int invert_cloverdoublet_eo(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) {
int iter = 0;
/* here comes the inversion using even/odd preconditioning */
if(g_proc_id == 0) {printf("# Using even/odd preconditioning!\n"); fflush(stdout);}
Msw_ee_inv_ndpsi(Even_new_s, Even_new_c,
Even_s, Even_c);
Hopping_Matrix(OE, g_spinor_field[DUM_DERI], Even_new_s);
Hopping_Matrix(OE, g_spinor_field[DUM_DERI+1], Even_new_c);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_mul_add_r(g_spinor_field[DUM_DERI], +1., Odd_s, VOLUME/2);
assign_mul_add_r(g_spinor_field[DUM_DERI+1], +1., Odd_c, VOLUME/2);
/* Do the inversion with the preconditioned */
/* matrix to get the odd sites */
/* Here we invert the hermitean operator squared */
if(g_proc_id == 0) {
printf("# Using CG for TMWILSON flavour doublet!\n");
fflush(stdout);
}
gamma5(g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI], VOLUME/2);
gamma5(g_spinor_field[DUM_DERI+1], g_spinor_field[DUM_DERI+1], VOLUME/2);
iter = cg_her_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec,
VOLUME/2, &Qsw_pm_ndpsi);
Qsw_dagger_ndpsi(Odd_new_s, Odd_new_c,
Odd_new_s, Odd_new_c);
/* Reconstruct the even sites */
Hopping_Matrix(EO, g_spinor_field[DUM_DERI], Odd_new_s);
Hopping_Matrix(EO, g_spinor_field[DUM_DERI+1], Odd_new_c);
Msw_ee_inv_ndpsi(g_spinor_field[DUM_DERI+2], g_spinor_field[DUM_DERI+3],
g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1]);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_add_mul_r(Even_new_s, g_spinor_field[DUM_DERI+2], +1., VOLUME/2);
assign_add_mul_r(Even_new_c, g_spinor_field[DUM_DERI+3], +1., VOLUME/2);
return(iter);
}
void M_full(spinor * const Even_new, spinor * const Odd_new,
spinor * const Even, spinor * const Odd) {
/* Even sites */
Hopping_Matrix(EO, g_spinor_field[DUM_DERI], Odd);
assign_mul_one_pm_imu(Even_new, Even, 1., VOLUME/2);
assign_add_mul_r(Even_new, g_spinor_field[DUM_DERI], -1., VOLUME/2);
/* Odd sites */
Hopping_Matrix(OE, g_spinor_field[DUM_DERI], Even);
assign_mul_one_pm_imu(Odd_new, Odd, 1., VOLUME/2);
assign_add_mul_r(Odd_new, g_spinor_field[DUM_DERI], -1., VOLUME/2);
}
// applies ((Q_h\tau_1 * R)^2 - 1)
void apply_Z_ndpsi(spinor * const k_up, spinor * const k_dn,
spinor * const l_up, spinor * const l_dn,
const int id, hamiltonian_field_t * const hf,
solver_params_t * solver_params) {
monomial * mnl = &monomial_list[id];
mnl->iter0 += solve_mms_nd(g_chi_up_spinor_field, g_chi_dn_spinor_field,
l_up, l_dn, solver_params);
// apply R to the pseudo-fermion fields
assign(k_up, l_up, VOLUME/2);
assign(k_dn, l_dn, VOLUME/2);
for(int j = (mnl->rat.np-1); j > -1; j--) {
assign_add_mul_r(k_up, g_chi_up_spinor_field[j],
mnl->rat.rmu[j], VOLUME/2);
assign_add_mul_r(k_dn, g_chi_dn_spinor_field[j],
mnl->rat.rmu[j], VOLUME/2);
}
// apply R a second time
mnl->iter0 += solve_mms_nd(g_chi_up_spinor_field, g_chi_dn_spinor_field,
k_up, k_dn,
solver_params);
for(int j = (mnl->rat.np-1); j > -1; j--) {
assign_add_mul_r(k_up, g_chi_up_spinor_field[j],
mnl->rat.rmu[j], VOLUME/2);
assign_add_mul_r(k_dn, g_chi_dn_spinor_field[j],
mnl->rat.rmu[j], VOLUME/2);
}
mul_r(g_chi_up_spinor_field[mnl->rat.np], mnl->rat.A*mnl->rat.A,
k_up, VOLUME/2);
mul_r(g_chi_dn_spinor_field[mnl->rat.np], mnl->rat.A*mnl->rat.A,
k_dn, VOLUME/2);
// apply Q^2 and compute the residue
solver_params->M_ndpsi(k_up, k_dn,
g_chi_up_spinor_field[mnl->rat.np], g_chi_dn_spinor_field[mnl->rat.np]);
diff(k_up, k_up, l_up, VOLUME/2);
diff(k_dn, k_dn, l_dn, VOLUME/2);
}
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;
}
double rat_acc(const int id, hamiltonian_field_t * const hf) {
solver_pm_t solver_pm;
monomial * mnl = &monomial_list[id];
double atime, etime, dummy;
atime = gettime();
// only for non-twisted operators
g_mu = 0.;
g_mu3 = 0.;
boundary(mnl->kappa);
if(mnl->type == CLOVERRAT) {
g_c_sw = mnl->c_sw;
sw_term((const su3**) hf->gaugefield, mnl->kappa, mnl->c_sw);
sw_invert(EE, 0.);
}
mnl->energy1 = 0.;
solver_pm.max_iter = mnl->maxiter;
solver_pm.squared_solver_prec = mnl->accprec;
solver_pm.no_shifts = mnl->rat.np;
solver_pm.shifts = mnl->rat.mu;
solver_pm.type = CGMMS;
solver_pm.M_psi = mnl->Qsq;
solver_pm.sdim = VOLUME/2;
solver_pm.rel_prec = g_relative_precision_flag;
mnl->iter0 += cg_mms_tm(g_chi_up_spinor_field, mnl->pf,
&solver_pm, &dummy);
// apply R to the pseudo-fermion fields
assign(mnl->w_fields[0], mnl->pf, VOLUME/2);
for(int j = (mnl->rat.np-1); j > -1; j--) {
assign_add_mul_r(mnl->w_fields[0], g_chi_up_spinor_field[j],
mnl->rat.rmu[j], VOLUME/2);
}
mnl->energy1 = scalar_prod_r(mnl->pf, mnl->w_fields[0], VOLUME/2, 1);
etime = gettime();
if(g_proc_id == 0) {
if(g_debug_level > 1) {
printf("# Time for %s monomial acc step: %e s\n", mnl->name, etime-atime);
}
if(g_debug_level > 0) { // shoud be 3
printf("called rat_acc for id %d dH = %1.10e\n", id, mnl->energy1 - mnl->energy0);
}
}
return(mnl->energy1 - mnl->energy0);
}
int bicg(spinor * const k, spinor * const l, double eps_sq) {
int iteration;
double xxx;
xxx=0.0;
gamma5(g_spinor_field[DUM_SOLVER+1], l, VOLUME/2);
/* main loop */
for(iteration=1;iteration<=ITER_MAX_BCG;iteration++) {
/* compute the residual*/
M_psi(DUM_SOLVER,k,q_off);
xxx=diff_and_square_norm(g_spinor_field[DUM_SOLVER], g_spinor_field[DUM_SOLVER+1], VOLUME/2);
/*apply the solver step for the residual*/
M_psi(DUM_SOLVER+2,DUM_SOLVER,q_off-(2.+2.*q_off));
assign_add_mul_r(k,-1./((1.+q_off)*(1.+q_off)),g_spinor_field[DUM_SOLVER+2], VOLUME/2);
if(xxx <= eps_sq) break;
}
if(g_proc_id==0) {
sout = fopen(solvout, "a");
fprintf(sout, "%d %e %f\n",iteration,xxx, g_mu);
fclose(sout);
}
/* if the geometric series fails, redo with conjugate gradient */
if(iteration>=ITER_MAX_BCG) {
if(ITER_MAX_BCG == 0) {
iteration = 0;
}
zero_spinor_field(k,VOLUME/2);
iteration += solve_cg(k,l,q_off,eps_sq);
Q_psi(k,k,q_off);
if(ITER_MAX_BCG != 0) {
iteration -= 1000000;
}
if(g_proc_id == 0) {
sout = fopen(solvout, "a");
fprintf(sout, "%d %e\n",iteration, g_mu);
fclose(sout);
}
}
return iteration;
}
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 ndratcor_heatbath(const int id, hamiltonian_field_t * const hf) {
monomial * mnl = &monomial_list[id];
double atime, etime, delta;
spinor * up0, * dn0, * up1, * dn1, * tup, * tdn, * Zup, * Zdn;
double coefs[6] = {1./4., -3./32., 7./128., -77./2048., 231./8192., -1463./65536.}; // series of (1+x)^(1/4)
double coefs_check[6] = {1./2., -1./8., 1./16., -5./128., 7./256., -21./1024.}; // series of (1+x)^(1/2)
atime = gettime();
nd_set_global_parameter(mnl);
g_mu3 = 0.;
mnl->iter0 = 0;
if(mnl->type == NDCLOVERRATCOR) {
init_sw_fields();
sw_term((const su3**)hf->gaugefield, mnl->kappa, mnl->c_sw);
sw_invert_nd(mnl->mubar*mnl->mubar - mnl->epsbar*mnl->epsbar);
copy_32_sw_fields();
}
// we measure before the trajectory!
