int mr(spinor * const P, spinor * const Q,
const int max_iter, const double eps_sq,
const int rel_prec, const int N, const int parallel,
matrix_mult f){
int i=0;
double norm_r,beta;
_Complex double alpha;
spinor * r;
spinor ** solver_field = NULL;
const int nr_sf = 3;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
}
r = solver_field[0];
zero_spinor_field(P, N);
f(solver_field[2], P);
diff(r, Q, solver_field[2], N);
norm_r=square_norm(solver_field[0], N, parallel);
if(g_proc_id == g_stdio_proc && g_debug_level > 2) {
printf("MR iteration number: %d, |res|^2 = %e\n", i, norm_r);
fflush( stdout );
}
while((norm_r > eps_sq) && (i < max_iter)){
i++;
f(solver_field[1], r);
alpha=scalar_prod(solver_field[1], r, N, parallel);
beta=square_norm(solver_field[1], N, parallel);
alpha /= beta;
assign_add_mul(P, r, alpha, N);
if(i%50 == 0){
f(solver_field[2], P);
}
else{
assign_add_mul(solver_field[2], solver_field[1], alpha, N);
}
diff(r, Q, solver_field[2], N);
norm_r=square_norm(solver_field[0], N, parallel);
if(g_proc_id == g_stdio_proc && g_debug_level > 2) {
printf("# MR iteration= %d |res|^2= %g\n", i, norm_r);
fflush(stdout);
}
}
finalize_solver(solver_field, nr_sf);
if(norm_r > eps_sq){
return(-1);
}
return(i);
}
void Msap(spinor * const P, spinor * const Q, const int Ncy, const int Niter) {
int blk, ncy = 0, eo, vol;
spinor * r, * a, * b;
double nrm;
spinor ** solver_field = NULL;
const int nr_sf = 6;
/*
* here it would be probably better to get the working fields as a parameter
* from the calling function
*/
init_solver_field(&solver_field, VOLUME, nr_sf);
r = solver_field[0];
a = solver_field[1];
b = solver_field[2];
for(ncy = 0; ncy < Ncy; ncy++) {
/* compute the global residue */
/* this can be done more efficiently */
/* here only a naive implementation */
for(eo = 0; eo < 2; eo++) {
D_psi(r, P);
diff(r, Q, r, VOLUME);
nrm = square_norm(r, VOLUME, 1);
if(g_proc_id == 0 && g_debug_level > 2 && eo == 1) { /* GG, was 1 */
printf("Msap: %d %1.3e\n", ncy, nrm);
fflush(stdout);
}
/* choose the even (odd) block */
/*blk = eolist[eo];*/
for (blk = 0; blk < nb_blocks; blk++) {
if(block_list[blk].evenodd == eo) {
vol = block_list[blk].volume;
/* get part of r corresponding to block blk into b */
copy_global_to_block(b, r, blk);
// does this work?? i.e. solver_field[3]
mrblk(a, b, solver_field[3], Niter, 1.e-31, 1, vol, &dummy_Di, blk);
/* add a up to full spinor P */
add_block_to_global(P, a, blk);
}
}
}
}
finalize_solver(solver_field, nr_sf);
return;
}
void CGeoSmoother(spinor * const P, spinor * const Q, const int Ncy, const int dummy) {
spinor ** solver_field = NULL;
const int nr_sf = 5;
double musave = g_mu;
g_mu = g_mu1;
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
convert_lexic_to_eo(solver_field[0], solver_field[1], Q);
if(g_c_sw > 0)
assign_mul_one_sw_pm_imu_inv(EE,solver_field[2], solver_field[0], g_mu);
else
assign_mul_one_pm_imu_inv(solver_field[2], solver_field[0], +1., VOLUME/2);
Hopping_Matrix(OE, solver_field[4], solver_field[2]);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_mul_add_r(solver_field[4], +1., solver_field[1], VOLUME/2);
/* Do the inversion with the preconditioned */
/* matrix to get the odd sites */
gamma5(solver_field[4], solver_field[4], VOLUME/2);
if(g_c_sw > 0) {
cg_her(solver_field[3], solver_field[4], Ncy, 1.e-8, 1,
VOLUME/2, &Qsw_pm_psi);
Qsw_minus_psi(solver_field[3], solver_field[3]);
/* Reconstruct the even sites */
Hopping_Matrix(EO, solver_field[2], solver_field[3]);
assign_mul_one_sw_pm_imu_inv(EE,solver_field[4],solver_field[2], g_mu);
}
else {
cg_her(solver_field[3], solver_field[4], Ncy, 1.e-8, 1,
VOLUME/2, &Qtm_pm_psi);
Qtm_minus_psi(solver_field[3], solver_field[3]);
/* Reconstruct the even sites */
Hopping_Matrix(EO, solver_field[4], solver_field[3]);
mul_one_pm_imu_inv(solver_field[4], +1., VOLUME/2);
}
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_add_mul_r(solver_field[2], solver_field[4], +1., VOLUME/2);
convert_eo_to_lexic(P, solver_field[2], solver_field[3]);
g_mu = musave;
finalize_solver(solver_field, nr_sf);
return;
}
/* P output = solution , Q input = source */
int cg_mms_tm(spinor ** const P, spinor * const Q,
solver_params_t * solver_params, double * cgmms_reached_prec) {
static double normsq, pro, err, squarenorm;
int iteration, N = solver_params->sdim, no_shifts = solver_params->no_shifts;
static double gamma, alpham1;
spinor ** solver_field = NULL;
double atime, etime;
const int nr_sf = 3;
atime = gettime();
if(solver_params->sdim == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
init_mms_tm(no_shifts, VOLUMEPLUSRAND);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
init_mms_tm(no_shifts, VOLUMEPLUSRAND/2);
}
zero_spinor_field(P[0], N);
alphas[0] = 1.0;
betas[0] = 0.0;
sigma[0] = solver_params->shifts[0]*solver_params->shifts[0];
if(g_proc_id == 0 && g_debug_level > 1) printf("# CGMMS: shift %d is %e\n", 0, sigma[0]);
for(int im = 1; im < no_shifts; im++) {
sigma[im] = solver_params->shifts[im]*solver_params->shifts[im] - sigma[0];
if(g_proc_id == 0 && g_debug_level > 1) printf("# CGMMS: shift %d is %e\n", im, sigma[im]);
// these will be the result spinor fields
zero_spinor_field(P[im], N);
// these are intermediate fields
assign(ps_mms_solver[im-1], Q, N);
zitam1[im] = 1.0;
zita[im] = 1.0;
alphas[im] = 1.0;
betas[im] = 0.0;
}
/* currently only implemented for P=0 */
squarenorm = square_norm(Q, N, 1);
/* if a starting solution vector equal to zero is chosen */
assign(solver_field[0], Q, N);
assign(solver_field[1], Q, N);
normsq = squarenorm;
/* main loop */
for(iteration = 0; iteration < solver_params->max_iter; iteration++) {
/* Q^2*p and then (p,Q^2*p) */
solver_params->M_psi(solver_field[2], solver_field[1]);
// add the zero's shift
assign_add_mul_r(solver_field[2], solver_field[1], sigma[0], N);
pro = scalar_prod_r(solver_field[1], solver_field[2], N, 1);
/* For the update of the coeff. of the shifted pol. we need alphas[0](i-1) and alpha_cg(i).
This is the reason why we need this double definition of alpha */
alpham1 = alphas[0];
/* Compute alphas[0](i+1) */
alphas[0] = normsq/pro;
for(int im = 1; im < no_shifts; im++) {
/* Now gamma is a temp variable that corresponds to zita(i+1) */
gamma = zita[im]*alpham1/(alphas[0]*betas[0]*(1.-zita[im]/zitam1[im])
+ alpham1*(1.+sigma[im]*alphas[0]));
// Now zita(i-1) is put equal to the old zita(i)
zitam1[im] = zita[im];
// Now zita(i+1) is updated
zita[im] = gamma;
// Update of alphas(i) = alphas[0](i)*zita(i+1)/zita(i)
alphas[im] = alphas[0]*zita[im]/zitam1[im];
// Compute xs(i+1) = xs(i) + alphas(i)*ps(i)
assign_add_mul_r(P[im], ps_mms_solver[im-1], alphas[im], N);
// in the CG the corrections are decreasing with the iteration number increasing
// therefore, we can remove shifts when the norm of the correction vector
// falls below a threshold
// this is useful for computing time and needed, because otherwise
// zita might get smaller than DOUBLE_EPS and, hence, zero
if(iteration > 0 && (iteration % 20 == 0) && (im == no_shifts-1)) {
double sn = square_norm(ps_mms_solver[im-1], N, 1);
if(alphas[no_shifts-1]*alphas[no_shifts-1]*sn <= solver_params->squared_solver_prec) {
no_shifts--;
if(g_debug_level > 2 && g_proc_id == 0) {
printf("# CGMMS: at iteration %d removed one shift, %d remaining\n", iteration, no_shifts);
}
}
}
}
/* Compute x_(i+1) = x_i + alphas[0](i+1) p_i */
assign_add_mul_r(P[0], solver_field[1], alphas[0], N);
/* Compute r_(i+1) = r_i - alphas[0](i+1) Qp_i */
assign_add_mul_r(solver_field[0], solver_field[2], -alphas[0], N);
/* Check whether the precision eps_sq is reached */
err = square_norm(solver_field[0], N, 1);
if(g_debug_level > 2 && g_proc_id == g_stdio_proc) {
printf("# CGMMS iteration: %d residue: %g\n", iteration, err); fflush( stdout );
}
if( ((err <= solver_params->squared_solver_prec) && (solver_params->rel_prec == 0)) ||
((err <= solver_params->squared_solver_prec*squarenorm) && (solver_params->rel_prec > 0)) ||
(iteration == solver_params->max_iter -1) ) {
/* FIXME temporary output of precision until a better solution can be found */
*cgmms_reached_prec = err;
break;
}
/* Compute betas[0](i+1) = (r(i+1),r(i+1))/(r(i),r(i))
Compute p(i+1) = r(i+1) + beta(i+1)*p(i) */
betas[0] = err/normsq;
assign_mul_add_r(solver_field[1], betas[0], solver_field[0], N);
normsq = err;
/* Compute betas(i+1) = betas[0](i+1)*(zita(i+1)*alphas(i))/(zita(i)*alphas[0](i))
Compute ps(i+1) = zita(i+1)*r(i+1) + betas(i+1)*ps(i) */
for(int im = 1; im < no_shifts; im++) {
betas[im] = betas[0]*zita[im]*alphas[im]/(zitam1[im]*alphas[0]);
assign_mul_add_mul_r(ps_mms_solver[im-1], solver_field[0], betas[im], zita[im], N);
}
}
etime = gettime();
g_sloppy_precision = 0;
if(iteration == solver_params->max_iter -1) iteration = -1;
else iteration++;
if(g_debug_level > 0 && g_proc_id == 0) {
printf("# CGMMS (%d shifts): iter: %d eps_sq: %1.4e %1.4e t/s\n", solver_params->no_shifts, iteration, solver_params->squared_solver_prec, etime - atime);
}
finalize_solver(solver_field, nr_sf);
return(iteration);
}
int incr_eigcg(const int N, const int nrhs, const int nrhs1, spinor * const x, spinor * const b,
const int ldh, matrix_mult f, const double eps_sq1, const double eps_sq, double restart_eps_sq,
const int rand_guess_opt, const int rel_prec, const int maxit, int nev, const int v_max)
{
/*Static variables and arrays.*/
static spinor **solver_field; /*4 spinor fields*/
static int ncurEvals=0; /* current number of stored eigenvectors */
static int ncurRHS=0; /* current number of the system being solved */
static spinor **evecs; /* accumulated eigenvectors for deflation. */
static void *_evals;
static double *evals; /* Ritz values */
static void *_v;
static spinor *V; /* work array for eigenvector search basis in eigCG */
static void *_h;
static _Complex double *H; /* The ncurEvals^2 matrix: H=evecs'*A*evecs */
static void *_hu;
static _Complex double *HU; /* used for diagonalization of H if eigenvalues requested
also used as a copy of H if needed*/
static void *_initwork;
static _Complex double *initwork; /* vector of size ldh using with init-CG */
static void *_ework;
static _Complex double *ework;
/* end of the thinking part */
static void *_work;
static _Complex double *work;
static void *_rwork;
static double *rwork;
static void *_IPIV;
static int *IPIV; /*integer array to store permutations when solving the small linear system*/
/* some constants */
char cU='U'; char cN='N'; char cV='V';
_Complex double tpone= 1.0e+00;
_Complex double tzero= 0.0e+00;
//tpone.re=+1.0e+00; tpone.im=0.0e+00;
//tzero.re=+0.0e+00; tzero.im=0.0e+00;
/* Timing vars */
double wt1,wt2,wE,wI;
double eps_sq_used;
/* Variables */
double machEps = 1e-15;
double normb, normsq, tmpd,tmpd2;
_Complex double tempz;
int i,j, ONE = 1;
int tmpsize,tmpi,info=0;
int numIts, flag, nAdded, nev_used;
int maxit_remain;
int esize,nrsf;
int parallel; /* for parallel processing of the scalar products */
/* leading dimension for spinor vectors */
int LDN;
if(N==VOLUME)
LDN = VOLUMEPLUSRAND;
else
LDN = VOLUMEPLUSRAND/2;
#ifdef MPI
parallel=1;
#else
parallel=0;
#endif
/*think more about this */
esize=2*12*N+4*nev*nev; /* fixed size for ework used for restarting in eigcg*/
nrsf=4; /*number of solver fields */
int lwork=3*ldh;
double cur_res; //current residual squared (initial value will be computed in eigcg)
/*increment the RHS counter*/
ncurRHS = ncurRHS +1;
//set the tolerance to be used for this right-hand side
if(ncurRHS > nrhs1){
eps_sq_used = eps_sq;
}
else{
eps_sq_used = eps_sq1;
}
if(ncurRHS==1)/* If this is the first system, allocate needed memory for the solver*/
{
init_solver_field(&solver_field, LDN, nrsf);
}
if(nev==0){ /*incremental eigcg is used as a cg solver. No need to restart forcing no-restart*/
if(g_proc_id == g_stdio_proc && g_debug_level > 0) {
fprintf(stdout, "CG won't be restarted in this mode since no deflation will take place (nev=0)\n");
fflush(stdout);
}
restart_eps_sq=0.0;
}
if((ncurRHS==1) && (nev >0) )/* If this is the first right-hand side and eigenvectors are needed, allocate needed memory*/
{
