Merge branch 'release-4-6' into master

[alexxy/gromacs.git] / src / gromacs / mdlib / coupling.c

/* -*- mode: c; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4; c-file-style: "stroustrup"; -*-
 *
 *                This source code is part of
 *
 *                 G   R   O   M   A   C   S
 *
 *          GROningen MAchine for Chemical Simulations
 *
 *                        VERSION 3.2.0
 * Written by David van der Spoel, Erik Lindahl, Berk Hess, and others.
 * Copyright (c) 1991-2000, University of Groningen, The Netherlands.
 * Copyright (c) 2001-2004, 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:
 * GROwing Monsters And Cloning Shrimps
 */
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <assert.h>

#include "typedefs.h"
#include "smalloc.h"
#include "update.h"
#include "vec.h"
#include "macros.h"
#include "physics.h"
#include "names.h"
#include "gmx_fatal.h"
#include "txtdump.h"
#include "nrnb.h"
#include "gmx_random.h"
#include "update.h"
#include "mdrun.h"

#define NTROTTERPARTS 3

/* Suzuki-Yoshida Constants, for n=3 and n=5, for symplectic integration  */
/* for n=1, w0 = 1 */
/* for n=3, w0 = w2 = 1/(2-2^-(1/3)), w1 = 1-2*w0 */
/* for n=5, w0 = w1 = w3 = w4 = 1/(4-4^-(1/3)), w1 = 1-4*w0 */

#define MAX_SUZUKI_YOSHIDA_NUM 5
#define SUZUKI_YOSHIDA_NUM  5

static const double  sy_const_1[] = { 1. };
static const double  sy_const_3[] = { 0.828981543588751, -0.657963087177502, 0.828981543588751 };
static const double  sy_const_5[] = { 0.2967324292201065, 0.2967324292201065, -0.186929716880426, 0.2967324292201065, 0.2967324292201065 };

static const double* sy_const[] = {
    NULL,
    sy_const_1,
    NULL,
    sy_const_3,
    NULL,
    sy_const_5
};

/*
   static const double sy_const[MAX_SUZUKI_YOSHIDA_NUM+1][MAX_SUZUKI_YOSHIDA_NUM+1] = {
    {},
    {1},
    {},
    {0.828981543588751,-0.657963087177502,0.828981543588751},
    {},
    {0.2967324292201065,0.2967324292201065,-0.186929716880426,0.2967324292201065,0.2967324292201065}
   };*/

/* these integration routines are only referenced inside this file */
static void NHC_trotter(t_grpopts *opts, int nvar, gmx_ekindata_t *ekind, real dtfull,
                        double xi[], double vxi[], double scalefac[], real *veta, t_extmass *MassQ, gmx_bool bEkinAveVel)

{
    /* general routine for both barostat and thermostat nose hoover chains */

    int           i, j, mi, mj, jmax;
    double        Ekin, Efac, reft, kT, nd;
    double        dt;
    t_grp_tcstat *tcstat;
    double       *ivxi, *ixi;
    double       *iQinv;
    double       *GQ;
    gmx_bool      bBarostat;
    int           mstepsi, mstepsj;
    int           ns = SUZUKI_YOSHIDA_NUM; /* set the degree of integration in the types/state.h file */
    int           nh = opts->nhchainlength;

    snew(GQ, nh);
    mstepsi = mstepsj = ns;

/* if scalefac is NULL, we are doing the NHC of the barostat */

    bBarostat = FALSE;
    if (scalefac == NULL)
    {
        bBarostat = TRUE;
    }

    for (i = 0; i < nvar; i++)
    {

        /* make it easier to iterate by selecting
           out the sub-array that corresponds to this T group */

        ivxi = &vxi[i*nh];
        ixi  = &xi[i*nh];
        if (bBarostat)
        {
            iQinv = &(MassQ->QPinv[i*nh]);
            nd    = 1.0; /* THIS WILL CHANGE IF NOT ISOTROPIC */
            reft  = max(0.0, opts->ref_t[0]);
            Ekin  = sqr(*veta)/MassQ->Winv;
        }
        else
        {
            iQinv  = &(MassQ->Qinv[i*nh]);
            tcstat = &ekind->tcstat[i];
            nd     = opts->nrdf[i];
            reft   = max(0.0, opts->ref_t[i]);
            if (bEkinAveVel)
            {
                Ekin = 2*trace(tcstat->ekinf)*tcstat->ekinscalef_nhc;
            }
            else
            {
                Ekin = 2*trace(tcstat->ekinh)*tcstat->ekinscaleh_nhc;
            }
        }
        kT = BOLTZ*reft;

        for (mi = 0; mi < mstepsi; mi++)
        {
            for (mj = 0; mj < mstepsj; mj++)
            {
                /* weighting for this step using Suzuki-Yoshida integration - fixed at 5 */
                dt = sy_const[ns][mj] * dtfull / mstepsi;

                /* compute the thermal forces */
                GQ[0] = iQinv[0]*(Ekin - nd*kT);

                for (j = 0; j < nh-1; j++)
                {
                    if (iQinv[j+1] > 0)
                    {
                        /* we actually don't need to update here if we save the
                           state of the GQ, but it's easier to just recompute*/
                        GQ[j+1] = iQinv[j+1]*((sqr(ivxi[j])/iQinv[j])-kT);
                    }
                    else
                    {
                        GQ[j+1] = 0;
                    }
                }

                ivxi[nh-1] += 0.25*dt*GQ[nh-1];
                for (j = nh-1; j > 0; j--)
                {
                    Efac      = exp(-0.125*dt*ivxi[j]);
                    ivxi[j-1] = Efac*(ivxi[j-1]*Efac + 0.25*dt*GQ[j-1]);
                }

                Efac = exp(-0.5*dt*ivxi[0]);
                if (bBarostat)
                {
                    *veta *= Efac;
                }
                else
                {
                    scalefac[i] *= Efac;
                }
                Ekin *= (Efac*Efac);

                /* Issue - if the KE is an average of the last and the current temperatures, then we might not be
                   able to scale the kinetic energy directly with this factor.  Might take more bookkeeping -- have to
                   think about this a bit more . . . */

                GQ[0] = iQinv[0]*(Ekin - nd*kT);

                /* update thermostat positions */
                for (j = 0; j < nh; j++)
                {
                    ixi[j] += 0.5*dt*ivxi[j];
                }

                for (j = 0; j < nh-1; j++)
                {
                    Efac    = exp(-0.125*dt*ivxi[j+1]);
                    ivxi[j] = Efac*(ivxi[j]*Efac + 0.25*dt*GQ[j]);
                    if (iQinv[j+1] > 0)
                    {
                        GQ[j+1] = iQinv[j+1]*((sqr(ivxi[j])/iQinv[j])-kT);
                    }
                    else
                    {
                        GQ[j+1] = 0;
                    }
                }
                ivxi[nh-1] += 0.25*dt*GQ[nh-1];
            }
        }
    }
    sfree(GQ);
}

static void boxv_trotter(t_inputrec *ir, real *veta, real dt, tensor box,
                         gmx_ekindata_t *ekind, tensor vir, real pcorr, t_extmass *MassQ)
{

    real   pscal;
    double alpha;
    int    i, j, d, n, nwall;
    real   T, GW, vol;
    tensor Winvm, ekinmod, localpres;

