minimize.cpp.preplumed

                           const MdrunOptions &mdrunOptions,
                           gmx_vsite_t *vsite, gmx_constr_t constr,
                           gmx::IMDOutputProvider *outputProvider,
                           t_inputrec *inputrec,
                           gmx_mtop_t *top_global, t_fcdata *fcd,
                           t_state *state_global,
                           gmx::MDAtoms *mdAtoms,
                           t_nrnb *nrnb, gmx_wallcycle_t wcycle,
                           gmx_edsam_t ed,
                           t_forcerec *fr,
                           const ReplicaExchangeParameters &replExParams,
                           gmx_membed_t gmx_unused *membed,
                           gmx_walltime_accounting_t walltime_accounting)
 */
double do_cg(FILE *fplog, t_commrec *cr, const gmx::MDLogger gmx_unused &mdlog,
             int nfile, const t_filenm fnm[],
             const gmx_output_env_t gmx_unused *oenv,
             const MdrunOptions &mdrunOptions,
             gmx_vsite_t *vsite, gmx_constr_t constr,
             gmx::IMDOutputProvider *outputProvider,
             t_inputrec *inputrec,
             gmx_mtop_t *top_global, t_fcdata *fcd,
             t_state *state_global,
             ObservablesHistory *observablesHistory,
             gmx::MDAtoms *mdAtoms,
             t_nrnb *nrnb, gmx_wallcycle_t wcycle,
             t_forcerec *fr,
             const ReplicaExchangeParameters gmx_unused &replExParams,
             gmx_membed_t gmx_unused *membed,
             gmx_walltime_accounting_t walltime_accounting)
{
    const char       *CG = "Polak-Ribiere Conjugate Gradients";

    gmx_localtop_t   *top;
    gmx_enerdata_t   *enerd;
    gmx_global_stat_t gstat;
    t_graph          *graph;
    double            tmp, minstep;
    real              stepsize;
    real              a, b, c, beta = 0.0;
    real              epot_repl = 0;
    real              pnorm;
    t_mdebin         *mdebin;
    gmx_bool          converged, foundlower;
    rvec              mu_tot;
    gmx_bool          do_log = FALSE, do_ene = FALSE, do_x, do_f;
    tensor            vir, pres;
    int               number_steps, neval = 0, nstcg = inputrec->nstcgsteep;
    gmx_mdoutf_t      outf;
    int               m, step, nminstep;
    auto              mdatoms = mdAtoms->mdatoms();

    step = 0;

    if (MASTER(cr))
    {
        // In CG, the state is extended with a search direction
        state_global->flags |= (1<<estCGP);

        // Ensure the extra per-atom state array gets allocated
        state_change_natoms(state_global, state_global->natoms);

        // Initialize the search direction to zero
        for (RVec &cg_p : state_global->cg_p)
        {
            cg_p = { 0, 0, 0 };
        }
    }

    /* Create 4 states on the stack and extract pointers that we will swap */
    em_state_t  s0 {}, s1 {}, s2 {}, s3 {};
    em_state_t *s_min = &s0;
    em_state_t *s_a   = &s1;
    em_state_t *s_b   = &s2;
    em_state_t *s_c   = &s3;

    /* Init em and store the local state in s_min */
    init_em(fplog, CG, cr, outputProvider, inputrec, mdrunOptions,
            state_global, top_global, s_min, &top,
            nrnb, mu_tot, fr, &enerd, &graph, mdAtoms, &gstat,
            vsite, constr, nullptr,
            nfile, fnm, &outf, &mdebin, wcycle);

    /* Print to log file */
    print_em_start(fplog, cr, walltime_accounting, wcycle, CG);

    /* Max number of steps */
    number_steps = inputrec->nsteps;

    if (MASTER(cr))
    {
        sp_header(stderr, CG, inputrec->em_tol, number_steps);
    }
    if (fplog)
    {
        sp_header(fplog, CG, inputrec->em_tol, number_steps);
    }