init_solver_field(&evecs, LDN, ldh);
#if (defined SSE || defined SSE2 || defined SSE3)
/*Extra elements are needed for allignment */
//_v = malloc(LDN*v_max*sizeof(spinor)+ALIGN_BASE);
_v = calloc(LDN*v_max+ALIGN_BASE,sizeof(spinor));
V = (spinor *)(((unsigned long int)(_v)+ALIGN_BASE)&~ALIGN_BASE);
//_h=malloc(ldh*ldh*sizeof(_Complex double )+ALIGN_BASE);
_h=calloc(ldh*ldh+ALIGN_BASE,sizeof(_Complex double ));
H = (_Complex double *)(((unsigned long int)(_h)+ALIGN_BASE)&~ALIGN_BASE);
//_hu=malloc(ldh*ldh*sizeof(_Complex double )+ALIGN_BASE);
_hu=calloc(ldh*ldh+ALIGN_BASE,sizeof(_Complex double ));
HU = (_Complex double *)(((unsigned long int)(_hu)+ALIGN_BASE)&~ALIGN_BASE);
//_ework = malloc(esize*sizeof(_Complex double )+ALIGN_BASE);
_ework = calloc(esize+ALIGN_BASE,sizeof(_Complex double ));
ework=(_Complex double *)(((unsigned long int)(_ework)+ALIGN_BASE)&~ALIGN_BASE);
//_initwork = malloc(ldh*sizeof(_Complex double )+ALIGN_BASE);
_initwork = calloc(ldh+ALIGN_BASE,sizeof(_Complex double ));
initwork = (_Complex double *)(((unsigned long int)(_initwork)+ALIGN_BASE)&~ALIGN_BASE);
//_work = malloc(lwork*sizeof(_Complex double )+ALIGN_BASE);
_work = calloc(lwork+ALIGN_BASE,sizeof(_Complex double ));
work = (_Complex double *)(((unsigned long int)(_work)+ALIGN_BASE)&~ALIGN_BASE);
//_rwork = malloc(3*ldh*sizeof(double)+ALIGN_BASE);
_rwork = calloc(3*ldh+ALIGN_BASE,sizeof(double));
rwork = (double *)(((unsigned long int)(_rwork)+ALIGN_BASE)&~ALIGN_BASE);
//_IPIV = malloc(ldh*sizeof(int)+ALIGN_BASE);
_IPIV = calloc(ldh+ALIGN_BASE,sizeof(int));
IPIV = (int *)(((unsigned long int)(_IPIV)+ALIGN_BASE)&~ALIGN_BASE);
//_evals = malloc(ldh*sizeof(double)+ALIGN_BASE);
_evals = calloc(ldh+ALIGN_BASE,sizeof(double));
evals = (double *)(((unsigned long int)(_evals)+ALIGN_BASE)&~ALIGN_BASE);
#else
V = (spinor *) calloc(LDN*v_max,sizeof(spinor));
H = calloc(ldh*ldh, sizeof(_Complex double ));
HU= calloc(ldh*ldh, sizeof(_Complex double ));
initwork = calloc(ldh, sizeof(_Complex double ));
ework = calloc(esize, sizeof(_Complex double ));
work = calloc(lwork,sizeof(_Complex double ));
rwork= calloc(3*ldh,sizeof(double));
IPIV = calloc(ldh, sizeof(int));
evals = (double *) calloc(ldh, sizeof(double));
#endif
} /*if(ncurRHS==1)*/
if(g_proc_id == g_stdio_proc && g_debug_level > 0) {
fprintf(stdout, "System %d, eps_sq %e\n",ncurRHS,eps_sq_used);
fflush(stdout);
}
/*---------------------------------------------------------------*/
/* Call eigCG until this right-hand side converges */
/*---------------------------------------------------------------*/
wE = 0.0; wI = 0.0; /* Start accumulator timers */
flag = -1; /* First time through. Run eigCG regularly */
maxit_remain = maxit; /* Initialize Max and current # of iters */
numIts = 0;
while( flag == -1 || flag == 3)
{
//if(g_proc_id==g_stdio_proc)
//printf("flag= %d, ncurEvals= %d\n",flag,ncurEvals);
if(ncurEvals > 0)
{
/* --------------------------------------------------------- */
/* Perform init-CG with evecs vectors */
/* xinit = xinit + evecs*Hinv*evec'*(b-Ax0) */
/* --------------------------------------------------------- */
wt1 = gettime();
/*r0=b-Ax0*/
normsq = square_norm(x,N,parallel);
if(normsq>0.0)
{
f(solver_field[0],x); /* solver_field[0]= A*x */
diff(solver_field[1],b,solver_field[0],N); /* solver_filed[1]=b-A*x */
}
else
assign(solver_field[1],b,N); /* solver_field[1]=b */
/* apply the deflation using init-CG */
/* evecs'*(b-Ax) */
for(i=0; i<ncurEvals; i++)
{
initwork[i]= scalar_prod(evecs[i],solver_field[1],N,parallel);
}
/* solve the linear system H y = c */
tmpsize=ldh*ncurEvals;
_FT(zcopy) (&tmpsize,H,&ONE,HU,&ONE); /* copy H into HU */
_FT(zgesv) (&ncurEvals,&ONE,HU,&ldh,IPIV,initwork,&ldh,&info);
if(info != 0)
{
if(g_proc_id == g_stdio_proc) {
fprintf(stderr, "Error in ZGESV:, info = %d\n",info);
fflush(stderr);
}
exit(1);
}
/* x = x + evecs*inv(H)*evecs'*r */
for(i=0; i<ncurEvals; i++)
{
assign_add_mul(x,evecs[i],initwork[i],N);
}
/* compute elapsed time and add to accumulator */
wt2 = gettime();
wI = wI + wt2-wt1;
}/* if(ncurEvals > 0) */
/* ------------------------------------------------------------ */
/* Adjust nev for eigcg according to available ldh/restart */
/* ------------------------------------------------------------ */
if (flag == 3) { /* restart with the same rhs, set nev_used = 0 */
nev_used = 0;
/* if convergence seems before next restart do not restart again */
if(rel_prec)
{
if (cur_res*(restart_eps_sq) < eps_sq*normb*normb)
restart_eps_sq=0.0;
}
else
{
if (cur_res*(restart_eps_sq) < eps_sq)
restart_eps_sq=0.0;
} /* if(rel_prec) */
}
else
{
/* First time through this rhs. Find nev evecs */
/* limited by the ldh evecs we can store in total */
if (ldh-ncurEvals < nev)
nev = ldh - ncurEvals;
nev_used = nev;
}
/* ------------------------------------------------------------ */
/* Solve Ax = b with x initial guess */
/* ------------------------------------------------------------ */
wt1 = gettime();
eigcg( N, LDN, x, b, &normb, eps_sq_used, restart_eps_sq, rel_prec, maxit_remain,
&numIts, &cur_res, &flag, solver_field, f,
nev_used, v_max, V, esize, ework);
//if(g_proc_id == g_stdio_proc)
//printf("eigcg flag= %d \n",flag);
wt2 = gettime();
wE = wE + wt2-wt1;
/* if flag == 3 update the remain max number of iterations */
maxit_remain = maxit - numIts;
}
/* end while (flag ==-1 || flag == 3) */
/* ------------------------------------------------ */
/* ---------- */
/* Reporting */
/* ---------- */
/* compute the exact residual */
f(solver_field[0],x); /* solver_field[0]= A*x */
diff(solver_field[1],b,solver_field[0],N); /* solver_filed[1]=b-A*x */
normsq=square_norm(solver_field[1],N,parallel);
if(g_debug_level > 0 && g_proc_id == g_stdio_proc)
{
fprintf(stdout, "For this rhs:\n");
fprintf(stdout, "Total initCG Wallclock : %-f\n", wI);
fprintf(stdout, "Total eigpcg Wallclock : %-f\n", wE);
fprintf(stdout, "Iterations: %-d\n", numIts);
fprintf(stdout, "Residual: %e, Actual Resid of LinSys : %e\n", cur_res,normsq);
if (flag != 0) {
fprintf(stderr, "Error: eigcg returned with nonzero exit status\n");
return flag;
fflush(stderr);
}
fflush(stdout);
}
/* ------------------------------------------------------------------- */
/* ------------------------------------------------------------------- */
/* Update the evecs and the factorization of evecs'*A*evecs */
/* ------------------------------------------------------------------- */
if (nev > 0)
{
wt1 = gettime();
/* Append new Ritz vectors to the basis and orthogonalize them to evecs */
for(i=0; i<nev_used; i++)
assign(evecs[i+ncurEvals],&V[i*LDN],N);
nAdded = ortho_new_vectors(evecs,N,ncurEvals,nev_used,machEps);
/* expand H */
for(j=ncurEvals; j< (ncurEvals+nAdded); j++)
{
f(solver_field[0],evecs[j]);
for(i=0; i<=j; i++)
{
H[i+j*ldh] = scalar_prod(evecs[i],solver_field[0],N,parallel);
H[j+i*ldh]= conj(H[i+j*ldh]);
//H[j+i*ldh].re = H[i+j*ldh].re;
//H[j+i*ldh].im = -H[i+j*ldh].im;
}
}
/* update the number of vectors in the basis */
ncurEvals = ncurEvals + nAdded;
/* ---------- */
/* Reporting */
/* ---------- */
wt2 = gettime();
if(g_proc_id == g_stdio_proc && g_debug_level > 0)
{
fprintf(stdout,"ncurRHS %d\n",ncurRHS);
fprintf(stdout,"ncurEvals %d \n",ncurEvals);
fprintf(stdout,"Update\n");
fprintf(stdout,"Added %d vecs\n",nAdded);
fprintf(stdout,"U Wallclock : %-f\n", wt2-wt1);
fprintf(stdout,"Note: Update Wall time doesn't include time for computing eigenvalues and their residuals.\n");
fflush(stdout);
}
if(g_debug_level > 3) /*compute eigenvalues and their residuals if requested*/
{
/* copy H into HU */
tmpsize=ldh*ncurEvals;
_FT(zcopy) (&tmpsize,H,&ONE,HU,&ONE);
/* compute eigenvalues and eigenvectors of HU (using V and spinor fields as tmp work spaces)*/
_FT(zheev)(&cV, &cU, &ncurEvals, HU, &ldh, evals, work, &lwork, rwork, &info,1,1);
if(info != 0)
{
if(g_proc_id == g_stdio_proc)
{
fprintf(stderr,"Error in ZHEEV:, info = %d\n",info);
fflush(stderr);
}
exit(1);
}
/* compute residuals and print out results */
for(i=0; i<ncurEvals; i++)
{
tmpi=12*N;
tmpsize=12*LDN;
_FT(zgemv)(&cN,&tmpi,&ncurEvals,&tpone,(_Complex double *)evecs[0],&tmpsize,
&HU[i*ldh], &ONE,&tzero,(_Complex double *) solver_field[0],&ONE,1);
normsq=square_norm(solver_field[0],N,parallel);
f(solver_field[1],solver_field[0]);
tempz = scalar_prod(solver_field[0],solver_field[1],N,parallel);
evals[i] = creal(tempz)/normsq;
mul_r(solver_field[2],evals[i],solver_field[0],N);
diff(solver_field[3],solver_field[1],solver_field[2], N);
tmpd2= square_norm(solver_field[3],N,parallel);
tmpd= sqrt(tmpd2/normsq);
if(g_proc_id == g_stdio_proc)
{fprintf(stdout,"RR Eval[%d]: %22.15E rnorm: %22.15E\n", i+1, evals[i], tmpd); fflush(stdout);}
}
}/*if(plvl >= 2)*/
} /* if(nev>0) */
/*--------------------------------------*/
/*free memory that is no longer needed */
/* and reset ncurRHS and ncurEvals */
/*--------------------------------------*/
if(ncurRHS == nrhs) /*this was the last system to be solved */
{
ncurRHS=0;
ncurEvals=0;
finalize_solver(solver_field,nrsf);
}
if( (ncurRHS == nrhs) && (nev >0) )/*this was the last system to be solved and there were allocated memory for eigenvector computation*/
{
finalize_solver(evecs,ldh);
#if (defined SSE || defined SSE2 || defined SSE3)
free(_v);
free(_h);
free(_hu);
free(_ework);
free(_initwork);
free(_IPIV);
free(_evals);
free(_rwork);
free(_work);
#else
free(V);
free(H);
free(HU);
free(ework);
free(initwork);
free(IPIV);
free(evals);
free(rwork);
free(work);
#endif
}
return numIts;
}
int gcr(spinor * const P, spinor * const Q,
const int m, const int max_restarts,
const double eps_sq, const int rel_prec,
const int N, const int precon, matrix_mult f) {
int k, l, restart, i, iter = 0;
double norm_sq, err;
spinor * rho, * tmp;
complex ctmp;
spinor ** solver_field = NULL;
const int nr_sf = 2;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
}
rho = solver_field[0];
tmp = solver_field[1];
init_gcr(m, N+RAND);
norm_sq = square_norm(Q, N, 1);
if(norm_sq < 1.e-32) {
norm_sq = 1.;
}
for(restart = 0; restart < max_restarts; restart++) {
dfl_sloppy_prec = 0;
f(tmp, P);
diff(rho, Q, tmp, N);
err = square_norm(rho, N, 1);
if(g_proc_id == g_stdio_proc && g_debug_level > 2){
printf("GCR: iteration number: %d, true residue: %g\n", iter, err);
fflush(stdout);
}
if(((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*norm_sq) && (rel_prec == 1))) {
finalize_solver(solver_field, nr_sf);
return(iter);
}
for(k = 0; k < m; k++) {
if(precon == 0) {
assign(xi[k], rho, N);
}
else {
zero_spinor_field(xi[k], N);
Msap_eo(xi[k], rho, 6);
/* Msap(xi[k], rho, 8); */
}
dfl_sloppy_prec = 1;
dfl_little_D_prec = 1.e-12;
f(tmp, xi[k]);
/* tmp will become chi[k] */
for(l = 0; l < k; l++) {
a[l][k] = scalar_prod(chi[l], tmp, N, 1);
assign_diff_mul(tmp, chi[l], a[l][k], N);
}
b[k] = sqrt(square_norm(tmp, N, 1));
mul_r(chi[k], 1./b[k], tmp, N);
c[k] = scalar_prod(chi[k], rho, N, 1);
assign_diff_mul(rho, chi[k], c[k], N);
err = square_norm(rho, N, 1);
iter ++;
if(g_proc_id == g_stdio_proc && g_debug_level > 0){
if(rel_prec == 1) printf("# GCR: %d\t%g >= %g iterated residue\n", iter, err, eps_sq*norm_sq);
else printf("# GCR: %d\t%g >= %giterated residue\n", iter, err, eps_sq);
fflush(stdout);
}
/* Precision reached? */
if((k == m-1) || ((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*norm_sq) && (rel_prec == 1))) {
break;
}
}
/* prepare for restart */
_mult_real(c[k], c[k], 1./b[k]);
assign_add_mul(P, xi[k], c[k], N);
for(l = k-1; l >= 0; l--) {
for(i = l+1; i <= k; i++) {
_mult_assign_complex(ctmp, a[l][i], c[i]);
/* c[l] -= ctmp */
_diff_complex(c[l], ctmp);
}
_mult_real(c[l], c[l], 1./b[l]);
assign_add_mul(P, xi[l], c[l], N);
}
}
finalize_solver(solver_field, nr_sf);
return(-1);
}
void Msap_eo(spinor * const P, spinor * const Q, const int Ncy, const int Niter) {
int ncy = 0, vol, vols;
spinor * r, * a, * b;
double nrm;
double musave = g_mu;
double kappasave = g_kappa;
spinor ** solver_field = NULL;
// also get space for mrblk! 6 = 3+3
const int nr_sf = 6;
if(kappa_Msap > 0) {
g_kappa = kappa_Msap;
}
if(mu_Msap > -10) {
g_mu = mu_Msap;
// make sure the sign is correct!