    /* The heat bath is coupled to a separate barostat, the last temperature group.  In the
       2006 Tuckerman et al paper., the order is iL_{T_baro} iL {T_part}
     */

    if (ir->epct == epctSEMIISOTROPIC)
    {
        nwall = 2;
    }
    else
    {
        nwall = 3;
    }

    /* eta is in pure units.  veta is in units of ps^-1. GW is in
       units of ps^-2.  However, eta has a reference of 1 nm^3, so care must be
       taken to use only RATIOS of eta in updating the volume. */

    /* we take the partial pressure tensors, modify the
       kinetic energy tensor, and recovert to pressure */

    if (ir->opts.nrdf[0] == 0)
    {
        gmx_fatal(FARGS, "Barostat is coupled to a T-group with no degrees of freedom\n");
    }
    /* alpha factor for phase space volume, then multiply by the ekin scaling factor.  */
    alpha  = 1.0 + DIM/((double)ir->opts.nrdf[0]);
    alpha *= ekind->tcstat[0].ekinscalef_nhc;
    msmul(ekind->ekin, alpha, ekinmod);
    /* for now, we use Elr = 0, because if you want to get it right, you
       really should be using PME. Maybe print a warning? */

    pscal   = calc_pres(ir->ePBC, nwall, box, ekinmod, vir, localpres)+pcorr;

    vol = det(box);
    GW  = (vol*(MassQ->Winv/PRESFAC))*(DIM*pscal - trace(ir->ref_p));  /* W is in ps^2 * bar * nm^3 */

    *veta += 0.5*dt*GW;
}

/*
 * This file implements temperature and pressure coupling algorithms:
 * For now only the Weak coupling and the modified weak coupling.
 *
 * Furthermore computation of pressure and temperature is done here
 *
 */

real calc_pres(int ePBC, int nwall, matrix box, tensor ekin, tensor vir,
               tensor pres)
{
    int  n, m;
    real fac;

    if (ePBC == epbcNONE || (ePBC == epbcXY && nwall != 2))
    {
        clear_mat(pres);
    }
    else
    {
        /* Uitzoeken welke ekin hier van toepassing is, zie Evans & Morris - E.
         * Wrs. moet de druktensor gecorrigeerd worden voor de netto stroom in
         * het systeem...
         */

        fac = PRESFAC*2.0/det(box);
        for (n = 0; (n < DIM); n++)
        {
            for (m = 0; (m < DIM); m++)
            {
                pres[n][m] = (ekin[n][m] - vir[n][m])*fac;
            }
        }

        if (debug)
        {
            pr_rvecs(debug, 0, "PC: pres", pres, DIM);
            pr_rvecs(debug, 0, "PC: ekin", ekin, DIM);
            pr_rvecs(debug, 0, "PC: vir ", vir, DIM);
            pr_rvecs(debug, 0, "PC: box ", box, DIM);
        }
    }
    return trace(pres)/DIM;
}

real calc_temp(real ekin, real nrdf)
{
    if (nrdf > 0)
    {
        return (2.0*ekin)/(nrdf*BOLTZ);
    }
    else
    {
        return 0;
    }
}

void parrinellorahman_pcoupl(FILE *fplog, gmx_large_int_t step,
                             t_inputrec *ir, real dt, tensor pres,
                             tensor box, tensor box_rel, tensor boxv,
                             tensor M, matrix mu, gmx_bool bFirstStep)
{
    /* This doesn't do any coordinate updating. It just
     * integrates the box vector equations from the calculated
     * acceleration due to pressure difference. We also compute
     * the tensor M which is used in update to couple the particle
     * coordinates to the box vectors.
     *
     * In Nose and Klein (Mol.Phys 50 (1983) no 5., p 1055) this is
     * given as
     *            -1    .           .     -1
     * M_nk = (h')   * (h' * h + h' h) * h
     *
     * with the dots denoting time derivatives and h is the transformation from
     * the scaled frame to the real frame, i.e. the TRANSPOSE of the box.
     * This also goes for the pressure and M tensors - they are transposed relative
     * to ours. Our equation thus becomes:
     *
     *                  -1       .    .           -1
     * M_gmx = M_nk' = b  * (b * b' + b * b') * b'
     *
     * where b is the gromacs box matrix.
     * Our box accelerations are given by
     *   ..                                    ..
     *   b = vol/W inv(box') * (P-ref_P)     (=h')
     */

    int    d, n;
    tensor winv;
    real   vol = box[XX][XX]*box[YY][YY]*box[ZZ][ZZ];
    real   atot, arel, change, maxchange, xy_pressure;
    tensor invbox, pdiff, t1, t2;

    real   maxl;

    m_inv_ur0(box, invbox);

    if (!bFirstStep)
    {
        /* Note that PRESFAC does not occur here.
         * The pressure and compressibility always occur as a product,
         * therefore the pressure unit drops out.
         */
        maxl = max(box[XX][XX], box[YY][YY]);
        maxl = max(maxl, box[ZZ][ZZ]);
        for (d = 0; d < DIM; d++)
        {
            for (n = 0; n < DIM; n++)
            {
                winv[d][n] =
                    (4*M_PI*M_PI*ir->compress[d][n])/(3*ir->tau_p*ir->tau_p*maxl);
            }
        }

        m_sub(pres, ir->ref_p, pdiff);

        if (ir->epct == epctSURFACETENSION)
        {
            /* Unlike Berendsen coupling it might not be trivial to include a z
             * pressure correction here? On the other hand we don't scale the
             * box momentarily, but change accelerations, so it might not be crucial.
             */
            xy_pressure = 0.5*(pres[XX][XX]+pres[YY][YY]);
            for (d = 0; d < ZZ; d++)
            {
                pdiff[d][d] = (xy_pressure-(pres[ZZ][ZZ]-ir->ref_p[d][d]/box[d][d]));
            }
        }

        tmmul(invbox, pdiff, t1);
        /* Move the off-diagonal elements of the 'force' to one side to ensure
         * that we obey the box constraints.
         */
        for (d = 0; d < DIM; d++)
        {
            for (n = 0; n < d; n++)
            {
                t1[d][n] += t1[n][d];
                t1[n][d]  = 0;
            }
        }

        switch (ir->epct)
        {
            case epctANISOTROPIC:
                for (d = 0; d < DIM; d++)
                {
                    for (n = 0; n <= d; n++)
                    {
                        t1[d][n] *= winv[d][n]*vol;
                    }
                }
                break;
            case epctISOTROPIC:
                /* calculate total volume acceleration */
                atot = box[XX][XX]*box[YY][YY]*t1[ZZ][ZZ]+
                    box[XX][XX]*t1[YY][YY]*box[ZZ][ZZ]+
                    t1[XX][XX]*box[YY][YY]*box[ZZ][ZZ];
                arel = atot/(3*vol);
                /* set all RELATIVE box accelerations equal, and maintain total V
                 * change speed */
                for (d = 0; d < DIM; d++)
                {
                    for (n = 0; n <= d; n++)
                    {
                        t1[d][n] = winv[0][0]*vol*arel*box[d][n];
                    }
                }
                break;
            case epctSEMIISOTROPIC:
            case epctSURFACETENSION:
                /* Note the correction to pdiff above for surftens. coupling  */

