colvarcomp_distances.C
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Created: Wed, Sep 18, 04:58

colvarcomp_distances.C
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	#include <cmath>

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



	/// \file cvc_distance.cpp \brief Collective variables
	/// determining various type of distances between two groups

	// "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;
	x.type (colvarvalue::type_scalar);
	}

	void colvar::distance::calc_value()
	{
	group1.reset_atoms_data();
	group2.reset_atoms_data();

	group1.read_positions();
	group2.read_positions();

	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);

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



	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()
	{
	group1.reset_atoms_data();
	group2.reset_atoms_data();

	group1.read_positions();
	group2.read_positions();

	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::fatal_error ("Error: wrapAround was defined in a distanceZ component,"
	" but its period has not been set.\n");
	}

	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::fatal_error ("Axis vector is zero!");
	axis = axis.unit();
	}
	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()
	{
	main.reset_atoms_data();
	ref1.reset_atoms_data();

	main.read_positions();
	ref1.read_positions();

	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 {
	ref2.reset_atoms_data();
	ref2.read_positions();

	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 ));
	}
	}
	}

	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()
	{
	ref1.reset_atoms_data();
	main.reset_atoms_data();

	ref1.read_positions();
	main.read_positions();

	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) {
	ref2.reset_atoms_data();
	ref2.read_positions();

	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::min_distance::min_distance (std::string const &conf)
	: distance (conf)
	{
	function_type = "min_distance";
	x.type (colvarvalue::type_scalar);

	get_keyval (conf, "smoothing", smoothing, (1.0 * cvm::unit_angstrom()));
	}

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

	void colvar::min_distance::calc_value()
	{
	group1.reset_atoms_data();
	group2.reset_atoms_data();

	group1.read_positions();
	group2.read_positions();

	x.real_value = 0.0;

	bool zero_dist = false;

	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 d = dv.norm();
	if (d > 0.0)
	x.real_value += std::exp (smoothing / d);
	else
	zero_dist = true;
	}
	}

	x.real_value = zero_dist ? 0.0 : smoothing/(std::log (x.real_value));
	}

	void colvar::min_distance::calc_gradients()
	{
	if (x.real_value > 0.0) {
	cvm::real const sum = std::exp (smoothing/x.real_value);
	cvm::real const dxdsum = -1.0 *
	(x.real_value/smoothing) * (x.real_value/smoothing) *
	(1.0 / sum);

	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 d = dv.norm();
	if (d > 0.0) {
	cvm::rvector const dvu = dv / dv.norm();
	ai1->grad += dxdsum * std::exp (smoothing / d) *
	smoothing * (-1.0/(dd)) (-1.0) * dvu;
	ai2->grad += dxdsum * std::exp (smoothing / d) *
	smoothing * (-1.0/(dd)) dvu;
	}
	}
	}
	}
	}

	void colvar::min_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_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()
	{
	group1.reset_atoms_data();
	group2.reset_atoms_data();

	group1.read_positions();
	group2.read_positions();

	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::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);
	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()
	{
	atoms.reset_atoms_data();
	atoms.read_positions();
	atoms.apply_translation ((-1.0) * atoms.center_of_geometry());

	x.real_value = 0.0;
	for (cvm::atom_iter ai = atoms.begin(); ai != atoms.end(); ai++) {
	x.real_value += (ai->mass/atoms.total_mass) * (ai->pos).norm2();
	}
	x.real_value = std::sqrt (x.real_value);
	}


	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;
	}
	}


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

	ref_pos_sum2 = 0.0;
	for (size_t i = 0; i < ref_pos.size(); i++) {
	ref_pos_sum2 += ref_pos[i].norm2();
	}
	}


	void colvar::rmsd::calc_value()
	{
	atoms.reset_atoms_data();
	atoms.read_positions();

	atoms_cog = atoms.center_of_geometry();
	rot.calc_optimal_rotation (ref_pos, atoms.positions_shifted (-1.0 * atoms_cog));

	cvm::real group_pos_sum2 = 0.0;
	for (size_t i = 0; i < atoms.size(); i++) {
	group_pos_sum2 += (atoms[i].pos - atoms_cog).norm2();
	}

