Merge branch 'rotation-4-5' into rotation

[gromacs/adressmacs.git] / src / mdlib / pull_rotation.c

/*
 * 
 *                This source code is part of
 * 
 *                 G   R   O   M   A   C   S
 * 
 *          GROningen MAchine for Chemical Simulations
 * 
 * Written by David van der Spoel, Erik Lindahl, Berk Hess, and others.
 * Copyright (c) 1991-2000, University of Groningen, The Netherlands.
 * Copyright (c) 2001-2008, The GROMACS development team,
 * check out http://www.gromacs.org for more information.
 
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 * 
 * If you want to redistribute modifications, please consider that
 * scientific software is very special. Version control is crucial -
 * bugs must be traceable. We will be happy to consider code for
 * inclusion in the official distribution, but derived work must not
 * be called official GROMACS. Details are found in the README & COPYING
 * files - if they are missing, get the official version at www.gromacs.org.
 * 
 * To help us fund GROMACS development, we humbly ask that you cite
 * the papers on the package - you can find them in the top README file.
 * 
 * For more info, check our website at http://www.gromacs.org
 * 
 * And Hey:
 * Gallium Rubidium Oxygen Manganese Argon Carbon Silicon
 */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "domdec.h"
#include "gmx_wallcycle.h"
#include "trnio.h"
#include "smalloc.h"
#include "network.h"
#include "pbc.h"
#include "futil.h"
#include "mdrun.h"
#include "txtdump.h"
#include "names.h"
#include "mtop_util.h"
#include "names.h"
#include "nrjac.h"
#include "vec.h"
#include "gmx_ga2la.h"
#include "xvgr.h"
#include "gmxfio.h"
#include "mpelogging.h"
#include "groupcoord.h"
#include "pull_rotation.h"
#include "gmx_sort.h"


static char *RotStr = {"Enforced rotation:"};


/* Set the minimum weight for the determination of the slab centers */
#define WEIGHT_MIN (10*GMX_FLOAT_MIN)

/* Helper structure for sorting positions along rotation vector             */
typedef struct {
    real xcproj;            /* Projection of xc on the rotation vector        */
    int ind;                /* Index of xc                                    */
    real m;                 /* Mass                                           */
    rvec x;                 /* Position                                       */
    rvec x_ref;             /* Reference position                             */
} sort_along_vec_t;


/* Enforced rotation / flexible: determine the angle of each slab             */
typedef struct gmx_slabdata
{
    int  nat;               /* Number of atoms belonging to this slab         */
    rvec *x;                /* The positions belonging to this slab. In 
                               general, this should be all positions of the 
                               whole rotation group, but we leave those away 
                               that have a small enough weight                */
    rvec *ref;              /* Same for reference                             */
    real *weight;           /* The weight for each atom                       */
} t_gmx_slabdata;


/* Enforced rotation data for all groups                                      */
typedef struct gmx_enfrot
{
    FILE  *out_rot;         /* Output file for rotation data                  */
    FILE  *out_torque;      /* Output file for torque data                    */
    FILE  *out_angles;      /* Output file for slab angles for flexible type  */
    FILE  *out_slabs;       /* Output file for slab centers                   */
    int   bufsize;          /* Allocation size of buf                         */
    rvec  *xbuf;            /* Coordinate buffer variable for sorting         */
    real  *mbuf;            /* Masses buffer variable for sorting             */
    sort_along_vec_t *data; /* Buffer variable needed for position sorting    */
    real  *mpi_inbuf;       /* MPI buffer                                     */
    real  *mpi_outbuf;      /* MPI buffer                                     */
    int   mpi_bufsize;      /* Allocation size of in & outbuf                 */
    real  Vrot;             /* (Local) part of the enf. rotation potential    */
} t_gmx_enfrot;


/* Global enforced rotation data for a single rotation group                  */
typedef struct gmx_enfrotgrp
{
    real    degangle;       /* Rotation angle in degree                       */
    matrix  rotmat;         /* Rotation matrix                                */
    atom_id *ind_loc;       /* Local rotation indices                         */
    int     nat_loc;        /* Number of local group atoms                    */
    int     nalloc_loc;     /* Allocation size for ind_loc and weight_loc     */

    real  V;                /* Rotation potential for this rotation group     */
    rvec  *f_rot_loc;       /* Array to store the forces on the local atoms
                               resulting from enforced rotation potential     */

    /* Collective coordinates for the whole rotation group */
    real  *xc_ref_length;   /* Length of each x_rotref vector after x_rotref 
                               has been put into origin                       */
    int   *xc_ref_ind;      /* Position of each local atom in the collective
                               array                                          */
    rvec  xc_center;        /* Center of the rotation group positions, may
                               be mass weighted                               */
    rvec  xc_ref_center;    /* dito, for the reference positions              */
    rvec  *xc;              /* Current (collective) positions                 */
    ivec  *xc_shifts;       /* Current (collective) shifts                    */
    ivec  *xc_eshifts;      /* Extra shifts since last DD step                */
    rvec  *xc_old;          /* Old (collective) positions                     */
    rvec  *xc_norm;         /* Normalized form of the current positions       */
    rvec  *xc_ref_sorted;   /* Reference positions (sorted in the same order 
                               as xc when sorted)                             */
    int   *xc_sortind;      /* Where is a position found after sorting?       */
    real  *mc;              /* Collective masses                              */
    real  *mc_sorted;
    real  invmass;          /* one over the total mass of the rotation group  */
    /* Fixed rotation only */
    rvec  *xr_loc;          /* Local reference coords, correctly rotated      */
    rvec  *x_loc_pbc;       /* Local current coords, correct PBC image        */
    real  *m_loc;           /* Masses of the current local atoms              */
    real  fix_torque_v;     /* Torque in the direction of rotation vector     */
    real  fix_angles_v;
    real  fix_weight_v;
    /* Flexible rotation only */
    int   nslabs_alloc;     /* For this many slabs memory is allocated        */
    int   slab_first;       /* Lowermost slab for that the calculation needs 
                               to be performed at a given time step           */
    int   slab_last;        /* Uppermost slab ...                             */
    int   slab_first_ref;   /* First slab for which reference COG is stored   */
    int   slab_last_ref;    /* Last ...                                       */
    int   slab_buffer;      /* Slab buffer region around reference slabs      */
    int   *firstatom;       /* First relevant atom for a slab                 */
    int   *lastatom;        /* Last relevant atom for a slab                  */
    rvec  *slab_center;     /* Gaussian-weighted slab center (COG)            */
    rvec  *slab_center_ref; /* Gaussian-weighted slab COG for the 
                               reference positions                            */
    real  *slab_weights;    /* Sum of gaussian weights in a slab              */
    real  *slab_torque_v;   /* Torque T = r x f for each slab.                */
                            /* torque_v = m.v = angular momentum in the 
                               direction of v                                 */
    real  max_beta;         /* min_gaussian from inputrec->rotgrp is the
                               minimum value the gaussian must have so that 
                               the force is actually evaluated max_beta is 
                               just another way to put it                     */
    real  *gn_atom;         /* Precalculated gaussians for a single atom      */
    int   *gn_slabind;      /* Tells to which slab each precalculated gaussian 
                               belongs                                        */
    rvec  *slab_innersumvec;/* Inner sum of the flexible2 potential per slab;
                               this is precalculated for optimization reasons */
    t_gmx_slabdata *slab_data; /* Holds atom positions and gaussian weights 
                               of atoms belonging to a slab                   */
} t_gmx_enfrotgrp;


static double** allocate_square_matrix(int dim)
{
    int i;
    double** mat = NULL; 
    
    
    snew(mat, dim);
    for(i=0; i<dim; i++)
        snew(mat[i], dim);

    return mat;
}


static void free_square_matrix(double** mat, int dim)
{
    int i;
    
    
    for (i=0; i<dim; i++)
        sfree(mat[i]);
    sfree(mat);
}


/* Output rotation energy and torque for each rotation group */
static void reduce_output(t_commrec *cr, t_rot *rot, real t)
{
    int      g,i,islab,nslabs=0;
    int      count;      /* MPI element counter                               */
    t_rotgrp *rotg;
    gmx_enfrot_t er;     /* Pointer to the enforced rotation buffer variables */
    gmx_enfrotgrp_t erg; /* Pointer to enforced rotation group data           */
    gmx_bool bFlex;

    
    er=rot->enfrot;
    
    /* Fill the MPI buffer with stuff to reduce: */
    if (PAR(cr))
    {
        count=0;
        for (g=0; g < rot->ngrp; g++)
        {
            rotg = &rot->grp[g];
            erg=rotg->enfrotgrp;
            nslabs = erg->slab_last - erg->slab_first + 1;
            er->mpi_inbuf[count++] = erg->V;
            switch (rotg->eType)
            {
                case erotgISO:
                case erotgISOPF:
                case erotgPM:
                case erotgPMPF:
                case erotgRM:
                case erotgRMPF:
                case erotgRM2:
                case erotgRM2PF:
                    er->mpi_inbuf[count++] = erg->fix_torque_v;
                    er->mpi_inbuf[count++] = erg->fix_angles_v;
                    er->mpi_inbuf[count++] = erg->fix_weight_v;
                    break;
                case erotgFLEX:
                case erotgFLEXT:
                case erotgFLEX2:
                case erotgFLEX2T:
                    /* (Re-)allocate memory for MPI buffer: */
                    if (er->mpi_bufsize < count+nslabs)
                    {
                        er->mpi_bufsize = count+nslabs;
                        srenew(er->mpi_inbuf , er->mpi_bufsize);
                        srenew(er->mpi_outbuf, er->mpi_bufsize);
                    }
                    for (i=0; i<nslabs; i++)
                        er->mpi_inbuf[count++] = erg->slab_torque_v[i];
                    break;
                default:
                    break;
            }
        }
#ifdef GMX_MPI
        MPI_Reduce(er->mpi_inbuf, er->mpi_outbuf, count, GMX_MPI_REAL, MPI_SUM, MASTERRANK(cr), cr->mpi_comm_mygroup);
#endif
        /* Copy back the reduced data from the buffer on the master */
        if (MASTER(cr))
        {
            count=0;
            for (g=0; g < rot->ngrp; g++)
            {
                rotg = &rot->grp[g];
                erg=rotg->enfrotgrp;
                nslabs = erg->slab_last - erg->slab_first + 1;
                erg->V = er->mpi_outbuf[count++];
                switch (rotg->eType)
                {
                    case erotgISO:
                    case erotgISOPF:
                    case erotgPM:
                    case erotgPMPF:
                    case erotgRM:
                    case erotgRMPF:
                    case erotgRM2:
                    case erotgRM2PF:
                        erg->fix_torque_v = er->mpi_outbuf[count++];
                        erg->fix_angles_v = er->mpi_outbuf[count++];
                        erg->fix_weight_v = er->mpi_outbuf[count++];
                        break;
                    case erotgFLEX:
                    case erotgFLEXT:
                    case erotgFLEX2:
                    case erotgFLEX2T:
                        for (i=0; i<nslabs; i++)
                            erg->slab_torque_v[i] = er->mpi_outbuf[count++];
                        break;
                    default:
                        break;
                }
            }
        }
    }
    
    /* Output */
    if (MASTER(cr))
    {
        /* Av. angle and total torque for each rotation group */
        for (g=0; g < rot->ngrp; g++)
        {
            rotg=&rot->grp[g];
            bFlex = (    (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
                      || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) );

            erg=rotg->enfrotgrp;
            
            /* Output to main rotation log file: */
            if (!bFlex)
            {
                fprintf(er->out_rot, "%12.4f%12.3e", 
                        (erg->fix_angles_v/erg->fix_weight_v)*180.0*M_1_PI,
                        erg->fix_torque_v);
            }
            fprintf(er->out_rot, "%12.3e", erg->V);
                        
            /* Output to torque log file: */
            if (bFlex)
            {
                fprintf(er->out_torque, "%12.3e%6d", t, g);
                for (i=erg->slab_first; i<=erg->slab_last; i++)
                {
                    islab = i - erg->slab_first;  /* slab index */
                    /* Only output if enough weight is in slab */
                    if (erg->slab_weights[islab] > rotg->min_gaussian)
                        fprintf(er->out_torque, "%6d%12.3e", i, erg->slab_torque_v[islab]);
                }
                fprintf(er->out_torque , "\n");
            }
        }
        fprintf(er->out_rot, "\n");
    }
}


/* Add the forces from enforced rotation potential to the local forces.
 * Should be called after the SR forces have been evaluated */
extern real add_rot_forces(t_rot *rot, rvec f[], t_commrec *cr, int step, real t)
{
    int g,l,ii;
    t_rotgrp *rotg;
    gmx_enfrot_t er;     /* Pointer to the enforced rotation buffer variables */
    gmx_enfrotgrp_t erg; /* Pointer to enforced rotation group data           */

    
    er=rot->enfrot;
    
    GMX_MPE_LOG(ev_add_rot_forces_start);
    
    /* Reduce energy,torque, angles etc. to get the sum values (per rotation group) 
     * on the master and output these values to file. */
    if (do_per_step(step, rot->nsttout))
        reduce_output(cr, rot, t);

    /* Total rotation potential is the sum over all rotation groups */
    er->Vrot = 0.0; 
        
    /* Loop over enforced rotation groups (usually 1, though)
     * Apply the forces from rotation potentials */
    for (g=0; g<rot->ngrp; g++)
    {
        rotg = &rot->grp[g];
        erg=rotg->enfrotgrp;
        er->Vrot += erg->V;
        for (l=0; l<erg->nat_loc; l++)
        {
            /* Get the right index of the local force */
            ii = erg->ind_loc[l];
            /* Add */
            rvec_inc(f[ii],erg->f_rot_loc[l]);
        }
    }
    
    GMX_MPE_LOG(ev_add_rot_forces_finish);

    return (MASTER(cr)? er->Vrot : 0.0);
}


/* Calculate the maximum beta that leads to a gaussian larger min_gaussian,
 * also does some checks
 */
static double calc_beta_max(real min_gaussian, real slab_dist)
{
    const double norm = 0.5698457353514458216;  /* = 1/1.7548609 */
    double sigma;
    double arg;
    
    
    /* Actually the next two checks are already made in grompp */
    if (slab_dist <= 0)
        gmx_fatal(FARGS, "Slab distance of flexible rotation groups must be >=0 !");
    if (min_gaussian <= 0)
        gmx_fatal(FARGS, "Cutoff value for Gaussian must be > 0. (You requested %f)");

    /* Define the sigma value */
    sigma = 0.7*slab_dist;

    /* Calculate the argument for the logarithm and check that the log() result is negative or 0 */
    arg = min_gaussian/norm;
    if (arg > 1.0)
        gmx_fatal(FARGS, "min_gaussian of flexible rotation groups must be <%g", norm);
    
    return sqrt(-2.0*sigma*sigma*log(min_gaussian/norm));
}


static inline real calc_beta(rvec curr_x, t_rotgrp *rotg, int n)
{
    return iprod(curr_x, rotg->vec) - rotg->slab_dist * n;
}


static inline real gaussian_weight(rvec curr_x, t_rotgrp *rotg, int n)
{
    /* norm is chosen such that the sum of the gaussians
     * over the slabs is approximately 1.0 everywhere */
    /* a previously used value was norm = 0.5698457353514458216 = 1/1.7548609 */
    const real norm = 0.569917543430618;      /* = 1/1.7546397922417 */
    real       sigma;

    
    /* Define the sigma value */
    sigma = 0.7*rotg->slab_dist;
    /* Calculate the Gaussian value of slab n for position curr_x */
    return norm * exp( -0.5 * sqr( calc_beta(curr_x, rotg, n)/sigma ) );
}


