extern "C" magma_int_t
magma_cpcgs_merge(
magma_c_matrix A, magma_c_matrix b, magma_c_matrix *x,
magma_c_solver_par *solver_par,
magma_c_preconditioner *precond_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// prepare solver feedback
solver_par->solver = Magma_PCGS;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// local variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE;
// solver variables
float nom0, r0, res, nomb;
magmaFloatComplex rho, rho_l = c_one, alpha, beta;
magma_int_t dofs = A.num_rows* b.num_cols;
// GPU workspace
magma_c_matrix r={Magma_CSR}, rt={Magma_CSR}, r_tld={Magma_CSR},
p={Magma_CSR}, q={Magma_CSR}, u={Magma_CSR}, v={Magma_CSR}, t={Magma_CSR},
p_hat={Magma_CSR}, q_hat={Magma_CSR}, u_hat={Magma_CSR}, v_hat={Magma_CSR};
CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &r_tld,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &p_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &q_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &u_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &v_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver setup
CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue));
magma_ccopy( dofs, r.dval, 1, r_tld.dval, 1, queue );
solver_par->init_res = nom0;
nomb = magma_scnrm2( dofs, b.dval, 1, queue );
if ( nomb == 0.0 ){
nomb=1.0;
}
if ( (r0 = nomb * solver_par->rtol) < ATOLERANCE ){
r0 = ATOLERANCE;
}
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = (real_Double_t)nom0;
solver_par->timing[0] = 0.0;
}
if ( nom0 < r0 ) {
info = MAGMA_SUCCESS;
goto cleanup;
}
//Chronometry
real_Double_t tempo1, tempo2, tempop1, tempop2;
tempo1 = magma_sync_wtime( queue );
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// start iteration
do
{
solver_par->numiter++;
rho = magma_cdotc( dofs, r.dval, 1, r_tld.dval, 1, queue );
// rho = < r,r_tld>
if ( MAGMA_C_ABS(rho) == 0.0 ) {
goto cleanup;
}
if ( solver_par->numiter > 1 ) { // direction vectors
beta = rho / rho_l;
magma_ccgs_1(
r.num_rows,
r.num_cols,
beta,
r.dval,
q.dval,
u.dval,
p.dval,
queue );
//u = r + beta*q;
//p = u + beta*( q + beta*p );
}
else{
magma_ccgs_2(
r.num_rows,
r.num_cols,
r.dval,
u.dval,
p.dval,
queue );
// u = r
// p = r
}
// preconditioner
tempop1 = magma_sync_wtime( queue );
CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, p, &rt, precond_par, queue ));
CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, rt, &p_hat, precond_par, queue ));
tempop2 = magma_sync_wtime( queue );
precond_par->runtime += tempop2-tempop1;
CHECK( magma_c_spmv( c_one, A, p_hat, c_zero, v_hat, queue )); // v = A p
solver_par->spmv_count++;
alpha = rho / magma_cdotc( dofs, r_tld.dval, 1, v_hat.dval, 1, queue );
magma_ccgs_3(
r.num_rows,
r.num_cols,
alpha,
v_hat.dval,
u.dval,
q.dval,
t.dval,
queue );
// q = u - alpha v_hat
// t = u + q
// preconditioner
tempop1 = magma_sync_wtime( queue );
CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, t, &rt, precond_par, queue ));
CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, rt, &u_hat, precond_par, queue ));
tempop2 = magma_sync_wtime( queue );
