data.assign(nt, t);
  }


  colvar_grid() : has_data(false)
  {
    nd = nt = 0;
    mult = 1;
    has_parent_data = false;
    this->setup();
  }

  virtual ~colvar_grid()
  {}

  colvar_grid(colvar_grid<T> const &g) : colvarparse(),
                                         nd(g.nd),
                                         nx(g.nx),
                                         mult(g.mult),
                                         data(),
                                         cv(g.cv),
                                         use_actual_value(g.use_actual_value),
                                         lower_boundaries(g.lower_boundaries),
                                         upper_boundaries(g.upper_boundaries),
                                         periodic(g.periodic),
                                         hard_lower_boundaries(g.hard_lower_boundaries),
                                         hard_upper_boundaries(g.hard_upper_boundaries),
                                         widths(g.widths),
                                         has_parent_data(false),
                                         has_data(false)
  {}

  colvar_grid(std::vector<int> const &nx_i,
              T const &t = T(),
              size_t mult_i = 1)
    : has_parent_data(false), has_data(false)
  {
    this->setup(nx_i, t, mult_i);
  }

  colvar_grid(std::vector<colvar *> const &colvars,
              T const &t = T(),
              size_t mult_i = 1,
              bool add_extra_bin = false)
    : has_parent_data(false), has_data(false)
  {
    (void) t;
    this->init_from_colvars(colvars, mult_i, add_extra_bin);
  }

  int init_from_colvars(std::vector<colvar *> const &colvars,
                        size_t mult_i = 1,
                        bool add_extra_bin = false)
  {
    if (cvm::debug()) {
      cvm::log("Reading grid configuration from collective variables.\n");
    }

    cv = colvars;
    nd = colvars.size();
    mult = mult_i;

    size_t i;

    if (cvm::debug()) {
      cvm::log("Allocating a grid for "+cvm::to_str(colvars.size())+
               " collective variables, multiplicity = "+cvm::to_str(mult_i)+".\n");
    }

    for (i =  0; i < cv.size(); i++) {

      if (cv[i]->value().type() != colvarvalue::type_scalar) {
        cvm::error("Colvar grids can only be automatically "
                   "constructed for scalar variables.  "
                   "ABF and histogram can not be used; metadynamics "
                   "can be used with useGrids disabled.\n", COLVARS_INPUT_ERROR);
        return COLVARS_ERROR;
      }

      if (cv[i]->width <= 0.0) {
        cvm::error("Tried to initialize a grid on a "
                   "variable with negative or zero width.\n", COLVARS_INPUT_ERROR);
        return COLVARS_ERROR;
      }

      widths.push_back(cv[i]->width);
      hard_lower_boundaries.push_back(cv[i]->is_enabled(colvardeps::f_cv_hard_lower_boundary));
      hard_upper_boundaries.push_back(cv[i]->is_enabled(colvardeps::f_cv_hard_upper_boundary));
      periodic.push_back(cv[i]->periodic_boundaries());

      // By default, get reported colvar value (for extended Lagrangian colvars)
      use_actual_value.push_back(false);

      // except if a colvar is specified twice in a row
      // then the first instance is the actual value
      // For histograms of extended-system coordinates
      if (i > 0 && cv[i-1] == cv[i]) {
        use_actual_value[i-1] = true;
      }

      if (add_extra_bin) {
        if (periodic[i]) {
          // Shift the grid by half the bin width (values at edges instead of center of bins)
          lower_boundaries.push_back(cv[i]->lower_boundary.real_value - 0.5 * widths[i]);
          upper_boundaries.push_back(cv[i]->upper_boundary.real_value - 0.5 * widths[i]);
        } else {
          // Make this grid larger by one bin width
          lower_boundaries.push_back(cv[i]->lower_boundary.real_value - 0.5 * widths[i]);
          upper_boundaries.push_back(cv[i]->upper_boundary.real_value + 0.5 * widths[i]);
        }
      } else {
        lower_boundaries.push_back(cv[i]->lower_boundary);
        upper_boundaries.push_back(cv[i]->upper_boundary);
      }
    }

    this->init_from_boundaries();
    return this->setup();
  }

  int init_from_boundaries()
  {
    if (cvm::debug()) {
      cvm::log("Configuring grid dimensions from colvars boundaries.\n");
    }