/* Returns the weight in a single slab, also calculates the Gaussian- and mass-
 * weighted sum of positions for that slab */
static real get_slab_weight(int j, t_rotgrp *rotg, rvec xc[], real mc[], rvec *x_weighted_sum)
{
    rvec curr_x;              /* The position of an atom                      */
    rvec curr_x_weighted;     /* The gaussian-weighted position               */
    real gaussian;            /* A single gaussian weight                     */
    real wgauss;              /* gaussian times current mass                  */
    real slabweight = 0.0;    /* The sum of weights in the slab               */
    int i,islab;
    gmx_enfrotgrp_t erg;      /* Pointer to enforced rotation group data      */

    
    erg=rotg->enfrotgrp;
    clear_rvec(*x_weighted_sum);
    
    /* Slab index */
    islab = j - erg->slab_first;
    
    /* Loop over all atoms in the rotation group */
     for (i=0; i<rotg->nat; i++)
     {
         copy_rvec(xc[i], curr_x);
         gaussian = gaussian_weight(curr_x, rotg, j);
         wgauss = gaussian * mc[i];
         svmul(wgauss, curr_x, curr_x_weighted);
         rvec_add(*x_weighted_sum, curr_x_weighted, *x_weighted_sum);
         slabweight += wgauss;
     } /* END of loop over rotation group atoms */

     return slabweight;
}


static void get_slab_centers(
        t_rotgrp *rotg,       /* The rotation group information               */
        rvec      *xc,        /* The rotation group positions; will 
                                 typically be enfrotgrp->xc, but at first call 
                                 it is enfrotgrp->xc_ref                      */
        real      *mc,        /* The masses of the rotation group atoms       */
        t_commrec *cr,        /* Communication record                         */
        int       g,          /* The number of the rotation group             */
        real      time,       /* Used for output only                         */
        FILE      *out_slabs, /* For outputting center per slab information   */
        gmx_bool  bOutStep,   /* Is this an output step?                      */
        gmx_bool  bReference) /* If this routine is called from
                                 init_rot_group we need to store
                                 the reference slab centers                   */
{
    int j,islab;
    gmx_enfrotgrp_t erg;      /* Pointer to enforced rotation group data */
    
    
    erg=rotg->enfrotgrp;

    /* Loop over slabs */
    for (j = erg->slab_first; j <= erg->slab_last; j++)
    {
        islab = j - erg->slab_first;
        erg->slab_weights[islab] = get_slab_weight(j, rotg, xc, mc, &erg->slab_center[islab]);
        
        /* We can do the calculations ONLY if there is weight in the slab! */
        if (erg->slab_weights[islab] > WEIGHT_MIN)
        {
            svmul(1.0/erg->slab_weights[islab], erg->slab_center[islab], erg->slab_center[islab]);
        }
        else
        {
            /* We need to check this here, since we divide through slab_weights
             * in the flexible low-level routines! */
            gmx_fatal(FARGS, "Not enough weight in slab %d. Slab center cannot be determined!", j);
        }
        
        /* At first time step: save the centers of the reference structure */
        if (bReference)
            copy_rvec(erg->slab_center[islab], erg->slab_center_ref[islab]);
    } /* END of loop over slabs */
    
    /* Output on the master */
    if (MASTER(cr) && bOutStep)
    {
        fprintf(out_slabs, "%12.3e%6d", time, g);
        for (j = erg->slab_first; j <= erg->slab_last; j++)
        {
            islab = j - erg->slab_first;
            fprintf(out_slabs, "%6d%12.3e%12.3e%12.3e",
                    j,erg->slab_center[islab][XX],erg->slab_center[islab][YY],erg->slab_center[islab][ZZ]);
        }
        fprintf(out_slabs, "\n");
    }
}


static void calc_rotmat(
        rvec vec,
        real degangle,  /* Angle alpha of rotation at time t in degrees       */
        matrix rotmat)  /* Rotation matrix                                    */
{
    real radangle;            /* Rotation angle in radians */
    real cosa;                /* cosine alpha              */
    real sina;                /* sine alpha                */
    real OMcosa;              /* 1 - cos(alpha)            */
    real dumxy, dumxz, dumyz; /* save computations         */
    rvec rot_vec;             /* Rotate around rot_vec ... */


    radangle = degangle * M_PI/180.0;
    copy_rvec(vec , rot_vec );

    /* Precompute some variables: */
    cosa   = cos(radangle);
    sina   = sin(radangle);
    OMcosa = 1.0 - cosa;
    dumxy  = rot_vec[XX]*rot_vec[YY]*OMcosa;
    dumxz  = rot_vec[XX]*rot_vec[ZZ]*OMcosa;
    dumyz  = rot_vec[YY]*rot_vec[ZZ]*OMcosa;

    /* Construct the rotation matrix for this rotation group: */
    /* 1st column: */
    rotmat[XX][XX] = cosa  + rot_vec[XX]*rot_vec[XX]*OMcosa;
    rotmat[YY][XX] = dumxy + rot_vec[ZZ]*sina;
    rotmat[ZZ][XX] = dumxz - rot_vec[YY]*sina;
    /* 2nd column: */
    rotmat[XX][YY] = dumxy - rot_vec[ZZ]*sina;
    rotmat[YY][YY] = cosa  + rot_vec[YY]*rot_vec[YY]*OMcosa;
    rotmat[ZZ][YY] = dumyz + rot_vec[XX]*sina;
    /* 3rd column: */
    rotmat[XX][ZZ] = dumxz + rot_vec[YY]*sina;
    rotmat[YY][ZZ] = dumyz - rot_vec[XX]*sina;
    rotmat[ZZ][ZZ] = cosa  + rot_vec[ZZ]*rot_vec[ZZ]*OMcosa;

#ifdef PRINTMATRIX
    int iii,jjj;

    for (iii=0; iii<3; iii++) {
        for (jjj=0; jjj<3; jjj++)
            fprintf(stderr, " %10.8f ",  rotmat[iii][jjj]);
        fprintf(stderr, "\n");
    }
#endif
}


/* Calculates torque on the rotation axis tau = position x force */
static inline real torque(
        rvec rotvec,  /* rotation vector; MUST be normalized!                 */
        rvec force,   /* force                                                */
        rvec x,       /* position of atom on which the force acts             */
        rvec pivot)   /* pivot point of rotation axis                         */
{
    rvec vectmp, tau;

    
    /* Subtract offset */
    rvec_sub(x,pivot,vectmp);
    
    /* position x force */
    cprod(vectmp, force, tau);
    
    /* Return the part of the torque which is parallel to the rotation vector */
    return iprod(tau, rotvec);
}


/* Right-aligned output of value with standard width */
static void print_aligned(FILE *fp, char *str)
{
    fprintf(fp, "%12s", str);
}


/* Right-aligned output of value with standard short width */
static void print_aligned_short(FILE *fp, char *str)
{
    fprintf(fp, "%6s", str);
}


/* Right-aligned output of value with standard width */
static void print_aligned_group(FILE *fp, char *str, int g)
{
    char sbuf[STRLEN];
    
    
    sprintf(sbuf, "%s%d", str, g);
    fprintf(fp, "%12s", sbuf);
}


static FILE *open_output_file(const char *fn, int steps)
{
    FILE *fp;
    
    
    fp = ffopen(fn, "w");

    fprintf(fp, "# Output is written every %d time steps.\n\n", steps);
    
    return fp;
}


/* Open output file for slab COG data. Call on master only */
static FILE *open_slab_out(t_rot *rot, const char *fn)
{
    FILE      *fp=NULL;
    int       g;
    t_rotgrp  *rotg;


    for (g=0; g<rot->ngrp; g++)
    {
        rotg = &rot->grp[g];
        if (   (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
            || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) )
        {
            if (NULL == fp)
                fp = open_output_file(fn, rot->nsttout);
            fprintf(fp, "# Rotation group %d (%s), slab distance %f nm\n", g, erotg_names[rotg->eType], rotg->slab_dist);
        }
    }
    
    if (fp != NULL)
    {
        fprintf(fp, "# The following columns will have the syntax: (COG = center of geometry, gaussian weighted)\n");
        fprintf(fp, "#     ");
        print_aligned_short(fp, "t");
        print_aligned_short(fp, "grp");
        print_aligned_short(fp, "slab");
        print_aligned(fp, "COG-X");
        print_aligned(fp, "COG-Y");
        print_aligned(fp, "COG-Z");
        print_aligned_short(fp, "slab");
        print_aligned(fp, "COG-X");
        print_aligned(fp, "COG-Y");
        print_aligned(fp, "COG-Z");
        print_aligned_short(fp, "slab");
        fprintf(fp, " ...\n");
        fflush(fp);
    }
    
    return fp;
}


/* Open output file and print some general information about the rotation groups.
 * Call on master only */
static FILE *open_rot_out(const char *fn, t_rot *rot, const output_env_t oenv, 
                          unsigned long Flags)
{
    FILE       *fp;
    int        g,nsets;
    t_rotgrp   *rotg;
    const char **setname;
    char       buf[50];
    gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */
    gmx_bool   bFlex;


    if (Flags & MD_APPENDFILES)
    {
        fp = gmx_fio_fopen(fn,"a");
    }
    else
    {
        fp = xvgropen(fn, "Rotation angles and energy", "Time [ps]", "angles [degree] and energies [kJ/mol]", oenv);
        fprintf(fp, "# The scalar tau is the torque [kJ/mol] in the direction of the rotation vector v.\n");
        fprintf(fp, "# To obtain the vectorial torque, multiply tau with the group's rot_vec.\n#\n");
        
        for (g=0; g<rot->ngrp; g++)
        {
            rotg = &rot->grp[g];
            erg=rotg->enfrotgrp;
            bFlex = (   (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
                     || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) );


            fprintf(fp, "# Rotation group %d, potential type '%s':\n"      , g, erotg_names[rotg->eType]);
            fprintf(fp, "# rot_massw%d          %s\n"                      , g, yesno_names[rotg->bMassW]);
            fprintf(fp, "# rot_vec%d            %12.5e %12.5e %12.5e\n"    , g, rotg->vec[XX], rotg->vec[YY], rotg->vec[ZZ]);
            fprintf(fp, "# rot_rate%d           %12.5e degree/ps\n"        , g, rotg->rate);
            fprintf(fp, "# rot_k%d              %12.5e kJ/(mol*nm^2)\n"    , g, rotg->k);
            if ( rotg->eType==erotgISO || rotg->eType==erotgPM || rotg->eType==erotgRM || rotg->eType==erotgRM2)
                fprintf(fp, "# rot_pivot%d          %12.5e %12.5e %12.5e  nm\n", g, rotg->pivot[XX], rotg->pivot[YY], rotg->pivot[ZZ]);

            if (bFlex)
            {
                fprintf(fp, "# rot_slab_distance%d   %f nm\n", g, rotg->slab_dist);
                fprintf(fp, "# rot_min_gaussian%d   %12.5e\n", g, rotg->min_gaussian);
            }

            /* Output the centers of the rotation groups for the pivot-free potentials */
            if ((rotg->eType==erotgISOPF) || (rotg->eType==erotgPMPF) || (rotg->eType==erotgRMPF) || (rotg->eType==erotgRM2PF
                || (rotg->eType==erotgFLEXT) || (rotg->eType==erotgFLEX2T)) )
            {
                fprintf(fp, "# %s of ref. grp. %d  %12.5e %12.5e %12.5e\n",
                        rotg->bMassW? "COM":"COG", g,
                                erg->xc_ref_center[XX], erg->xc_ref_center[YY], erg->xc_ref_center[ZZ]);

                fprintf(fp, "# initial %s grp. %d  %12.5e %12.5e %12.5e\n",
                        rotg->bMassW? "COM":"COG", g,
                                erg->xc_center[XX], erg->xc_center[YY], erg->xc_center[ZZ]);
            }

            if ( (rotg->eType == erotgRM2) || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) )
            {
                fprintf(fp, "# rot_eps%d            %12.5e nm^2\n", g, rotg->eps);
            }
        }
        
        fprintf(fp, "#\n# Legend for the following data columns:\n");
        fprintf(fp, "#     ");
        print_aligned_short(fp, "t");
        nsets = 0;
        snew(setname, 4*rot->ngrp);
        
        for (g=0; g<rot->ngrp; g++)
        {
            rotg = &rot->grp[g];
            sprintf(buf, "theta_ref%d [degree]", g);
            print_aligned_group(fp, "theta_ref", g);
            setname[nsets] = strdup(buf);
            nsets++;
        }
        for (g=0; g<rot->ngrp; g++)
        {
            rotg = &rot->grp[g];
            bFlex = (   (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
                     || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) );

            /* For flexible axis rotation we use RMSD fitting to determine the
             * actual angle of the rotation group */
            if (!bFlex)
            {
                sprintf(buf, "theta-av%d [degree]", g);
                print_aligned_group(fp, "theta_av", g);
                setname[nsets] = strdup(buf);
                nsets++;
                sprintf(buf, "tau%d [kJ/mol]", g);
                print_aligned_group(fp, "tau", g);
                setname[nsets] = strdup(buf);
                nsets++;
            }
            sprintf(buf, "energy%d [kJ/mol]", g);
            print_aligned_group(fp, "energy", g);
            setname[nsets] = strdup(buf);
            nsets++;
        }
        fprintf(fp, "\n#\n");
        
        if (nsets > 1)
            xvgr_legend(fp, nsets, setname, oenv);
        sfree(setname);
        
        fflush(fp);
    }
    
    return fp;
}


/* Call on master only */
static FILE *open_angles_out(t_rot *rot, const char *fn)
{
    int      g;
    FILE     *fp=NULL;
    t_rotgrp *rotg;


    /* Open output file and write some information about it's structure: */
    fp = open_output_file(fn, rot->nstrout);
    fprintf(fp, "# All angles given in degrees, time in ps\n");
    for (g=0; g<rot->ngrp; g++)
    {
        rotg = &rot->grp[g];
        if (   (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
            || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) )
        {
            fprintf(fp, "# Rotation group %d (%s), slab distance %f nm, fit type %s\n", 
                    g, erotg_names[rotg->eType], rotg->slab_dist, erotg_fitnames[rotg->eFittype]);
        }
    }
    fprintf(fp, "# The following columns will have the syntax:\n");
    fprintf(fp, "#     ");
    print_aligned_short(fp, "t");
    print_aligned_short(fp, "grp");
    print_aligned(fp, "theta_ref");
    print_aligned(fp, "theta_fit");
    print_aligned_short(fp, "slab");
    print_aligned_short(fp, "atoms");
    print_aligned(fp, "theta_fit");
    print_aligned_short(fp, "slab");
    print_aligned_short(fp, "atoms");
    print_aligned(fp, "theta_fit");
    fprintf(fp, " ...\n");
    fflush(fp);
    return fp;
}


/* Open torque output file and write some information about it's structure.
 * Call on master only */
static FILE *open_torque_out(t_rot *rot, const char *fn)
{
    FILE      *fp;
    int       g;
    t_rotgrp  *rotg;


    fp = open_output_file(fn, rot->nsttout);

    for (g=0; g<rot->ngrp; g++)
    {
        rotg = &rot->grp[g];
        if (   (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
            || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) )
        {
            fprintf(fp, "# Rotation group %d (%s), slab distance %f nm\n", g, erotg_names[rotg->eType], rotg->slab_dist);
            fprintf(fp, "# The scalar tau is the torque [kJ/mol] in the direction of the rotation vector.\n");
            fprintf(fp, "# To obtain the vectorial torque, multiply tau with\n");
            fprintf(fp, "# rot_vec%d            %10.3e %10.3e %10.3e\n", g, rotg->vec[XX], rotg->vec[YY], rotg->vec[ZZ]);
            fprintf(fp, "#\n");
        }
    }
    fprintf(fp, "# The following columns will have the syntax (tau=torque for that slab):\n");
    fprintf(fp, "#     ");
    print_aligned_short(fp, "t");
    print_aligned_short(fp, "grp");
    print_aligned_short(fp, "slab");
    print_aligned(fp, "tau");
    print_aligned_short(fp, "slab");
    print_aligned(fp, "tau");
    fprintf(fp, " ...\n");
    fflush(fp);

    return fp;
}


static void swap_val(double* vec, int i, int j)
{
    double tmp = vec[j];
    
    
    vec[j]=vec[i];
    vec[i]=tmp;
}


static void swap_col(double **mat, int i, int j)
{
    double tmp[3] = {mat[0][j], mat[1][j], mat[2][j]};
    
    
    mat[0][j]=mat[0][i];
    mat[1][j]=mat[1][i];
    mat[2][j]=mat[2][i];
    
    mat[0][i]=tmp[0];
    mat[1][i]=tmp[1];
    mat[2][i]=tmp[2];
} 


/* Eigenvectors are stored in columns of eigen_vec */
static void diagonalize_symmetric(
        double **matrix,
        double **eigen_vec,
        double eigenval[3])
{
    int n_rot;
    
    
    jacobi(matrix,3,eigenval,eigen_vec,&n_rot);
    
