/// -*- c++ -*-

#ifndef COLVARCOMP_H
#define COLVARCOMP_H

// Declaration of colvar::cvc base class and derived ones.
//
// Future cvc's could be declared on additional header files.
// After the declaration of a new derived class, its metric
// functions must be reimplemented as well.
// If the new cvc has no symmetry or periodicity,
// this can be done straightforwardly by using the macro:
// simple_scalar_dist_functions (derived_class)


#include <fstream>
#include <cmath>


#include "colvarmodule.h"
#include "colvar.h"
#include "colvaratoms.h"


/// \brief Colvar component (base class); most implementations of
/// \link cvc \endlink utilize one or more \link
/// colvarmodule::atom \endlink or \link colvarmodule::atom_group
/// \endlink objects to access atoms.
///
/// A \link cvc \endlink object (or an object of a
/// cvc-derived class) specifies how to calculate a collective
/// variable, its gradients and other related physical quantities
/// which do not depend only on the numeric value (the \link colvar
/// \endlink class already serves this purpose).
///
/// No restriction is set to what kind of calculation a \link
/// cvc \endlink object performs (usually calculate an
/// analytical function of atomic coordinates).  The only constraint
/// is that the value calculated is implemented as a \link colvarvalue
/// \endlink object.  This serves to provide a unique way to calculate
/// scalar and non-scalar collective variables, and specify if and how
/// they can be combined together by the parent \link colvar \endlink
/// object.
///
/// <b> If you wish to implement a new collective variable component, you
/// should write your own class by inheriting directly from \link
/// cvc \endlink, or one of its derived classes (for instance,
/// \link distance \endlink is frequently used, because it provides
/// useful data and function members for any colvar based on two
/// atom groups).  The steps are: \par
/// 1. add the name of this class under colvar.h \par
/// 2. add a call to the parser in colvar.C, within the function colvar::colvar() \par
/// 3. declare the class in colvarcomp.h \par
/// 4. implement the class in one of the files colvarcomp_*.C
///
/// </b>
/// The cvm::atom and cvm::atom_group classes are available to
/// transparently communicate with the simulation program.  However,
/// they are not strictly needed, as long as all the degrees of
/// freedom associated to the cvc are properly evolved by a simple
/// call to e.g. apply_force().

class colvar::cvc
  : public colvarparse
{
public:

  /// \brief The name of the object (helps to identify this
  /// cvc instance when debugging)
  std::string name;

  /// \brief Description of the type of collective variable
  ///
  /// Normally this string is set by the parent \link colvar \endlink
  /// object within its constructor, when all \link cvc \endlink
  /// objects are initialized; therefore the main "config string"
  /// constructor does not need to define it.  If a \link cvc
  /// \endlink is initialized and/or a different constructor is used,
  /// this variable definition should be set within the constructor.
  std::string function_type;

  /// \brief Type of \link colvarvalue \endlink that this cvc
  /// provides
  colvarvalue::Type type() const;

  /// \brief Coefficient in the polynomial combination (default: 1.0)
  cvm::real sup_coeff;
  /// \brief Exponent in the polynomial combination (default: 1)
  int       sup_np;

  /// \brief Period of this cvc value, (default: 0.0, non periodic)
  cvm::real period;

  /// \brief If the component is periodic, wrap around this value (default: 0.0)
  cvm::real wrap_center;

  bool b_periodic;

  /// \brief Constructor
  ///
  /// At least one constructor which reads a string should be defined
  /// for every class inheriting from cvc \param conf Contents
  /// of the configuration file pertaining to this \link cvc
  /// \endlink
  cvc (std::string const &conf);

  /// \brief Within the constructor, make a group parse its own
  /// options from the provided configuration string
  void parse_group (std::string const &conf,
                    char const *group_key,
                    cvm::atom_group &group,
                    bool optional = false);

  /// \brief Default constructor (used when \link cvc \endlink
  /// objects are declared within other ones)
  cvc();

  /// Destructor
  virtual ~cvc();


  /// \brief If this flag is false (default), inverse gradients
  /// (derivatives of atom coordinates with respect to x) are
  /// unavailable; it should be set to true by the constructor of each
  /// derived object capable of calculating them
  bool b_inverse_gradients;

  /// \brief If this flag is false (default), the Jacobian derivative
  /// (divergence of the inverse gradients) is unavailable; it should
  /// be set to true by the constructor of each derived object capable
  /// of calculating it
  bool b_Jacobian_derivative;

  /// \brief Calculate the variable
  virtual void calc_value() = 0;

  /// \brief Calculate the atomic gradients, to be reused later in
  /// order to apply forces
  virtual void calc_gradients() = 0;

  /// \brief If true, calc_gradients() will call debug_gradients() for every group needed
  bool b_debug_gradients;

  /// \brief Calculate finite-difference gradients alongside the analytical ones, for each Cartesian component
  virtual void debug_gradients (cvm::atom_group &group);