    // these will have to be updated
    nx.clear();
    nxc.clear();
    nt = 0;

    for (size_t i =  0; i < lower_boundaries.size(); i++) {
      // Re-compute periodicity using current grid boundaries
      periodic[i] = cv[i]->periodic_boundaries(lower_boundaries[i].real_value,
                                               upper_boundaries[i].real_value);

      cvm::real nbins = ( upper_boundaries[i].real_value -
                          lower_boundaries[i].real_value ) / widths[i];
      int nbins_round = (int)(nbins+0.5);

      if (cvm::fabs(nbins - cvm::real(nbins_round)) > 1.0E-10) {
        cvm::log("Warning: grid interval("+
                 cvm::to_str(lower_boundaries[i], cvm::cv_width, cvm::cv_prec)+" - "+
                 cvm::to_str(upper_boundaries[i], cvm::cv_width, cvm::cv_prec)+
                 ") is not commensurate to its bin width("+
                 cvm::to_str(widths[i], cvm::cv_width, cvm::cv_prec)+").\n");
        upper_boundaries[i].real_value = lower_boundaries[i].real_value +
          (nbins_round * widths[i]);
      }

      if (cvm::debug())
        cvm::log("Number of points is "+cvm::to_str((int) nbins_round)+
                 " for the colvar no. "+cvm::to_str(i+1)+".\n");

      nx.push_back(nbins_round);
    }

    return COLVARS_OK;
  }

  inline void wrap(std::vector<int> & ix) const
  {
    for (size_t i = 0; i < nd; i++) {
      if (periodic[i]) {
        ix[i] = (ix[i] + nx[i]) % nx[i]; //to ensure non-negative result
      } else {
        if (ix[i] < 0 || ix[i] >= nx[i]) {
          cvm::error("Trying to wrap illegal index vector (non-PBC) for a grid point: "
                     + cvm::to_str(ix), COLVARS_BUG_ERROR);
          return;
        }
      }
    }
  }

  inline bool wrap_edge(std::vector<int> & ix) const
  {
    bool edge = false;
    for (size_t i = 0; i < nd; i++) {
      if (periodic[i]) {
        ix[i] = (ix[i] + nx[i]) % nx[i]; //to ensure non-negative result
      } else if (ix[i] == -1 || ix[i] == nx[i]) {
        edge = true;
      }
    }
    return edge;
  }

  inline int current_bin_scalar(int const i) const
  {
    return value_to_bin_scalar(use_actual_value[i] ? cv[i]->actual_value() : cv[i]->value(), i);
  }

  inline int current_bin_scalar_bound(int const i) const
  {
    return value_to_bin_scalar_bound(use_actual_value[i] ? cv[i]->actual_value() : cv[i]->value(), i);
  }

  inline int current_bin_scalar(int const i, int const iv) const
  {
    return value_to_bin_scalar(use_actual_value[i] ?
                               cv[i]->actual_value().vector1d_value[iv] :
                               cv[i]->value().vector1d_value[iv], i);
  }

  inline int value_to_bin_scalar(colvarvalue const &value, const int i) const
  {
    return (int) cvm::floor( (value.real_value - lower_boundaries[i].real_value) / widths[i] );
  }

  inline cvm::real current_bin_scalar_fraction(int const i) const
  {
    return value_to_bin_scalar_fraction(use_actual_value[i] ? cv[i]->actual_value() : cv[i]->value(), i);
  }

  inline cvm::real value_to_bin_scalar_fraction(colvarvalue const &value, const int i) const
  {
    cvm::real x = (value.real_value - lower_boundaries[i].real_value) / widths[i];
    return x - cvm::floor(x);
  }

  inline int value_to_bin_scalar_bound(colvarvalue const &value, const int i) const
  {
    int bin_index = cvm::floor( (value.real_value - lower_boundaries[i].real_value) / widths[i] );
    if (bin_index < 0) bin_index=0;
    if (bin_index >=int(nx[i])) bin_index=int(nx[i])-1;
    return (int) bin_index;
  }

  inline int value_to_bin_scalar(colvarvalue const &value,
                                 colvarvalue const &new_offset,
                                 cvm::real   const &new_width) const
  {
    return (int) cvm::floor( (value.real_value - new_offset.real_value) / new_width );
  }

  inline colvarvalue bin_to_value_scalar(int const &i_bin, int const i) const
  {
    return lower_boundaries[i].real_value + widths[i] * (0.5 + i_bin);
  }

  inline colvarvalue bin_to_value_scalar(int const &i_bin,
                                         colvarvalue const &new_offset,
                                         cvm::real const &new_width) const
  {
    return new_offset.real_value + new_width * (0.5 + i_bin);
  }

  inline void set_value(std::vector<int> const &ix,
                        T const &t,
                        size_t const &imult = 0)
  {
    data[this->address(ix)+imult] = t;
    has_data = true;
  }

  inline void set_value(size_t i, T const &t)
  {
    data[i] = t;
  }

  void delta_grid(colvar_grid<T> const &other_grid)
  {

    if (other_grid.multiplicity() != this->multiplicity()) {
      cvm::error("Error: trying to subtract two grids with "
                 "different multiplicity.\n");
      return;
    }

    if (other_grid.data.size() != this->data.size()) {
      cvm::error("Error: trying to subtract two grids with "
                 "different size.\n");
      return;
    }

    for (size_t i = 0; i < data.size(); i++) {
      data[i] = other_grid.data[i] - data[i];
    }
    has_data = true;
  }

  void copy_grid(colvar_grid<T> const &other_grid)
  {
    if (other_grid.multiplicity() != this->multiplicity()) {
      cvm::error("Error: trying to copy two grids with "
                 "different multiplicity.\n");
      return;
    }