if(g_mu*musave < 0) g_mu *= -1.;
}
boundary(g_kappa);
/*
* here it would be probably better to get the working fields as a parameter
* from the calling function
*/
vols = block_list[0].volume/2+block_list[0].spinpad;
vol = block_list[0].volume/2;
init_solver_field(&solver_field, nb_blocks*2*vols, nr_sf);
r = solver_field[0];
a = solver_field[1];
b = solver_field[2];
int * blk_e_list = malloc(nb_blocks/2*sizeof(int));
int * blk_o_list = malloc(nb_blocks/2*sizeof(int));
int iblke = 0, iblko = 0;
for(int blk = 0; blk < nb_blocks; blk++) {
if (block_list[blk].evenodd == 0) {
blk_e_list[iblke] = blk;
iblke++;
}
else {
blk_o_list[iblko] = blk;
iblko++;
}
}
for(ncy = 0; ncy < Ncy; ncy++) {
/* compute the global residue */
/* this can be done more efficiently */
/* here only a naive implementation */
for(int eo = 0; eo < 2; eo++) {
D_psi(r, P);
diff(r, Q, r, VOLUME);
nrm = square_norm(r, VOLUME, 1);
if(g_proc_id == 0 && g_debug_level > 2 && eo == 0) {
printf("Msap_eo: %d %1.3e mu = %e\n", ncy, nrm, g_mu/2./g_kappa);
fflush(stdout);
}
int * blk_eo_list;
if(eo == 0) {
blk_eo_list = blk_e_list;
}
else {
blk_eo_list = blk_o_list;
}
/* choose the even (odd) block */
// rely on nested parallelism
//
#ifdef TM_USE_OMP
# pragma omp parallel for
#endif
for (int iblk = 0; iblk < nb_blocks/2; iblk++) {
int blk = blk_eo_list[iblk];
spinor32 * b_even = (spinor32*) (b + blk*2*vols);
spinor32 * b_odd = (spinor32*) (b +blk*2*vols + vols);
spinor32 * a_even = (spinor32*) (a + blk*2*vols);
spinor32 * a_odd = (spinor32*) (a + blk*2*vols + vols);
// mrblk needs 3 solver fields which we distribute according to the block number
spinor32 * c = (spinor32*) (solver_field[3] + blk*2*3*vols);
/* get part of r corresponding to block blk into b_even and b_odd */
copy_global_to_block_eo_32(b_even, b_odd, r, blk);
if(g_c_sw > 0) {
assign_mul_one_sw_pm_imu_inv_block_32(EE, a_even, b_even, g_mu, &block_list[blk]);
Block_H_psi_32(&block_list[blk], a_odd, a_even, OE);
/* a_odd = b_odd - a_odd */
diff_32(a_odd, b_odd, a_odd, vol);
mrblk_32(b_odd, a_odd, c,
Niter, 1.e-31, 1, vol, &Msw_plus_block_psi_32, blk);
Block_H_psi_32(&block_list[blk], b_even, b_odd, EO);
assign_32(c, b_even, vol);
assign_mul_one_sw_pm_imu_inv_block_32(EE, b_even, c, g_mu, &block_list[blk]);
}
else {
assign_mul_one_pm_imu_inv_32(a_even, b_even, +1., vol);
Block_H_psi_32(&block_list[blk], a_odd, a_even, OE);
/* a_odd = b_odd - a_odd */
diff_32(a_odd, b_odd, a_odd, vol);
mrblk_32(b_odd, a_odd, c,
Niter, 1.e-31, 1, vol, &Mtm_plus_block_psi_32, blk);
Block_H_psi_32(&block_list[blk], b_even, b_odd, EO);
mul_one_pm_imu_inv_32(b_even, +1., vol);
}
/* a_even = a_even - b_even */
diff_32(a_even, a_even, b_even, vol);
/* add even and odd part up to full spinor P */
add_eo_block_32_to_global(P, a_even, b_odd, blk);
}
}
}
free(blk_e_list);
free(blk_o_list);
finalize_solver(solver_field, nr_sf);
g_mu = musave;
g_kappa = kappasave;
boundary(g_kappa);
return;
}
/* P output = solution , Q input = source */
int pcg_her(spinor * const P, spinor * const Q, const int max_iter,
double eps_sq, const int rel_prec, const int N, matrix_mult f) {
double normsp, pro, pro2, err, alpha_cg, beta_cg, squarenorm;
int iteration;
spinor ** solver_field = NULL;
const int nr_sf = 5;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
}
squarenorm = square_norm(Q, N, 1);
/* !!!! INITIALIZATION !!!! */
assign(solver_field[0], P, N);
/* (r_0,r_0) = normsq */
normsp = square_norm(P, N, 1);
assign(solver_field[3], Q, N);
/* initialize residue r and search vector p */
if(normsp==0){
/* if a starting solution vector equal to zero is chosen */
/* r0 */
assign(solver_field[1], solver_field[3], N);
/* p0 */
}
else{
/* if a starting solution vector different from zero is chosen */
/* r0 = b - A x0 */
f(solver_field[2], solver_field[0]);
diff(solver_field[1], solver_field[3], solver_field[2], N);
}
/* z0 = M^-1 r0 */
invert_eigenvalue_part(solver_field[3], solver_field[1], 10, N);
/* p0 = z0 */
assign(solver_field[2], solver_field[3], N);
/* Is this really real? */
pro2 = scalar_prod_r(solver_field[1], solver_field[3], N, 1);
/* main loop */
for(iteration = 0; iteration < max_iter; iteration++) {
/* A p */
f(solver_field[4], solver_field[2]);
pro = scalar_prod_r(solver_field[2], solver_field[4], N, 1);
/* Compute alpha_cg(i+1) */
alpha_cg=pro2/pro;
/* Compute x_(i+1) = x_i + alpha_cg(i+1) p_i */
assign_add_mul_r(solver_field[0], solver_field[2], alpha_cg, N);
/* Compute r_(i+1) = r_i - alpha_cg(i+1) Qp_i */
assign_add_mul_r(solver_field[1], solver_field[4], -alpha_cg, N);
/* Check whether the precision is reached ... */
err=square_norm(solver_field[1], N, 1);
if(g_debug_level > 1 && g_proc_id == g_stdio_proc) {
printf("%d\t%g\n",iteration,err); fflush( stdout);
}
if(((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*squarenorm) && (rel_prec == 1))) {
assign(P, solver_field[0], N);
g_sloppy_precision = 0;
finalize_solver(solver_field, nr_sf);
return(iteration+1);
}
#ifdef _USE_HALFSPINOR
if(((err*err <= eps_sq) && (rel_prec == 0)) || ((err*err <= eps_sq*squarenorm) && (rel_prec == 1)) || iteration > 1400) {
g_sloppy_precision = 1;
if(g_debug_level > 2 && g_proc_id == g_stdio_proc) {
printf("sloppy precision on\n"); fflush( stdout);
}
}
#endif
/* z_j */
beta_cg = 1/pro2;
/* invert_eigenvalue_part(solver_field[3], solver_field[1], 10, N); */
/* Compute beta_cg(i+1)
Compute p_(i+1) = r_i+1 + beta_(i+1) p_i */
pro2 = scalar_prod_r(solver_field[1], solver_field[3], N, 1);
beta_cg *= pro2;
assign_mul_add_r(solver_field[2], beta_cg, solver_field[3], N);
}
assign(P, solver_field[0], N);
g_sloppy_precision = 0;
/* return(-1); */
finalize_solver(solver_field, nr_sf);
return(1);
}
int cr(spinor * const P, spinor * const Q,
const int m, const int max_restarts,
const double eps_sq, const int rel_prec,
const int N, const int precon, matrix_mult f) {
int k, l, restart, i, iter = 0;
double norm_sq, err;
spinor * xi, * Axi, * chi, * Achi, *tmp;
_Complex double alpha, beta;
static _Complex double one = 1.0;
double norm, rAr, newrAr;
double atime, etime;
spinor ** solver_field = NULL;
const int nr_sf = 5;
int save_sloppy = g_sloppy_precision;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
}
atime = gettime();
xi = solver_field[0];
Axi = solver_field[1];
chi = solver_field[2];
Achi = solver_field[3];
tmp = solver_field[4];
norm_sq = square_norm(Q, N, 1);
if(norm_sq < 1.e-32) {
norm_sq = 1.;
}
dfl_sloppy_prec = 0;
f(tmp, P);
diff(chi, Q, tmp, N);
assign(xi, chi, N);
f(Axi, xi);
f(Achi, chi);
rAr = scalar_prod(chi, Achi, N, 1);
err = square_norm(chi, N, 1);
if(((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*norm_sq) && (rel_prec == 1))) {
finalize_solver(solver_field, nr_sf);
return(iter);
}
for(k = 0; k < m; k++) {
dfl_sloppy_prec = 1;
norm = square_norm(Axi, N, 1);
alpha = rAr/norm;
assign_add_mul(P, xi, alpha, N);
/* get the new residual */
assign_diff_mul(chi, Axi, alpha, N);
err = square_norm(chi, N, 1);
iter ++;
etime = gettime();
if(g_proc_id == g_stdio_proc && g_debug_level > 3){
printf("# CR: %d\t%g iterated residue, time spent %f s\n", iter, err, (etime - atime));
fflush(stdout);
}
/* Precision reached? */
if((k == m-1) || ((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*norm_sq) && (rel_prec == 1))) {
break;
}
#ifdef _USE_HALFSPINOR
if(((err*err <= eps_sq) && (rel_prec == 0)) || ((err*err <= eps_sq*norm_sq) && (rel_prec == 1))) {
if (g_sloppy_precision_flag == 1) {
g_sloppy_precision = 1;
if(g_debug_level > 2 && g_proc_id == g_stdio_proc) {
printf("sloppy precision on\n"); fflush( stdout);
}
}
}
#endif
f(Achi, chi);
newrAr = scalar_prod(chi, Achi, N, 1);
beta = newrAr/rAr;
assign_mul_add_mul(xi, beta, chi, one, N);
assign_mul_add_mul(Axi,beta, Achi, one, N);
rAr = newrAr;
}
g_sloppy_precision = save_sloppy;
finalize_solver(solver_field, nr_sf);
return(-1);
}
/* P inout (guess for the solving spinor)
Q input
*/
int bicgstab_complex(spinor * const P,spinor * const Q, const int max_iter,
double eps_sq, const int rel_prec,
const int N, matrix_mult f){
double err, d1, squarenorm;
complex rho0, rho1, omega, alpha, beta, nom, denom;
int i;
spinor * r, * p, * v, *hatr, * s, * t;
spinor ** solver_field = NULL;
const int nr_sf = 6;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
}
hatr = solver_field[0];
r = solver_field[1];
v = solver_field[2];
p = solver_field[3];
s = solver_field[4];
t = solver_field[5];
f(r, P);
diff(p, Q, r, N);
assign(r, p, N);
assign(hatr, p, N);
rho0 = scalar_prod(hatr, r, N, 1);
squarenorm = square_norm(Q, N, 1);
for(i = 0; i < max_iter; i++){
err = square_norm(r, N, 1);
if(g_proc_id == g_stdio_proc && g_debug_level > 1) {
printf("%d %e\n", i, err);
fflush(stdout);
}
if((((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*squarenorm) && (rel_prec == 1))) && i>0) {
finalize_solver(solver_field, nr_sf);
return(i);
}
f(v, p);
denom = scalar_prod(hatr, v, N, 1);
_div_complex(alpha, rho0, denom);
assign(s, r, N);
assign_diff_mul(s, v, alpha, N);
f(t, s);
omega = scalar_prod(t,s, N, 1);
d1 = square_norm(t, N, 1);
omega.re/=d1; omega.im/=d1;
assign_add_mul_add_mul(P, p, s, alpha, omega, N);
assign(r, s, N);
assign_diff_mul(r, t, omega, N);
rho1 = scalar_prod(hatr, r, N, 1);
if(fabs(rho1.re) < 1.e-25 && fabs(rho1.im) < 1.e-25) {
finalize_solver(solver_field, nr_sf);
return(-1);
}
_mult_assign_complex(nom, alpha, rho1);
_mult_assign_complex(denom, omega, rho0);
_div_complex(beta, nom, denom);
omega.re=-omega.re; omega.im=-omega.im;
assign_mul_bra_add_mul_ket_add(p, v, r, omega, beta, N);
rho0.re = rho1.re; rho0.im = rho1.im;
}
finalize_solver(solver_field, nr_sf);
return -1;
}
int bicgstab2(spinor * const x0, spinor * const b, const int max_iter,
double eps_sq, const int rel_prec, const int N, matrix_mult f) {
const int l = 2;
double err;
int i, j, k;
int update_app = 0, update_res = 0;
double rho0, rho1, beta, alpha, omega, gamma_hat,
sigma, kappa0, kappal, rho, zeta0;
double squarenorm, Mx=0., Mr=0.;
spinor * r[5], * u[5], * r0_tilde, * u0, * x, * xp, * bp;
double Z[3][3], y0[3], yl[3], yp[3], ypp[3];