                /* calculate total XY volume acceleration */
                atot = box[XX][XX]*t1[YY][YY]+t1[XX][XX]*box[YY][YY];
                arel = atot/(2*box[XX][XX]*box[YY][YY]);
                /* set RELATIVE XY box accelerations equal, and maintain total V
                 * change speed. Dont change the third box vector accelerations */
                for (d = 0; d < ZZ; d++)
                {
                    for (n = 0; n <= d; n++)
                    {
                        t1[d][n] = winv[d][n]*vol*arel*box[d][n];
                    }
                }
                for (n = 0; n < DIM; n++)
                {
                    t1[ZZ][n] *= winv[d][n]*vol;
                }
                break;
            default:
                gmx_fatal(FARGS, "Parrinello-Rahman pressure coupling type %s "
                          "not supported yet\n", EPCOUPLTYPETYPE(ir->epct));
                break;
        }

        maxchange = 0;
        for (d = 0; d < DIM; d++)
        {
            for (n = 0; n <= d; n++)
            {
                boxv[d][n] += dt*t1[d][n];

                /* We do NOT update the box vectors themselves here, since
                 * we need them for shifting later. It is instead done last
                 * in the update() routine.
                 */

                /* Calculate the change relative to diagonal elements-
                   since it's perfectly ok for the off-diagonal ones to
                   be zero it doesn't make sense to check the change relative
                   to its current size.
                 */

                change = fabs(dt*boxv[d][n]/box[d][d]);

                if (change > maxchange)
                {
                    maxchange = change;
                }
            }
        }

        if (maxchange > 0.01 && fplog)
        {
            char buf[22];
            fprintf(fplog,
                    "\nStep %s  Warning: Pressure scaling more than 1%%. "
                    "This may mean your system\n is not yet equilibrated. "
                    "Use of Parrinello-Rahman pressure coupling during\n"
                    "equilibration can lead to simulation instability, "
                    "and is discouraged.\n",
                    gmx_step_str(step, buf));
        }
    }

    preserve_box_shape(ir, box_rel, boxv);

    mtmul(boxv, box, t1);   /* t1=boxv * b' */
    mmul(invbox, t1, t2);
    mtmul(t2, invbox, M);

    /* Determine the scaling matrix mu for the coordinates */
    for (d = 0; d < DIM; d++)
    {
        for (n = 0; n <= d; n++)
        {
            t1[d][n] = box[d][n] + dt*boxv[d][n];
        }
    }
    preserve_box_shape(ir, box_rel, t1);
    /* t1 is the box at t+dt, determine mu as the relative change */
    mmul_ur0(invbox, t1, mu);
}

void berendsen_pcoupl(FILE *fplog, gmx_large_int_t step,
                      t_inputrec *ir, real dt, tensor pres, matrix box,
                      matrix mu)
{
    int     d, n;
    real    scalar_pressure, xy_pressure, p_corr_z;
    char   *ptr, buf[STRLEN];

    /*
     *  Calculate the scaling matrix mu
     */
    scalar_pressure = 0;
    xy_pressure     = 0;
    for (d = 0; d < DIM; d++)
    {
        scalar_pressure += pres[d][d]/DIM;
        if (d != ZZ)
        {
            xy_pressure += pres[d][d]/(DIM-1);
        }
    }
    /* Pressure is now in bar, everywhere. */
#define factor(d, m) (ir->compress[d][m]*dt/ir->tau_p)

    /* mu has been changed from pow(1+...,1/3) to 1+.../3, since this is
     * necessary for triclinic scaling
     */
    clear_mat(mu);
    switch (ir->epct)
    {
        case epctISOTROPIC:
            for (d = 0; d < DIM; d++)
            {
                mu[d][d] = 1.0 - factor(d, d)*(ir->ref_p[d][d] - scalar_pressure) /DIM;
            }
            break;
        case epctSEMIISOTROPIC:
            for (d = 0; d < ZZ; d++)
            {
                mu[d][d] = 1.0 - factor(d, d)*(ir->ref_p[d][d]-xy_pressure)/DIM;
            }
            mu[ZZ][ZZ] =
                1.0 - factor(ZZ, ZZ)*(ir->ref_p[ZZ][ZZ] - pres[ZZ][ZZ])/DIM;
            break;
        case epctANISOTROPIC:
            for (d = 0; d < DIM; d++)
            {
                for (n = 0; n < DIM; n++)
                {
                    mu[d][n] = (d == n ? 1.0 : 0.0)
                        -factor(d, n)*(ir->ref_p[d][n] - pres[d][n])/DIM;
                }
            }
            break;
        case epctSURFACETENSION:
            /* ir->ref_p[0/1] is the reference surface-tension times *
             * the number of surfaces                                */
            if (ir->compress[ZZ][ZZ])
            {
                p_corr_z = dt/ir->tau_p*(ir->ref_p[ZZ][ZZ] - pres[ZZ][ZZ]);
            }
            else
            {
                /* when the compressibity is zero, set the pressure correction   *
                 * in the z-direction to zero to get the correct surface tension */
                p_corr_z = 0;
            }
            mu[ZZ][ZZ] = 1.0 - ir->compress[ZZ][ZZ]*p_corr_z;
            for (d = 0; d < DIM-1; d++)
            {
                mu[d][d] = 1.0 + factor(d, d)*(ir->ref_p[d][d]/(mu[ZZ][ZZ]*box[ZZ][ZZ])
                                               - (pres[ZZ][ZZ]+p_corr_z - xy_pressure))/(DIM-1);
            }
            break;
        default:
            gmx_fatal(FARGS, "Berendsen pressure coupling type %s not supported yet\n",
                      EPCOUPLTYPETYPE(ir->epct));
            break;
    }
    /* To fullfill the orientation restrictions on triclinic boxes
     * we will set mu_yx, mu_zx and mu_zy to 0 and correct
     * the other elements of mu to first order.
     */
    mu[YY][XX] += mu[XX][YY];
    mu[ZZ][XX] += mu[XX][ZZ];
    mu[ZZ][YY] += mu[YY][ZZ];
    mu[XX][YY]  = 0;
    mu[XX][ZZ]  = 0;
    mu[YY][ZZ]  = 0;

    if (debug)
    {
        pr_rvecs(debug, 0, "PC: pres ", pres, 3);
        pr_rvecs(debug, 0, "PC: mu   ", mu, 3);
    }

    if (mu[XX][XX] < 0.99 || mu[XX][XX] > 1.01 ||
        mu[YY][YY] < 0.99 || mu[YY][YY] > 1.01 ||
        mu[ZZ][ZZ] < 0.99 || mu[ZZ][ZZ] > 1.01)
    {
        char buf2[22];
        sprintf(buf, "\nStep %s  Warning: pressure scaling more than 1%%, "
                "mu: %g %g %g\n",
                gmx_step_str(step, buf2), mu[XX][XX], mu[YY][YY], mu[ZZ][ZZ]);
        if (fplog)
        {
            fprintf(fplog, "%s", buf);
        }
        fprintf(stderr, "%s", buf);
    }
}

void berendsen_pscale(t_inputrec *ir, matrix mu,
                      matrix box, matrix box_rel,
                      int start, int nr_atoms,
                      rvec x[], unsigned short cFREEZE[],
                      t_nrnb *nrnb)
{
    ivec   *nFreeze = ir->opts.nFreeze;
    int     n, d, g = 0;