    /* sort in ascending order */
    if (eigenval[0] > eigenval[1])
    {
        swap_val(eigenval, 0, 1);
        swap_col(eigen_vec, 0, 1);
    } 
    if (eigenval[1] > eigenval[2])
    {
        swap_val(eigenval, 1, 2);
        swap_col(eigen_vec, 1, 2);
    }
    if (eigenval[0] > eigenval[1])
    {
        swap_val(eigenval, 0, 1);
        swap_col(eigen_vec, 0, 1);
    }
}


static void align_with_z(
        rvec* s,           /* Structure to align */
        int natoms,
        rvec axis)
{
    int    i, j, k;
    rvec   zet = {0.0, 0.0, 1.0};
    rvec   rot_axis={0.0, 0.0, 0.0};
    rvec   *rotated_str=NULL;
    real   ooanorm;
    real   angle;
    matrix rotmat;
    
    
    snew(rotated_str, natoms);

    /* Normalize the axis */
    ooanorm = 1.0/norm(axis);
    svmul(ooanorm, axis, axis);
    
    /* Calculate the angle for the fitting procedure */
    cprod(axis, zet, rot_axis);
    angle = acos(axis[2]);
    if (angle < 0.0)
        angle += M_PI;
    
    /* Calculate the rotation matrix */
    calc_rotmat(rot_axis, angle*180.0/M_PI, rotmat);
    
    /* Apply the rotation matrix to s */
    for (i=0; i<natoms; i++)
    {    
        for(j=0; j<3; j++)
        {
            for(k=0; k<3; k++)
            {
                rotated_str[i][j] += rotmat[j][k]*s[i][k];
            }
        }
    }
    
    /* Rewrite the rotated structure to s */
    for(i=0; i<natoms; i++)
    {
        for(j=0; j<3; j++)
        {
            s[i][j]=rotated_str[i][j];
        }
    }
    
    sfree(rotated_str);
} 


static void calc_correl_matrix(rvec* Xstr, rvec* Ystr, double** Rmat, int natoms)
{    
    int i, j, k;
 
    
    for (i=0; i<3; i++)
        for (j=0; j<3; j++)
            Rmat[i][j] = 0.0;
    
    for (i=0; i<3; i++) 
        for (j=0; j<3; j++) 
            for (k=0; k<natoms; k++) 
                Rmat[i][j] += Ystr[k][i] * Xstr[k][j];
}


static void weigh_coords(rvec* str, real* weight, int natoms)
{
    int i, j;
    
    
    for(i=0; i<natoms; i++)
    {
        for(j=0; j<3; j++)
            str[i][j] *= sqrt(weight[i]);
    }  
}


static double opt_angle_analytic(
        rvec* ref_s,
        rvec* act_s,
        real* weight, 
        int natoms,
        rvec ref_com,
        rvec act_com,
        rvec axis)
{    
    int    i, j, k;
    rvec   *ref_s_1=NULL;
    rvec   *act_s_1=NULL;
    rvec   shift;
    double **Rmat, **RtR, **eigvec;
    double eigval[3];
    double V[3][3], WS[3][3];
    double rot_matrix[3][3];
    double opt_angle;
    
    
    /* Do not change the original coordinates */ 
    snew(ref_s_1, natoms);
    snew(act_s_1, natoms);
    for(i=0; i<natoms; i++)
    {
        copy_rvec(ref_s[i], ref_s_1[i]);
        copy_rvec(act_s[i], act_s_1[i]);
    }
    
    /* Translate the structures to the origin */
    shift[XX] = -ref_com[XX];
    shift[YY] = -ref_com[YY];
    shift[ZZ] = -ref_com[ZZ];
    translate_x(ref_s_1, natoms, shift);
    
    shift[XX] = -act_com[XX];
    shift[YY] = -act_com[YY];
    shift[ZZ] = -act_com[ZZ];
    translate_x(act_s_1, natoms, shift);
    
    /* Align rotation axis with z */
    align_with_z(ref_s_1, natoms, axis);
    align_with_z(act_s_1, natoms, axis);
    
    /* Correlation matrix */
    Rmat = allocate_square_matrix(3);
    
    for (i=0; i<natoms; i++)
    {
        ref_s_1[i][2]=0.0;
        act_s_1[i][2]=0.0;
    }
    
    /* Weight positions with sqrt(weight) */
    if (weight)
    {
        weigh_coords(ref_s_1, weight, natoms);
        weigh_coords(act_s_1, weight, natoms);
    }
    
    /* Calculate correlation matrices R=YXt (X=ref_s; Y=act_s) */
    calc_correl_matrix(ref_s_1, act_s_1, Rmat, natoms);
    
    /* Calculate RtR */
    RtR = allocate_square_matrix(3);
    for (i=0; i<3; i++)
    {
        for (j=0; j<3; j++)
        {
            for (k=0; k<3; k++)
            {
                RtR[i][j] += Rmat[k][i] * Rmat[k][j];
            }
        }
    }
    /* Diagonalize RtR */
    snew(eigvec,3);
    for (i=0; i<3; i++)
        snew(eigvec[i],3);
    
    diagonalize_symmetric(RtR, eigvec, eigval);
    swap_col(eigvec,0,1);
    swap_col(eigvec,1,2);
    swap_val(eigval,0,1);
    swap_val(eigval,1,2);
    
    /* Calculate V */
    for(i=0; i<3; i++)
    {
        for(j=0; j<3; j++)
        {
            V[i][j]  = 0.0;
            WS[i][j] = 0.0;
        }
    }
    
    for (i=0; i<2; i++)
        for (j=0; j<2; j++)
            WS[i][j] = eigvec[i][j] / sqrt(eigval[j]);
    
    for (i=0; i<3; i++)
    {
        for (j=0; j<3; j++)
        {
            for (k=0; k<3; k++)
            {
                V[i][j] += Rmat[i][k]*WS[k][j];
            }
        }
    }
    free_square_matrix(Rmat, 3);
    
    /* Calculate optimal rotation matrix */
    for (i=0; i<3; i++)
        for (j=0; j<3; j++)
            rot_matrix[i][j] = 0.0;
    
    for (i=0; i<3; i++)
    {
        for(j=0; j<3; j++)
        {
            for(k=0; k<3; k++){
                rot_matrix[i][j] += eigvec[i][k]*V[j][k];
            }
        }
    }
    rot_matrix[2][2] = 1.0;
        
    /* Determine the optimal rotation angle: */
    opt_angle = (-1.0)*acos(rot_matrix[0][0])*180.0/M_PI;
    if (rot_matrix[0][1] < 0.0)
        opt_angle = (-1.0)*opt_angle;
        
    /* Give back some memory */
    free_square_matrix(RtR, 3);
    sfree(ref_s_1);
    sfree(act_s_1);
    for (i=0; i<3; i++)
        sfree(eigvec[i]);
    sfree(eigvec);
    
    return opt_angle;
}


/* Determine actual angle of this slab by RMSD fit to the reference */
/* Not parallelized, call this routine only on the master */
static void flex_fit_angle(
        int  g,
        t_rotgrp *rotg,
        double t,
        real degangle,
        FILE *fp)
{
    int         i,l,n,islab,ind;
    rvec        curr_x, ref_x;
    rvec        *fitcoords=NULL;
    rvec        act_center;  /* Center of actual positions that are passed to the fit routine */
    rvec        ref_center;  /* Same for the reference positions */
    double      fitangle;    /* This will be the actual angle of the rotation group derived
                              * from an RMSD fit to the reference structure at t=0 */
    t_gmx_slabdata *sd;
    rvec        coord;
    real        scal;
    gmx_enfrotgrp_t erg;     /* Pointer to enforced rotation group data */
    real        OOm_av;      /* 1/average_mass of a rotation group atom */
    real        m_rel;       /* Relative mass of a rotation group atom  */

    
    erg=rotg->enfrotgrp;

    /* Average mass of a rotation group atom: */
    OOm_av = erg->invmass*rotg->nat;

    /**********************************/
    /* First collect the data we need */
    /**********************************/

    /* Collect the data for the individual slabs */
    for (n = erg->slab_first; n <= erg->slab_last; n++)
    {
        islab = n - erg->slab_first; /* slab index */
        sd = &(rotg->enfrotgrp->slab_data[islab]);
        sd->nat = erg->lastatom[islab]-erg->firstatom[islab]+1;
        ind = 0;
        
        /* Loop over the relevant atoms in the slab */
        for (l=erg->firstatom[islab]; l<=erg->lastatom[islab]; l++)
        {            
            /* Current position of this atom: x[ii][XX/YY/ZZ] */
            copy_rvec(erg->xc[l], curr_x);
            
            /* The (unrotated) reference position of this atom is copied to ref_x.
             * Beware, the xc coords have been sorted in do_flexible */
            copy_rvec(erg->xc_ref_sorted[l], ref_x);
            
            /* Save data for doing angular RMSD fit later */
            /* Save the current atom position */
            copy_rvec(curr_x, sd->x[ind]);
            /* Save the corresponding reference position */
            copy_rvec(ref_x , sd->ref[ind]);
            
            /* Maybe also mass-weighting was requested. If yes, additionally
             * multiply the weights with the relative mass of the atom. If not,
             * multiply with unity. */
            m_rel = erg->mc_sorted[l]*OOm_av;

            /* Save the weight for this atom in this slab */
            sd->weight[ind] = gaussian_weight(curr_x, rotg, n) * m_rel;

            /* Next atom in this slab */
            ind++;
        }
    }

    /* Get the center of the whole rotation group. Note, again, the erg->xc have
     * been sorted in do_flexible */
    get_center(erg->xc, erg->mc_sorted, rotg->nat, act_center);

    /******************************/
    /* Now do the fit calculation */
    /******************************/

    /* === Determine the optimal fit angle for the whole rotation group === */
    if (rotg->eFittype == erotgFitNORM)
    {
        /* Normalize every position to it's reference length 
         * prior to performing the fit */
        for (i=0; i<rotg->nat; i++)
        {
            /* First put the center of the positions into the origin */
            rvec_sub(erg->xc[i], act_center, coord);
            /* Determine the scaling factor for the length: */
            scal = erg->xc_ref_length[erg->xc_sortind[i]] / norm(coord);
            /* Get position, multiply with the scaling factor and save in buf[i] */
            svmul(scal, coord, erg->xc_norm[i]);
        }
        fitcoords = erg->xc_norm;
    }
    else
    {
        fitcoords = erg->xc;
    }
    /* Note that from the point of view of the current positions, the reference has rotated backwards,
     * but we want to output the angle relative to the fixed reference, therefore the minus sign. */
    fitangle = -opt_angle_analytic(erg->xc_ref_sorted, fitcoords, erg->mc_sorted,
                                   rotg->nat, erg->xc_ref_center, act_center, rotg->vec);
    fprintf(fp, "%12.3e%6d%12.3f%12.3lf", t, g, degangle, fitangle);


    /* === Now do RMSD fitting for each slab === */
    /* We require at least SLAB_MIN_ATOMS in a slab, such that the fit makes sense. */
#define SLAB_MIN_ATOMS 4

    for (n = erg->slab_first; n <= erg->slab_last; n++)
    {
        islab = n - erg->slab_first; /* slab index */
        sd = &(rotg->enfrotgrp->slab_data[islab]);
        if (sd->nat >= SLAB_MIN_ATOMS)
        {
            /* Get the center of the slabs reference and current positions */
            get_center(sd->ref, sd->weight, sd->nat, ref_center);
            get_center(sd->x  , sd->weight, sd->nat, act_center);
            if (rotg->eFittype == erotgFitNORM)
            {
                /* Normalize every position to it's reference length 
                 * prior to performing the fit */
                for (i=0; i<sd->nat;i++) /* Center */
                {
                    rvec_dec(sd->ref[i], ref_center);
                    rvec_dec(sd->x[i]  , act_center);
                    /* Normalize x_i such that it gets the same length as ref_i */
                    svmul( norm(sd->ref[i])/norm(sd->x[i]), sd->x[i], sd->x[i] );
                }
                /* We already subtracted the centers */
                clear_rvec(ref_center);
                clear_rvec(act_center);
            }
            fitangle = -opt_angle_analytic(sd->ref, sd->x, sd->weight, sd->nat, ref_center, act_center, rotg->vec);
            fprintf(fp, "%6d%6d%12.3f", n, sd->nat, fitangle);
        }
    }
    fprintf(fp     , "\n");

#undef SLAB_MIN_ATOMS
}


/* Shift x with is */
static inline void shift_single_coord(matrix box, rvec x, const ivec is)
{
    int tx,ty,tz;


    tx=is[XX];
    ty=is[YY];
    tz=is[ZZ];

    if(TRICLINIC(box))
    {
        x[XX] += tx*box[XX][XX]+ty*box[YY][XX]+tz*box[ZZ][XX];
        x[YY] += ty*box[YY][YY]+tz*box[ZZ][YY];
        x[ZZ] += tz*box[ZZ][ZZ];
    } else
    {
        x[XX] += tx*box[XX][XX];
        x[YY] += ty*box[YY][YY];
        x[ZZ] += tz*box[ZZ][ZZ];
    }
}


/* Determine the 'home' slab of this atom which is the
 * slab with the highest Gaussian weight of all */
#define round(a) (int)(a+0.5)
static inline int get_homeslab(
        rvec curr_x,   /* The position for which the home slab shall be determined */ 
        rvec rotvec,   /* The rotation vector */
        real slabdist) /* The slab distance */
{
    real dist;
    
    
    /* The distance of the atom to the coordinate center (where the
     * slab with index 0) is */
    dist = iprod(rotvec, curr_x);
    
    return round(dist / slabdist); 
}


/* For a local atom determine the relevant slabs, i.e. slabs in
 * which the gaussian is larger than min_gaussian
 */
static int get_single_atom_gaussians(
        rvec      curr_x,
        t_commrec *cr,
        t_rotgrp  *rotg)
{
   int slab, homeslab;
   real g;
   int count = 0;
   gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */

   
   erg=rotg->enfrotgrp;
   
   /* Determine the 'home' slab of this atom: */
   homeslab = get_homeslab(curr_x, rotg->vec, rotg->slab_dist);

   /* First determine the weight in the atoms home slab: */
   g = gaussian_weight(curr_x, rotg, homeslab);
   
   erg->gn_atom[count] = g;
   erg->gn_slabind[count] = homeslab;
   count++;
   
   
   /* Determine the max slab */
   slab = homeslab;
   while (g > rotg->min_gaussian)
   {
       slab++;
       g = gaussian_weight(curr_x, rotg, slab);
       erg->gn_slabind[count]=slab;
       erg->gn_atom[count]=g;
       count++;
   }
   count--;
   
