/* Estimate the reciprocal space part error of the SPME Ewald sum. */
static real estimate_reciprocal(
t_inputinfo *info,
rvec x[], /* array of particles */
real q[], /* array of charges */
int nr, /* number of charges = size of the charge array */
FILE *fp_out,
gmx_bool bVerbose,
unsigned int seed, /* The seed for the random number generator */
int *nsamples, /* Return the number of samples used if Monte Carlo
* algorithm is used for self energy error estimate */
t_commrec *cr)
{
real e_rec=0; /* reciprocal error estimate */
real e_rec1=0; /* Error estimate term 1*/
real e_rec2=0; /* Error estimate term 2*/
real e_rec3=0; /* Error estimate term 3 */
real e_rec3x=0; /* part of Error estimate term 3 in x */
real e_rec3y=0; /* part of Error estimate term 3 in y */
real e_rec3z=0; /* part of Error estimate term 3 in z */
int i,ci;
int nx,ny,nz; /* grid coordinates */
real q2_all=0; /* sum of squared charges */
rvec gridpx; /* reciprocal grid point in x direction*/
rvec gridpxy; /* reciprocal grid point in x and y direction*/
rvec gridp; /* complete reciprocal grid point in 3 directions*/
rvec tmpvec; /* template to create points from basis vectors */
rvec tmpvec2; /* template to create points from basis vectors */
real coeff=0; /* variable to compute coefficients of the error estimate */
real coeff2=0; /* variable to compute coefficients of the error estimate */
real tmp=0; /* variables to compute different factors from vectors */
real tmp1=0;
real tmp2=0;
gmx_bool bFraction;
/* Random number generator */
gmx_rng_t rng=NULL;
int *numbers=NULL;
/* Index variables for parallel work distribution */
int startglobal,stopglobal;
int startlocal, stoplocal;
int x_per_core;
int xtot;
#ifdef TAKETIME
double t0=0.0;
double t1=0.0;
#endif
rng=gmx_rng_init(seed);
clear_rvec(gridpx);
clear_rvec(gridpxy);
clear_rvec(gridp);
clear_rvec(tmpvec);
clear_rvec(tmpvec2);
for(i=0;i<nr;i++)
{
q2_all += q[i]*q[i];
}
/* Calculate indices for work distribution */
startglobal=-info->nkx[0]/2;
stopglobal = info->nkx[0]/2;
xtot = stopglobal*2+1;
if (PAR(cr))
{
x_per_core = ceil((real)xtot / (real)cr->nnodes);
startlocal = startglobal + x_per_core*cr->nodeid;
stoplocal = startlocal + x_per_core -1;
if (stoplocal > stopglobal)
stoplocal = stopglobal;
}
else
{
startlocal = startglobal;
stoplocal = stopglobal;
x_per_core = xtot;
}
/*
#ifdef GMX_LIB_MPI
MPI_Barrier(MPI_COMM_WORLD);
#endif
*/
#ifdef GMX_LIB_MPI
#ifdef TAKETIME
if (MASTER(cr))
t0 = MPI_Wtime();
#endif
#endif
if (MASTER(cr)){
fprintf(stderr, "Calculating reciprocal error part 1 ...");
}
for(nx=startlocal; nx<=stoplocal; nx++)
{
svmul(nx,info->recipbox[XX],gridpx);
for(ny=-info->nky[0]/2; ny<info->nky[0]/2+1; ny++)