    /* Call the force routine and some auxiliary (neighboursearching etc.) */
    /* do_force always puts the charge groups in the box and shifts again
     * We do not unshift, so molecules are always whole in congrad.c
     */
    evaluate_energy(fplog, cr,
                    top_global, s_min, top,
                    inputrec, nrnb, wcycle, gstat,
                    vsite, constr, fcd, graph, mdAtoms, fr,
                    mu_tot, enerd, vir, pres, -1, TRUE);
    where();

    if (MASTER(cr))
    {
        /* Copy stuff to the energy bin for easy printing etc. */
        upd_mdebin(mdebin, FALSE, FALSE, (double)step,
                   mdatoms->tmass, enerd, &s_min->s, inputrec->fepvals, inputrec->expandedvals, s_min->s.box,
                   nullptr, nullptr, vir, pres, nullptr, mu_tot, constr);

        print_ebin_header(fplog, step, step);
        print_ebin(mdoutf_get_fp_ene(outf), TRUE, FALSE, FALSE, fplog, step, step, eprNORMAL,
                   mdebin, fcd, &(top_global->groups), &(inputrec->opts), nullptr);
    }
    where();

    /* Estimate/guess the initial stepsize */
    stepsize = inputrec->em_stepsize/s_min->fnorm;

    if (MASTER(cr))
    {
        double sqrtNumAtoms = sqrt(static_cast<double>(state_global->natoms));
        fprintf(stderr, "   F-max             = %12.5e on atom %d\n",
                s_min->fmax, s_min->a_fmax+1);
        fprintf(stderr, "   F-Norm            = %12.5e\n",
                s_min->fnorm/sqrtNumAtoms);
        fprintf(stderr, "\n");
        /* and copy to the log file too... */
        fprintf(fplog, "   F-max             = %12.5e on atom %d\n",
                s_min->fmax, s_min->a_fmax+1);
        fprintf(fplog, "   F-Norm            = %12.5e\n",
                s_min->fnorm/sqrtNumAtoms);
        fprintf(fplog, "\n");
    }
    /* Start the loop over CG steps.
     * Each successful step is counted, and we continue until
     * we either converge or reach the max number of steps.
     */
    converged = FALSE;
    for (step = 0; (number_steps < 0 || step <= number_steps) && !converged; step++)
    {

        /* start taking steps in a new direction
         * First time we enter the routine, beta=0, and the direction is
         * simply the negative gradient.
         */

        /* Calculate the new direction in p, and the gradient in this direction, gpa */
        rvec       *pm  = as_rvec_array(s_min->s.cg_p.data());
        const rvec *sfm = as_rvec_array(s_min->f.data());
        double      gpa = 0;
        int         gf  = 0;
        for (int i = 0; i < mdatoms->homenr; i++)
        {
            if (mdatoms->cFREEZE)
            {
                gf = mdatoms->cFREEZE[i];
            }
            for (m = 0; m < DIM; m++)
            {
                if (!inputrec->opts.nFreeze[gf][m])
                {
                    pm[i][m] = sfm[i][m] + beta*pm[i][m];
                    gpa     -= pm[i][m]*sfm[i][m];
                    /* f is negative gradient, thus the sign */
                }
                else
                {
                    pm[i][m] = 0;
                }
            }
        }

        /* Sum the gradient along the line across CPUs */
        if (PAR(cr))
        {
            gmx_sumd(1, &gpa, cr);
        }

        /* Calculate the norm of the search vector */
        get_f_norm_max(cr, &(inputrec->opts), mdatoms, pm, &pnorm, nullptr, nullptr);

        /* Just in case stepsize reaches zero due to numerical precision... */
        if (stepsize <= 0)
        {
            stepsize = inputrec->em_stepsize/pnorm;
        }

        /*
         * Double check the value of the derivative in the search direction.
         * If it is positive it must be due to the old information in the
         * CG formula, so just remove that and start over with beta=0.
         * This corresponds to a steepest descent step.
         */
        if (gpa > 0)
        {
            beta = 0;
            step--;   /* Don't count this step since we are restarting */
            continue; /* Go back to the beginning of the big for-loop */
        }

        /* Calculate minimum allowed stepsize, before the average (norm)
         * relative change in coordinate is smaller than precision
         */
        minstep = 0;
        for (int i = 0; i < mdatoms->homenr; i++)
        {
            for (m = 0; m < DIM; m++)
            {
                tmp = fabs(s_min->s.x[i][m]);
                if (tmp < 1.0)
                {
                    tmp = 1.0;
                }
                tmp      = pm[i][m]/tmp;
                minstep += tmp*tmp;
            }
        }
        /* Add up from all CPUs */
        if (PAR(cr))
        {
            gmx_sumd(1, &minstep, cr);
        }

        minstep = GMX_REAL_EPS/sqrt(minstep/(3*top_global->natoms));

        if (stepsize < minstep)
        {
            converged = TRUE;
            break;
        }