    /* Scale the positions */
    for (n = start; n < start+nr_atoms; n++)
    {
        if (cFREEZE)
        {
            g = cFREEZE[n];
        }

        if (!nFreeze[g][XX])
        {
            x[n][XX] = mu[XX][XX]*x[n][XX]+mu[YY][XX]*x[n][YY]+mu[ZZ][XX]*x[n][ZZ];
        }
        if (!nFreeze[g][YY])
        {
            x[n][YY] = mu[YY][YY]*x[n][YY]+mu[ZZ][YY]*x[n][ZZ];
        }
        if (!nFreeze[g][ZZ])
        {
            x[n][ZZ] = mu[ZZ][ZZ]*x[n][ZZ];
        }
    }
    /* compute final boxlengths */
    for (d = 0; d < DIM; d++)
    {
        box[d][XX] = mu[XX][XX]*box[d][XX]+mu[YY][XX]*box[d][YY]+mu[ZZ][XX]*box[d][ZZ];
        box[d][YY] = mu[YY][YY]*box[d][YY]+mu[ZZ][YY]*box[d][ZZ];
        box[d][ZZ] = mu[ZZ][ZZ]*box[d][ZZ];
    }

    preserve_box_shape(ir, box_rel, box);

    /* (un)shifting should NOT be done after this,
     * since the box vectors might have changed
     */
    inc_nrnb(nrnb, eNR_PCOUPL, nr_atoms);
}

void berendsen_tcoupl(t_inputrec *ir, gmx_ekindata_t *ekind, real dt)
{
    t_grpopts *opts;
    int        i;
    real       T, reft = 0, lll;

    opts = &ir->opts;

    for (i = 0; (i < opts->ngtc); i++)
    {
        if (ir->eI == eiVV)
        {
            T = ekind->tcstat[i].T;
        }
        else
        {
            T = ekind->tcstat[i].Th;
        }

        if ((opts->tau_t[i] > 0) && (T > 0.0))
        {
            reft                    = max(0.0, opts->ref_t[i]);
            lll                     = sqrt(1.0 + (dt/opts->tau_t[i])*(reft/T-1.0));
            ekind->tcstat[i].lambda = max(min(lll, 1.25), 0.8);
        }
        else
        {
            ekind->tcstat[i].lambda = 1.0;
        }

        if (debug)
        {
            fprintf(debug, "TC: group %d: T: %g, Lambda: %g\n",
                    i, T, ekind->tcstat[i].lambda);
        }
    }
}

static int poisson_variate(real lambda, gmx_rng_t rng)
{

    real L;
    int  k = 0;
    real p = 1.0;

    L = exp(-lambda);

    do
    {
        k  = k+1;
        p *= gmx_rng_uniform_real(rng);
    }
    while (p > L);

    return k-1;
}

void andersen_tcoupl(t_inputrec *ir, t_mdatoms *md, t_state *state, gmx_rng_t rng, real rate, t_idef *idef, int nblocks, int *sblock, gmx_bool *randatom, int *randatom_list, gmx_bool *randomize, real *boltzfac)
{
    t_grpopts *opts;
    int        i, j, k, d, len, n, ngtc, gc = 0;
    int        nshake, nsettle, nrandom, nrand_group;
    real       boltz, scal, reft, prand;
    t_iatom   *iatoms;

    /* convenience variables */
    opts = &ir->opts;
    ngtc = opts->ngtc;

    /* idef is only passed in if it's chance-per-particle andersen, so
       it essentially serves as a boolean to determine which type of
       andersen is being used */
    if (idef)
    {

        /* randomly atoms to randomize.  However, all constraint
           groups have to have either all of the atoms or none of the
           atoms randomize.

           Algorithm:
           1. Select whether or not to randomize each atom to get the correct probability.
           2. Cycle through the constraint groups.
              2a. for each constraint group, determine the fraction f of that constraint group that are
                  chosen to be randomized.
              2b. all atoms in the constraint group are randomized with probability f.
         */

        nrandom = 0;
        if ((rate < 0.05) && (md->homenr > 50))
        {
            /* if the rate is relatively high, use a standard method, if low rate,
             * use poisson */
            /* poisson distributions approxmation, more efficient for
             * low rates, fewer random numbers required */
            nrandom = poisson_variate(md->homenr*rate, rng);  /* how many do we randomize? Use Poisson. */
            /* now we know how many, choose them randomly. No worries about repeats, at this rate, it's negligible.
               worst thing that happens, it lowers the true rate an negligible amount */
            for (i = 0; i < nrandom; i++)
            {
                randatom[(int)(gmx_rng_uniform_real(rng)*md->homenr)] = TRUE;
            }
        }
        else
        {
            for (i = 0; i < md->homenr; i++)
            {
                if (gmx_rng_uniform_real(rng) < rate)
                {
                    randatom[i] = TRUE;
                    nrandom++;
                }
            }
        }

        /* instead of looping over the constraint groups, if we had a
           list of which atoms were in which constraint groups, we
           could then loop over only the groups that are randomized
           now.  But that is not available now.  Create later after
           determining whether there actually is any slowing. */

        /* first, loop through the settles to make sure all groups either entirely randomized, or not randomized. */

        nsettle  = idef->il[F_SETTLE].nr/2;
        for (i = 0; i < nsettle; i++)
        {
            iatoms      = idef->il[F_SETTLE].iatoms;
            nrand_group = 0;
            for (k = 0; k < 3; k++)  /* settles are always 3 atoms, hardcoded */
            {
                if (randatom[iatoms[2*i+1]+k])
                {
                    nrand_group++;     /* count the number of atoms to be shaken in the settles group */
                    randatom[iatoms[2*i+1]+k] = FALSE;
                    nrandom--;
                }
            }
            if (nrand_group > 0)
            {
                prand = (nrand_group)/3.0;  /* use this fraction to compute the probability the
                                               whole group is randomized */
                if (gmx_rng_uniform_real(rng) < prand)
                {
                    for (k = 0; k < 3; k++)
                    {
                        randatom[iatoms[2*i+1]+k] = TRUE;   /* mark them all to be randomized */
                    }
                    nrandom += 3;
                }
            }
        }

        /* now loop through the shake groups */
        nshake = nblocks;
        for (i = 0; i < nshake; i++)
        {
            iatoms      = &(idef->il[F_CONSTR].iatoms[sblock[i]]);
            len         = sblock[i+1]-sblock[i];
            nrand_group = 0;
            for (k = 0; k < len; k++)
            {
                if (k%3 != 0)
                {   /* only 2/3 of the sblock items are atoms, the others are labels */
                    if (randatom[iatoms[k]])
                    {
                        nrand_group++;
                        randatom[iatoms[k]] = FALSE;  /* need to mark it false here in case the atom is in more than
                                                         one group in the shake block */
                        nrandom--;
                    }
                }
            }
            if (nrand_group > 0)
            {
                prand = (nrand_group)/(1.0*(2*len/3));
                if (gmx_rng_uniform_real(rng) < prand)
                {
                    for (k = 0; k < len; k++)
                    {
                        if (k%3 != 0)
                        {                               /* only 2/3 of the sblock items are atoms, the others are labels */
                            randatom[iatoms[k]] = TRUE; /* randomize all of them */
                            nrandom++;
                        }
                    }
                }
            }
        }
        if (nrandom > 0)
        {
            n = 0;
            for (i = 0; i < md->homenr; i++)  /* now loop over the list of atoms */
            {
                if (randatom[i])
                {
                    randatom_list[n] = i;
                    n++;
                }
            }
            nrandom = n;  /* there are some values of nrandom for which
                             this algorithm won't work; for example all
                             water molecules and nrandom =/= 3.  Better to
                             recount and use this number (which we
                             calculate anyway: it will not affect
                             the average number of atoms accepted.
                           */
        }
    }
    else
    {
        /* if it's andersen-massive, then randomize all the atoms */
        nrandom = md->homenr;
        for (i = 0; i < nrandom; i++)
        {
            randatom_list[i] = i;
        }
    }

