extern "C" magma_int_t
magma_zqmr_merge(
magma_z_matrix A, magma_z_matrix b, magma_z_matrix *x,
magma_z_solver_par *solver_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// prepare solver feedback
solver_par->solver = Magma_QMRMERGE;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// local variables
magmaDoubleComplex c_zero = MAGMA_Z_ZERO, c_one = MAGMA_Z_ONE;
// solver variables
double nom0, r0, res=0, nomb;
magmaDoubleComplex rho = c_one, rho1 = c_one, eta = -c_one , pds = c_one,
thet = c_one, thet1 = c_one, epsilon = c_one,
beta = c_one, delta = c_one, pde = c_one, rde = c_one,
gamm = c_one, gamm1 = c_one, psi = c_one;
magma_int_t dofs = A.num_rows* b.num_cols;
// need to transpose the matrix
magma_z_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR};
// GPU workspace
magma_z_matrix r={Magma_CSR}, r_tld={Magma_CSR},
v={Magma_CSR}, w={Magma_CSR}, wt={Magma_CSR},
d={Magma_CSR}, s={Magma_CSR}, z={Magma_CSR}, q={Magma_CSR},
p={Magma_CSR}, pt={Magma_CSR}, y={Magma_CSR};
CHECK( magma_zvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &r_tld, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &w, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &wt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver setup
CHECK( magma_zresidualvec( A, b, *x, &r, &nom0, queue));
solver_par->init_res = nom0;
magma_zcopy( dofs, r.dval, 1, r_tld.dval, 1, queue );
magma_zcopy( dofs, r.dval, 1, y.dval, 1, queue );
magma_zcopy( dofs, r.dval, 1, v.dval, 1, queue );
magma_zcopy( dofs, r.dval, 1, wt.dval, 1, queue );
magma_zcopy( dofs, r.dval, 1, z.dval, 1, queue );
// transpose the matrix
magma_zmtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue );
magma_zmconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue );
magma_zmfree(&Ah1, queue );
magma_zmtransposeconjugate( Ah2, &Ah1, queue );
magma_zmfree(&Ah2, queue );
Ah2.blocksize = A.blocksize;
Ah2.alignment = A.alignment;
magma_zmconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue );
magma_zmfree(&Ah1, queue );
magma_zmtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue );
magma_zmfree(&Ah2, queue );
nomb = magma_dznrm2( 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;
}
psi = magma_zsqrt( magma_zdotc( dofs, z.dval, 1, z.dval, 1, queue ));
rho = magma_zsqrt( magma_zdotc( dofs, y.dval, 1, y.dval, 1, queue ));
// v = y / rho
// y = y / rho
// w = wt / psi
// z = z / psi
magma_zqmr_1(
r.num_rows,
r.num_cols,
rho,
psi,
y.dval,
z.dval,
v.dval,
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++;
if( magma_z_isnan_inf( rho ) || magma_z_isnan_inf( psi ) ){
info = MAGMA_DIVERGENCE;
break;
}
// delta = z' * y;
delta = magma_zdotc( dofs, z.dval, 1, y.dval, 1, queue );
if( magma_z_isnan_inf( delta ) ){
info = MAGMA_DIVERGENCE;
break;
}
// no precond: yt = y, zt = z
//magma_zcopy( dofs, y.dval, 1, yt.dval, 1 );