   /* Determine the max slab */
   slab = homeslab;
   do
   {
       slab--;
       g = gaussian_weight(curr_x, rotg, slab);       
       erg->gn_slabind[count]=slab;
       erg->gn_atom[count]=g;
       count++;
   }
   while (g > rotg->min_gaussian);
   count--;
   
   return count;
}


static void flex2_precalc_inner_sum(t_rotgrp *rotg, t_commrec *cr)
{
    int  i,n,islab;
    rvec  xi;                /* positions in the i-sum                        */
    rvec  xcn, ycn;          /* the current and the reference slab centers    */
    real gaussian_xi;
    rvec yi0;
    rvec  rin;               /* Helper variables                              */
    real  fac,fac2;
    rvec innersumvec;
    real OOpsii,OOpsiistar;
    real sin_rin;          /* s_ii.r_ii */
    rvec s_in,tmpvec,tmpvec2;
    real mi,wi;            /* Mass-weighting of the positions                 */
    real N_M;              /* N/M                                             */
    gmx_enfrotgrp_t erg;    /* Pointer to enforced rotation group data */


    erg=rotg->enfrotgrp;
    N_M = rotg->nat * erg->invmass;

    /* Loop over all slabs that contain something */
    for (n=erg->slab_first; n <= erg->slab_last; n++)
    {
        islab = n - erg->slab_first; /* slab index */

        /* The current center of this slab is saved in xcn: */
        copy_rvec(erg->slab_center[islab], xcn);
        /* ... and the reference center in ycn: */
        copy_rvec(erg->slab_center_ref[islab+erg->slab_buffer], ycn);

        /*** D. Calculate the whole inner sum used for second and third sum */
        /* For slab n, we need to loop over all atoms i again. Since we sorted
         * the atoms with respect to the rotation vector, we know that it is sufficient
         * to calculate from firstatom to lastatom only. All other contributions will
         * be very small. */
        clear_rvec(innersumvec);
        for (i = erg->firstatom[islab]; i <= erg->lastatom[islab]; i++)
        {
            /* Coordinate xi of this atom */
            copy_rvec(erg->xc[i],xi);

            /* The i-weights */
            gaussian_xi = gaussian_weight(xi,rotg,n);
            mi = erg->mc_sorted[i];  /* need the sorted mass here */
            wi = N_M*mi;

            /* Calculate rin */
            copy_rvec(erg->xc_ref_sorted[i],yi0); /* Reference position yi0   */
            rvec_sub(yi0, ycn, tmpvec2);          /* tmpvec2 = yi0 - ycn      */
            mvmul(erg->rotmat, tmpvec2, rin);     /* rin = Omega.(yi0 - ycn)  */

            /* Calculate psi_i* and sin */
            rvec_sub(xi, xcn, tmpvec2);           /* tmpvec2 = xi - xcn       */
            cprod(rotg->vec, tmpvec2, tmpvec);    /* tmpvec = v x (xi - xcn)  */
            OOpsiistar = norm2(tmpvec)+rotg->eps; /* OOpsii* = 1/psii* = |v x (xi-xcn)|^2 + eps */
            OOpsii = norm(tmpvec);                /* OOpsii = 1 / psii = |v x (xi - xcn)| */

                                       /*         v x (xi - xcn)          */
            unitv(tmpvec, s_in);       /*  sin = ----------------         */
                                       /*        |v x (xi - xcn)|         */

            sin_rin=iprod(s_in,rin);   /* sin_rin = sin . rin             */

            /* Now the whole sum */
            fac = OOpsii/OOpsiistar;
            svmul(fac, rin, tmpvec);
            fac2 = fac*fac*OOpsii;
            svmul(fac2*sin_rin, s_in, tmpvec2);
            rvec_dec(tmpvec, tmpvec2);

            svmul(wi*gaussian_xi*sin_rin, tmpvec, tmpvec2);

            rvec_inc(innersumvec,tmpvec2);
        } /* now we have the inner sum, used both for sum2 and sum3 */

        /* Save it to be used in do_flex2_lowlevel */
        copy_rvec(innersumvec, erg->slab_innersumvec[islab]);
    } /* END of loop over slabs */
}


static void flex_precalc_inner_sum(t_rotgrp *rotg, t_commrec *cr)
{
    int   i,n,islab;
    rvec  xi;                /* position                                      */
    rvec  xcn, ycn;          /* the current and the reference slab centers    */
    rvec  qin,rin;           /* q_i^n and r_i^n                               */
    real  bin;
    rvec  tmpvec;
    rvec  innersumvec;       /* Inner part of sum_n2                          */
    real  gaussian_xi;       /* Gaussian weight gn(xi)                        */
    real  mi,wi;             /* Mass-weighting of the positions               */
    real  N_M;               /* N/M                                           */

    gmx_enfrotgrp_t erg;    /* Pointer to enforced rotation group data */


    erg=rotg->enfrotgrp;
    N_M = rotg->nat * erg->invmass;

    /* Loop over all slabs that contain something */
    for (n=erg->slab_first; n <= erg->slab_last; n++)
    {
        islab = n - erg->slab_first; /* slab index */

        /* The current center of this slab is saved in xcn: */
        copy_rvec(erg->slab_center[islab], xcn);
        /* ... and the reference center in ycn: */
        copy_rvec(erg->slab_center_ref[islab+erg->slab_buffer], ycn);

        /* For slab n, we need to loop over all atoms i again. Since we sorted
         * the atoms with respect to the rotation vector, we know that it is sufficient
         * to calculate from firstatom to lastatom only. All other contributions will
         * be very small. */
        clear_rvec(innersumvec);
        for (i=erg->firstatom[islab]; i<=erg->lastatom[islab]; i++)
        {
            /* Coordinate xi of this atom */
            copy_rvec(erg->xc[i],xi);

            /* The i-weights */
            gaussian_xi = gaussian_weight(xi,rotg,n);
            mi = erg->mc_sorted[i];  /* need the sorted mass here */
            wi = N_M*mi;

            /* Calculate rin and qin */
            rvec_sub(erg->xc_ref_sorted[i], ycn, tmpvec); /* tmpvec = yi0-ycn */
            mvmul(erg->rotmat, tmpvec, rin);      /* rin = Omega.(yi0 - ycn)  */
            cprod(rotg->vec, rin, tmpvec);    /* tmpvec = v x Omega*(yi0-ycn) */

                                             /*        v x Omega*(yi0-ycn)    */
            unitv(tmpvec, qin);              /* qin = ---------------------   */
                                             /*       |v x Omega*(yi0-ycn)|   */

            /* Calculate bin */
            rvec_sub(xi, xcn, tmpvec);            /* tmpvec = xi-xcn          */
            bin = iprod(qin, tmpvec);             /* bin  = qin*(xi-xcn)      */

            svmul(wi*gaussian_xi*bin, qin, tmpvec);

            /* Add this contribution to the inner sum: */
            rvec_add(innersumvec, tmpvec, innersumvec);
        } /* now we have the inner sum vector S^n for this slab */
        /* Save it to be used in do_flex_lowlevel */
        copy_rvec(innersumvec, erg->slab_innersumvec[islab]);
    }
}


static real do_flex2_lowlevel(
        t_rotgrp  *rotg,
        real      sigma,    /* The Gaussian width sigma */
        rvec      x[],
        gmx_bool  bCalcTorque,
        matrix    box,
        t_commrec *cr)
{
    int  count,ic,ii,j,m,n,islab,iigrp;
    rvec  xj;                /* position in the i-sum                         */
    rvec  yj0;               /* the reference position in the j-sum           */
    rvec  xcn, ycn;          /* the current and the reference slab centers    */
    real V;                  /* This node's part of the rotation pot. energy  */
    real gaussian_xj;        /* Gaussian weight                               */
    real beta;

    real  numerator;
    rvec  rjn;               /* Helper variables                              */
    real  fac,fac2;

    real OOpsij,OOpsijstar;
    real OOsigma2;           /* 1/(sigma^2)                                   */
    real sjn_rjn;
    real betasigpsi;
    rvec sjn,tmpvec,tmpvec2;
    rvec sum1vec_part,sum1vec,sum2vec_part,sum2vec,sum3vec,sum4vec,innersumvec;
    real sum3,sum4;
    gmx_enfrotgrp_t erg;     /* Pointer to enforced rotation group data       */
    real mj,wj;              /* Mass-weighting of the positions               */
    real N_M;                /* N/M                                           */
    real Wjn;                /* g_n(x_j) m_j / Mjn                            */

    /* To calculate the torque per slab */
    rvec slab_force;         /* Single force from slab n on one atom          */
    rvec slab_sum1vec_part;
    real slab_sum3part,slab_sum4part;
    rvec slab_sum1vec, slab_sum2vec, slab_sum3vec, slab_sum4vec;


    erg=rotg->enfrotgrp;

    /* Pre-calculate the inner sums, so that we do not have to calculate
     * them again for every atom */
    flex2_precalc_inner_sum(rotg, cr);

    /********************************************************/
    /* Main loop over all local atoms of the rotation group */
    /********************************************************/
    N_M = rotg->nat * erg->invmass;
    V = 0.0;
    OOsigma2 = 1.0 / (sigma*sigma);
    for (j=0; j<erg->nat_loc; j++)
    {
        /* Local index of a rotation group atom  */
        ii = erg->ind_loc[j];
        /* Position of this atom in the collective array */
        iigrp = erg->xc_ref_ind[j];
        /* Mass-weighting */
        mj = erg->mc[iigrp];  /* need the unsorted mass here */
        wj = N_M*mj;
        
        /* Current position of this atom: x[ii][XX/YY/ZZ]
         * Note that erg->xc_center contains the center of mass in case the flex2-t
         * potential was chosen. For the flex2 potential erg->xc_center must be
         * zero. */
        rvec_sub(x[ii], erg->xc_center, xj);

        /* Shift this atom such that it is near its reference */
        shift_single_coord(box, xj, erg->xc_shifts[iigrp]);

        /* Determine the slabs to loop over, i.e. the ones with contributions
         * larger than min_gaussian */
        count = get_single_atom_gaussians(xj, cr, rotg);
        
        clear_rvec(sum1vec_part);
        clear_rvec(sum2vec_part);
        sum3 = 0.0;
        sum4 = 0.0;
        /* Loop over the relevant slabs for this atom */
        for (ic=0; ic < count; ic++)  
        {
            n = erg->gn_slabind[ic];
            
            /* Get the precomputed Gaussian value of curr_slab for curr_x */
            gaussian_xj = erg->gn_atom[ic];

            islab = n - erg->slab_first; /* slab index */
            
            /* The (unrotated) reference position of this atom is copied to yj0: */
            copy_rvec(rotg->x_ref[iigrp], yj0);

            beta = calc_beta(xj, rotg,n);

            /* The current center of this slab is saved in xcn: */
            copy_rvec(erg->slab_center[islab], xcn);
            /* ... and the reference center in ycn: */
            copy_rvec(erg->slab_center_ref[islab+erg->slab_buffer], ycn);
            
            rvec_sub(yj0, ycn, tmpvec2);          /* tmpvec2 = yj0 - ycn      */

            /* Rotate: */
            mvmul(erg->rotmat, tmpvec2, rjn);     /* rjn = Omega.(yj0 - ycn)  */
            
            /* Subtract the slab center from xj */
            rvec_sub(xj, xcn, tmpvec2);           /* tmpvec2 = xj - xcn       */

            /* Calculate sjn */
            cprod(rotg->vec, tmpvec2, tmpvec);    /* tmpvec = v x (xj - xcn)  */

            OOpsijstar = norm2(tmpvec)+rotg->eps; /* OOpsij* = 1/psij* = |v x (xj-xcn)|^2 + eps */

            numerator = sqr(iprod(tmpvec, rjn));
            
            /*********************************/
            /* Add to the rotation potential */
            /*********************************/
            V += 0.5*rotg->k*wj*gaussian_xj*numerator/OOpsijstar;


            /*************************************/
            /* Now calculate the force on atom j */
            /*************************************/

            OOpsij = norm(tmpvec);    /* OOpsij = 1 / psij = |v x (xj - xcn)| */

                                           /*         v x (xj - xcn)          */
            unitv(tmpvec, sjn);            /*  sjn = ----------------         */
                                           /*        |v x (xj - xcn)|         */

            sjn_rjn=iprod(sjn,rjn);        /* sjn_rjn = sjn . rjn             */


            /*** A. Calculate the first of the four sum terms: ****************/
            fac = OOpsij/OOpsijstar;
            svmul(fac, rjn, tmpvec);
            fac2 = fac*fac*OOpsij;
            svmul(fac2*sjn_rjn, sjn, tmpvec2);
            rvec_dec(tmpvec, tmpvec2);
            fac2 = wj*gaussian_xj; /* also needed for sum4 */
            svmul(fac2*sjn_rjn, tmpvec, slab_sum1vec_part);
            /********************/
            /*** Add to sum1: ***/
            /********************/
            rvec_inc(sum1vec_part, slab_sum1vec_part); /* sum1 still needs to vector multiplied with v */

            /*** B. Calculate the forth of the four sum terms: ****************/
            betasigpsi = beta*OOsigma2*OOpsij; /* this is also needed for sum3 */
            /********************/
            /*** Add to sum4: ***/
            /********************/
            slab_sum4part = fac2*betasigpsi*fac*sjn_rjn*sjn_rjn; /* Note that fac is still valid from above */
            sum4 += slab_sum4part;

            /*** C. Calculate Wjn for second and third sum */
            /* Note that we can safely divide by slab_weights since we check in
             * get_slab_centers that it is non-zero. */
            Wjn = gaussian_xj*mj/erg->slab_weights[islab];

            /* We already have precalculated the inner sum for slab n */
            copy_rvec(erg->slab_innersumvec[islab], innersumvec);

            /* Weigh the inner sum vector with Wjn */
            svmul(Wjn, innersumvec, innersumvec);

            /*** E. Calculate the second of the four sum terms: */
            /********************/
            /*** Add to sum2: ***/
            /********************/
            rvec_inc(sum2vec_part, innersumvec); /* sum2 still needs to be vector crossproduct'ed with v */
            
            /*** F. Calculate the third of the four sum terms: */
            slab_sum3part = betasigpsi * iprod(sjn, innersumvec);
            sum3 += slab_sum3part; /* still needs to be multiplied with v */

            /*** G. Calculate the torque on the local slab's axis: */
            if (bCalcTorque)
            {
                /* Sum1 */
                cprod(slab_sum1vec_part, rotg->vec, slab_sum1vec);
                /* Sum2 */
                cprod(innersumvec, rotg->vec, slab_sum2vec);
                /* Sum3 */
                svmul(slab_sum3part, rotg->vec, slab_sum3vec);
                /* Sum4 */
                svmul(slab_sum4part, rotg->vec, slab_sum4vec);

                /* The force on atom ii from slab n only: */
                for (m=0; m<DIM; m++)
                    slab_force[m] = rotg->k * (-slab_sum1vec[m] + slab_sum2vec[m] - slab_sum3vec[m] + 0.5*slab_sum4vec[m]);

                erg->slab_torque_v[islab] += torque(rotg->vec, slab_force, xj, xcn);
            }
        } /* END of loop over slabs */

        /* Construct the four individual parts of the vector sum: */
        cprod(sum1vec_part, rotg->vec, sum1vec);      /* sum1vec =   { } x v  */
        cprod(sum2vec_part, rotg->vec, sum2vec);      /* sum2vec =   { } x v  */
        svmul(sum3, rotg->vec, sum3vec);              /* sum3vec =   { } . v  */
        svmul(sum4, rotg->vec, sum4vec);              /* sum4vec =   { } . v  */

        /* Store the additional force so that it can be added to the force
         * array after the normal forces have been evaluated */
        for (m=0; m<DIM; m++)
            erg->f_rot_loc[j][m] = rotg->k * (-sum1vec[m] + sum2vec[m] - sum3vec[m] + 0.5*sum4vec[m]);