        /* Write coordinates if necessary */
        do_x = do_per_step(step, inputrec->nstxout);
        do_f = do_per_step(step, inputrec->nstfout);

        write_em_traj(fplog, cr, outf, do_x, do_f, nullptr,
                      top_global, inputrec, step,
                      s_min, state_global, observablesHistory);

        /* Take a step downhill.
         * In theory, we should minimize the function along this direction.
         * That is quite possible, but it turns out to take 5-10 function evaluations
         * for each line. However, we dont really need to find the exact minimum -
         * it is much better to start a new CG step in a modified direction as soon
         * as we are close to it. This will save a lot of energy evaluations.
         *
         * In practice, we just try to take a single step.
         * If it worked (i.e. lowered the energy), we increase the stepsize but
         * the continue straight to the next CG step without trying to find any minimum.
         * If it didn't work (higher energy), there must be a minimum somewhere between
         * the old position and the new one.
         *
         * Due to the finite numerical accuracy, it turns out that it is a good idea
         * to even accept a SMALL increase in energy, if the derivative is still downhill.
         * This leads to lower final energies in the tests I've done. / Erik
         */
        s_a->epot = s_min->epot;
        a         = 0.0;
        c         = a + stepsize; /* reference position along line is zero */

        if (DOMAINDECOMP(cr) && s_min->s.ddp_count < cr->dd->ddp_count)
        {
            em_dd_partition_system(fplog, step, cr, top_global, inputrec,
                                   s_min, top, mdAtoms, fr, vsite, constr,
                                   nrnb, wcycle);
        }

        /* Take a trial step (new coords in s_c) */
        do_em_step(cr, inputrec, mdatoms, fr->bMolPBC, s_min, c, &s_min->s.cg_p, s_c,
                   constr, top, nrnb, wcycle, -1);

        neval++;
        /* Calculate energy for the trial step */
        evaluate_energy(fplog, cr,
                        top_global, s_c, top,
                        inputrec, nrnb, wcycle, gstat,
                        vsite, constr, fcd, graph, mdAtoms, fr,
                        mu_tot, enerd, vir, pres, -1, FALSE);

        /* Calc derivative along line */
        const rvec *pc  = as_rvec_array(s_c->s.cg_p.data());
        const rvec *sfc = as_rvec_array(s_c->f.data());
        double      gpc = 0;
        for (int i = 0; i < mdatoms->homenr; i++)
        {
            for (m = 0; m < DIM; m++)
            {
                gpc -= pc[i][m]*sfc[i][m]; /* f is negative gradient, thus the sign */
            }
        }
        /* Sum the gradient along the line across CPUs */
        if (PAR(cr))
        {
            gmx_sumd(1, &gpc, cr);
        }

        /* This is the max amount of increase in energy we tolerate */
        tmp = sqrt(GMX_REAL_EPS)*fabs(s_a->epot);

        /* Accept the step if the energy is lower, or if it is not significantly higher
         * and the line derivative is still negative.
         */
        if (s_c->epot < s_a->epot || (gpc < 0 && s_c->epot < (s_a->epot + tmp)))
        {
            foundlower = TRUE;
            /* Great, we found a better energy. Increase step for next iteration
             * if we are still going down, decrease it otherwise
             */
            if (gpc < 0)
            {
                stepsize *= 1.618034; /* The golden section */
            }
            else
            {
                stepsize *= 0.618034; /* 1/golden section */
            }
        }
        else
        {
            /* New energy is the same or higher. We will have to do some work
             * to find a smaller value in the interval. Take smaller step next time!
             */
            foundlower = FALSE;
            stepsize  *= 0.618034;
        }




        /* OK, if we didn't find a lower value we will have to locate one now - there must
         * be one in the interval [a=0,c].
         * The same thing is valid here, though: Don't spend dozens of iterations to find
         * the line minimum. We try to interpolate based on the derivative at the endpoints,
         * and only continue until we find a lower value. In most cases this means 1-2 iterations.
         *
         * I also have a safeguard for potentially really pathological functions so we never
         * take more than 20 steps before we give up ...
         *
         * If we already found a lower value we just skip this step and continue to the update.
         */
        double gpb;
        if (!foundlower)
        {
            nminstep = 0;

            do
            {
                /* Select a new trial point.
                 * If the derivatives at points a & c have different sign we interpolate to zero,
                 * otherwise just do a bisection.
                 */
                if (gpa < 0 && gpc > 0)
                {
                    b = a + gpa*(a-c)/(gpc-gpa);
                }
                else
                {
                    b = 0.5*(a+c);
                }