spinor ** solver_field = NULL;
const int nr_sf = 10;
k = -l;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
}
r0_tilde = solver_field[0];
u0 = solver_field[1];
r[0] = solver_field[2];
u[0] = solver_field[3];
r[1] = solver_field[4];
u[1] = solver_field[5];
r[2] = solver_field[6];
u[2] = solver_field[7];
bp = solver_field[8];
xp = x0;
x = solver_field[9];
zero_spinor_field(x, N);
assign(u[0], b, N);
f(r0_tilde, xp);
diff(r[0], u[0], r0_tilde, N);
zero_spinor_field(u0, N);
assign(r0_tilde, r[0], N);
/* random_spinor_field(r0_tilde, N); */
assign(bp, r[0], N);
squarenorm = square_norm(b, N, 1);
rho0 = 1.;
alpha = rho0;
omega = rho0;
err = square_norm(r[0], N, 1);
Mr = err;
Mx = err;
zeta0 = err;
while( k < max_iter && (((err > eps_sq) && (rel_prec == 0))
|| ((err > eps_sq*squarenorm) && (rel_prec == 1))
)) {
k+=l;
/* The BiCG part */
rho0 *= -omega;
for(j = 0; j < l; j++) {
rho1 = scalar_prod_r(r[j], r0_tilde, N, 1);
beta = alpha*(rho1/rho0);
rho0 = rho1;
/* if(g_proc_id == 0) {printf("beta = %e, alpha = %e, rho0 = %e\n", beta, alpha, rho0);fflush(stdout);} */
for(i = 0; i <= j; i++) {
/* u_i = r_i - \beta u_i */
assign_mul_add_r(u[i], -beta, r[i], N);
}
f(u[j+1], u[j]);
sigma = scalar_prod_r(u[j+1], r0_tilde, N, 1);
alpha = rho1/sigma;
/* if(g_proc_id == 0) {printf("sigma = %e, alpha = %e\n", sigma, alpha);fflush(stdout);} */
/* x = x + \alpha u_0 */
assign_add_mul_r(x, u[0], alpha, N);
/* r_i = r_i - \alpha u_{i+1} */
for(i = 0; i <= j; i++) {
assign_add_mul_r(r[i], u[i+1], -alpha, N);
}
f(r[j+1], r[j]);
err = square_norm(r[j+1], N, 1);
if(g_proc_id == 0 && g_debug_level > 1) {printf("%d %d err = %e\n", k, j, err);fflush(stdout);}
if(err > Mr) Mr = err;
if(err > Mx) Mx = err;
}
/* The polynomial part */
/* Z = R* R */
for(i = 0; i <= l; i++){
for(j = 0; j <= i; j++){
Z[i][j] = scalar_prod_r(r[j], r[i], N, 1);
Z[j][i] = Z[i][j];
}
}
/* r0tilde and rl_tilde */
y0[0] = -1;
y0[2] = 0.;
y0[1] = Z[1][0]/Z[1][1];
yl[0] = 0.;
yl[2] = -1.;
yl[1] = Z[1][2]/Z[1][1];
/* Convex combination */
for(i = 0; i < l+1; i++){
yp[i] = 0.;
ypp[i] = 0.;
for(j = 0; j < l+1; j++) {
yp[i] +=Z[i][j]*y0[j];
ypp[i] +=Z[i][j]*yl[j];
}
}
kappa0 = sqrt( y0[0]*yp[0] + y0[1]*yp[1] + y0[2]*yp[2] );
kappal = sqrt( yl[0]*ypp[0] + yl[1]*ypp[1] + yl[2]*ypp[2] );
rho = (yl[0]*yp[0] + yl[1]*yp[1] + yl[2]*yp[2])/kappa0/kappal;
if(fabs(rho) > 0.7) {
gamma_hat = rho;
}
else {
gamma_hat = rho*0.7/fabs(rho);
}
for(i = 0; i <= l; i++) {
y0[i] -= gamma_hat*kappa0*yl[i]/kappal;
}
/* Update */
omega = y0[l];
for(i = 1; i < l+1; i++) {
assign_add_mul_r(u[0], u[i], -y0[i], N);
assign_add_mul_r(x, r[i-1], y0[i], N);
assign_add_mul_r(r[0], r[i], -y0[i], N);
}
err = kappa0*kappa0;
/* Reliable update part */
if(err > Mr) Mr = err;
if(err > Mx) Mx = err;
update_app = (err < 1.e-4*zeta0 && zeta0 <= Mx);
update_res = ((err < 1.e-4*Mr && zeta0 <= Mr) || update_app);
if(update_res) {
if(g_proc_id == 0 && g_debug_level > 1) printf("Update res\n");
f(r[0], x);
diff(r[0], bp, r[0], N);
Mr = err;
if(update_app) {
if(g_proc_id == 0 && g_debug_level > 1) printf("Update app\n");
Mx = err;
assign_add_mul_r(xp, x, 1., N);
zero_spinor_field(x, N);
assign(bp, r[0], N);
}
}
update_app = 0;
update_res = 0;
if(g_proc_id == 0 && g_debug_level > 0){
printf(" BiCGstab(2)convex iterated %d %d, %e rho0 = %e, alpha = %e, gamma_hat= %e\n",
l, k, err, rho0, alpha, gamma_hat);
fflush( stdout );
}
}
assign_add_mul_r(x, xp, 1., N);
assign(x0, x, N);
if(k == max_iter) return(-1);
return(k);
}
/* P output = solution , Q input = source */
int mixed_cg_her(spinor * const P, spinor * const Q, solver_params_t solver_params,
const int max_iter, double eps_sq, const int rel_prec, const int N,
matrix_mult f, matrix_mult32 f32) {
int i = 0, iter = 0, j = 0;
float sqnrm = 0., sqnrm2, squarenorm;
float pro, err, alpha_cg, beta_cg;
double sourcesquarenorm, sqnrm_d, squarenorm_d;
spinor *delta, *y, *xhigh;
spinor32 *x, *stmp;
spinor ** solver_field = NULL;
spinor32 ** solver_field32 = NULL;
const int nr_sf = 3;
const int nr_sf32 = 4;
int max_inner_it = mixcg_maxinnersolverit;
int N_outer = max_iter/max_inner_it;
//to be on the save side we allow at least 10 outer iterations
if(N_outer < 10) N_outer = 10;
int save_sloppy = g_sloppy_precision_flag;
double atime, etime, flops;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
init_solver_field_32(&solver_field32, VOLUMEPLUSRAND, nr_sf32);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
init_solver_field_32(&solver_field32, VOLUMEPLUSRAND/2, nr_sf32);
}
squarenorm_d = square_norm(Q, N, 1);
sourcesquarenorm = squarenorm_d;
sqnrm_d = squarenorm_d;
delta = solver_field[0];
y = solver_field[1];
xhigh = solver_field[2];
x = solver_field32[3];
assign(delta, Q, N);
//set solution to zero
zero_spinor_field(P, N);
atime = gettime();
for(i = 0; i < N_outer; i++) {
/* main CG loop in lower precision */
zero_spinor_field_32(x, N);
zero_spinor_field_32(solver_field32[0], N);
assign_to_32(solver_field32[1], delta, N);
assign_to_32(solver_field32[2], delta, N);
sqnrm = (float) sqnrm_d;
sqnrm2 = sqnrm;
/*inner CG loop */
for(j = 0; j <= max_inner_it; j++) {
f32(solver_field32[0], solver_field32[2]);
pro = scalar_prod_r_32(solver_field32[2], solver_field32[0], N, 1);
alpha_cg = sqnrm2 / pro;
assign_add_mul_r_32(x, solver_field32[2], alpha_cg, N);
assign_mul_add_r_32(solver_field32[0], -alpha_cg, solver_field32[1], N);
err = square_norm_32(solver_field32[0], N, 1);
if(g_proc_id == g_stdio_proc && g_debug_level > 2) {
printf("inner CG: %d res^2 %g\n", iter+j, err);
fflush(stdout);
}
//if (((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*squarenorm) && (rel_prec == 1))){
if((err <= mixcg_innereps*sqnrm)|| (j==max_inner_it) || ((1.3*err <= eps_sq) && (rel_prec == 0)) || ((1.3*err <= eps_sq*sourcesquarenorm) && (rel_prec == 1))) {
break;
}
beta_cg = err / sqnrm2;
assign_mul_add_r_32(solver_field32[2], beta_cg, solver_field32[0], N);
stmp = solver_field32[0];
solver_field32[0] = solver_field32[1];
solver_field32[1] = stmp;
sqnrm2 = err;
}
/* end inner CG loop */
iter += j;
/* we want to apply a true double matrix with f(y,P) -> set sloppy off here*/
g_sloppy_precision_flag = 0;
/* calculate defect in double precision */
assign_to_64(xhigh, x, N);
add(P, P, xhigh, N);
f(y, P);
diff(delta, Q, y, N);
sqnrm_d = square_norm(delta, N, 1);
if(g_debug_level > 2 && g_proc_id == 0) {
printf("mixed CG: last inner residue: %g\t\n", err);
printf("mixed CG: true residue %d %g\t\n",iter, sqnrm_d); fflush(stdout);
}
/* here we can reset it to its initial value*/
g_sloppy_precision_flag = save_sloppy;
if(((sqnrm_d <= eps_sq) && (rel_prec == 0)) || ((sqnrm_d <= eps_sq*sourcesquarenorm) && (rel_prec == 1))) {
etime = gettime();
if(g_debug_level > 0 && g_proc_id == 0) {
if(N != VOLUME){
/* 2 A + 2 Nc Ns + N_Count ( 2 A + 10 Nc Ns ) */
/* 2*1608.0 because the linalg is over VOLUME/2 */
flops = (2*(2*1608.0+2*3*4) + 2*3*4 + iter*(2.*(2*1608.0+2*3*4) + 10*3*4))*N/1.0e6f;
printf("# mixed CG: iter: %d eps_sq: %1.4e t/s: %1.4e\n", iter, eps_sq, etime-atime);
printf("# mixed CG: flopcount (for e/o tmWilson only): t/s: %1.4e mflops_local: %.1f mflops: %.1f\n",
etime-atime, flops/(etime-atime), g_nproc*flops/(etime-atime));
}
else{
/* 2 A + 2 Nc Ns + N_Count ( 2 A + 10 Nc Ns ) */
flops = (2*(1608.0+2*3*4) + 2*3*4 + iter*(2.*(1608.0+2*3*4) + 10*3*4))*N/1.0e6f;
printf("# mixed CG: iter: %d eps_sq: %1.4e t/s: %1.4e\n", iter, eps_sq, etime-atime);
printf("# mixed CG: flopcount (for non-e/o tmWilson only): t/s: %1.4e mflops_local: %.1f mflops: %.1f\n",
etime-atime, flops/(etime-atime), g_nproc*flops/(etime-atime));
}
}
finalize_solver(solver_field, nr_sf);
finalize_solver_32(solver_field32, nr_sf32);
return(iter+i);
}
iter++;
}
finalize_solver(solver_field, nr_sf);
finalize_solver_32(solver_field32, nr_sf32);
return(-1);
}
void Msap_eo(spinor * const P, spinor * const Q, const int Ncy) {
int blk, ncy = 0, eo, vol;
spinor * r, * a, * b;
double nrm;
spinor * b_even, * b_odd, * a_even, * a_odd;
spinor ** solver_field = NULL;
const int nr_sf = 3;
/*
* here it would be probably better to get the working fields as a parameter
* from the calling function
*/
init_solver_field(&solver_field, VOLUME, nr_sf);
r = solver_field[0];
a = solver_field[1];
b = solver_field[2];
vol = block_list[0].volume/2;
b_even = b;
b_odd = b + vol + 1;
a_even = a;
a_odd = a + vol + 1;
for(ncy = 0; ncy < Ncy; ncy++) {
/* compute the global residue */
/* this can be done more efficiently */
/* here only a naive implementation */
for(eo = 0; eo < 2; eo++) {
D_psi(r, P);
diff(r, Q, r, VOLUME);
nrm = square_norm(r, VOLUME, 1);
if(g_proc_id == 0 && g_debug_level > 1 && eo == 1) {
printf("Msap: %d %1.3e\n", ncy, nrm);
}
/* choose the even (odd) block */
for (blk = 0; blk < nb_blocks; blk++) {
if(block_list[blk].evenodd == eo) {
/* get part of r corresponding to block blk into b_even and b_odd */
copy_global_to_block_eo(b_even, b_odd, r, blk);
assign_mul_one_pm_imu_inv(a_even, b_even, +1., vol);
Block_H_psi(&block_list[blk], a_odd, a_even, OE);
/* a_odd = a_odd - b_odd */
assign_mul_add_r(a_odd, -1., b_odd, vol);
mrblk(b_odd, a_odd, 3, 1.e-31, 1, vol, &Mtm_plus_block_psi, blk);
Block_H_psi(&block_list[blk], b_even, b_odd, EO);
mul_one_pm_imu_inv(b_even, +1., vol);
/* a_even = a_even - b_even */
assign_add_mul_r(a_even, b_even, -1., vol);
/* add even and odd part up to full spinor P */
add_eo_block_to_global(P, a_even, b_odd, blk);
}
}
}
}
finalize_solver(solver_field, nr_sf);
return;
}
int mixed_cg_mms_tm_nd(spinor ** const Pup, spinor ** const Pdn,
spinor * const Qup, spinor * const Qdn,
solver_pm_t * solver_pm) {
double eps_sq = solver_pm->squared_solver_prec;
int noshifts = solver_pm->no_shifts;
int rel_prec = solver_pm->rel_prec;
int max_iter = solver_pm->max_iter;
int check_abs, check_rel;
double * shifts = solver_pm->shifts;
int Nshift = noshifts;
// algorithm
double rr_up, rr_dn, rr, rr_old, r0r0, dAd_up, dAd_dn, dAd;
if(rel_prec){
check_rel = 1;
check_abs = 0;
}
else{
check_rel = 0;
check_abs = 1;
}
int use_eo=1, eofactor=2;
//not even-odd?