//magma_zcopy( dofs, z.dval, 1, zt.dval, 1 );
if( solver_par->numiter == 1 ){
// p = y;
// q = z;
magma_zcopy( dofs, y.dval, 1, p.dval, 1, queue );
magma_zcopy( dofs, z.dval, 1, q.dval, 1, queue );
}
else{
pde = psi * delta / epsilon;
rde = rho * MAGMA_Z_CONJ(delta/epsilon);
// p = y - pde * p
// q = z - rde * q
magma_zqmr_2(
r.num_rows,
r.num_cols,
pde,
rde,
y.dval,
z.dval,
p.dval,
q.dval,
queue );
}
if( magma_z_isnan_inf( rho ) || magma_z_isnan_inf( psi ) ){
info = MAGMA_DIVERGENCE;
break;
}
CHECK( magma_z_spmv( c_one, A, p, c_zero, pt, queue ));
solver_par->spmv_count++;
// epsilon = q' * pt;
epsilon = magma_zdotc( dofs, q.dval, 1, pt.dval, 1, queue );
beta = epsilon / delta;
if( magma_z_isnan_inf( epsilon ) || magma_z_isnan_inf( beta ) ){
info = MAGMA_DIVERGENCE;
break;
}
// v = pt - beta * v
// y = v
magma_zqmr_3(
r.num_rows,
r.num_cols,
beta,
pt.dval,
v.dval,
y.dval,
queue );
rho1 = rho;
// rho = norm(y);
rho = magma_zsqrt( magma_zdotc( dofs, y.dval, 1, y.dval, 1, queue ));
// wt = A' * q - beta' * w;
CHECK( magma_z_spmv( c_one, AT, q, c_zero, wt, queue ));
solver_par->spmv_count++;
magma_zaxpy( dofs, - MAGMA_Z_CONJ( beta ), w.dval, 1, wt.dval, 1, queue );
// no precond: z = wt
magma_zcopy( dofs, wt.dval, 1, z.dval, 1, queue );
thet1 = thet;
thet = rho / (gamm * MAGMA_Z_MAKE( MAGMA_Z_ABS(beta), 0.0 ));
gamm1 = gamm;
gamm = c_one / magma_zsqrt(c_one + thet*thet);
eta = - eta * rho1 * gamm * gamm / (beta * gamm1 * gamm1);
if( magma_z_isnan_inf( thet ) || magma_z_isnan_inf( gamm ) || magma_z_isnan_inf( eta ) ){
info = MAGMA_DIVERGENCE;
break;
}
if( solver_par->numiter == 1 ){
// d = eta * p + pds * d;
// s = eta * pt + pds * d;
// x = x + d;
// r = r - s;
magma_zqmr_4(
r.num_rows,
r.num_cols,
eta,
p.dval,
pt.dval,
d.dval,
s.dval,
x->dval,
r.dval,
queue );
}
else{
pds = (thet1 * gamm) * (thet1 * gamm);
// d = eta * p + pds * d;
// s = eta * pt + pds * d;
// x = x + d;
// r = r - s;
magma_zqmr_5(
r.num_rows,
r.num_cols,
eta,
pds,
p.dval,
pt.dval,
d.dval,
s.dval,
x->dval,
r.dval,
queue );
}
// psi = norm(z);
psi = magma_zsqrt( magma_zdotc( dofs, z.dval, 1, z.dval, 1, queue ) );
res = magma_dznrm2( dofs, r.dval, 1, queue );
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;
}
}
// v = y / rho
// y = y / rho
// w = wt / psi
// z = z / psi
magma_zqmr_1(
r.num_rows,
r.num_cols,
rho,
psi,
y.dval,
z.dval,
v.dval,
w.dval,
queue );
if ( res/nomb <= solver_par->rtol || res <= solver_par->atol ){
break;
}
}
while ( solver_par->numiter+1 <= solver_par->maxiter );
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
CHECK( magma_zresidualvec( 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 ) {
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_zmfree(&r, queue );
magma_zmfree(&r_tld, queue );
magma_zmfree(&v, queue );
magma_zmfree(&w, queue );
