// -----------------------------------------------------------------
// Return a_i * b_i for two complex vectors (no conjugation!)
double_complex inner(complex *a, complex *b) {
int i, Ndat = 16 * DIMF;
double_complex dot;
dot.real = a[0].real * b[0].real - a[0].imag * b[0].imag;
dot.imag = a[0].imag * b[0].real + a[0].real * b[0].imag;
for (i = 1; i < sites_on_node * Ndat; i++) {
dot.real += a[i].real * b[i].real - a[i].imag * b[i].imag;
dot.imag += a[i].imag * b[i].real + a[i].real * b[i].imag;
}
// Accumulate inner product across all nodes
g_dcomplexsum(&dot);
return dot;
}
static void chem_pot_print1(double_complex pb_dMdmu_p_e, double_complex pb_dMdmu_p_o,
double_complex pb_d2Mdmu2_p_e, double_complex pb_d2Mdmu2_p_o,
Real mass, int jpbp_reps, int npbp_reps)
{
Real r_pb_dMdmu_p_e = 0.0;
Real i_pb_dMdmu_p_e = 0.0;
Real r_pb_dMdmu_p_o = 0.0;
Real i_pb_dMdmu_p_o = 0.0;
Real r_pb_d2Mdmu2_p_e = 0.0;
Real i_pb_d2Mdmu2_p_e = 0.0;
Real r_pb_d2Mdmu2_p_o = 0.0;
Real i_pb_d2Mdmu2_p_o = 0.0;
g_dcomplexsum( &pb_dMdmu_p_e );
g_dcomplexsum( &pb_dMdmu_p_o );
g_dcomplexsum( &pb_d2Mdmu2_p_e );
g_dcomplexsum( &pb_d2Mdmu2_p_o );
r_pb_dMdmu_p_e = pb_dMdmu_p_e.real*(2.0/(double)volume) ;
i_pb_dMdmu_p_e = pb_dMdmu_p_e.imag*(2.0/(double)volume) ;
r_pb_dMdmu_p_o = pb_dMdmu_p_o.real*(2.0/(double)volume) ;
i_pb_dMdmu_p_o = pb_dMdmu_p_o.imag*(2.0/(double)volume) ;
r_pb_d2Mdmu2_p_e = pb_d2Mdmu2_p_e.real*(2.0/(double)volume) ;
i_pb_d2Mdmu2_p_e = pb_d2Mdmu2_p_e.imag*(2.0/(double)volume) ;
r_pb_d2Mdmu2_p_o = pb_d2Mdmu2_p_o.real*(2.0/(double)volume) ;
i_pb_d2Mdmu2_p_o = pb_d2Mdmu2_p_o.imag*(2.0/(double)volume) ;
node0_printf("PB_DMDMU_P: mass %e %e %e %e %e ( %d of %d )\n", mass,
r_pb_dMdmu_p_e, r_pb_dMdmu_p_o,
i_pb_dMdmu_p_e, i_pb_dMdmu_p_o,
jpbp_reps+1, npbp_reps);
node0_printf("PB_D2MDMU2_P: mass %e %e %e %e %e ( %d of %d )\n", mass,
r_pb_d2Mdmu2_p_e, r_pb_d2Mdmu2_p_o,
i_pb_d2Mdmu2_p_e, i_pb_d2Mdmu2_p_o,
jpbp_reps+1, npbp_reps);
}
/* Assume the first Nvecs_curr eigenvectors have been already orthonormalized.
If norm of an eigenvector is less than ORTHO_EPS, remove it.
Rturn the number of new eigenvectors to be added.