  /// \brief Calculate the total force from the system using the
  /// inverse atomic gradients
  virtual void calc_force_invgrads();

  /// \brief Calculate the divergence of the inverse atomic gradients
  virtual void calc_Jacobian_derivative();


  /// \brief Return the previously calculated value
  virtual colvarvalue value() const;

  /// \brief Return const pointer to the previously calculated value
  virtual const colvarvalue *p_value() const;

  /// \brief Return the previously calculated system force
  virtual colvarvalue system_force() const;

  /// \brief Return the previously calculated divergence of the
  /// inverse atomic gradients
  virtual colvarvalue Jacobian_derivative() const;

  /// \brief Apply the collective variable force, by communicating the
  /// atomic forces to the simulation program (\b Note: the \link ft
  /// \endlink member is not altered by this function)
  ///
  /// Note: multiple calls to this function within the same simulation
  /// step will add the forces altogether \param cvforce The
  /// collective variable force, usually coming from the biases and
  /// eventually manipulated by the parent \link colvar \endlink
  /// object
  virtual void apply_force (colvarvalue const &cvforce) = 0;

  /// \brief Square distance between x1 and x2 (can be redefined to
  /// transparently implement constraints, symmetries and
  /// periodicities)
  ///
  /// colvar::cvc::dist2() and the related functions are
  /// declared as "const" functions, but not "static", because
  /// additional parameters defining the metrics (e.g. the
  /// periodicity) may be specific to each colvar::cvc object.
  ///
  /// If symmetries or periodicities are present, the
  /// colvar::cvc::dist2() should be redefined to return the
  /// "closest distance" value and colvar::cvc::dist2_lgrad(),
  /// colvar::cvc::dist2_rgrad() to return its gradients.
  ///
  /// If constraints are present (and not already implemented by any
  /// of the \link colvarvalue \endlink types), the
  /// colvar::cvc::dist2_lgrad() and
  /// colvar::cvc::dist2_rgrad() functions should be redefined
  /// to provide a gradient which is compatible with the constraint,
  /// i.e. already deprived of its component normal to the constraint
  /// hypersurface.
  ///
  /// Finally, another useful application, if you are performing very
  /// many operations with these functions, could be to override the
  /// \link colvarvalue \endlink member functions and access directly
  /// its member data.  For instance: to define dist2(x1,x2) as
  /// (x2.real_value-x1.real_value)*(x2.real_value-x1.real_value) in
  /// case of a scalar \link colvarvalue \endlink type.
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;

  /// \brief Gradient (with respect to x1) of the square distance (can
  /// be redefined to transparently implement constraints, symmetries
  /// and periodicities)
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;

  /// \brief Gradient (with respect to x2) of the square distance (can
  /// be redefined to transparently implement constraints, symmetries
  /// and periodicities)
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;

  /// \brief Return a positive number if x2>x1, zero if x2==x1,
  /// negative otherwise (can be redefined to transparently implement
  /// constraints, symmetries and periodicities) \b Note: \b it \b
  /// only \b works \b with \b scalar \b variables, otherwise raises
  /// an error
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;

  /// \brief Wrapp value (for periodic/symmetric cvcs)
  virtual void wrap (colvarvalue &x) const;

  /// \brief Pointers to all atom groups, to let colvars collect info
  /// e.g. atomic gradients
  std::vector<cvm::atom_group *> atom_groups;

protected:

  /// \brief Cached value
  colvarvalue x;

  /// \brief Value at the previous step
  colvarvalue x_old;

  /// \brief Calculated system force (\b Note: this is calculated from
  /// the total atomic forces read from the program, subtracting fromt
  /// the "internal" forces of the system the "external" forces from
  /// the colvar biases)
  colvarvalue ft;

  /// \brief Calculated Jacobian derivative (divergence of the inverse
  /// gradients): serves to calculate the phase space correction
  colvarvalue jd;
};




inline colvarvalue::Type colvar::cvc::type() const
{
  return x.type();
}

inline colvarvalue colvar::cvc::value() const
{
  return x;
}

inline const colvarvalue * colvar::cvc::p_value() const
{
  return &x;
}

inline colvarvalue colvar::cvc::system_force() const
{
  return ft;
}

inline colvarvalue colvar::cvc::Jacobian_derivative() const
{
  return jd;
}


inline cvm::real colvar::cvc::dist2 (colvarvalue const &x1,
                                     colvarvalue const &x2) const
{
  return x1.dist2 (x2);
}

inline colvarvalue colvar::cvc::dist2_lgrad (colvarvalue const &x1,
                                             colvarvalue const &x2) const
{
  return x1.dist2_grad (x2);
}

inline colvarvalue colvar::cvc::dist2_rgrad (colvarvalue const &x1,
                                             colvarvalue const &x2) const
{
  return x2.dist2_grad (x1);
}

