colvarcomp_distances.cpp
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Created: Thu, Jul 18, 03:22

colvarcomp_distances.cpp
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	/// -- c++ --

	#include <cmath>

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



	// "twogroup" flag defaults to true; set to false by selfCoordNum
	// (only distance-derived component based on only one group)

	colvar::distance::distance (std::string const &conf, bool twogroups)
	: cvc (conf)
	{
	function_type = "distance";
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	if (get_keyval (conf, "forceNoPBC", b_no_PBC, false)) {
	cvm::log ("Computing distance using absolute positions (not minimal-image)");
	}
	if (twogroups && get_keyval (conf, "oneSiteSystemForce", b_1site_force, false)) {
	cvm::log ("Computing system force on group 1 only");
	}
	parse_group (conf, "group1", group1);
	atom_groups.push_back (&group1);
	if (twogroups) {
	parse_group (conf, "group2", group2);
	atom_groups.push_back (&group2);
	}
	x.type (colvarvalue::type_scalar);
	}


	colvar::distance::distance()
	: cvc ()
	{
	function_type = "distance";
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	b_1site_force = false;
	b_no_PBC = false;
	x.type (colvarvalue::type_scalar);
	}

	void colvar::distance::calc_value()
	{
	if (b_no_PBC) {
	dist_v = group2.center_of_mass() - group1.center_of_mass();
	} else {
	dist_v = cvm::position_distance (group1.center_of_mass(),
	group2.center_of_mass());
	}
	x.real_value = dist_v.norm();
	}

	void colvar::distance::calc_gradients()
	{
	cvm::rvector const u = dist_v.unit();
	group1.set_weighted_gradient (-1.0 * u);
	group2.set_weighted_gradient ( u);
	}

	void colvar::distance::calc_force_invgrads()
	{
	group1.read_system_forces();
	if ( b_1site_force ) {
	ft.real_value = -1.0 * (group1.system_force() * dist_v.unit());
	} else {
	group2.read_system_forces();
	ft.real_value = 0.5 * ((group2.system_force() - group1.system_force()) * dist_v.unit());
	}
	}

	void colvar::distance::calc_Jacobian_derivative()
	{
	jd.real_value = x.real_value ? (2.0 / x.real_value) : 0.0;
	}

	void colvar::distance::apply_force (colvarvalue const &force)
	{
	if (!group1.noforce)
	group1.apply_colvar_force (force.real_value);

	if (!group2.noforce)
	group2.apply_colvar_force (force.real_value);
	}



	colvar::distance_vec::distance_vec (std::string const &conf)
	: distance (conf)
	{
	function_type = "distance_vec";
	x.type (colvarvalue::type_vector);
	}

	colvar::distance_vec::distance_vec()
	: distance()
	{
	function_type = "distance_vec";
	x.type (colvarvalue::type_vector);
	}

	void colvar::distance_vec::calc_value()
	{
	if (b_no_PBC) {
	x.rvector_value = group2.center_of_mass() - group1.center_of_mass();
	} else {
	x.rvector_value = cvm::position_distance (group1.center_of_mass(),
	group2.center_of_mass());
	}
	}

	void colvar::distance_vec::calc_gradients()
	{
	// gradients are not stored: a 3x3 matrix for each atom would be
	// needed to store just the identity matrix
	}

	void colvar::distance_vec::apply_force (colvarvalue const &force)
	{
	if (!group1.noforce)
	group1.apply_force (-1.0 * force.rvector_value);

	if (!group2.noforce)
	group2.apply_force ( force.rvector_value);
	}



	colvar::distance_z::distance_z (std::string const &conf)
	: cvc (conf)
	{
	function_type = "distance_z";
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	x.type (colvarvalue::type_scalar);

	// TODO detect PBC from MD engine (in simple cases)
	// and then update period in real time
	if (period != 0.0)
	b_periodic = true;

	if ((wrap_center != 0.0) && (period == 0.0)) {
	cvm::error ("Error: wrapAround was defined in a distanceZ component,"
	" but its period has not been set.\n");
	return;
	}

	parse_group (conf, "main", main);
	parse_group (conf, "ref", ref1);
	atom_groups.push_back (&main);
	atom_groups.push_back (&ref1);
	// this group is optional
	parse_group (conf, "ref2", ref2, true);

	if (ref2.size()) {
	atom_groups.push_back (&ref2);
	cvm::log ("Using axis joining the centers of mass of groups \"ref\" and \"ref2\"");
	fixed_axis = false;
	if (key_lookup (conf, "axis"))
	cvm::log ("Warning: explicit axis definition will be ignored!");
	} else {
	if (get_keyval (conf, "axis", axis, cvm::rvector (0.0, 0.0, 1.0))) {
	if (axis.norm2() == 0.0) {
	cvm::error ("Axis vector is zero!");
	return;
	}
	if (axis.norm2() != 1.0) {
	axis = axis.unit();
	cvm::log ("The normalized axis is: "+cvm::to_str (axis)+".\n");
	}
	}
	fixed_axis = true;
	}