                /* safeguard if interpolation close to machine accuracy causes errors:
                 * never go outside the interval
                 */
                if (b <= a || b >= c)
                {
                    b = 0.5*(a+c);
                }

                if (DOMAINDECOMP(cr) && s_min->s.ddp_count != cr->dd->ddp_count)
                {
                    /* Reload the old state */
                    em_dd_partition_system(fplog, -1, cr, top_global, inputrec,
                                           s_min, top, mdAtoms, fr, vsite, constr,
                                           nrnb, wcycle);
                }

                /* Take a trial step to this new point - new coords in s_b */
                do_em_step(cr, inputrec, mdatoms, fr->bMolPBC, s_min, b, &s_min->s.cg_p, s_b,
                           constr, top, nrnb, wcycle, -1);

                neval++;
                /* Calculate energy for the trial step */
                evaluate_energy(fplog, cr,
                                top_global, s_b, top,
                                inputrec, nrnb, wcycle, gstat,
                                vsite, constr, fcd, graph, mdAtoms, fr,
                                mu_tot, enerd, vir, pres, -1, FALSE);

                /* p does not change within a step, but since the domain decomposition
                 * might change, we have to use cg_p of s_b here.
                 */
                const rvec *pb  = as_rvec_array(s_b->s.cg_p.data());
                const rvec *sfb = as_rvec_array(s_b->f.data());
                gpb             = 0;
                for (int i = 0; i < mdatoms->homenr; i++)
                {
                    for (m = 0; m < DIM; m++)
                    {
                        gpb -= pb[i][m]*sfb[i][m]; /* f is negative gradient, thus the sign */
                    }
                }
                /* Sum the gradient along the line across CPUs */
                if (PAR(cr))
                {
                    gmx_sumd(1, &gpb, cr);
                }

                if (debug)
                {
                    fprintf(debug, "CGE: EpotA %f EpotB %f EpotC %f gpb %f\n",
                            s_a->epot, s_b->epot, s_c->epot, gpb);
                }

                epot_repl = s_b->epot;

                /* Keep one of the intervals based on the value of the derivative at the new point */
                if (gpb > 0)
                {
                    /* Replace c endpoint with b */
                    swap_em_state(&s_b, &s_c);
                    c   = b;
                    gpc = gpb;
                }
                else
                {
                    /* Replace a endpoint with b */
                    swap_em_state(&s_b, &s_a);
                    a   = b;
                    gpa = gpb;
                }

                /*
                 * Stop search as soon as we find a value smaller than the endpoints.
                 * Never run more than 20 steps, no matter what.
                 */
                nminstep++;
            }
            while ((epot_repl > s_a->epot || epot_repl > s_c->epot) &&
                   (nminstep < 20));

            if (fabs(epot_repl - s_min->epot) < fabs(s_min->epot)*GMX_REAL_EPS ||
                nminstep >= 20)
            {
                /* OK. We couldn't find a significantly lower energy.
                 * If beta==0 this was steepest descent, and then we give up.
                 * If not, set beta=0 and restart with steepest descent before quitting.
                 */
                if (beta == 0.0)
                {
                    /* Converged */
                    converged = TRUE;
                    break;
                }
                else
                {
                    /* Reset memory before giving up */
                    beta = 0.0;
                    continue;
                }
            }

            /* Select min energy state of A & C, put the best in B.
             */
            if (s_c->epot < s_a->epot)
            {
                if (debug)
                {
                    fprintf(debug, "CGE: C (%f) is lower than A (%f), moving C to B\n",
                            s_c->epot, s_a->epot);
                }
                swap_em_state(&s_b, &s_c);
                gpb = gpc;
            }
            else
            {
                if (debug)
                {
                    fprintf(debug, "CGE: A (%f) is lower than C (%f), moving A to B\n",
                            s_a->epot, s_c->epot);
                }
                swap_em_state(&s_b, &s_a);
                gpb = gpa;
            }

        }
        else
        {
            if (debug)
            {
                fprintf(debug, "CGE: Found a lower energy %f, moving C to B\n",
                        s_c->epot);
            }
            swap_em_state(&s_b, &s_c);
            gpb = gpc;
        }

        /* new search direction */
        /* beta = 0 means forget all memory and restart with steepest descents. */
        if (nstcg && ((step % nstcg) == 0))
        {
            beta = 0.0;
        }
        else
        {
            /* s_min->fnorm cannot be zero, because then we would have converged
             * and broken out.
             */