inline cvm::real colvar::cvc::compare (colvarvalue const &x1,
                                       colvarvalue const &x2) const
{
  if (this->type() == colvarvalue::type_scalar) {
    return cvm::real (x1 - x2);
  } else {
    cvm::error ("Error: you requested an operation which requires "
                "comparison between two non-scalar values.\n");
    return 0.0;
  }
}

inline void colvar::cvc::wrap (colvarvalue &x) const
{
  return;
}


/// \brief Colvar component: distance between the centers of mass of
/// two groups (colvarvalue::type_scalar type, range [0:*))
///
/// This class also serves as the template for many collective
/// variables with two atom groups: in this case, the
/// distance::distance() constructor should be called on the same
/// configuration string, to make the same member data and functions
/// available to the derived object
class colvar::distance
  : public colvar::cvc
{
protected:
  /// First atom group
  cvm::atom_group  group1;
  /// Second atom group
  cvm::atom_group  group2;
  /// Vector distance, cached to be recycled
  cvm::rvector     dist_v;
  /// Use absolute positions, ignoring PBCs when present
  bool b_no_PBC;
  /// Compute system force on first site only to avoid unwanted
  /// coupling to other colvars (see e.g. Ciccotti et al., 2005)
  bool b_1site_force;
public:
  distance (std::string const &conf, bool twogroups = true);
  distance();
  virtual inline ~distance() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void calc_force_invgrads();
  virtual void calc_Jacobian_derivative();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


// \brief Colvar component: distance vector between centers of mass
// of two groups (\link colvarvalue::type_vector \endlink type,
// range (-*:*)x(-*:*)x(-*:*))
class colvar::distance_vec
  : public colvar::distance
{
public:
  distance_vec (std::string const &conf);
  distance_vec();
  virtual inline ~distance_vec() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  /// Redefined to handle the box periodicity
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  /// Redefined to handle the box periodicity
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  /// Redefined to handle the box periodicity
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  /// Redefined to handle the box periodicity
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: distance unit vector (direction) between
/// centers of mass of two groups (colvarvalue::type_unitvector type,
/// range [-1:1]x[-1:1]x[-1:1])
class colvar::distance_dir
  : public colvar::distance
{
public:
  distance_dir (std::string const &conf);
  distance_dir();
  virtual inline ~distance_dir() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: projection of the distance vector along
/// an axis (colvarvalue::type_scalar type, range (-*:*))
class colvar::distance_z
  : public colvar::cvc
{
protected:
  /// Main atom group
  cvm::atom_group  main;
  /// Reference atom group
  cvm::atom_group  ref1;
  /// Optional, second ref atom group
  cvm::atom_group  ref2;
  /// Use absolute positions, ignoring PBCs when present
  bool b_no_PBC;
  /// Compute system force on one site only to avoid unwanted
  /// coupling to other colvars (see e.g. Ciccotti et al., 2005)
  bool b_1site_force;
  /// Vector on which the distance vector is projected
  cvm::rvector axis;
  /// Norm of the axis
  cvm::real axis_norm;
  /// Vector distance, cached to be recycled
  cvm::rvector     dist_v;
  /// Flag: using a fixed axis vector?
  bool fixed_axis;
public:
  distance_z (std::string const &conf);
  distance_z();
  virtual inline ~distance_z() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void calc_force_invgrads();
  virtual void calc_Jacobian_derivative();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
  /// \brief Redefined to make use of the user-provided period
  virtual void wrap (colvarvalue &x) const;
};


/// \brief Colvar component: projection of the distance vector on a
/// plane (colvarvalue::type_scalar type, range [0:*))
class colvar::distance_xy
  : public colvar::distance_z
{
protected:
  /// Components of the distance vector orthogonal to the axis
  cvm::rvector dist_v_ortho;
  /// Vector distances
  cvm::rvector v12, v13;
public:
  distance_xy (std::string const &conf);
  distance_xy();
  virtual inline ~distance_xy() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void calc_force_invgrads();
  virtual void calc_Jacobian_derivative();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: average distance between two groups of atoms, weighted as the sixth power,
/// as in NMR refinements (colvarvalue::type_scalar type, range (0:*))
class colvar::distance_inv
  : public colvar::distance
{
protected:
  /// Components of the distance vector orthogonal to the axis
  int exponent;
public:
  distance_inv (std::string const &conf);
  distance_inv();
  virtual inline ~distance_inv() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};