#ifdef INFOF
        fprintf(stderr," FORCE on ATOM %d/%d  = (%15.8f %15.8f %15.8f)  \n",
                j,ii,erg->f_rot_loc[j][XX], erg->f_rot_loc[j][YY], erg->f_rot_loc[j][ZZ]);
#endif

#ifdef SUM_PARTS
        fprintf(stderr, "sum1: %15.8f %15.8f %15.8f\n",    -rotg->k*sum1vec[XX],    -rotg->k*sum1vec[YY],    -rotg->k*sum1vec[ZZ]);
        fprintf(stderr, "sum2: %15.8f %15.8f %15.8f\n",     rotg->k*sum2vec[XX],     rotg->k*sum2vec[YY],     rotg->k*sum2vec[ZZ]);
        fprintf(stderr, "sum3: %15.8f %15.8f %15.8f\n",    -rotg->k*sum3vec[XX],    -rotg->k*sum3vec[YY],    -rotg->k*sum3vec[ZZ]);
        fprintf(stderr, "sum4: %15.8f %15.8f %15.8f\n", 0.5*rotg->k*sum4vec[XX], 0.5*rotg->k*sum4vec[YY], 0.5*rotg->k*sum4vec[ZZ]);
#endif
    } /* END of loop over local atoms */

#ifdef INFOF
    fprintf(stderr, "THE POTENTIAL IS  V=%f\n", V);
#endif

    return V;
}


static real do_flex_lowlevel(
        t_rotgrp *rotg,
        real      sigma,     /* The Gaussian width sigma                      */
        rvec      x[],
        gmx_bool  bCalcTorque,
        matrix    box,
        t_commrec *cr)
{
    int   count,ic,ii,j,m,n,islab,iigrp;
    rvec  xj,yj0;            /* current and reference position                */
    rvec  xcn, ycn;          /* the current and the reference slab centers    */
    rvec  xj_xcn;            /* xj - xcn                                      */
    rvec  qjn;               /* q_i^n                                         */
    rvec  sum_n1,sum_n2;     /* Two contributions to the rotation force       */
    rvec  innersumvec;       /* Inner part of sum_n2                          */
    rvec  s_n;
    rvec  force_n;           /* Single force from slab n on one atom          */
    rvec  tmpvec,tmpvec2,tmp_f;   /* Helper variables            */
    real  V;                 /* The rotation potential energy                 */
    real  OOsigma2;          /* 1/(sigma^2)                                   */
    real  beta;              /* beta_n(xj)                                    */
    real  bjn;               /* b_j^n                                         */
    real  gaussian_xj;       /* Gaussian weight gn(xj)                        */
    real  betan_xj_sigma2;
    real  mj,wj;             /* Mass-weighting of the positions               */
    real  N_M;               /* N/M                                           */
    gmx_enfrotgrp_t erg;     /* Pointer to enforced rotation group data       */

    
    erg=rotg->enfrotgrp;

    /* Pre-calculate the inner sums, so that we do not have to calculate
     * them again for every atom */
    flex_precalc_inner_sum(rotg, cr);

    /********************************************************/
    /* Main loop over all local atoms of the rotation group */
    /********************************************************/
    OOsigma2 = 1.0/(sigma*sigma);
    N_M = rotg->nat * erg->invmass;
    V = 0.0;
    for (j=0; j<erg->nat_loc; j++)
    {
        /* Local index of a rotation group atom  */
        ii = erg->ind_loc[j];
        /* Position of this atom in the collective array */
        iigrp = erg->xc_ref_ind[j];
        /* Mass-weighting */
        mj = erg->mc[iigrp];  /* need the unsorted mass here */
        wj = N_M*mj;
        
        /* Current position of this atom: x[ii][XX/YY/ZZ]
         * Note that erg->xc_center contains the center of mass in case the flex-t
         * potential was chosen. For the flex potential erg->xc_center must be
         * zero. */
        rvec_sub(x[ii], erg->xc_center, xj);
        
        /* Shift this atom such that it is near its reference */
        shift_single_coord(box, xj, erg->xc_shifts[iigrp]);

        /* Determine the slabs to loop over, i.e. the ones with contributions
         * larger than min_gaussian */
        count = get_single_atom_gaussians(xj, cr, rotg);

        clear_rvec(sum_n1);
        clear_rvec(sum_n2);

        /* Loop over the relevant slabs for this atom */
        for (ic=0; ic < count; ic++)  
        {
            n = erg->gn_slabind[ic];
                
            /* Get the precomputed Gaussian for xj in slab n */
            gaussian_xj = erg->gn_atom[ic];

            islab = n - erg->slab_first; /* slab index */
            
            /* The (unrotated) reference position of this atom is saved in yj0: */
            copy_rvec(rotg->x_ref[iigrp], yj0);

            beta = calc_beta(xj, rotg, n);

            /* The current center of this slab is saved in xcn: */
            copy_rvec(erg->slab_center[islab], xcn);
            /* ... and the reference center in ycn: */
            copy_rvec(erg->slab_center_ref[islab+erg->slab_buffer], ycn);
            
            rvec_sub(yj0, ycn, tmpvec); /* tmpvec = yj0 - ycn */

            /* Rotate: */
            mvmul(erg->rotmat, tmpvec, tmpvec2); /* tmpvec2 = Omega.(yj0-ycn) */
            
            /* Subtract the slab center from xj */
            rvec_sub(xj, xcn, xj_xcn);           /* xj_xcn = xj - xcn         */
            
            /* Calculate qjn */
            cprod(rotg->vec, tmpvec2, tmpvec); /* tmpvec = v x Omega.(xj-xcn) */

                                 /*         v x Omega.(xj-xcn)    */
            unitv(tmpvec,qjn);   /*  qjn = --------------------   */
                                 /*        |v x Omega.(xj-xcn)|   */

            bjn = iprod(qjn, xj_xcn);   /* bjn = qjn * (xj - xcn) */
            
            /*********************************/
            /* Add to the rotation potential */
            /*********************************/
            V += 0.5*rotg->k*wj*gaussian_xj*sqr(bjn);
            
            /****************************************************************/
            /* sum_n1 will typically be the main contribution to the force: */
            /****************************************************************/
            betan_xj_sigma2 = beta*OOsigma2;  /*  beta_n(xj)/sigma^2  */

            /* The next lines calculate
             *  qjn - (bjn*beta(xj)/(2sigma^2))v  */
            svmul(bjn*0.5*betan_xj_sigma2, rotg->vec, tmpvec2);
            rvec_sub(qjn,tmpvec2,tmpvec);

            /* Multiply with gn(xj)*bjn: */
            svmul(gaussian_xj*bjn,tmpvec,tmpvec2);

            /* Sum over n: */
            rvec_inc(sum_n1,tmpvec2);
            
            /* We already have precalculated the Sn term for slab n */
            copy_rvec(erg->slab_innersumvec[islab], s_n);
                                                                          /*          beta_n(xj)              */
            svmul(betan_xj_sigma2*iprod(s_n, xj_xcn), rotg->vec, tmpvec); /* tmpvec = ---------- s_n (xj-xcn) */
                                                                          /*            sigma^2               */

            rvec_sub(s_n, tmpvec, innersumvec);
            
            /* We can safely divide by slab_weights since we check in get_slab_centers
             * that it is non-zero. */
            svmul(gaussian_xj/erg->slab_weights[islab], innersumvec, innersumvec);

            rvec_add(sum_n2, innersumvec, sum_n2);
            
            GMX_MPE_LOG(ev_inner_loop_finish);

            /* Calculate the torque: */
            if (bCalcTorque)
            {
                /* The force on atom ii from slab n only: */
                rvec_sub(innersumvec, tmpvec2, force_n);
                svmul(rotg->k, force_n, force_n);
                erg->slab_torque_v[islab] += torque(rotg->vec, force_n, xj, xcn);
            }
        } /* END of loop over slabs */

        /* Put both contributions together: */
        svmul(wj, sum_n1, sum_n1);
        svmul(mj, sum_n2, sum_n2);
        rvec_sub(sum_n2,sum_n1,tmp_f); /* F = -grad V */

        /* Store the additional force so that it can be added to the force
         * array after the normal forces have been evaluated */
        for(m=0; m<DIM; m++)
            erg->f_rot_loc[j][m] = rotg->k*tmp_f[m];
#ifdef INFOF
        fprintf(stderr," FORCE on atom %d  = %15.8f %15.8f %15.8f   1: %15.8f %15.8f %15.8f   2: %15.8f %15.8f %15.8f\n", iigrp,
                rotg->k*tmp_f[XX] ,  rotg->k*tmp_f[YY] ,  rotg->k*tmp_f[ZZ] ,
               -rotg->k*sum_n1[XX], -rotg->k*sum_n1[YY], -rotg->k*sum_n1[ZZ],
                rotg->k*sum_n2[XX],  rotg->k*sum_n2[YY],  rotg->k*sum_n2[ZZ]);
#endif
    } /* END of loop over local atoms */

    return V;
}

#ifdef PRINT_COORDS
static void print_coordinates(t_commrec *cr, t_rotgrp *rotg, rvec x[], matrix box, int step)
{
    int i;
    static FILE *fp;
    static char buf[STRLEN];
    static gmx_bool bFirst=1;


    if (bFirst)
    {
        sprintf(buf, "coords%d.txt", cr->nodeid);
        fp = fopen(buf, "w");
        bFirst = 0;
    }

    fprintf(fp, "\nStep %d\n", step);
    fprintf(fp, "box: %f %f %f %f %f %f %f %f %f\n",
            box[XX][XX], box[XX][YY], box[XX][ZZ],
            box[YY][XX], box[YY][YY], box[YY][ZZ],
            box[ZZ][XX], box[ZZ][ZZ], box[ZZ][ZZ]);
    for (i=0; i<rotg->nat; i++)
    {
        fprintf(fp, "%4d  %f %f %f\n", i,
                erg->xc[i][XX], erg->xc[i][YY], erg->xc[i][ZZ]);
    }
    fflush(fp);

}
#endif


static int projection_compare(const void *a, const void *b)
{
    sort_along_vec_t *xca, *xcb;
    
    
    xca = (sort_along_vec_t *)a;
    xcb = (sort_along_vec_t *)b;
    
    if (xca->xcproj < xcb->xcproj)
        return -1;
    else if (xca->xcproj > xcb->xcproj)
        return 1;
    else
        return 0;
}


static void sort_collective_coordinates(
        t_rotgrp *rotg,         /* Rotation group */
        sort_along_vec_t *data) /* Buffer for sorting the positions */
{
    int i;
    gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */

    
    erg=rotg->enfrotgrp;
    
    /* The projection of the position vector on the rotation vector is
     * the relevant value for sorting. Fill the 'data' structure */
    for (i=0; i<rotg->nat; i++)
    {
        data[i].xcproj = iprod(erg->xc[i], rotg->vec);  /* sort criterium */
        data[i].m      = erg->mc[i];
        data[i].ind    = i;
        copy_rvec(erg->xc[i]    , data[i].x    );
        copy_rvec(rotg->x_ref[i], data[i].x_ref);
    }
    /* Sort the 'data' structure */
    gmx_qsort(data, rotg->nat, sizeof(sort_along_vec_t), projection_compare);
    
    /* Copy back the sorted values */
    for (i=0; i<rotg->nat; i++)
    {
        copy_rvec(data[i].x    , erg->xc[i]           );
        copy_rvec(data[i].x_ref, erg->xc_ref_sorted[i]);
        erg->mc_sorted[i]  = data[i].m;
        erg->xc_sortind[i] = data[i].ind;
    }
}


/* For each slab, get the first and the last index of the sorted atom
 * indices */
static void get_firstlast_atom_per_slab(t_rotgrp *rotg, t_commrec *cr)
{
    int i,islab,n;
    real beta;
    gmx_enfrotgrp_t erg;     /* Pointer to enforced rotation group data */

    
    erg=rotg->enfrotgrp;

    GMX_MPE_LOG(ev_get_firstlast_start);
    
    /* Find the first atom that needs to enter the calculation for each slab */
    n = erg->slab_first;  /* slab */
    i = 0; /* start with the first atom */
    do
    {
        /* Find the first atom that significantly contributes to this slab */
        do /* move forward in position until a large enough beta is found */
        {
            beta = calc_beta(erg->xc[i], rotg, n);
            i++;
        } while ((beta < -erg->max_beta) && (i < rotg->nat));
        i--;
        islab = n - erg->slab_first;  /* slab index */
        erg->firstatom[islab] = i;
        /* Proceed to the next slab */
        n++;
    } while (n <= erg->slab_last);
    
    /* Find the last atom for each slab */
     n = erg->slab_last; /* start with last slab */
     i = rotg->nat-1;  /* start with the last atom */
     do
     {
         do /* move backward in position until a large enough beta is found */
         {
             beta = calc_beta(erg->xc[i], rotg, n);
             i--;
         } while ((beta > erg->max_beta) && (i > -1));
         i++;
         islab = n - erg->slab_first;  /* slab index */
         erg->lastatom[islab] = i;
         /* Proceed to the next slab */
         n--;
     } while (n >= erg->slab_first);
    
     GMX_MPE_LOG(ev_get_firstlast_finish);
}


/* Determine the very first and very last slab that needs to be considered 
 * For the first slab that needs to be considered, we have to find the smallest
 * n that obeys:
 * 
 * x_first * v - n*Delta_x <= beta_max
 * 
 * slab index n, slab distance Delta_x, rotation vector v. For the last slab we 
 * have to find the largest n that obeys
 * 
 * x_last * v - n*Delta_x >= -beta_max
 *  
 */
static inline int get_first_slab(
        t_rotgrp *rotg,     /* The rotation group (inputrec data) */
        real     max_beta,  /* The max_beta value, instead of min_gaussian */
        rvec     firstatom) /* First atom after sorting along the rotation vector v */
{
    /* Find the first slab for the first atom */   
    return ceil((iprod(firstatom, rotg->vec) - max_beta)/rotg->slab_dist);
}


static inline int get_last_slab(
        t_rotgrp *rotg,     /* The rotation group (inputrec data) */
        real     max_beta,  /* The max_beta value, instead of min_gaussian */
        rvec     lastatom)  /* Last atom along v */
{
    /* Find the last slab for the last atom */
    return floor((iprod(lastatom, rotg->vec) + max_beta)/rotg->slab_dist);    
}


static void get_firstlast_slab_check(
        t_rotgrp        *rotg,     /* The rotation group (inputrec data) */
        t_gmx_enfrotgrp *erg,      /* The rotation group (data only accessible in this file) */
        rvec            firstatom, /* First atom after sorting along the rotation vector v */
        rvec            lastatom,  /* Last atom along v */
        int             g,         /* The rotation group number */
        t_commrec       *cr)
{
    erg->slab_first = get_first_slab(rotg, erg->max_beta, firstatom);
    erg->slab_last  = get_last_slab(rotg, erg->max_beta, lastatom);

    /* Check whether we have reference data to compare against */
    if (erg->slab_first < erg->slab_first_ref)
        gmx_fatal(FARGS, "%s No reference data for first slab (n=%d), unable to proceed.",
                  RotStr, erg->slab_first);
    
    /* Check whether we have reference data to compare against */
    if (erg->slab_last > erg->slab_last_ref)
        gmx_fatal(FARGS, "%s No reference data for last slab (n=%d), unable to proceed.",
                  RotStr, erg->slab_last);
}