*/
static int orthogonalize(int Nvecs, int Nvecs_curr, su3_vector **eigVec, int parity){
register int i;
int j, k, Nvecs_add, n;
double norm;
double_complex cc;
double_complex *c;
j = Nvecs_curr;
Nvecs_add = Nvecs;
n = Nvecs_curr + Nvecs_add;
c = (double_complex *)malloc(n*sizeof(double_complex));
while(j < n){
/* Modified Gram-Schmidt
Orthogonality is better but more communications are needed */
for(k = 0; k < j; k++){
// c[k] = dcmplx((double)0.0,(double)0.0);
// FORSOMEFIELDPARITY_OMP(i, parity, private(cc) reduction(+:c[k])){
// cc = su3_dot(eigVec[k]+i, eigVec[j]+i);
// CSUM(c[k], cc);
// } END_LOOP_OMP;
double cctotr=0., cctoti=0.;
FORSOMEFIELDPARITY_OMP(i, parity, private(cc) reduction(+:cctotr,cctoti)){
cc = su3_dot(eigVec[k]+i, eigVec[j]+i);
cctotr += cc.real;
cctoti += cc.imag;
} END_LOOP_OMP;
c[k].real = cctotr;
c[k].imag = cctoti;
g_dcomplexsum(c+k);
FORSOMEFIELDPARITY_OMP(i, parity, default(shared)){
c_scalar_mult_sub_su3vec(eigVec[j]+i, c+k, eigVec[k]+i);
} END_LOOP_OMP
}
/* Gram-Schmidt
Less communications but
poor orthogonality might happen if the number of vectors is too large. */
/*
for(k = 0; k < j; k++){
c[k] = dcmplx((double)0.0,(double)0.0);
FORSOMEFIELDPARITY_OMP(i, parity, private(cc) reduction(+:c[k])){
cc = su3_dot(eigVec[k]+i, eigVec[j]+i);
CSUM(c[k], cc);
} END_LOOP_OMP
}
g_vecdcomplexsum(c, j);
for(k = 0; k < j; k++){
FORSOMEFIELDPARITY_OMP(i, parity, default(shared)){
c_scalar_mult_sub_su3vec(eigVec[j]+i, c+k, eigVec[k]+i);
} END_LOOP_OMP
}
*/
norm = (double)0.0;
FORSOMEFIELDPARITY_OMP(i, parity, reduction(+:norm)){
norm += magsq_su3vec(eigVec[j]+i);
} END_LOOP_OMP
g_doublesum(&norm);
norm = sqrt(norm);
if( norm < ORTHO_EPS ){
Nvecs_add--;
n--;
for(k = j; k < n; k++){
FORSOMEFIELDPARITY_OMP(i, parity, default(shared)){
eigVec[k][i] = eigVec[k+1][i];
} END_LOOP_OMP
}
}
else{
void f_meas_imp_field( int npbp_reps, quark_invert_control *qic, Real mass,
int naik_term_epsilon_index, fermion_links_t *fl){
imp_ferm_links_t* fn = get_fm_links(fl)[naik_term_epsilon_index];
#ifdef DM_DU0
imp_ferm_links_t* fn_du0 = get_fm_du0_links(fl)[naik_term_epsilon_index];
#endif
#if ( FERM_ACTION == HISQ || FERM_ACTION == HYPISQ ) & defined(DM_DEPS)
imp_ferm_links_t *fn_deps = get_fn_deps_links(fl);
#endif
Real r_psi_bar_psi_even, i_psi_bar_psi_even;
Real r_psi_bar_psi_odd, i_psi_bar_psi_odd;
Real r_ferm_action;
/* local variables for accumulators */
register int i;
double rfaction;
double_complex pbp_e, pbp_o;
complex cc;
int jpbp_reps;
su3_vector *gr = NULL;
su3_vector *M_gr = NULL;
su3_vector *M_inv_gr = NULL;
#ifdef DM_DU0
double r_pb_dMdu_p_even, r_pb_dMdu_p_odd;
su3_vector *dMdu_x = NULL;
#endif
#if ( FERM_ACTION == HISQ || FERM_ACTION == HYPISQ ) & defined(DM_DEPS)
double r_pb_dMdeps_p_even, r_pb_dMdeps_p_odd;
su3_vector *dMdeps_x = NULL;
#endif
#ifdef CHEM_POT
double_complex pb_dMdmu_p_e, pb_dMdmu_p_o;
double_complex pb_d2Mdmu2_p_e, pb_d2Mdmu2_p_o;
double MidM_MidM;
