void sf_gauge_derivative(const int id, hamiltonian_field_t * const hf) {
int i, mu;
static su3 v, w;
su3 *z;
su3adj *xm;
monomial * mnl = &monomial_list[id];
double factor = -1. * g_beta/3.0;
if(mnl->use_rectangles) {
factor = -mnl->c0 * g_beta/3.0;
}
for(i = 0; i < VOLUME; i++) {
for(mu=0;mu<4;mu++) {
z=&hf->gaugefield[i][mu];
xm=&hf->derivative[i][mu];
get_staples(&v,i,mu, (const su3**) hf->gaugefield);
_su3_times_su3d(w,*z,v);
_trace_lambda_mul_add_assign((*xm), factor, w);
if(mnl->use_rectangles) {
get_rectangle_staples(&v, i, mu);
_su3_times_su3d(w, *z, v);
_trace_lambda_mul_add_assign((*xm), factor*mnl->c1/mnl->c0, w);
}
}
}
return;
}
/* this function calculates the derivative of the momenta: equation 13 of Gottlieb */
void gauge_derivative(const int id, hamiltonian_field_t * const hf) {
monomial * mnl = &monomial_list[id];
double factor = -1. * g_beta/3.0;
if(mnl->use_rectangles) {
mnl->forcefactor = 1.;
factor = -mnl->c0 * g_beta/3.0;
}
double atime, etime;
atime = gettime();
#ifdef OMP
#pragma omp parallel
{
#endif
su3 ALIGN v, w;
int i, mu;
su3 *z;
su3adj *xm;
#ifdef OMP
#pragma omp for
#endif
for(i = 0; i < VOLUME; i++) {
for(mu=0;mu<4;mu++) {
z=&hf->gaugefield[i][mu];
xm=&hf->derivative[i][mu];
get_staples(&v,i,mu, (const su3**) hf->gaugefield);
_su3_times_su3d(w,*z,v);
_trace_lambda_mul_add_assign((*xm), factor, w);
if(mnl->use_rectangles) {
get_rectangle_staples(&v, i, mu);
_su3_times_su3d(w, *z, v);
_trace_lambda_mul_add_assign((*xm), factor*mnl->c1/mnl->c0, w);
}
}
}
#ifdef OMP
} /* OpenMP closing brace */
#endif
etime = gettime();
if(g_debug_level > 1 && g_proc_id == 0) {
printf("# Time for %s monomial derivative: %e s\n", mnl->name, etime-atime);
}
return;
}
void sw_all(hamiltonian_field_t * const hf, const double kappa,
const double c_sw) {
int k,l;
int x,xpk,xpl,xmk,xml,xpkml,xplmk,xmkml;
su3 *w1,*w2,*w3,*w4;
double ka_csw_8 = kappa*c_sw/8.;
static su3 v1,v2,vv1,vv2,plaq;
static su3 vis[4][4];
for(x = 0; x < VOLUME; x++) {
_minus_itimes_su3_plus_su3(vis[0][1],swm[x][1],swm[x][3]);
_su3_minus_su3(vis[0][2],swm[x][1],swm[x][3]);
_itimes_su3_minus_su3(vis[0][3],swm[x][2],swm[x][0]);
_minus_itimes_su3_plus_su3(vis[2][3],swp[x][1],swp[x][3]);
_su3_minus_su3(vis[1][3],swp[x][3],swp[x][1]);
_itimes_su3_minus_su3(vis[1][2],swp[x][2],swp[x][0]);
// project to the traceless anti-hermitian part
_su3_dagger(v1,vis[0][1]);
_su3_minus_su3(vis[0][1],vis[0][1],v1);
_su3_dagger(v1,vis[0][2]);
_su3_minus_su3(vis[0][2],vis[0][2],v1);
_su3_dagger(v1,vis[0][3]);
_su3_minus_su3(vis[0][3],vis[0][3],v1);
_su3_dagger(v1,vis[2][3]);