	if (get_keyval (conf, "forceNoPBC", b_no_PBC, false)) {
	cvm::log ("Computing distance using absolute positions (not minimal-image)");
	}
	if (get_keyval (conf, "oneSiteSystemForce", b_1site_force, false)) {
	cvm::log ("Computing system force on group \"main\" only");
	}
	}

	colvar::distance_z::distance_z()
	{
	function_type = "distance_z";
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	x.type (colvarvalue::type_scalar);
	}

	void colvar::distance_z::calc_value()
	{
	if (fixed_axis) {
	if (b_no_PBC) {
	dist_v = main.center_of_mass() - ref1.center_of_mass();
	} else {
	dist_v = cvm::position_distance (ref1.center_of_mass(),
	main.center_of_mass());
	}
	} else {

	if (b_no_PBC) {
	dist_v = main.center_of_mass() -
	(0.5 * (ref1.center_of_mass() + ref2.center_of_mass()));
	axis = ref2.center_of_mass() - ref1.center_of_mass();
	} else {
	dist_v = cvm::position_distance (0.5 * (ref1.center_of_mass() +
	ref2.center_of_mass()), main.center_of_mass());
	axis = cvm::position_distance (ref1.center_of_mass(), ref2.center_of_mass());
	}
	axis_norm = axis.norm();
	axis = axis.unit();
	}
	x.real_value = axis * dist_v;
	this->wrap (x);
	}

	void colvar::distance_z::calc_gradients()
	{
	main.set_weighted_gradient ( axis );

	if (fixed_axis) {
	ref1.set_weighted_gradient (-1.0 * axis);
	} else {
	if (b_no_PBC) {
	ref1.set_weighted_gradient ( 1.0 / axis_norm * (main.center_of_mass() - ref2.center_of_mass() -
	x.real_value * axis ));
	ref2.set_weighted_gradient ( 1.0 / axis_norm * (ref1.center_of_mass() - main.center_of_mass() +
	x.real_value * axis ));
	} else {
	ref1.set_weighted_gradient ( 1.0 / axis_norm * (
	cvm::position_distance (ref2.center_of_mass(), main.center_of_mass()) - x.real_value * axis ));
	ref2.set_weighted_gradient ( 1.0 / axis_norm * (
	cvm::position_distance (main.center_of_mass(), ref1.center_of_mass()) + x.real_value * axis ));
	}
	}

	if (b_debug_gradients) {
	cvm::log ("Debugging gradients for group main:\n");
	debug_gradients (main);
	cvm::log ("Debugging gradients for group ref1:\n");
	debug_gradients (ref1);
	cvm::log ("Debugging gradients for group ref2:\n");
	debug_gradients (ref2);
	}
	}

	void colvar::distance_z::calc_force_invgrads()
	{
	main.read_system_forces();

	if (fixed_axis && !b_1site_force) {
	ref1.read_system_forces();
	ft.real_value = 0.5 * ((main.system_force() - ref1.system_force()) * axis);
	} else {
	ft.real_value = main.system_force() * axis;
	}
	}

	void colvar::distance_z::calc_Jacobian_derivative()
	{
	jd.real_value = 0.0;
	}

	void colvar::distance_z::apply_force (colvarvalue const &force)
	{
	if (!ref1.noforce)
	ref1.apply_colvar_force (force.real_value);

	if (ref2.size() && !ref2.noforce)
	ref2.apply_colvar_force (force.real_value);

	if (!main.noforce)
	main.apply_colvar_force (force.real_value);
	}



	colvar::distance_xy::distance_xy (std::string const &conf)
	: distance_z (conf)
	{
	function_type = "distance_xy";
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	x.type (colvarvalue::type_scalar);
	}

	colvar::distance_xy::distance_xy()
	: distance_z()
	{
	function_type = "distance_xy";
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	x.type (colvarvalue::type_scalar);
	}

	void colvar::distance_xy::calc_value()
	{
	if (b_no_PBC) {
	dist_v = main.center_of_mass() - ref1.center_of_mass();
	} else {
	dist_v = cvm::position_distance (ref1.center_of_mass(),
	main.center_of_mass());
	}
	if (!fixed_axis) {
	if (b_no_PBC) {
	v12 = ref2.center_of_mass() - ref1.center_of_mass();
	} else {
	v12 = cvm::position_distance (ref1.center_of_mass(), ref2.center_of_mass());
	}
	axis_norm = v12.norm();
	axis = v12.unit();
	}

	dist_v_ortho = dist_v - (dist_v * axis) * axis;
	x.real_value = dist_v_ortho.norm();
	}

	void colvar::distance_xy::calc_gradients()
	{
	// Intermediate quantity (r_P3 / r_12 where P is the projection
	// of 3 (main) on the plane orthogonal to 12, containing 1 (ref1))
	cvm::real A;
	cvm::real x_inv;

	if (x.real_value == 0.0) return;
	x_inv = 1.0 / x.real_value;