/// \brief Colvar component: Radius of gyration of an atom group
/// (colvarvalue::type_scalar type, range [0:*))
class colvar::gyration
  : public colvar::cvc
{
protected:
  /// Atoms involved
  cvm::atom_group atoms;
public:
  /// Constructor
  gyration (std::string const &conf);
  gyration();
  virtual inline ~gyration() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void calc_force_invgrads();
  virtual void calc_Jacobian_derivative();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: moment of inertia of an atom group
/// (colvarvalue::type_scalar type, range [0:*))
class colvar::inertia
  : public colvar::gyration
{
public:
  /// Constructor
  inertia (std::string const &conf);
  inertia();
  virtual inline ~inertia() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: moment of inertia of an atom group
/// around a user-defined axis (colvarvalue::type_scalar type, range [0:*))
class colvar::inertia_z
  : public colvar::inertia
{
protected:
  /// Vector on which the inertia tensor is projected
  cvm::rvector axis;
public:
  /// Constructor
  inertia_z (std::string const &conf);
  inertia_z();
  virtual inline ~inertia_z() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: projection of 3N coordinates onto an
/// eigenvector (colvarvalue::type_scalar type, range (-*:*))
class colvar::eigenvector
  : public colvar::cvc
{
protected:

  /// Atom group
  cvm::atom_group             atoms;

  /// Reference coordinates
  std::vector<cvm::atom_pos>  ref_pos;

  /// Geometric center of the reference coordinates
  cvm::atom_pos                ref_pos_center;

  /// Eigenvector (of a normal or essential mode): will always have zero center
  std::vector<cvm::rvector>   eigenvec;

  /// Inverse square norm of the eigenvector
  cvm::real                   eigenvec_invnorm2;

public:

  /// Constructor
  eigenvector (std::string const &conf);
  virtual inline ~eigenvector() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void calc_force_invgrads();
  virtual void calc_Jacobian_derivative();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};



/// \brief Colvar component: angle between the centers of mass of
/// three groups (colvarvalue::type_scalar type, range [0:PI])
class colvar::angle
  : public colvar::cvc
{
protected:

  /// Atom group
  cvm::atom_group group1;
  /// Atom group
  cvm::atom_group group2;
  /// Atom group
  cvm::atom_group group3;

  /// Inter site vectors
  cvm::rvector r21, r23;
  /// Inter site vector norms
  cvm::real r21l, r23l;
  /// Derivatives wrt group centers of mass
  cvm::rvector dxdr1, dxdr3;

  /// Compute system force on first site only to avoid unwanted
  /// coupling to other colvars (see e.g. Ciccotti et al., 2005)
  /// (or to allow dummy atoms)
  bool b_1site_force;
public:

  /// Initialize by parsing the configuration
  angle (std::string const &conf);
  /// \brief Initialize the three groups after three atoms
  angle (cvm::atom const &a1, cvm::atom const &a2, cvm::atom const &a3);
  angle();
  virtual inline ~angle() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void calc_force_invgrads();
  virtual void calc_Jacobian_derivative();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: dihedral between the centers of mass of
/// four groups (colvarvalue::type_scalar type, range [-PI:PI])
class colvar::dihedral
  : public colvar::cvc
{
protected:

  /// Atom group
  cvm::atom_group group1;
  /// Atom group
  cvm::atom_group group2;
  /// Atom group
  cvm::atom_group group3;
  /// Atom group
  cvm::atom_group group4;
  /// Inter site vectors
  cvm::rvector r12, r23, r34;

  /// \brief Compute system force on first site only to avoid unwanted
  /// coupling to other colvars (see e.g. Ciccotti et al., 2005)
  bool b_1site_force;

public:

  /// Initialize by parsing the configuration
  dihedral (std::string  const &conf);
  /// \brief Initialize the four groups after four atoms
  dihedral (cvm::atom const &a1, cvm::atom const &a2, cvm::atom const &a3, cvm::atom const &a4);
  dihedral();
  virtual inline ~dihedral() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void calc_force_invgrads();
  virtual void calc_Jacobian_derivative();
  virtual void apply_force (colvarvalue const &force);

  /// Redefined to handle the 2*PI periodicity
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  /// Redefined to handle the 2*PI periodicity
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  /// Redefined to handle the 2*PI periodicity
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  /// Redefined to handle the 2*PI periodicity
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
  /// Redefined to handle the 2*PI periodicity
  virtual void wrap (colvarvalue &x) const;
};


/// \brief Colvar component: coordination number between two groups
/// (colvarvalue::type_scalar type, range [0:N1*N2])
class colvar::coordnum
  : public colvar::distance
{
protected:
  /// \brief "Cutoff" for isotropic calculation (default)
  cvm::real     r0;
  /// \brief "Cutoff vector" for anisotropic calculation
  cvm::rvector  r0_vec;
  /// \brief Wheter dist/r0 or \vec{dist}*\vec{1/r0_vec} should ne be
  /// used
  bool b_anisotropic;
  /// Integer exponent of the function numerator
  int en;
  /// Integer exponent of the function denominator
  int ed;
  /// \brief If true, group2 will be treated as a single atom
  /// (default: loop over all pairs of atoms in group1 and group2)
  bool b_group2_center_only;
public:
  /// Constructor
  coordnum (std::string const &conf);
  coordnum();
  virtual inline ~coordnum() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  template<bool b_gradients>
  /// \brief Calculate a coordination number through the function
  /// (1-x**n)/(1-x**m), x = |A1-A2|/r0 \param r0 "cutoff" for the
  /// coordination number \param exp_num \i n exponent \param exp_den
  /// \i m exponent \param A1 atom \param A2 atom
  static cvm::real switching_function (cvm::real const &r0,
                                       int const &exp_num, int const &exp_den,
                                       cvm::atom &A1, cvm::atom &A2);