precond_par->runtime += tempop2-tempop1;
CHECK( magma_c_spmv( c_one, A, u_hat, c_zero, t, queue )); // t = A u_hat
solver_par->spmv_count++;
magma_ccgs_4(
r.num_rows,
r.num_cols,
alpha,
u_hat.dval,
t.dval,
x->dval,
r.dval,
queue );
// r = r -alpha*A u_hat
// x = x + alpha u_hat
res = magma_scnrm2( dofs, r.dval, 1, queue );
if ( solver_par->verbose > 0 ) {
tempo2 = magma_sync_wtime( queue );
if ( (solver_par->numiter)%solver_par->verbose == 0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( res/nomb <= solver_par->rtol || res <= solver_par->atol ){
break;
}
rho_l = rho;
}
while ( solver_par->numiter+1 <= solver_par->maxiter );
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
float residual;
CHECK( magma_cresidualvec( A, b, *x, &r, &residual, queue));
solver_par->iter_res = res;
solver_par->final_res = residual;
if ( solver_par->numiter < solver_par->maxiter ) {
info = MAGMA_SUCCESS;
} else if ( solver_par->init_res > solver_par->final_res ) {
if ( solver_par->verbose > 0 ) {
if ( (solver_par->numiter)%solver_par->verbose == 0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_SLOW_CONVERGENCE;
if( solver_par->iter_res < solver_par->rtol*solver_par->init_res ||
solver_par->iter_res < solver_par->atol ) {
info = MAGMA_SUCCESS;
}
}
else {
if ( solver_par->verbose > 0 ) {
if ( (solver_par->numiter)%solver_par->verbose == 0 ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
cleanup:
magma_cmfree(&r, queue );
magma_cmfree(&rt, queue );
magma_cmfree(&r_tld, queue );
magma_cmfree(&p, queue );
magma_cmfree(&q, queue );
magma_cmfree(&u, queue );
magma_cmfree(&v, queue );
magma_cmfree(&t, queue );
magma_cmfree(&p_hat, queue );
magma_cmfree(&q_hat, queue );
magma_cmfree(&u_hat, queue );
magma_cmfree(&v_hat, queue );
solver_par->info = info;
return info;
} /* magma_cpcgs_merge */
extern "C" magma_int_t
magma_cbombard(
magma_c_matrix A, magma_c_matrix b,
magma_c_matrix *x, magma_c_solver_par *solver_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// 1=QMR, 2=CGS, 3+BiCGSTAB
magma_int_t flag = 0;
// prepare solver feedback
solver_par->solver = Magma_BOMBARD;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// local variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE;
// solver variables
float nom0, r0, res, Q_res, T_res, C_res, B_res, nomb;
//QMR
magmaFloatComplex Q_rho = c_one, Q_rho1 = c_one, Q_eta = -c_one , Q_pds = c_one,
Q_thet = c_one, Q_thet1 = c_one, Q_epsilon = c_one,
Q_beta = c_one, Q_delta = c_one, Q_pde = c_one, Q_rde = c_one,
Q_gamm = c_one, Q_gamm1 = c_one, Q_psi = c_one;
//TFQMR
magmaFloatComplex T_rho = c_one, T_rho_l = c_one, T_eta = c_zero , T_c = c_zero ,
T_theta = c_zero , T_tau = c_zero, T_alpha = c_one, T_beta = c_zero,
T_sigma = c_zero;
//CGS
magmaFloatComplex C_rho, C_rho_l = c_one, C_alpha, C_beta = c_zero;
//BiCGSTAB
magmaFloatComplex B_alpha, B_beta, B_omega, B_rho_old, B_rho_new;
magma_int_t dofs = A.num_rows* b.num_cols;
// need to transpose the matrix
// GPU workspace
// QMR
magma_c_matrix AT = {Magma_CSR}, Ah1 = {Magma_CSR}, Ah2 = {Magma_CSR},
Q_r={Magma_CSR}, r_tld={Magma_CSR}, Q_x={Magma_CSR},