	if (fixed_axis) {
	ref1.set_weighted_gradient (-1.0 * x_inv * dist_v_ortho);
	main.set_weighted_gradient ( x_inv * dist_v_ortho);
	} else {
	if (b_no_PBC) {
	v13 = main.center_of_mass() - ref1.center_of_mass();
	} else {
	v13 = cvm::position_distance (ref1.center_of_mass(), main.center_of_mass());
	}
	A = (dist_v * axis) / axis_norm;

	ref1.set_weighted_gradient ( (A - 1.0) * x_inv * dist_v_ortho);
	ref2.set_weighted_gradient ( -A * x_inv * dist_v_ortho);
	main.set_weighted_gradient ( 1.0 * x_inv * dist_v_ortho);
	}
	}

	void colvar::distance_xy::calc_force_invgrads()
	{
	main.read_system_forces();

	if (fixed_axis && !b_1site_force) {
	ref1.read_system_forces();
	ft.real_value = 0.5 / x.real_value * ((main.system_force() - ref1.system_force()) * dist_v_ortho);
	} else {
	ft.real_value = 1.0 / x.real_value * main.system_force() * dist_v_ortho;
	}
	}

	void colvar::distance_xy::calc_Jacobian_derivative()
	{
	jd.real_value = x.real_value ? (1.0 / x.real_value) : 0.0;
	}

	void colvar::distance_xy::apply_force (colvarvalue const &force)
	{
	if (!ref1.noforce)
	ref1.apply_colvar_force (force.real_value);

	if (ref2.size() && !ref2.noforce)
	ref2.apply_colvar_force (force.real_value);

	if (!main.noforce)
	main.apply_colvar_force (force.real_value);
	}



	colvar::distance_dir::distance_dir (std::string const &conf)
	: distance (conf)
	{
	function_type = "distance_dir";
	x.type (colvarvalue::type_unitvector);
	}


	colvar::distance_dir::distance_dir()
	: distance()
	{
	function_type = "distance_dir";
	x.type (colvarvalue::type_unitvector);
	}


	void colvar::distance_dir::calc_value()
	{
	if (b_no_PBC) {
	dist_v = group2.center_of_mass() - group1.center_of_mass();
	} else {
	dist_v = cvm::position_distance (group1.center_of_mass(),
	group2.center_of_mass());
	}
	x.rvector_value = dist_v.unit();
	}


	void colvar::distance_dir::calc_gradients()
	{
	// gradients are computed on the fly within apply_force()
	// Note: could be a problem if a future bias relies on gradient
	// calculations...
	}


	void colvar::distance_dir::apply_force (colvarvalue const &force)
	{
	// remove the radial force component
	cvm::real const iprod = force.rvector_value * x.rvector_value;
	cvm::rvector const force_tang = force.rvector_value - iprod * x.rvector_value;

	if (!group1.noforce)
	group1.apply_force (-1.0 * force_tang);

	if (!group2.noforce)
	group2.apply_force ( force_tang);
	}



	colvar::distance_inv::distance_inv (std::string const &conf)
	: distance (conf)
	{
	function_type = "distance_inv";
	get_keyval (conf, "exponent", exponent, 6);
	if (exponent%2) {
	cvm::error ("Error: odd exponent provided, can only use even ones.\n");
	return;
	}
	if (exponent <= 0) {
	cvm::error ("Error: negative or zero exponent provided.\n");
	return;
	}

	for (cvm::atom_iter ai1 = group1.begin(); ai1 != group1.end(); ai1++) {
	for (cvm::atom_iter ai2 = group2.begin(); ai2 != group2.end(); ai2++) {
	if (ai1->id == ai2->id)
	cvm::error ("Error: group1 and group1 have some atoms in common: this is not allowed for distanceInv.\n");
	return;
	}
	}

	b_inverse_gradients = false;
	b_Jacobian_derivative = false;
	x.type (colvarvalue::type_scalar);
	}

	colvar::distance_inv::distance_inv()
	{
	function_type = "distance_inv";
	exponent = 6;
	b_inverse_gradients = false;
	b_Jacobian_derivative = false;
	b_1site_force = false;
	x.type (colvarvalue::type_scalar);
	}