_su3_minus_su3(vis[2][3],vis[2][3],v1);
_su3_dagger(v1,vis[1][3]);
_su3_minus_su3(vis[1][3],vis[1][3],v1);
_su3_dagger(v1,vis[1][2]);
_su3_minus_su3(vis[1][2],vis[1][2],v1);
for(k = 0; k < 4; k++) {
for(l = k+1; l < 4; l++) {
xpk=g_iup[x][k];
xpl=g_iup[x][l];
xmk=g_idn[x][k];
xml=g_idn[x][l];
xpkml=g_idn[xpk][l];
xplmk=g_idn[xpl][k];
xmkml=g_idn[xml][k];
w1=&hf->gaugefield[x][k];
w2=&hf->gaugefield[xpk][l];
w3=&hf->gaugefield[xpl][k]; /*dag*/
w4=&hf->gaugefield[x][l]; /*dag*/
_su3_times_su3(v1,*w1,*w2);
_su3_times_su3(v2,*w4,*w3);
_su3_times_su3d(plaq,v1,v2);
_su3_times_su3(vv1,plaq,vis[k][l]);
_trace_lambda_mul_add_assign(hf->derivative[x][k], -2.*ka_csw_8, vv1);
_su3d_times_su3(vv2,*w1,vv1);
_su3_times_su3(vv1,vv2,*w1);
_trace_lambda_mul_add_assign(hf->derivative[xpk][l], -2.*ka_csw_8, vv1);
_su3_times_su3(vv2,vis[k][l],plaq);
_su3_dagger(vv1,vv2);
_trace_lambda_mul_add_assign(hf->derivative[x][l], -2.*ka_csw_8, vv1);
_su3d_times_su3(vv2,*w4,vv1);
_su3_times_su3(vv1,vv2,*w4);
_trace_lambda_mul_add_assign(hf->derivative[xpl][k], -2.*ka_csw_8, vv1);
w1=&hf->gaugefield[x][l];
w2=&hf->gaugefield[xplmk][k]; /*dag*/
w3=&hf->gaugefield[xmk][l]; /*dag*/
w4=&hf->gaugefield[xmk][k];
_su3_times_su3d(v1,*w1,*w2);
_su3d_times_su3(v2,*w3,*w4);
_su3_times_su3(plaq,v1,v2);
_su3_times_su3(vv1,plaq,vis[k][l]);
_trace_lambda_mul_add_assign(hf->derivative[x][l], -2.*ka_csw_8, vv1);
_su3_dagger(vv1,v1);
_su3_times_su3d(vv2,vv1,vis[k][l]);
_su3_times_su3d(vv1,vv2,v2);
_trace_lambda_mul_add_assign(hf->derivative[xplmk][k], -2.*ka_csw_8, vv1);
_su3_times_su3(vv2,*w3,vv1);
_su3_times_su3d(vv1,vv2,*w3);
_trace_lambda_mul_add_assign(hf->derivative[xmk][l], -2.*ka_csw_8, vv1);
_su3_dagger(vv2,vv1);
_trace_lambda_mul_add_assign(hf->derivative[xmk][k], -2.*ka_csw_8, vv2);
w1=&hf->gaugefield[xmk][k]; /*dag*/
w2=&hf->gaugefield[xmkml][l]; /*dag*/
w3=&hf->gaugefield[xmkml][k];
w4=&hf->gaugefield[xml][l];
_su3_times_su3(v1,*w2,*w1);
_su3_times_su3(v2,*w3,*w4);
_su3_times_su3d(vv1,*w1,vis[k][l]);
_su3_times_su3d(vv2,vv1,v2);
_su3_times_su3(vv1,vv2,*w2);
_trace_lambda_mul_add_assign(hf->derivative[xmk][k], -2.*ka_csw_8, vv1);
_su3_times_su3(vv2,*w2,vv1);
_su3_times_su3d(vv1,vv2,*w2);
_trace_lambda_mul_add_assign(hf->derivative[xmkml][l], -2.*ka_csw_8, vv1);
_su3_dagger(vv2,vv1);
_trace_lambda_mul_add_assign(hf->derivative[xmkml][k], -2.*ka_csw_8, vv2);
_su3d_times_su3(vv1,*w3,vv2);
_su3_times_su3(vv2,vv1,*w3);
_trace_lambda_mul_add_assign(hf->derivative[xml][l], -2.*ka_csw_8, vv2);
w1=&hf->gaugefield[xml][l]; /*dag*/
w2=&hf->gaugefield[xml][k];
w3=&hf->gaugefield[xpkml][l];