  template<bool b_gradients>
  /// \brief Calculate a coordination number through the function
  /// (1-x**n)/(1-x**m), x = |(A1-A2)*(r0_vec)^-|1 \param r0_vec
  /// vector of different cutoffs in the three directions \param
  /// exp_num \i n exponent \param exp_den \i m exponent \param A1
  /// atom \param A2 atom
  static cvm::real switching_function (cvm::rvector const &r0_vec,
                                       int const &exp_num, int const &exp_den,
                                       cvm::atom &A1, cvm::atom &A2);

  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};

/// \brief Colvar component: self-coordination number within a group
/// (colvarvalue::type_scalar type, range [0:N*(N-1)/2])
class colvar::selfcoordnum
  : public colvar::distance
{
protected:
  /// \brief "Cutoff" for isotropic calculation (default)
  cvm::real     r0;
  /// Integer exponent of the function numerator
  int en;
  /// Integer exponent of the function denominator
  int ed;
public:
  /// Constructor
  selfcoordnum (std::string const &conf);
  selfcoordnum();
  virtual inline ~selfcoordnum() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  template<bool b_gradients>
  /// \brief Calculate a coordination number through the function
  /// (1-x**n)/(1-x**m), x = |A1-A2|/r0 \param r0 "cutoff" for the
  /// coordination number \param exp_num \i n exponent \param exp_den
  /// \i m exponent \param A1 atom \param A2 atom
  static cvm::real switching_function (cvm::real const &r0,
                                       int const &exp_num, int const &exp_den,
                                       cvm::atom &A1, cvm::atom &A2);

  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};

/// \brief Colvar component: hydrogen bond, defined as the product of
/// a colvar::coordnum and 1/2*(1-cos((180-ang)/ang_tol))
/// (colvarvalue::type_scalar type, range [0:1])
class colvar::h_bond
  : public colvar::cvc
{
protected:
  /// Atoms involved in the component
  cvm::atom     acceptor, donor;
  /// \brief "Cutoff" distance between acceptor and donor
  cvm::real     r0;
  /// Integer exponent of the function numerator
  int en;
  /// Integer exponent of the function denominator
  int ed;
public:
  h_bond (std::string const &conf);
  /// Constructor for atoms already allocated
  h_bond (cvm::atom const &acceptor,
          cvm::atom const &donor,
          cvm::real r0, int en, int ed);
  h_bond();
  virtual ~h_bond();
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);

  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: alpha helix content of a contiguous
/// segment of 5 or more residues, implemented as a sum of phi/psi
/// dihedral angles and hydrogen bonds (colvarvalue::type_scalar type,
/// range [0:1])
// class colvar::alpha_dihedrals
//   : public colvar::cvc
// {
// protected:

//   /// Alpha-helical reference phi value
//   cvm::real phi_ref;

//   /// Alpha-helical reference psi value
//   cvm::real psi_ref;

//   /// List of phi dihedral angles
//   std::vector<dihedral *> phi;

//   /// List of psi dihedral angles
//   std::vector<dihedral *> psi;

//   /// List of hydrogen bonds
//   std::vector<h_bond *>   hb;

// public:

//   alpha_dihedrals (std::string const &conf);
//   alpha_dihedrals();
//   virtual inline ~alpha_dihedrals() {}
//   virtual void calc_value();
//   virtual void calc_gradients();
//   virtual void apply_force (colvarvalue const &force);
//   virtual cvm::real dist2 (colvarvalue const &x1,
//                            colvarvalue const &x2) const;
//   virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
//                                    colvarvalue const &x2) const;
//   virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
//                                    colvarvalue const &x2) const;
//   virtual cvm::real compare (colvarvalue const &x1,
//                              colvarvalue const &x2) const;
// };


/// \brief Colvar component: alpha helix content of a contiguous
/// segment of 5 or more residues, implemented as a sum of Ca-Ca-Ca
/// angles and hydrogen bonds (colvarvalue::type_scalar type, range
/// [0:1])
class colvar::alpha_angles
  : public colvar::cvc
{
protected:

  /// Reference Calpha-Calpha angle (default: 88 degrees)
  cvm::real theta_ref;

  /// Tolerance on the Calpha-Calpha angle
  cvm::real theta_tol;