	void colvar::distance_inv::calc_value()
	{
	x.real_value = 0.0;
	if (b_no_PBC) {
	for (cvm::atom_iter ai1 = group1.begin(); ai1 != group1.end(); ai1++) {
	for (cvm::atom_iter ai2 = group2.begin(); ai2 != group2.end(); ai2++) {
	cvm::rvector const dv = ai2->pos - ai1->pos;
	cvm::real const d2 = dv.norm2();
	cvm::real dinv = 1.0;
	for (int ne = 0; ne < exponent/2; ne++)
	dinv *= 1.0/d2;
	x.real_value += dinv;
	cvm::rvector const dsumddv = -(cvm::real (exponent)) * dinv/d2 * dv;
	ai1->grad += -1.0 * dsumddv;
	ai2->grad += dsumddv;
	}
	}
	} else {
	for (cvm::atom_iter ai1 = group1.begin(); ai1 != group1.end(); ai1++) {
	for (cvm::atom_iter ai2 = group2.begin(); ai2 != group2.end(); ai2++) {
	cvm::rvector const dv = cvm::position_distance (ai1->pos, ai2->pos);
	cvm::real const d2 = dv.norm2();
	cvm::real dinv = 1.0;
	for (int ne = 0; ne < exponent/2; ne++)
	dinv *= 1.0/d2;
	x.real_value += dinv;
	cvm::rvector const dsumddv = -(cvm::real (exponent)) * dinv/d2 * dv;
	ai1->grad += -1.0 * dsumddv;
	ai2->grad += dsumddv;
	}
	}
	}

	x.real_value = 1.0 / cvm::real (group1.size() group2.size());
	x.real_value = std::pow (x.real_value, -1.0/(cvm::real (exponent)));
	}

	void colvar::distance_inv::calc_gradients()
	{
	cvm::real const dxdsum = (-1.0/(cvm::real (exponent))) * std::pow (x.real_value, exponent+1) / cvm::real (group1.size() * group2.size());
	for (cvm::atom_iter ai1 = group1.begin(); ai1 != group1.end(); ai1++) {
	ai1->grad *= dxdsum;
	}
	for (cvm::atom_iter ai2 = group2.begin(); ai2 != group2.end(); ai2++) {
	ai2->grad *= dxdsum;
	}
	}

	void colvar::distance_inv::apply_force (colvarvalue const &force)
	{
	if (!group1.noforce)
	group1.apply_colvar_force (force.real_value);

	if (!group2.noforce)
	group2.apply_colvar_force (force.real_value);
	}



	colvar::gyration::gyration (std::string const &conf)
	: cvc (conf)
	{
	function_type = "gyration";
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	parse_group (conf, "atoms", atoms);
	atom_groups.push_back (&atoms);

	if (atoms.b_user_defined_fit) {
	cvm::log ("WARNING: explicit fitting parameters were provided for atom group \"atoms\".");
	} else {
	atoms.b_center = true;
	atoms.ref_pos.assign (1, cvm::atom_pos (0.0, 0.0, 0.0));
	}

	x.type (colvarvalue::type_scalar);
	}


	colvar::gyration::gyration()
	{
	function_type = "gyration";
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	x.type (colvarvalue::type_scalar);
	}


	void colvar::gyration::calc_value()
	{
	x.real_value = 0.0;
	for (cvm::atom_iter ai = atoms.begin(); ai != atoms.end(); ai++) {
	x.real_value += (ai->pos).norm2();
	}
	x.real_value = std::sqrt (x.real_value / cvm::real (atoms.size()));
	}


	void colvar::gyration::calc_gradients()
	{
	cvm::real const drdx = 1.0/(cvm::real (atoms.size()) * x.real_value);
	for (cvm::atom_iter ai = atoms.begin(); ai != atoms.end(); ai++) {
	ai->grad = drdx * ai->pos;
	}

	if (b_debug_gradients) {
	cvm::log ("Debugging gradients:\n");
	debug_gradients (atoms);
	}
	}


	void colvar::gyration::calc_force_invgrads()
	{
	atoms.read_system_forces();

	cvm::real const dxdr = 1.0/x.real_value;
	ft.real_value = 0.0;

	for (cvm::atom_iter ai = atoms.begin(); ai != atoms.end(); ai++) {
	ft.real_value += dxdr * ai->pos * ai->system_force;
	}
	}


	void colvar::gyration::calc_Jacobian_derivative()
	{
	jd = x.real_value ? (3.0 * cvm::real (atoms.size()) - 4.0) / x.real_value : 0.0;
	}


	void colvar::gyration::apply_force (colvarvalue const &force)
	{
	if (!atoms.noforce)
	atoms.apply_colvar_force (force.real_value);
	}



	colvar::inertia::inertia (std::string const &conf)
	: gyration (conf)
	{
	function_type = "inertia";
	b_inverse_gradients = false;
	b_Jacobian_derivative = false;
	x.type (colvarvalue::type_scalar);
	}


	colvar::inertia::inertia()
	{
	function_type = "inertia";
	x.type (colvarvalue::type_scalar);
	}


	void colvar::inertia::calc_value()
	{
	x.real_value = 0.0;
	for (cvm::atom_iter ai = atoms.begin(); ai != atoms.end(); ai++) {
	x.real_value += (ai->pos).norm2();
	}
	}


	void colvar::inertia::calc_gradients()
	{
	for (cvm::atom_iter ai = atoms.begin(); ai != atoms.end(); ai++) {
	ai->grad = 2.0 * ai->pos;
	}

	if (b_debug_gradients) {
	cvm::log ("Debugging gradients:\n");
	debug_gradients (atoms);
	}
	}