magma_zmfree(&wt, queue );
magma_zmfree(&d, queue );
magma_zmfree(&s, queue );
magma_zmfree(&z, queue );
magma_zmfree(&q, queue );
magma_zmfree(&p, queue );
magma_zmfree(&pt, queue );
magma_zmfree(&y, queue );
magma_zmfree(&AT, queue );
magma_zmfree(&Ah1, queue );
magma_zmfree(&Ah2, queue );
solver_par->info = info;
return info;
} /* magma_zqmr_merge */
extern "C" magma_int_t
magma_zbombard_merge(
magma_z_matrix A, magma_z_matrix b,
magma_z_matrix *x, magma_z_solver_par *solver_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// queue variables
const magma_queue_t squeue = 0; // synchronous kernel queues
const magma_int_t nqueues = 3; // number of queues
magma_queue_t queues[nqueues];
magma_int_t q1flag = 0;
// set asynchronous kernel queues
//printf("%% Kernel queues: (orig, queue) = (%p, %p)\n", (void *)orig_queue, (void *)queue);
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
if ( queue != squeue ) {
queues[1] = queue;
q1flag = 0;
} else {
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &(queues[1]) );
queue = queues[1];
q1flag = 1;
}
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &(queues[2]) );
for (int i = 0; i < nqueues; ++i ) {
; //printf("Kernel queue #%d = %p\n", i, (void *)queues[i]);
}
// 1=QMR, 2=CGS, 3+BiCGSTAB
magma_int_t flag = 0;
int mdot = 1;
// prepare solver feedback
solver_par->solver = Magma_BOMBARD;
solver_par->numiter = 0;
// constants
const magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
// solver variables
double nom0, r0, res, Q_res, C_res, B_res, nomb;
//QMR
magmaDoubleComplex 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;
//CGS
magmaDoubleComplex C_rho, C_rho_l = c_one, C_alpha, C_beta;
//BiCGSTAB
magmaDoubleComplex 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
// overall initial residual
magma_z_matrix r_tld={Magma_CSR};
// QMR
magma_z_matrix AT = {Magma_CSR}, Q_r={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};
// CGS
magma_z_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_z_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};
// multi-vector for block-SpMV
magma_z_matrix SpMV_in_1={Magma_CSR}, SpMV_out_1={Magma_CSR},
SpMV_in_2={Magma_CSR}, SpMV_out_2={Magma_CSR};
// workspace for zmzdotc
magma_z_matrix d1={Magma_CSR}, d2={Magma_CSR}, skp={Magma_CSR};
CHECK( magma_zvinit( &r_tld, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &SpMV_in_1, Magma_DEV, A.num_rows, b.num_cols * 3, c_zero, queue ));
CHECK( magma_zvinit( &SpMV_out_1, Magma_DEV, A.num_rows, b.num_cols * 3, c_zero, queue ));
CHECK( magma_zvinit( &SpMV_in_2, Magma_DEV, A.num_rows, b.num_cols * 3, c_zero, queue ));
CHECK( magma_zvinit( &SpMV_out_2, Magma_DEV, A.num_rows, b.num_cols * 3, c_zero, queue ));
CHECK( magma_zvinit( &d1, Magma_DEV, A.num_rows, b.num_cols * 4, c_zero, queue ));