    if (other_grid.data.size() != this->data.size()) {
      cvm::error("Error: trying to copy two grids with "
                 "different size.\n");
      return;
    }


    for (size_t i = 0; i < data.size(); i++) {
      data[i] = other_grid.data[i];
    }
    has_data = true;
  }

  void raw_data_out(T* out_data) const
  {
    for (size_t i = 0; i < data.size(); i++) out_data[i] = data[i];
  }
  void raw_data_out(std::vector<T>& out_data) const
  {
    out_data = data;
  }
  void raw_data_in(const T* in_data)
  {
    for (size_t i = 0; i < data.size(); i++) data[i] = in_data[i];
    has_data = true;
  }
  void raw_data_in(const std::vector<T>& in_data)
  {
    data = in_data;
    has_data = true;
  }
  size_t raw_data_num() const { return data.size(); }


  inline T const & value(std::vector<int> const &ix,
                         size_t const &imult = 0) const
  {
    return data[this->address(ix) + imult];
  }

  inline T const & value(size_t i) const
  {
    return data[i];
  }

  inline void add_constant(T const &t)
  {
    for (size_t i = 0; i < nt; i++)
      data[i] += t;
    has_data = true;
  }

  inline void multiply_constant(cvm::real const &a)
  {
    for (size_t i = 0; i < nt; i++)
      data[i] *= a;
  }

  inline void remove_small_values(cvm::real const &a)
  {
    for (size_t i = 0; i < nt; i++)
      if(data[i]<a) data[i] = a;
  }


  inline std::vector<int> const get_colvars_index(std::vector<colvarvalue> const &values) const
  {
    std::vector<int> index = new_index();
    for (size_t i = 0; i < nd; i++) {
      index[i] = value_to_bin_scalar(values[i], i);
    }
    return index;
  }

  inline std::vector<int> const get_colvars_index() const
  {
    std::vector<int> index = new_index();
    for (size_t i = 0; i < nd; i++) {
      index[i] = current_bin_scalar(i);
    }
    return index;
  }

  inline std::vector<int> const get_colvars_index_bound() const
  {
    std::vector<int> index = new_index();
    for (size_t i = 0; i < nd; i++) {
      index[i] = current_bin_scalar_bound(i);
    }
    return index;
  }

  inline cvm::real bin_distance_from_boundaries(std::vector<colvarvalue> const &values,
                                                bool skip_hard_boundaries = false)
  {
    cvm::real minimum = 1.0E+16;
    for (size_t i = 0; i < nd; i++) {

      if (periodic[i]) continue;

      cvm::real dl = cvm::sqrt(cv[i]->dist2(values[i], lower_boundaries[i])) / widths[i];
      cvm::real du = cvm::sqrt(cv[i]->dist2(values[i], upper_boundaries[i])) / widths[i];

      if (values[i].real_value < lower_boundaries[i])
        dl *= -1.0;
      if (values[i].real_value > upper_boundaries[i])
        du *= -1.0;

      if ( ((!skip_hard_boundaries) || (!hard_lower_boundaries[i])) && (dl < minimum))
        minimum = dl;
      if ( ((!skip_hard_boundaries) || (!hard_upper_boundaries[i])) && (du < minimum))
        minimum = du;
    }

    return minimum;
  }


  void map_grid(colvar_grid<T> const &other_grid)
  {
    if (other_grid.multiplicity() != this->multiplicity()) {
      cvm::error("Error: trying to merge two grids with values of "
                 "different multiplicity.\n");
      return;
    }

    std::vector<colvarvalue> const &gb  = this->lower_boundaries;
    std::vector<cvm::real> const &gw    = this->widths;
    std::vector<colvarvalue> const &ogb = other_grid.lower_boundaries;
    std::vector<cvm::real> const &ogw   = other_grid.widths;

    std::vector<int> ix = this->new_index();
    std::vector<int> oix = other_grid.new_index();

    if (cvm::debug())
      cvm::log("Remapping grid...\n");
    for ( ; this->index_ok(ix); this->incr(ix)) {

      for (size_t i = 0; i < nd; i++) {
        oix[i] =
          value_to_bin_scalar(bin_to_value_scalar(ix[i], gb[i], gw[i]),
                              ogb[i],
                              ogw[i]);
      }

      if (! other_grid.index_ok(oix)) {
        continue;
      }

      for (size_t im = 0; im < mult; im++) {
        this->set_value(ix, other_grid.value(oix, im), im);
      }
    }

    has_data = true;
    if (cvm::debug())
      cvm::log("Remapping done.\n");
  }

  void add_grid(colvar_grid<T> const &other_grid,
                cvm::real scale_factor = 1.0)
  {
    if (other_grid.multiplicity() != this->multiplicity()) {
      cvm::error("Error: trying to sum togetehr two grids with values of "
                 "different multiplicity.\n");
      return;
    }
    if (scale_factor != 1.0)
      for (size_t i = 0; i < data.size(); i++) {
        data[i] += static_cast<T>(scale_factor * other_grid.data[i]);
      }
    else
      // skip multiplication if possible
      for (size_t i = 0; i < data.size(); i++) {
        data[i] += other_grid.data[i];
      }
    has_data = true;
  }

  virtual T value_output(std::vector<int> const &ix,
                         size_t const &imult = 0) const
  {
    return value(ix, imult);
  }

  virtual void value_input(std::vector<int> const &ix,
                           T const &t,
                           size_t const &imult = 0,
                           bool add = false)
  {
    if ( add )
      data[address(ix) + imult] += t;
    else
      data[address(ix) + imult] = t;
    has_data = true;
  }