/* Enforced rotation with a flexible axis */
static void do_flexible(
        t_commrec *cr,
        gmx_enfrot_t enfrot,  /* Other rotation data            */
        t_rotgrp  *rotg,      /* The rotation group             */
        int       g,          /* Group number                   */
        rvec      x[],        /* The local positions            */
        matrix    box,
        double    t,          /* Time in picoseconds            */
        int       step,       /* The time step                  */
        gmx_bool  bOutstep)
{
    int          l,nslabs;
    real         sigma;       /* The Gaussian width sigma */
    gmx_enfrotgrp_t erg;      /* Pointer to enforced rotation group data */

    
    erg=rotg->enfrotgrp;

    /* Define the sigma value */
    sigma = 0.7*rotg->slab_dist;
    
    /* Sort the collective coordinates erg->xc along the rotation vector. This is
     * an optimization for the inner loop.
     */
    sort_collective_coordinates(rotg, enfrot->data);
    
    /* Determine the first relevant slab for the first atom and the last
     * relevant slab for the last atom */
    get_firstlast_slab_check(rotg, erg, erg->xc[0], erg->xc[rotg->nat-1], g, cr);
    
    /* Determine for each slab depending on the min_gaussian cutoff criterium,
     * a first and a last atom index inbetween stuff needs to be calculated */
    get_firstlast_atom_per_slab(rotg, cr);

    /* Determine the gaussian-weighted center of positions for all slabs */
    get_slab_centers(rotg,erg->xc,erg->mc_sorted,cr,g,t,enfrot->out_slabs,bOutstep,FALSE);
        
    /* Clear the torque per slab from last time step: */
    nslabs = erg->slab_last - erg->slab_first + 1;
    for (l=0; l<nslabs; l++)
        erg->slab_torque_v[l] = 0.0;
    
    /* Call the rotational forces kernel */
    GMX_MPE_LOG(ev_flexll_start);
    if (rotg->eType == erotgFLEX || rotg->eType == erotgFLEXT)
        erg->V = do_flex_lowlevel(rotg, sigma, x, bOutstep, box, cr);
    else if (rotg->eType == erotgFLEX2 || rotg->eType == erotgFLEX2T)
        erg->V = do_flex2_lowlevel(rotg, sigma, x, bOutstep, box, cr);
    else
        gmx_fatal(FARGS, "Unknown flexible rotation type");
    GMX_MPE_LOG(ev_flexll_finish);
    
    /* Determine actual angle of this slab by RMSD fit and output to file - Let's hope */
    /* this only happens once in a while, since this is not parallelized! */
    if (bOutstep && MASTER(cr))
        flex_fit_angle(g, rotg, t, erg->degangle, enfrot->out_angles);
}


/* Calculate the angle between reference and actual rotation group atom,
 * both projected into a plane perpendicular to the rotation vector: */
static void angle(t_rotgrp *rotg,
        rvec x_act,
        rvec x_ref,
        real *alpha,
        real *weight)  /* atoms near the rotation axis should count less than atoms far away */
{
    rvec xp, xrp;  /* current and reference positions projected on a plane perpendicular to pg->vec */
    rvec dum;


    /* Project x_ref and x into a plane through the origin perpendicular to rot_vec: */
    /* Project x_ref: xrp = x_ref - (vec * x_ref) * vec */
    svmul(iprod(rotg->vec, x_ref), rotg->vec, dum);
    rvec_sub(x_ref, dum, xrp);
    /* Project x_act: */
    svmul(iprod(rotg->vec, x_act), rotg->vec, dum);
    rvec_sub(x_act, dum, xp);

    /* Retrieve information about which vector precedes. gmx_angle always
     * returns a positive angle. */
    cprod(xp, xrp, dum); /* if reference precedes, this is pointing into the same direction as vec */

    if (iprod(rotg->vec, dum) >= 0)
        *alpha = -gmx_angle(xrp, xp);
    else
        *alpha = +gmx_angle(xrp, xp);
    
    /* Also return the weight */
    *weight = norm(xp);
}


/* Project first vector onto a plane perpendicular to the second vector 
 * dr = dr - (dr.v)v
 * Note that v must be of unit length.
 */
static inline void project_onto_plane(rvec dr, const rvec v)
{
    rvec tmp;
    
    
    svmul(iprod(dr,v),v,tmp);  /* tmp = (dr.v)v */
    rvec_dec(dr, tmp);         /* dr = dr - (dr.v)v */
}


/* Fixed rotation: The rotation reference group rotates around an axis */
/* The atoms of the actual rotation group are attached with imaginary  */
/* springs to the reference atoms.                                     */
static void do_fixed(
        t_commrec *cr,
        t_rotgrp  *rotg,        /* The rotation group          */
        rvec      x[],          /* The positions               */
        matrix    box,          /* The simulation box          */
        double    t,            /* Time in picoseconds         */
        int       step,         /* The time step               */
        gmx_bool  bTorque)
{
    int       i,m;
    rvec      dr;
    rvec      tmp_f;           /* Force */
    real      alpha;           /* a single angle between an actual and a reference position */
    real      weight;          /* single weight for a single angle */
    gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */
    rvec      tmpvec;

    /* for mass weighting: */
    real      wi;              /* Mass-weighting of the positions */
    real      N_M;             /* N/M */
    real      k_wi;            /* k times wi */

    gmx_bool  bProject;

    
    erg=rotg->enfrotgrp;
    bProject = (rotg->eType==erotgPM) || (rotg->eType==erotgPMPF);

    /* Clear values from last time step */
    erg->V            = 0.0;
    erg->fix_torque_v = 0.0;
    erg->fix_angles_v = 0.0;
    erg->fix_weight_v = 0.0;

    N_M = rotg->nat * erg->invmass;

    /* Each process calculates the forces on its local atoms */
    for (i=0; i<erg->nat_loc; i++)
    {
        /* Calculate (x_i-x_c) resp. (x_i-u) */
        rvec_sub(erg->x_loc_pbc[i], erg->xc_center, tmpvec);

        /* Calculate Omega*(y_i-y_c)-(x_i-x_c) */
        rvec_sub(erg->xr_loc[i], tmpvec, dr);
        
        if (bProject)
            project_onto_plane(dr, rotg->vec);
            
        /* Mass-weighting */
        wi = N_M*erg->m_loc[i];

        /* Store the additional force so that it can be added to the force
         * array after the normal forces have been evaluated */
        k_wi = rotg->k*wi;
        for (m=0; m<DIM; m++)
        {
            tmp_f[m]             = k_wi*dr[m];
            erg->f_rot_loc[i][m] = tmp_f[m];
            erg->V              += 0.5*k_wi*sqr(dr[m]);
        }
        
        if (bTorque)
        {
            /* Add to the torque of this rotation group */
            erg->fix_torque_v += torque(rotg->vec, tmp_f, erg->x_loc_pbc[i], erg->xc_center);
            
            /* Calculate the angle between reference and actual rotation group atom. */
            angle(rotg, tmpvec, erg->xr_loc[i], &alpha, &weight);  /* angle in rad, weighted */
            erg->fix_angles_v += alpha * weight;
            erg->fix_weight_v += weight;
        }
        /* If you want enforced rotation to contribute to the virial,
         * activate the following lines:
            if (MASTER(cr))
            {
               Add the rotation contribution to the virial
              for(j=0; j<DIM; j++)
                for(m=0;m<DIM;m++)
                  vir[j][m] += 0.5*f[ii][j]*dr[m];
            }
         */
#ifdef INFOF
        fprintf(stderr,"step %d node%d FORCE on ATOM %d = (%15.8f %15.8f %15.8f)  torque=%15.8f\n", step, cr->nodeid,
                erg->xc_ref_ind[i],erg->f_rot_loc[i][XX], erg->f_rot_loc[i][YY], erg->f_rot_loc[i][ZZ],erg->fix_torque_v);
#endif
    } /* end of loop over local rotation group atoms */
}


/* Calculate the radial motion potential and forces */
static void do_radial_motion(
        t_commrec *cr,
        t_rotgrp  *rotg,        /* The rotation group          */
        rvec      x[],          /* The positions               */
        matrix    box,          /* The simulation box          */
        double    t,            /* Time in picoseconds         */
        int       step,         /* The time step               */
        gmx_bool  bTorque)
{
    int       j;
    rvec      tmp_f;           /* Force */
    real      alpha;           /* a single angle between an actual and a reference position */
    real      weight;          /* single weight for a single angle */
    gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */
    rvec      xj_u;            /* xj - u */
    rvec      tmpvec;
    real      fac,fac2,sum;
    rvec      pj;

    /* For mass weighting: */
    real      wj;              /* Mass-weighting of the positions */
    real      N_M;             /* N/M */


    erg=rotg->enfrotgrp;

    /* Clear values from last time step */
    erg->V            = 0.0;
    sum               = 0.0;
    erg->fix_torque_v = 0.0;
    erg->fix_angles_v = 0.0;
    erg->fix_weight_v = 0.0;

    N_M = rotg->nat * erg->invmass;

    /* Each process calculates the forces on its local atoms */
    for (j=0; j<erg->nat_loc; j++)
    {
        /* Calculate (xj-u) */
        rvec_sub(erg->x_loc_pbc[j], erg->xc_center, xj_u);  /* xj_u = xj-u */

        /* Calculate Omega.(yj-u) */
        cprod(rotg->vec, erg->xr_loc[j], tmpvec);  /* tmpvec = v x Omega.(yj-u) */

                              /*         v x Omega.(yj-u)     */
        unitv(tmpvec, pj);    /*  pj = --------------------   */
                              /*       | v x Omega.(yj-u) |   */

        fac = iprod(pj, xj_u);  /* fac = pj.(xj-u) */
        fac2 = fac*fac;

        /* Mass-weighting */
        wj = N_M*erg->m_loc[j];

        /* Store the additional force so that it can be added to the force
         * array after the normal forces have been evaluated */
        svmul(-rotg->k*wj*fac, pj, tmp_f);
        copy_rvec(tmp_f, erg->f_rot_loc[j]);
        sum += wj*fac2;
        if (bTorque)
        {
            /* Add to the torque of this rotation group */
            erg->fix_torque_v += torque(rotg->vec, tmp_f, erg->x_loc_pbc[j], erg->xc_center);

            /* Calculate the angle between reference and actual rotation group atom. */
            angle(rotg, xj_u, erg->xr_loc[j], &alpha, &weight);  /* angle in rad, weighted */
            erg->fix_angles_v += alpha * weight;
            erg->fix_weight_v += weight;
        }
#ifdef INFOF
        fprintf(stderr,"RM: step %d node%d FORCE on ATOM %d = (%15.8f %15.8f %15.8f)  torque=%15.8f\n", step, cr->nodeid,
                erg->xc_ref_ind[j],erg->f_rot_loc[j][XX], erg->f_rot_loc[j][YY], erg->f_rot_loc[j][ZZ],erg->fix_torque_v);
#endif
    } /* end of loop over local rotation group atoms */
    erg->V = 0.5*rotg->k*sum;
}


/* Calculate the radial motion pivot-free potential and forces */
static void do_radial_motion_pf(
        t_commrec *cr,
        t_rotgrp  *rotg,        /* The rotation group          */
        rvec      x[],          /* The positions               */
        matrix    box,          /* The simulation box          */
        double    t,            /* Time in picoseconds         */
        int       step,         /* The time step               */
        gmx_bool  bTorque)
{
    int       i,ii,iigrp,j;
    rvec      xj;              /* Current position */
    rvec      xj_xc;           /* xj  - xc  */
    rvec      yj0_yc0;         /* yj0 - yc0 */
    rvec      tmp_f;           /* Force */
    real      alpha;           /* a single angle between an actual and a reference position */
    real      weight;          /* single weight for a single angle */
    gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */
    rvec      tmpvec, tmpvec2;
    rvec      innersumvec;     /* Precalculation of the inner sum */
    rvec      innersumveckM;
    real      fac,fac2,V;
    rvec      qi,qj;

    /* For mass weighting: */
    real      mj,wi,wj;        /* Mass-weighting of the positions */
    real      N_M;             /* N/M */


    erg=rotg->enfrotgrp;

    /* Clear values from last time step */
    erg->V            = 0.0;
    V                 = 0.0;
    erg->fix_torque_v = 0.0;
    erg->fix_angles_v = 0.0;
    erg->fix_weight_v = 0.0;

    N_M = rotg->nat * erg->invmass;

    /* Get the current center of the rotation group: */
    get_center(erg->xc, erg->mc, rotg->nat, erg->xc_center);

    /* Precalculate Sum_i [ wi qi.(xi-xc) qi ] which is needed for every single j */
    clear_rvec(innersumvec);
    for (i=0; i < rotg->nat; i++)
    {
        /* Mass-weighting */
        wi = N_M*erg->mc[i];

        /* Calculate qi. Note that xc_ref_center has already been subtracted from
         * x_ref in init_rot_group.*/
        mvmul(erg->rotmat, rotg->x_ref[i], tmpvec);  /* tmpvec  = Omega.(yi0-yc0) */

        cprod(rotg->vec, tmpvec, tmpvec2);          /* tmpvec2 = v x Omega.(yi0-yc0) */

                              /*         v x Omega.(yi0-yc0)     */
        unitv(tmpvec2, qi);   /*  qi = -----------------------   */
                              /*       | v x Omega.(yi0-yc0) |   */

        rvec_sub(erg->xc[i], erg->xc_center, tmpvec);  /* tmpvec = xi-xc */

        svmul(wi*iprod(qi, tmpvec), qi, tmpvec2);

        rvec_inc(innersumvec, tmpvec2);
    }
    svmul(rotg->k*erg->invmass, innersumvec, innersumveckM);

    /* Each process calculates the forces on its local atoms */
    for (j=0; j<erg->nat_loc; j++)
    {
        /* Local index of a rotation group atom  */
        ii = erg->ind_loc[j];
        /* Position of this atom in the collective array */
        iigrp = erg->xc_ref_ind[j];
        /* Mass-weighting */
        mj = erg->mc[iigrp];  /* need the unsorted mass here */
        wj = N_M*mj;

        /* Current position of this atom: x[ii][XX/YY/ZZ] */
        copy_rvec(x[ii], xj);

        /* Shift this atom such that it is near its reference */
        shift_single_coord(box, xj, erg->xc_shifts[iigrp]);

        /* The (unrotated) reference position is yj0. yc0 has already
         * been subtracted in init_rot_group */
        copy_rvec(rotg->x_ref[iigrp], yj0_yc0);   /* yj0_yc0 = yj0 - yc0      */

        /* Calculate Omega.(yj0-yc0) */
        mvmul(erg->rotmat, yj0_yc0, tmpvec2);     /* tmpvec2 = Omega.(yj0 - yc0)  */

        cprod(rotg->vec, tmpvec2, tmpvec);  /* tmpvec = v x Omega.(yj0-yc0) */

                              /*         v x Omega.(yj0-yc0)     */
        unitv(tmpvec, qj);    /*  qj = -----------------------   */
                              /*       | v x Omega.(yj0-yc0) |   */

        /* Calculate (xj-xc) */
        rvec_sub(xj, erg->xc_center, xj_xc);  /* xj_xc = xj-xc */

        fac = iprod(qj, xj_xc);  /* fac = qj.(xj-xc) */
        fac2 = fac*fac;

        /* Store the additional force so that it can be added to the force
         * array after the normal forces have been evaluated */
        svmul(-rotg->k*wj*fac, qj, tmp_f); /* part 1 of force */
        svmul(mj, innersumveckM, tmpvec);  /* part 2 of force */
        rvec_inc(tmp_f, tmpvec);
        copy_rvec(tmp_f, erg->f_rot_loc[j]);
        V += wj*fac2;
        if (bTorque)
        {
            /* Add to the torque of this rotation group */
            erg->fix_torque_v += torque(rotg->vec, tmp_f, xj, erg->xc_center);