CHECK( magma_zvinit( &d2, Magma_DEV, A.num_rows, b.num_cols * 4, c_zero, queue ));
CHECK( magma_zvinit( &skp, Magma_CPU, 4, 1, c_zero, queue ));
// QMR
CHECK( magma_zvinit( &Q_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_w, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_wt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &Q_x, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// QMR
CHECK( magma_zvinit( &C_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_x,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_p_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_q_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_u_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_v_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &C_t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// BiCGSTAB
CHECK( magma_zvinit( &B_r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &B_x,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &B_p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &B_v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &B_s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_zvinit( &B_t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver setup
CHECK( magma_zresidualvec( A, b, *x, &r_tld, &nom0, queue));
solver_par->init_res = nom0;
res = nom0;
// QMR
magma_zcopy( dofs, r_tld.dval, 1, Q_r.dval, 1, queue );
magma_zcopy( dofs, r_tld.dval, 1, Q_y.dval, 1, queue );
magma_zcopy( dofs, r_tld.dval, 1, Q_v.dval, 1, queue );
magma_zcopy( dofs, r_tld.dval, 1, Q_wt.dval, 1, queue );
magma_zcopy( dofs, r_tld.dval, 1, Q_z.dval, 1, queue );
magma_zcopy( dofs, x->dval, 1, Q_x.dval, 1, queue );
// transpose the matrix
magma_zmtransposeconjugate( A, &AT, queue );
// CGS
magma_zcopy( dofs, r_tld.dval, 1, C_r.dval, 1, queue );
magma_zcopy( dofs, x->dval, 1, C_x.dval, 1, queue );
// BiCGSTAB
magma_zcopy( dofs, r_tld.dval, 1, B_r.dval, 1, queue );
magma_zcopy( dofs, x->dval, 1, B_x.dval, 1, queue );
CHECK( magma_z_spmv( c_one, A, B_r, c_zero, B_v, queue ));
magma_zcopy( dofs, B_v.dval, 1, SpMV_out_1.dval+2*dofs, 1, queue );
nomb = magma_dznrm2( 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;
}
Q_psi = magma_zsqrt( magma_zdotc( dofs, Q_z.dval, 1, Q_z.dval, 1), queue );
Q_rho = magma_zsqrt( magma_zdotc( dofs, Q_y.dval, 1, Q_y.dval, 1), queue );
// BiCGSTAB
B_rho_new = magma_zdotc( dofs, B_r.dval, 1, B_r.dval, 1, queue );
B_rho_old = B_omega = B_alpha = MAGMA_Z_MAKE( 1.0, 0. );
// v = y / rho
// y = y / rho
// w = wt / psi
// z = z / psi
magma_zqmr_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;
// start iteration
do
{
solver_par->numiter++;
if(mdot == 0){
//QMR: delta = z' * y;
Q_delta = magma_zdotc( dofs, Q_z.dval, 1, Q_y.dval, 1, queue );
//CGS: rho = r' * r_tld
C_rho = magma_zdotc( dofs, C_r.dval, 1, r_tld.dval, 1, queue );