	void colvar::inertia::apply_force (colvarvalue const &force)
	{
	if (!atoms.noforce)
	atoms.apply_colvar_force (force.real_value);
	}


	colvar::inertia_z::inertia_z (std::string const &conf)
	: inertia (conf)
	{
	function_type = "inertia_z";
	if (get_keyval (conf, "axis", axis, cvm::rvector (0.0, 0.0, 1.0))) {
	if (axis.norm2() == 0.0) {
	cvm::error ("Axis vector is zero!");
	return;
	}
	if (axis.norm2() != 1.0) {
	axis = axis.unit();
	cvm::log ("The normalized axis is: "+cvm::to_str (axis)+".\n");
	}
	}
	x.type (colvarvalue::type_scalar);
	}


	colvar::inertia_z::inertia_z()
	{
	function_type = "inertia_z";
	x.type (colvarvalue::type_scalar);
	}


	void colvar::inertia_z::calc_value()
	{
	x.real_value = 0.0;
	for (cvm::atom_iter ai = atoms.begin(); ai != atoms.end(); ai++) {
	cvm::real const iprod = ai->pos * axis;
	x.real_value += iprod * iprod;
	}
	}


	void colvar::inertia_z::calc_gradients()
	{
	for (cvm::atom_iter ai = atoms.begin(); ai != atoms.end(); ai++) {
	ai->grad = 2.0 * (ai->pos * axis) * axis;
	}

	if (b_debug_gradients) {
	cvm::log ("Debugging gradients:\n");
	debug_gradients (atoms);
	}
	}


	void colvar::inertia_z::apply_force (colvarvalue const &force)
	{
	if (!atoms.noforce)
	atoms.apply_colvar_force (force.real_value);
	}



	colvar::rmsd::rmsd (std::string const &conf)
	: cvc (conf)
	{
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	function_type = "rmsd";
	x.type (colvarvalue::type_scalar);

	parse_group (conf, "atoms", atoms);
	atom_groups.push_back (&atoms);

	if (atoms.b_dummy) {
	cvm::error ("Error: \"atoms\" cannot be a dummy atom.");
	return;
	}

	if (atoms.ref_pos_group != NULL) {
	cvm::log ("The option \"refPositionsGroup\" (alternative group for fitting) was enabled: "
	"Jacobian derivatives of the RMSD will not be calculated.\n");
	b_Jacobian_derivative = false;
	}

	// the following is a simplified version of the corresponding atom group options;
	// we need this because the reference coordinates defined inside the atom group
	// may be used only for fitting, and even more so if ref_pos_group is used
	if (get_keyval (conf, "refPositions", ref_pos, ref_pos)) {
	cvm::log ("Using reference positions from configuration file to calculate the variable.\n");
	if (ref_pos.size() != atoms.size()) {
	cvm::error ("Error: the number of reference positions provided ("+
	cvm::to_str (ref_pos.size())+
	") does not match the number of atoms of group \"atoms\" ("+
	cvm::to_str (atoms.size())+").\n");
	return;
	}
	}
	{
	std::string ref_pos_file;
	if (get_keyval (conf, "refPositionsFile", ref_pos_file, std::string (""))) {

	if (ref_pos.size()) {
	cvm::error ("Error: cannot specify \"refPositionsFile\" and "
	"\"refPositions\" at the same time.\n");
	return;
	}

	std::string ref_pos_col;
	double ref_pos_col_value;

	if (get_keyval (conf, "refPositionsCol", ref_pos_col, std::string (""))) {
	// if provided, use PDB column to select coordinates
	bool found = get_keyval (conf, "refPositionsColValue", ref_pos_col_value, 0.0);
	if (found && !ref_pos_col_value)
	cvm::error ("Error: refPositionsColValue, "
	"if provided, must be non-zero.\n");
	return;
	} else {
	// if not, rely on existing atom indices for the group
	atoms.create_sorted_ids();
	}

	ref_pos.resize (atoms.size());
	cvm::load_coords (ref_pos_file.c_str(), ref_pos, atoms.sorted_ids,
	ref_pos_col, ref_pos_col_value);
	}
	}

	if (atoms.b_user_defined_fit) {
	cvm::log ("WARNING: explicit fitting parameters were provided for atom group \"atoms\".");
	} else {
	// Default: fit everything
	cvm::log ("Enabling \"centerReference\" and \"rotateReference\", to minimize RMSD before calculating it as a variable: "
	"if this is not the desired behavior, disable them explicitly within the \"atoms\" block.\n");
	atoms.b_center = true;
	atoms.b_rotate = true;
	// default case: reference positions for calculating the rmsd are also those used
	// for fitting
	atoms.ref_pos = ref_pos;
	atoms.center_ref_pos();