            /* Calculate the angle between reference and actual rotation group atom. */
            angle(rotg, xj_xc, yj0_yc0, &alpha, &weight);  /* angle in rad, weighted */
            erg->fix_angles_v += alpha * weight;
            erg->fix_weight_v += weight;
        }
#ifdef INFOF
        fprintf(stderr,"RM-PF: step %d node%d FORCE on ATOM %d = (%15.8f %15.8f %15.8f)  torque=%15.8f\n", step, cr->nodeid,
                erg->xc_ref_ind[j],erg->f_rot_loc[j][XX], erg->f_rot_loc[j][YY], erg->f_rot_loc[j][ZZ],erg->fix_torque_v);
#endif
    } /* end of loop over local rotation group atoms */
    erg->V = 0.5*rotg->k*V;
}


/* Precalculate the inner sum for the radial motion 2 forces */
static void radial_motion2_precalc_inner_sum(t_rotgrp  *rotg, rvec innersumvec)
{
    int       i;
    gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */
    rvec      xi_xc;           /* xj - xc */
    rvec      tmpvec,tmpvec2;
    real      fac,fac2;
    rvec      ri,si;
    real      siri;
    rvec      v_xi_xc;          /* v x (xj - u) */
    real      psii,psiistar;
    real      wi;              /* Mass-weighting of the positions */
    real      N_M;             /* N/M */
    rvec      sumvec;

    erg=rotg->enfrotgrp;
    N_M = rotg->nat * erg->invmass;

    /* Loop over the collective set of positions */
    clear_rvec(sumvec);
    for (i=0; i<rotg->nat; i++)
    {
        /* Mass-weighting */
        wi = N_M*erg->mc[i];

        rvec_sub(erg->xc[i], erg->xc_center, xi_xc); /* xi_xc = xi-xc         */

        /* Calculate ri. Note that xc_ref_center has already been subtracted from
         * x_ref in init_rot_group.*/
        mvmul(erg->rotmat, rotg->x_ref[i], ri);      /* ri  = Omega.(yi0-yc0) */

        cprod(rotg->vec, xi_xc, v_xi_xc);            /* v_xi_xc = v x (xi-u)  */

        fac = norm2(v_xi_xc);
                                          /*                      1           */
        psiistar = 1.0/(fac + rotg->eps); /* psiistar = --------------------- */
                                          /*            |v x (xi-xc)|^2 + eps */

        psii = gmx_invsqrt(fac);          /*                 1                */
                                          /*  psii    = -------------         */
                                          /*            |v x (xi-xc)|         */

        svmul(psii, v_xi_xc, si);          /*  si = psii * (v x (xi-xc) )     */

        fac = iprod(v_xi_xc, ri);                   /* fac = (v x (xi-xc)).ri */
        fac2 = fac*fac;

        siri = iprod(si, ri);                       /* siri = si.ri           */

        svmul(psiistar/psii, ri, tmpvec);
        svmul(psiistar*psiistar/(psii*psii*psii) * siri, si, tmpvec2);
        rvec_dec(tmpvec, tmpvec2);
        cprod(tmpvec, rotg->vec, tmpvec2);

        svmul(wi*siri, tmpvec2, tmpvec);

        rvec_inc(sumvec, tmpvec);
    }
    svmul(rotg->k*erg->invmass, sumvec, innersumvec);
}


/* Calculate the radial motion 2 potential and forces */
static void do_radial_motion2(
        t_commrec *cr,
        t_rotgrp  *rotg,        /* The rotation group          */
        rvec      x[],          /* The positions               */
        matrix    box,          /* The simulation box          */
        double    t,            /* Time in picoseconds         */
        int       step,         /* The time step               */
        gmx_bool  bTorque)
{
    int       ii,iigrp,j;
    rvec      xj;              /* Position */
    real      alpha;           /* a single angle between an actual and a reference position */
    real      weight;          /* single weight for a single angle */
    gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */
    rvec      xj_u;            /* xj - u */
    rvec      tmpvec,tmpvec2;
    real      fac,fac2,Vpart;
    rvec      rj,sj;
    real      sjrj;
    rvec      v_xj_u;          /* v x (xj - u) */
    real      psij,psijstar;
    real      mj,wj;           /* For mass-weighting of the positions */
    real      N_M;             /* N/M */
    gmx_bool  bPF;
    rvec      innersumvec;


    erg=rotg->enfrotgrp;

    bPF = rotg->eType==erotgRM2PF;
    clear_rvec(innersumvec);
    if (bPF)
    {
        /* For the pivot-free variant we have to use the current center of
         * mass of the rotation group instead of the pivot u */
        get_center(erg->xc, erg->mc, rotg->nat, erg->xc_center);

        /* Also, we precalculate the second term of the forces that is identical
         * (up to the weight factor mj) for all forces */
        radial_motion2_precalc_inner_sum(rotg,innersumvec);
    }

    /* Clear values from last time step */
    erg->V            = 0.0;
    Vpart             = 0.0;
    erg->fix_torque_v = 0.0;
    erg->fix_angles_v = 0.0;
    erg->fix_weight_v = 0.0;

    N_M = rotg->nat * erg->invmass;

    /* Each process calculates the forces on its local atoms */
    for (j=0; j<erg->nat_loc; j++)
    {
        if (bPF)
        {
            /* Local index of a rotation group atom  */
            ii = erg->ind_loc[j];
            /* Position of this atom in the collective array */
            iigrp = erg->xc_ref_ind[j];
            /* Mass-weighting */
            mj = erg->mc[iigrp];

            /* Current position of this atom: x[ii] */
            copy_rvec(x[ii], xj);

            /* Shift this atom such that it is near its reference */
            shift_single_coord(box, xj, erg->xc_shifts[iigrp]);

            /* The (unrotated) reference position is yj0. yc0 has already
             * been subtracted in init_rot_group */
            copy_rvec(rotg->x_ref[iigrp], tmpvec);     /* tmpvec = yj0 - yc0  */

            /* Calculate Omega.(yj0-yc0) */
            mvmul(erg->rotmat, tmpvec, rj);          /* rj = Omega.(yj0-yc0)  */
        }
        else
        {
            mj = erg->m_loc[j];
            copy_rvec(erg->x_loc_pbc[j], xj);
            copy_rvec(erg->xr_loc[j], rj);           /* rj = Omega.(yj0-u)    */
        }
        /* Mass-weighting */
        wj = N_M*mj;

        /* Calculate (xj-u) resp. (xj-xc) */
        rvec_sub(xj, erg->xc_center, xj_u);          /* xj_u = xj-u           */

        cprod(rotg->vec, xj_u, v_xj_u);              /* v_xj_u = v x (xj-u)   */

        fac = norm2(v_xj_u);
                                          /*                      1           */
        psijstar = 1.0/(fac + rotg->eps); /*  psistar = --------------------  */
                                          /*            |v x (xj-u)|^2 + eps  */

        psij = gmx_invsqrt(fac);          /*                 1                */
                                          /*  psij    = ------------          */
                                          /*            |v x (xj-u)|          */

        svmul(psij, v_xj_u, sj);          /*  sj = psij * (v x (xj-u) )       */

        fac = iprod(v_xj_u, rj);                     /* fac = (v x (xj-u)).rj */
        fac2 = fac*fac;

        sjrj = iprod(sj, rj);                        /* sjrj = sj.rj          */

        svmul(psijstar/psij, rj, tmpvec);
        svmul(psijstar*psijstar/(psij*psij*psij) * sjrj, sj, tmpvec2);
        rvec_dec(tmpvec, tmpvec2);
        cprod(tmpvec, rotg->vec, tmpvec2);

        /* Store the additional force so that it can be added to the force
         * array after the normal forces have been evaluated */
        svmul(-rotg->k*wj*sjrj, tmpvec2, tmpvec);
        svmul(mj, innersumvec, tmpvec2);  /* This is != 0 only for the pivot-free variant */

        rvec_add(tmpvec2, tmpvec, erg->f_rot_loc[j]);
        Vpart += wj*psijstar*fac2;
        if (bTorque)
        {
            /* Add to the torque of this rotation group */
            erg->fix_torque_v += torque(rotg->vec, erg->f_rot_loc[j], xj, erg->xc_center);

            /* Calculate the angle between reference and actual rotation group atom. */
            angle(rotg, xj_u, rj, &alpha, &weight);  /* angle in rad, weighted */
            erg->fix_angles_v += alpha * weight;
            erg->fix_weight_v += weight;
        }
#ifdef INFOF
        fprintf(stderr,"RM2: step %d node%d FORCE on ATOM %d = (%15.8f %15.8f %15.8f)  torque=%15.8f\n", step, cr->nodeid,
                erg->xc_ref_ind[j],erg->f_rot_loc[j][XX], erg->f_rot_loc[j][YY], erg->f_rot_loc[j][ZZ],erg->fix_torque_v);
#endif
    } /* end of loop over local rotation group atoms */
    erg->V = 0.5*rotg->k*Vpart;
}


/* Determine the smallest and largest position vector (with respect to the 
 * rotation vector) for the reference group */
static void get_firstlast_atom_ref(
        t_rotgrp  *rotg, 
        int       *firstindex, 
        int       *lastindex)
{
    gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */
    int i;
    real xcproj;               /* The projection of a reference position on the 
                                  rotation vector */
    real minproj, maxproj;     /* Smallest and largest projection on v */
    

    
    erg=rotg->enfrotgrp;

    /* Start with some value */
    minproj = iprod(rotg->x_ref[0], rotg->vec);
    maxproj = minproj;
    
    /* This is just to ensure that it still works if all the atoms of the 
     * reference structure are situated in a plane perpendicular to the rotation 
     * vector */
    *firstindex = 0;
    *lastindex  = rotg->nat-1;
    
    /* Loop over all atoms of the reference group, 
     * project them on the rotation vector to find the extremes */
    for (i=0; i<rotg->nat; i++)
    {
        xcproj = iprod(rotg->x_ref[i], rotg->vec);
        if (xcproj < minproj)
        {
            minproj = xcproj;
            *firstindex = i;
        }
        if (xcproj > maxproj)
        {
            maxproj = xcproj;
            *lastindex = i;
        }
    }
}


/* Allocate memory for the slabs */
static void allocate_slabs(
        t_rotgrp  *rotg, 
        FILE      *fplog, 
        int       g, 
        gmx_bool  bVerbose,
        t_commrec *cr)
{
    gmx_enfrotgrp_t erg;      /* Pointer to enforced rotation group data */
    int i, nslabs;
    
    
    erg=rotg->enfrotgrp;
    
    /* More slabs than are defined for the reference are never needed */
    nslabs = erg->slab_last_ref - erg->slab_first_ref + 1;
    
    /* Remember how many we allocated */
    erg->nslabs_alloc = nslabs;

    if (MASTER(cr) && bVerbose)
        fprintf(fplog, "%s allocating memory to store data for %d slabs (rotation group %d).\n",
                RotStr, nslabs,g);
    snew(erg->slab_center     , nslabs);
    snew(erg->slab_center_ref , nslabs);
    snew(erg->slab_weights    , nslabs);
    snew(erg->slab_torque_v   , nslabs);
    snew(erg->slab_data       , nslabs);
    snew(erg->gn_atom         , nslabs);
    snew(erg->gn_slabind      , nslabs);
    snew(erg->slab_innersumvec, nslabs);
    for (i=0; i<nslabs; i++)
    {
        snew(erg->slab_data[i].x     , rotg->nat);
        snew(erg->slab_data[i].ref   , rotg->nat);
        snew(erg->slab_data[i].weight, rotg->nat);
    }
    snew(erg->xc_ref_sorted, rotg->nat);
    snew(erg->xc_sortind   , rotg->nat);
    snew(erg->firstatom    , nslabs);
    snew(erg->lastatom     , nslabs);
}


/* From the extreme coordinates of the reference group, determine the first 
 * and last slab of the reference. We can never have more slabs in the real
 * simulation than calculated here for the reference.
 */
static void get_firstlast_slab_ref(t_rotgrp *rotg, real mc[], int ref_firstindex, int ref_lastindex)
{
    gmx_enfrotgrp_t erg;      /* Pointer to enforced rotation group data */
    int first,last,firststart;
    rvec dummy;

    
    erg=rotg->enfrotgrp;
    first = get_first_slab(rotg, erg->max_beta, rotg->x_ref[ref_firstindex]);
    last  = get_last_slab( rotg, erg->max_beta, rotg->x_ref[ref_lastindex ]);
    firststart = first;

    while (get_slab_weight(first, rotg, rotg->x_ref, mc, &dummy) > WEIGHT_MIN)
    {
        first--;
    }
    erg->slab_first_ref = first+1;
    while (get_slab_weight(last, rotg, rotg->x_ref, mc, &dummy) > WEIGHT_MIN)
    {
        last++;
    }
    erg->slab_last_ref  = last-1;
    
    erg->slab_buffer = firststart - erg->slab_first_ref;
}



static void init_rot_group(FILE *fplog,t_commrec *cr,int g,t_rotgrp *rotg,
        rvec *x,gmx_mtop_t *mtop,gmx_bool bVerbose,FILE *out_slabs)
{
    int i,ii;
    rvec        coord,*xdum;
    gmx_bool    bFlex,bColl;
    t_atom      *atom;
    gmx_enfrotgrp_t erg;      /* Pointer to enforced rotation group data */
    int         ref_firstindex, ref_lastindex;
    real        mass,totalmass;
    

    /* Do we have a flexible axis? */
    bFlex = (    (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
              || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) );

    /* Do we use a global set of coordinates? */
    bColl = bFlex || (rotg->eType==erotgRMPF) || (rotg->eType==erotgRM2PF);

    erg=rotg->enfrotgrp;
    
    /* Allocate space for collective coordinates if needed */
    if (bColl)
    {
        snew(erg->xc        , rotg->nat);
        snew(erg->xc_shifts , rotg->nat);
        snew(erg->xc_eshifts, rotg->nat);

        /* Save the original (whole) set of positions such that later the
         * molecule can always be made whole again */
        snew(erg->xc_old    , rotg->nat);        
        if (MASTER(cr))
        {
            for (i=0; i<rotg->nat; i++)
            {
                ii = rotg->ind[i];
                copy_rvec(x[ii], erg->xc_old[i]);
            }
        }
#ifdef GMX_MPI
        if (PAR(cr))
            gmx_bcast(rotg->nat*sizeof(erg->xc_old[0]),erg->xc_old, cr);
#endif

        if (rotg->eFittype == erotgFitNORM)
        {
            snew(erg->xc_ref_length, rotg->nat); /* in case fit type NORM is chosen */
            snew(erg->xc_norm      , rotg->nat);
        }
    }
    else
    {
        snew(erg->xr_loc   , rotg->nat);
        snew(erg->x_loc_pbc, rotg->nat);
    }
    
    snew(erg->f_rot_loc , rotg->nat);
    snew(erg->xc_ref_ind, rotg->nat);
    
    /* xc_ref_ind needs to be set to identity in the serial case */
    if (!PAR(cr))
        for (i=0; i<rotg->nat; i++)
            erg->xc_ref_ind[i] = i;

    /* Copy the masses so that the COM can be determined. For all types of
     * enforced rotation, we store the masses in the erg->mc array. */
    snew(erg->mc, rotg->nat);
    if (bFlex)
        snew(erg->mc_sorted, rotg->nat);
    if (!bColl)
        snew(erg->m_loc, rotg->nat);
    totalmass=0.0;
    for (i=0; i<rotg->nat; i++)
    {
        if (rotg->bMassW)
        {
            gmx_mtop_atomnr_to_atom(mtop,rotg->ind[i],&atom);
            mass=atom->m;
        }
        else
        {
            mass=1.0;
        }
        erg->mc[i] = mass;
        totalmass += mass;
    }
    erg->invmass = 1.0/totalmass;
    