su3_vector *dM_M_inv_gr = NULL;
su3_vector *d2M_M_inv_gr = NULL;
su3_vector *M_inv_dM_M_inv_gr = NULL;
su3_vector *dM_M_inv_dM_M_inv_gr = NULL;
#endif
/* Loop over random sources */
for(jpbp_reps = 0; jpbp_reps < npbp_reps; jpbp_reps++){
rfaction = (double)0.0;
pbp_e = pbp_o = dcmplx((double)0.0,(double)0.0);
/* Make random source, and do inversion */
/* generate gr random; M_gr = M gr */
gr = create_v_field();
#ifndef Z2RSOURCE
grsource_plain_field( gr, EVENANDODD );
#else
z2rsource_plain_field( gr, EVENANDODD );
#endif
/* The following operation is done in the prevailing
precision. The algorithm needs to be fixed! */
M_gr = create_v_field();
ks_dirac_adj_op( gr, M_gr, mass, EVENANDODD, fn );
/* M_inv_gr = M^{-1} gr */
M_inv_gr = create_v_field();
mat_invert_uml_field( gr, M_inv_gr, qic, mass, fn );
#ifdef DM_DU0
r_pb_dMdu_p_even = r_pb_dMdu_p_odd = (double)0.0;
/* dMdu_x = dM/du0 M^{-1} gr */
dMdu_x = create_v_field();
dslash_fn_field( M_inv_gr, dMdu_x, EVENANDODD, fn_du0 );
#endif
#if ( FERM_ACTION == HISQ || FERM_ACTION == HYPISQ ) & defined(DM_DEPS)
r_pb_dMdeps_p_even = r_pb_dMdeps_p_odd = (double)0.0;
/* dMdeps_x = dM/deps0 M^{-1} gr */
dMdeps_x = create_v_field();
dslash_fn_field( M_inv_gr, dMdeps_x, EVENANDODD, fn_deps );
#endif
#ifdef CHEM_POT
pb_dMdmu_p_e = pb_dMdmu_p_o = dcmplx((double)0.0,(double)0.0);
pb_d2Mdmu2_p_e = pb_d2Mdmu2_p_o = dcmplx((double)0.0,(double)0.0);
/* dM_M_inv_gr = dM/dmu * M_inv_gr */
/* d2M_M_inv_gr = d2M/dmu2 * M_inv_gr */
dM_M_inv_gr = create_v_field();
chem_pot_tshift(fn, dM_M_inv_gr, M_inv_gr, 3., -1.);
d2M_M_inv_gr = create_v_field();
chem_pot_tshift(fn, d2M_M_inv_gr, M_inv_gr, 9., 1.);
#endif
/* fermion action = M_gr.M_inv_gr */
/* psi-bar-psi on even sites = gr.M_inv_gr */
FOREVENFIELDSITES(i){
rfaction += su3_rdot( M_gr+i, M_inv_gr+i );
cc = su3_dot( gr+i, M_inv_gr+i );
CSUM(pbp_e, cc);
#ifdef DM_DU0
/* r_pb_dMdu_p_even = gr * dM/du0 M^{-1} gr |even*/
r_pb_dMdu_p_even += su3_rdot( gr+i, dMdu_x+i );
#endif
#if ( FERM_ACTION == HISQ || FERM_ACTION == HYPISQ ) & defined(DM_DEPS)
/* r_pb_dMdu_p_even = gr * dM/du0 M^{-1} gr |even*/
r_pb_dMdeps_p_even += su3_rdot( gr+i, dMdeps_x+i );
#endif
#ifdef CHEM_POT
/* Compute pb_dMdmu_p, pb_d2Mdmu2_p and dM_M_inv on even sites */
cc = su3_dot( gr+i, dM_M_inv_gr+i);
CSUM(pb_dMdmu_p_e, cc);
cc = su3_dot( gr+i, d2M_M_inv_gr+i);
CSUM(pb_d2Mdmu2_p_e, cc);
#endif
}
/* psi-bar-psi on odd sites */
FORODDFIELDSITES(i){
cc = su3_dot( gr+i, M_inv_gr+i );
CSUM(pbp_o, cc);
#ifdef DM_DU0
/* r_pb_dMdu_p_odd = gr * dM/du0 M^{-1} gr |odd*/
r_pb_dMdu_p_odd += su3_rdot( gr+i, dMdu_x+i );
#endif
#if ( FERM_ACTION == HISQ || FERM_ACTION == HYPISQ ) & defined(DM_DEPS)
/* r_pb_dMdu_p_odd = gr * dM/du0 M^{-1} gr |odd*/
r_pb_dMdeps_p_odd += su3_rdot( gr+i, dMdeps_x+i );
#endif
#ifdef CHEM_POT
/* Compute pb_dMdmu_P, pb_d2Mdmu2_p and dM_M_inv on odd sites */
cc = su3_dot( gr+i, dM_M_inv_gr+i);
CSUM(pb_dMdmu_p_o, cc);