if((mnl->rec_ev != 0) && (hf->traj_counter%mnl->rec_ev == 0)) {
if(mnl->type != NDCLOVERRAT) phmc_compute_ev(hf->traj_counter-1, id, &Qtm_pm_ndbipsi);
else phmc_compute_ev(hf->traj_counter-1, id, &Qsw_pm_ndbipsi);
}
// the Gaussian distributed random fields
mnl->energy0 = 0.;
random_spinor_field_eo(mnl->pf, mnl->rngrepro, RN_GAUSS);
mnl->energy0 = square_norm(mnl->pf, VOLUME/2, 1);
random_spinor_field_eo(mnl->pf2, mnl->rngrepro, RN_GAUSS);
mnl->energy0 += square_norm(mnl->pf2, VOLUME/2, 1);
mnl->solver_params.max_iter = mnl->maxiter;
mnl->solver_params.squared_solver_prec = mnl->accprec;
mnl->solver_params.no_shifts = mnl->rat.np;
mnl->solver_params.shifts = mnl->rat.mu;
mnl->solver_params.type = mnl->solver;
mnl->solver_params.M_ndpsi = &Qtm_pm_ndpsi;
mnl->solver_params.M_ndpsi32 = &Qtm_pm_ndpsi_32;
if(mnl->type == NDCLOVERRATCOR) {
mnl->solver_params.M_ndpsi = &Qsw_pm_ndpsi;
mnl->solver_params.M_ndpsi32 = &Qsw_pm_ndpsi_32;
}
mnl->solver_params.sdim = VOLUME/2;
mnl->solver_params.rel_prec = g_relative_precision_flag;
// apply B to the random field to generate pseudo-fermion fields
up0 = mnl->w_fields[0]; dn0 = mnl->w_fields[1];
up1 = mnl->w_fields[2]; dn1 = mnl->w_fields[3];
Zup = mnl->w_fields[4]; Zdn = mnl->w_fields[5];
apply_Z_ndpsi(up0, dn0, mnl->pf, mnl->pf2, id, hf, &(mnl->solver_params));
// computing correction to energy1
delta = coefs_check[0]*(scalar_prod_r(mnl->pf, up0, VOLUME/2, 1) + scalar_prod_r(mnl->pf2, dn0, VOLUME/2, 1));
if(g_debug_level > 2 && g_proc_id == 0)
printf("# NDRATCOR heatbath: c_%d*(R * Z^%d * R) = %e\n", 1, 1, delta);
// debug for showing that the old check was giving a smaller delta
if(g_debug_level > 3) {
double delta_old = square_norm(up0, VOLUME/2, 1) + square_norm(dn0, VOLUME/2, 1);
if(g_proc_id == 0) {
printf("# NDRATCOR old check: || Z^%d * R ||^2 = %e\n", 1, delta_old);
printf("# NDRATCOR new check: (c_%d*(R * Z^%d * R))^2 = %e\n", 1, 1, delta*delta);
}
}
if(delta*delta > mnl->accprec) {
assign_add_mul_r(mnl->pf, up0, coefs[0], VOLUME/2);
assign_add_mul_r(mnl->pf2, dn0, coefs[0], VOLUME/2);
// saving first application
assign(Zup, up0, VOLUME/2);
assign(Zdn, dn0, VOLUME/2);
for(int i = 2; i < 8; i++) {
// computing next order correction to energy1
delta = coefs_check[i-1]*(scalar_prod_r(Zup, up0, VOLUME/2, 1) + scalar_prod_r(Zup, dn0, VOLUME/2, 1));
if(g_debug_level > 2 && g_proc_id == 0)
printf("# NDRATCOR heatbath: c_%d*(R * Z^%d * R) = %e\n", i, i, delta);
// debug for showing that the old check was giving a smaller delta
if(g_debug_level > 3) {
double delta_old = square_norm(up0, VOLUME/2, 1) + square_norm(dn0, VOLUME/2, 1);
if(g_proc_id == 0) {
printf("# NDRATCOR old check: || Z^%d * R ||^2 = %e\n", 1, delta_old);
printf("# NDRATCOR new check: (c_%d*(R * Z^%d * R))^2 = %e\n", 1, 1, delta*delta);
}
}
if(delta*delta < mnl->accprec) break;
apply_Z_ndpsi(up1, dn1, up0, dn0, id, hf, &(mnl->solver_params));
assign_add_mul_r(mnl->pf, up1, coefs[i-1], VOLUME/2);
assign_add_mul_r(mnl->pf2, dn1, coefs[i-1], VOLUME/2);
tup = up0; tdn = dn0;
up0 = up1; dn0 = dn1;
up1 = tup; dn1 = tdn;
}
}
etime = gettime();
if(g_proc_id == 0) {
if(g_debug_level > 1) {
printf("# Time for %s monomial heatbath: %e s\n", mnl->name, etime-atime);
}
if(g_debug_level > 3) {
printf("called ndratcor_heatbath for id %d energy %f\n", id, mnl->energy0);
}
}
return;
}
// computes ||(1 - C^dagger R C) phi||
void check_C_ndpsi(spinor * const k_up, spinor * const k_dn,
spinor * const l_up, spinor * const l_dn,
const int id, hamiltonian_field_t * const hf,
solver_params_t * solver_params) {
monomial * mnl = &monomial_list[id];
mnl->iter0 = solve_mms_nd(g_chi_up_spinor_field, g_chi_dn_spinor_field,
l_up, l_dn, solver_params);
assign(k_up, l_up, VOLUME/2);
assign(k_dn, l_dn, VOLUME/2);
// apply C to the random field to generate pseudo-fermion fields
for(int j = (mnl->rat.np-1); j > -1; j--) {
// Q_h * tau^1 - i nu_j
// this needs phmc_Cpol = 1 to work!
if(mnl->type == NDCLOVERRATCOR || mnl->type == NDCLOVERRAT) {
Qsw_tau1_sub_const_ndpsi(g_chi_up_spinor_field[mnl->rat.np], g_chi_dn_spinor_field[mnl->rat.np],
g_chi_up_spinor_field[j], g_chi_dn_spinor_field[j],
I*mnl->rat.nu[j], 1., mnl->EVMaxInv);
}
else {
Q_tau1_sub_const_ndpsi(g_chi_up_spinor_field[mnl->rat.np], g_chi_dn_spinor_field[mnl->rat.np],
g_chi_up_spinor_field[j], g_chi_dn_spinor_field[j],
I*mnl->rat.nu[j], 1., mnl->EVMaxInv);
}
assign_add_mul(k_up, g_chi_up_spinor_field[mnl->rat.np], I*mnl->rat.rnu[j], VOLUME/2);
assign_add_mul(k_dn, g_chi_dn_spinor_field[mnl->rat.np], I*mnl->rat.rnu[j], VOLUME/2);
}
//apply R
solver_params->shifts = mnl->rat.mu;
solve_mms_nd(g_chi_up_spinor_field, g_chi_dn_spinor_field,
k_up, k_dn,
solver_params);
for(int j = (mnl->rat.np-1); j > -1; j--) {
assign_add_mul_r(k_up, g_chi_up_spinor_field[j],
mnl->rat.rmu[j], VOLUME/2);
assign_add_mul_r(k_dn, g_chi_dn_spinor_field[j],
mnl->rat.rmu[j], VOLUME/2);
}
// apply C^dagger
solver_params->shifts = mnl->rat.nu;
solve_mms_nd(g_chi_up_spinor_field, g_chi_dn_spinor_field,
k_up, k_dn, solver_params);
for(int j = (mnl->rat.np-1); j > -1; j--) {
// Q_h * tau^1 + i nu_j
if(mnl->type == NDCLOVERRATCOR || mnl->type == NDCLOVERRAT) {
Qsw_tau1_sub_const_ndpsi(g_chi_up_spinor_field[mnl->rat.np], g_chi_dn_spinor_field[mnl->rat.np],
g_chi_up_spinor_field[j], g_chi_dn_spinor_field[j],
-I*mnl->rat.nu[j], 1., mnl->EVMaxInv);
}
else {
Q_tau1_sub_const_ndpsi(g_chi_up_spinor_field[mnl->rat.np], g_chi_dn_spinor_field[mnl->rat.np],
g_chi_up_spinor_field[j], g_chi_dn_spinor_field[j],
-I*mnl->rat.nu[j], 1., mnl->EVMaxInv);
}
assign_add_mul(k_up, g_chi_up_spinor_field[mnl->rat.np], -I*mnl->rat.rnu[j], VOLUME/2);
assign_add_mul(k_dn, g_chi_dn_spinor_field[mnl->rat.np], -I*mnl->rat.rnu[j], VOLUME/2);
}
diff(k_up, k_up, l_up, VOLUME/2);
diff(k_dn, k_dn, l_dn, VOLUME/2);
double resi = square_norm(k_up, VOLUME/2, 1);
resi += square_norm(k_dn, VOLUME/2, 1);
if(g_proc_id == 0) printf("|| (1-C^dagger R C)*phi|| = %e\n", resi);
return;
}
void eigcg(int n, int lde, spinor * const x, spinor * const b, double *normb,
const double eps_sq, double restart_eps_sq, const int rel_prec, int maxit, int *iter,
double *reshist, int *flag, spinor **work, matrix_mult f,
int nev, int v_max, spinor *V, int esize, _Complex double *ework)
{
double tolb;
double alpha, beta; /* CG scalars */
double rho, rhoprev;
double pAp;
int it; /* current iteration number */
int i, j; /* loop variables */
int zs,ds,tmpsize;
spinor *r, *p, *Ap; /* ptrs in work for CG vectors */
_Complex double tempz; /* double precision complex temp var */
double tempd; /* double temp var */
int tempi; /* int temp var */
int ONE = 1; /* var for passing 1 into BLAS routines */
/*----------------------------------------------------------------------
Eigen variables and setup
----------------------------------------------------------------------*/
/* Some constants */
char cR = 'R'; char cL = 'L'; char cN ='N';
char cV = 'V'; char cU = 'U'; char cC ='C';
double betaprev, alphaprev; /* remember the previous iterations scalars */
int v_size; /* tracks the size of V */
int lwork = 3*v_max; /* the size of zwork */
spinor *Ap_prev;
void *_h;
_Complex double *H; /* the V'AV projection matrix */
void *_hevecs;
_Complex double *Hevecs; /* the eigenvectors of H */
void *_hevecsold;
_Complex double *Hevecsold; /* the eigenvectors of H(v_max-1,v_max-1) */
void *_hevals;
double *Hevals; /* the eigenvalues of H */
void *_hevalsold;
double *Hevalsold; /* the eigenvalues of H(m-1,m-1) */
void *_tau;
_Complex double *TAU;
void *_zwork;
_Complex double *zwork; /* double complex work array needed by zheev */
void *_rwork;
double *rwork; /* double work array needed by zheev */
int parallel;
double tmpd;
_Complex double tmpz;
zs = sizeof(_Complex double);
ds = sizeof(double);
int info, allelems = v_max*v_max;
#ifdef MPI
parallel=1;
#else
parallel=0;
#endif
if(nev > 0) /*allocate memory only if eigenvalues will be used */
{
#if (defined SSE || defined SSE2 || defined SSE3)
if ((_h = calloc(v_max*v_max+ALIGN_BASE,zs)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr,"ERROR Could not allocate H\n"); exit(1);}
}
else
H = (_Complex double *)(((unsigned long int)(_h)+ALIGN_BASE)&~ALIGN_BASE);
if ((_hevecs = calloc(v_max*v_max+ALIGN_BASE,zs)) == NULL)
{
if( g_proc_id == g_stdio_proc )
{fprintf(stderr, "ERROR Could not allocate Hevecs\n"); exit(1);}