	// request the calculation of the derivatives of the rotation defined by the atom group
	atoms.rot.request_group1_gradients (atoms.size());
	// request derivatives of optimal rotation wrt reference coordinates for Jacobian:
	// this is only required for ABF, but we do both groups here for better caching
	atoms.rot.request_group2_gradients (atoms.size());
	}
	}


	void colvar::rmsd::calc_value()
	{
	// rotational-translational fit is handled by the atom group

	x.real_value = 0.0;
	for (size_t ia = 0; ia < atoms.size(); ia++) {
	x.real_value += (atoms[ia].pos - ref_pos[ia]).norm2();
	}
	x.real_value /= cvm::real (atoms.size()); // MSD
	x.real_value = std::sqrt (x.real_value);
	}


	void colvar::rmsd::calc_gradients()
	{
	cvm::real const drmsddx2 = (x.real_value > 0.0) ?
	0.5 / (x.real_value * cvm::real (atoms.size())) :
	0.0;

	for (size_t ia = 0; ia < atoms.size(); ia++) {
	atoms[ia].grad = (drmsddx2 * 2.0 * (atoms[ia].pos - ref_pos[ia]));
	}

	if (b_debug_gradients) {
	cvm::log ("Debugging gradients:\n");
	debug_gradients (atoms);
	}
	}


	void colvar::rmsd::apply_force (colvarvalue const &force)
	{
	if (!atoms.noforce)
	atoms.apply_colvar_force (force.real_value);
	}


	void colvar::rmsd::calc_force_invgrads()
	{
	atoms.read_system_forces();
	ft.real_value = 0.0;

	// Note: gradient square norm is 1/N_atoms

	for (size_t ia = 0; ia < atoms.size(); ia++) {
	ft.real_value += atoms[ia].grad * atoms[ia].system_force;
	}
	ft.real_value *= atoms.size();
	}


	void colvar::rmsd::calc_Jacobian_derivative()
	{
	// divergence of the rotated coordinates (including only derivatives of the rotation matrix)
	cvm::real divergence = 0.0;

	if (atoms.b_rotate) {

	// gradient of the rotation matrix
	cvm::matrix2d <cvm::rvector, 3, 3> grad_rot_mat;
	// gradients of products of 2 quaternion components
	cvm::rvector g11, g22, g33, g01, g02, g03, g12, g13, g23;
	for (size_t ia = 0; ia < atoms.size(); ia++) {

	// Gradient of optimal quaternion wrt current Cartesian position
	cvm::vector1d< cvm::rvector, 4 > &dq = atoms.rot.dQ0_1[ia];

	g11 = 2.0 * (atoms.rot.q)[1]*dq[1];
	g22 = 2.0 * (atoms.rot.q)[2]*dq[2];
	g33 = 2.0 * (atoms.rot.q)[3]*dq[3];
	g01 = (atoms.rot.q)[0]dq[1] + (atoms.rot.q)[1]dq[0];
	g02 = (atoms.rot.q)[0]dq[2] + (atoms.rot.q)[2]dq[0];
	g03 = (atoms.rot.q)[0]dq[3] + (atoms.rot.q)[3]dq[0];
	g12 = (atoms.rot.q)[1]dq[2] + (atoms.rot.q)[2]dq[1];
	g13 = (atoms.rot.q)[1]dq[3] + (atoms.rot.q)[3]dq[1];
	g23 = (atoms.rot.q)[2]dq[3] + (atoms.rot.q)[3]dq[2];

	// Gradient of the rotation matrix wrt current Cartesian position
	grad_rot_mat[0][0] = -2.0 * (g22 + g33);
	grad_rot_mat[1][0] = 2.0 * (g12 + g03);
	grad_rot_mat[2][0] = 2.0 * (g13 - g02);
	grad_rot_mat[0][1] = 2.0 * (g12 - g03);
	grad_rot_mat[1][1] = -2.0 * (g11 + g33);
	grad_rot_mat[2][1] = 2.0 * (g01 + g23);
	grad_rot_mat[0][2] = 2.0 * (g02 + g13);
	grad_rot_mat[1][2] = 2.0 * (g23 - g01);
	grad_rot_mat[2][2] = -2.0 * (g11 + g22);

	cvm::atom_pos &y = ref_pos[ia];

	for (size_t alpha = 0; alpha < 3; alpha++) {
	for (size_t beta = 0; beta < 3; beta++) {
	divergence += grad_rot_mat[beta][alpha][alpha] * y[beta];
	// Note: equation was derived for inverse rotation (see colvars paper)
	// so here the matrix is transposed
	// (eq would give divergence += grad_rot_mat[alpha][beta][alpha] * y[beta];)
	}
	}
	}
	}

	jd.real_value = x.real_value > 0.0 ? (3.0 * atoms.size() - 4.0 - divergence) / x.real_value : 0.0;
	}




	colvar::eigenvector::eigenvector (std::string const &conf)
	: cvc (conf)
	{
	b_inverse_gradients = true;
	b_Jacobian_derivative = true;
	function_type = "eigenvector";
	x.type (colvarvalue::type_scalar);

	parse_group (conf, "atoms", atoms);
	atom_groups.push_back (&atoms);