  //   /// Get the pointer to the binned value indexed by ix
  //   inline T const *value_p (std::vector<int> const &ix)
  //   {
  //     return &(data[address (ix)]);
  //   }

  inline std::vector<int> const new_index() const
  {
    return std::vector<int> (nd, 0);
  }

  inline bool index_ok(std::vector<int> const &ix) const
  {
    for (size_t i = 0; i < nd; i++) {
      if ( (ix[i] < 0) || (ix[i] >= int(nx[i])) )
        return false;
    }
    return true;
  }

  inline void incr(std::vector<int> &ix) const
  {
    for (int i = ix.size()-1; i >= 0; i--) {

      ix[i]++;

      if (ix[i] >= nx[i]) {

        if (i > 0) {
          ix[i] = 0;
          continue;
        } else {
          // this is the last iteration, a non-valid index is being
          // set for the outer index, which will be caught by
          // index_ok()
          ix[0] = nx[0];
          return;
        }
      } else {
        return;
      }
    }
  }

  std::ostream & write_params(std::ostream &os)
  {
    size_t i;
    os << "grid_parameters {\n  n_colvars " << nd << "\n";

    os << "  lower_boundaries ";
    for (i = 0; i < nd; i++)
      os << " " << lower_boundaries[i];
    os << "\n";

    os << "  upper_boundaries ";
    for (i = 0; i < nd; i++)
      os << " " << upper_boundaries[i];
    os << "\n";

    os << "  widths ";
    for (i = 0; i < nd; i++)
      os << " " << widths[i];
    os << "\n";

    os << "  sizes ";
    for (i = 0; i < nd; i++)
      os << " " << nx[i];
    os << "\n";

    os << "}\n";
    return os;
  }

  int parse_params(std::string const &conf,
                   colvarparse::Parse_Mode const parse_mode = colvarparse::parse_normal)
  {
    if (cvm::debug()) cvm::log("Reading grid configuration from string.\n");

    std::vector<int> old_nx = nx;
    std::vector<colvarvalue> old_lb = lower_boundaries;
    std::vector<colvarvalue> old_ub = upper_boundaries;
    std::vector<cvm::real> old_w = widths;

    {
      size_t nd_in = 0;
      // this is only used in state files
      colvarparse::get_keyval(conf, "n_colvars", nd_in, nd, colvarparse::parse_silent);
      if (nd_in != nd) {
        cvm::error("Error: trying to read data for a grid "
                   "that contains a different number of colvars ("+
                   cvm::to_str(nd_in)+") than the grid defined "
                   "in the configuration file("+cvm::to_str(nd)+
                   ").\n");
        return COLVARS_ERROR;
      }
    }

    // underscore keywords are used in state file
    colvarparse::get_keyval(conf, "lower_boundaries",
                            lower_boundaries, lower_boundaries, colvarparse::parse_silent);
    colvarparse::get_keyval(conf, "upper_boundaries",
                            upper_boundaries, upper_boundaries, colvarparse::parse_silent);

    // camel case keywords are used in config file
    colvarparse::get_keyval(conf, "lowerBoundaries",
                            lower_boundaries, lower_boundaries, parse_mode);
    colvarparse::get_keyval(conf, "upperBoundaries",
                            upper_boundaries, upper_boundaries, parse_mode);

    colvarparse::get_keyval(conf, "widths", widths, widths, parse_mode);

    // only used in state file
    colvarparse::get_keyval(conf, "sizes", nx, nx, colvarparse::parse_silent);

    if (nd < lower_boundaries.size()) nd = lower_boundaries.size();

    if (! use_actual_value.size()) use_actual_value.assign(nd, false);
    if (! periodic.size()) periodic.assign(nd, false);
    if (! widths.size()) widths.assign(nd, 1.0);

    cvm::real eps = 1.e-10;

    bool new_params = false;
    if (old_nx.size()) {
      for (size_t i = 0; i < nd; i++) {
        if (old_nx[i] != nx[i] ||
            cvm::sqrt(cv[i]->dist2(old_lb[i], lower_boundaries[i])) > eps ||
            cvm::sqrt(cv[i]->dist2(old_ub[i], upper_boundaries[i])) > eps ||
            cvm::fabs(old_w[i] - widths[i]) > eps) {
          new_params = true;
        }
      }
    } else {
      new_params = true;
    }