Q_v={Magma_CSR}, Q_w={Magma_CSR}, Q_wt={Magma_CSR},
Q_d={Magma_CSR}, Q_s={Magma_CSR}, Q_z={Magma_CSR}, Q_q={Magma_CSR},
Q_p={Magma_CSR}, Q_pt={Magma_CSR}, Q_y={Magma_CSR}, d1={Magma_CSR}, d2={Magma_CSR};
//TFQMR
// GPU workspace
magma_c_matrix T_r={Magma_CSR}, T_pu_m={Magma_CSR}, T_x={Magma_CSR},
T_d={Magma_CSR}, T_w={Magma_CSR}, T_v={Magma_CSR},
T_u_mp1={Magma_CSR}, T_u_m={Magma_CSR}, T_Au={Magma_CSR},
T_Ad={Magma_CSR}, T_Au_new={Magma_CSR};
// CGS
magma_c_matrix C_r={Magma_CSR}, C_rt={Magma_CSR}, C_x={Magma_CSR},
C_p={Magma_CSR}, C_q={Magma_CSR}, C_u={Magma_CSR}, C_v={Magma_CSR}, C_t={Magma_CSR},
C_p_hat={Magma_CSR}, C_q_hat={Magma_CSR}, C_u_hat={Magma_CSR}, C_v_hat={Magma_CSR};
//BiCGSTAB
magma_c_matrix B_r={Magma_CSR}, B_x={Magma_CSR}, B_p={Magma_CSR}, B_v={Magma_CSR},
B_s={Magma_CSR}, B_t={Magma_CSR};
CHECK( magma_cvinit( &r_tld, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &d1, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &d2, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// QMR
CHECK( magma_cvinit( &Q_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_w, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_wt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Q_x, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// TFQMR
CHECK( magma_cvinit( &T_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &T_u_mp1,Magma_DEV, A.num_rows, b.num_cols, c_one, queue ));
CHECK( magma_cvinit( &T_u_m, Magma_DEV, A.num_rows, b.num_cols, c_one, queue ));
CHECK( magma_cvinit( &T_pu_m, Magma_DEV, A.num_rows, b.num_cols, c_one, queue ));
CHECK( magma_cvinit( &T_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &T_d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &T_w, Magma_DEV, A.num_rows, b.num_cols, c_one, queue ));
CHECK( magma_cvinit( &T_Ad, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &T_Au_new, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &T_Au, Magma_DEV, A.num_rows, b.num_cols, c_one, queue ));
CHECK( magma_cvinit( &T_x, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// CGS
CHECK( magma_cvinit( &C_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_x,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_p_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_q_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_u_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_v_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &C_t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// BiCGSTAB
CHECK( magma_cvinit( &B_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &B_x,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &B_p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &B_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &B_s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &B_t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver setup
CHECK( magma_cresidualvec( A, b, *x, &r_tld, &nom0, queue));
solver_par->init_res = nom0;
res = nom0;
// QMR
magma_ccopy( dofs, r_tld.dval, 1, Q_r.dval, 1, queue );
magma_ccopy( dofs, r_tld.dval, 1, Q_y.dval, 1, queue );