{
svmul(ny,info->recipbox[YY],tmpvec);
rvec_add(gridpx,tmpvec,gridpxy);
for(nz=-info->nkz[0]/2; nz<info->nkz[0]/2+1; nz++)
{
if ( 0 == nx && 0 == ny && 0 == nz )
continue;
svmul(nz,info->recipbox[ZZ],tmpvec);
rvec_add(gridpxy,tmpvec,gridp);
tmp=norm2(gridp);
coeff=exp(-1.0 * M_PI * M_PI * tmp / info->ewald_beta[0] / info->ewald_beta[0] ) ;
coeff/= 2.0 * M_PI * info->volume * tmp;
coeff2=tmp ;
tmp=eps_poly2(nx,info->nkx[0],info->pme_order[0]);
tmp+=eps_poly2(ny,info->nkx[0],info->pme_order[0]);
tmp+=eps_poly2(nz,info->nkx[0],info->pme_order[0]);
tmp1=eps_poly1(nx,info->nkx[0],info->pme_order[0]);
tmp2=eps_poly1(ny,info->nky[0],info->pme_order[0]);
tmp+=2.0 * tmp1 * tmp2;
tmp1=eps_poly1(nz,info->nkz[0],info->pme_order[0]);
tmp2=eps_poly1(ny,info->nky[0],info->pme_order[0]);
tmp+=2.0 * tmp1 * tmp2;
tmp1=eps_poly1(nz,info->nkz[0],info->pme_order[0]);
tmp2=eps_poly1(nx,info->nkx[0],info->pme_order[0]);
tmp+=2.0 * tmp1 * tmp2;
tmp1=eps_poly1(nx,info->nkx[0],info->pme_order[0]);
tmp1+=eps_poly1(ny,info->nky[0],info->pme_order[0]);
tmp1+=eps_poly1(nz,info->nkz[0],info->pme_order[0]);
tmp+= tmp1 * tmp1;
e_rec1+= 32.0 * M_PI * M_PI * coeff * coeff * coeff2 * tmp * q2_all * q2_all / nr ;
tmp1=eps_poly3(nx,info->nkx[0],info->pme_order[0]);
tmp1*=info->nkx[0];
tmp2=iprod(gridp,info->recipbox[XX]);
tmp=tmp1*tmp2;
tmp1=eps_poly3(ny,info->nky[0],info->pme_order[0]);
tmp1*=info->nky[0];
tmp2=iprod(gridp,info->recipbox[YY]);
tmp+=tmp1*tmp2;
tmp1=eps_poly3(nz,info->nkz[0],info->pme_order[0]);
tmp1*=info->nkz[0];
tmp2=iprod(gridp,info->recipbox[ZZ]);
tmp+=tmp1*tmp2;
tmp*=4.0 * M_PI;
tmp1=eps_poly4(nx,info->nkx[0],info->pme_order[0]);
tmp1*=norm2(info->recipbox[XX]);
tmp1*=info->nkx[0] * info->nkx[0];
tmp+=tmp1;
tmp1=eps_poly4(ny,info->nky[0],info->pme_order[0]);
tmp1*=norm2(info->recipbox[YY]);
tmp1*=info->nky[0] * info->nky[0];
tmp+=tmp1;
tmp1=eps_poly4(nz,info->nkz[0],info->pme_order[0]);
tmp1*=norm2(info->recipbox[ZZ]);
tmp1*=info->nkz[0] * info->nkz[0];
tmp+=tmp1;
e_rec2+= 4.0 * coeff * coeff * tmp * q2_all * q2_all / nr ;
}
}
if (MASTER(cr))
fprintf(stderr, "\rCalculating reciprocal error part 1 ... %3.0f%%", 100.0*(nx-startlocal+1)/(x_per_core));
}
if (MASTER(cr))
fprintf(stderr, "\n");
/* Use just a fraction of all charges to estimate the self energy error term? */
bFraction = (info->fracself > 0.0) && (info->fracself < 1.0);
if (bFraction)
{
/* Here xtot is the number of samples taken for the Monte Carlo calculation
* of the average of term IV of equation 35 in Wang2010. Round up to a
* number of samples that is divisible by the number of nodes */
x_per_core = ceil(info->fracself * nr / (real)cr->nnodes);
xtot = x_per_core * cr->nnodes;