if(solver_pm->sdim == VOLUME) {
eofactor = 1;
use_eo = 0;
}
int N = VOLUME/eofactor;
int Vol = VOLUMEPLUSRAND/eofactor;
// norm of source
rr_up = square_norm(Qup, N, 1);
rr_dn = square_norm(Qdn, N, 1);
rr = rr_up + rr_dn;
if( (g_cart_id == 0 && g_debug_level > 2)) printf("# CGMMSND_mixed: Initial mms residue: %.6e\n", rr);
if(rr < 1.0e-4){
if( (g_cart_id == 0 && g_debug_level > 2)) printf("# CGMMSND_mixed: norm of source too low: falling back to double mms solver %.6e\n", rr);
return(cg_mms_tm_nd(Pup, Pdn, Qup, Qdn, solver_pm));
}
r0r0 = rr; // for relative precision
rr_old = rr; // for the first iteration
//allocate an auxiliary solver fields
spinor ** sf = NULL;
const int nr_sf = 6;
init_solver_field(&sf, Vol, nr_sf);
spinor32 ** sf32 = NULL;
const int nr_sf32 = 8;
init_solver_field_32(&sf32, Vol, nr_sf32);
//spinor fields
//we need one less than shifts, since one field is cared of by the usual cg fields
init_mms_tm_nd_32(noshifts-1, Vol);
// Pup/dn can be used as auxiliary field to work on, as it is not later used (could be used as initial guess at the very start)
// Q_up/dn can be used as feedback, or if not, also as auxiliary field
//allocate cg constants
double * sigma;
double * zitam1, * zita;
double * alphas, * betas;
double gamma;
double alpham1;
sigma = (double*)calloc((noshifts), sizeof(double));
zitam1 = (double*)calloc((noshifts), sizeof(double));
zita = (double*)calloc((noshifts), sizeof(double));
alphas = (double*)calloc((noshifts), sizeof(double));
betas = (double*)calloc((noshifts), sizeof(double));
spinor32 * r_up, * r_dn, * Ad_up, * Ad_dn, * x_up, * x_dn, * d_up, * d_dn;
spinor * r_up_d, * r_dn_d, * x_up_d, * x_dn_d, * Ax_up_d, * Ax_dn_d;
// iteration counter
int j;
//reliable update flag
int rel_update = 0;
//no of reliable updates done
int no_rel_update = 0;
//use reliable update flag
int use_reliable = 1;
double rel_delta = 1.0e-10;
int trigger_shift = -1;
double * res;
double * res0;
double * maxres;
res = (double*)calloc((noshifts), sizeof(double));
res0 = (double*)calloc((noshifts), sizeof(double));
maxres = (double*)calloc((noshifts), sizeof(double));
/////////////////
// ASSIGNMENTS //
/////////////////
x_up = sf32[0];
x_dn = sf32[1];
r_up = sf32[2];
r_dn = sf32[3];
d_up = sf32[4];
d_dn = sf32[5];
Ad_up = sf32[6];
Ad_dn = sf32[7];
x_up_d = sf[0];
x_dn_d = sf[1];
r_up_d = sf[2];
r_dn_d = sf[3];
Ax_up_d = sf[4];
Ax_dn_d = sf[5];
/*
//matrix test
spinor32 * help_low_up = sf32[0];
spinor32 * help_low_dn = sf32[1];
spinor * help_high_up = sf[0];
spinor * help_high_dn = sf[1];
assign_to_32(help_low_up, Qup, N);
assign_to_32(help_low_dn, Qdn, N);
assign(help_high_up, Qup, N);
assign(help_high_dn, Qdn, N);
double sqn_high = square_norm(help_high_up,N,1) +
square_norm(help_high_dn,N,1);
printf("square_norm(Q_high) = %e\n", sqn_high);
float sqn_low = square_norm_32(help_low_up,N,1) +
square_norm_32(help_low_dn,N,1);
printf("square_norm(Q_low) = %e\n", sqn_low);
solver_pm->M_ndpsi32(sf32[2], sf32[3], help_low_up, help_low_dn);
solver_pm->M_ndpsi(sf[2], sf[3], help_high_up, help_high_dn);
assign_to_64(sf[4], sf32[2], N);
assign_to_64(sf[5], sf32[3], N);
diff(sf[0], sf[4], sf[2], N);
diff(sf[1], sf[5], sf[3], N);
double sqnrm = square_norm(sf[0], N, 1) +
square_norm(sf[1], N, 1);
printf("Operator 32 test: (square_norm) / (spinor component) = %.8e\n", sqnrm/24.0/N);
exit(1);
*/
// r(0) = b
assign_to_32(r_up, Qup, N);
assign_to_32(r_dn, Qdn, N);
// d(0) = b
assign_to_32(d_up, Qup, N);
assign_to_32(d_dn, Qdn, N);
maxres[0] = rr;
res[0] = rr;
res0[0] = rr;
alphas[0] = 1.0;
betas[0] = 0.0;
sigma[0] = shifts[0]*shifts[0];
if(g_cart_id == 0 && g_debug_level > 2) printf("# CGMMSND_mixed: shift %d is %e\n", 0, sigma[0]);
// currently only implemented for P=0
for(int im = 1; im < noshifts; im++) {
maxres[im] = rr;
res[im] = rr;
res0[im] = rr;
sigma[im] = shifts[im]*shifts[im] - sigma[0];
if(g_cart_id == 0 && g_debug_level > 2) printf("# CGMMSND_mixed: shift %d is %e\n", im, sigma[im]);
// these will be the result spinor fields
zero_spinor_field_32(mms_x_up[im-1], N);
zero_spinor_field_32(mms_x_dn[im-1], N);
assign_to_32(mms_d_up[im-1], Qup, N);
assign_to_32(mms_d_dn[im-1], Qdn, N);
zitam1[im] = 1.0;
zita[im] = 1.0;
alphas[im] = 1.0;
betas[im] = 0.0;
}
//zero fields for solution Pup, Pdn
for(int im = 0; im < noshifts; im++){
zero_spinor_field(Pup[im], N);
zero_spinor_field(Pdn[im], N);
}
//////////
// LOOP //
//////////
for (j = 0; j < max_iter; j++) {
// A*d(k)
solver_pm->M_ndpsi32(Ad_up, Ad_dn, d_up, d_dn);
//add zero'th shift
assign_add_mul_r_32(Ad_up, d_up, (float) sigma[0], N);
assign_add_mul_r_32(Ad_dn, d_dn, (float) sigma[0], N);
// alpha = r(k)*r(k) / d(k)*A*d(k)
dAd_up = scalar_prod_r_32(d_up, Ad_up, N, 1);
dAd_dn = scalar_prod_r_32(d_dn, Ad_dn, N, 1);
dAd = dAd_up + dAd_dn;
alpham1 = alphas[0];
alphas[0] = rr_old / dAd; // rr_old is taken from the last iteration respectively
// r(k+1)
assign_add_mul_r_32(r_up, Ad_up, (float) -alphas[0],N);
assign_add_mul_r_32(r_dn, Ad_dn, (float) -alphas[0],N);
// r(k+1)*r(k+1)
rr_up = square_norm_32(r_up, N, 1);
rr_dn = square_norm_32(r_dn, N, 1);
rr = rr_up + rr_dn;
if((g_cart_id == 0) && (g_debug_level > 2)) printf("# CGMMSND_mixed: mms iteration j = %i: rr = %.6e\n", j, rr);
// aborting ?? // check wether precision is reached ...
if ( ((check_abs)&&(rr <= eps_sq)) || ((check_rel)&&(rr <= eps_sq*r0r0)) )
{
if ((check_rel)&&(rr <= eps_sq*r0r0)) {
if((g_cart_id == 0) && (g_debug_level > 3)) printf("# CGMMSND_mixed: Reached relative solver precision of eps_rel = %.2e\n", eps_sq);
}
break;
}
// update alphas and zitas
// used later
for(int im = 1; im < noshifts; im++) {
gamma = zita[im]*alpham1/(alphas[0]*betas[0]*(1.-zita[im]/zitam1[im])
+ alpham1*(1.+sigma[im]*alphas[0]));
zitam1[im] = zita[im];
zita[im] = gamma;
alphas[im] = alphas[0]*zita[im]/zitam1[im];
}
//check for reliable update
res[0] = rr;
for(int im=1; im<noshifts; im++) res[im] = rr * zita[im];
rel_update = 0;
for(int im = (noshifts-1); im >= 0; im--) {
if( res[im] > maxres[im] ) maxres[im] = res[im];
if( (res[im] < rel_delta*res0[im]) && (res0[im]<=maxres[im]) && (use_reliable) ) rel_update=1;
if( rel_update && ( trigger_shift == -1) ) trigger_shift = im;
}
if(!rel_update)
{
// x_j(k+1) = x_j(k) + alpha_j*d_j(k)
// alphas are set above
assign_add_mul_r_32(x_up, d_up, (float) alphas[0], N);
assign_add_mul_r_32(x_dn, d_dn, (float) alphas[0], N);
for(int im = 1; im < noshifts; im++) {
assign_add_mul_r_32(mms_x_up[im-1], mms_d_up[im-1], (float) alphas[im], N);
assign_add_mul_r_32(mms_x_dn[im-1], mms_d_dn[im-1], (float) alphas[im], N);
}
// beta = r(k+1)*r(k+1) / r(k)*r(k)
betas[0] = rr / rr_old;
rr_old = rr; // for next iteration
// d_0(k+1) = r(k+1) + beta*d_0(k)
assign_mul_add_r_32(d_up, (float) betas[0], r_up, N);
assign_mul_add_r_32(d_dn, (float) betas[0], r_dn, N);
// d_j(k+1) = zita*r(k+1) + beta*d_j(k)
for(int im = 1; im < noshifts; im++) {
betas[im] = betas[0]*zita[im]*alphas[im]/(zitam1[im]*alphas[0]);
assign_mul_add_mul_r_32(mms_d_up[im-1], r_up, (float) betas[im], (float) zita[im], N);
assign_mul_add_mul_r_32(mms_d_dn[im-1], r_dn, (float) betas[im], (float) zita[im], N);
}
}
else{
//reliable update
if( (g_cart_id == 0) && (g_debug_level > 3) ){
printf("# CGMMSND_mixed: Shift %d with offset squared %e triggered a reliable update\n", trigger_shift, sigma[trigger_shift]);
}
//add low prec solutions
assign_add_mul_r_32(x_up, d_up, (float) alphas[0], N);
assign_add_mul_r_32(x_dn, d_dn, (float) alphas[0], N);
addto_32(Pup[0], x_up, N);
addto_32(Pdn[0], x_dn, N);
for(int im = 1; im < noshifts; im++) {
assign_add_mul_r_32(mms_x_up[im-1], mms_d_up[im-1], alphas[im], N);
assign_add_mul_r_32(mms_x_dn[im-1], mms_d_dn[im-1], alphas[im], N);
addto_32(Pup[im], mms_x_up[im-1], N);
addto_32(Pdn[im], mms_x_dn[im-1], N);
}
//add low precision for shift 0 only
addto_32(x_up_d, x_up, N);
addto_32(x_dn_d, x_dn, N);
solver_pm->M_ndpsi(Ax_up_d, Ax_dn_d, x_up_d, x_dn_d);
//add zero'th shift
assign_add_mul_r(Ax_up_d, x_up_d, sigma[0], N);
assign_add_mul_r(Ax_dn_d, x_dn_d, sigma[0], N);
diff(r_up_d, Qup, Ax_up_d, N);
diff(r_dn_d, Qdn, Ax_dn_d, N);
rr_up = square_norm(r_up_d, N, 1);
rr_dn = square_norm(r_dn_d, N, 1);
rr = rr_up + rr_dn;
if ((g_cart_id == 0) && (g_debug_level > 3) ) printf("# CGMMSND_mixed: New residue after reliable update: %.6e\n", rr);
//update res[im]
res[0] = rr;
if(res[trigger_shift] > res0[trigger_shift]){
if(g_cart_id == 0) printf("# CGMMSND_mixed: Warning: residue of shift no %d got larger after rel. update\n", trigger_shift);
//if this is the zero'th shift not getting better -> no further convergence, break
if(trigger_shift == 0) break;
}
//zero float fields
zero_spinor_field_32(x_up, N);
zero_spinor_field_32(x_dn, N);
for(int im = 1; im < noshifts; im++) {
zero_spinor_field_32(mms_x_up[im-1], N);
zero_spinor_field_32(mms_x_dn[im-1], N);
}
//update the source
assign_to_32(r_up, r_up_d, N);
assign_to_32(r_dn, r_dn_d, N);
betas[0] = res[0]/rr_old;
rr_old = rr;
// d_0(k+1) = r(k+1) + beta*d_0(k)
assign_mul_add_r_32(d_up, betas[0], r_up, N);
assign_mul_add_r_32(d_dn, betas[0], r_dn, N);
// d_j(k+1) = r(k+1) + beta*d_j(k)
for(int im = 1; im < noshifts; im++) {
betas[im] = betas[0]*zita[im]*alphas[im]/(zitam1[im]*alphas[0]);
assign_mul_add_mul_r_32(mms_d_up[im-1], r_up, (float) betas[im], (float) zita[im], N);
assign_mul_add_mul_r_32(mms_d_dn[im-1], r_dn, (float) betas[im], (float) zita[im], N);
}
//new maxres for the shift that initiated the reliable update
res[trigger_shift] = res[0]*zita[trigger_shift]*zita[trigger_shift];
res0[trigger_shift] = res[trigger_shift];
maxres[trigger_shift] = res[trigger_shift];
trigger_shift = -1;
no_rel_update ++;
} //reliable update
//check if some shift is converged
for(int im = 1; im < noshifts; im++) {
if(j > 0 && (j % 10 == 0) && (im == noshifts-1)) {
double sn = square_norm_32(mms_d_up[im-1], N, 1);
sn += square_norm_32(mms_d_dn[im-1], N, 1);
if(alphas[noshifts-1]*alphas[noshifts-1]*sn <= eps_sq) {
noshifts--;
if( (g_debug_level > 1) && (g_cart_id == 0) ) {
printf("# CGMMSND_mixed: at iteration %d removed one shift, %d remaining\n", j, noshifts);
}
//if removed we add the latest solution vector for this shift
addto_32(Pup[im], mms_x_up[im-1], N);
addto_32(Pdn[im], mms_x_dn[im-1], N);
}
}
}
}//LOOP
if( (g_cart_id == 0) && (g_debug_level > 1) ) printf("Final mms residue: %.6e\n", rr);
//add the latest solutions
for(int im = 0; im < noshifts; im++) {
if(im == 0){
addto_32(Pup[0], x_up, N);
addto_32(Pdn[0], x_dn, N);
}
else{
addto_32(Pup[im], mms_x_up[im-1], N);
addto_32(Pdn[im], mms_x_dn[im-1], N);
}
}
if(g_debug_level > 4){
if(g_cart_id == 0) printf("# CGMMSND_mixed: Checking mms result:\n");
//loop over all shifts (-> Nshift)
for(int im = 0; im < Nshift; im++){
solver_pm->M_ndpsi(sf[0], sf[1], Pup[im], Pdn[im]);
assign_add_mul_r(sf[0], Pup[im] , shifts[im]*shifts[im], N);
assign_add_mul_r(sf[1], Pdn[im] , shifts[im]*shifts[im], N);
diff(sf[2], sf[0], Qup, N);
diff(sf[3], sf[1], Qdn, N);
rr_up = square_norm(sf[2], N, 1);
rr_dn = square_norm(sf[3], N, 1);
rr = rr_up + rr_dn;
if(g_cart_id == 0) printf("# CGMMSND_mixed: Shift[%d] squared residue: %e\n", im, rr);
}
}
finalize_solver(sf, nr_sf);
finalize_solver_32(sf32, nr_sf32);
//free cg constants
free(sigma); free(zitam1); free(zita); free(alphas); free(betas);
//free reliable update stuff
free(res); free(res0); free(maxres);
//if not converged -> return(-1)
if(j<max_iter){
return(j);
}
else{
return(-1);
}
}//
int invert_doublet_eo_quda(spinor * const Even_new_s, spinor * const Odd_new_s,
spinor * const Even_new_c, spinor * const Odd_new_c,
spinor * const Even_s, spinor * const Odd_s,
spinor * const Even_c, spinor * const Odd_c,
const double precision, const int max_iter,
const int solver_flag, const int rel_prec, const int even_odd_flag,
const SloppyPrecision sloppy_precision,
CompressionType compression) {
spinor ** solver_field = NULL;
const int nr_sf = 4;
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
convert_eo_to_lexic(solver_field[0], Even_s, Odd_s);
convert_eo_to_lexic(solver_field[1], Even_c, Odd_c);
// convert_eo_to_lexic(g_spinor_field[DUM_DERI+1], Even_new, Odd_new);
void *spinorIn = (void*)solver_field[0]; // source
void *spinorIn_c = (void*)solver_field[1]; // charme source
void *spinorOut = (void*)solver_field[2]; // solution
void *spinorOut_c = (void*)solver_field[3]; // charme solution
if ( rel_prec )
inv_param.residual_type = QUDA_L2_RELATIVE_RESIDUAL;
else
inv_param.residual_type = QUDA_L2_ABSOLUTE_RESIDUAL;
inv_param.kappa = g_kappa;
// IMPORTANT: use opposite TM mu-flavor since gamma5 -> -gamma5
inv_param.mu = -g_mubar /2./g_kappa;
inv_param.epsilon = g_epsbar/2./g_kappa;
// figure out which BC to use (theta, trivial...)
