extern "C" magma_int_t
magma_cresidualvec(
magma_c_matrix A, magma_c_matrix b, magma_c_matrix x,
magma_c_matrix *r, float *res,
magma_queue_t queue )
{
magma_int_t info =0;
// some useful variables
magmaFloatComplex zero = MAGMA_C_ZERO, one = MAGMA_C_ONE,
mone = MAGMA_C_NEG_ONE;
magma_int_t dofs = A.num_rows;
if ( A.num_rows == b.num_rows ) {
CHECK( magma_c_spmv( mone, A, x, zero, *r, queue )); // r = A x
magma_caxpy( dofs, one, b.dval, 1, r->dval, 1, queue ); // r = r - b
*res = magma_scnrm2( dofs, r->dval, 1, queue ); // res = ||r||
// /magma_scnrm2( dofs, b.dval, 1, queue ); /||b||
//printf( "relative residual: %e\n", *res );
} else if ((b.num_rows*b.num_cols)%A.num_rows== 0 ) {
magma_int_t num_vecs = b.num_rows*b.num_cols/A.num_rows;
CHECK( magma_c_spmv( mone, A, x, zero, *r, queue )); // r = A x
for( magma_int_t i=0; i<num_vecs; i++) {
magma_caxpy( dofs, one, b(i), 1, r(i), 1, queue ); // r = r - b
res[i] = magma_scnrm2( dofs, r(i), 1, queue ); // res = ||r||
}
// /magma_scnrm2( dofs, b.dval, 1, queue ); /||b||
//printf( "relative residual: %e\n", *res );
} else {
printf("%%error: dimensions do not match.\n");
info = MAGMA_ERR_NOT_SUPPORTED;
}
cleanup:
return info;
}
extern "C" magma_int_t
magma_cpbicgstab(
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 = 0;
// set queue for old dense routines
magma_queue_t orig_queue=NULL;
magmablasGetKernelStream( &orig_queue );
// prepare solver feedback
solver_par->solver = Magma_PBICGSTAB;
solver_par->numiter = 0;
solver_par->info = MAGMA_SUCCESS;
// some useful variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE,
c_mone = MAGMA_C_NEG_ONE;
magma_int_t dofs = A.num_rows*b.num_cols;
// workspace
magma_c_matrix r={Magma_CSR}, rr={Magma_CSR}, p={Magma_CSR}, v={Magma_CSR}, s={Magma_CSR}, t={Magma_CSR}, ms={Magma_CSR}, mt={Magma_CSR}, y={Magma_CSR}, z={Magma_CSR};
CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &rr,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( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &s, 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 ));
CHECK( magma_cvinit( &ms,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &mt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver variables
magmaFloatComplex alpha, beta, omega, rho_old, rho_new;
float nom, betanom, nom0, r0, den, res;
// solver setup
CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue));
magma_ccopy( dofs, r.dval, 1, rr.dval, 1 ); // rr = r
betanom = nom0;
nom = nom0*nom0;
rho_new = omega = alpha = MAGMA_C_MAKE( 1.0, 0. );
solver_par->init_res = nom0;
CHECK( magma_c_spmv( c_one, A, r, c_zero, v, queue )); // z = A r
den = MAGMA_C_REAL( magma_cdotc(dofs, v.dval, 1, r.dval, 1) ); // den = z' * r
if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE )
r0 = ATOLERANCE;
if ( nom < r0 ) {
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
goto cleanup;
}
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = nom0;
solver_par->timing[0] = 0.0;
}
solver_par->numiter = 0;
// start iteration
do
{
solver_par->numiter++;
rho_old = rho_new; // rho_old=rho
rho_new = magma_cdotc( dofs, rr.dval, 1, r.dval, 1 ); // rho=<rr,r>
