/* Put antihermitian traceless part into momentum */
static void
add_forces_to_mom(QDP_ColorVector **back_qdp, QDP_ColorVector **forw_qdp,
int dir, REAL coeff[], int nsrc)
{
REAL tmp_coeff[nsrc];
QDP_ColorMatrix *tm[nsrc];
int i;
QOP_trace("test 481\n");
if(GOES_BACKWARDS(dir)) {
dir = OPP_DIR(dir);
for(i=0; i<nsrc; i++) {
tmp_coeff[i] = -coeff[i];
}
} else {
for(i=0; i<nsrc; i++) {
tmp_coeff[i] = coeff[i];
}
}
QOP_trace("test 482\n");
for(i=0; i<nsrc; i++) {
QDP_V_eq_r_times_V(tv[i], &tmp_coeff[i], forw_qdp[i], QDP_all);
tm[i] = tempmom_qdp[dir];
}
QOP_trace("test 483\n");
QDP_M_vpeq_V_times_Va(tm, back_qdp, tv, QDP_all, nsrc);
QOP_trace("test 484\n");
}
/* normalizes the vecror vec. Work only on subset. */
void
normalize_qdp(QDP_ColorVector *vec, QDP_Subset subset)
{
QLA_Real norm;
QDP_r_eq_norm2_V(&norm, vec, subset);
norm = 1.0/sqrt(norm);
QDP_V_eq_r_times_V(vec, &norm, vec, subset);
}
int
Rayleigh_min_qdp(QDP_ColorVector *vec, QDP_ColorVector **eigVec,
Real Tolerance, Real RelTol, int Nvecs, int MaxIter,
int Restart, QDP_Subset subset)
{
QLA_Complex cc;
QLA_Real beta, cos_theta, sin_theta;
QLA_Real quot, P_norm, theta, real_vecMp, pMp;
QLA_Real g_norm, old_g_norm, start_g_norm;
QDP_ColorVector *Mvec, *grad, *P, *MP;
int iter;
#ifdef DEBUG
if(QDP_this_node==0) printf("begin Rayleigh_min_qdp\n");
#endif
Mvec = QDP_create_V();
grad = QDP_create_V();
//oldgrad = QDP_create_V();
P = QDP_create_V();
MP = QDP_create_V();
project_out_qdp(vec, eigVec, Nvecs, subset);
normalize_qdp(vec, subset);
Matrix_Vec_mult_qdp(vec, Mvec, subset);
project_out_qdp(Mvec, eigVec, Nvecs, subset);
/* Compute the quotient quot=vev*M*vec */
QDP_r_eq_re_V_dot_V(", vec, Mvec, subset);
/* quot is real since M is hermitian. quot = vec*M*vec */
#ifdef DEBUG
if(QDP_this_node==0) printf("Rayleigh_min: Start -- quot=%g\n", quot);
#endif
/* Compute the grad=M*vec - quot*vec */
QDP_V_eq_V(grad, Mvec, QDP_all);
QDP_V_meq_r_times_V(grad, ", vec, subset);
/* set P (the search direction) equal to grad */
QDP_V_eq_V(P, grad, QDP_all);
/* compute the norms of P and grad */
QDP_r_eq_norm2_V(&P_norm, P, subset);
P_norm = sqrt(P_norm);
QDP_r_eq_norm2_V(&g_norm, grad, subset);
g_norm = sqrt(g_norm);
start_g_norm = g_norm;
//QDP_V_eq_V(oldgrad, grad, subset);
#ifdef DEBUG
if(QDP_this_node==0) printf("Rayleigh_min: Start -- g_norm=%g\n", g_norm);
#endif
iter = 0;
while( (g_norm>Tolerance*quot) &&
( ((iter<MaxIter)&&(g_norm/start_g_norm>RelTol)) || (iter<MINITER) )
) {
iter++;
Matrix_Vec_mult_qdp(P, MP, subset);
QDP_r_eq_re_V_dot_V(&real_vecMp, vec, MP, subset);
QDP_r_eq_re_V_dot_V(&pMp, P, MP, subset);
theta = 0.5*atan(2.0*real_vecMp/(quot*P_norm - pMp/P_norm));
sin_theta = sin(theta);
cos_theta = cos(theta);
if(sin_theta*cos_theta*real_vecMp>0) {
theta = theta - 0.5*M_PI; /* chose the minimum not the maximum */
sin_theta = sin(theta); /* the sin,cos calls can be avoided */