}else
Hevecs = (_Complex double *)(((unsigned long int)(_hevecs)+ALIGN_BASE)&~ALIGN_BASE);
if ((_hevecsold = calloc(v_max*v_max+ALIGN_BASE,zs)) == NULL)
{
if( g_proc_id == g_stdio_proc )
{fprintf(stderr, "ERROR Could not allocate Hevecsold\n"); exit(1);}
}else
Hevecsold = (_Complex double *)(((unsigned long int)(_hevecsold)+ALIGN_BASE)&~ALIGN_BASE);
if ((_hevals = calloc(v_max+ALIGN_BASE,ds)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr, "ERROR Could not allocate Hevals\n"); exit(1);}
}else
Hevals = (double *)(((unsigned long int)(_hevals)+ALIGN_BASE)&~ALIGN_BASE);
if ((_hevalsold = calloc(v_max+ALIGN_BASE,ds)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr, "ERROR Could not allocate Hevalsold\n"); exit(1); }
}else
Hevalsold = (double *)(((unsigned long int)(_hevalsold)+ALIGN_BASE)&~ALIGN_BASE);
if ((_tau = calloc(2*nev+ALIGN_BASE,zs)) == NULL)
{
if( g_proc_id == g_stdio_proc )
{fprintf(stderr, "ERROR Could not allocate TAU\n"); exit(1); }
}else
TAU = (_Complex double *)(((unsigned long int)(_tau)+ALIGN_BASE)&~ALIGN_BASE);
if ((_zwork = calloc(lwork+ALIGN_BASE,zs)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr, "ERROR Could not allocate zwork\n"); exit(1);}
}else
zwork = (_Complex double *)(((unsigned long int)(_zwork)+ALIGN_BASE)&~ALIGN_BASE);
if ((_rwork = calloc(3*v_max+ALIGN_BASE,ds)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr, "ERROR Could not allocate rwork\n"); exit(1);}
}else
rwork = (double *)(((unsigned long int)(_rwork)+ALIGN_BASE)&~ALIGN_BASE);
#else
if ((H = (_Complex double *) calloc(v_max*v_max, zs)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr, "ERROR Could not allocate H\n"); exit(1);}
}
if ((Hevecs = (_Complex double *) calloc(v_max*v_max, zs)) == NULL)
{
if( g_proc_id == g_stdio_proc )
{fprintf(stderr, "ERROR Could not allocate Hevecs\n"); exit(1);}
}
if ((Hevecsold = (_Complex double *) calloc(v_max*v_max, zs)) == NULL)
{
if( g_proc_id == g_stdio_proc )
{fprintf(stderr, "ERROR Could not allocate Hevecsold\n"); exit(1);}
}
if ((Hevals = (double *) calloc(v_max, ds)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr, "ERROR Could not allocate Hevals\n"); exit(1);}
}
if ((Hevalsold = (double *) calloc(v_max, ds)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr, "ERROR Could not allocate Hevalsold\n"); exit(1); }
}
if ((TAU = (_Complex double *) calloc(2*nev, zs)) == NULL)
{
if( g_proc_id == g_stdio_proc )
{fprintf(stderr, "ERROR Could not allocate TAU\n"); exit(1); }
}
if ((zwork = (_Complex double *) calloc(lwork, zs)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr, "ERROR Could not allocate zwork\n"); exit(1);}
}
if ((rwork = (double *) calloc(3*v_max, ds)) == NULL)
{
if( g_proc_id == g_stdio_proc)
{fprintf(stderr, "ERROR Could not allocate rwork\n"); exit(1);}
}
#endif
} /* end if (nev > 0) */
/*----------------------------------------------------------------------*/
/* setup pointers into work */
r = work[0];
p = work[1];
Ap = work[2];
Ap_prev = work[3];
/*--------------------------------------------------------------------
Initialization phase
--------------------------------------------------------------------*/
if (*flag != 3)
{
/* If flag == 3, the eigCG is called after restart with the same b
* whose norm is already known in normb, so no need for these */
tempd = square_norm(b,n,parallel); /* Norm of rhs, b */
*normb = sqrt(tempd);
/* If right hand side is zero return zero solution. ITER stays the same */
if (*normb == 0.0)
{
for (i=0; i<n; i++)
{
_vector_null(x[i].s0);
_vector_null(x[i].s1);
_vector_null(x[i].s2);
_vector_null(x[i].s3);
}
*flag = 0;
*reshist = 0.0;
if( g_debug_level > 0 && g_proc_id == g_stdio_proc)
displayInfo(eps_sq,maxit,*flag,*iter,*reshist);
return;
}
}
/* Set up for the method */
*flag = 1;
tolb = eps_sq * (*normb)*(*normb); /* Relative to b tolerance */
/* Zero-th residual: r = b - A*x */
f(r,x);
diff(r,b,r,n);
rho = 0.0;
alpha = 1.0;
beta = 0.0;
v_size = 0;
double reshist_init=square_norm(r,n,parallel);
//if( g_proc_id == g_stdio_proc )
//fprintf(stdout, "reshist init %f\n", reshist_init);
/*--------------------------------------------------------------------
main CG loop
--------------------------------------------------------------------*/
for (it = 0; it < maxit; it++) {
rhoprev = rho;
rho=square_norm(r,n,parallel);
*reshist = rho;
if ( (g_debug_level > 2) && (g_proc_id == g_stdio_proc) )
{ fprintf(stdout, " Linsys res( %d ): %g\n",*iter+it,*reshist); fflush(stdout); }
/* Convergence test */
if ( ( (*reshist < eps_sq) && (rel_prec==0) ) || ( (*reshist < eps_sq*(*normb)*(*normb)) && (rel_prec ==1 ) ) )
{
*flag = 0;
break; /* break do not return */
}
/* Restart test */
if(nev==0)
{
if (*reshist < (restart_eps_sq*reshist_init) )
{
*flag = 3;
break; /* break do not return */
}
}
if (it == 0)
assign(p,r,n);
else {
betaprev = beta;
beta = rho / rhoprev;
if (beta == 0.0) {
*flag = 2;
break;
}
assign_mul_add_r(p,beta,r,n); /* p = beta*p + r */
}
/*----- eigCG specific code -------------------------------------------*/
/* Remember Ap from previous iteration to be used at restart */
if (nev > 0 && v_size == v_max)
assign(Ap_prev,Ap,n);
/*---------------------------------------------------------------------*/
f(Ap,p);
/*----- eigCG specific code -------------------------------------------*/
if (nev > 0) {
/* record the diagonal vAv for the previous vector */
if (it > 0) {
H[(v_size-1)*v_max+v_size-1]= 1.0/alpha + betaprev/alphaprev;
//H[(v_size-1)*v_max+v_size-1].im = 0.0;
}
/* Restarting V */
if (v_size == v_max) {
/* Solve (v_max) and (v_max-1) eigenproblems */
tempi = v_max;
allelems=v_max*v_max;
_FT(zcopy)(&allelems, H, &ONE, Hevecs, &ONE);
_FT(zheev)(&cV,&cU,&tempi,Hevecs,&v_max,Hevals,zwork,&lwork,rwork,&info,1,1);
if( (info != 0 ) && (g_proc_id==g_stdio_proc))
{fprintf(stderr, "Error: ZHEEV in eigcg at v_max step, info %d\n",info); exit(1);}
tempi = v_max-1;
_FT(zcopy)(&allelems, H, &ONE, Hevecsold, &ONE);
_FT(zheev)(&cV,&cU,&tempi,Hevecsold,&v_max,Hevalsold,zwork,&lwork,rwork,&info,1,1);
if( (info != 0 ) && (g_proc_id==g_stdio_proc))
{fprintf(stderr, "Error: ZHEEV in eigcg at (v_max-1) step, info %d\n",info); exit(1);}
/* fill 0s in vmax-th elem of oldevecs to match Hevecs */
for(i=1; i <= v_max ; i++)
{Hevecsold[i*v_max-1] = 0.0 ;}
/* Attach the first nev oldevecs at the end of the nev latest ones */
tempi = nev*v_max;
_FT(zcopy)(&tempi,Hevecsold,&ONE,&Hevecs[tempi],&ONE);
/* Orthogonalize the 2*nev (new+old) vectors Hevecs=QR */
v_size = 2*nev;
_FT(zgeqrf)(&v_max,&v_size,Hevecs,&v_max,TAU,zwork,&lwork,&info) ;
if( (info != 0 ) && (g_proc_id==g_stdio_proc))
{fprintf(stderr, "Error: ZGEQRF in eigcg info %d\n",info); exit(1);}
/* use as a temp space Hevecsold = Q^THQ */
_FT(zcopy)(&allelems,H,&ONE,Hevecsold,&ONE);
_FT(zunmqr)(&cR,&cN,&v_max,&v_max,&v_size,Hevecs,&v_max,
TAU,Hevecsold,&v_max,zwork,&lwork,&info);
if( (info != 0 ) && (g_proc_id==g_stdio_proc))
{fprintf(stderr, "Error: ZGEQRF call 1 in eigcg info %d\n",info); exit(1);}
_FT(zunmqr)(&cL,&cC,&v_max,&v_size,&v_size,Hevecs,&v_max,
TAU,Hevecsold,&v_max,zwork,&lwork,&info);
if( (info != 0 ) && (g_proc_id==g_stdio_proc))
{fprintf(stderr, "Error: ZGEQRF call 2 in eigcg info %d\n",info); exit(1);}
/* solve the small Hevecsold v_size x v_size eigenproblem */
_FT(zheev)(&cV,&cU,&v_size,Hevecsold,&v_max,Hevals, zwork,&lwork,rwork,&info,1,1);
if( (info != 0 ) && (g_proc_id==g_stdio_proc))
{fprintf(stderr, "Error: ZHEEV in eigcg info %d\n",info); exit(1);}
/* zero out unused part of eigenectors in Hevecsold */
tempi = 0;
for(i = 0; i < v_size; i++ )
{
for(j = v_size; j < v_max; j++)
{Hevecsold[tempi + j]=0.0;}
tempi += v_max;
}
/* Compute the Hevecsold = Hevecs*Hevecsold */
_FT(zunmqr)(&cL,&cN,&v_max,&v_size,&v_size,Hevecs,&v_max,
TAU,Hevecsold,&v_max,zwork,&lwork,&info);
if( (info != 0 ) && (g_proc_id==g_stdio_proc))
{fprintf(stderr, "Error: ZUNMQR, info %d\n",info); exit(1);}
/* Restart V = V(n,v_max)*Hevecsold(v_max,v_size) */
Zrestart_X((_Complex double *) V, 12*lde, Hevecsold, 12*n, v_max, v_size, ework, esize);
/* Restart H = diag(Hevals) plus a column and a row */
for (i = 0; i < allelems; i++ ) {H[i] = 0.0; }
for (i = 0; i < v_size; i++) H[i*(v_max+1)]= Hevals[i];
/* The next residual to be added (v = r/sqrt(rho))
* needs the (nev+1)-th column and row, through V(:,1:vs)'*A*v.