}
else
{
/* In this case we use all nr particle positions */
xtot = nr;
x_per_core = ceil( (real)xtot / (real)cr->nnodes );
}
startlocal = x_per_core * cr->nodeid;
stoplocal = min(startlocal + x_per_core, xtot); /* min needed if xtot == nr */
if (bFraction)
{
/* Make shure we get identical results in serial and parallel. Therefore,
* take the sample indices from a single, global random number array that
* is constructed on the master node and that only depends on the seed */
snew(numbers, xtot);
if (MASTER(cr))
{
for (i=0; i<xtot; i++)
{
numbers[i] = floor(gmx_rng_uniform_real(rng) * nr );
}
}
/* Broadcast the random number array to the other nodes */
if (PAR(cr))
{
nblock_bc(cr,xtot,numbers);
}
if (bVerbose && MASTER(cr))
{
fprintf(stdout, "Using %d sample%s to approximate the self interaction error term",
xtot, xtot==1?"":"s");
if (PAR(cr))
fprintf(stdout, " (%d sample%s per node)", x_per_core, x_per_core==1?"":"s");
fprintf(stdout, ".\n");
}
}
/* Return the number of positions used for the Monte Carlo algorithm */
*nsamples = xtot;
for(i=startlocal;i<stoplocal;i++)
{
e_rec3x=0;
e_rec3y=0;
e_rec3z=0;
if (bFraction)
{
/* Randomly pick a charge */
ci = numbers[i];
}
else
{
/* Use all charges */
ci = i;
}
/* for(nx=startlocal; nx<=stoplocal; nx++)*/
for(nx=-info->nkx[0]/2; nx<info->nkx[0]/2+1; nx++)
{
svmul(nx,info->recipbox[XX],gridpx);
for(ny=-info->nky[0]/2; ny<info->nky[0]/2+1; ny++)
{
svmul(ny,info->recipbox[YY],tmpvec);
rvec_add(gridpx,tmpvec,gridpxy);
for(nz=-info->nkz[0]/2; nz<info->nkz[0]/2+1; nz++)
{
if ( 0 == nx && 0 == ny && 0 == nz)
continue;
svmul(nz,info->recipbox[ZZ],tmpvec);
rvec_add(gridpxy,tmpvec,gridp);
tmp=norm2(gridp);
coeff=exp(-1.0 * M_PI * M_PI * tmp / info->ewald_beta[0] / info->ewald_beta[0] );
coeff/= tmp ;
e_rec3x+=coeff*eps_self(nx,info->nkx[0],info->recipbox[XX],info->pme_order[0],x[ci]);
e_rec3y+=coeff*eps_self(ny,info->nky[0],info->recipbox[YY],info->pme_order[0],x[ci]);
e_rec3z+=coeff*eps_self(nz,info->nkz[0],info->recipbox[ZZ],info->pme_order[0],x[ci]);
}
}
}
clear_rvec(tmpvec2);
svmul(e_rec3x,info->recipbox[XX],tmpvec);
rvec_inc(tmpvec2,tmpvec);
svmul(e_rec3y,info->recipbox[YY],tmpvec);
rvec_inc(tmpvec2,tmpvec);
svmul(e_rec3z,info->recipbox[ZZ],tmpvec);
rvec_inc(tmpvec2,tmpvec);
e_rec3 += q[ci]*q[ci]*q[ci]*q[ci]*norm2(tmpvec2) / ( xtot * M_PI * info->volume * M_PI * info->volume);
if (MASTER(cr)){
fprintf(stderr, "\rCalculating reciprocal error part 2 ... %3.0f%%",
100.0*(i+1)/stoplocal);
}
}
if (MASTER(cr))
fprintf(stderr, "\n");
#ifdef GMX_LIB_MPI
#ifdef TAKETIME
if (MASTER(cr))
{
t1= MPI_Wtime() - t0;
fprintf(fp_out, "Recip. err. est. took : %lf s\n", t1);
}
#endif
#endif
#ifdef DEBUG