set_boundary_conditions(&compression);
// set the sloppy precision of the mixed prec solver
set_sloppy_prec(sloppy_precision);
// load gauge after setting precision
_loadGaugeQuda(compression);
// choose dslash type
if( g_c_sw > 0.0 ) {
inv_param.dslash_type = QUDA_TWISTED_CLOVER_DSLASH;
inv_param.matpc_type = QUDA_MATPC_EVEN_EVEN;
inv_param.solution_type = QUDA_MAT_SOLUTION;
inv_param.clover_order = QUDA_PACKED_CLOVER_ORDER;
inv_param.clover_coeff = g_c_sw*g_kappa;
}
else {
inv_param.dslash_type = QUDA_TWISTED_MASS_DSLASH;
inv_param.matpc_type = QUDA_MATPC_EVEN_EVEN_ASYMMETRIC;
inv_param.solution_type = QUDA_MAT_SOLUTION;
}
// choose solver
if(solver_flag == BICGSTAB) {
if(g_proc_id == 0) {printf("# QUDA: Using BiCGstab!\n"); fflush(stdout);}
inv_param.inv_type = QUDA_BICGSTAB_INVERTER;
}
else {
/* Here we invert the hermitean operator squared */
inv_param.inv_type = QUDA_CG_INVERTER;
if(g_proc_id == 0) {
printf("# QUDA: Using mixed precision CG!\n");
printf("# QUDA: mu = %f, kappa = %f\n", g_mu/2./g_kappa, g_kappa);
fflush(stdout);
}
}
if( even_odd_flag ) {
inv_param.solve_type = QUDA_NORMOP_PC_SOLVE;
if(g_proc_id == 0) printf("# QUDA: Using preconditioning!\n");
}
else {
inv_param.solve_type = QUDA_NORMOP_SOLVE;
if(g_proc_id == 0) printf("# QUDA: Not using preconditioning!\n");
}
inv_param.tol = sqrt(precision)*0.25;
inv_param.maxiter = max_iter;
inv_param.twist_flavor = QUDA_TWIST_NONDEG_DOUBLET;
inv_param.Ls = 2;
// NULL pointers to host fields to force
// construction instead of download of the clover field:
if( g_c_sw > 0.0 )
loadCloverQuda(NULL, NULL, &inv_param);
// reorder spinor
reorder_spinor_toQuda( (double*)spinorIn, inv_param.cpu_prec, 1, (double*)spinorIn_c );
// perform the inversion
invertQuda(spinorOut, spinorIn, &inv_param);
if( inv_param.verbosity == QUDA_VERBOSE )
if(g_proc_id == 0)
printf("# QUDA: Device memory used: Spinor: %f GiB, Gauge: %f GiB, Clover: %f GiB\n",
inv_param.spinorGiB, gauge_param.gaugeGiB, inv_param.cloverGiB);
if( inv_param.verbosity > QUDA_SILENT )
if(g_proc_id == 0)
printf("# QUDA: Done: %i iter / %g secs = %g Gflops\n",
inv_param.iter, inv_param.secs, inv_param.gflops/inv_param.secs);
// number of CG iterations
int iteration = inv_param.iter;
// reorder spinor
reorder_spinor_fromQuda( (double*)spinorIn, inv_param.cpu_prec, 1, (double*)spinorIn_c );
reorder_spinor_fromQuda( (double*)spinorOut, inv_param.cpu_prec, 1, (double*)spinorOut_c );
convert_lexic_to_eo(Even_s, Odd_s, solver_field[0]);
convert_lexic_to_eo(Even_c, Odd_c, solver_field[1]);
convert_lexic_to_eo(Even_new_s, Odd_new_s, solver_field[2]);
convert_lexic_to_eo(Even_new_c, Odd_new_c, solver_field[3]);
finalize_solver(solver_field, nr_sf);
freeGaugeQuda();
if(iteration >= max_iter)
return(-1);
return(iteration);
}
/* P output = solution , Q input = source */
int cg_her_nd(spinor * const P_up,spinor * P_dn, spinor * const Q_up, spinor * const Q_dn,
const int max_iter, double eps_sq, const int rel_prec,
const int N, matrix_mult_nd f) {
double normsp, normsq, pro, err, alpha_cg, beta_cg, squarenorm;
int iteration;
double err1, err2;
spinor ** up_field = NULL;
spinor ** dn_field = NULL;
const int nr_sf = 5;
/* do we really need so many fields??? */
init_solver_field(&up_field, VOLUMEPLUSRAND, nr_sf);
init_solver_field(&dn_field, VOLUMEPLUSRAND, nr_sf);
squarenorm = square_norm(Q_up, N, 1);
squarenorm+= square_norm(Q_dn, N, 1);
/* !!!! INITIALIZATION !!!! */
assign(up_field[0], P_up, N);
assign(dn_field[0], P_dn, N);
/* (r_0,r_0) = normsq */
normsp =square_norm(P_up, N, 1);
normsp+=square_norm(P_dn, N, 1);
/* assign(up_field[5], Q_up, N); */
/* assign(dn_field[5], Q_dn, N); */
/* initialize residue r and search vector p */
if(normsp==0){
/* if a starting solution vector equal to zero is chosen */
assign(up_field[1], Q_up, N);
assign(dn_field[1], Q_dn, N);
assign(up_field[2], Q_up, N);
assign(dn_field[2], Q_dn, N);
normsq =square_norm(Q_up, N, 1);
normsq+=square_norm(Q_dn, N, 1);
}
else {
/* if a starting solution vector different from zero is chosen */
f(up_field[3],dn_field[3],
up_field[0],dn_field[0]);
diff(up_field[1], Q_up, up_field[3], N);
diff(dn_field[1], Q_dn, dn_field[3], N);
assign(up_field[2], up_field[1], N);
assign(dn_field[2], dn_field[1], N);
normsq =square_norm(up_field[2], N, 1);
normsq+=square_norm(dn_field[2], N, 1);
}
/* main loop */
for(iteration=0;iteration<max_iter;iteration++){
f(up_field[4],dn_field[4],
up_field[2],dn_field[2]);
pro =scalar_prod_r(up_field[2], up_field[4], N, 1);
pro+=scalar_prod_r(dn_field[2], dn_field[4], N, 1);
/* Compute alpha_cg(i+1) */
alpha_cg=normsq/pro;
/* Compute x_(i+1) = x_i + alpha_cg(i+1) p_i */
assign_add_mul_r(up_field[0], up_field[2], alpha_cg, N);
assign_add_mul_r(dn_field[0], dn_field[2], alpha_cg, N);
/* Compute r_(i+1) = r_i - alpha_cg(i+1) Qp_i */
assign_add_mul_r(up_field[1], up_field[4], -alpha_cg, N);
assign_add_mul_r(dn_field[1], dn_field[4], -alpha_cg, N);
/* Check whether the precision is reached ... */
err1 =square_norm(up_field[1], N, 1);
err2 =square_norm(dn_field[1], N, 1);
err = err1 + err2;
if(g_debug_level > 1 && g_proc_id == g_stdio_proc) {
printf("cg_her_nd : i = %d esqr %e = %e + %e \n",iteration,err, err1, err2); fflush( stdout);
}
if(((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*squarenorm) && (rel_prec == 1))) {
assign(P_up, up_field[0], N);
assign(P_dn, dn_field[0], N);
g_sloppy_precision = 0;
finalize_solver(up_field, nr_sf);
finalize_solver(dn_field, nr_sf);
return(iteration+1);
}
#ifdef _USE_HALFSPINOR
if(((err*err <= eps_sq) && (rel_prec == 0)) || ((err*err <= eps_sq*squarenorm) && (rel_prec == 1))) {
g_sloppy_precision = 1;
if(g_debug_level > 2 && g_proc_id == g_stdio_proc) {
printf("sloppy precision on\n"); fflush( stdout);
}
}
#endif
/* Compute beta_cg(i+1)
Compute p_(i+1) = r_i+1 + beta_(i+1) p_i */
beta_cg=err/normsq;
assign_mul_add_r(up_field[2], beta_cg, up_field[1], N);
assign_mul_add_r(dn_field[2], beta_cg, dn_field[1], N);
normsq=err;
}
assign(P_up, up_field[0], N);
assign(P_dn, dn_field[0], N);
g_sloppy_precision = 0;
finalize_solver(up_field, nr_sf);
finalize_solver(dn_field, nr_sf);
return(-1);
}
int gmres_dr(spinor * const P,spinor * const Q,
const int m, const int nr_ev, const int max_restarts,
const double eps_sq, const int rel_prec,
const int N, matrix_mult f){
int restart=0, i, j, k, l;
double beta, eps, norm, beta2=0.;
complex *lswork = NULL;
int lwork;
complex tmp1, tmp2;
int info=0;
int _m = m, mp1 = m+1, np1 = nr_ev+1, ne = nr_ev, V2 = 12*(VOLUMEPLUSRAND)/2, _N = 12*N;
spinor ** solver_field = NULL;
const int nr_sf = 3;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
}
double err=0.;
spinor * r0, * x0;
cmone.re = -1.; cmone.im=0.;
cpone.re = 1.; cpone.im=0.;
czero.re = 0.; czero.im = 0.;
r0 = solver_field[0];
x0 = solver_field[2];
eps=sqrt(eps_sq);
init_gmres_dr(m, (VOLUMEPLUSRAND));
norm = sqrt(square_norm(Q, N, 1));
assign(x0, P, N);
/* first normal GMRES cycle */
/* r_0=Q-AP (b=Q, x+0=P) */
f(r0, x0);
diff(r0, Q, r0, N);
/* v_0=r_0/||r_0|| */
alpha[0].re=sqrt(square_norm(r0, N, 1));
err = alpha[0].re;
if(g_proc_id == g_stdio_proc && g_debug_level > 0){
printf("%d\t%e true residue\n", restart*m, alpha[0].re*alpha[0].re);
fflush(stdout);
}
if(alpha[0].re==0.){
assign(P, x0, N);
finalize_solver(solver_field, nr_sf);
return(restart*m);
}
mul_r(V[0], 1./alpha[0].re, r0, N);
for(j = 0; j < m; j++){
/* solver_field[0]=A*v_j */
/* Set h_ij and omega_j */
/* solver_field[1] <- omega_j */
f(solver_field[1], V[j]);
/* assign(solver_field[1], solver_field[0], N); */
for(i = 0; i <= j; i++){
H[i][j] = scalar_prod(V[i], solver_field[1], N, 1);
/* G, work and work2 are in Fortran storage: columns first */
G[j][i] = H[i][j];
work2[j][i] = H[i][j];
work[i][j].re = H[i][j].re;
work[i][j].im = -H[i][j].im;
assign_diff_mul(solver_field[1], V[i], H[i][j], N);
}
_complex_set(H[j+1][j], sqrt(square_norm(solver_field[1], N, 1)), 0.);
G[j][j+1] = H[j+1][j];
work2[j][j+1] = H[j+1][j];
work[j+1][j].re = H[j+1][j].re;
work[j+1][j].im = -H[j+1][j].im;
beta2 = H[j+1][j].re*H[j+1][j].re;
for(i = 0; i < j; i++){
tmp1 = H[i][j];
tmp2 = H[i+1][j];
_mult_real(H[i][j], tmp2, s[i]);
_add_assign_complex_conj(H[i][j], c[i], tmp1);
_mult_real(H[i+1][j], tmp1, s[i]);
_diff_assign_complex(H[i+1][j], c[i], tmp2);
}
/* Set beta, s, c, alpha[j],[j+1] */
beta = sqrt(_complex_square_norm(H[j][j]) + _complex_square_norm(H[j+1][j]));
s[j] = H[j+1][j].re / beta;
_mult_real(c[j], H[j][j], 1./beta);
_complex_set(H[j][j], beta, 0.);
_mult_real(alpha[j+1], alpha[j], s[j]);
tmp1 = alpha[j];
_mult_assign_complex_conj(alpha[j], c[j], tmp1);
/* precision reached? */
if(g_proc_id == g_stdio_proc && g_debug_level > 0){
printf("%d\t%e residue\n", restart*m+j, alpha[j+1].re*alpha[j+1].re);
fflush(stdout);
}
if(((alpha[j+1].re <= eps) && (rel_prec == 0)) || ((alpha[j+1].re <= eps*norm) && (rel_prec == 1))){
_mult_real(alpha[j], alpha[j], 1./H[j][j].re);
assign_add_mul(x0, V[j], alpha[j], N);
for(i = j-1; i >= 0; i--){
for(k = i+1; k <= j; k++){
_mult_assign_complex(tmp1, H[i][k], alpha[k]);
/* alpha[i] -= tmp1 */
_diff_complex(alpha[i], tmp1);
}
_mult_real(alpha[i], alpha[i], 1./H[i][i].re);
assign_add_mul(x0, V[i], alpha[i], N);
}
for(i = 0; i < m; i++){
alpha[i].im = 0.;
}
assign(P, x0, N);
finalize_solver(solver_field, nr_sf);
return(restart*m+j);
}
/* if not */
else {
mul_r(V[(j+1)], 1./H[j+1][j].re, solver_field[1], N);
}
}
j=m-1;
/* prepare for restart */
_mult_real(alpha[j], alpha[j], 1./H[j][j].re);
assign_add_mul(x0, V[j], alpha[j], N);