beta = rho_new/rho_old * alpha/omega; // beta=rho/rho_old *alpha/omega
magma_cscal( dofs, beta, p.dval, 1 ); // p = beta*p
magma_caxpy( dofs, c_mone * omega * beta, v.dval, 1 , p.dval, 1 );
// p = p-omega*beta*v
magma_caxpy( dofs, c_one, r.dval, 1, p.dval, 1 ); // p = p+r
// preconditioner
CHECK( magma_c_applyprecond_left( A, p, &mt, precond_par, queue ));
CHECK( magma_c_applyprecond_right( A, mt, &y, precond_par, queue ));
CHECK( magma_c_spmv( c_one, A, y, c_zero, v, queue )); // v = Ap
alpha = rho_new / magma_cdotc( dofs, rr.dval, 1, v.dval, 1 );
magma_ccopy( dofs, r.dval, 1 , s.dval, 1 ); // s=r
magma_caxpy( dofs, c_mone * alpha, v.dval, 1 , s.dval, 1 ); // s=s-alpha*v
// preconditioner
CHECK( magma_c_applyprecond_left( A, s, &ms, precond_par, queue ));
CHECK( magma_c_applyprecond_right( A, ms, &z, precond_par, queue ));
CHECK( magma_c_spmv( c_one, A, z, c_zero, t, queue )); // t=As
// preconditioner
CHECK( magma_c_applyprecond_left( A, s, &ms, precond_par, queue ));
CHECK( magma_c_applyprecond_left( A, t, &mt, precond_par, queue ));
// omega = <ms,mt>/<mt,mt>
omega = magma_cdotc( dofs, mt.dval, 1, ms.dval, 1 )
/ magma_cdotc( dofs, mt.dval, 1, mt.dval, 1 );
magma_caxpy( dofs, alpha, y.dval, 1 , x->dval, 1 ); // x=x+alpha*p
magma_caxpy( dofs, omega, z.dval, 1 , x->dval, 1 ); // x=x+omega*s
magma_ccopy( dofs, s.dval, 1 , r.dval, 1 ); // r=s
magma_caxpy( dofs, c_mone * omega, t.dval, 1 , r.dval, 1 ); // r=r-omega*t
res = betanom = magma_scnrm2( dofs, r.dval, 1 );
nom = betanom*betanom;
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/nom0 < solver_par->epsilon ) {
break;
}
}
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->final_res = residual;
solver_par->iter_res = res;
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) betanom;
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->epsilon*solver_par->init_res ){
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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
cleanup:
magma_cmfree(&r, queue );
magma_cmfree(&rr, queue );
magma_cmfree(&p, queue );
magma_cmfree(&v, queue );
magma_cmfree(&s, queue );
magma_cmfree(&t, queue );
magma_cmfree(&ms, queue );
magma_cmfree(&mt, queue );
magma_cmfree(&y, queue );
magma_cmfree(&z, queue );
magmablasSetKernelStream( orig_queue );
solver_par->info = info;
return info;
} /* magma_cbicgstab */
extern "C" magma_int_t
magma_cpqmr_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_QMR;
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=0.0, nomb;
magmaFloatComplex 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_c_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR};
// GPU workspace
magma_c_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},
vt={Magma_CSR}, yt={Magma_CSR}, zt={Magma_CSR};
CHECK( magma_cvinit( &r, 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( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &w, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &wt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &z, 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( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &yt, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &vt, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &zt, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver setup
CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue));
solver_par->init_res = nom0;
magma_ccopy( dofs, r.dval, 1, r_tld.dval, 1, queue );
magma_ccopy( dofs, r.dval, 1, vt.dval, 1, queue );
magma_ccopy( dofs, r.dval, 1, wt.dval, 1, queue );
// 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 );
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;
}
// no precond: y = vt, z = wt
// magma_ccopy( dofs, vt.dval, 1, y.dval, 1, queue );
// magma_ccopy( dofs, wt.dval, 1, z.dval, 1, queue );
CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, vt, &y, precond_par, queue ));
CHECK( magma_c_applyprecond_right( MagmaTrans, A, wt, &z, precond_par, queue ));
psi = magma_csqrt( magma_cdotc( dofs, z.dval, 1, z.dval, 1, queue ));
rho = magma_csqrt( magma_cdotc( dofs, y.dval, 1, y.dval, 1, queue ));
// v = vt / rho
// y = y / rho
// w = wt / psi
// z = z / psi
magma_cqmr_8(
r.num_rows,
r.num_cols,
rho,
psi,
vt.dval,
wt.dval,
y.dval,
z.dval,
v.dval,
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( magma_c_isnan_inf( rho ) || magma_c_isnan_inf( psi ) ){
info = MAGMA_DIVERGENCE;
break;
}
// delta = z' * y;
delta = magma_cdotc( dofs, z.dval, 1, y.dval, 1, queue );
if( magma_c_isnan_inf( delta ) ){
info = MAGMA_DIVERGENCE;
break;
}
// no precond: yt = y, zt = z
// magma_ccopy( dofs, y.dval, 1, yt.dval, 1, queue );
// magma_ccopy( dofs, z.dval, 1, zt.dval, 1, queue );
CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, y, &yt, precond_par, queue ));
CHECK( magma_c_applyprecond_left( MagmaTrans, A, z, &zt, precond_par, queue ));
if( solver_par->numiter == 1 ){
// p = y;
// q = z;
magma_ccopy( dofs, yt.dval, 1, p.dval, 1, queue );
magma_ccopy( dofs, zt.dval, 1, q.dval, 1, queue );
}
else{
pde = psi * delta / epsilon;
rde = rho * MAGMA_C_CONJ(delta/epsilon);
// p = yt - pde * p
// q = zt - rde * q
magma_cqmr_2(
r.num_rows,
r.num_cols,
pde,
rde,
yt.dval,
zt.dval,
p.dval,
q.dval,
queue );
}
if( magma_c_isnan_inf( rho ) || magma_c_isnan_inf( psi ) ){
info = MAGMA_DIVERGENCE;
break;
}
CHECK( magma_c_spmv( c_one, A, p, c_zero, pt, queue ));
solver_par->spmv_count++;
// epsilon = q' * pt;
epsilon = magma_cdotc( dofs, q.dval, 1, pt.dval, 1, queue );
beta = epsilon / delta;
if( magma_c_isnan_inf( epsilon ) || magma_c_isnan_inf( beta ) ){
info = MAGMA_DIVERGENCE;
break;
}
// vt = pt - beta * v;
magma_cqmr_7(
r.num_rows,
r.num_cols,
beta,
pt.dval,
v.dval,
vt.dval,
queue );
magma_ccopy( dofs, v.dval, 1, vt.dval, 1, queue );
magma_cscal( dofs, -beta, vt.dval, 1, queue );
magma_caxpy( dofs, c_one, pt.dval, 1, vt.dval, 1, queue );
// no precond: y = vt
// magma_ccopy( dofs, vt.dval, 1, y.dval, 1, queue );
CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, vt, &y, precond_par, queue ));
rho1 = rho;
// rho = norm(y);
rho = magma_csqrt( magma_cdotc( dofs, y.dval, 1, y.dval, 1, queue ));
// wt = A' * q - beta' * w;
CHECK( magma_c_spmv( c_one, AT, q, c_zero, wt, queue ));
solver_par->spmv_count++;
magma_caxpy( dofs, - MAGMA_C_CONJ( beta ), w.dval, 1, wt.dval, 1, queue );