// BiCGSTAB
B_rho_old = B_rho_new;
B_rho_new = magma_zdotc( 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
}else{
B_rho_old = B_rho_new;
magma_zmdotc4(
b.num_rows,
Q_z.dval,
Q_y.dval,
r_tld.dval,
C_r.dval,
r_tld.dval,
B_r.dval,
r_tld.dval,
B_r.dval,
d1.dval,
d2.dval,
skp.val,
queue );
Q_delta = skp.val[0];
C_rho = skp.val[1];
B_rho_new = skp.val[2];
B_beta = B_rho_new/B_rho_old * B_alpha/B_omega;
}
if( solver_par->numiter == 1 ){
//QMR: p = y;
//QMR: q = z;
magma_zcopy( dofs, Q_y.dval, 1, SpMV_in_1.dval, 1, queue );
magma_zcopy( dofs, Q_z.dval, 1, SpMV_in_2.dval, 1, queue );
//QMR: u = r;
//QMR: p = r;
magma_zcgs_2(
b.num_rows,
b.num_cols,
C_r.dval,
C_u.dval,
SpMV_in_1.dval+dofs,
queue );
}
else{
Q_pde = Q_psi * Q_delta / Q_epsilon;
Q_rde = Q_rho * MAGMA_Z_CNJG(Q_delta/Q_epsilon);
C_beta = C_rho / C_rho_l;
//QMR p = y - pde * p
//QMR q = z - rde * q
magma_zqmr_2(
b.num_rows,
b.num_cols,
Q_pde,
Q_rde,
Q_y.dval,
Q_z.dval,
SpMV_in_1.dval,
SpMV_in_2.dval,
queue );
//CGS: u = r + beta*q;
//CGS: p = u + beta*( q + beta*p );
magma_zcgs_1(
b.num_rows,
b.num_cols,
C_beta,
C_r.dval,
C_q.dval,
C_u.dval,
SpMV_in_1.dval+dofs,
queue );
}
// BiCGSTAB: p = r + beta * ( p - omega * v )
magma_zbicgstab_1(
b.num_rows,
b.num_cols,
B_beta,
B_omega,
B_r.dval,
SpMV_out_1.dval+2*dofs,
SpMV_in_1.dval+2*dofs,
queue );
/*
//QMR
CHECK( magma_z_spmv( c_one, A, Q_p, c_zero, Q_pt, queue ));
//CGS
CHECK( magma_z_spmv( c_one, A, C_p, c_zero, C_v_hat, queue ));
// BiCGSTAB
CHECK( magma_z_spmv( c_one, A, B_p, c_zero, B_v, queue ));
*/
// gather everything for a block-SpMV
//magma_zcopy( dofs, Q_p.dval, 1, SpMV_in_1.dval , 1, queue );
//magma_zcopy( dofs, C_p.dval, 1, SpMV_in_1.dval+dofs , 1, queue );
//magma_zcopy( dofs, B_p.dval, 1, SpMV_in_1.dval+2*dofs , 1, queue );
// block SpMV
CHECK( magma_z_spmv( c_one, A, SpMV_in_1, c_zero, SpMV_out_1, queue ));
// scatter results
//magma_zcopy( dofs, SpMV_out_1.dval , 1, Q_pt.dval, 1, queue );
//magma_zcopy( dofs, SpMV_out_1.dval+dofs , 1, C_v_hat.dval, 1, queue );
//magma_zcopy( dofs, SpMV_out_1.dval+2*dofs , 1, B_v.dval, 1, queue );
if( mdot == 0 ) {
//QMR: epsilon = q' * pt;
Q_epsilon = magma_zdotc( dofs, SpMV_in_2.dval, 1, SpMV_out_1.dval, 1, queue );
Q_beta = Q_epsilon / Q_delta;
//CGS: alpha = r_tld' * v_hat
C_alpha = C_rho / magma_zdotc( dofs, r_tld.dval, 1, SpMV_out_1.dval+dofs, 1, queue );
C_rho_l = C_rho;
//BiCGSTAB
B_alpha = B_rho_new / magma_zdotc( dofs, r_tld.dval, 1, SpMV_out_1.dval+2*dofs, 1, queue );
}else{
magma_zmdotc4(
b.num_rows,
SpMV_in_2.dval,
SpMV_out_1.dval,
r_tld.dval,
SpMV_out_1.dval+dofs,
r_tld.dval,
SpMV_out_1.dval+2*dofs,
r_tld.dval,
SpMV_out_1.dval+2*dofs,
d1.dval,
d2.dval,
skp.val,
queue );
Q_epsilon = skp.val[0];
Q_beta = Q_epsilon / Q_delta;
C_alpha = C_rho / skp.val[1];
C_rho_l = C_rho;
B_alpha = B_rho_new / skp.val[2];