magma_ccopy( dofs, r_tld.dval, 1, Q_v.dval, 1, queue );
magma_ccopy( dofs, r_tld.dval, 1, Q_wt.dval, 1, queue );
magma_ccopy( dofs, r_tld.dval, 1, Q_z.dval, 1, queue );
magma_ccopy( dofs, x->dval, 1, Q_x.dval, 1, queue );
// transpose the matrix
// transpose the matrix
magma_cmtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue );
magma_cmconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue );
magma_cmfree(&Ah1, queue );
magma_cmtransposeconjugate( Ah2, &Ah1, queue );
magma_cmfree(&Ah2, queue );
Ah2.blocksize = A.blocksize;
Ah2.alignment = A.alignment;
magma_cmconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue );
magma_cmfree(&Ah1, queue );
magma_cmtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue );
magma_cmfree(&Ah2, queue );
// TFQMR
solver_par->init_res = nom0;
magma_ccopy( dofs, r_tld.dval, 1, T_r.dval, 1, queue );
magma_ccopy( dofs, T_r.dval, 1, T_w.dval, 1, queue );
magma_ccopy( dofs, T_r.dval, 1, T_u_m.dval, 1, queue );
magma_ccopy( dofs, T_r.dval, 1, T_u_mp1.dval, 1, queue );
magma_ccopy( dofs, T_u_m.dval, 1, T_pu_m.dval, 1, queue );
CHECK( magma_c_spmv( c_one, A, T_pu_m, c_zero, T_v, queue ));
magma_ccopy( dofs, T_v.dval, 1, T_Au.dval, 1, queue );
// CGS
magma_ccopy( dofs, r_tld.dval, 1, C_r.dval, 1, queue );
magma_ccopy( dofs, x->dval, 1, C_x.dval, 1, queue );
// BiCGSTAB
magma_ccopy( dofs, r_tld.dval, 1, B_r.dval, 1, queue );
magma_ccopy( dofs, x->dval, 1, B_x.dval, 1, queue );
CHECK( magma_c_spmv( c_one, A, B_r, c_zero, B_v, queue ));
nomb = magma_scnrm2( dofs, b.dval, 1, queue );
if ( nomb == 0.0 ){
nomb=1.0;
}
if ( (r0 = nomb * solver_par->rtol) < ATOLERANCE ){
r0 = ATOLERANCE;
}
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = (real_Double_t)nom0;
solver_par->timing[0] = 0.0;
}
if ( nom0 < r0 ) {
info = MAGMA_SUCCESS;
goto cleanup;
}
T_tau = magma_csqrt( magma_cdotc( dofs, T_r.dval, 1, r_tld.dval, 1, queue) );
T_rho = magma_cdotc( dofs, T_r.dval, 1, r_tld.dval, 1, queue );
T_rho_l = T_rho;
Q_psi = magma_csqrt( magma_cdotc( dofs, Q_z.dval, 1, Q_z.dval, 1, queue ));
Q_rho = magma_csqrt( magma_cdotc( dofs, Q_y.dval, 1, Q_y.dval, 1, queue ));
// BiCGSTAB
B_rho_new = magma_cdotc( dofs, B_r.dval, 1, B_r.dval, 1, queue );
B_rho_old = B_omega = B_alpha = MAGMA_C_MAKE( 1.0, 0. );
// v = y / rho
// y = y / rho
// w = wt / psi
// z = z / psi
magma_cqmr_1(
b.num_rows,
b.num_cols,
Q_rho,
Q_psi,
Q_y.dval,
Q_z.dval,
Q_v.dval,
Q_w.dval,
queue );
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// start iteration
do
{
solver_par->numiter++;
//QMR: delta = z' * y;
Q_delta = magma_cdotc( dofs, Q_z.dval, 1, Q_y.dval, 1, queue );
// TFQMR
T_alpha = T_rho / magma_cdotc( dofs, T_v.dval, 1, r_tld.dval, 1, queue );
T_sigma = T_theta * T_theta / T_alpha * T_eta;
//CGS: rho = r' * r_tld
C_rho = magma_cdotc( dofs, C_r.dval, 1, r_tld.dval, 1, queue );
// BiCGSTAB
B_rho_old = B_rho_new;
B_rho_new = magma_cdotc( dofs, r_tld.dval, 1, B_r.dval, 1, queue ); // rho=<rr,r>
B_beta = B_rho_new/B_rho_old * B_alpha/B_omega; // beta=rho/rho_old *alpha/omega
if( solver_par->numiter == 1 ){
//QMR: p = y;