    // reallocate the array in case the grid params have just changed
    if (new_params) {
      init_from_boundaries();
      // data.clear(); // no longer needed: setup calls clear()
      return this->setup(nx, T(), mult);
    }

    return COLVARS_OK;
  }

  void check_consistency()
  {
    for (size_t i = 0; i < nd; i++) {
      if ( (cvm::sqrt(cv[i]->dist2(cv[i]->lower_boundary,
                                   lower_boundaries[i])) > 1.0E-10) ||
           (cvm::sqrt(cv[i]->dist2(cv[i]->upper_boundary,
                                   upper_boundaries[i])) > 1.0E-10) ||
           (cvm::sqrt(cv[i]->dist2(cv[i]->width,
                                   widths[i])) > 1.0E-10) ) {
        cvm::error("Error: restart information for a grid is "
                   "inconsistent with that of its colvars.\n");
        return;
      }
    }
  }


  void check_consistency(colvar_grid<T> const &other_grid)
  {
    for (size_t i = 0; i < nd; i++) {
      // we skip dist2(), because periodicities and the like should
      // matter: boundaries should be EXACTLY the same (otherwise,
      // map_grid() should be used)
      if ( (cvm::fabs(other_grid.lower_boundaries[i] -
                      lower_boundaries[i]) > 1.0E-10) ||
           (cvm::fabs(other_grid.upper_boundaries[i] -
                      upper_boundaries[i]) > 1.0E-10) ||
           (cvm::fabs(other_grid.widths[i] -
                      widths[i]) > 1.0E-10) ||
           (data.size() != other_grid.data.size()) ) {
        cvm::error("Error: inconsistency between "
                   "two grids that are supposed to be equal, "
                   "aside from the data stored.\n");
        return;
      }
    }
  }


  std::istream & read_restart(std::istream &is)
  {
    std::streampos const start_pos = is.tellg();
    std::string key, conf;
    if ((is >> key) && (key == std::string("grid_parameters"))) {
      is.seekg(start_pos, std::ios::beg);
      is >> colvarparse::read_block("grid_parameters", &conf);
      parse_params(conf, colvarparse::parse_silent);
    } else {
      cvm::log("Grid parameters are missing in the restart file, using those from the configuration.\n");
      is.seekg(start_pos, std::ios::beg);
    }
    read_raw(is);
    return is;
  }

  std::ostream & write_restart(std::ostream &os)
  {
    write_params(os);
    write_raw(os);
    return os;
  }


  std::ostream & write_raw(std::ostream &os,
                           size_t const buf_size = 3) const
  {
    std::streamsize const w = os.width();
    std::streamsize const p = os.precision();

    std::vector<int> ix = new_index();
    size_t count = 0;
    for ( ; index_ok(ix); incr(ix)) {
      for (size_t imult = 0; imult < mult; imult++) {
        os << " "
           << std::setw(w) << std::setprecision(p)
           << value_output(ix, imult);
        if (((++count) % buf_size) == 0)
          os << "\n";
      }
    }
    // write a final newline only if buffer is not empty
    if ((count % buf_size) != 0)
      os << "\n";

    return os;
  }

  std::istream & read_raw(std::istream &is)
  {
    std::streampos const start_pos = is.tellg();

    for (std::vector<int> ix = new_index(); index_ok(ix); incr(ix)) {
      for (size_t imult = 0; imult < mult; imult++) {
        T new_value;
        if (is >> new_value) {
          value_input(ix, new_value, imult);
        } else {
          is.clear();
          is.seekg(start_pos, std::ios::beg);
          is.setstate(std::ios::failbit);
          cvm::error("Error: failed to read all of the grid points from file.  Possible explanations: grid parameters in the configuration (lowerBoundary, upperBoundary, width) are different from those in the file, or the file is corrupt/incomplete.\n");
          return is;
        }
      }
    }

    has_data = true;
    return is;
  }

  std::istream & read_multicol(std::istream &is, bool add = false);

  int read_multicol(std::string const &filename,
                    std::string description = "grid file",
                    bool add = false);

  std::ostream & write_multicol(std::ostream &os) const;

  int write_multicol(std::string const &filename,
                     std::string description = "grid file") const;

  std::ostream & write_opendx(std::ostream &os) const;

  int write_opendx(std::string const &filename,
                   std::string description = "grid file") const;
};



class colvar_grid_count : public colvar_grid<size_t>
{
public:

  colvar_grid_count();

  virtual ~colvar_grid_count()
  {}

  colvar_grid_count(std::vector<int> const &nx_i,
                    size_t const           &def_count = 0);

  colvar_grid_count(std::vector<colvar *>  &colvars,
                    size_t const           &def_count = 0,
                    bool                   add_extra_bin = false);

  inline void incr_count(std::vector<int> const &ix)
  {
    ++(data[this->address(ix)]);
  }