}
//QMR: v = pt - beta * v
//QMR: y = v
magma_zqmr_3(
b.num_rows,
b.num_cols,
Q_beta,
SpMV_out_1.dval,
Q_v.dval,
Q_y.dval,
queue );
//CGS: q = u - alpha v_hat
//CGS: t = u + q
magma_zcgs_3(
b.num_rows,
b.num_cols,
C_alpha,
SpMV_out_1.dval+dofs,
C_u.dval,
C_q.dval,
SpMV_in_2.dval+dofs,
queue );
// BiCGSTAB: s = r - alpha v
magma_zbicgstab_2(
b.num_rows,
b.num_cols,
B_alpha,
B_r.dval,
SpMV_out_1.dval+2*dofs,
SpMV_in_2.dval+2*dofs,
queue );
// gather everything for a block-SpMV
//magma_zcopy( dofs, Q_q.dval, 1, SpMV_in_2.dval , 1, queue );
//magma_zcopy( dofs, C_t.dval, 1, SpMV_in_2.dval+dofs , 1, queue );
//magma_zcopy( dofs, B_s.dval, 1, SpMV_in_2.dval+2*dofs , 1, queue );
// block SpMV
CHECK( magma_z_spmv( c_one, A, SpMV_in_2, c_zero, SpMV_out_2, queue ));
// scatter results
//magma_zcopy( dofs, SpMV_out_2.dval , 1, Q_wt.dval, 1, queue );
//magma_zcopy( dofs, SpMV_out_2.dval+dofs , 1, C_rt.dval, 1, queue );
//magma_zcopy( dofs, SpMV_out_2.dval+2*dofs , 1, B_t.dval, 1, queue );
Q_rho1 = Q_rho;
if( mdot == 0 ) {
//QMR rho = norm(y);
Q_rho = magma_zsqrt( magma_zdotc( dofs, Q_y.dval, 1, Q_y.dval, 1), queue );
// BiCGSTAB
B_omega = magma_zdotc( dofs, SpMV_out_2.dval+2*dofs, 1, SpMV_in_2.dval+2*dofs, 1 ) // omega = <s,t>/<t,t>
/ magma_zdotc( dofs, SpMV_out_2.dval+2*dofs, 1, SpMV_out_2.dval+2*dofs, 1, queue );
}else{
magma_zmdotc4(
b.num_rows,
Q_y.dval,
Q_y.dval,
Q_y.dval,
Q_y.dval,
SpMV_out_2.dval+2*dofs,
SpMV_in_2.dval+2*dofs,
SpMV_out_2.dval+2*dofs,
SpMV_out_2.dval+2*dofs,
d1.dval,
d2.dval,
skp.val,
queue );
Q_rho = magma_zsqrt(skp.val[0]);
B_omega = skp.val[2]/skp.val[3];
}
// QMR
Q_thet1 = Q_thet;
Q_thet = Q_rho / (Q_gamm * MAGMA_Z_MAKE( MAGMA_Z_ABS(Q_beta), 0.0 ));
Q_gamm1 = Q_gamm;
Q_gamm = c_one / magma_zsqrt(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_zqmr_4(
b.num_rows,
b.num_cols,
Q_eta,
SpMV_in_1.dval,
SpMV_out_1.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);
//QMR: d = eta * p + pds * d;
//QMR: s = eta * pt + pds * d;
//QMR: x = x + d;
//QMR: r = r - s;
magma_zqmr_5(
b.num_rows,
b.num_cols,
Q_eta,
Q_pds,
SpMV_in_1.dval,
SpMV_out_1.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_zcgs_4(
b.num_rows,
b.num_cols,
C_alpha,
SpMV_in_2.dval+dofs,
SpMV_out_2.dval+dofs,
C_x.dval,
C_r.dval,
queue );
// BiCGSTAB: x = x + alpha * p + omega * s
// BiCGSTAB: r = s - omega * t
magma_zbicgstab_3(
b.num_rows,
b.num_cols,
B_alpha,
B_omega,
SpMV_in_1.dval+2*dofs,
SpMV_in_2.dval+2*dofs,
SpMV_out_2.dval+2*dofs,
B_x.dval,
B_r.dval,
queue );
if( mdot == 0 ){
Q_res = magma_dznrm2( dofs, Q_r.dval, 1, queue );
C_res = magma_dznrm2( dofs, C_r.dval, 1, queue );
B_res = magma_dznrm2( dofs, B_r.dval, 1, queue );
//QMR: psi = norm(z);
Q_psi = magma_zsqrt( magma_zdotc( dofs, Q_z.dval, 1, Q_z.dval, 1), queue );
}else{
magma_zmdotc4(
b.num_rows,