if(g_proc_id == 0 && g_debug_level > 3) {
printf("alpha: %e %e\n", alpha[j].re, alpha[j].im);
}
for(i = j-1; i >= 0; i--){
for(k = i+1; k <= j; k++){
_mult_assign_complex(tmp1, H[i][k], alpha[k]);
_diff_complex(alpha[i], tmp1);
}
_mult_real(alpha[i], alpha[i], 1./H[i][i].re);
if(g_proc_id == 0 && g_debug_level > 3) {
printf("alpha: %e %e\n", alpha[i].re, alpha[i].im);
}
assign_add_mul(x0, V[i], alpha[i], N);
}
/* This produces c=V_m+1*r0 */
for(i = 0; i < mp1; i++) {
c[i] = scalar_prod(V[i], r0, N, 1);
if(g_proc_id == 0 && g_debug_level > 3) {
printf("c: %e %e err = %e\n", c[i].re, c[i].im, err);
}
}
for(restart = 1; restart < max_restarts; restart++) {
/* compute c-\bar H \alpha */
_FT(zgemv) ("N", &mp1, &_m, &cmone, G[0], &mp1, alpha, &one, &cpone, c, &one, 1);
err = sqrt(short_scalar_prod(c, c, mp1).re);
if(g_proc_id == 0 && g_debug_level > 0) {
printf("%d\t %e short residue\n", m*restart, err*err);
}
/* Compute new residual r0 */
/* r_0=Q-AP (b=Q, x+0=P) */
if(g_debug_level > 0) {
f(r0, x0);
diff(r0, Q, r0, N);
tmp1.im=sqrt(square_norm(r0, N, 1));
if(g_proc_id == g_stdio_proc){
printf("%d\t%e true residue\n", m*restart, tmp1.im*tmp1.im);
fflush(stdout);
}
}
mul(r0, c[0], V[0], N);
for(i = 1; i < mp1; i++) {
assign_add_mul(r0, V[i], c[i], N);
}
if(g_debug_level > 3) {
tmp1.im=sqrt(square_norm(r0, N, 1));
if(g_proc_id == g_stdio_proc){
printf("%d\t%e residue\n", m*restart, tmp1.im*tmp1.im);
fflush(stdout);
}
}
/* Stop if satisfied */
if(err < eps){
assign(P, x0, N);
finalize_solver(solver_field, nr_sf);
return(restart*m);
}
/* Prepare to compute harmonic Ritz pairs */
for(i = 0; i < m-1; i++){
alpha[i].re = 0.;
alpha[i].im = 0.;
}
alpha[m-1].re = 1.;
alpha[m-1].im = 0.;
_FT(zgesv) (&_m, &one, work[0], &mp1, idx, alpha, &_m, &info);
for(i = 0; i < m; i++) {
G[m-1][i].re += (beta2*alpha[idx[i]-1].re);
G[m-1][i].im += (beta2*alpha[idx[i]-1].im);
}
if(g_proc_id == 0 && g_debug_level > 3){
printf("zgesv returned info = %d, c[m-1]= %e, %e , idx[m-1]=%d\n",
info, alpha[idx[m-1]-1].re, alpha[idx[m-1]-1].im, idx[m-1]);
}
/* c - \bar H * d -> c */
/* G contains H + \beta^2 H^-He_n e_n^H */
/* Compute harmonic Ritz pairs */
diagonalise_general_matrix(m, G[0], mp1, alpha, evalues);
for(i = 0; i < m; i++) {
sortarray[i] = _complex_square_norm(evalues[i]);
idx[i] = i;
}
quicksort(m, sortarray, idx);
if(g_proc_id == g_stdio_proc && g_debug_level > 1) {
for(i = 0; i < m; i++) {
printf("# Evalues %d %e %e \n", i, evalues[idx[i]].re, evalues[idx[i]].im);
}
fflush(stdout);
}
/* Copy the first nr_ev eigenvectors to work */
for(i = 0; i < ne; i++) {
for(l = 0; l < m; l++) {
work[i][l] = G[idx[i]][l];
}
}
/* Orthonormalize them */
for(i = 0; i < ne; i++) {
work[i][m].re = 0.;
work[i][m].im = 0.;
short_ModifiedGS(work[i], m, i, work[0], mp1);
}
/* Orthonormalize c - \bar H d to work */
short_ModifiedGS(c, m+1, ne, work[0], mp1);
for(i = 0; i < mp1; i++) {
work[nr_ev][i] = c[i];
}
/* Now compute \bar H = P^T_k+1 \bar H_m P_k */
for(i = 0; i < mp1; i++) {
for(l = 0; l < mp1; l++) {
H[i][l].re = 0.;
H[i][l].im = 0.;
}
}
_FT(zgemm) ("N", "N", &mp1, &ne, &_m, &cpone, work2[0], &mp1, work[0], &mp1, &czero, G[0], &mp1, 1, 1);
_FT(zgemm) ("C", "N", &np1, &ne , &mp1, &cpone, work[0], &mp1, G[0], &mp1, &czero, H[0], &mp1, 1, 1);
if(g_debug_level > 3) {
for(i = 0; i < ne+1; i++) {
for(l = 0; l < ne+1; l++) {
if(g_proc_id == 0) {
printf("(g[%d], g[%d]) = %e, %e\n", i, l, short_scalar_prod(work[i], work[l], m+1).re,
short_scalar_prod(work[i], work[l], m+1).im);
printf("(g[%d], g[%d]) = %e, %e\n", l, i, short_scalar_prod(work[l], work[i], m+1).re,
short_scalar_prod(work[l], work[i], m+1).im);
}
}
}
}
/* V_k+1 = V_m+1 P_k+1 */
/* _FT(zgemm) ("N", "N", &_N, &np1, &mp1, &cpone, (complex*)V[0], &V2, work[0], &mp1, &czero, (complex*)Z[0], &V2, 1, 1); */
for(l = 0; l < np1; l++) {
mul(Z[l], work[l][0], V[0], N);
for(i = 1; i < mp1; i++) {
assign_add_mul(Z[l], V[i], work[l][i], N);
}
}
/* copy back to V */
for(i = 0; i < np1; i++) {
assign(V[i], Z[i], N);
}
/* Reorthogonalise v_nr_ev */
ModifiedGS((complex*)V[nr_ev], _N, nr_ev, (complex*)V[0], V2);
if(g_debug_level > 3) {
for(i = 0; i < np1; i++) {
for(l = 0; l < np1; l++) {
tmp1 = scalar_prod(V[l], V[i], N, 1);
if(g_proc_id == 0) {
printf("(V[%d], V[%d]) = %e %e %d %d %d %d %d %d %e %e\n", l, i, tmp1.re, tmp1.im, np1, mp1, ne, _m, _N, V2, H[l][i].re, H[l][i].im);
}
}
}
}
/* Copy the content of H to work, work2 and G */
for(i=0; i < mp1; i++) {
for(l = 0; l < mp1; l++) {
G[i][l] = H[i][l];
work2[i][l] = H[i][l];
work[l][i].re = H[i][l].re;
work[l][i].im = -H[i][l].im;
}
}
for(j = ne; j < m; j++) {
/* solver_field[0]=A*v_j */
f(solver_field[1], V[j]);
/* Set h_ij and omega_j */
/* solver_field[1] <- omega_j */
/* assign(solver_field[1], solver_field[0], N); */
for(i = 0; i <= j; i++){
H[j][i] = scalar_prod(V[i], solver_field[1], N, 1);
/* H, G, work and work2 are now all in Fortran storage: columns first */
G[j][i] = H[j][i];
work2[j][i] = H[j][i];
work[i][j].re = H[j][i].re;
work[i][j].im = -H[j][i].im;
assign_diff_mul(solver_field[1], V[i], H[j][i], N);
}
beta2 = square_norm(solver_field[1], N, 1);
_complex_set(H[j][j+1], sqrt(beta2), 0.);
G[j][j+1] = H[j][j+1];
work2[j][j+1] = H[j][j+1];
work[j+1][j].re = H[j][j+1].re;
work[j+1][j].im = -H[j][j+1].im;
mul_r(V[(j+1)], 1./H[j][j+1].re, solver_field[1], N);
}
/* Solve the least square problem for alpha*/
/* This produces c=V_m+1*r0 */
for(i = 0; i < mp1; i++) {
c[i] = scalar_prod(V[i], r0, N, 1);
alpha[i] = c[i];
if(g_proc_id == 0 && g_debug_level > 3) {
printf("c: %e %e err = %e\n", c[i].re, c[i].im, err);
}
}
if(lswork == NULL) {
lwork = -1;
_FT(zgels) ("N", &mp1, &_m, &one, H[0], &mp1, alpha, &mp1, &tmp1, &lwork, &info, 1);
lwork = (int)tmp1.re;
lswork = (complex*)malloc(lwork*sizeof(complex));
}
_FT(zgels) ("N", &mp1, &_m, &one, H[0], &mp1, alpha, &mp1, lswork, &lwork, &info, 1);
if(g_proc_id == 0 && g_debug_level > 3) {
printf("zgels returned info = %d\n", info);
fflush(stdout);
}
/* Compute the new solution vector */
for(i = 0; i < m; i++){
if(g_proc_id == 0 && g_debug_level > 3) {
printf("alpha: %e %e\n", alpha[i].re, alpha[i].im);
}
assign_add_mul(x0, V[i], alpha[i], N);
}
}
/* If maximal number of restart is reached */
assign(P, x0, N);
finalize_solver(solver_field, nr_sf);
return(-1);
}
int bicgstabell(spinor * const x0, spinor * const b, const int max_iter,
double eps_sq, const int rel_prec, const int _l, const int N, matrix_mult f) {
double err;
int i, j, k, l;
double rho0, rho1, beta, alpha, omega, gamma0 = 0., squarenorm;
spinor * r[5], * u[5], * r0_tilde, * x;
double tau[5][5], gamma[25], gammap[25], gammapp[25], sigma[25];
spinor ** solver_field = NULL;
const int nr_sf = 2*(_l+1)+2;
l = _l;
k = -l;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
}
r0_tilde = solver_field[0];
for(i = 0; i <= l; i++){
r[i] = solver_field[2+2*i];
u[i] = solver_field[3+2*i];
}
x = x0;
assign(u[0], b, N);
f(r0_tilde, x);
diff(r[0], u[0], r0_tilde, N);
zero_spinor_field(solver_field[1], N);
assign(r0_tilde, r[0], N);
squarenorm = square_norm(b, N, 1);
rho0 = 1.;
alpha = 0.;
omega = 1.;
err = square_norm(r0_tilde, N, 1);
while( k < max_iter && (((err > eps_sq) && (rel_prec == 0))
|| ((err > eps_sq*squarenorm) && (rel_prec == 1))
)) {
k+=l;
/* The BiCG part */
rho0 *= -omega;
for(j = 0; j < l; j++) {
rho1 = scalar_prod_r(r[j], r0_tilde, N, 1);
beta = (rho1/rho0);
beta *= alpha;
rho0 = rho1;
for(i = 0; i <= j; i++) {
/* u_i = r_i - \beta u_i */
assign_mul_add_r(u[i], -beta, r[i], N);
}
f(u[j+1], u[j]);
gamma0 = scalar_prod_r(u[j+1], r0_tilde, N, 1);
alpha = rho0/gamma0;
/* r_i = r_i - \alpha u_{i+1} */
for(i = 0; i <= j; i++) {
assign_add_mul_r(r[i], u[i+1], -alpha, N);
}
f(r[j+1], r[j]);
/* x = x + \alpha u_0 */
assign_add_mul_r(x, u[0], alpha, N);
err = square_norm(r[j+1], N, 1);
if(g_proc_id == 0 && g_debug_level > 1) {printf("%d %d err = %e\n", k, j, err);fflush(stdout);}
}
/* The MR part */
for(j = 1; j <= l; j++){
for(i = 1; i < j; i++){
tau[i][j] = scalar_prod_r(r[j], r[i], N, 1)/sigma[i];
assign_add_mul_r(r[j], r[i], -tau[i][j], N);
}
sigma[j] = scalar_prod_r(r[j], r[j], N, 1);
gammap[j] = scalar_prod_r(r[0], r[j], N, 1)/sigma[j];
}
gamma[l] = gammap[l];
omega = gamma[l];
for(j = l-1; j > 0; j--) {
gamma[j] = gammap[j];
for(i = j+1; i <= l; i++) {
gamma[j] -= (tau[j][i]*gamma[i]);
}
}
for(j = 1; j < l; j++) {
gammapp[j] = gamma[j+1];
for(i = j+1; i < l; i++){
gammapp[j] += (tau[j][i]*gamma[i+1]);
}
}
assign_add_mul_r(x, r[0], gamma[1], N);
assign_add_mul_r(r[0], r[l], -gammap[l], N);
for(j = 1; j < l; j++){
assign_add_mul_r(x, r[j], gammapp[j], N);
assign_add_mul_r(r[0], r[j], -gammap[j], N);
}
assign_add_mul_r(u[0], u[l], -gamma[l], N);
for(j = 1; j < l; j++){
assign_add_mul_r(u[0], u[j], -gamma[j], N);
}
err = square_norm(r[0], N, 1);
if(g_proc_id == 0 && g_debug_level > 0){
printf(" BiCGstabell iterated %d %d, %e rho0 = %e, alpha = %e, gamma0= %e\n", l, k, err, rho0, alpha, gamma0);
fflush( stdout );
}
}
finalize_solver(solver_field, nr_sf);
if(k == max_iter) return(-1);
return(k);
}
void Msap_eo_old(spinor * const P, spinor * const Q, const int Ncy, const int Niter) {
int blk, ncy = 0, eo, vol, vols;
spinor * r, * a, * b, * c;
double nrm;
double musave = g_mu;
double kappasave = g_kappa;
spinor * b_even, * b_odd, * a_even, * a_odd;
spinor ** solver_field = NULL;
// also get space for mrblk! 6 = 3+3
const int nr_sf = 6;
if(kappa_dflgen > 0) {
g_kappa = kappa_dfl;
}
if(mu_dflgen > -10) {
g_mu = mu_dfl;
// make sure the sign is correct!