  inline size_t const & new_count(std::vector<int> const &ix,
                                  size_t const &imult = 0)
  {
    return new_data[address(ix) + imult];
  }

  std::istream & read_multicol(std::istream &is, bool add = false);

  int read_multicol(std::string const &filename,
                            std::string description = "grid file",
                            bool add = false);

  std::ostream & write_multicol(std::ostream &os) const;

  int write_multicol(std::string const &filename,
                     std::string description = "grid file") const;

  std::ostream & write_opendx(std::ostream &os) const;

  int write_opendx(std::string const &filename,
                   std::string description = "grid file") const;

  virtual void value_input(std::vector<int> const &ix,
                           size_t const &t,
                           size_t const &imult = 0,
                           bool add = false)
  {
    (void) imult;
    if (add) {
      data[address(ix)] += t;
      if (this->has_parent_data) {
        // save newly read data for inputting parent grid
        new_data[address(ix)] = t;
      }
    } else {
      data[address(ix)] = t;
    }
    has_data = true;
  }

  inline cvm::real log_gradient_finite_diff(const std::vector<int> &ix0,
                                            int n = 0)
  {
    cvm::real A0, A1, A2;
    std::vector<int> ix = ix0;

    // TODO this can be rewritten more concisely with wrap_edge()
    if (periodic[n]) {
      ix[n]--; wrap(ix);
      A0 = value(ix);
      ix = ix0;
      ix[n]++; wrap(ix);
      A1 = value(ix);
      if (A0 * A1 == 0) {
        return 0.; // can't handle empty bins
      } else {
        return (cvm::logn(A1) - cvm::logn(A0))
          / (widths[n] * 2.);
      }
    } else if (ix[n] > 0 && ix[n] < nx[n]-1) { // not an edge
      ix[n]--;
      A0 = value(ix);
      ix = ix0;
      ix[n]++;
      A1 = value(ix);
      if (A0 * A1 == 0) {
        return 0.; // can't handle empty bins
      } else {
        return (cvm::logn(A1) - cvm::logn(A0))
          / (widths[n] * 2.);
      }
    } else {
      // edge: use 2nd order derivative
      int increment = (ix[n] == 0 ? 1 : -1);
      // move right from left edge, or the other way around
      A0 = value(ix);
      ix[n] += increment; A1 = value(ix);
      ix[n] += increment; A2 = value(ix);
      if (A0 * A1 * A2 == 0) {
        return 0.; // can't handle empty bins
      } else {
        return (-1.5 * cvm::logn(A0) + 2. * cvm::logn(A1)
          - 0.5 * cvm::logn(A2)) * increment / widths[n];
      }
    }
  }

  inline cvm::real gradient_finite_diff(const std::vector<int> &ix0,
                                        int n = 0)
  {
    cvm::real A0, A1, A2;
    std::vector<int> ix = ix0;

    // FIXME this can be rewritten more concisely with wrap_edge()
    if (periodic[n]) {
      ix[n]--; wrap(ix);
      A0 = value(ix);
      ix = ix0;
      ix[n]++; wrap(ix);
      A1 = value(ix);
      if (A0 * A1 == 0) {
        return 0.; // can't handle empty bins
      } else {
        return (A1 - A0) / (widths[n] * 2.);
      }
    } else if (ix[n] > 0 && ix[n] < nx[n]-1) { // not an edge
      ix[n]--;
      A0 = value(ix);
      ix = ix0;
      ix[n]++;
      A1 = value(ix);
      if (A0 * A1 == 0) {
        return 0.; // can't handle empty bins
      } else {
        return (A1 - A0) / (widths[n] * 2.);
      }
    } else {
      // edge: use 2nd order derivative
      int increment = (ix[n] == 0 ? 1 : -1);
      // move right from left edge, or the other way around
      A0 = value(ix);
      ix[n] += increment; A1 = value(ix);
      ix[n] += increment; A2 = value(ix);
      return (-1.5 * A0 + 2. * A1
          - 0.5 * A2) * increment / widths[n];
    }
  }
};


class colvar_grid_scalar : public colvar_grid<cvm::real>
{
public:

  colvar_grid_count *samples;

  colvar_grid_scalar();

  colvar_grid_scalar(colvar_grid_scalar const &g);

  virtual ~colvar_grid_scalar();

  colvar_grid_scalar(std::vector<int> const &nx_i);

  colvar_grid_scalar(std::vector<colvar *> &colvars,
                     bool add_extra_bin = false);

  inline void acc_value(std::vector<int> const &ix,
                        cvm::real const &new_value,
                        size_t const &imult = 0)
  {
    (void) imult;
    // only legal value of imult here is 0
    data[address(ix)] += new_value;
    if (samples)
      samples->incr_count(ix);
    has_data = true;
  }

  std::istream & read_multicol(std::istream &is, bool add = false);

  int read_multicol(std::string const &filename,
                    std::string description = "grid file",
                    bool add = false);

  std::ostream & write_multicol(std::ostream &os) const;