if (PAR(cr))
{
fprintf(stderr, "Node %3d: nx=[%3d...%3d] e_rec3=%e\n",
cr->nodeid, startlocal, stoplocal, e_rec3);
}
#endif
if (PAR(cr))
{
gmx_sum(1,&e_rec1,cr);
gmx_sum(1,&e_rec2,cr);
gmx_sum(1,&e_rec3,cr);
}
/* e_rec1*=8.0 * q2_all / info->volume / info->volume / nr ;
e_rec2*= q2_all / M_PI / M_PI / info->volume / info->volume / nr ;
e_rec3/= M_PI * M_PI * info->volume * info->volume * nr ;
*/
e_rec=sqrt(e_rec1+e_rec2+e_rec3);
return ONE_4PI_EPS0 * e_rec;
}
/* Estimate the reciprocal space part error of the SPME Ewald sum. */
static real estimate_reciprocal(
t_inputinfo *info,
rvec x[], /* array of particles */
real q[], /* array of charges */
int nr, /* number of charges = size of the charge array */
FILE *fp_out,
t_commrec *cr)
{
real e_rec=0; /* reciprocal error estimate */
real e_rec1=0; /* Error estimate term 1*/
real e_rec2=0; /* Error estimate term 2*/
real e_rec3=0; /* Error estimate term 3 */
real e_rec3x=0; /* part of Error estimate term 3 in x */
real e_rec3y=0; /* part of Error estimate term 3 in y */
real e_rec3z=0; /* part of Error estimate term 3 in z */
int i,ci;
int nx,ny,nz; /* grid coordinates */
real q2_all=0; /* sum of squared charges */
rvec gridpx; /* reciprocal grid point in x direction*/
rvec gridpxy; /* reciprocal grid point in x and y direction*/
rvec gridp; /* complete reciprocal grid point in 3 directions*/
rvec tmpvec; /* template to create points from basis vectors */
rvec tmpvec2; /* template to create points from basis vectors */
real coeff=0; /* variable to compute coefficients of the error estimate */
real coeff2=0; /* variable to compute coefficients of the error estimate */
real tmp=0; /* variables to compute different factors from vectors */
real tmp1=0;
real tmp2=0;
real xtmp=0;
real ytmp=0;
real ztmp=0;
double ewald_error;
/* Random number generator */
gmx_rng_t rng=NULL;
/*rng=gmx_rng_init(gmx_rng_make_seed()); */
/* Index variables for parallel work distribution */
int startglobal,stopglobal;
int startlocal, stoplocal;
int x_per_core;
int nrsamples;
real xtot;
/* #define TAKETIME */
#ifdef TAKETIME
double t0=0.0;
double t1=0.0;
double t2=0.0;
#endif
rng=gmx_rng_init(cr->nodeid);
clear_rvec(gridpx);
clear_rvec(gridpxy);
clear_rvec(gridp);
clear_rvec(tmpvec);
clear_rvec(tmpvec2);
for(i=0;i<nr;i++)
{
q2_all += q[i]*q[i];
}
/* Calculate indices for work distribution */
startglobal=-info->nkx[0]/2;
stopglobal = info->nkx[0]/2;
xtot = stopglobal*2+1;
if (PAR(cr))
{
x_per_core = ceil(xtot / cr->nnodes);
startlocal = startglobal + x_per_core*cr->nodeid;
stoplocal = startlocal + x_per_core -1;
if (stoplocal > stopglobal)
stoplocal = stopglobal;
}
else
{
startlocal = startglobal;
stoplocal = stopglobal;