	{
	bool const b_inline = get_keyval (conf, "refPositions", ref_pos, ref_pos);

	if (b_inline) {
	cvm::log ("Using reference positions from input file.\n");
	if (ref_pos.size() != atoms.size()) {
	cvm::error ("Error: reference positions do not "
	"match the number of requested atoms.\n");
	return;
	}
	}

	std::string file_name;
	if (get_keyval (conf, "refPositionsFile", file_name)) {

	if (b_inline) {
	cvm::error ("Error: refPositions and refPositionsFile cannot be specified at the same time.\n");
	return;
	}

	std::string file_col;
	double file_col_value;
	if (get_keyval (conf, "refPositionsCol", file_col, std::string (""))) {
	// use PDB flags if column is provided
	bool found = get_keyval (conf, "refPositionsColValue", file_col_value, 0.0);
	if (found && !file_col_value) {
	cvm::error ("Error: refPositionsColValue, "
	"if provided, must be non-zero.\n");
	return;
	}
	} else {
	// if not, use atom indices
	atoms.create_sorted_ids();
	}

	ref_pos.resize (atoms.size());
	cvm::load_coords (file_name.c_str(), ref_pos, atoms.sorted_ids, file_col, file_col_value);
	}
	}

	// save for later the geometric center of the provided positions (may not be the origin)
	cvm::rvector ref_pos_center (0.0, 0.0, 0.0);
	for (size_t i = 0; i < atoms.size(); i++) {
	ref_pos_center += ref_pos[i];
	}
	ref_pos_center *= 1.0 / atoms.size();

	if (atoms.b_user_defined_fit) {
	cvm::log ("WARNING: explicit fitting parameters were provided for atom group \"atoms\".\n");
	} else {
	// default: fit everything
	cvm::log ("Enabling \"centerReference\" and \"rotateReference\", to minimize RMSD before calculating the vector projection: "
	"if this is not the desired behavior, disable them explicitly within the \"atoms\" block.\n");
	atoms.b_center = true;
	atoms.b_rotate = true;
	atoms.ref_pos = ref_pos;
	atoms.center_ref_pos();

	// request the calculation of the derivatives of the rotation defined by the atom group
	atoms.rot.request_group1_gradients (atoms.size());
	// request derivatives of optimal rotation wrt reference coordinates for Jacobian:
	// this is only required for ABF, but we do both groups here for better caching
	atoms.rot.request_group2_gradients (atoms.size());
	}

	{
	bool const b_inline = get_keyval (conf, "vector", eigenvec, eigenvec);
	// now load the eigenvector
	if (b_inline) {
	cvm::log ("Using vector components from input file.\n");
	if (eigenvec.size() != atoms.size()) {
	cvm::fatal_error ("Error: vector components do not "
	"match the number of requested atoms.\n");
	}
	}

	std::string file_name;
	if (get_keyval (conf, "vectorFile", file_name)) {

	if (b_inline) {
	cvm::error ("Error: vector and vectorFile cannot be specified at the same time.\n");
	return;
	}

	std::string file_col;
	double file_col_value;
	if (get_keyval (conf, "vectorCol", file_col, std::string (""))) {
	// use PDB flags if column is provided
	bool found = get_keyval (conf, "vectorColValue", file_col_value, 0.0);
	if (found && !file_col_value) {
	cvm::error ("Error: vectorColValue, if provided, must be non-zero.\n");
	return;
	}
	} else {
	// if not, use atom indices
	atoms.create_sorted_ids();
	}

	eigenvec.resize (atoms.size());
	cvm::load_coords (file_name.c_str(), eigenvec, atoms.sorted_ids, file_col, file_col_value);
	}
	}

	if (!ref_pos.size() \|\| !eigenvec.size()) {
	cvm::error ("Error: both reference coordinates"
	"and eigenvector must be defined.\n");
	return;
	}

	cvm::atom_pos eig_center (0.0, 0.0, 0.0);
	for (size_t eil = 0; eil < atoms.size(); eil++) {
	eig_center += eigenvec[eil];
	}
	eig_center *= 1.0 / atoms.size();
	cvm::log ("Geometric center of the provided vector: "+cvm::to_str (eig_center)+"\n");

	bool b_difference_vector = false;
	get_keyval (conf, "differenceVector", b_difference_vector, false);

	if (b_difference_vector) {

	if (atoms.b_center) {
	// both sets should be centered on the origin for fitting
	for (size_t i = 0; i < atoms.size(); i++) {
	eigenvec[i] -= eig_center;
	ref_pos[i] -= ref_pos_center;
	}
	}
	if (atoms.b_rotate) {
	atoms.rot.calc_optimal_rotation (eigenvec, ref_pos);
	for (size_t i = 0; i < atoms.size(); i++) {
	eigenvec[i] = atoms.rot.rotate (eigenvec[i]);
	}
	}
	cvm::log ("\"differenceVector\" is on: subtracting the reference positions from the provided vector: v = v - x0.\n");
	for (size_t i = 0; i < atoms.size(); i++) {
	eigenvec[i] -= ref_pos[i];
	}
	if (atoms.b_center) {
	// bring back the ref positions to where they were
	for (size_t i = 0; i < atoms.size(); i++) {
	ref_pos[i] += ref_pos_center;
	}
	}