if(g_mu*musave < 0) g_mu *= -1.;
}
boundary(g_kappa);
/*
* here it would be probably better to get the working fields as a parameter
* from the calling function
*/
vols = block_list[0].volume/2+block_list[0].spinpad;
vol = block_list[0].volume/2;
init_solver_field(&solver_field, nb_blocks*2*vols, nr_sf);
r = solver_field[0];
a = solver_field[1];
b = solver_field[2];
for(ncy = 0; ncy < Ncy; ncy++) {
/* compute the global residue */
/* this can be done more efficiently */
/* here only a naive implementation */
for(eo = 0; eo < 2; eo++) {
D_psi(r, P);
diff(r, Q, r, VOLUME);
nrm = square_norm(r, VOLUME, 1);
if(g_proc_id == 0 && g_debug_level > 2 && eo == 0) {
printf("Msap_eo: %d %1.3e mu = %e\n", ncy, nrm, g_mu/2./g_kappa);
fflush(stdout);
}
/* choose the even (odd) block */
// rely on nested parallelism
//
#ifdef TM_USE_OMP
# pragma omp parallel for private (a_even, a_odd, b_even, b_odd, c)
#endif
for (blk = 0; blk < nb_blocks; blk++) {
b_even = b + blk*2*vols;
b_odd = b +blk*2*vols + vols;
a_even = a + blk*2*vols;
a_odd = a + blk*2*vols + vols;
c = solver_field[3] + blk*vols;
if(block_list[blk].evenodd == eo) {
/* get part of r corresponding to block blk into b_even and b_odd */
copy_global_to_block_eo(b_even, b_odd, r, blk);
if(g_c_sw > 0) {
assign_mul_one_sw_pm_imu_inv_block(EE, a_even, b_even, g_mu, &block_list[blk]);
Block_H_psi(&block_list[blk], a_odd, a_even, OE);
/* a_odd = b_odd - a_odd */
diff(a_odd, b_odd, a_odd, vol);
mrblk(b_odd, a_odd, solver_field[3] + blk*2*3*vols, Niter, 1.e-31, 1, vol, &Msw_plus_block_psi, blk);
Block_H_psi(&block_list[blk], b_even, b_odd, EO);
assign(c, b_even, vol);
assign_mul_one_sw_pm_imu_inv_block(EE, b_even, c, g_mu, &block_list[blk]);
}
else {
assign_mul_one_pm_imu_inv(a_even, b_even, +1., vol);
Block_H_psi(&block_list[blk], a_odd, a_even, OE);
/* a_odd = b_odd - a_odd */
diff(a_odd, b_odd, a_odd, vol);
mrblk(b_odd, a_odd, solver_field[3] + blk*2*3*vols, Niter, 1.e-31, 1, vol, &Mtm_plus_block_psi, blk);
Block_H_psi(&block_list[blk], b_even, b_odd, EO);
mul_one_pm_imu_inv(b_even, +1., vol);
}
/* a_even = a_even - b_even */
diff(a_even, a_even, b_even, vol);
/* add even and odd part up to full spinor P */
add_eo_block_to_global(P, a_even, b_odd, blk);
}
}
}
}
finalize_solver(solver_field, nr_sf);
g_mu = musave;
g_kappa = kappasave;
boundary(g_kappa);
return;
}
/* P output = solution , Q input = source */
int cg_mms_tm(spinor * const P, spinor * const Q, const int max_iter,
double eps_sq, const int rel_prec, const int N, matrix_mult f) {
static double normsq, pro, err, alpha_cg = 1., beta_cg = 0., squarenorm;
int iteration, im, append = 0;
char filename[100];
static double gamma, alpham1;
int const cg_mms_default_precision = 32;
double tmp_mu = g_mu;
WRITER * writer = NULL;
paramsInverterInfo *inverterInfo = NULL;
paramsPropagatorFormat *propagatorFormat = NULL;
spinor * temp_save; //used to save all the masses
spinor ** solver_field = NULL;
const int nr_sf = 5;
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
init_mms_tm(g_no_extra_masses);
/* currently only implemented for P=0 */
zero_spinor_field(P, N);
/* Value of the bare MMS-masses (\mu^2 - \mu_0^2) */
for(im = 0; im < g_no_extra_masses; im++) {
sigma[im] = g_extra_masses[im]*g_extra_masses[im] - g_mu*g_mu;
assign(xs_mms_solver[im], P, N);
assign(ps_mms_solver[im], Q, N);
zitam1[im] = 1.0;
zita[im] = 1.0;
alphas[im] = 1.0;
betas[im] = 0.0;
}
squarenorm = square_norm(Q, N, 1);
assign(solver_field[0], P, N);
/* normsp = square_norm(P, N, 1); */
/* initialize residue r and search vector p */
/* if(normsp == 0){ */
/* currently only implemented for P=0 */
if(1) {
/* if a starting solution vector equal to zero is chosen */
assign(solver_field[1], Q, N);
assign(solver_field[2], Q, N);
normsq = square_norm(Q, N, 1);
}
else{
/* if a starting solution vector different from zero is chosen */
f(solver_field[3], solver_field[0]);
diff(solver_field[1], Q, solver_field[3], N);
assign(solver_field[2], solver_field[1], N);
normsq = square_norm(solver_field[2], N, 1);
}
/* main loop */
for(iteration = 0; iteration < max_iter; iteration++) {
/* Q^2*p and then (p,Q^2*p) */
f(solver_field[4], solver_field[2]);
pro = scalar_prod_r(solver_field[2], solver_field[4], N, 1);
/* For the update of the coeff. of the shifted pol. we need alpha_cg(i-1) and alpha_cg(i).
This is the reason why we need this double definition of alpha */
alpham1 = alpha_cg;
/* Compute alpha_cg(i+1) */
alpha_cg = normsq/pro;
for(im = 0; im < g_no_extra_masses; im++) {
/* Now gamma is a temp variable that corresponds to zita(i+1) */
gamma = zita[im]*alpham1/(alpha_cg*beta_cg*(1.-zita[im]/zitam1[im])
+ alpham1*(1.+sigma[im]*alpha_cg));
/* Now zita(i-1) is put equal to the old zita(i) */
zitam1[im] = zita[im];
/* Now zita(i+1) is updated */
zita[im] = gamma;
/* Update of alphas(i) = alpha_cg(i)*zita(i+1)/zita(i) */
alphas[im] = alpha_cg*zita[im]/zitam1[im];
/* Compute xs(i+1) = xs(i) + alphas(i)*ps(i) */
assign_add_mul_r(xs_mms_solver[im], ps_mms_solver[im], alphas[im], N);
}
/* Compute x_(i+1) = x_i + alpha_cg(i+1) p_i */
assign_add_mul_r(solver_field[0], solver_field[2], alpha_cg, N);
/* Compute r_(i+1) = r_i - alpha_cg(i+1) Qp_i */
assign_add_mul_r(solver_field[1], solver_field[4], -alpha_cg, N);
/* Check whether the precision eps_sq is reached */
err = square_norm(solver_field[1], N, 1);
if(g_debug_level > 2 && g_proc_id == g_stdio_proc) {
printf("CGMMS iteration: %d residue: %g\n", iteration, err); fflush( stdout );
}
if( ((err <= eps_sq) && (rel_prec == 0)) ||
((err <= eps_sq*squarenorm) && (rel_prec == 1)) ) {
assign(P, solver_field[0], N);
f(solver_field[2], P);
diff(solver_field[3], solver_field[2], Q, N);
err = square_norm(solver_field[3], N, 1);
if(g_debug_level > 0 && g_proc_id == g_stdio_proc) {
printf("# CG MMS true residue at final iteration (%d) was %g.\n", iteration, err);
fflush( stdout);
}
g_sloppy_precision = 0;
g_mu = tmp_mu;
/* save all the results of (Q^dagger Q)^(-1) \gamma_5 \phi */
/* here ... */
/* when im == -1 save the base mass*/
for(im = -1; im < g_no_extra_masses; im++) {
if(im==-1) {
temp_save=solver_field[0];
} else {
temp_save=xs_mms_solver[im];
}
if(SourceInfo.type != 1) {
if (PropInfo.splitted) {
sprintf(filename, "%s.%.4d.%.2d.%.2d.cgmms.%.2d.inverted", SourceInfo.basename, SourceInfo.nstore, SourceInfo.t, SourceInfo.ix, im+1);
} else {
sprintf(filename, "%s.%.4d.%.2d.cgmms.%.2d.inverted", SourceInfo.basename, SourceInfo.nstore, SourceInfo.t, im+1);
}
}
else {
sprintf(filename, "%s.%.4d.%.5d.cgmms.%.2d.0", SourceInfo.basename, SourceInfo.nstore, SourceInfo.sample, im+1);
}
if(g_kappa != 0) {
mul_r(temp_save, (2*g_kappa)*(2*g_kappa), temp_save, N);
}
append = !PropInfo.splitted;
construct_writer(&writer, filename, append);
if (PropInfo.splitted || SourceInfo.ix == index_start) {
//Create the inverter info NOTE: always set to TWILSON=12 and 1 flavour (to be adjusted)
inverterInfo = construct_paramsInverterInfo(err, iteration+1, 12, 1);
if (im == -1) {
inverterInfo->cgmms_mass = inverterInfo->mu;
} else {
inverterInfo->cgmms_mass = g_extra_masses[im]/(2 * inverterInfo->kappa);
}
write_spinor_info(writer, PropInfo.format, inverterInfo, append);
//Create the propagatorFormat NOTE: always set to 1 flavour (to be adjusted)
propagatorFormat = construct_paramsPropagatorFormat(cg_mms_default_precision, 1);
write_propagator_format(writer, propagatorFormat);
free(inverterInfo);
free(propagatorFormat);
}
convert_lexic_to_eo(solver_field[2], solver_field[1], temp_save);
write_spinor(writer, &solver_field[2], &solver_field[1], 1, 32);
destruct_writer(writer);
}
finalize_solver(solver_field, nr_sf);
return(iteration+1);
}
/* Compute beta_cg(i+1) = (r(i+1),r(i+1))/(r(i),r(i))
Compute p(i+1) = r(i+1) + beta(i+1)*p(i) */
beta_cg = err/normsq;
assign_mul_add_r(solver_field[2], beta_cg, solver_field[1], N);
normsq = err;
/* Compute betas(i+1) = beta_cg(i)*(zita(i+1)*alphas(i))/(zita(i)*alpha_cg(i))
Compute ps(i+1) = zita(i+1)*r(i+1) + betas(i+1)*ps(i) */
for(im = 0; im < g_no_extra_masses; im++) {
betas[im] = beta_cg*zita[im]*alphas[im]/(zitam1[im]*alpha_cg);
assign_mul_add_mul_r(ps_mms_solver[im], solver_field[1], betas[im], zita[im], N);
}
}
assign(P, solver_field[0], N);
g_sloppy_precision = 0;
finalize_solver(solver_field, nr_sf);
return(-1);
}
int gmres(spinor * const P,spinor * const Q,
const int m, const int max_restarts,
const double eps_sq, const int rel_prec,
const int N, const int parallel, matrix_mult f){
int restart, i, j, k;
double beta, eps, norm;
complex tmp1, tmp2;
spinor ** solver_field = NULL;
const int nr_sf = 3;
if(N == VOLUME) {
init_solver_field(&solver_field, VOLUMEPLUSRAND, nr_sf);
}
else {
init_solver_field(&solver_field, VOLUMEPLUSRAND/2, nr_sf);
}
eps=sqrt(eps_sq);
init_gmres(m, VOLUMEPLUSRAND);
norm = sqrt(square_norm(Q, N, parallel));
assign(solver_field[2], P, N);
for(restart = 0; restart < max_restarts; restart++){
/* r_0=Q-AP (b=Q, x+0=P) */
f(solver_field[0], solver_field[2]);
diff(solver_field[0], Q, solver_field[0], N);
/* v_0=r_0/||r_0|| */
alpha[0].re=sqrt(square_norm(solver_field[0], N, parallel));
if(g_proc_id == g_stdio_proc && g_debug_level > 1){
printf("%d\t%g true residue\n", restart*m, alpha[0].re*alpha[0].re);
fflush(stdout);
}
if(alpha[0].re==0.){
assign(P, solver_field[2], N);
finalize_solver(solver_field, nr_sf);
return(restart*m);
}
mul_r(V[0], 1./alpha[0].re, solver_field[0], N);
for(j = 0; j < m; j++){
/* solver_field[0]=A*v_j */
f(solver_field[0], V[j]);
/* Set h_ij and omega_j */
/* solver_field[1] <- omega_j */
assign(solver_field[1], solver_field[0], N);
for(i = 0; i <= j; i++){
H[i][j] = scalar_prod(V[i], solver_field[1], N, parallel);
assign_diff_mul(solver_field[1], V[i], H[i][j], N);
}
_complex_set(H[j+1][j], sqrt(square_norm(solver_field[1], N, parallel)), 0.);
for(i = 0; i < j; i++){
tmp1 = H[i][j];
tmp2 = H[i+1][j];
_mult_real(H[i][j], tmp2, s[i]);
_add_assign_complex_conj(H[i][j], c[i], tmp1);
_mult_real(H[i+1][j], tmp1, s[i]);
_diff_assign_complex(H[i+1][j], c[i], tmp2);
}
/* Set beta, s, c, alpha[j],[j+1] */
beta = sqrt(_complex_square_norm(H[j][j]) + _complex_square_norm(H[j+1][j]));
s[j] = H[j+1][j].re / beta;
_mult_real(c[j], H[j][j], 1./beta);
_complex_set(H[j][j], beta, 0.);
_mult_real(alpha[j+1], alpha[j], s[j]);
tmp1 = alpha[j];
_mult_assign_complex_conj(alpha[j], c[j], tmp1);
/* precision reached? */
if(g_proc_id == g_stdio_proc && g_debug_level > 1){
printf("%d\t%g residue\n", restart*m+j, alpha[j+1].re*alpha[j+1].re);
fflush(stdout);
}
if(((alpha[j+1].re <= eps) && (rel_prec == 0)) || ((alpha[j+1].re <= eps*norm) && (rel_prec == 1))){
_mult_real(alpha[j], alpha[j], 1./H[j][j].re);
assign_add_mul(solver_field[2], V[j], alpha[j], N);
for(i = j-1; i >= 0; i--){
for(k = i+1; k <= j; k++){
_mult_assign_complex(tmp1, H[i][k], alpha[k]);
_diff_complex(alpha[i], tmp1);
}
_mult_real(alpha[i], alpha[i], 1./H[i][i].re);
assign_add_mul(solver_field[2], V[i], alpha[i], N);
}
for(i = 0; i < m; i++){
alpha[i].im = 0.;
}
assign(P, solver_field[2], N);
finalize_solver(solver_field, nr_sf);
return(restart*m+j);
}
/* if not */
else{
if(j != m-1){
mul_r(V[(j+1)], 1./H[j+1][j].re, solver_field[1], N);
}
}
}
j=m-1;
/* prepare for restart */
_mult_real(alpha[j], alpha[j], 1./H[j][j].re);
assign_add_mul(solver_field[2], V[j], alpha[j], N);
for(i = j-1; i >= 0; i--){
for(k = i+1; k <= j; k++){
_mult_assign_complex(tmp1, H[i][k], alpha[k]);
_diff_complex(alpha[i], tmp1);
}
_mult_real(alpha[i], alpha[i], 1./H[i][i].re);
assign_add_mul(solver_field[2], V[i], alpha[i], N);
}
for(i = 0; i < m; i++){
alpha[i].im = 0.;
}
}
/* If maximal number of restarts is reached */
assign(P, solver_field[2], N);
finalize_solver(solver_field, nr_sf);
return(-1);
}