    /* Set xc_ref_center for any rotation potential */
    if ((rotg->eType==erotgISO) || (rotg->eType==erotgPM) || (rotg->eType==erotgRM) || (rotg->eType==erotgRM2))
    {
        /* Set the pivot point for the fixed, stationary-axis potentials. This
         * won't change during the simulation */
        copy_rvec(rotg->pivot, erg->xc_ref_center);
        copy_rvec(rotg->pivot, erg->xc_center    );
    }
    else
    {
        /* Center of the reference positions */
        get_center(rotg->x_ref, erg->mc, rotg->nat, erg->xc_ref_center);

        /* Center of the actual positions */
        if (MASTER(cr))
        {
            snew(xdum, rotg->nat);
            for (i=0; i<rotg->nat; i++)
            {
                ii = rotg->ind[i];
                copy_rvec(x[ii], xdum[i]);
            }
            get_center(xdum, erg->mc, rotg->nat, erg->xc_center);
            sfree(xdum);
        }
#ifdef GMX_MPI
        if (PAR(cr))
            gmx_bcast(sizeof(erg->xc_center), erg->xc_center, cr);
#endif
    }

    if ( (rotg->eType != erotgFLEX) && (rotg->eType != erotgFLEX2) )
    {
        /* Put the reference positions into origin: */
        for (i=0; i<rotg->nat; i++)
            rvec_dec(rotg->x_ref[i], erg->xc_ref_center);
    }

    /* Enforced rotation with flexible axis */
    if (bFlex)
    {
        /* Calculate maximum beta value from minimum gaussian (performance opt.) */
        erg->max_beta = calc_beta_max(rotg->min_gaussian, rotg->slab_dist);

        /* Determine the smallest and largest coordinate with respect to the rotation vector */
        get_firstlast_atom_ref(rotg, &ref_firstindex, &ref_lastindex);
        
        /* From the extreme coordinates of the reference group, determine the first 
         * and last slab of the reference. */
        get_firstlast_slab_ref(rotg, erg->mc, ref_firstindex, ref_lastindex);
                
        /* Allocate memory for the slabs */
        allocate_slabs(rotg, fplog, g, bVerbose, cr);

        /* Flexible rotation: determine the reference centers for the rest of the simulation */
        erg->slab_first = erg->slab_first_ref;
        erg->slab_last = erg->slab_last_ref;
        get_slab_centers(rotg,rotg->x_ref,erg->mc,cr,g,-1,out_slabs,TRUE,TRUE);

        /* Length of each x_rotref vector from center (needed if fit routine NORM is chosen): */
        if (rotg->eFittype == erotgFitNORM)
        {
            for (i=0; i<rotg->nat; i++)
            {
                rvec_sub(rotg->x_ref[i], erg->xc_ref_center, coord);
                erg->xc_ref_length[i] = norm(coord);
            }
        }
    }
}


extern void dd_make_local_rotation_groups(gmx_domdec_t *dd,t_rot *rot)
{
    gmx_ga2la_t ga2la;
    int g;
    t_rotgrp *rotg;
    gmx_enfrotgrp_t erg;      /* Pointer to enforced rotation group data */
    
    ga2la = dd->ga2la;

    for(g=0; g<rot->ngrp; g++)
    {
        rotg = &rot->grp[g];
        erg  = rotg->enfrotgrp;


        dd_make_local_group_indices(ga2la,rotg->nat,rotg->ind,
                &erg->nat_loc,&erg->ind_loc,&erg->nalloc_loc,erg->xc_ref_ind);
    }
}


extern void init_rot(FILE *fplog,t_inputrec *ir,int nfile,const t_filenm fnm[],
        t_commrec *cr, rvec *x, matrix box, gmx_mtop_t *mtop, const output_env_t oenv,
        gmx_bool bVerbose, unsigned long Flags)
{
    t_rot    *rot;
    t_rotgrp *rotg;
    int      g;
    int      nat_max=0;     /* Size of biggest rotation group */
    gmx_enfrot_t er;        /* Pointer to the enforced rotation buffer variables */    
    gmx_enfrotgrp_t erg;    /* Pointer to enforced rotation group data */
    rvec     *x_pbc;        /* Space for the pbc-correct atom positions */


    if ( (PAR(cr)) && !DOMAINDECOMP(cr) )
        gmx_fatal(FARGS, "Enforced rotation is only implemented for domain decomposition!");

    if ( MASTER(cr) && bVerbose)
        fprintf(stdout, "%s Initializing ...\n", RotStr);


    rot = ir->rot;
    snew(rot->enfrot, 1);
    er=rot->enfrot;
    
    /* Output every step for reruns */
    if (Flags & MD_RERUN)
    {
        if (fplog)
            fprintf(fplog, "%s rerun - will write rotation output every available step.\n", RotStr);
        rot->nstrout = 1;
        rot->nsttout = 1;
    }

    er->out_slabs = NULL;
    if (MASTER(cr))
        er->out_slabs = open_slab_out(rot, opt2fn("-rs",nfile,fnm));

    if (MASTER(cr))
    {
        /* Remove pbc, make molecule whole.
         * When ir->bContinuation=TRUE this has already been done, but ok. */
        snew(x_pbc,mtop->natoms);
        m_rveccopy(mtop->natoms,x,x_pbc);
        do_pbc_first_mtop(NULL,ir->ePBC,box,mtop,x_pbc);
    }

    for(g=0; g<rot->ngrp; g++)
    {
        rotg = &rot->grp[g];

        if (fplog)
            fprintf(fplog,"%s group %d type '%s'\n", RotStr, g, erotg_names[rotg->eType]);
        
        if (rotg->nat > 0)
        {
            /* Allocate space for the rotation group's data: */
            snew(rotg->enfrotgrp, 1);
            erg  = rotg->enfrotgrp;

            nat_max=max(nat_max, rotg->nat);
            
            if (PAR(cr))
            {
                erg->nat_loc    = 0;
                erg->nalloc_loc = 0;
                erg->ind_loc    = NULL;
            }
            else
            {
                erg->nat_loc = rotg->nat;
                erg->ind_loc = rotg->ind;
            }
            init_rot_group(fplog,cr,g,rotg,x_pbc,mtop,bVerbose,er->out_slabs);
        }
    }
    
    /* Allocate space for enforced rotation buffer variables */
    er->bufsize = nat_max;
    snew(er->data, nat_max);
    snew(er->xbuf, nat_max);
    snew(er->mbuf, nat_max);

    /* Buffers for MPI reducing torques, angles, weights (for each group), and V */
    er->mpi_bufsize = 4*rot->ngrp; /* To start with */
    snew(er->mpi_inbuf , er->mpi_bufsize);
    snew(er->mpi_outbuf, er->mpi_bufsize);

    /* Only do I/O on the MASTER */
    er->out_angles  = NULL;
    er->out_rot     = NULL;
    er->out_torque  = NULL;
    if (MASTER(cr))
    {
        er->out_rot = open_rot_out(opt2fn("-ro",nfile,fnm), rot, oenv, Flags);
        if (   (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
            || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) )
        {
            if (rot->nstrout > 0)
                er->out_angles  = open_angles_out(rot, opt2fn("-ra",nfile,fnm));
            if (rot->nsttout > 0)
                er->out_torque  = open_torque_out(rot, opt2fn("-rt",nfile,fnm));
        }
        sfree(x_pbc);
    }
}


extern void finish_rot(FILE *fplog,t_rot *rot)
{
    gmx_enfrot_t er;        /* Pointer to the enforced rotation buffer variables */    

    
    er=rot->enfrot;
    if (er->out_rot)
        gmx_fio_fclose(er->out_rot);
    if (er->out_slabs)
        gmx_fio_fclose(er->out_slabs);
    if (er->out_angles)
        gmx_fio_fclose(er->out_angles);
    if (er->out_torque)
        gmx_fio_fclose(er->out_torque);
}


/* Rotate the local reference positions and store them in
 * erg->xr_loc[0...(nat_loc-1)]
 *
 * Note that we already subtracted u or y_c from the reference positions
 * in init_rot_group().
 */
static void rotate_local_reference(t_rotgrp *rotg)
{
    gmx_enfrotgrp_t erg;
    int i,ii;

    
    erg=rotg->enfrotgrp;
    
    for (i=0; i<erg->nat_loc; i++)
    {
        /* Index of this rotation group atom with respect to the whole rotation group */
        ii = erg->xc_ref_ind[i];
        /* Rotate */
        mvmul(erg->rotmat, rotg->x_ref[ii], erg->xr_loc[i]);
    }
}


/* Select the PBC representation for each local x position and store that
 * for later usage. We assume the right PBC image of an x is the one nearest to
 * its rotated reference */
static void choose_pbc_image(rvec x[], t_rotgrp *rotg, matrix box, int npbcdim)
{
    int d,i,ii,m;
    gmx_enfrotgrp_t erg;       /* Pointer to enforced rotation group data */
    rvec xref,xcurr,dx;
    ivec shift;


    erg=rotg->enfrotgrp;
    
    for (i=0; i<erg->nat_loc; i++)
    {
        clear_ivec(shift);
        
        /* Index of a rotation group atom  */
        ii = erg->ind_loc[i];

        /* Get the reference position. The pivot (or COM or COG) was already
         * subtracted in init_rot_group() from the reference positions. Also,
         * the reference positions have already been rotated in
         * rotate_local_reference() */
        copy_rvec(erg->xr_loc[i], xref);
        
        /* Subtract the (old) center from the current positions
         * (just to determine the shifts!) */
        rvec_sub(x[ii], erg->xc_center, xcurr);
        
        /* Shortest PBC distance between the atom and its reference */
        rvec_sub(xcurr, xref, dx);
        
        /* Determine the shift for this atom */
        for(m=npbcdim-1; m>=0; m--)
        {
            while (dx[m] < -0.5*box[m][m])
            {
                for(d=0; d<DIM; d++)
                    dx[d] += box[m][d];
                shift[m]++;
            }
            while (dx[m] >= 0.5*box[m][m])
            {
                for(d=0; d<DIM; d++)
                    dx[d] -= box[m][d];
                shift[m]--;
            }
        }
        
        /* Apply the shift to the current atom */
        copy_rvec(x[ii], erg->x_loc_pbc[i]);
        shift_single_coord(box, erg->x_loc_pbc[i], shift); 
    }
}


extern void do_rotation(
        t_commrec *cr,
        t_inputrec *ir,
        matrix box,
        rvec x[],
        real t,
        int step,
        gmx_wallcycle_t wcycle,
        gmx_bool bNS)
{
    int      g,i,ii;
    t_rot    *rot;
    t_rotgrp *rotg;
    gmx_bool outstep_torque;
    gmx_bool bFlex,bColl;
    float    cycles_rot;
    gmx_enfrot_t er;     /* Pointer to the enforced rotation buffer variables */
    gmx_enfrotgrp_t erg; /* Pointer to enforced rotation group data           */
    rvec     transvec;
#ifdef TAKETIME
    double t0;
#endif
    
    
    rot=ir->rot;
    er=rot->enfrot;
    
    /* At which time steps do we want to output the torque */
    outstep_torque = do_per_step(step, rot->nsttout);
    
    /* Output time into rotation output file */
    if (outstep_torque && MASTER(cr))
        fprintf(er->out_rot, "%12.3e",t);

    /**************************************************************************/
    /* First do ALL the communication! */
    for(g=0; g<rot->ngrp; g++)
    {
        rotg = &rot->grp[g];
        erg=rotg->enfrotgrp;

        /* Do we have a flexible axis? */
        bFlex = (    (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
                  || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) );

        /* Do we use a collective (global) set of coordinates? */
        bColl = bFlex || (rotg->eType==erotgRMPF) || (rotg->eType==erotgRM2PF);

        /* Calculate the rotation matrix for this angle: */
        erg->degangle = rotg->rate * t;
        calc_rotmat(rotg->vec,erg->degangle,erg->rotmat);

        if (bColl)
        {
            /* Transfer the rotation group's positions such that every node has
             * all of them. Every node contributes its local positions x and stores
             * it in the collective erg->xc array. */
            communicate_group_positions(cr,erg->xc, erg->xc_shifts, erg->xc_eshifts, bNS,
                    x, rotg->nat, erg->nat_loc, erg->ind_loc, erg->xc_ref_ind, erg->xc_old, box);
        }
        else
        {
            /* Fill the local masses array;
             * this array changes in DD/neighborsearching steps */
            if (bNS)
            {
                for (i=0; i<erg->nat_loc; i++)
                {
                    /* Index of local atom w.r.t. the collective rotation group */
                    ii = erg->xc_ref_ind[i];
                    erg->m_loc[i] = erg->mc[ii];
                }
            }

            /* Calculate Omega*(y_i-y_c) for the local positions */
            rotate_local_reference(rotg);

            /* Choose the nearest PBC images of the group atoms with respect
             * to the rotated reference positions */
            choose_pbc_image(x, rotg, box, 3);

            /* Get the center of the rotation group */
            if ( (rotg->eType==erotgISOPF) || (rotg->eType==erotgPMPF) )
                get_center_comm(cr, erg->x_loc_pbc, erg->m_loc, erg->nat_loc, rotg->nat, erg->xc_center);
        }

    } /* End of loop over rotation groups */

    /**************************************************************************/
    /* Done communicating, we can start to count cycles now ... */
    wallcycle_start(wcycle, ewcROT);
    GMX_MPE_LOG(ev_rotcycles_start);

#ifdef TAKETIME
    t0 = MPI_Wtime();
#endif

    for(g=0; g<rot->ngrp; g++)
    {
        rotg = &rot->grp[g];
        erg=rotg->enfrotgrp;

        bFlex = (    (rotg->eType==erotgFLEX ) || (rotg->eType==erotgFLEXT )
                  || (rotg->eType==erotgFLEX2) || (rotg->eType==erotgFLEX2T) );

        bColl = bFlex || (rotg->eType==erotgRMPF) || (rotg->eType==erotgRM2PF);

        if (outstep_torque && MASTER(cr))
            fprintf(er->out_rot, "%12.4f", erg->degangle);

        switch(rotg->eType)
        {
            case erotgISO:
            case erotgISOPF:
            case erotgPM:
            case erotgPMPF:
                do_fixed(cr,rotg,x,box,t,step,outstep_torque);
                break;
            case erotgRM:
                do_radial_motion(cr,rotg,x,box,t,step,outstep_torque);
                break;
            case erotgRMPF:
                do_radial_motion_pf(cr,rotg,x,box,t,step,outstep_torque);
                break;
            case erotgRM2:
            case erotgRM2PF:
                do_radial_motion2(cr,rotg,x,box,t,step,outstep_torque);
                break;
            case erotgFLEXT:
            case erotgFLEX2T:
                /* Subtract the center of the rotation group from the collective positions array
                 * Also store the center in erg->xc_center since it needs to be subtracted
                 * in the low level routines from the local coordinates as well */
                get_center(erg->xc, erg->mc, rotg->nat, erg->xc_center);
                svmul(-1.0, erg->xc_center, transvec);
                translate_x(erg->xc, rotg->nat, transvec);
                do_flexible(cr,er,rotg,g,x,box,t,step,outstep_torque);
                break;
            case erotgFLEX:
            case erotgFLEX2:
                /* Do NOT subtract the center of mass in the low level routines! */
                clear_rvec(erg->xc_center);
                do_flexible(cr,er,rotg,g,x,box,t,step,outstep_torque);
                break;
            default:
                gmx_fatal(FARGS, "No such rotation potential.");
                break;
        }
    }

#ifdef TAKETIME
    if (MASTER(cr))
        fprintf(stderr, "%s calculation (step %d) took %g seconds.\n", RotStr, step, MPI_Wtime()-t0);
#endif

    /* Stop the cycle counter and add to the force cycles for load balancing */
    cycles_rot = wallcycle_stop(wcycle,ewcROT);
    if (DOMAINDECOMP(cr) && wcycle)
        dd_cycles_add(cr->dd,cycles_rot,ddCyclF);
    GMX_MPE_LOG(ev_rotcycles_finish);
}