    /* randomize the velocities of the selected particles */

    for (i = 0; i < nrandom; i++)  /* now loop over the list of atoms */
    {
        n = randatom_list[i];
        if (md->cTC)
        {
            gc   = md->cTC[n];  /* assign the atom to a temperature group if there are more than one */
        }
        if (randomize[gc])
        {
            scal = sqrt(boltzfac[gc]*md->invmass[n]);
            for (d = 0; d < DIM; d++)
            {
                state->v[n][d] = scal*gmx_rng_gaussian_table(rng);
            }
        }
        randatom[n] = FALSE; /* unmark this atom for randomization */
    }
}


void nosehoover_tcoupl(t_grpopts *opts, gmx_ekindata_t *ekind, real dt,
                       double xi[], double vxi[], t_extmass *MassQ)
{
    int   i;
    real  reft, oldvxi;

    /* note that this routine does not include Nose-hoover chains yet. Should be easy to add. */

    for (i = 0; (i < opts->ngtc); i++)
    {
        reft     = max(0.0, opts->ref_t[i]);
        oldvxi   = vxi[i];
        vxi[i]  += dt*MassQ->Qinv[i]*(ekind->tcstat[i].Th - reft);
        xi[i]   += dt*(oldvxi + vxi[i])*0.5;
    }
}

t_state *init_bufstate(const t_state *template_state)
{
    t_state *state;
    int      nc = template_state->nhchainlength;
    snew(state, 1);
    snew(state->nosehoover_xi, nc*template_state->ngtc);
    snew(state->nosehoover_vxi, nc*template_state->ngtc);
    snew(state->therm_integral, template_state->ngtc);
    snew(state->nhpres_xi, nc*template_state->nnhpres);
    snew(state->nhpres_vxi, nc*template_state->nnhpres);

    return state;
}

void destroy_bufstate(t_state *state)
{
    sfree(state->x);
    sfree(state->v);
    sfree(state->nosehoover_xi);
    sfree(state->nosehoover_vxi);
    sfree(state->therm_integral);
    sfree(state->nhpres_xi);
    sfree(state->nhpres_vxi);
    sfree(state);
}

void trotter_update(t_inputrec *ir, gmx_large_int_t step, gmx_ekindata_t *ekind,
                    gmx_enerdata_t *enerd, t_state *state,
                    tensor vir, t_mdatoms *md,
                    t_extmass *MassQ, int **trotter_seqlist, int trotter_seqno)
{

    int             n, i, j, d, ntgrp, ngtc, gc = 0;
    t_grp_tcstat   *tcstat;
    t_grpopts      *opts;
    gmx_large_int_t step_eff;
    real            ecorr, pcorr, dvdlcorr;
    real            bmass, qmass, reft, kT, dt, nd;
    tensor          dumpres, dumvir;
    double         *scalefac, dtc;
    int            *trotter_seq;
    rvec            sumv = {0, 0, 0}, consk;
    gmx_bool        bCouple;

    if (trotter_seqno <= ettTSEQ2)
    {
        step_eff = step-1;  /* the velocity verlet calls are actually out of order -- the first half step
                               is actually the last half step from the previous step.  Thus the first half step
                               actually corresponds to the n-1 step*/

    }
    else
    {
        step_eff = step;
    }

    bCouple = (ir->nsttcouple == 1 ||
               do_per_step(step_eff+ir->nsttcouple, ir->nsttcouple));

    trotter_seq = trotter_seqlist[trotter_seqno];

    if ((trotter_seq[0] == etrtSKIPALL) || (!bCouple))
    {
        return;
    }
    dtc  = ir->nsttcouple*ir->delta_t; /* This is OK for NPT, because nsttcouple == nstpcouple is enforcesd */
    opts = &(ir->opts);                /* just for ease of referencing */
    ngtc = opts->ngtc;
    assert(ngtc > 0);
    snew(scalefac, opts->ngtc);
    for (i = 0; i < ngtc; i++)
    {
        scalefac[i] = 1;
    }
    /* execute the series of trotter updates specified in the trotterpart array */

    for (i = 0; i < NTROTTERPARTS; i++)
    {
        /* allow for doubled intgrators by doubling dt instead of making 2 calls */
        if ((trotter_seq[i] == etrtBAROV2) || (trotter_seq[i] == etrtBARONHC2) || (trotter_seq[i] == etrtNHC2))
        {
            dt = 2 * dtc;
        }
        else
        {
            dt = dtc;
        }

        switch (trotter_seq[i])
        {
            case etrtBAROV:
            case etrtBAROV2:
                boxv_trotter(ir, &(state->veta), dt, state->box, ekind, vir,
                             enerd->term[F_PDISPCORR], MassQ);
                break;
            case etrtBARONHC:
            case etrtBARONHC2:
                NHC_trotter(opts, state->nnhpres, ekind, dt, state->nhpres_xi,
                            state->nhpres_vxi, NULL, &(state->veta), MassQ, FALSE);
                break;
            case etrtNHC:
            case etrtNHC2:
                NHC_trotter(opts, opts->ngtc, ekind, dt, state->nosehoover_xi,
                            state->nosehoover_vxi, scalefac, NULL, MassQ, (ir->eI == eiVV));
                /* need to rescale the kinetic energies and velocities here.  Could
                   scale the velocities later, but we need them scaled in order to
                   produce the correct outputs, so we'll scale them here. */

                for (i = 0; i < ngtc; i++)
                {
                    tcstat                  = &ekind->tcstat[i];
                    tcstat->vscale_nhc      = scalefac[i];
                    tcstat->ekinscaleh_nhc *= (scalefac[i]*scalefac[i]);
                    tcstat->ekinscalef_nhc *= (scalefac[i]*scalefac[i]);
                }
                /* now that we've scaled the groupwise velocities, we can add them up to get the total */
                /* but do we actually need the total? */