	} else {
	cvm::log ("Centering the provided vector to zero.\n");
	for (size_t i = 0; i < atoms.size(); i++) {
	eigenvec[i] -= eig_center;
	}
	}

	// cvm::log ("The first three components (v1x, v1y, v1z) of the resulting vector are: "+cvm::to_str (eigenvec[0])+".\n");

	// for inverse gradients
	eigenvec_invnorm2 = 0.0;
	for (size_t ein = 0; ein < atoms.size(); ein++) {
	eigenvec_invnorm2 += eigenvec[ein].norm2();
	}
	eigenvec_invnorm2 = 1.0 / eigenvec_invnorm2;

	if (b_difference_vector) {
	cvm::log ("\"differenceVector\" is on: normalizing the vector.\n");
	for (size_t i = 0; i < atoms.size(); i++) {
	eigenvec[i] *= eigenvec_invnorm2;
	}
	} else {
	cvm::log ("The norm of the vector is \|v\| = "+cvm::to_str (eigenvec_invnorm2)+".\n");
	}
	}


	void colvar::eigenvector::calc_value()
	{
	x.real_value = 0.0;
	for (size_t i = 0; i < atoms.size(); i++) {
	x.real_value += (atoms[i].pos - ref_pos[i]) * eigenvec[i];
	}
	}


	void colvar::eigenvector::calc_gradients()
	{
	for (size_t ia = 0; ia < atoms.size(); ia++) {
	atoms[ia].grad = eigenvec[ia];
	}

	if (b_debug_gradients) {
	cvm::log ("Debugging gradients:\n");
	debug_gradients (atoms);
	}
	}


	void colvar::eigenvector::apply_force (colvarvalue const &force)
	{
	if (!atoms.noforce)
	atoms.apply_colvar_force (force.real_value);
	}


	void colvar::eigenvector::calc_force_invgrads()
	{
	atoms.read_system_forces();
	ft.real_value = 0.0;

	for (size_t ia = 0; ia < atoms.size(); ia++) {
	ft.real_value += eigenvec_invnorm2 * atoms[ia].grad *
	atoms[ia].system_force;
	}
	}


	void colvar::eigenvector::calc_Jacobian_derivative()
	{
	// gradient of the rotation matrix
	cvm::matrix2d <cvm::rvector, 3, 3> grad_rot_mat;
	cvm::quaternion &quat0 = atoms.rot.q;

	// gradients of products of 2 quaternion components
	cvm::rvector g11, g22, g33, g01, g02, g03, g12, g13, g23;

	cvm::real sum = 0.0;

	for (size_t ia = 0; ia < atoms.size(); ia++) {

	// Gradient of optimal quaternion wrt current Cartesian position
	// trick: d(R^-1)/dx = d(R^t)/dx = (dR/dx)^t
	// we can just transpose the derivatives of the direct matrix
	cvm::vector1d< cvm::rvector, 4 > &dq_1 = atoms.rot.dQ0_1[ia];

	g11 = 2.0 * quat0[1]*dq_1[1];
	g22 = 2.0 * quat0[2]*dq_1[2];
	g33 = 2.0 * quat0[3]*dq_1[3];
	g01 = quat0[0]dq_1[1] + quat0[1]dq_1[0];
	g02 = quat0[0]dq_1[2] + quat0[2]dq_1[0];
	g03 = quat0[0]dq_1[3] + quat0[3]dq_1[0];
	g12 = quat0[1]dq_1[2] + quat0[2]dq_1[1];
	g13 = quat0[1]dq_1[3] + quat0[3]dq_1[1];
	g23 = quat0[2]dq_1[3] + quat0[3]dq_1[2];

	// Gradient of the inverse rotation matrix wrt current Cartesian position
	// (transpose of the gradient of the direct rotation)
	grad_rot_mat[0][0] = -2.0 * (g22 + g33);
	grad_rot_mat[0][1] = 2.0 * (g12 + g03);
	grad_rot_mat[0][2] = 2.0 * (g13 - g02);
	grad_rot_mat[1][0] = 2.0 * (g12 - g03);
	grad_rot_mat[1][1] = -2.0 * (g11 + g33);
	grad_rot_mat[1][2] = 2.0 * (g01 + g23);
	grad_rot_mat[2][0] = 2.0 * (g02 + g13);
	grad_rot_mat[2][1] = 2.0 * (g23 - g01);
	grad_rot_mat[2][2] = -2.0 * (g11 + g22);

	for (size_t i = 0; i < 3; i++) {
	for (size_t j = 0; j < 3; j++) {
	sum += grad_rot_mat[i][j][i] * eigenvec[ia][j];
	}
	}
	}

	jd.real_value = sum * std::sqrt (eigenvec_invnorm2);
	}

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