Q_r.dval,
Q_r.dval,
C_r.dval,
C_r.dval,
B_r.dval,
B_r.dval,
Q_z.dval,
Q_z.dval,
d1.dval,
d2.dval,
skp.val,
queue );
Q_res = MAGMA_Z_ABS(magma_zsqrt(skp.val[0]));
C_res = MAGMA_Z_ABS(magma_zsqrt(skp.val[1]));
B_res = MAGMA_Z_ABS(magma_zsqrt(skp.val[2]));
//QMR: psi = norm(z);
Q_psi = magma_zsqrt(skp.val[3]);
}
//QMR: v = y / rho
//QMR: y = y / rho
//QMR: w = wt / psi
//QMR: z = z / psi
//QMR: wt = A' * q - beta' * w
//QMR: no precond: z = wt
magma_zqmr_6(
b.num_rows,
b.num_cols,
Q_beta,
Q_rho,
Q_psi,
Q_y.dval,
Q_z.dval,
Q_v.dval,
Q_w.dval,
SpMV_out_2.dval,
queue );
// printf(" %e %e %e\n", Q_res, C_res, B_res);
if( Q_res < res ){
res = Q_res;
flag = 1;
}
if( C_res < res ){
res = C_res;
flag = 2;
}
if( B_res < res ){
res = B_res;
flag = 3;
}
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 ){
break;
}
}
while ( solver_par->numiter+1 <= solver_par->maxiter );
// copy back the best solver
switch ( flag ) {
case 1:
printf("%% QMR fastest solver.\n");
magma_zcopy( dofs, Q_x.dval, 1, x->dval, 1, queue );
break;
case 2:
printf("%% CGS fastest solver.\n");
magma_zcopy( dofs, C_x.dval, 1, x->dval, 1, queue );
break;
case 3:
printf("%% BiCGSTAB fastest solver.\n");
magma_zcopy( dofs, B_x.dval, 1, x->dval, 1, queue );
break;
}
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
CHECK( magma_zresidualvec( 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;
} 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_zmfree(&r_tld, queue );
magma_zmfree(&SpMV_in_1, queue );
magma_zmfree(&SpMV_out_1, queue );
magma_zmfree(&SpMV_in_2, queue );
magma_zmfree(&SpMV_out_2, queue );
magma_zmfree(&d1, queue );
magma_zmfree(&d2, queue );
magma_zmfree(&skp, queue );
magma_zmfree(&AT, queue );
// QMR
magma_zmfree(&Q_r, queue );
magma_zmfree(&Q_v, queue );
magma_zmfree(&Q_w, queue );
magma_zmfree(&Q_wt, queue );
magma_zmfree(&Q_d, queue );
magma_zmfree(&Q_s, queue );
magma_zmfree(&Q_z, queue );
magma_zmfree(&Q_q, queue );
magma_zmfree(&Q_p, queue );
magma_zmfree(&Q_pt, queue );
magma_zmfree(&Q_y, queue );
magma_zmfree(&Q_x, queue );
// CGS
magma_zmfree(&C_r, queue );
magma_zmfree(&C_rt, queue );
magma_zmfree(&C_x, queue );
magma_zmfree(&C_p, queue );
magma_zmfree(&C_q, queue );
magma_zmfree(&C_u, queue );
magma_zmfree(&C_v, queue );
magma_zmfree(&C_t, queue );
magma_zmfree(&C_p_hat, queue );
magma_zmfree(&C_q_hat, queue );
magma_zmfree(&C_u_hat, queue );
magma_zmfree(&C_v_hat, queue );
// BiCGSTAB
magma_zmfree(&B_r, queue );
magma_zmfree(&B_x, queue );
magma_zmfree(&B_p, queue );
magma_zmfree(&B_v, queue );
magma_zmfree(&B_s, queue );
magma_zmfree(&B_t, queue );
// destroy asynchronous queues
magma_queue_destroy( queues[0] );
if ( q1flag == 1 ) {
magma_queue_destroy( queues[1] );
}
magma_queue_destroy( queues[2] );
solver_par->info = info;
return info;
} /* magma_zbombard_merge */