* Instead of a matvec, we use the Ap and Ap_prev to obtain this:
* V(:,1:vs)'*A*V(:,vs+1) = V(:,1:vs)'*A*r/sqrt(rho) =
* V'(A(p-beta*p_prev))/sqrt(rho) = V'(Ap - beta*Ap_prev)/sqrt(rho)*/
tmpd=-beta;
assign_mul_add_r(Ap_prev,tmpd,Ap,n); /* Ap_prev=Ap-beta*Ap_prev */
tempi=v_size*v_max;
for (i=0; i<v_size; i++){
tmpz=scalar_prod(&V[i*lde],Ap_prev,n,parallel);
H[v_size+i*v_max]=tmpz/sqrt(rho);
H[i+tempi]=conj(tmpz)/sqrt(rho);
}
} /* end of if v_size == v_max */
else
{
/* update (vs+1,vs),(vs,vs+1) elements of tridigonal which are real*/
if ( it > 0)
{
H[(v_size-1)*v_max + v_size]= -sqrt(beta)/alpha;
H[v_size*v_max + v_size-1] = creal(H[(v_size-1)*v_max + v_size]);
}
} /* of else */
/* Augment V with the current CG residual r normalized by sqrt(rho) */
tmpd=1.0/sqrt(rho);
mul_r(&V[v_size*lde],tmpd,r,n);
v_size++;
} /* end of if nev >0 , ie., the eigCG specific code */
/*---------------------------------------------------------------------*/
/* pAp = p' * Ap */
tempz=scalar_prod(p,Ap,n,parallel);
pAp = creal(tempz);
if (pAp == 0.0) {
*flag = 2;
break;
}
alphaprev = alpha;
alpha = rho / pAp;
assign_add_mul_r(x,p,alpha,n); /*update x*/
tmpd=-alpha;
assign_add_mul_r(r,Ap,tmpd,n); /*update r*/
//next line useful for debugging
//printf("%d beta, alpha, rho, pAp %le %le %le %le\n",it,beta,alpha,rho,pAp);
} /* for it = 0 : maxit-1 */
*iter = *iter + it+1; /* record the number of CG iterations plus any older */
if( g_proc_id == g_stdio_proc && g_debug_level > 0)
displayInfo(eps_sq,maxit,*flag,*iter-1,*reshist);
if(nev > 0 )
{
#if (defined SSE || defined SSE2 || defined SSE3)
H= NULL;
free(_h);
Hevecs=NULL;
free(_hevecs);
Hevecsold=NULL;
free(_hevecsold);
Hevals=NULL;
free(_hevals);
Hevalsold=NULL;
free(_hevalsold);
TAU=NULL;
free(_tau);
zwork=NULL;
free(_zwork);
rwork=NULL;
free(_rwork);
#else
free(H);
free(Hevecs);
free(Hevecsold);
free(Hevals);
free(Hevalsold);
free(TAU);
free(zwork);
free(rwork);
#endif
}
return;
}
int invert_doublet_eo(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,
solver_params_t solver_params, const ExternalInverter external_inverter,
const SloppyPrecision sloppy, const CompressionType compression) {
int iter = 0;
#ifdef TM_USE_QUDA
if( external_inverter==QUDA_INVERTER ) {
return invert_doublet_eo_quda( Even_new_s, Odd_new_s, Even_new_c, Odd_new_c,
Even_s, Odd_s, Even_c, Odd_c,
precision, max_iter,
solver_flag, rel_prec, 1,
sloppy, compression );
}
#endif
#ifdef HAVE_GPU
# ifdef TEMPORALGAUGE
if (usegpu_flag) {
gtrafo_eo_nd(Even_s, Odd_s, Even_c, Odd_c,
(spinor*const)NULL, (spinor*const)NULL, (spinor*const)NULL, (spinor*const)NULL,
GTRAFO_APPLY);
}
# endif
#endif /* HAVE_GPU*/
/* here comes the inversion using even/odd preconditioning */
if(g_proc_id == 0) {printf("# Using even/odd preconditioning!\n"); fflush(stdout);}
M_ee_inv_ndpsi(Even_new_s, Even_new_c,
Even_s, Even_c,
g_mubar, g_epsbar);
Hopping_Matrix(OE, g_spinor_field[DUM_DERI], Even_new_s);
Hopping_Matrix(OE, g_spinor_field[DUM_DERI+1], Even_new_c);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_mul_add_r(g_spinor_field[DUM_DERI], +1., Odd_s, VOLUME/2);
assign_mul_add_r(g_spinor_field[DUM_DERI+1], +1., Odd_c, VOLUME/2);
/* Do the inversion with the preconditioned */
/* matrix to get the odd sites */
/* Here we invert the hermitean operator squared */
if(g_proc_id == 0) {
printf("# Using CG for TMWILSON flavour doublet!\n");
fflush(stdout);
}
if ( external_inverter == NO_EXT_INV ){
gamma5(g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI], VOLUME/2);
gamma5(g_spinor_field[DUM_DERI+1], g_spinor_field[DUM_DERI+1], VOLUME/2);
#ifdef HAVE_GPU
if (usegpu_flag) { // GPU, mixed precision solver
# if ( defined TM_USE_MPI && defined PARALLELT )
iter = mixedsolve_eo_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec);
# elif ( !defined TM_USE_MPI && !defined PARALLELT )
iter = mixedsolve_eo_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec);
# else
printf("MPI and/or PARALLELT are not appropriately set for the GPU implementation. Aborting...\n");
exit(-1);
# endif
}
else { // CPU, conjugate gradient
iter = cg_her_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec,
VOLUME/2, &Qtm_pm_ndpsi);
}
#else // CPU, conjugate gradient
if(solver_flag == RGMIXEDCG){
iter = rg_mixed_cg_her_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
solver_params, max_iter, precision, rel_prec, VOLUME/2,
&Qtm_pm_ndpsi, &Qtm_pm_ndpsi_32);
}
else {
iter = cg_her_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec, VOLUME/2, &Qtm_pm_ndpsi);
}
#endif
Qtm_dagger_ndpsi(Odd_new_s, Odd_new_c,
Odd_new_s, Odd_new_c);
} // if(NO_EXT_INV)
#ifdef TM_USE_QPHIX
else if (external_inverter == QPHIX_INVERTER ) {
// using QPhiX, we invert M M^dagger y = b, so we don't need gamma_5 multiplications
iter = invert_eo_qphix_twoflavour(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, solver_flag, rel_prec,
solver_params, sloppy, compression);
// and it multiplies y internally by M^dagger, returning M^{-1} b as required
}
#endif // TM_USE_QPHIX
/* Reconstruct the even sites */
Hopping_Matrix(EO, g_spinor_field[DUM_DERI], Odd_new_s);
Hopping_Matrix(EO, g_spinor_field[DUM_DERI+1], Odd_new_c);
M_ee_inv_ndpsi(g_spinor_field[DUM_DERI+2], g_spinor_field[DUM_DERI+3],
g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
g_mubar, g_epsbar);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_add_mul_r(Even_new_s, g_spinor_field[DUM_DERI+2], +1., VOLUME/2);
assign_add_mul_r(Even_new_c, g_spinor_field[DUM_DERI+3], +1., VOLUME/2);
#ifdef HAVE_GPU
/* return from temporal gauge again */
# ifdef TEMPORALGAUGE
if (usegpu_flag) {
gtrafo_eo_nd(Even_s, Odd_s, Even_c, Odd_c, Even_new_s, Odd_new_s, Even_new_c, Odd_new_c,
GTRAFO_REVERT);
}
# endif
#endif
return(iter);
}
int invert_cloverdoublet_eo(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, solver_params_t solver_params,
const ExternalInverter external_inverter, const SloppyPrecision sloppy, const CompressionType compression) {
int iter = 0;
#ifdef TM_USE_QUDA
if( external_inverter==QUDA_INVERTER ) {
return invert_doublet_eo_quda( Even_new_s, Odd_new_s, Even_new_c, Odd_new_c,
Even_s, Odd_s, Even_c, Odd_c,
precision, max_iter,
solver_flag, rel_prec, 1,
sloppy, compression );
}
#endif
/* here comes the inversion using even/odd preconditioning */
if(g_proc_id == 0) {printf("# Using even/odd preconditioning!\n"); fflush(stdout);}
Msw_ee_inv_ndpsi(Even_new_s, Even_new_c,
Even_s, Even_c);
Hopping_Matrix(OE, g_spinor_field[DUM_DERI], Even_new_s);
Hopping_Matrix(OE, g_spinor_field[DUM_DERI+1], Even_new_c);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_mul_add_r(g_spinor_field[DUM_DERI], +1., Odd_s, VOLUME/2);
assign_mul_add_r(g_spinor_field[DUM_DERI+1], +1., Odd_c, VOLUME/2);
if( external_inverter == NO_EXT_INV ){
/* Do the inversion with the preconditioned */
/* matrix to get the odd sites */
/* Here we invert the hermitean operator squared */
if(g_proc_id == 0) {
printf("# Using CG for TMWILSON flavour doublet!\n");
fflush(stdout);
}
gamma5(g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI], VOLUME/2);
gamma5(g_spinor_field[DUM_DERI+1], g_spinor_field[DUM_DERI+1], VOLUME/2);
if(solver_flag == RGMIXEDCG){
iter = rg_mixed_cg_her_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
solver_params, max_iter, precision, rel_prec, VOLUME/2,
&Qsw_pm_ndpsi, &Qsw_pm_ndpsi_32);
} else {
iter = cg_her_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec,
VOLUME/2, &Qsw_pm_ndpsi);
}
Qsw_dagger_ndpsi(Odd_new_s, Odd_new_c,
Odd_new_s, Odd_new_c);
} // if(NO_EXT_INV)
#ifdef TM_USE_QPHIX
else if (external_inverter == QPHIX_INVERTER ) {
// using QPhiX, we invert M M^dagger y = b, so we don't need gamma_5 multiplications
iter = invert_eo_qphix_twoflavour(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, solver_flag, rel_prec,
solver_params, sloppy, compression);
// and it multiplies y internally by M^dagger, returning M^{-1} b as required