  int write_multicol(std::string const &filename,
                     std::string description = "grid file") const;

  std::ostream & write_opendx(std::ostream &os) const;

  int write_opendx(std::string const &filename,
                   std::string description = "grid file") const;

  inline void vector_gradient_finite_diff( const std::vector<int> &ix0, std::vector<cvm::real> &grad)
  {
    cvm::real A0, A1;
    std::vector<int> ix;
    size_t i, j, k, n;

    if (nd == 2) {
      for (n = 0; n < 2; n++) {
        ix = ix0;
        A0 = value(ix);
        ix[n]++; wrap(ix);
        A1 = value(ix);
        ix[1-n]++; wrap(ix);
        A1 += value(ix);
        ix[n]--; wrap(ix);
        A0 += value(ix);
        grad[n] = 0.5 * (A1 - A0) / widths[n];
      }
    } else if (nd == 3) {

      cvm::real p[8]; // potential values within cube, indexed in binary (4 i + 2 j + k)
      ix = ix0;
      int index = 0;
      for (i = 0; i<2; i++) {
        ix[1] = ix0[1];
        for (j = 0; j<2; j++) {
          ix[2] = ix0[2];
          for (k = 0; k<2; k++) {
            wrap(ix);
            p[index++] = value(ix);
            ix[2]++;
          }
          ix[1]++;
        }
        ix[0]++;
      }

      // The following would be easier to read using binary literals
      //                  100    101    110    111      000    001    010   011
      grad[0] = 0.25 * ((p[4] + p[5] + p[6] + p[7]) - (p[0] + p[1] + p[2] + p[3])) / widths[0];
      //                  010     011    110   111      000    001    100   101
      grad[1] = 0.25 * ((p[2] + p[3] + p[6] + p[7]) - (p[0] + p[1] + p[4] + p[5])) / widths[1];
      //                  001    011     101   111      000    010   100    110
      grad[2] = 0.25 * ((p[1] + p[3] + p[5] + p[7]) - (p[0] + p[2] + p[4] + p[6])) / widths[2];
    } else {
      cvm::error("Finite differences available in dimension 2 and 3 only.");
    }
  }

  inline cvm::real gradient_finite_diff(const std::vector<int> &ix0,
                                        int n = 0)
  {
    cvm::real A0, A1, A2;
    std::vector<int> ix = ix0;

    // FIXME this can be rewritten more concisely with wrap_edge()
    if (periodic[n]) {
      ix[n]--; wrap(ix);
      A0 = value(ix);
      ix = ix0;
      ix[n]++; wrap(ix);
      A1 = value(ix);
      if (A0 * A1 == 0) {
        return 0.; // can't handle empty bins
      } else {
        return (A1 - A0) / (widths[n] * 2.);
      }
    } else if (ix[n] > 0 && ix[n] < nx[n]-1) { // not an edge
      ix[n]--;
      A0 = value(ix);
      ix = ix0;
      ix[n]++;
      A1 = value(ix);
      if (A0 * A1 == 0) {
        return 0.; // can't handle empty bins
      } else {
        return (A1 - A0) / (widths[n] * 2.);
      }
    } else {
      // edge: use 2nd order derivative
      int increment = (ix[n] == 0 ? 1 : -1);
      // move right from left edge, or the other way around
      A0 = value(ix);
      ix[n] += increment; A1 = value(ix);
      ix[n] += increment; A2 = value(ix);
      return (-1.5 * A0 + 2. * A1
          - 0.5 * A2) * increment / widths[n];
    }
  }

  virtual cvm::real value_output(std::vector<int> const &ix,
                                 size_t const &imult = 0) const
  {
    if (imult > 0) {
      cvm::error("Error: trying to access a component "
                 "larger than 1 in a scalar data grid.\n");
      return 0.;
    }
    if (samples) {
      return (samples->value(ix) > 0) ?
        (data[address(ix)] / cvm::real(samples->value(ix))) :
        0.0;
    } else {
      return data[address(ix)];
    }
  }

  virtual void value_input(std::vector<int> const &ix,
                           cvm::real const &new_value,
                           size_t const &imult = 0,
                           bool add = false)
  {
    if (imult > 0) {
      cvm::error("Error: trying to access a component "
                 "larger than 1 in a scalar data grid.\n");
      return;
    }
    if (add) {
      if (samples)
        data[address(ix)] += new_value * samples->new_count(ix);
      else
        data[address(ix)] += new_value;
    } else {
      if (samples)
        data[address(ix)] = new_value * samples->value(ix);
      else
        data[address(ix)] = new_value;
    }
    has_data = true;
  }

  cvm::real maximum_value() const;

  cvm::real minimum_value() const;

  cvm::real minimum_pos_value() const;

  cvm::real integral() const;

  cvm::real entropy() const;
};



class colvar_grid_gradient : public colvar_grid<cvm::real>
{
public:

  colvar_grid_count *samples;

  colvar_grid_scalar *weights;

  colvar_grid_gradient();