w4=&hf->gaugefield[x][k]; /*dag*/
_su3d_times_su3(v1,*w1,*w2);
_su3_times_su3d(v2,*w3,*w4);
_su3_times_su3d(vv1,*w1,vis[k][l]);
_su3_times_su3d(vv2,vv1,v2);
_su3_times_su3d(vv1,vv2,*w2);
_trace_lambda_mul_add_assign(hf->derivative[xml][l], -2.*ka_csw_8, vv1);
_su3_dagger(vv2,vv1);
_trace_lambda_mul_add_assign(hf->derivative[xml][k], -2.*ka_csw_8, vv2);
_su3d_times_su3(vv1,*w2,vv2);
_su3_times_su3(vv2,vv1,*w2);
_trace_lambda_mul_add_assign(hf->derivative[xpkml][l], -2.*ka_csw_8, vv2);
_su3_dagger(vv2,v2);
_su3_times_su3d(vv1,vv2,v1);
_su3_times_su3d(vv2,vv1,vis[k][l]);
_trace_lambda_mul_add_assign(hf->derivative[x][k], -2.*ka_csw_8, vv2);
}
}
}
return;
}
void deriv_Sb_D_psi(spinor * const l, spinor * const k,
hamiltonian_field_t * const hf, const double factor) {
int ix,iy;
su3 * restrict up ALIGN;
su3 * restrict um ALIGN;
static su3 v1,v2;
static su3_vector psia,psib,phia,phib;
static spinor rr;
/* spinor * restrict r ALIGN; */
spinor * restrict sp ALIGN;
spinor * restrict sm ALIGN;
#ifdef _KOJAK_INST
#pragma pomp inst begin(derivSb)
#endif
#ifdef XLC
#pragma disjoint(*sp, *sm, *up, *um)
#endif
#ifdef BGL
__alignx(16, l);
__alignx(16, k);
#endif
/* for parallelization */
#ifdef MPI
xchange_lexicfield(k);
xchange_lexicfield(l);
#endif
/************** loop over all lattice sites ****************/
for(ix = 0; ix < (VOLUME); ix++){
rr = (*(l + ix));
/* rr=g_spinor_field[l][icx-ioff]; */
/*multiply the left vector with gamma5*/
_vector_minus_assign(rr.s2, rr.s2);
_vector_minus_assign(rr.s3, rr.s3);
/*********************** direction +0 ********************/
iy=g_iup[ix][0];
sp = k + iy;
up=&hf->gaugefield[ix][0];
_vector_add(psia,(*sp).s0,(*sp).s2);
_vector_add(psib,(*sp).s1,(*sp).s3);
_vector_add(phia,rr.s0,rr.s2);
_vector_add(phib,rr.s1,rr.s3);
_vector_tensor_vector_add(v1, phia, psia, phib, psib);
_su3_times_su3d(v2,*up,v1);
_complex_times_su3(v1,ka0,v2);
_trace_lambda_mul_add_assign(hf->derivative[ix][0], 2.*factor, v1);
/************** direction -0 ****************************/
iy=g_idn[ix][0];
sm = k + iy;
um=&hf->gaugefield[iy][0];
_vector_sub(psia,(*sm).s0,(*sm).s2);
_vector_sub(psib,(*sm).s1,(*sm).s3);
_vector_sub(phia,rr.s0,rr.s2);
_vector_sub(phib,rr.s1,rr.s3);
_vector_tensor_vector_add(v1, psia, phia, psib, phib);
_su3_times_su3d(v2,*um,v1);
_complex_times_su3(v1,ka0,v2);
_trace_lambda_mul_add_assign(hf->derivative[iy][0], 2.*factor, v1);
/*************** direction +1 **************************/
iy=g_iup[ix][1];
sp = k + iy;
up=&hf->gaugefield[ix][1];
_vector_i_add(psia,(*sp).s0,(*sp).s3);
_vector_i_add(psib,(*sp).s1,(*sp).s2);