}
#endif // TM_USE_QPHIX
/* Reconstruct the even sites */
Hopping_Matrix(EO, g_spinor_field[DUM_DERI], Odd_new_s);
Hopping_Matrix(EO, g_spinor_field[DUM_DERI+1], Odd_new_c);
Msw_ee_inv_ndpsi(g_spinor_field[DUM_DERI+2], g_spinor_field[DUM_DERI+3],
g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1]);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_add_mul_r(Even_new_s, g_spinor_field[DUM_DERI+2], +1., VOLUME/2);
assign_add_mul_r(Even_new_c, g_spinor_field[DUM_DERI+3], +1., VOLUME/2);
return(iter);
}
int invert_clover_eo(spinor * const Even_new, spinor * const Odd_new,
spinor * const Even, spinor * const Odd,
const double precision, const int max_iter,
const int solver_flag, const int rel_prec,solver_params_t solver_params,
su3 *** gf, matrix_mult Qsq, matrix_mult Qm) {
int iter;
if(g_proc_id == 0 && g_debug_level > 0) {
printf("# Using even/odd preconditioning!\n");
fflush(stdout);
}
assign_mul_one_sw_pm_imu_inv(EE, Even_new, Even, +g_mu);
Hopping_Matrix(OE, g_spinor_field[DUM_DERI], Even_new);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_mul_add_r(g_spinor_field[DUM_DERI], +1., Odd, VOLUME/2);
/* Do the inversion with the preconditioned */
/* matrix to get the odd sites */
/* Here we invert the hermitean operator squared */
gamma5(g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI], VOLUME/2);
if(g_proc_id == 0) {
//printf("# Using CG!\n");
printf("# mu = %f, kappa = %f, csw = %f\n",
g_mu/2./g_kappa, g_kappa, g_c_sw);
fflush(stdout);
}
if(solver_flag == CG) {
if(g_proc_id == 0) {
printf("# Using CG!\n");
fflush(stdout);
}
iter = cg_her(Odd_new, g_spinor_field[DUM_DERI], max_iter,
precision, rel_prec,
VOLUME/2, Qsq);
Qm(Odd_new, Odd_new);
} else if(solver_flag == INCREIGCG) {
if(g_proc_id == 0) {
printf("# Using Incremental Eig-CG!\n");
fflush(stdout);
}
iter = incr_eigcg(VOLUME/2,solver_params.eigcg_nrhs, solver_params.eigcg_nrhs1, Odd_new, g_spinor_field[DUM_DERI], solver_params.eigcg_ldh, Qsq,
solver_params.eigcg_tolsq1, solver_params.eigcg_tolsq, solver_params.eigcg_restolsq , solver_params.eigcg_rand_guess_opt,
rel_prec, max_iter, solver_params.eigcg_nev, solver_params.eigcg_vmax);
Qm(Odd_new, Odd_new);
} else {
if(g_proc_id == 0) {
printf("# This solver is not available for this operator. Exisiting!\n");
fflush(stdout);
}
return 0;
}
/* Reconstruct the even sites */
Hopping_Matrix(EO, g_spinor_field[DUM_DERI], Odd_new);
clover_inv(g_spinor_field[DUM_DERI], +1, g_mu);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_add_mul_r(Even_new, g_spinor_field[DUM_DERI], +1., VOLUME/2);
return(iter);
}
/*lambda: largest eigenvalue, k eigenvector */
int evamax(double *rz, int k, double q_off, double eps_sq) {
static double ritz,norm0,normg,normg0,beta_cg;
static double costh,sinth,cosd,sind,aaa,normp,xxx;
static double xs1,xs2,xs3;
int iteration;
/* Initialize k to be gaussian */
random_spinor_field(g_spinor_field[k], VOLUME/2);
norm0=square_norm(g_spinor_field[k], VOLUME/2, 1);
/*normalize k */
assign_mul_bra_add_mul_r( g_spinor_field[k], 1./sqrt(norm0),0., g_spinor_field[k], VOLUME/2);
Q_psi(DUM_SOLVER,k,q_off);
Q_psi(DUM_SOLVER,DUM_SOLVER,q_off);
/*compute the ritz functional */
/*put g on DUM_SOLVER+2 and p on DUM_SOLVER+1*/
ritz=scalar_prod_r(g_spinor_field[DUM_SOLVER], g_spinor_field[k], VOLUME/2, 1);
zero_spinor_field(g_spinor_field[DUM_SOLVER+2],VOLUME/2);
assign_add_mul_r_add_mul(g_spinor_field[DUM_SOLVER+2], g_spinor_field[DUM_SOLVER], g_spinor_field[k],
1., -ritz, VOLUME/2);
assign(g_spinor_field[DUM_SOLVER+1], g_spinor_field[DUM_SOLVER+2], VOLUME/2);
normg0=square_norm(g_spinor_field[DUM_SOLVER+2], VOLUME/2, 1);
/* main loop */
for(iteration=1;iteration<=ITER_MAX_BCG;iteration++) {
if(normg0 <= eps_sq) break;
Q_psi(DUM_SOLVER+2,DUM_SOLVER+1,q_off);
Q_psi(DUM_SOLVER+2,DUM_SOLVER+2,q_off);
/* compute costh and sinth */
normp=square_norm(g_spinor_field[DUM_SOLVER+1], VOLUME/2, 1);
xxx=scalar_prod_r(g_spinor_field[DUM_SOLVER+2], g_spinor_field[DUM_SOLVER+1], VOLUME/2, 1);
xs1=0.5*(ritz+xxx/normp);
xs2=0.5*(ritz-xxx/normp);
normp=sqrt(normp);
xs3=normg0/normp;
aaa=sqrt(xs2*xs2+xs3*xs3);
cosd=xs2/aaa;
sind=xs3/aaa;
if(cosd>=0.) {
costh=sqrt(0.5*(1.+cosd));
sinth=0.5*sind/costh;
}
else {
sinth=sqrt(0.5*(1.-cosd));
costh=0.5*sind/sinth;
}
ritz=xs1+aaa;
assign_add_mul_r_add_mul(g_spinor_field[k], g_spinor_field[k], g_spinor_field[DUM_SOLVER+1],
costh-1., sinth/normp, VOLUME/2);
assign_add_mul_r_add_mul(g_spinor_field[DUM_SOLVER], g_spinor_field[DUM_SOLVER], g_spinor_field[DUM_SOLVER+2],
costh-1., sinth/normp, VOLUME/2);
/* compute g */
zero_spinor_field(g_spinor_field[DUM_SOLVER+2],VOLUME/2);
assign_add_mul_r_add_mul(g_spinor_field[DUM_SOLVER+2], g_spinor_field[DUM_SOLVER], g_spinor_field[k],
1., -ritz, VOLUME/2);
/* calculate the norm of g' and beta_cg=costh g'^2/g^2 */
normg=square_norm(g_spinor_field[DUM_SOLVER+2], VOLUME/2, 1);
beta_cg=costh*normg/normg0;
if(beta_cg*costh*normp>20.*sqrt(normg)) beta_cg=0.;
normg0=normg;
/* compute the new value of p */
assign_add_mul_r(g_spinor_field[DUM_SOLVER+1], g_spinor_field[k], -scalar_prod_r(g_spinor_field[k], g_spinor_field[DUM_SOLVER+1], VOLUME/2), VOLUME/2, 1);
assign_mul_add_r(g_spinor_field[DUM_SOLVER+1],beta_cg, g_spinor_field[DUM_SOLVER+2], VOLUME/2);
/* restore the state of the iteration */
if(iteration%20==0) {
/* readjust x */
xxx=sqrt(square_norm(g_spinor_field[k], VOLUME/2), 1);
assign_mul_bra_add_mul_r( g_spinor_field[k], 1./xxx,0., g_spinor_field[k], VOLUME/2);
Q_psi(DUM_SOLVER,k,q_off);
Q_psi(DUM_SOLVER,DUM_SOLVER,q_off);
/*compute the ritz functional */
ritz=scalar_prod_r(g_spinor_field[DUM_SOLVER], g_spinor_field[k], VOLUME/2, 1);
/*put g on DUM_SOLVER+2 and p on DUM_SOLVER+1*/
zero_spinor_field(g_spinor_field[DUM_SOLVER+2],VOLUME/2);
assign_add_mul_r_add_mul(g_spinor_field[DUM_SOLVER+2], g_spinor_field[DUM_SOLVER], g_spinor_field[k],
1., -ritz, VOLUME/2);
normg0=square_norm(g_spinor_field[DUM_SOLVER+2], VOLUME/2, 1);
/*subtract a linear combination of x and g from p to
insure (x,p)=0 and (p,g)=(g,g) */
cosd=scalar_prod_r(g_spinor_field[k], g_spinor_field[DUM_SOLVER+1], VOLUME/2, 1);
assign_add_mul_r(g_spinor_field[DUM_SOLVER+1], g_spinor_field[k], -cosd, VOLUME/2);
cosd=scalar_prod_r(g_spinor_field[DUM_SOLVER+1], g_spinor_field[DUM_SOLVER+2], VOLUME/2, 1)-normg0;
assign_add_mul_r(g_spinor_field[DUM_SOLVER+1], g_spinor_field[DUM_SOLVER+2], -cosd/sqrt(normg0), VOLUME/2);
}
}
*rz=ritz;
return iteration;
}
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);
}
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);
}
}//
/* 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);
}
void op_invert(const int op_id, const int index_start, const int write_prop) {
operator * optr = &operator_list[op_id];
double atime = 0., etime = 0., nrm1 = 0., nrm2 = 0.;
int i;
optr->iterations = 0;
optr->reached_prec = -1.;
g_kappa = optr->kappa;
boundary(g_kappa);
atime = gettime();
if(optr->type == TMWILSON || optr->type == WILSON || optr->type == CLOVER) {
g_mu = optr->mu;
g_c_sw = optr->c_sw;
if(optr->type == CLOVER) {
if (g_cart_id == 0 && g_debug_level > 1) {
printf("#\n# csw = %e, computing clover leafs\n", g_c_sw);
}
init_sw_fields(VOLUME);
sw_term( (const su3**) g_gauge_field, optr->kappa, optr->c_sw);
/* this must be EE here! */
/* to match clover_inv in Qsw_psi */
sw_invert(EE, optr->mu);
}
for(i = 0; i < 2; i++) {
if (g_cart_id == 0) {
printf("#\n# 2 kappa mu = %e, kappa = %e, c_sw = %e\n", g_mu, g_kappa, g_c_sw);
}
if(optr->type != CLOVER) {
if(use_preconditioning){
g_precWS=(void*)optr->precWS;
}
else {
g_precWS=NULL;
}
optr->iterations = invert_eo( optr->prop0, optr->prop1, optr->sr0, optr->sr1,
optr->eps_sq, optr->maxiter,
optr->solver, optr->rel_prec,
0, optr->even_odd_flag,optr->no_extra_masses, optr->extra_masses, optr->id );
/* check result */
M_full(g_spinor_field[4], g_spinor_field[5], optr->prop0, optr->prop1);