  virtual ~colvar_grid_gradient()
  {}

  colvar_grid_gradient(std::vector<int> const &nx_i);

  colvar_grid_gradient(std::vector<colvar *>  &colvars);

  colvar_grid_gradient(std::string &filename);

  virtual std::istream & read_multicol(std::istream &is, bool add = false);

  virtual int read_multicol(std::string const &filename,
                            std::string description = "grid file",
                            bool add = false);

  virtual std::ostream & write_multicol(std::ostream &os) const;

  virtual int write_multicol(std::string const &filename,
                             std::string description = "grid file") const;

  virtual std::ostream & write_opendx(std::ostream &os) const;

  virtual int write_opendx(std::string const &filename,
                           std::string description = "grid file") const;

  inline void vector_value(std::vector<int> const &ix, std::vector<cvm::real> &v) const
  {
    cvm::real const * p = &value(ix);
    if (samples) {
      int count = samples->value(ix);
      if (count) {
        cvm::real invcount = 1.0 / count;
        for (size_t i = 0; i < mult; i++) {
          v[i] = invcount * p[i];
        }
      } else {
        for (size_t i = 0; i < mult; i++) {
          v[i] = 0.0;
        }
      }
    } else {
      for (size_t i = 0; i < mult; i++) {
        v[i] = p[i];
      }
    }
  }

  inline void acc_value(std::vector<int> const &ix, std::vector<colvarvalue> const &values) {
    for (size_t imult = 0; imult < mult; imult++) {
      data[address(ix) + imult] += values[imult].real_value;
    }
    if (samples)
      samples->incr_count(ix);
  }

  inline void acc_force(std::vector<int> const &ix, cvm::real const *forces) {
    for (size_t imult = 0; imult < mult; imult++) {
      data[address(ix) + imult] -= forces[imult];
    }
    if (samples)
      samples->incr_count(ix);
  }

  inline void acc_force_weighted(std::vector<int> const &ix,
                                 cvm::real const *forces,
                                 cvm::real weight) {
    for (size_t imult = 0; imult < mult; imult++) {
      data[address(ix) + imult] -= forces[imult] * weight;
    }
    weights->acc_value(ix, weight);
  }

  virtual cvm::real value_output(std::vector<int> const &ix,
                                 size_t const &imult = 0) const
  {
    if (samples)
      return (samples->value(ix) > 0) ?
        (data[address(ix) + imult] / cvm::real(samples->value(ix))) :
        0.0;
    else
      return data[address(ix) + imult];
  }

  virtual void value_input(std::vector<int> const &ix,
                           cvm::real const &new_value,
                           size_t const &imult = 0,
                           bool add = false)
  {
    if (add) {
      if (samples)
        data[address(ix) + imult] += new_value * samples->new_count(ix);
      else
        data[address(ix) + imult] += new_value;
    } else {
      if (samples)
        data[address(ix) + imult] = new_value * samples->value(ix);
      else
        data[address(ix) + imult] = new_value;
    }
    has_data = true;
  }


  inline cvm::real average()
  {
    size_t n = 0;

    if (nd != 1 || nx[0] == 0) {
      return 0.0;
    }

    cvm::real sum = 0.0;
    std::vector<int> ix = new_index();
    if (samples) {
      for ( ; index_ok(ix); incr(ix)) {
        if ( (n = samples->value(ix)) )
          sum += value(ix) / n;
      }
    } else {
      for ( ; index_ok(ix); incr(ix)) {
        sum += value(ix);
      }
    }
    return (sum / cvm::real(nx[0]));
  }

  void write_1D_integral(std::ostream &os);

};




class integrate_potential : public colvar_grid_scalar
{
  public:

  integrate_potential();

  virtual ~integrate_potential()
  {}

  integrate_potential(std::vector<colvar *> &colvars, colvar_grid_gradient * gradients);

  integrate_potential(colvar_grid_gradient * gradients);

  int integrate(const int itmax, const cvm::real & tol, cvm::real & err);

  void update_div_neighbors(const std::vector<int> &ix);

  void set_div();

  inline void set_zero_minimum() {
    add_constant(-1.0 * minimum_value());
  }

  protected:

  // Reference to gradient grid
  colvar_grid_gradient *gradients;

  std::vector<cvm::real> divergence;

//   std::vector<cvm::real> inv_lap_diag; // Inverse of the diagonal of the Laplacian; for conditioning

  void update_div_local(const std::vector<int> &ix);

  void get_grad(cvm::real * g, std::vector<int> &ix);

  void nr_linbcg_sym(const std::vector<cvm::real> &b, std::vector<cvm::real> &x,
                     const cvm::real &tol, const int itmax, int &iter, cvm::real &err);

  cvm::real l2norm(const std::vector<cvm::real> &x);

  void atimes(const std::vector<cvm::real> &x, std::vector<cvm::real> &r);

//   /// Inversion of preconditioner matrix
//   void asolve(const std::vector<cvm::real> &b, std::vector<cvm::real> &x);
};

#endif

---