x_per_core = xtot;
}
/*
#ifdef GMX_MPI
MPI_Barrier(MPI_COMM_WORLD);
#endif
*/
#ifdef TAKETIME
if (MASTER(cr))
t0 = MPI_Wtime();
#endif
if (MASTER(cr)){
fprintf(stderr, "Calculating reciprocal error part 1 ...");
}
for(nx=startlocal; nx<=stoplocal; nx++)
{
svmul(nx,info->recipbox[XX],gridpx);
for(ny=-info->nky[0]/2; ny<info->nky[0]/2+1; ny++)
{
svmul(ny,info->recipbox[YY],tmpvec);
rvec_add(gridpx,tmpvec,gridpxy);
for(nz=-info->nkz[0]/2; nz<info->nkz[0]/2+1; nz++)
{
if ( 0 == nx && 0 == ny && 0 == nz )
continue;
svmul(nz,info->recipbox[ZZ],tmpvec);
rvec_add(gridpxy,tmpvec,gridp);
tmp=norm2(gridp);
coeff=exp(-1.0 * M_PI * M_PI * tmp / info->ewald_beta[0] / info->ewald_beta[0] ) ;
coeff/= 2.0 * M_PI * info->volume * tmp;
coeff2=tmp ;
tmp=eps_poly2(nx,info->nkx[0],info->pme_order[0]);
tmp+=eps_poly2(ny,info->nkx[0],info->pme_order[0]);
tmp+=eps_poly2(nz,info->nkx[0],info->pme_order[0]);
tmp1=eps_poly1(nx,info->nkx[0],info->pme_order[0]);
tmp2=eps_poly1(ny,info->nky[0],info->pme_order[0]);
tmp+=2.0 * tmp1 * tmp2;
tmp1=eps_poly1(nz,info->nkz[0],info->pme_order[0]);
tmp2=eps_poly1(ny,info->nky[0],info->pme_order[0]);
tmp+=2.0 * tmp1 * tmp2;
tmp1=eps_poly1(nz,info->nkz[0],info->pme_order[0]);
tmp2=eps_poly1(nx,info->nkx[0],info->pme_order[0]);
tmp+=2.0 * tmp1 * tmp2;
tmp1=eps_poly1(nx,info->nkx[0],info->pme_order[0]);
tmp1+=eps_poly1(ny,info->nky[0],info->pme_order[0]);
tmp1+=eps_poly1(nz,info->nkz[0],info->pme_order[0]);
tmp+= tmp1 * tmp1;
e_rec1+= 32.0 * M_PI * M_PI * coeff * coeff * coeff2 * tmp * q2_all * q2_all / nr ;
tmp1=eps_poly3(nx,info->nkx[0],info->pme_order[0]);
tmp1*=info->nkx[0];
tmp2=iprod(gridp,info->recipbox[XX]);
tmp=tmp1*tmp2;
tmp1=eps_poly3(ny,info->nky[0],info->pme_order[0]);
tmp1*=info->nky[0];
tmp2=iprod(gridp,info->recipbox[YY]);
tmp+=tmp1*tmp2;
tmp1=eps_poly3(nz,info->nkz[0],info->pme_order[0]);
tmp1*=info->nkz[0];
tmp2=iprod(gridp,info->recipbox[ZZ]);
tmp+=tmp1*tmp2;
tmp*=4.0 * M_PI;
tmp1=eps_poly4(nx,info->nkx[0],info->pme_order[0]);
tmp1*=norm2(info->recipbox[XX]);
tmp1*=info->nkx[0] * info->nkx[0];
tmp+=tmp1;
tmp1=eps_poly4(ny,info->nky[0],info->pme_order[0]);
tmp1*=norm2(info->recipbox[YY]);
tmp1*=info->nky[0] * info->nky[0];
tmp+=tmp1;
tmp1=eps_poly4(nz,info->nkz[0],info->pme_order[0]);
tmp1*=norm2(info->recipbox[ZZ]);
tmp1*=info->nkz[0] * info->nkz[0];
tmp+=tmp1;
e_rec2+= 4.0 * coeff * coeff * tmp * q2_all * q2_all / nr ;
}
}
if (MASTER(cr))
fprintf(stderr, "\rCalculating reciprocal error part 1 ... %3.0f%%", 100.0*(nx-startlocal+1)/(x_per_core));
}
/*
#ifdef GMX_MPI
MPI_Barrier(MPI_COMM_WORLD);
#endif
*/
if (MASTER(cr))
fprintf(stderr, "\n");
if (info->fracself>0)
{
nrsamples=ceil(info->fracself*nr);