  /// List of Calpha-Calpha angles
  std::vector<angle *> theta;

  /// List of hydrogen bonds
  std::vector<h_bond *>   hb;

  /// Contribution of the hb terms
  cvm::real hb_coeff;

public:

  alpha_angles (std::string const &conf);
  alpha_angles();
  virtual ~alpha_angles();
  void calc_value();
  void calc_gradients();
  void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};

/// \brief Colvar component: dihedPC
/// Projection of the config onto a dihedral principal component
/// See e.g. Altis et al., J. Chem. Phys 126, 244111 (2007)
/// Based on a set of 'dihedral' cvcs
class colvar::dihedPC
  : public colvar::cvc
{
protected:

  std::vector<dihedral *> theta;
  std::vector<cvm::real> coeffs;

public:

  dihedPC (std::string const &conf);
  dihedPC();
  virtual  ~dihedPC();
  void calc_value();
  void calc_gradients();
  void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};

/// \brief Colvar component: orientation in space of an atom group,
/// with respect to a set of reference coordinates
/// (colvarvalue::type_quaternion type, range
/// [-1:1]x[-1:1]x[-1:1]x[-1:1])
class colvar::orientation
  : public colvar::cvc
{
protected:

  /// Atom group
  cvm::atom_group            atoms;
  /// Center of geometry of the group
  cvm::atom_pos              atoms_cog;

  /// Reference coordinates
  std::vector<cvm::atom_pos> ref_pos;

  /// Rotation object
  cvm::rotation              rot;

  /// \brief This is used to remove jumps in the sign of the
  /// quaternion, which may be annoying in the colvars trajectory
  cvm::quaternion            ref_quat;

public:

  orientation (std::string const &conf);
  orientation();
  virtual inline ~orientation() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: angle of rotation with respect to a set
/// of reference coordinates (colvarvalue::type_scalar type, range
/// [0:PI))
class colvar::orientation_angle
  : public colvar::orientation
{
public:

  orientation_angle (std::string const &conf);
  orientation_angle();
  virtual inline ~orientation_angle() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: cosine of the angle of rotation with respect to a set
/// of reference coordinates (colvarvalue::type_scalar type, range
/// [-1:1])
class colvar::orientation_proj
  : public colvar::orientation
{
public:

  orientation_proj (std::string const &conf);
  orientation_proj();
  virtual inline ~orientation_proj() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};


/// \brief Colvar component: projection of the orientation vector onto
/// a predefined axis (colvarvalue::type_scalar type, range [-1:1])
class colvar::tilt
  : public colvar::orientation
{
protected:

  cvm::rvector axis;

public:

  tilt (std::string const &conf);
  tilt();
  virtual inline ~tilt() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};



/// \brief Colvar component: angle of rotation around a predefined
/// axis (colvarvalue::type_scalar type, range [-PI:PI])
class colvar::spin_angle
  : public colvar::orientation
{
protected:

  cvm::rvector axis;

public:

  spin_angle (std::string const &conf);
  spin_angle();
  virtual inline ~spin_angle() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void apply_force (colvarvalue const &force);
  /// Redefined to handle the 2*PI periodicity
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  /// Redefined to handle the 2*PI periodicity
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  /// Redefined to handle the 2*PI periodicity
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  /// Redefined to handle the 2*PI periodicity
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
  /// Redefined to handle the 2*PI periodicity
  virtual void wrap (colvarvalue &x) const;
};



/// \brief Colvar component: root mean square deviation (RMSD) of a
/// group with respect to a set of reference coordinates; uses \link
/// colvar::orientation \endlink to calculate the rotation matrix
/// (colvarvalue::type_scalar type, range [0:*))
class colvar::rmsd
  : public colvar::cvc
{
protected:

  /// Atom group
  cvm::atom_group             atoms;

  /// Reference coordinates (for RMSD calculation only)
  std::vector<cvm::atom_pos>  ref_pos;

public:

  /// Constructor
  rmsd (std::string const &conf);
  virtual inline ~rmsd() {}
  virtual void calc_value();
  virtual void calc_gradients();
  virtual void calc_force_invgrads();
  virtual void calc_Jacobian_derivative();
  virtual void apply_force (colvarvalue const &force);
  virtual cvm::real dist2 (colvarvalue const &x1,
                           colvarvalue const &x2) const;
  virtual colvarvalue dist2_lgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual colvarvalue dist2_rgrad (colvarvalue const &x1,
                                   colvarvalue const &x2) const;
  virtual cvm::real compare (colvarvalue const &x1,
                             colvarvalue const &x2) const;
};



// metrics functions for cvc implementations

// simple definitions of the distance functions; these are useful only
// for optimization (the type check performed in the default
// colvarcomp functions is skipped)