cos_theta = cos(theta);
}
sin_theta = sin_theta/P_norm;
/* vec = cos(theta)*vec +sin(theta)*P/p_norm */
//dax_p_by_qdp(cos_theta, vec, sin_theta, P, subset);
QDP_V_eq_r_times_V(vec, &cos_theta, vec, subset);
QDP_V_peq_r_times_V(vec, &sin_theta, P, subset);
/* Mvec = cos(theta)*Mvec +sin(theta)*MP/p_norm */
//dax_p_by_qdp(cos_theta, Mvec, sin_theta, MP, subset);
QDP_V_eq_r_times_V(Mvec, &cos_theta, Mvec, subset);
QDP_V_peq_r_times_V(Mvec, &sin_theta, MP, subset);
/* renormalize vec ... */
if( iter%Restart == 0 ) {
#ifdef DEBUG
{
QLA_Real vec_norm;
if(QDP_this_node==0) printf("Renormalizing...");
QDP_r_eq_norm2_V(&vec_norm, vec, subset);
if(QDP_this_node==0) printf(" norm: %g\n", sqrt(vec_norm));
}
#endif
/* Project vec on the orthogonal complement of eigVec */
project_out_qdp(vec, eigVec, Nvecs, subset);
normalize_qdp(vec, subset);
Matrix_Vec_mult_qdp(vec, Mvec, subset);
/* Recompute the quotient */
QDP_r_eq_re_V_dot_V(", vec, Mvec, subset);
/* Recompute the grad */
QDP_V_eq_V(grad, Mvec, QDP_all);
QDP_V_meq_r_times_V(grad, ", vec, subset);
//QDP_r_eq_norm2_V(&g_norm, grad, subset);
//printf("g_norm = %g\n", g_norm);
/* Project P on the orthogonal complement of eigVec */
//QDP_r_eq_norm2_V(&P_norm, P, subset);
//printf("P_norm = %g\n", P_norm);
project_out_qdp(P, eigVec, Nvecs, subset);
//QDP_r_eq_norm2_V(&P_norm, P, subset);
//printf("P_norm = %g\n", P_norm);
/* make P orthogonal to vec */
QDP_c_eq_V_dot_V(&cc, vec, P, subset);
//printf("cc = %g\n", QLA_real(cc));
QDP_V_meq_c_times_V(P, &cc, vec, subset);
//QDP_r_eq_norm2_V(&P_norm, P, subset);
//printf("P_norm = %g\n", P_norm);
/* make P orthogonal to grad */
QDP_c_eq_V_dot_V(&cc, grad, P, subset);
//printf("cc = %g\n", QLA_real(cc));
QDP_V_meq_c_times_V(P, &cc, grad, subset);
QDP_r_eq_norm2_V(&P_norm, P, subset);
P_norm = sqrt(P_norm);
}
QDP_r_eq_re_V_dot_V(", vec, Mvec, subset);
#ifdef DEBUG
node0_printf("Rayleigh_min: %i, quot=%8g g=%8g b=%6g P:%6g\n",
iter, quot, g_norm, beta, P_norm);
#endif
old_g_norm = g_norm;
QDP_V_eq_V(grad, Mvec, QDP_all);
QDP_V_meq_r_times_V(grad, ", vec, subset);
//QDP_V_meq_V(oldgrad, grad, subset);
//QDP_r_eq_re_V_dot_V(&g_norm, oldgrad, grad, subset);
//QDP_V_eq_V(oldgrad, grad, subset);
QDP_r_eq_norm2_V(&g_norm, grad, subset);
g_norm = sqrt(g_norm);
beta = cos_theta*g_norm*g_norm/(old_g_norm*old_g_norm);
if( beta>2.0 ) beta = 2.0; /* Cut off beta */
QDP_c_eq_V_dot_V(&cc, vec, P, subset);
QLA_real(cc) *= beta;
QLA_imag(cc) *= beta;
QDP_V_eq_r_times_V_plus_V(P, &beta, P, grad, subset);
QDP_V_meq_c_times_V(P, &cc, vec, subset);
QDP_r_eq_norm2_V(&P_norm, P, subset);
P_norm = sqrt(P_norm);
}
project_out_qdp(vec, eigVec, Nvecs, subset);
normalize_qdp(vec, subset);
QDP_destroy_V(MP);
QDP_destroy_V(P);
//QDP_destroy_V(oldgrad);
QDP_destroy_V(grad);
QDP_destroy_V(Mvec);
iter++;
#ifdef DEBUG
if(QDP_this_node==0) printf("end Rayleigh_min_qdp\n");
#endif
return iter;
}