}
else
{
nrsamples=nr;
}
xtot=nrsamples;
startglobal=0;
stopglobal=nr;
if(PAR(cr))
{
x_per_core=ceil(xtot/cr->nnodes);
startlocal=startglobal+x_per_core*cr->nodeid;
stoplocal=startglobal+x_per_core*(cr->nodeid+1);
if (stoplocal>stopglobal)
stoplocal=stopglobal;
}
else
{
startlocal=startglobal;
stoplocal=stopglobal;
x_per_core=xtot;
}
for(i=startlocal;i<stoplocal;i++)
{
e_rec3x=0;
e_rec3y=0;
e_rec3z=0;
if (info->fracself<0) {
ci=i;
}else {
ci=floor(gmx_rng_uniform_real(rng) * nr );
if (ci==nr)
{
ci=nr-1;
}
}
/* for(nx=startlocal; nx<=stoplocal; nx++)*/
for(nx=-info->nkx[0]/2; nx<info->nkx[0]/2+1; nx++)
{
svmul(nx,info->recipbox[XX],gridpx);
for(ny=-info->nky[0]/2; ny<info->nky[0]/2+1; ny++)
{
svmul(ny,info->recipbox[YY],tmpvec);
rvec_add(gridpx,tmpvec,gridpxy);
for(nz=-info->nkz[0]/2; nz<info->nkz[0]/2+1; nz++)
{
if ( 0 == nx && 0 == ny && 0 == nz)
continue;
svmul(nz,info->recipbox[ZZ],tmpvec);
rvec_add(gridpxy,tmpvec,gridp);
tmp=norm2(gridp);
coeff=exp(-1.0 * M_PI * M_PI * tmp / info->ewald_beta[0] / info->ewald_beta[0] );
coeff/= tmp ;
e_rec3x+=coeff*eps_self(nx,info->nkx[0],info->recipbox[XX],info->pme_order[0],x[ci]);
e_rec3y+=coeff*eps_self(ny,info->nky[0],info->recipbox[YY],info->pme_order[0],x[ci]);
e_rec3z+=coeff*eps_self(nz,info->nkz[0],info->recipbox[ZZ],info->pme_order[0],x[ci]);
}
}
}
clear_rvec(tmpvec2);
svmul(e_rec3x,info->recipbox[XX],tmpvec);
rvec_inc(tmpvec2,tmpvec);
svmul(e_rec3y,info->recipbox[YY],tmpvec);
rvec_inc(tmpvec2,tmpvec);
svmul(e_rec3z,info->recipbox[ZZ],tmpvec);
rvec_inc(tmpvec2,tmpvec);
e_rec3 += q[ci]*q[ci]*q[ci]*q[ci]*norm2(tmpvec2) / ( nrsamples * M_PI * info->volume * M_PI * info->volume);
if (MASTER(cr)){
fprintf(stderr, "\rCalculating reciprocal error part 2 ... %3.0f%%",
100.0*(i+1)/stoplocal);
}
}
if (MASTER(cr))
fprintf(stderr, "\n");
#ifdef TAKETIME
if (MASTER(cr))
{
t1= MPI_Wtime() - t0;
fprintf(fp_out, "Recip. err. est. took : %lf s\n", t1);
}
#endif
#ifdef DEBUG
if (PAR(cr))
{
fprintf(stderr, "Node %3d: nx=[%3d...%3d] e_rec3=%e\n",
cr->nodeid, startlocal, stoplocal, e_rec3);
}
#endif
/*
#ifdef GMX_MPI
MPI_Barrier(MPI_COMM_WORLD);
#endif
*/
#ifdef TAKETIME
if (MASTER(cr))
{
t2= MPI_Wtime() - t0;
fprintf(fp_out, "barrier : %lf s\n", t2-t1);
}
#endif
if (PAR(cr))
{
gmx_sum(1,&e_rec1,cr);
gmx_sum(1,&e_rec2,cr);
gmx_sum(1,&e_rec3,cr);
}
#ifdef TAKETIME
if (MASTER(cr))
fprintf(fp_out, "final reduce : %lf s\n", MPI_Wtime() - t0-t2);
#endif
/* e_rec1*=8.0 * q2_all / info->volume / info->volume / nr ;
e_rec2*= q2_all / M_PI / M_PI / info->volume / info->volume / nr ;
e_rec3/= M_PI * M_PI * info->volume * info->volume * nr ;
*/
e_rec=sqrt(e_rec1+e_rec2+e_rec3);
return ONE_4PI_EPS0 * e_rec;
}