// definitions assuming the scalar type

#define simple_scalar_dist_functions(TYPE)                              \
                                                                        \
  inline cvm::real colvar::TYPE::dist2 (colvarvalue const &x1,          \
                                        colvarvalue const &x2) const    \
  {                                                                     \
    return (x1.real_value - x2.real_value)*(x1.real_value - x2.real_value); \
  }                                                                     \
                                                                        \
  inline colvarvalue colvar::TYPE::dist2_lgrad (colvarvalue const &x1,  \
                                                colvarvalue const &x2) const \
  {                                                                     \
    return 2.0 * (x1.real_value - x2.real_value);                       \
  }                                                                     \
                                                                        \
  inline colvarvalue colvar::TYPE::dist2_rgrad (colvarvalue const &x1,  \
                                                colvarvalue const &x2) const \
  {                                                                     \
    return this->dist2_lgrad (x2, x1);                                  \
  }                                                                     \
                                                                        \
  inline cvm::real colvar::TYPE::compare (colvarvalue const &x1,        \
                                          colvarvalue const &x2) const  \
  {                                                                     \
    return this->dist2_lgrad (x1, x2);                                  \
  }                                                                     \
                                                                        \

  simple_scalar_dist_functions (distance)
  // NOTE: distance_z has explicit functions, see below
  simple_scalar_dist_functions (distance_xy)
  simple_scalar_dist_functions (distance_inv)
  simple_scalar_dist_functions (angle)
  simple_scalar_dist_functions (coordnum)
  simple_scalar_dist_functions (selfcoordnum)
  simple_scalar_dist_functions (h_bond)
  simple_scalar_dist_functions (gyration)
  simple_scalar_dist_functions (inertia)
  simple_scalar_dist_functions (inertia_z)
  simple_scalar_dist_functions (rmsd)
  simple_scalar_dist_functions (orientation_angle)
  simple_scalar_dist_functions (orientation_proj)
  simple_scalar_dist_functions (tilt)
  simple_scalar_dist_functions (eigenvector)
  //  simple_scalar_dist_functions (alpha_dihedrals)
  simple_scalar_dist_functions (alpha_angles)
  simple_scalar_dist_functions (dihedPC)


// metrics functions for cvc implementations with a periodicity

inline cvm::real colvar::dihedral::dist2 (colvarvalue const &x1,
                                          colvarvalue const &x2) const
{
  cvm::real diff = x1.real_value - x2.real_value;
  diff = (diff < -180.0 ? diff + 360.0 : (diff > 180.0 ? diff - 360.0 : diff));
  return diff * diff;
}

inline colvarvalue colvar::dihedral::dist2_lgrad (colvarvalue const &x1,
                                                  colvarvalue const &x2) const
{
  cvm::real diff = x1.real_value - x2.real_value;
  diff = (diff < -180.0 ? diff + 360.0 : (diff > 180.0 ? diff - 360.0 : diff));
  return 2.0 * diff;
}

inline colvarvalue colvar::dihedral::dist2_rgrad (colvarvalue const &x1,
                                                  colvarvalue const &x2) const
{
  cvm::real diff = x1.real_value - x2.real_value;
  diff = (diff < -180.0 ? diff + 360.0 : (diff > 180.0 ? diff - 360.0 : diff));
  return (-2.0) * diff;
}

inline cvm::real colvar::dihedral::compare (colvarvalue const &x1,
                                            colvarvalue const &x2) const
{
  return dist2_lgrad (x1, x2);
}

inline void colvar::dihedral::wrap (colvarvalue &x) const
{
  if ((x.real_value - wrap_center) >= 180.0) {
    x.real_value -= 360.0;
    return;
  }

  if ((x.real_value - wrap_center) < -180.0) {
    x.real_value += 360.0;
    return;
  }

  return;
}

inline cvm::real colvar::spin_angle::dist2 (colvarvalue const &x1,
                                          colvarvalue const &x2) const
{
  cvm::real diff = x1.real_value - x2.real_value;
  diff = (diff < -180.0 ? diff + 360.0 : (diff > 180.0 ? diff - 360.0 : diff));
  return diff * diff;
}

inline colvarvalue colvar::spin_angle::dist2_lgrad (colvarvalue const &x1,
                                                  colvarvalue const &x2) const
{
  cvm::real diff = x1.real_value - x2.real_value;
  diff = (diff < -180.0 ? diff + 360.0 : (diff > 180.0 ? diff - 360.0 : diff));
  return 2.0 * diff;
}

inline colvarvalue colvar::spin_angle::dist2_rgrad (colvarvalue const &x1,
                                                  colvarvalue const &x2) const
{
  cvm::real diff = x1.real_value - x2.real_value;
  diff = (diff < -180.0 ? diff + 360.0 : (diff > 180.0 ? diff - 360.0 : diff));
  return (-2.0) * diff;
}

inline cvm::real colvar::spin_angle::compare (colvarvalue const &x1,
                                            colvarvalue const &x2) const
{
  return dist2_lgrad (x1, x2);
}