//QMR: q = z;
magma_ccopy( dofs, Q_y.dval, 1, Q_p.dval, 1, queue );
magma_ccopy( dofs, Q_z.dval, 1, Q_q.dval, 1, queue );
//QMR: u = r;
//QMR: p = r;
magma_ccgs_2(
b.num_rows,
b.num_cols,
C_r.dval,
C_u.dval,
C_p.dval,
queue );
}
else{
Q_pde = Q_psi * Q_delta / Q_epsilon;
Q_rde = Q_rho * MAGMA_C_CONJ(Q_delta/Q_epsilon);
C_beta = C_rho / C_rho_l;
//QMR p = y - pde * p
//QMR q = z - rde * q
magma_cqmr_2(
b.num_rows,
b.num_cols,
Q_pde,
Q_rde,
Q_y.dval,
Q_z.dval,
Q_p.dval,
Q_q.dval,
queue );
//CGS: u = r + beta*q;
//CGS: p = u + beta*( q + beta*p );
magma_ccgs_1(
b.num_rows,
b.num_cols,
C_beta,
C_r.dval,
C_q.dval,
C_u.dval,
C_p.dval,
queue );
}
// TFQMR
magma_ctfqmr_1(
b.num_rows,
b.num_cols,
T_alpha,
T_sigma,
T_v.dval,
T_Au.dval,
T_u_m.dval,
T_pu_m.dval,
T_u_mp1.dval,
T_w.dval,
T_d.dval,
T_Ad.dval,
queue );
T_theta = magma_csqrt( magma_cdotc(dofs, T_w.dval, 1, T_w.dval, 1, queue) ) / T_tau;
T_c = c_one / magma_csqrt( c_one + T_theta*T_theta );
T_tau = T_tau * T_theta *T_c;
T_eta = T_c * T_c * T_alpha;
T_sigma = T_theta * T_theta / T_alpha * T_eta;
magma_ctfqmr_2(
b.num_rows,
b.num_cols,
T_eta,
T_d.dval,
T_Ad.dval,
T_x.dval,
T_r.dval,
queue );
magma_ccopy( dofs, T_u_mp1.dval, 1, T_pu_m.dval, 1, queue );
// BiCGSTAB: p = r + beta * ( p - omega * v )
magma_cbicgstab_1(
b.num_rows,
b.num_cols,
B_beta,
B_omega,
B_r.dval,
B_v.dval,
B_p.dval,
queue );
//QMR
CHECK( magma_c_spmv( c_one, A, Q_p, c_zero, Q_pt, queue ));
//TFQMR
CHECK( magma_c_spmv( c_one, A, T_pu_m, c_zero, T_Au_new, queue ));
//CGS
CHECK( magma_c_spmv( c_one, A, C_p, c_zero, C_v_hat, queue ));
// BiCGSTAB
CHECK( magma_c_spmv( c_one, A, B_p, c_zero, B_v, queue )); // v = Ap
solver_par->spmv_count++;
//QMR: epsilon = q' * pt;
Q_epsilon = magma_cdotc( dofs, Q_q.dval, 1, Q_pt.dval, 1, queue );
Q_beta = Q_epsilon / Q_delta;
//TFQMR
magma_ccopy( dofs, T_Au_new.dval, 1, T_Au.dval, 1, queue );
magma_ccopy( dofs, T_u_mp1.dval, 1, T_u_m.dval, 1, queue );
//CGS: alpha = r_tld' * v_hat
C_alpha = C_rho / magma_cdotc( dofs, r_tld.dval, 1, C_v_hat.dval, 1, queue );
//BiCGSTAB
B_alpha = B_rho_new / magma_cdotc( dofs, r_tld.dval, 1, B_v.dval, 1, queue );
//QMR: v = pt - beta * v
//QMR: y = v
magma_cqmr_3(
b.num_rows,
b.num_cols,
Q_beta,
Q_pt.dval,
Q_v.dval,
Q_y.dval,
queue );
// TFQMR
magma_ctfqmr_5(
b.num_rows,
b.num_cols,
T_alpha,
T_sigma,
T_v.dval,
T_Au.dval,
T_pu_m.dval,
T_w.dval,
T_d.dval,
T_Ad.dval,
queue );
// TFQMR
T_sigma = T_theta * T_theta / T_alpha * T_eta;
T_theta = magma_csqrt( magma_cdotc(dofs, T_w.dval, 1, T_w.dval, 1, queue) ) / T_tau;
T_c = c_one / magma_csqrt( c_one + T_theta*T_theta );
T_tau = T_tau * T_theta *T_c;
T_eta = T_c * T_c * T_alpha;
// TFQMR
magma_ctfqmr_2(
b.num_rows,
b.num_cols,
T_eta,
T_d.dval,
T_Ad.dval,
T_x.dval,
T_r.dval,
queue );
T_rho = magma_cdotc( dofs, T_w.dval, 1, r_tld.dval, 1, queue );
T_beta = T_rho / T_rho_l;
T_rho_l = T_rho;
magma_ctfqmr_3(
b.num_rows,
b.num_cols,
T_beta,
T_w.dval,
T_u_m.dval,
T_u_mp1.dval,
queue );
magma_ccopy( dofs, T_u_mp1.dval, 1, T_pu_m.dval, 1, queue );
//CGS: q = u - alpha v_hat
//CGS: t = u + q
magma_ccgs_3(
b.num_rows,
b.num_cols,