                /* modify the velocities as well */
                for (n = md->start; n < md->start+md->homenr; n++)
                {
                    if (md->cTC) /* does this conditional need to be here? is this always true?*/
                    {
                        gc = md->cTC[n];
                    }
                    for (d = 0; d < DIM; d++)
                    {
                        state->v[n][d] *= scalefac[gc];
                    }

                    if (debug)
                    {
                        for (d = 0; d < DIM; d++)
                        {
                            sumv[d] += (state->v[n][d])/md->invmass[n];
                        }
                    }
                }
                break;
            default:
                break;
        }
    }
    /* check for conserved momentum -- worth looking at this again eventually, but not working right now.*/
#if 0
    if (debug)
    {
        if (bFirstHalf)
        {
            for (d = 0; d < DIM; d++)
            {
                consk[d] = sumv[d]*exp((1 + 1.0/opts->nrdf[0])*((1.0/DIM)*log(det(state->box)/state->vol0)) + state->nosehoover_xi[0]);
            }
            fprintf(debug, "Conserved kappa: %15.8f %15.8f %15.8f\n", consk[0], consk[1], consk[2]);
        }
    }
#endif
    sfree(scalefac);
}


extern void init_npt_masses(t_inputrec *ir, t_state *state, t_extmass *MassQ, gmx_bool bInit)
{
    int           n, i, j, d, ntgrp, ngtc, nnhpres, nh, gc = 0;
    t_grp_tcstat *tcstat;
    t_grpopts    *opts;
    real          ecorr, pcorr, dvdlcorr;
    real          bmass, qmass, reft, kT, dt, ndj, nd;
    tensor        dumpres, dumvir;

    opts    = &(ir->opts); /* just for ease of referencing */
    ngtc    = ir->opts.ngtc;
    nnhpres = state->nnhpres;
    nh      = state->nhchainlength;

    if (ir->eI == eiMD)
    {
        if (bInit)
        {
            snew(MassQ->Qinv, ngtc);
        }
        for (i = 0; (i < ngtc); i++)
        {
            if ((opts->tau_t[i] > 0) && (opts->ref_t[i] > 0))
            {
                MassQ->Qinv[i] = 1.0/(sqr(opts->tau_t[i]/M_2PI)*opts->ref_t[i]);
            }
            else
            {
                MassQ->Qinv[i] = 0.0;
            }
        }
    }
    else if (EI_VV(ir->eI))
    {
        /* Set pressure variables */

        if (bInit)
        {
            if (state->vol0 == 0)
            {
                state->vol0 = det(state->box);
                /* because we start by defining a fixed
                   compressibility, we need the volume at this
                   compressibility to solve the problem. */
            }
        }

        /* units are nm^3 * ns^2 / (nm^3 * bar / kJ/mol) = kJ/mol  */
        /* Consider evaluating eventually if this the right mass to use.  All are correct, some might be more stable  */
        MassQ->Winv = (PRESFAC*trace(ir->compress)*BOLTZ*opts->ref_t[0])/(DIM*state->vol0*sqr(ir->tau_p/M_2PI));
        /* An alternate mass definition, from Tuckerman et al. */
        /* MassQ->Winv = 1.0/(sqr(ir->tau_p/M_2PI)*(opts->nrdf[0]+DIM)*BOLTZ*opts->ref_t[0]); */
        for (d = 0; d < DIM; d++)
        {
            for (n = 0; n < DIM; n++)
            {
                MassQ->Winvm[d][n] = PRESFAC*ir->compress[d][n]/(state->vol0*sqr(ir->tau_p/M_2PI));
                /* not clear this is correct yet for the anisotropic case. Will need to reevaluate
                   before using MTTK for anisotropic states.*/
            }
        }
        /* Allocate space for thermostat variables */
        if (bInit)
        {
            snew(MassQ->Qinv, ngtc*nh);
        }

        /* now, set temperature variables */
        for (i = 0; i < ngtc; i++)
        {
            if ((opts->tau_t[i] > 0) && (opts->ref_t[i] > 0))
            {
                reft = max(0.0, opts->ref_t[i]);
                nd   = opts->nrdf[i];
                kT   = BOLTZ*reft;
                for (j = 0; j < nh; j++)
                {
                    if (j == 0)
                    {
                        ndj = nd;
                    }
                    else
                    {
                        ndj = 1;
                    }
                    MassQ->Qinv[i*nh+j]   = 1.0/(sqr(opts->tau_t[i]/M_2PI)*ndj*kT);
                }
            }
            else
            {
                reft = 0.0;
                for (j = 0; j < nh; j++)
                {
                    MassQ->Qinv[i*nh+j] = 0.0;
                }
            }
        }
    }
}

int **init_npt_vars(t_inputrec *ir, t_state *state, t_extmass *MassQ, gmx_bool bTrotter)
{
    int           n, i, j, d, ntgrp, ngtc, nnhpres, nh, gc = 0;
    t_grp_tcstat *tcstat;
    t_grpopts    *opts;
    real          ecorr, pcorr, dvdlcorr;
    real          bmass, qmass, reft, kT, dt, ndj, nd;
    tensor        dumpres, dumvir;
    int         **trotter_seq;

    opts    = &(ir->opts); /* just for ease of referencing */
    ngtc    = state->ngtc;
    nnhpres = state->nnhpres;
    nh      = state->nhchainlength;

    init_npt_masses(ir, state, MassQ, TRUE);

    /* first, initialize clear all the trotter calls */
    snew(trotter_seq, ettTSEQMAX);
    for (i = 0; i < ettTSEQMAX; i++)
    {
        snew(trotter_seq[i], NTROTTERPARTS);
        for (j = 0; j < NTROTTERPARTS; j++)
        {
            trotter_seq[i][j] = etrtNONE;
        }
        trotter_seq[i][0] = etrtSKIPALL;
    }

    if (!bTrotter)
    {
        /* no trotter calls, so we never use the values in the array.
         * We access them (so we need to define them, but ignore
         * then.*/

        return trotter_seq;
    }

    /* compute the kinetic energy by using the half step velocities or
     * the kinetic energies, depending on the order of the trotter calls */

    if (ir->eI == eiVV)
    {
        if (IR_NPT_TROTTER(ir))
        {
            /* This is the complicated version - there are 4 possible calls, depending on ordering.
               We start with the initial one. */
            /* first, a round that estimates veta. */
            trotter_seq[0][0] = etrtBAROV;

            /* trotter_seq[1] is etrtNHC for 1/2 step velocities - leave zero */

            /* The first half trotter update */
            trotter_seq[2][0] = etrtBAROV;
            trotter_seq[2][1] = etrtNHC;
            trotter_seq[2][2] = etrtBARONHC;

            /* The second half trotter update */
            trotter_seq[3][0] = etrtBARONHC;
            trotter_seq[3][1] = etrtNHC;
            trotter_seq[3][2] = etrtBAROV;

            /* trotter_seq[4] is etrtNHC for second 1/2 step velocities - leave zero */

        }
        else if (IR_NVT_TROTTER(ir))
        {
            /* This is the easy version - there are only two calls, both the same.
               Otherwise, even easier -- no calls  */
            trotter_seq[2][0] = etrtNHC;
            trotter_seq[3][0] = etrtNHC;
        }
        else if (IR_NPH_TROTTER(ir))
        {
            /* This is the complicated version - there are 4 possible calls, depending on ordering.
               We start with the initial one. */
            /* first, a round that estimates veta. */
            trotter_seq[0][0] = etrtBAROV;

            /* trotter_seq[1] is etrtNHC for 1/2 step velocities - leave zero */

            /* The first half trotter update */
            trotter_seq[2][0] = etrtBAROV;
            trotter_seq[2][1] = etrtBARONHC;

            /* The second half trotter update */
            trotter_seq[3][0] = etrtBARONHC;
            trotter_seq[3][1] = etrtBAROV;

            /* trotter_seq[4] is etrtNHC for second 1/2 step velocities - leave zero */
        }
    }
    else if (ir->eI == eiVVAK)
    {
        if (IR_NPT_TROTTER(ir))
        {
            /* This is the complicated version - there are 4 possible calls, depending on ordering.
               We start with the initial one. */
            /* first, a round that estimates veta. */
            trotter_seq[0][0] = etrtBAROV;