_vector_i_add(phia,rr.s0,rr.s3);
_vector_i_add(phib,rr.s1,rr.s2);
_vector_tensor_vector_add(v1, phia, psia, phib, psib);
_su3_times_su3d(v2,*up,v1);
_complex_times_su3(v1,ka1,v2);
_trace_lambda_mul_add_assign(hf->derivative[ix][1], 2.*factor, v1);
/**************** direction -1 *************************/
iy=g_idn[ix][1];
sm = k + iy;
um=&hf->gaugefield[iy][1];
_vector_i_sub(psia,(*sm).s0,(*sm).s3);
_vector_i_sub(psib,(*sm).s1,(*sm).s2);
_vector_i_sub(phia,rr.s0,rr.s3);
_vector_i_sub(phib,rr.s1,rr.s2);
_vector_tensor_vector_add(v1, psia, phia, psib, phib);
_su3_times_su3d(v2,*um,v1);
_complex_times_su3(v1,ka1,v2);
_trace_lambda_mul_add_assign(hf->derivative[iy][1], 2.*factor, v1);
/*************** direction +2 **************************/
iy=g_iup[ix][2];
sp = k + iy;
up=&hf->gaugefield[ix][2];
_vector_add(psia,(*sp).s0,(*sp).s3);
_vector_sub(psib,(*sp).s1,(*sp).s2);
_vector_add(phia,rr.s0,rr.s3);
_vector_sub(phib,rr.s1,rr.s2);
_vector_tensor_vector_add(v1, phia, psia, phib, psib);
_su3_times_su3d(v2,*up,v1);
_complex_times_su3(v1,ka2,v2);
_trace_lambda_mul_add_assign(hf->derivative[ix][2], 2.*factor, v1);
/***************** direction -2 ************************/
iy=g_idn[ix][2];
sm = k + iy;
um=&hf->gaugefield[iy][2];
_vector_sub(psia,(*sm).s0,(*sm).s3);
_vector_add(psib,(*sm).s1,(*sm).s2);
_vector_sub(phia,rr.s0,rr.s3);
_vector_add(phib,rr.s1,rr.s2);
_vector_tensor_vector_add(v1, psia, phia, psib, phib);
_su3_times_su3d(v2,*um,v1);
_complex_times_su3(v1,ka2,v2);
_trace_lambda_mul_add_assign(hf->derivative[iy][2], 2.*factor, v1);
/****************** direction +3 ***********************/
iy=g_iup[ix][3];
sp = k + iy;
up=&hf->gaugefield[ix][3];
_vector_i_add(psia,(*sp).s0,(*sp).s2);
_vector_i_sub(psib,(*sp).s1,(*sp).s3);
_vector_i_add(phia,rr.s0,rr.s2);
_vector_i_sub(phib,rr.s1,rr.s3);
_vector_tensor_vector_add(v1, phia, psia, phib, psib);
_su3_times_su3d(v2,*up,v1);
_complex_times_su3(v1,ka3,v2);
_trace_lambda_mul_add_assign(hf->derivative[ix][3], 2.*factor, v1);
/***************** direction -3 ************************/
iy=g_idn[ix][3];
sm = k + iy;
um=&hf->gaugefield[iy][3];
_vector_i_sub(psia,(*sm).s0,(*sm).s2);
_vector_i_add(psib,(*sm).s1,(*sm).s3);
_vector_i_sub(phia,rr.s0,rr.s2);
_vector_i_add(phib,rr.s1,rr.s3);
_vector_tensor_vector_add(v1, psia, phia, psib, phib);
_su3_times_su3d(v2,*um,v1);
_complex_times_su3(v1,ka3,v2);
_trace_lambda_mul_add_assign(hf->derivative[iy][3], 2.*factor, v1);
/****************** end of loop ************************/
}
#ifdef _KOJAK_INST
#pragma pomp inst end(derivSb)
#endif
}