}
else {
optr->iterations = invert_clover_eo(optr->prop0, optr->prop1, optr->sr0, optr->sr1,
optr->eps_sq, optr->maxiter,
optr->solver, optr->rel_prec,
&g_gauge_field, &Qsw_pm_psi, &Qsw_minus_psi);
/* check result */
Msw_full(g_spinor_field[4], g_spinor_field[5], optr->prop0, optr->prop1);
}
diff(g_spinor_field[4], g_spinor_field[4], optr->sr0, VOLUME / 2);
diff(g_spinor_field[5], g_spinor_field[5], optr->sr1, VOLUME / 2);
nrm1 = square_norm(g_spinor_field[4], VOLUME / 2, 1);
nrm2 = square_norm(g_spinor_field[5], VOLUME / 2, 1);
optr->reached_prec = nrm1 + nrm2;
/* convert to standard normalisation */
/* we have to mult. by 2*kappa */
if (optr->kappa != 0.) {
mul_r(optr->prop0, (2*optr->kappa), optr->prop0, VOLUME / 2);
mul_r(optr->prop1, (2*optr->kappa), optr->prop1, VOLUME / 2);
}
if (optr->solver != CGMMS && write_prop) /* CGMMS handles its own I/O */
optr->write_prop(op_id, index_start, i);
if(optr->DownProp) {
optr->mu = -optr->mu;
} else
break;
}
}
else if(optr->type == DBTMWILSON || optr->type == DBCLOVER) {
g_mubar = optr->mubar;
g_epsbar = optr->epsbar;
g_c_sw = 0.;
if(optr->type == DBCLOVER) {
g_c_sw = optr->c_sw;
if (g_cart_id == 0 && g_debug_level > 1) {
printf("#\n# csw = %e, computing clover leafs\n", g_c_sw);
}
init_sw_fields(VOLUME);
sw_term( (const su3**) g_gauge_field, optr->kappa, optr->c_sw);
sw_invert_nd(optr->mubar*optr->mubar-optr->epsbar*optr->epsbar);
}
for(i = 0; i < SourceInfo.no_flavours; i++) {
if(optr->type != DBCLOVER) {
optr->iterations = invert_doublet_eo( optr->prop0, optr->prop1, optr->prop2, optr->prop3,
optr->sr0, optr->sr1, optr->sr2, optr->sr3,
optr->eps_sq, optr->maxiter,
optr->solver, optr->rel_prec);
}
else {
optr->iterations = invert_cloverdoublet_eo( optr->prop0, optr->prop1, optr->prop2, optr->prop3,
optr->sr0, optr->sr1, optr->sr2, optr->sr3,
optr->eps_sq, optr->maxiter,
optr->solver, optr->rel_prec);
}
g_mu = optr->mubar;
if(optr->type != DBCLOVER) {
M_full(g_spinor_field[DUM_DERI+1], g_spinor_field[DUM_DERI+2], optr->prop0, optr->prop1);
}
else {
Msw_full(g_spinor_field[DUM_DERI+1], g_spinor_field[DUM_DERI+2], optr->prop0, optr->prop1);
}
assign_add_mul_r(g_spinor_field[DUM_DERI+1], optr->prop2, -optr->epsbar, VOLUME/2);
assign_add_mul_r(g_spinor_field[DUM_DERI+2], optr->prop3, -optr->epsbar, VOLUME/2);
g_mu = -g_mu;
if(optr->type != DBCLOVER) {
M_full(g_spinor_field[DUM_DERI+3], g_spinor_field[DUM_DERI+4], optr->prop2, optr->prop3);
}
else {
Msw_full(g_spinor_field[DUM_DERI+3], g_spinor_field[DUM_DERI+4], optr->prop2, optr->prop3);
}
assign_add_mul_r(g_spinor_field[DUM_DERI+3], optr->prop0, -optr->epsbar, VOLUME/2);
assign_add_mul_r(g_spinor_field[DUM_DERI+4], optr->prop1, -optr->epsbar, VOLUME/2);
diff(g_spinor_field[DUM_DERI+1], g_spinor_field[DUM_DERI+1], optr->sr0, VOLUME/2);
diff(g_spinor_field[DUM_DERI+2], g_spinor_field[DUM_DERI+2], optr->sr1, VOLUME/2);
diff(g_spinor_field[DUM_DERI+3], g_spinor_field[DUM_DERI+3], optr->sr2, VOLUME/2);
diff(g_spinor_field[DUM_DERI+4], g_spinor_field[DUM_DERI+4], optr->sr3, VOLUME/2);
nrm1 = square_norm(g_spinor_field[DUM_DERI+1], VOLUME/2, 1);
nrm1 += square_norm(g_spinor_field[DUM_DERI+2], VOLUME/2, 1);
nrm1 += square_norm(g_spinor_field[DUM_DERI+3], VOLUME/2, 1);
nrm1 += square_norm(g_spinor_field[DUM_DERI+4], VOLUME/2, 1);
optr->reached_prec = nrm1;
g_mu = g_mu1;
/* For standard normalisation */
/* we have to mult. by 2*kappa */
mul_r(g_spinor_field[DUM_DERI], (2*optr->kappa), optr->prop0, VOLUME/2);
mul_r(g_spinor_field[DUM_DERI+1], (2*optr->kappa), optr->prop1, VOLUME/2);
mul_r(g_spinor_field[DUM_DERI+2], (2*optr->kappa), optr->prop2, VOLUME/2);
mul_r(g_spinor_field[DUM_DERI+3], (2*optr->kappa), optr->prop3, VOLUME/2);
/* the final result should be stored in the convention used in */
/* hep-lat/0606011 */
/* this requires multiplication of source with */
/* (1+itau_2)/sqrt(2) and the result with (1-itau_2)/sqrt(2) */
mul_one_pm_itau2(optr->prop0, optr->prop2, g_spinor_field[DUM_DERI],
g_spinor_field[DUM_DERI+2], -1., VOLUME/2);
mul_one_pm_itau2(optr->prop1, optr->prop3, g_spinor_field[DUM_DERI+1],
g_spinor_field[DUM_DERI+3], -1., VOLUME/2);
/* write propagator */
if(write_prop) optr->write_prop(op_id, index_start, i);
mul_r(optr->prop0, 1./(2*optr->kappa), g_spinor_field[DUM_DERI], VOLUME/2);
mul_r(optr->prop1, 1./(2*optr->kappa), g_spinor_field[DUM_DERI+1], VOLUME/2);
mul_r(optr->prop2, 1./(2*optr->kappa), g_spinor_field[DUM_DERI+2], VOLUME/2);
mul_r(optr->prop3, 1./(2*optr->kappa), g_spinor_field[DUM_DERI+3], VOLUME/2);
/* mirror source, but not for volume sources */
if(i == 0 && SourceInfo.no_flavours == 2 && SourceInfo.type != 1) {
if (g_cart_id == 0) {
fprintf(stdout, "# Inversion done in %d iterations, squared residue = %e!\n",
optr->iterations, optr->reached_prec);
}
mul_one_pm_itau2(g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+2], optr->sr0, optr->sr2, -1., VOLUME/2);
mul_one_pm_itau2(g_spinor_field[DUM_DERI+1], g_spinor_field[DUM_DERI+3], optr->sr1, optr->sr3, -1., VOLUME/2);
mul_one_pm_itau2(optr->sr0, optr->sr2, g_spinor_field[DUM_DERI+2], g_spinor_field[DUM_DERI], +1., VOLUME/2);
mul_one_pm_itau2(optr->sr1, optr->sr3, g_spinor_field[DUM_DERI+3], g_spinor_field[DUM_DERI+1], +1., VOLUME/2);
}
/* volume sources need only one inversion */
else if(SourceInfo.type == 1) i++;
}
}
else if(optr->type == OVERLAP) {
g_mu = 0.;
m_ov=optr->m;
eigenvalues(&optr->no_ev, 5000, optr->ev_prec, 0, optr->ev_readwrite, nstore, optr->even_odd_flag);
/* ov_check_locality(); */
/* index_jd(&optr->no_ev_index, 5000, 1.e-12, optr->conf_input, nstore, 4); */
ov_n_cheby=optr->deg_poly;
if(use_preconditioning==1)
g_precWS=(void*)optr->precWS;
else
g_precWS=NULL;
if(g_debug_level > 3) ov_check_ginsparg_wilson_relation_strong();
invert_overlap(op_id, index_start);
if(write_prop) optr->write_prop(op_id, index_start, 0);
}
etime = gettime();
if (g_cart_id == 0 && g_debug_level > 0) {
fprintf(stdout, "# Inversion done in %d iterations, squared residue = %e!\n",
optr->iterations, optr->reached_prec);
fprintf(stdout, "# Inversion done in %1.2e sec. \n", etime - atime);
}
return;
}
void Q_over_sqrt_Q_sqr(spinor * const R, double * const c,
const int n, spinor * const S,
const double rnorm, const double minev) {
int j;
double fact1, fact2, temp1, temp2, temp3, temp4, maxev, tnorm;
spinor *sv, *d, *dd, *aux, *aux3;
double ap_eps_sq = 0.;
sv=lock_Dov_WS_spinor(2);
d=lock_Dov_WS_spinor(3);
dd=lock_Dov_WS_spinor(4);
aux=lock_Dov_WS_spinor(5);
aux3=lock_Dov_WS_spinor(6);
eigenvalues_for_cg_computed = no_eigenvalues - 1;
if(eigenvalues_for_cg_computed < 0) eigenvalues_for_cg_computed = 0;
maxev=1.0;
fact1=4/(maxev-minev);
fact2=-2*(maxev+minev)/(maxev-minev);
zero_spinor_field(d, VOLUME);
zero_spinor_field(dd, VOLUME);
if(1) assign_sub_lowest_eigenvalues(aux3, S, no_eigenvalues-1, VOLUME);
else assign(aux3, S, VOLUME);
/* Check whether switch for adaptive precision is on */
/* this might be implemented again in the future */
/* Use the 'old' version using Clenshaw's recursion for the
Chebysheff polynomial
*/
if(1) {
for (j = n-1; j >= 1; j--) {
assign(sv, d, VOLUME);
if ( (j%10) == 0 ) {
assign_sub_lowest_eigenvalues(aux, d, no_eigenvalues-1, VOLUME);
}
else {
assign(aux, d, VOLUME);
}
norm_Q_sqr_psi(R, aux, rnorm);
/* printf("%d %e %e\n", j, R[0].s0.c0.re, R[0].s0.c0.im); */
/* printf("%e %e\n", R[0].s1.c0.re, R[0].s1.c0.im); */
temp1=-1.0;
temp2=c[j];
assign_mul_add_mul_add_mul_add_mul_r(d, R, dd, aux3, fact2, fact1, temp1, temp2, VOLUME);
assign(dd, sv, VOLUME);
}
if(1) assign_sub_lowest_eigenvalues(R, d, no_eigenvalues-1, VOLUME);
else assign(R, d, VOLUME);
norm_Q_sqr_psi(aux, R, rnorm);
temp1=-1.0;
temp2=c[0]/2.;
temp3=fact1/2.;
temp4=fact2/2.;
assign_mul_add_mul_add_mul_add_mul_r(aux, d, dd, aux3, temp3, temp4, temp1, temp2, VOLUME);
norm_Q_n_psi(R, aux, 1, rnorm);
}
else {
/* Use the adaptive precision version using the forward recursion