	// value of the RMSD (Coutsias et al)
	cvm::real const MSD = 1.0/(cvm::real (atoms.size())) *
	( group_pos_sum2 + ref_pos_sum2 - 2.0 * rot.lambda );

	x.real_value = (MSD > 0.0) ? std::sqrt (MSD) : 0.0;
	}


	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 - atoms_cog -
	rot.q.rotate (ref_pos[ia])));
	}
	}


	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 back-rotated target coordinates
	cvm::real divergence = 0.0;

	// 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 = rot.dQ0_2[ia];

	g11 = 2.0 * (rot.q)[1]*dq[1];
	g22 = 2.0 * (rot.q)[2]*dq[2];
	g33 = 2.0 * (rot.q)[3]*dq[3];
	g01 = (rot.q)[0]dq[1] + (rot.q)[1]dq[0];
	g02 = (rot.q)[0]dq[2] + (rot.q)[2]dq[0];
	g03 = (rot.q)[0]dq[3] + (rot.q)[3]dq[0];
	g12 = (rot.q)[1]dq[2] + (rot.q)[2]dq[1];
	g13 = (rot.q)[1]dq[3] + (rot.q)[3]dq[1];
	g23 = (rot.q)[2]dq[3] + (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 i = 0; i < 3; i++) {
	for (size_t j = 0; j < 3; j++) {
	divergence += grad_rot_mat[i][j][i] * y[j];
	}
	}
	}

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



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

	ref_pos_sum2 = 0.0;
	for (size_t i = 0; i < ref_pos.size(); i++) {
	ref_pos_sum2 += ref_pos[i].norm2();
	}
	}


	void colvar::logmsd::calc_value()
	{
	atoms.reset_atoms_data();
	atoms.read_positions();

	if (cvm::debug())
	cvm::log ("colvar::logmsd: current com: "+
	cvm::to_str (atoms.center_of_mass())+"\n");

	atoms_cog = atoms.center_of_geometry();
	rot.calc_optimal_rotation (ref_pos, atoms.positions_shifted (-1.0 * atoms_cog));

	cvm::real group_pos_sum2 = 0.0;
	for (size_t i = 0; i < atoms.size(); i++) {
	group_pos_sum2 += (atoms[i].pos-atoms_cog).norm2();
	}

	// value of the MSD (Coutsias et al)
	MSD = 1.0/(cvm::real (atoms.size())) *
	( group_pos_sum2 + ref_pos_sum2 - 2.0 * rot.lambda );

	x.real_value = (MSD > 0.0) ? std::log(MSD) : 0.0;
	}


	void colvar::logmsd::calc_gradients()
	{
	cvm::real fact = (MSD > 0.0) ? 2.0/(cvm::real (atoms.size()) * MSD) : 0.0;

	for (size_t ia = 0; ia < atoms.size(); ia++) {
	atoms[ia].grad = fact * (atoms[ia].pos - atoms_cog - rot.dL0_2[ia]);
	}
	}


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


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

	// Note: gradient square norm is 4.0 / (N_atoms * E)

	for (size_t ia = 0; ia < atoms.size(); ia++) {
	ft.real_value += atoms[ia].grad * atoms[ia].system_force;
	}
	ft.real_value = atoms.size() MSD / 4.0;
	}


	void colvar::logmsd::calc_Jacobian_derivative()
	{
	// divergence of the back-rotated target coordinates
	cvm::real divergence = 0.0;

	// 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 = rot.dQ0_2[ia];