            /* The first half trotter update, part 1 -- double update, because it commutes */
            trotter_seq[1][0] = etrtNHC;

            /* The first half trotter update, part 2 */
            trotter_seq[2][0] = etrtBAROV;
            trotter_seq[2][1] = etrtBARONHC;

            /* The second half trotter update, part 1 */
            trotter_seq[3][0] = etrtBARONHC;
            trotter_seq[3][1] = etrtBAROV;

            /* The second half trotter update */
            trotter_seq[4][0] = etrtNHC;
        }
        else if (IR_NVT_TROTTER(ir))
        {
            /* This is the easy version - there is only one call, both the same.
               Otherwise, even easier -- no calls  */
            trotter_seq[1][0] = etrtNHC;
            trotter_seq[4][0] = etrtNHC;
        }
        else if (IR_NPH_TROTTER(ir))
        {
            /* This is the complicated version - there are 4 possible calls, depending on ordering.
               We start with the initial one. */
            /* first, a round that estimates veta. */
            trotter_seq[0][0] = etrtBAROV;

            /* The first half trotter update, part 1 -- leave zero */
            trotter_seq[1][0] = etrtNHC;

            /* The first half trotter update, part 2 */
            trotter_seq[2][0] = etrtBAROV;
            trotter_seq[2][1] = etrtBARONHC;

            /* The second half trotter update, part 1 */
            trotter_seq[3][0] = etrtBARONHC;
            trotter_seq[3][1] = etrtBAROV;

            /* The second half trotter update -- blank for now */
        }
    }

    switch (ir->epct)
    {
        case epctISOTROPIC:
        default:
            bmass = DIM*DIM; /* recommended mass parameters for isotropic barostat */
    }

    snew(MassQ->QPinv, nnhpres*opts->nhchainlength);

    /* barostat temperature */
    if ((ir->tau_p > 0) && (opts->ref_t[0] > 0))
    {
        reft = max(0.0, opts->ref_t[0]);
        kT   = BOLTZ*reft;
        for (i = 0; i < nnhpres; i++)
        {
            for (j = 0; j < nh; j++)
            {
                if (j == 0)
                {
                    qmass = bmass;
                }
                else
                {
                    qmass = 1;
                }
                MassQ->QPinv[i*opts->nhchainlength+j]   = 1.0/(sqr(opts->tau_t[0]/M_2PI)*qmass*kT);
            }
        }
    }
    else
    {
        for (i = 0; i < nnhpres; i++)
        {
            for (j = 0; j < nh; j++)
            {
                MassQ->QPinv[i*nh+j] = 0.0;
            }
        }
    }
    return trotter_seq;
}

real NPT_energy(t_inputrec *ir, t_state *state, t_extmass *MassQ)
{
    int     i, j, nd, ndj, bmass, qmass, ngtcall;
    real    ener_npt, reft, eta, kT, tau;
    double *ivxi, *ixi;
    double *iQinv;
    real    vol, dbaro, W, Q;
    int     nh = state->nhchainlength;

    ener_npt = 0;

    /* now we compute the contribution of the pressure to the conserved quantity*/

    if (ir->epc == epcMTTK)
    {
        /* find the volume, and the kinetic energy of the volume */

        switch (ir->epct)
        {

            case epctISOTROPIC:
                /* contribution from the pressure momenenta */
                ener_npt += 0.5*sqr(state->veta)/MassQ->Winv;

                /* contribution from the PV term */
                vol       = det(state->box);
                ener_npt += vol*trace(ir->ref_p)/(DIM*PRESFAC);

                break;
            case epctANISOTROPIC:

                break;

            case epctSURFACETENSION:

                break;
            case epctSEMIISOTROPIC:

                break;
            default:
                break;
        }
    }

    if (IR_NPT_TROTTER(ir) || IR_NPH_TROTTER(ir))
    {
        /* add the energy from the barostat thermostat chain */
        for (i = 0; i < state->nnhpres; i++)
        {

            /* note -- assumes only one degree of freedom that is thermostatted in barostat */
            ivxi  = &state->nhpres_vxi[i*nh];
            ixi   = &state->nhpres_xi[i*nh];
            iQinv = &(MassQ->QPinv[i*nh]);
            reft  = max(ir->opts.ref_t[0], 0); /* using 'System' temperature */
            kT    = BOLTZ * reft;

            for (j = 0; j < nh; j++)
            {
                if (iQinv[j] > 0)
                {
                    ener_npt += 0.5*sqr(ivxi[j])/iQinv[j];
                    /* contribution from the thermal variable of the NH chain */
                    ener_npt += ixi[j]*kT;
                }
                if (debug)
                {
                    fprintf(debug, "P-T-group: %10d Chain %4d ThermV: %15.8f ThermX: %15.8f", i, j, ivxi[j], ixi[j]);
                }
            }
        }
    }

    if (ir->etc)
    {
        for (i = 0; i < ir->opts.ngtc; i++)
        {
            ixi   = &state->nosehoover_xi[i*nh];
            ivxi  = &state->nosehoover_vxi[i*nh];
            iQinv = &(MassQ->Qinv[i*nh]);

            nd   = ir->opts.nrdf[i];
            reft = max(ir->opts.ref_t[i], 0);
            kT   = BOLTZ * reft;

            if (nd > 0)
            {
                if (IR_NVT_TROTTER(ir))
                {
                    /* contribution from the thermal momenta of the NH chain */
                    for (j = 0; j < nh; j++)
                    {
                        if (iQinv[j] > 0)
                        {
                            ener_npt += 0.5*sqr(ivxi[j])/iQinv[j];
                            /* contribution from the thermal variable of the NH chain */
                            if (j == 0)
                            {
                                ndj = nd;
                            }
                            else
                            {
                                ndj = 1;
                            }
                            ener_npt += ndj*ixi[j]*kT;
                        }
                    }
                }
                else  /* Other non Trotter temperature NH control  -- no chains yet. */
                {
                    ener_npt += 0.5*BOLTZ*nd*sqr(ivxi[0])/iQinv[0];
                    ener_npt += nd*ixi[0]*kT;
                }
            }
        }
    }
    return ener_npt;
}

static real vrescale_gamdev(int ia, gmx_rng_t rng)
/* Gamma distribution, adapted from numerical recipes */
{
    int  j;
    real am, e, s, v1, v2, x, y;

    if (ia < 6)
    {
        do
        {
            x = 1.0;
            for (j = 1; j <= ia; j++)
            {
                x *= gmx_rng_uniform_real(rng);
            }
        }
        while (x == 0);
        x = -log(x);
    }
    else
    {
        do
        {
            do
            {
                do
                {
                    v1 = gmx_rng_uniform_real(rng);
                    v2 = 2.0*gmx_rng_uniform_real(rng)-1.0;
                }
                while (v1*v1 + v2*v2 > 1.0 ||
                       v1*v1*GMX_REAL_MAX < 3.0*ia);
                /* The last check above ensures that both x (3.0 > 2.0 in s)
                 * and the pre-factor for e do not go out of range.
                 */
                y  = v2/v1;
                am = ia - 1;
                s  = sqrt(2.0*am + 1.0);
                x  = s*y + am;
            }
            while (x <= 0.0);
            e = (1.0 + y*y)*exp(am*log(x/am) - s*y);
        }
        while (gmx_rng_uniform_real(rng) > e);
    }