            /* Polak-Ribiere update.
             * Change to fnorm2/fnorm2_old for Fletcher-Reeves
             */
            beta = pr_beta(cr, &inputrec->opts, mdatoms, top_global, s_min, s_b);
        }
        /* Limit beta to prevent oscillations */
        if (fabs(beta) > 5.0)
        {
            beta = 0.0;
        }


        /* update positions */
        swap_em_state(&s_min, &s_b);
        gpa = gpb;

        /* Print it if necessary */
        if (MASTER(cr))
        {
            if (mdrunOptions.verbose)
            {
                double sqrtNumAtoms = sqrt(static_cast<double>(state_global->natoms));
                fprintf(stderr, "\rStep %d, Epot=%12.6e, Fnorm=%9.3e, Fmax=%9.3e (atom %d)\n",
                        step, s_min->epot, s_min->fnorm/sqrtNumAtoms,
                        s_min->fmax, s_min->a_fmax+1);
                fflush(stderr);
            }
            /* Store the new (lower) energies */
            upd_mdebin(mdebin, FALSE, FALSE, (double)step,
                       mdatoms->tmass, enerd, &s_min->s, inputrec->fepvals, inputrec->expandedvals, s_min->s.box,
                       nullptr, nullptr, vir, pres, nullptr, mu_tot, constr);

            do_log = do_per_step(step, inputrec->nstlog);
            do_ene = do_per_step(step, inputrec->nstenergy);

            /* Prepare IMD energy record, if bIMD is TRUE. */
            IMD_fill_energy_record(inputrec->bIMD, inputrec->imd, enerd, step, TRUE);

            if (do_log)
            {
                print_ebin_header(fplog, step, step);
            }
            print_ebin(mdoutf_get_fp_ene(outf), do_ene, FALSE, FALSE,
                       do_log ? fplog : nullptr, step, step, eprNORMAL,
                       mdebin, fcd, &(top_global->groups), &(inputrec->opts), nullptr);
        }

        /* Send energies and positions to the IMD client if bIMD is TRUE. */
        if (MASTER(cr) && do_IMD(inputrec->bIMD, step, cr, TRUE, state_global->box, as_rvec_array(state_global->x.data()), inputrec, 0, wcycle))
        {
            IMD_send_positions(inputrec->imd);
        }

        /* Stop when the maximum force lies below tolerance.
         * If we have reached machine precision, converged is already set to true.
         */
        converged = converged || (s_min->fmax < inputrec->em_tol);

    }   /* End of the loop */

    /* IMD cleanup, if bIMD is TRUE. */
    IMD_finalize(inputrec->bIMD, inputrec->imd);

    if (converged)
    {
        step--; /* we never took that last step in this case */

    }
    if (s_min->fmax > inputrec->em_tol)
    {
        if (MASTER(cr))
        {
            warn_step(stderr, inputrec->em_tol, step-1 == number_steps, FALSE);
            warn_step(fplog, inputrec->em_tol, step-1 == number_steps, FALSE);
        }
        converged = FALSE;
    }

    if (MASTER(cr))
    {
        /* If we printed energy and/or logfile last step (which was the last step)
         * we don't have to do it again, but otherwise print the final values.
         */
        if (!do_log)
        {
            /* Write final value to log since we didn't do anything the last step */
            print_ebin_header(fplog, step, step);
        }
        if (!do_ene || !do_log)
        {
            /* Write final energy file entries */
            print_ebin(mdoutf_get_fp_ene(outf), !do_ene, FALSE, FALSE,
                       !do_log ? fplog : nullptr, step, step, eprNORMAL,
                       mdebin, fcd, &(top_global->groups), &(inputrec->opts), nullptr);
        }
    }

    /* Print some stuff... */
    if (MASTER(cr))
    {
        fprintf(stderr, "\nwriting lowest energy coordinates.\n");
    }

    /* IMPORTANT!
     * For accurate normal mode calculation it is imperative that we
     * store the last conformation into the full precision binary trajectory.
     *
     * However, we should only do it if we did NOT already write this step
     * above (which we did if do_x or do_f was true).
     */
    /* Note that with 0 < nstfout != nstxout we can end up with two frames
     * in the trajectory with the same step number.
     */
    do_x = !do_per_step(step, inputrec->nstxout);
    do_f = (inputrec->nstfout > 0 && !do_per_step(step, inputrec->nstfout));

    write_em_traj(fplog, cr, outf, do_x, do_f, ftp2fn(efSTO, nfile, fnm),
                  top_global, inputrec, step,
                  s_min, state_global, observablesHistory);


    if (MASTER(cr))
    {
        double sqrtNumAtoms = sqrt(static_cast<double>(state_global->natoms));
        print_converged(stderr, CG, inputrec->em_tol, step, converged, number_steps,
                        s_min, sqrtNumAtoms);
        print_converged(fplog, CG, inputrec->em_tol, step, converged, number_steps,
                        s_min, sqrtNumAtoms);

        fprintf(fplog, "\nPerformed %d energy evaluations in total.\n", neval);
    }

    finish_em(cr, outf, walltime_accounting, wcycle);