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

	// Gradient of the rotation matrix wrt current Cartesian position
	// Note: we are only going to use "diagonal" terms: grad_rot_mat[i][j][i]
	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 i = 0; i < 3; i++) {
	for (size_t j = 0; j < 3; j++) {
	divergence += grad_rot_mat[i][j][i] * y[j];
	}
	}
	}

	jd.real_value = (3.0 * atoms.size() - 3.0 - divergence) / 2.0;
	}



	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);

	if (atoms.b_rotate) {
	cvm::fatal_error ("Error: rotateReference should be disabled:"
	"eigenvector component will set it internally.");
	}

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

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

	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::fatal_error ("Error: refPositionsColValue, "
	"if provided, must be non-zero.\n");
	} 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);
	}
	}

	// Set mobile frame of reference for atom group
	atoms.b_center = true;
	atoms.b_rotate = true;
	atoms.ref_pos = ref_pos;

	// now load the eigenvector
	if (get_keyval (conf, "vector", eigenvec, eigenvec)) {
	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)) {

	std::string file_col;
	if (!get_keyval (conf, "vectorCol", file_col, std::string (""))) {
	cvm::fatal_error ("Error: parameter vectorCol is required if vectorFile is set.\n");
	}

	double file_col_value;
	bool found = get_keyval (conf, "vectorColValue", file_col_value, 0.0);
	if (found && !file_col_value)
	cvm::fatal_error ("Error: eigenvectorColValue, "
	"if provided, must be non-zero.\n");

	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::fatal_error ("Error: both reference coordinates"
	"and eigenvector must be defined.\n");
	}

	cvm::rvector center (0.0, 0.0, 0.0);
	eigenvec_invnorm2 = 0.0;

	for (size_t i = 0; i < atoms.size(); i++) {
	center += eigenvec[i];
	}

	cvm::log ("Subtracting sum of eigenvector components: " + cvm::to_str (center) + "\n");

	for (size_t i = 0; i < atoms.size(); i++) {
	eigenvec[i] = eigenvec[i] - center;
	eigenvec_invnorm2 += eigenvec[i].norm2();
	}
	eigenvec_invnorm2 = 1.0 / eigenvec_invnorm2;

	// request derivatives of optimal rotation wrt 2nd group
	// for Jacobian
	atoms.rot.request_group1_gradients(atoms.size());
	atoms.rot.request_group2_gradients(atoms.size());
	}


	void colvar::eigenvector::calc_value()
	{
	atoms.reset_atoms_data();
	atoms.read_positions(); // this will also update atoms.rot

	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()
	{
	// There are two versions of this code
	// The simple version is not formally exact, but its
	// results are numerically indistinguishable from the
	// exact one. The exact one is more expensive and possibly
	// less stable in cases where the optimal rotation
	// becomes ill-defined.

	// Version A: simple, intuitive, cheap, robust. Wrong.
	// Works just fine in practice.
	for (size_t ia = 0; ia < atoms.size(); ia++) {
	atoms[ia].grad = eigenvec[ia];
	}

	/*
	// Version B: complex, expensive, fragile. Right.

	// 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;

	// a term that involves the rotation gradients
	cvm::rvector rot_grad_term;

	cvm::atom_pos x_relative;
	cvm::atom_pos atoms_cog = atoms.center_of_geometry();

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

	// Gradient of optimal quaternion wrt current Cartesian position
	// WARNING: we want derivatives wrt the FIRST group here (unlike RMSD)
	cvm::vector1d< cvm::rvector, 4 > &dq = atoms.rot.dQ0_1[ia];

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

	// this term needs to be rotated back, so we sum it separately
	rot_grad_term.reset();

	for (size_t ja = 0; ja < atoms.size(); ja++) {
	x_relative = atoms[ja].pos - atoms_cog;

	for (size_t i = 0; i < 3; i++) {
	for (size_t j = 0; j < 3; j++) {
	rot_grad_term += eigenvec[ja][i] * grad_rot_mat[i][j] * x_relative[j];
	}
	}
	}

	// Rotate correction term back to reference frame
	atoms[ia].grad = eigenvec[ia] + quat0.rotate (rot_grad_term);
	}
	*/
	}


	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::atom_pos x_relative;
	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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