    return x;
}

static real vrescale_sumnoises(int nn, gmx_rng_t rng)
{
/*
 * Returns the sum of n independent gaussian noises squared
 * (i.e. equivalent to summing the square of the return values
 * of nn calls to gmx_rng_gaussian_real).xs
 */
    real rr;

    if (nn == 0)
    {
        return 0.0;
    }
    else if (nn == 1)
    {
        rr = gmx_rng_gaussian_real(rng);
        return rr*rr;
    }
    else if (nn % 2 == 0)
    {
        return 2.0*vrescale_gamdev(nn/2, rng);
    }
    else
    {
        rr = gmx_rng_gaussian_real(rng);
        return 2.0*vrescale_gamdev((nn-1)/2, rng) + rr*rr;
    }
}

static real vrescale_resamplekin(real kk, real sigma, int ndeg, real taut,
                                 gmx_rng_t rng)
{
/*
 * Generates a new value for the kinetic energy,
 * according to Bussi et al JCP (2007), Eq. (A7)
 * kk:    present value of the kinetic energy of the atoms to be thermalized (in arbitrary units)
 * sigma: target average value of the kinetic energy (ndeg k_b T/2)  (in the same units as kk)
 * ndeg:  number of degrees of freedom of the atoms to be thermalized
 * taut:  relaxation time of the thermostat, in units of 'how often this routine is called'
 */
    real factor, rr;

    if (taut > 0.1)
    {
        factor = exp(-1.0/taut);
    }
    else
    {
        factor = 0.0;
    }
    rr = gmx_rng_gaussian_real(rng);
    return
        kk +
        (1.0 - factor)*(sigma*(vrescale_sumnoises(ndeg-1, rng) + rr*rr)/ndeg - kk) +
        2.0*rr*sqrt(kk*sigma/ndeg*(1.0 - factor)*factor);
}

void vrescale_tcoupl(t_inputrec *ir, gmx_ekindata_t *ekind, real dt,
                     double therm_integral[], gmx_rng_t rng)
{
    t_grpopts *opts;
    int        i;
    real       Ek, Ek_ref1, Ek_ref, Ek_new;

    opts = &ir->opts;

    for (i = 0; (i < opts->ngtc); i++)
    {
        if (ir->eI == eiVV)
        {
            Ek = trace(ekind->tcstat[i].ekinf);
        }
        else
        {
            Ek = trace(ekind->tcstat[i].ekinh);
        }

        if (opts->tau_t[i] >= 0 && opts->nrdf[i] > 0 && Ek > 0)
        {
            Ek_ref1 = 0.5*opts->ref_t[i]*BOLTZ;
            Ek_ref  = Ek_ref1*opts->nrdf[i];

            Ek_new  = vrescale_resamplekin(Ek, Ek_ref, opts->nrdf[i],
                                           opts->tau_t[i]/dt, rng);

            /* Analytically Ek_new>=0, but we check for rounding errors */
            if (Ek_new <= 0)
            {
                ekind->tcstat[i].lambda = 0.0;
            }
            else
            {
                ekind->tcstat[i].lambda = sqrt(Ek_new/Ek);
            }

            therm_integral[i] -= Ek_new - Ek;

            if (debug)
            {
                fprintf(debug, "TC: group %d: Ekr %g, Ek %g, Ek_new %g, Lambda: %g\n",
                        i, Ek_ref, Ek, Ek_new, ekind->tcstat[i].lambda);
            }
        }
        else
        {
            ekind->tcstat[i].lambda = 1.0;
        }
    }
}

real vrescale_energy(t_grpopts *opts, double therm_integral[])
{
    int  i;
    real ener;

    ener = 0;
    for (i = 0; i < opts->ngtc; i++)
    {
        ener += therm_integral[i];
    }

    return ener;
}

void rescale_velocities(gmx_ekindata_t *ekind, t_mdatoms *mdatoms,
                        int start, int end, rvec v[])
{
    t_grp_acc      *gstat;
    t_grp_tcstat   *tcstat;
    unsigned short *cACC, *cTC;
    int             ga, gt, n, d;
    real            lg;
    rvec            vrel;

    tcstat = ekind->tcstat;
    cTC    = mdatoms->cTC;

    if (ekind->bNEMD)
    {
        gstat  = ekind->grpstat;
        cACC   = mdatoms->cACC;

        ga = 0;
        gt = 0;
        for (n = start; n < end; n++)
        {
            if (cACC)
            {
                ga   = cACC[n];
            }
            if (cTC)
            {
                gt   = cTC[n];
            }
            /* Only scale the velocity component relative to the COM velocity */
            rvec_sub(v[n], gstat[ga].u, vrel);
            lg = tcstat[gt].lambda;
            for (d = 0; d < DIM; d++)
            {
                v[n][d] = gstat[ga].u[d] + lg*vrel[d];
            }
        }
    }
    else
    {
        gt = 0;
        for (n = start; n < end; n++)
        {
            if (cTC)
            {
                gt   = cTC[n];
            }
            lg = tcstat[gt].lambda;
            for (d = 0; d < DIM; d++)
            {
                v[n][d] *= lg;
            }
        }
    }
}


/* set target temperatures if we are annealing */
void update_annealing_target_temp(t_grpopts *opts, real t)
{
    int  i, j, n, npoints;
    real pert, thist = 0, x;

    for (i = 0; i < opts->ngtc; i++)
    {
        npoints = opts->anneal_npoints[i];
        switch (opts->annealing[i])
        {
            case eannNO:
                continue;
            case  eannPERIODIC:
                /* calculate time modulo the period */
                pert  = opts->anneal_time[i][npoints-1];
                n     = t / pert;
                thist = t - n*pert; /* modulo time */
                /* Make sure rounding didn't get us outside the interval */
                if (fabs(thist-pert) < GMX_REAL_EPS*100)
                {
                    thist = 0;
                }
                break;
            case eannSINGLE:
                thist = t;
                break;
            default:
                gmx_fatal(FARGS, "Death horror in update_annealing_target_temp (i=%d/%d npoints=%d)", i, opts->ngtc, npoints);
        }
        /* We are doing annealing for this group if we got here,
         * and we have the (relative) time as thist.
         * calculate target temp */
        j = 0;
        while ((j < npoints-1) && (thist > (opts->anneal_time[i][j+1])))
        {
            j++;
        }
        if (j < npoints-1)
        {
            /* Found our position between points j and j+1.
             * Interpolate: x is the amount from j+1, (1-x) from point j
             * First treat possible jumps in temperature as a special case.
             */
            if ((opts->anneal_time[i][j+1]-opts->anneal_time[i][j]) < GMX_REAL_EPS*100)
            {
                opts->ref_t[i] = opts->anneal_temp[i][j+1];
            }
            else
            {
                x = ((thist-opts->anneal_time[i][j])/
                     (opts->anneal_time[i][j+1]-opts->anneal_time[i][j]));
                opts->ref_t[i] = x*opts->anneal_temp[i][j+1]+(1-x)*opts->anneal_temp[i][j];
            }
        }
        else
        {
            opts->ref_t[i] = opts->anneal_temp[i][npoints-1];
        }
    }
}