for the Chebysheff polynomial
*/
/* d = T_0(Q^2) */
assign(d, aux3, VOLUME);
/* dd = T_1(Q^2) */
norm_Q_sqr_psi(dd, d, rnorm);
temp3 = fact1/2.;
temp4 = fact2/2.;
assign_mul_add_mul_r(dd, d, temp3, temp4, VOLUME);
/* r = c_1 T_1(Q^2) + 1./2 c_0 */
temp1 = c[1];
temp2 = c[0]/2.;
mul_add_mul_r(R, dd, d, temp1, temp2, VOLUME);
temp1=-1.0;
for (j = 2; j <= n-1; j++) {
/* aux = T_j(Q^2) = 2 Q^2 T_{j-1}(Q^2) - T_{j-2}(Q^2) */
norm_Q_sqr_psi(aux, dd, rnorm);
assign_mul_add_mul_add_mul_r(aux, dd, d, fact1, fact2, temp1, VOLUME);
/* r = r + c_j T_j(Q^2) */
temp2 = c[j];
assign_add_mul_r(R, aux, temp2, VOLUME);
/* The stoppping criterio tnorm = |T_j(Q^2)| */
tnorm=square_norm(aux, VOLUME, 1);
tnorm*=(temp2*temp2);
/*
auxnorm=square_norm(R);
if(g_proc_id == g_stdio_proc){printf("j= %d\t|c T|^2= %g\t c_j= %g\t|r|^2= %g\n",j,tnorm,temp2,auxnorm); fflush( stdout);};
*/
if(tnorm < ap_eps_sq) break;
/* d = T_{j-1}(Q^2) */
assign(d, dd, VOLUME);
/* dd = T_{j}(Q^2) */
assign(dd, aux, VOLUME);
}
if(g_proc_id == g_stdio_proc && g_debug_level > 0) {
printf("Order of Chebysheff approximation = %d\n",j);
fflush( stdout);
}
/* r = Q r */
assign(aux, R, VOLUME);
norm_Q_n_psi(R, aux, 1, rnorm);
}
/* add in piece from projected subspace */
addproj_q_invsqrt(R, S, no_eigenvalues-1, VOLUME);
unlock_Dov_WS_spinor(2);
unlock_Dov_WS_spinor(3);
unlock_Dov_WS_spinor(4);
unlock_Dov_WS_spinor(5);
unlock_Dov_WS_spinor(6);
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 invert_doublet_eo(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) {
int iter = 0;
#ifdef HAVE_GPU
# ifdef TEMPORALGAUGE
/* initialize temporal gauge here */
int retval;
double dret1, dret2;
double plaquette1 = 0.0;
double plaquette2 = 0.0;
if (usegpu_flag) {
/* need VOLUME here (not N=VOLUME/2)*/
if ((retval = init_temporalgauge_trafo(VOLUME, g_gauge_field)) != 0 ) { // initializes the transformation matrices
if (g_proc_id == 0) printf("Error while gauge fixing to temporal gauge. Aborting...\n"); // g_tempgauge_field as a copy of g_gauge_field
exit(200);
}
/* do trafo */
plaquette1 = measure_plaquette(g_gauge_field);
apply_gtrafo(g_gauge_field, g_trafo); // transformation of the gauge field
plaquette2 = measure_plaquette(g_gauge_field);
if (g_proc_id == 0) printf("\tPlaquette before gauge fixing: %.16e\n", plaquette1/6./VOLUME);
if (g_proc_id == 0) printf("\tPlaquette after gauge fixing: %.16e\n", plaquette2/6./VOLUME);
/* do trafo to odd_s part of source */
dret1 = square_norm(Odd_s, VOLUME/2 , 1);
apply_gtrafo_spinor_odd(Odd_s, g_trafo); // odd spinor transformation, strange
dret2 = square_norm(Odd_s, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
/* do trafo to odd_c part of source */
dret1 = square_norm(Odd_c, VOLUME/2 , 1);
apply_gtrafo_spinor_odd(Odd_c, g_trafo); // odd spinor transformation, charm
dret2 = square_norm(Odd_c, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
/* do trafo to even_s part of source */
dret1 = square_norm(Even_s, VOLUME/2 , 1);
apply_gtrafo_spinor_even(Even_s, g_trafo); // even spinor transformation, strange
dret2 = square_norm(Even_s, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
/* do trafo to even_c part of source */
dret1 = square_norm(Even_c, VOLUME/2 , 1);
apply_gtrafo_spinor_even(Even_c, g_trafo); // even spinor transformation, charm
dret2 = square_norm(Even_c, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
# ifdef MPI
xchange_gauge(g_gauge_field);
# endif
}
# endif
#endif /* HAVE_GPU*/
/* here comes the inversion using even/odd preconditioning */
if(g_proc_id == 0) {printf("# Using even/odd preconditioning!\n"); fflush(stdout);}
M_ee_inv_ndpsi(Even_new_s, Even_new_c,
Even_s, Even_c,
g_mubar, g_epsbar);
Hopping_Matrix(OE, g_spinor_field[DUM_DERI], Even_new_s);
Hopping_Matrix(OE, g_spinor_field[DUM_DERI+1], Even_new_c);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_mul_add_r(g_spinor_field[DUM_DERI], +1., Odd_s, VOLUME/2);
assign_mul_add_r(g_spinor_field[DUM_DERI+1], +1., Odd_c, VOLUME/2);
/* Do the inversion with the preconditioned */
/* matrix to get the odd sites */
/* Here we invert the hermitean operator squared */
if(g_proc_id == 0) {
printf("# Using CG for TMWILSON flavour doublet!\n");
fflush(stdout);
}
gamma5(g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI], VOLUME/2);
gamma5(g_spinor_field[DUM_DERI+1], g_spinor_field[DUM_DERI+1], VOLUME/2);
#ifdef HAVE_GPU
if (usegpu_flag) { // GPU, mixed precision solver
# if defined(MPI) && defined(PARALLELT)
iter = mixedsolve_eo_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec);
# elif !defined(MPI) && !defined(PARALLELT)
iter = mixedsolve_eo_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec);
# else
printf("MPI and/or PARALLELT are not appropriately set for the GPU implementation. Aborting...\n");
exit(-1);
# endif
}
else { // CPU, conjugate gradient
iter = cg_her_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec,
VOLUME/2, &Qtm_pm_ndpsi);
}
#else // CPU, conjugate gradient
iter = cg_her_nd(Odd_new_s, Odd_new_c, g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
max_iter, precision, rel_prec,
VOLUME/2, &Qtm_pm_ndpsi);
#endif
Qtm_dagger_ndpsi(Odd_new_s, Odd_new_c,
Odd_new_s, Odd_new_c);
/* Reconstruct the even sites */
Hopping_Matrix(EO, g_spinor_field[DUM_DERI], Odd_new_s);
Hopping_Matrix(EO, g_spinor_field[DUM_DERI+1], Odd_new_c);
M_ee_inv_ndpsi(g_spinor_field[DUM_DERI+2], g_spinor_field[DUM_DERI+3],
g_spinor_field[DUM_DERI], g_spinor_field[DUM_DERI+1],
g_mubar, g_epsbar);
/* The sign is plus, since in Hopping_Matrix */
/* the minus is missing */
assign_add_mul_r(Even_new_s, g_spinor_field[DUM_DERI+2], +1., VOLUME/2);
assign_add_mul_r(Even_new_c, g_spinor_field[DUM_DERI+3], +1., VOLUME/2);
#ifdef HAVE_GPU
/* return from temporal gauge again */
# ifdef TEMPORALGAUGE
if (usegpu_flag) {
/* undo trafo */
/* apply_inv_gtrafo(g_gauge_field, g_trafo);*/
/* copy back the saved original field located in g_tempgauge_field -> update necessary*/
plaquette1 = measure_plaquette(g_gauge_field);
copy_gauge_field(g_gauge_field, g_tempgauge_field);
g_update_gauge_copy = 1;
plaquette2 = measure_plaquette(g_gauge_field);
if (g_proc_id == 0) printf("\tPlaquette before inverse gauge fixing: %.16e\n", plaquette1/6./VOLUME);
if (g_proc_id == 0) printf("\tPlaquette after inverse gauge fixing: %.16e\n", plaquette2/6./VOLUME);
/* undo trafo to source Even_s */
dret1 = square_norm(Even_s, VOLUME/2 , 1);
apply_inv_gtrafo_spinor_even(Even_s, g_trafo);
dret2 = square_norm(Even_s, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
/* undo trafo to source Even_c */
dret1 = square_norm(Even_c, VOLUME/2 , 1);
apply_inv_gtrafo_spinor_even(Even_c, g_trafo);
dret2 = square_norm(Even_c, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
/* undo trafo to source Odd_s */
dret1 = square_norm(Odd_s, VOLUME/2 , 1);
apply_inv_gtrafo_spinor_odd(Odd_s, g_trafo);
dret2 = square_norm(Odd_s, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
/* undo trafo to source Odd_c */
dret1 = square_norm(Odd_c, VOLUME/2 , 1);
apply_inv_gtrafo_spinor_odd(Odd_c, g_trafo);
dret2 = square_norm(Odd_c, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
// Even_new_s
dret1 = square_norm(Even_new_s, VOLUME/2 , 1);
apply_inv_gtrafo_spinor_even(Even_new_s, g_trafo);
dret2 = square_norm(Even_new_s, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
// Even_new_c
dret1 = square_norm(Even_new_c, VOLUME/2 , 1);
apply_inv_gtrafo_spinor_even(Even_new_c, g_trafo);
dret2 = square_norm(Even_new_c, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
// Odd_new_s
dret1 = square_norm(Odd_new_s, VOLUME/2 , 1);
apply_inv_gtrafo_spinor_odd(Odd_new_s, g_trafo);
dret2 = square_norm(Odd_new_s, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
// Odd_new_c
dret1 = square_norm(Odd_new_c, VOLUME/2 , 1);
apply_inv_gtrafo_spinor_odd(Odd_new_c, g_trafo);
dret2 = square_norm(Odd_new_c, VOLUME/2, 1);