cc = su3_dot( gr+i, d2M_M_inv_gr+i);
CSUM(pb_d2Mdmu2_p_o, cc);
#endif
}
#ifdef CHEM_POT
destroy_v_field(d2M_M_inv_gr); d2M_M_inv_gr = NULL;
#endif
destroy_v_field(M_gr); M_gr = NULL;
g_dcomplexsum( &pbp_o );
g_dcomplexsum( &pbp_e );
g_doublesum( &rfaction );
#ifdef DM_DU0
destroy_v_field( dMdu_x ); dMdu_x = NULL;
g_doublesum( &r_pb_dMdu_p_even );
g_doublesum( &r_pb_dMdu_p_odd );
r_pb_dMdu_p_even *= (2.0/(double)volume);
r_pb_dMdu_p_odd *= (2.0/(double)volume);
node0_printf("PB_DMDU_P: mass %e %e %e ( %d of %d )\n", mass,
r_pb_dMdu_p_even, r_pb_dMdu_p_odd, jpbp_reps+1, npbp_reps);
#endif
#if ( FERM_ACTION == HISQ || FERM_ACTION == HYPISQ ) & defined(DM_DEPS)
destroy_v_field( dMdeps_x ); dMdeps_x = NULL;
g_doublesum( &r_pb_dMdeps_p_even );
g_doublesum( &r_pb_dMdeps_p_odd );
r_pb_dMdeps_p_even *= (2.0/(double)volume);
r_pb_dMdeps_p_odd *= (2.0/(double)volume);
node0_printf("PB_DMDEPS_P: mass %e %e %e ( %d of %d )\n", mass,
r_pb_dMdeps_p_even, r_pb_dMdeps_p_odd, jpbp_reps+1, npbp_reps);
#endif
r_psi_bar_psi_odd = pbp_o.real*(2.0/(double)volume) ;
i_psi_bar_psi_odd = pbp_o.imag*(2.0/(double)volume) ;
r_psi_bar_psi_even = pbp_e.real*(2.0/(double)volume) ;
i_psi_bar_psi_even = pbp_e.imag*(2.0/(double)volume) ;
r_ferm_action = rfaction*(1.0/(double)volume) ;
node0_printf("PBP: mass %e %e %e %e %e ( %d of %d )\n", mass,
r_psi_bar_psi_even, r_psi_bar_psi_odd,
i_psi_bar_psi_even, i_psi_bar_psi_odd,
jpbp_reps+1, npbp_reps);
node0_printf("FACTION: mass = %e, %e ( %d of %d )\n", mass,
r_ferm_action, jpbp_reps+1, npbp_reps);
#ifdef CHEM_POT
/* Print results for pb_dMdmu_p and pb_d2Mdmu2_p */
chem_pot_print1(pb_dMdmu_p_e, pb_dMdmu_p_o, pb_d2Mdmu2_p_e, pb_d2Mdmu2_p_o,
mass, jpbp_reps, npbp_reps);
#endif
#ifdef TR_MM_INV
if(npbp_reps > 1){
su3_vector *MM_inv_gr = create_v_field();
double pbp_pbp = 0.0;
mat_invert_uml_field( M_inv_gr, MM_inv_gr, qic, mass, fn );
FORALLFIELDSITES(i){
pbp_pbp += su3_rdot( gr+i, MM_inv_gr+i );
}
g_doublesum( &pbp_pbp );
pbp_pbp = pbp_pbp*(1.0/(double)volume) ;
node0_printf("TR_MM_INV: mass %e, %e ( %d of %d )\n", mass,
pbp_pbp, jpbp_reps+1, npbp_reps);
destroy_v_field(MM_inv_gr);
}
#endif
destroy_v_field(M_inv_gr); M_inv_gr = NULL;
#ifdef CHEM_POT
/* M_inv_dM_M_inv_gr = M^{-1} dM_M_inv_gr */
M_inv_dM_M_inv_gr = create_v_field();
mat_invert_uml_field( dM_M_inv_gr, M_inv_dM_M_inv_gr, qic, mass, fn );
destroy_v_field(dM_M_inv_gr); dM_M_inv_gr = NULL;
/* dM_M_inv_dM_M_inv_gr = dM/dmu M_inv_dM_M_inv_gr */
dM_M_inv_dM_M_inv_gr = create_v_field();
chem_pot_tshift(fn, dM_M_inv_dM_M_inv_gr, M_inv_dM_M_inv_gr, 3., -1.);
destroy_v_field(M_inv_dM_M_inv_gr); M_inv_dM_M_inv_gr = NULL;
/* Compute MidM_MidM */
MidM_MidM = (double)0.0;
FORALLFIELDSITES(i){
MidM_MidM += su3_rdot( gr+i, dM_M_inv_dM_M_inv_gr+i);
}
destroy_v_field(dM_M_inv_dM_M_inv_gr); dM_M_inv_dM_M_inv_gr = NULL;
chem_pot_print2(MidM_MidM, jpbp_reps, npbp_reps, mass);
#endif
destroy_v_field(gr); gr = NULL;
} /* jpbp_reps */