C_alpha,
C_v_hat.dval,
C_u.dval,
C_q.dval,
C_t.dval,
queue );
// BiCGSTAB: s = r - alpha v
magma_cbicgstab_2(
b.num_rows,
b.num_cols,
B_alpha,
B_r.dval,
B_v.dval,
B_s.dval,
queue );
Q_rho1 = Q_rho;
//QMR rho = norm(y);
Q_rho = magma_csqrt( magma_cdotc( dofs, Q_y.dval, 1, Q_y.dval, 1, queue ) );
//QMR wt = A' * q - beta' * w;
CHECK( magma_c_spmv( c_one, AT, Q_q, c_zero, Q_wt, queue ));
//TFQMR
CHECK( magma_c_spmv( c_one, A, T_pu_m, c_zero, T_Au_new, queue ));
//CGS t = A u_hat
CHECK( magma_c_spmv( c_one, A, C_t, c_zero, C_rt, queue ));
//BiCGSTAB
CHECK( magma_c_spmv( c_one, A, B_s, c_zero, B_t, queue )); // t=As
solver_par->spmv_count++;
//BiCGSTAB
B_omega = magma_cdotc( dofs, B_t.dval, 1, B_s.dval, 1, queue ) // omega = <s,t>/<t,t>
/ magma_cdotc( dofs, B_t.dval, 1, B_t.dval, 1, queue );
// QMR
magma_caxpy( dofs, - MAGMA_C_CONJ( Q_beta ), Q_w.dval, 1, Q_wt.dval, 1, queue );
// no precond: z = wt
magma_ccopy( dofs, Q_wt.dval, 1, Q_z.dval, 1, queue );
//TFQMR
magma_ctfqmr_4(
b.num_rows,
b.num_cols,
T_beta,
T_Au_new.dval,
T_v.dval,
T_Au.dval,
queue );
magma_ccopy( dofs, T_u_mp1.dval, 1, T_u_m.dval, 1, queue );
// QMR
Q_thet1 = Q_thet;
Q_thet = Q_rho / (Q_gamm * MAGMA_C_MAKE( MAGMA_C_ABS(Q_beta), 0.0 ));
Q_gamm1 = Q_gamm;
Q_gamm = c_one / magma_csqrt(c_one + Q_thet*Q_thet);
Q_eta = - Q_eta * Q_rho1 * Q_gamm * Q_gamm / (Q_beta * Q_gamm1 * Q_gamm1);
if ( solver_par->numiter == 1 ) {
//QMR: d = eta * p + pds * d;
//QMR: s = eta * pt + pds * d;
//QMR: x = x + d;
//QMR: r = r - s;
magma_cqmr_4(
b.num_rows,
b.num_cols,
Q_eta,
Q_p.dval,
Q_pt.dval,
Q_d.dval,
Q_s.dval,
Q_x.dval,
Q_r.dval,
queue );
}
else {
Q_pds = (Q_thet1 * Q_gamm) * (Q_thet1 * Q_gamm);
// d = eta * p + pds * d;
// s = eta * pt + pds * d;
// x = x + d;
// r = r - s;
magma_cqmr_5(
b.num_rows,
b.num_cols,
Q_eta,
Q_pds,
Q_p.dval,
Q_pt.dval,
Q_d.dval,
Q_s.dval,
Q_x.dval,
Q_r.dval,
queue );
}
// CGS: r = r -alpha*A u_hat
// CGS: x = x + alpha u_hat
magma_ccgs_4(
b.num_rows,
b.num_cols,
C_alpha,
C_t.dval,
C_rt.dval,
C_x.dval,
C_r.dval,
queue );
C_rho_l = C_rho;
// BiCGSTAB: x = x + alpha * p + omega * s
// BiCGSTAB: r = s - omega * t
magma_cbicgstab_3(
b.num_rows,
b.num_cols,
B_alpha,
B_omega,
B_p.dval,
B_s.dval,
B_t.dval,
B_x.dval,
B_r.dval,
queue );
//QMR: psi = norm(z);
Q_psi = magma_csqrt( magma_cdotc( dofs, Q_z.dval, 1, Q_z.dval, 1, queue ) );
//QMR: v = y / rho
//QMR: y = y / rho
//QMR: w = wt / psi
//QMR: z = z / psi
magma_cqmr_1(
b.num_rows,
b.num_cols,
Q_rho,
Q_psi,
Q_y.dval,
Q_z.dval,
Q_v.dval,
Q_w.dval,
queue );
Q_res = magma_scnrm2( dofs, Q_r.dval, 1, queue );
T_res = magma_scnrm2( dofs, T_r.dval, 1, queue );
C_res = magma_scnrm2( dofs, C_r.dval, 1, queue );
B_res = magma_scnrm2( dofs, B_r.dval, 1, queue );
// printf(" %e %e %e\n", Q_res, C_res, B_res);
if( Q_res < res ){
res = Q_res;
flag = 1;
}
if( T_res < res ){
res = Q_res;
flag = 2;
}
if( C_res < res ){
res = C_res;
flag = 3;
}
if( B_res < res ){
res = B_res;
flag = 4;
}
if ( solver_par->verbose > 0 ) {
tempo2 = magma_sync_wtime( queue );