if (g_proc_id == 0) printf("\tsquare norm before gauge fixing: %.16e\n", dret1);
if (g_proc_id == 0) printf("\tsquare norm after gauge fixing: %.16e\n", dret2);
finalize_temporalgauge();
# ifdef MPI
xchange_gauge(g_gauge_field);
# endif
}
# endif
#endif
return(iter);
}
/* k output , l input */
int solve_cg(spinor * const k, spinor * const l, double eps_sq, const int rel_prec) {
static double normsq, pro, err, alpha_cg, beta_cg, squarenorm, sqnrm, sqnrm2;
int iteration = 0, i, j;
int save_sloppy = g_sloppy_precision;
double atime, etime, flops;
spinor *x, *delta, *y;
/* initialize residue r and search vector p */
#ifdef MPI
atime = MPI_Wtime();
#else
atime = ((double)clock())/((double)(CLOCKS_PER_SEC));
#endif
squarenorm = square_norm(l, VOLUME/2, 1);
if(g_sloppy_precision_flag == 1) {
delta = g_spinor_field[DUM_SOLVER+3];
x = g_spinor_field[DUM_SOLVER+4];
y = g_spinor_field[DUM_SOLVER+5];
assign(delta, l, VOLUME/2);
Qtm_pm_psi(y, k);
diff(delta, l, y, VOLUME/2);
sqnrm = square_norm(delta, VOLUME/2, 1);
if(((sqnrm <= eps_sq) && (rel_prec == 0)) || ((sqnrm <= eps_sq*squarenorm) && (rel_prec == 1))) {
return(0);
}
for(i = 0; i < 20; i++) {
g_sloppy_precision = 1;
/* main CG loop in lower precision */
zero_spinor_field(x, VOLUME/2);
assign(g_spinor_field[DUM_SOLVER+1], delta, VOLUME/2);
assign(g_spinor_field[DUM_SOLVER+2], delta, VOLUME/2);
sqnrm2 = sqnrm;
for(j = 0; j <= ITER_MAX_CG; j++) {
Qtm_pm_psi(g_spinor_field[DUM_SOLVER], g_spinor_field[DUM_SOLVER+2]);
pro = scalar_prod_r(g_spinor_field[DUM_SOLVER+2], g_spinor_field[DUM_SOLVER], VOLUME/2, 1);
alpha_cg = sqnrm2 / pro;
assign_add_mul_r(x, g_spinor_field[DUM_SOLVER+2], alpha_cg, VOLUME/2);
assign_mul_add_r(g_spinor_field[DUM_SOLVER], -alpha_cg, g_spinor_field[DUM_SOLVER+1], VOLUME/2);
err = square_norm(g_spinor_field[DUM_SOLVER], VOLUME/2, 1);
if(g_proc_id == g_stdio_proc && g_debug_level > 1) {
printf("inner CG: %d res^2 %g\n", iteration+j+1, err);
fflush(stdout);
}
if (((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*squarenorm) && (rel_prec == 1))){
break;
}
beta_cg = err / sqnrm2;
assign_mul_add_r(g_spinor_field[DUM_SOLVER+2], beta_cg, g_spinor_field[DUM_SOLVER], VOLUME/2);
assign(g_spinor_field[DUM_SOLVER+1], g_spinor_field[DUM_SOLVER], VOLUME/2);
sqnrm2 = err;
}
/* end main CG loop */
iteration += j;
g_sloppy_precision = 0;
add(k, k, x, VOLUME/2);
Qtm_pm_psi(y, x);
diff(delta, delta, y, VOLUME/2);
sqnrm = square_norm(delta, VOLUME/2, 1);
if(g_debug_level > 0 && g_proc_id == g_stdio_proc) {
printf("mixed CG(linsolve): true residue %d\t%g\t\n",iteration, sqnrm); fflush( stdout);
}
if(((sqnrm <= eps_sq) && (rel_prec == 0)) || ((sqnrm <= eps_sq*squarenorm) && (rel_prec == 1))) {
break;
}
iteration++;
}
}
else {
Qtm_pm_psi(g_spinor_field[DUM_SOLVER], k);
diff(g_spinor_field[DUM_SOLVER+1], l, g_spinor_field[DUM_SOLVER], VOLUME/2);
assign(g_spinor_field[DUM_SOLVER+2], g_spinor_field[DUM_SOLVER+1], VOLUME/2);
normsq=square_norm(g_spinor_field[DUM_SOLVER+1], VOLUME/2, 1);
/* main loop */
for(iteration = 1; iteration <= ITER_MAX_CG; iteration++) {
Qtm_pm_psi(g_spinor_field[DUM_SOLVER], g_spinor_field[DUM_SOLVER+2]);
pro=scalar_prod_r(g_spinor_field[DUM_SOLVER+2], g_spinor_field[DUM_SOLVER], VOLUME/2, 1);
alpha_cg=normsq/pro;
assign_add_mul_r(k, g_spinor_field[DUM_SOLVER+2], alpha_cg, VOLUME/2);
assign_mul_add_r(g_spinor_field[DUM_SOLVER], -alpha_cg, g_spinor_field[DUM_SOLVER+1], VOLUME/2);
err=square_norm(g_spinor_field[DUM_SOLVER], VOLUME/2, 1);
if(g_proc_id == g_stdio_proc && g_debug_level > 1) {
printf("CG (linsolve): iterations: %d res^2 %e\n", iteration, err);
fflush(stdout);
}
if (((err <= eps_sq) && (rel_prec == 0)) || ((err <= eps_sq*squarenorm) && (rel_prec == 1))){
break;
}
beta_cg = err/normsq;
assign_mul_add_r(g_spinor_field[DUM_SOLVER+2], beta_cg, g_spinor_field[DUM_SOLVER], VOLUME/2);
assign(g_spinor_field[DUM_SOLVER+1], g_spinor_field[DUM_SOLVER], VOLUME/2);
normsq=err;
}
}
#ifdef MPI
etime = MPI_Wtime();
#else
etime = ((double)clock())/((double)(CLOCKS_PER_SEC));
#endif
/* 2 A + 2 Nc Ns + N_Count ( 2 A + 10 Nc Ns ) */
/* 2*1320.0 because the linalg is over VOLUME/2 */
flops = (2*(2*1320.0+2*3*4) + 2*3*4 + iteration*(2.*(2*1320.0+2*3*4) + 10*3*4))*VOLUME/2/1.0e6f;
if(g_proc_id==0 && g_debug_level > 0) {
printf("CG: iter: %d eps_sq: %1.4e t/s: %1.4e\n", iteration, eps_sq, etime-atime);
printf("CG: flopcount: t/s: %1.4e mflops_local: %.1f mflops: %.1f\n",
etime-atime, flops/(etime-atime), g_nproc*flops/(etime-atime));
}
g_sloppy_precision = save_sloppy;
return(iteration);
}
/* 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);
}
/* 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);
}
void poly_precon(spinor * const R, spinor * const S, const double prec, const int n) {
int j;
double fact1, fact2, temp1, temp2, temp3, temp4, invmaxev = 1./4., maxev=4., tnorm, minev=g_mu*g_mu, auxnorm;
static spinor *sv_, *sv, *d_, *d, *dd_, *dd, *aux_, *aux, *aux3_, *aux3;
static int initp = 0;
static double * c;
const int N = VOLUME;
maxev = 4.0;
invmaxev = 1./maxev;
minev = 0.1;
/* minev = 1.5*1.5*g_mu*g_mu; */
if(initp == 0) {
c = (double*)calloc(1000, sizeof(double));
#if (defined SSE || defined SSE2 || defined SSE3)
sv_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
sv = (spinor *)(((unsigned long int)(sv_)+ALIGN_BASE)&~ALIGN_BASE);
d_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
d = (spinor *)(((unsigned long int)(d_)+ALIGN_BASE)&~ALIGN_BASE);
dd_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
dd = (spinor *)(((unsigned long int)(dd_)+ALIGN_BASE)&~ALIGN_BASE);
aux_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
aux = (spinor *)(((unsigned long int)(aux_)+ALIGN_BASE)&~ALIGN_BASE);
aux3_= calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
aux3 = (spinor *)(((unsigned long int)(aux3_)+ALIGN_BASE)&~ALIGN_BASE);
#else
sv_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
sv = sv_;
d_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
d = d_;
dd_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
dd = dd_;
aux_ = calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
aux = aux_;
aux3_= calloc(VOLUMEPLUSRAND+1, sizeof(spinor));
aux3 = aux3_;
#endif
get_c(minev, maxev, c, 100);
initp = 1;
}
fact1 = 4. / (maxev - minev);
fact2 = -2 * (maxev + minev) / (maxev - minev);
zero_spinor_field(&d[0], N);
zero_spinor_field(&dd[0], N);
assign(&aux3[0], &S[0], N);
/* gamma5(&aux3[0], &S[0], N); */
/* Use the adaptive precision version using the forward recursion
for the Chebysheff polynomial
*/
/* d = T_0(Q^2) */
assign(&d[0], &aux3[0], N);
/* dd = T_1(Q^2) */
Q_pm_psi(&dd[0], &d[0]);
/* mul_r(dd, invmaxev, dd, N); */
/* norm_Q_sqr_psi(&dd[0], &d[0], g_m_D_psi, rnorm); */
temp3 = fact1/2;
temp4 = fact2/2;
assign_mul_add_mul_r(&dd[0], &d[0], temp3, temp4, N);
/* r = c_1 T_1(Q^2) + 1/2 c_0 */
temp1 = c[1];
temp2 = c[0]/2;
mul_add_mul_r(&R[0], &dd[0], &d[0], temp1, temp2, N);
temp1 = -1.0;
for (j=2; j<=n-1; j++) {
/* aux = T_j(Q^2) = 2 Q^2 T_{j-1}(Q^2) - T_{j-2}(Q^2) */
Q_pm_psi(&aux[0], &dd[0]);
/* mul_r(aux, invmaxev, aux, N); */
/* norm_Q_sqr_psi(&aux[0], &dd[0], g_m_D_psi, rnorm); */
assign_mul_add_mul_add_mul_r(&aux[0],&dd[0],&d[0],fact1,fact2,temp1, N);
/* r = r + c_j T_j(Q^2) */
temp2=c[j];
assign_add_mul_r(&R[0],&aux[0],temp2, N);
/* The stoppping criterio tnorm = |T_j(Q^2)| */
tnorm = square_norm(aux, N, 1);
tnorm *= (temp2*temp2);
auxnorm = square_norm(R, N, 1);
if(g_proc_id == g_stdio_proc) {
printf("j= %d\t|c T|^2= %g\t%g\t c_j= %g\t|r|^2= %g\n",j,tnorm,prec, temp2,auxnorm); fflush( stdout);
fflush(stdout);
}
if(tnorm < prec) break;
/* d = T_{j-1}(Q^2) */
assign(&d[0], &dd[0], N);
/* dd = T_{j}(Q^2) */
assign(&dd[0], &aux[0], N);
}
if(g_proc_id == g_stdio_proc) {
printf("Order of Chebysheff approximation = %d\n",j);
fflush( stdout);
}
/* r = Q r */
/* assign(aux, R, N); */
/* Q_minus_psi(R, aux); */
return;
}