// no precond: z = wt
// magma_ccopy( dofs, wt.dval, 1, z.dval, 1, queue );
CHECK( magma_c_applyprecond_right( MagmaTrans, A, wt, &z, precond_par, queue ));
thet1 = thet;
thet = rho / (gamm * MAGMA_C_MAKE( MAGMA_C_ABS(beta), 0.0 ));
gamm1 = gamm;
gamm = c_one / magma_csqrt(c_one + thet*thet);
eta = - eta * rho1 * gamm * gamm / (beta * gamm1 * gamm1);
if( magma_c_isnan_inf( thet ) || magma_c_isnan_inf( gamm ) || magma_c_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_cqmr_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)^2;
pds = (thet1 * gamm) * (thet1 * gamm);
// d = eta * p + pds * d;
// s = eta * pt + pds * d;
// x = x + d;
// r = r - s;
magma_cqmr_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_csqrt( magma_cdotc( dofs, z.dval, 1, z.dval, 1, queue ) );
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 == 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 = vt / rho
// y = y / rho
// w = wt / psi
// z = z / psi
magma_cqmr_8(
r.num_rows,
r.num_cols,
rho,
psi,
vt.dval,
wt.dval,
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;
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 ) {
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, queue );
magma_cmfree(&r_tld, queue );
magma_cmfree(&v, queue );
magma_cmfree(&w, queue );
magma_cmfree(&wt, queue );
magma_cmfree(&d, queue );
magma_cmfree(&s, queue );
magma_cmfree(&z, queue );
magma_cmfree(&q, queue );
magma_cmfree(&p, queue );
magma_cmfree(&zt, queue );
magma_cmfree(&vt, queue );
magma_cmfree(&yt, queue );
magma_cmfree(&pt, queue );
magma_cmfree(&y, queue );
magma_cmfree(&AT, queue );
magma_cmfree(&Ah1, queue );
magma_cmfree(&Ah2, queue );
solver_par->info = info;
return info;
} /* magma_cqmr */
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 */
extern "C" magma_int_t
magma_cgmres(
magma_c_sparse_matrix A,
magma_c_vector b,
magma_c_vector *x,
magma_c_solver_par *solver_par,
magma_queue_t queue )
{
magma_int_t stat = 0;
// set queue for old dense routines
magma_queue_t orig_queue;
magmablasGetKernelStream( &orig_queue );
magma_int_t stat_cpu = 0, stat_dev = 0;
// prepare solver feedback
solver_par->solver = Magma_GMRES;
solver_par->numiter = 0;
solver_par->info = MAGMA_SUCCESS;
// local variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE,
c_mone = MAGMA_C_NEG_ONE;
magma_int_t dofs = A.num_rows;
magma_int_t i, j, k, m = 0;
magma_int_t restart = min( dofs-1, solver_par->restart );
magma_int_t ldh = restart+1;
float nom, rNorm, RNorm, nom0, betanom, r0 = 0.;
// CPU workspace
//magma_setdevice(0);
magmaFloatComplex *H, *HH, *y, *h1;
stat_cpu += magma_cmalloc_pinned( &H, (ldh+1)*ldh );
stat_cpu += magma_cmalloc_pinned( &y, ldh );
stat_cpu += magma_cmalloc_pinned( &HH, ldh*ldh );
stat_cpu += magma_cmalloc_pinned( &h1, ldh );
if( stat_cpu != 0){
magma_free_pinned( H );
magma_free_pinned( y );
magma_free_pinned( HH );
magma_free_pinned( h1 );
magmablasSetKernelStream( orig_queue );
return MAGMA_ERR_HOST_ALLOC;
}
// GPU workspace
magma_c_vector r, q, q_t;
magma_c_vinit( &r, Magma_DEV, dofs, c_zero, queue );
magma_c_vinit( &q, Magma_DEV, dofs*(ldh+1), c_zero, queue );