inline void colvar::spin_angle::wrap (colvarvalue &x) const
{
  if ((x.real_value - wrap_center) >= 180.0) {
    x.real_value -= 360.0;
    return;
  }

  if ((x.real_value - wrap_center) < -180.0) {
    x.real_value += 360.0;
    return;
  }

  return;
}


// Projected distance
// Differences should always be wrapped around 0 (ignoring wrap_center)
inline cvm::real colvar::distance_z::dist2 (colvarvalue const &x1,
                                            colvarvalue const &x2) const
{
  cvm::real diff = x1.real_value - x2.real_value;
  if (period != 0.0) {
    cvm::real shift = std::floor (diff/period + 0.5);
    diff -= shift * period;
  }
  return diff * diff;
}

inline colvarvalue colvar::distance_z::dist2_lgrad (colvarvalue const &x1,
                                                    colvarvalue const &x2) const
{
  cvm::real diff = x1.real_value - x2.real_value;
  if (period != 0.0) {
    cvm::real shift = std::floor (diff/period + 0.5);
    diff -= shift * period;
  }
  return 2.0 * diff;
}

inline colvarvalue colvar::distance_z::dist2_rgrad (colvarvalue const &x1,
                                                    colvarvalue const &x2) const
{
  cvm::real diff = x1.real_value - x2.real_value;
  if (period != 0.0) {
    cvm::real shift = std::floor (diff/period + 0.5);
    diff -= shift * period;
  }
  return (-2.0) * diff;
}

inline cvm::real colvar::distance_z::compare (colvarvalue const &x1,
                                              colvarvalue const &x2) const
{
  return dist2_lgrad (x1, x2);
}

inline void colvar::distance_z::wrap (colvarvalue &x) const
{
  if (! this->b_periodic) {
    // don't wrap if the period has not been set
    return;
  }

  cvm::real shift = std::floor ((x.real_value - wrap_center) / period + 0.5);
  x.real_value -= shift * period;
  return;
}


// distance between three dimensional vectors
//
// TODO apply PBC to distance_vec
// Note: differences should be centered around (0, 0, 0)!

inline cvm::real colvar::distance_vec::dist2 (colvarvalue const &x1,
                                              colvarvalue const &x2) const
{
  return cvm::position_dist2 (x1.rvector_value, x2.rvector_value);
}

inline colvarvalue colvar::distance_vec::dist2_lgrad (colvarvalue const &x1,
                                                      colvarvalue const &x2) const
{
  return 2.0 * cvm::position_distance(x2.rvector_value, x1.rvector_value);
}

inline colvarvalue colvar::distance_vec::dist2_rgrad (colvarvalue const &x1,
                                                      colvarvalue const &x2) const
{
  return 2.0 * cvm::position_distance(x2.rvector_value, x1.rvector_value);
}

inline cvm::real colvar::distance_vec::compare (colvarvalue const &x1,
                                                colvarvalue const &x2) const
{
  cvm::error ("Error: cannot compare() two distance vectors.\n");
  return 0.0;
}

inline cvm::real colvar::distance_dir::dist2 (colvarvalue const &x1,
                                              colvarvalue const &x2) const
{
  return (x1.rvector_value - x2.rvector_value).norm2();
}

inline colvarvalue colvar::distance_dir::dist2_lgrad (colvarvalue const &x1,
                                                      colvarvalue const &x2) const
{
  return colvarvalue ((x1.rvector_value - x2.rvector_value), colvarvalue::type_unitvector);
}

inline colvarvalue colvar::distance_dir::dist2_rgrad (colvarvalue const &x1,
                                                      colvarvalue const &x2) const
{
  return colvarvalue ((x2.rvector_value - x1.rvector_value), colvarvalue::type_unitvector);
}

inline cvm::real colvar::distance_dir::compare (colvarvalue const &x1,
                                                colvarvalue const &x2) const
{
  cvm::error ("Error: cannot compare() two distance directions.\n");
  return 0.0;
}

// distance between quaternions

inline cvm::real colvar::orientation::dist2 (colvarvalue const &x1,
                                             colvarvalue const &x2) const
{
  return x1.quaternion_value.dist2 (x2);
}

inline colvarvalue colvar::orientation::dist2_lgrad (colvarvalue const &x1,
                                                     colvarvalue const &x2) const
{
  return x1.quaternion_value.dist2_grad (x2);
}

inline colvarvalue colvar::orientation::dist2_rgrad (colvarvalue const &x1,
                                                     colvarvalue const &x2) const
{
  return x2.quaternion_value.dist2_grad (x1);
}

inline cvm::real colvar::orientation::compare (colvarvalue const &x1,
                                               colvarvalue const &x2) const
{
  cvm::error ("Error: cannot compare() two quaternions.\n");
  return 0.0;
}


#endif