if ( (solver_par->numiter)%solver_par->verbose == c_zero ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( res/nomb <= solver_par->rtol || res <= solver_par->atol ){
info = MAGMA_SUCCESS;
break;
}
if( magma_c_isnan_inf( Q_beta ) && magma_c_isnan_inf( C_beta ) && magma_c_isnan_inf( B_beta ) ){
info = MAGMA_DIVERGENCE;
break;
}
}
while ( solver_par->numiter+1 <= solver_par->maxiter );
// copy back the best solver
switch ( flag ) {
case 1:
printf("%% QMR fastest solver.\n");
magma_ccopy( dofs, Q_x.dval, 1, x->dval, 1, queue );
break;
case 2:
printf("%% TFQMR fastest solver.\n");
magma_ccopy( dofs, T_x.dval, 1, x->dval, 1, queue );
break;
case 3:
printf("%% CGS fastest solver.\n");
magma_ccopy( dofs, C_x.dval, 1, x->dval, 1, queue );
break;
case 4:
printf("%% BiCGSTAB fastest solver.\n");
magma_ccopy( dofs, B_x.dval, 1, x->dval, 1, queue );
break;
}
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
float residual;
CHECK( magma_cresidualvec( A, b, *x, &r_tld, &residual, queue));
solver_par->iter_res = res;
solver_par->final_res = residual;
if ( solver_par->numiter < solver_par->maxiter && info == MAGMA_SUCCESS ) {
info = MAGMA_SUCCESS;
} else if ( solver_par->init_res > solver_par->final_res ) {
if ( solver_par->verbose > 0 ) {
if ( (solver_par->numiter)%solver_par->verbose == c_zero ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_SLOW_CONVERGENCE;
if( solver_par->iter_res < solver_par->rtol*solver_par->init_res ||
solver_par->iter_res < solver_par->atol ) {
info = MAGMA_SUCCESS;
}
}
else {
if ( solver_par->verbose > 0 ) {
if ( (solver_par->numiter)%solver_par->verbose == c_zero ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
cleanup:
magma_cmfree(&r_tld, queue );
magma_cmfree(&d1, queue );
magma_cmfree(&d2, queue );
magma_cmfree(&AT, queue );
// QMR
magma_cmfree(&Q_r, queue );
magma_cmfree(&Q_v, queue );
magma_cmfree(&Q_w, queue );
magma_cmfree(&Q_wt, queue );
magma_cmfree(&Q_d, queue );
magma_cmfree(&Q_s, queue );
magma_cmfree(&Q_z, queue );
magma_cmfree(&Q_q, queue );
magma_cmfree(&Q_p, queue );
magma_cmfree(&Q_pt, queue );
magma_cmfree(&Q_y, queue );
magma_cmfree(&Q_x, queue );
magma_cmfree(&Ah1, queue );
magma_cmfree(&Ah2, queue );
// TFQMR
magma_cmfree(&T_r, queue );
magma_cmfree(&T_x, queue );
magma_cmfree(&T_d, queue );
magma_cmfree(&T_w, queue );
magma_cmfree(&T_v, queue );
magma_cmfree(&T_u_m, queue );
magma_cmfree(&T_u_mp1, queue );
magma_cmfree(&T_pu_m, queue );
magma_cmfree(&T_d, queue );
magma_cmfree(&T_Au, queue );
magma_cmfree(&T_Au_new, queue );
magma_cmfree(&T_Ad, queue );
// CGS
magma_cmfree(&C_r, queue );
magma_cmfree(&C_rt, queue );
magma_cmfree(&C_x, queue );
magma_cmfree(&C_p, queue );
magma_cmfree(&C_q, queue );
magma_cmfree(&C_u, queue );
magma_cmfree(&C_v, queue );
magma_cmfree(&C_t, queue );
magma_cmfree(&C_p_hat, queue );
magma_cmfree(&C_q_hat, queue );
magma_cmfree(&C_u_hat, queue );
magma_cmfree(&C_v_hat, queue );
// BiCGSTAB
magma_cmfree(&B_r, queue );
magma_cmfree(&B_x, queue );
magma_cmfree(&B_p, queue );
magma_cmfree(&B_v, queue );
magma_cmfree(&B_s, queue );
magma_cmfree(&B_t, queue );
solver_par->info = info;
return info;
} /* magma_cbombard */