    /* To print the actual number of steps we needed somewhere */
    walltime_accounting_set_nsteps_done(walltime_accounting, step);

    return 0;
}   /* That's all folks */


/*! \brief Do L-BFGS conjugate gradients minimization
    \copydoc integrator_t(FILE *fplog, t_commrec *cr, const gmx::MDLogger &mdlog,
                          int nfile, const t_filenm fnm[],
                          const gmx_output_env_t *oenv,
                          const MdrunOptions &mdrunOptions,
                          gmx_vsite_t *vsite, gmx_constr_t constr,
                          gmx::IMDOutputProvider *outputProvider,
                          t_inputrec *inputrec,
                          gmx_mtop_t *top_global, t_fcdata *fcd,
                          t_state *state_global,
                          gmx::MDAtoms *mdAtoms,
                          t_nrnb *nrnb, gmx_wallcycle_t wcycle,
                          gmx_edsam_t ed,
                          t_forcerec *fr,
                          const ReplicaExchangeParameters &replExParams,
                          gmx_membed_t gmx_unused *membed,
                          gmx_walltime_accounting_t walltime_accounting)
 */
double do_lbfgs(FILE *fplog, t_commrec *cr, const gmx::MDLogger gmx_unused &mdlog,
                int nfile, const t_filenm fnm[],
                const gmx_output_env_t gmx_unused *oenv,
                const MdrunOptions &mdrunOptions,
                gmx_vsite_t *vsite, gmx_constr_t constr,
                gmx::IMDOutputProvider *outputProvider,
                t_inputrec *inputrec,
                gmx_mtop_t *top_global, t_fcdata *fcd,
                t_state *state_global,
                ObservablesHistory *observablesHistory,
                gmx::MDAtoms *mdAtoms,
                t_nrnb *nrnb, gmx_wallcycle_t wcycle,
                t_forcerec *fr,
                const ReplicaExchangeParameters gmx_unused &replExParams,
                gmx_membed_t gmx_unused *membed,
                gmx_walltime_accounting_t walltime_accounting)
{
    static const char *LBFGS = "Low-Memory BFGS Minimizer";
    em_state_t         ems;
    gmx_localtop_t    *top;
    gmx_enerdata_t    *enerd;
    gmx_global_stat_t  gstat;
    t_graph           *graph;
    int                ncorr, nmaxcorr, point, cp, neval, nminstep;
    double             stepsize, step_taken, gpa, gpb, gpc, tmp, minstep;
    real              *rho, *alpha, *p, *s, **dx, **dg;
    real               a, b, c, maxdelta, delta;
    real               diag, Epot0;
    real               dgdx, dgdg, sq, yr, beta;
    t_mdebin          *mdebin;
    gmx_bool           converged;
    rvec               mu_tot;
    gmx_bool           do_log, do_ene, do_x, do_f, foundlower, *frozen;
    tensor             vir, pres;
    int                start, end, number_steps;
    gmx_mdoutf_t       outf;
    int                i, k, m, n, gf, step;
    int                mdof_flags;
    auto               mdatoms = mdAtoms->mdatoms();

    if (PAR(cr))
    {
        gmx_fatal(FARGS, "Cannot do parallel L-BFGS Minimization - yet.\n");
    }

    if (nullptr != constr)
    {
        gmx_fatal(FARGS, "The combination of constraints and L-BFGS minimization is not implemented. Either do not use constraints, or use another minimizer (e.g. steepest descent).");
    }

    n        = 3*state_global->natoms;
    nmaxcorr = inputrec->nbfgscorr;

    snew(frozen, n);

    snew(p, n);
    snew(rho, nmaxcorr);
    snew(alpha, nmaxcorr);

    snew(dx, nmaxcorr);
    for (i = 0; i < nmaxcorr; i++)
    {
        snew(dx[i], n);
    }

    snew(dg, nmaxcorr);
    for (i = 0; i < nmaxcorr; i++)
    {
        snew(dg[i], n);
    }

    step  = 0;
    neval = 0;

    /* Init em */
    init_em(fplog, LBFGS, cr, outputProvider, inputrec, mdrunOptions,
            state_global, top_global, &ems, &top,
            nrnb, mu_tot, fr, &enerd, &graph, mdAtoms, &gstat,
            vsite, constr, nullptr,
            nfile, fnm, &outf, &mdebin, wcycle);

    start = 0;
    end   = mdatoms->homenr;

    /* We need 4 working states */
    em_state_t  s0 {}, s1 {}, s2 {}, s3 {};
    em_state_t *sa   = &s0;
    em_state_t *sb   = &s1;
    em_state_t *sc   = &s2;
    em_state_t *last = &s3;
    /* Initialize by copying the state from ems (we could skip x and f here) */
    *sa              = ems;
    *sb              = ems;
    *sc              = ems;

    /* Print to log file */
    print_em_start(fplog, cr, walltime_accounting, wcycle, LBFGS);

    do_log = do_ene = do_x = do_f = TRUE;

    /* Max number of steps */
    number_steps = inputrec->nsteps;

    /* Create a 3*natoms index to tell whether each degree of freedom is frozen */
    gf = 0;
    for (i = start; i < end; i++)
    {
        if (mdatoms->cFREEZE)
        {
            gf = mdatoms->cFREEZE[i];
        }
        for (m = 0; m < DIM; m++)
        {
            frozen[3*i+m] = inputrec->opts.nFreeze[gf][m];
        }
    }
    if (MASTER(cr))
    {
        sp_header(stderr, LBFGS, inputrec->em_tol, number_steps);
    }
    if (fplog)
    {
        sp_header(fplog, LBFGS, inputrec->em_tol, number_steps);
    }

    if (vsite)
    {
        construct_vsites(vsite, as_rvec_array(state_global->x.data()), 1, nullptr,
                         top->idef.iparams, top->idef.il,
                         fr->ePBC, fr->bMolPBC, cr, state_global->box);
    }

    /* Call the force routine and some auxiliary (neighboursearching etc.) */
    /* do_force always puts the charge groups in the box and shifts again
     * We do not unshift, so molecules are always whole
     */
    neval++;
    evaluate_energy(fplog, cr,
                    top_global, &ems, top,
                    inputrec, nrnb, wcycle, gstat,
                    vsite, constr, fcd, graph, mdAtoms, fr,
                    mu_tot, enerd, vir, pres, -1, TRUE);
    where();

    if (MASTER(cr))
    {
        /* Copy stuff to the energy bin for easy printing etc. */
        upd_mdebin(mdebin, FALSE, FALSE, (double)step,
                   mdatoms->tmass, enerd, state_global, inputrec->fepvals, inputrec->expandedvals, state_global->box,
                   nullptr, nullptr, vir, pres, nullptr, mu_tot, constr);

        print_ebin_header(fplog, step, step);
        print_ebin(mdoutf_get_fp_ene(outf), TRUE, FALSE, FALSE, fplog, step, step, eprNORMAL,
                   mdebin, fcd, &(top_global->groups), &(inputrec->opts), nullptr);
    }
    where();

    /* Set the initial step.
     * since it will be multiplied by the non-normalized search direction
     * vector (force vector the first time), we scale it by the
     * norm of the force.
     */

    if (MASTER(cr))
    {
        double sqrtNumAtoms = sqrt(static_cast<double>(state_global->natoms));
        fprintf(stderr, "Using %d BFGS correction steps.\n\n", nmaxcorr);
        fprintf(stderr, "   F-max             = %12.5e on atom %d\n", ems.fmax, ems.a_fmax + 1);
        fprintf(stderr, "   F-Norm            = %12.5e\n", ems.fnorm/sqrtNumAtoms);
        fprintf(stderr, "\n");
        /* and copy to the log file too... */
        fprintf(fplog, "Using %d BFGS correction steps.\n\n", nmaxcorr);
        fprintf(fplog, "   F-max             = %12.5e on atom %d\n", ems.fmax, ems.a_fmax + 1);
        fprintf(fplog, "   F-Norm            = %12.5e\n", ems.fnorm/sqrtNumAtoms);
        fprintf(fplog, "\n");
    }

    // Point is an index to the memory of search directions, where 0 is the first one.
    point = 0;

    // Set initial search direction to the force (-gradient), or 0 for frozen particles.
    real *fInit = static_cast<real *>(as_rvec_array(ems.f.data())[0]);
    for (i = 0; i < n; i++)
    {
        if (!frozen[i])
        {
            dx[point][i] = fInit[i]; /* Initial search direction */
        }
        else
        {
            dx[point][i] = 0;
        }
    }

    // Stepsize will be modified during the search, and actually it is not critical
    // (the main efficiency in the algorithm comes from changing directions), but
    // we still need an initial value, so estimate it as the inverse of the norm
    // so we take small steps where the potential fluctuates a lot.
    stepsize  = 1.0/ems.fnorm;

    /* Start the loop over BFGS steps.
     * Each successful step is counted, and we continue until
     * we either converge or reach the max number of steps.
     */

    ncorr = 0;

    /* Set the gradient from the force */
    converged = FALSE;
    for (step = 0; (number_steps < 0 || step <= number_steps) && !converged; step++)
    {

        /* Write coordinates if necessary */
        do_x = do_per_step(step, inputrec->nstxout);
        do_f = do_per_step(step, inputrec->nstfout);

        mdof_flags = 0;
        if (do_x)
        {
            mdof_flags |= MDOF_X;
        }

        if (do_f)
        {
            mdof_flags |= MDOF_F;
        }

        if (inputrec->bIMD)
        {
            mdof_flags |= MDOF_IMD;
        }

        mdoutf_write_to_trajectory_files(fplog, cr, outf, mdof_flags,
                                         top_global, step, (real)step, &ems.s, state_global, observablesHistory, ems.f);

        /* Do the linesearching in the direction dx[point][0..(n-1)] */

        /* make s a pointer to current search direction - point=0 first time we get here */
        s = dx[point];

        real *xx = static_cast<real *>(as_rvec_array(ems.s.x.data())[0]);
        real *ff = static_cast<real *>(as_rvec_array(ems.f.data())[0]);

        // calculate line gradient in position A
        for (gpa = 0, i = 0; i < n; i++)
        {
            gpa -= s[i]*ff[i];
        }

        /* Calculate minimum allowed stepsize along the line, before the average (norm)
         * relative change in coordinate is smaller than precision
         */
        for (minstep = 0, i = 0; i < n; i++)
        {
            tmp = fabs(xx[i]);
            if (tmp < 1.0)
            {
                tmp = 1.0;
            }
            tmp      = s[i]/tmp;
            minstep += tmp*tmp;
        }
        minstep = GMX_REAL_EPS/sqrt(minstep/n);

        if (stepsize < minstep)
        {
            converged = TRUE;
            break;
        }

        // Before taking any steps along the line, store the old position
        *last       = ems;
        real *lastx = static_cast<real *>(as_rvec_array(last->s.x.data())[0]);
        real *lastf = static_cast<real *>(as_rvec_array(last->f.data())[0]);
        Epot0       = ems.epot;

        *sa         = ems;

        /* Take a step downhill.
         * In theory, we should find the actual minimum of the function in this
         * direction, somewhere along the line.
         * That is quite possible, but it turns out to take 5-10 function evaluations
         * for each line. However, we dont really need to find the exact minimum -
         * it is much better to start a new BFGS step in a modified direction as soon
         * as we are close to it. This will save a lot of energy evaluations.
         *
         * In practice, we just try to take a single step.
         * If it worked (i.e. lowered the energy), we increase the stepsize but
         * continue straight to the next BFGS step without trying to find any minimum,
         * i.e. we change the search direction too. If the line was smooth, it is
         * likely we are in a smooth region, and then it makes sense to take longer
         * steps in the modified search direction too.
         *
         * If it didn't work (higher energy), there must be a minimum somewhere between
         * the old position and the new one. Then we need to start by finding a lower
         * value before we change search direction. Since the energy was apparently
         * quite rough, we need to decrease the step size.
         *
         * Due to the finite numerical accuracy, it turns out that it is a good idea
         * to accept a SMALL increase in energy, if the derivative is still downhill.
         * This leads to lower final energies in the tests I've done. / Erik
         */

        // State "A" is the first position along the line.
        // reference position along line is initially zero
        a          = 0.0;

        // Check stepsize first. We do not allow displacements
        // larger than emstep.
        //
        do
        {
            // Pick a new position C by adding stepsize to A.
            c        = a + stepsize;

            // Calculate what the largest change in any individual coordinate
            // would be (translation along line * gradient along line)
            maxdelta = 0;
            for (i = 0; i < n; i++)
            {
                delta = c*s[i];
                if (delta > maxdelta)
                {
                    maxdelta = delta;
                }
            }