q_t.memory_location = Magma_DEV;
q_t.dval = NULL;
q_t.num_rows = q_t.nnz = dofs; q_t.num_cols = 1;
magmaFloatComplex *dy = NULL, *dH = NULL;
stat_dev += magma_cmalloc( &dy, ldh );
stat_dev += magma_cmalloc( &dH, (ldh+1)*ldh );
if( stat_dev != 0){
magma_free_pinned( H );
magma_free_pinned( y );
magma_free_pinned( HH );
magma_free_pinned( h1 );
magma_free( dH );
magma_free( dy );
magma_free( dH );
magma_free( dy );
magmablasSetKernelStream( orig_queue );
return MAGMA_ERR_DEVICE_ALLOC;
}
// GPU stream
magma_queue_t stream[2];
magma_event_t event[1];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
magma_event_create( &event[0] );
//magmablasSetKernelStream(stream[0]);
magma_cscal( dofs, c_zero, x->dval, 1 ); // x = 0
magma_ccopy( dofs, b.dval, 1, r.dval, 1 ); // r = b
nom0 = betanom = magma_scnrm2( dofs, r.dval, 1 ); // nom0= || r||
nom = nom0 * nom0;
solver_par->init_res = nom0;
H(1,0) = MAGMA_C_MAKE( nom0, 0. );
magma_csetvector(1, &H(1,0), 1, &dH(1,0), 1);
if ( (r0 = nom0 * solver_par->epsilon ) < ATOLERANCE ){
r0 = solver_par->epsilon;
}
if ( nom < r0 ) {
magmablasSetKernelStream( orig_queue );
return MAGMA_SUCCESS;
}
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = nom0;
solver_par->timing[0] = 0.0;
}
// start iteration
for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter;
solver_par->numiter++ ) {
for(k=1; k<=restart; k++) {
magma_ccopy(dofs, r.dval, 1, q(k-1), 1); // q[0] = 1.0/||r||
magma_cscal(dofs, 1./H(k,k-1), q(k-1), 1); // (to be fused)
q_t.dval = q(k-1);
//magmablasSetKernelStream(stream[0]);
magma_c_spmv( c_one, A, q_t, c_zero, r, queue ); // r = A q[k]
// if (solver_par->ortho == Magma_MGS ) {
// modified Gram-Schmidt
for (i=1; i<=k; i++) {
H(i,k) =magma_cdotc(dofs, q(i-1), 1, r.dval, 1);
// H(i,k) = q[i] . r
magma_caxpy(dofs,-H(i,k), q(i-1), 1, r.dval, 1);
// r = r - H(i,k) q[i]
}
H(k+1,k) = MAGMA_C_MAKE( magma_scnrm2(dofs, r.dval, 1), 0. ); // H(k+1,k) = ||r||
/*} else if (solver_par->ortho == Magma_FUSED_CGS ) {
// fusing cgemv with scnrm2 in classical Gram-Schmidt
magmablasSetKernelStream(stream[0]);
magma_ccopy(dofs, r.dval, 1, q(k), 1);
// dH(1:k+1,k) = q[0:k] . r
magmablas_cgemv(MagmaTrans, dofs, k+1, c_one, q(0),
dofs, r.dval, 1, c_zero, &dH(1,k), 1);
// r = r - q[0:k-1] dH(1:k,k)
magmablas_cgemv(MagmaNoTrans, dofs, k, c_mone, q(0),
dofs, &dH(1,k), 1, c_one, r.dval, 1);
// 1) dH(k+1,k) = sqrt( dH(k+1,k) - dH(1:k,k) )
magma_ccopyscale( dofs, k, r.dval, q(k), &dH(1,k) );
// 2) q[k] = q[k] / dH(k+1,k)
magma_event_record( event[0], stream[0] );
magma_queue_wait_event( stream[1], event[0] );
magma_cgetvector_async(k+1, &dH(1,k), 1, &H(1,k), 1, stream[1]);
// asynch copy dH(1:(k+1),k) to H(1:(k+1),k)
} else {
// classical Gram-Schmidt (default)
// > explicitly calling magmabls
magmablasSetKernelStream(stream[0]);
magmablas_cgemv(MagmaTrans, dofs, k, c_one, q(0),
dofs, r.dval, 1, c_zero, &dH(1,k), 1, queue );
// dH(1:k,k) = q[0:k-1] . r
#ifndef SCNRM2SCALE
// start copying dH(1:k,k) to H(1:k,k)
magma_event_record( event[0], stream[0] );
magma_queue_wait_event( stream[1], event[0] );
magma_cgetvector_async(k, &dH(1,k), 1, &H(1,k),
1, stream[1]);
#endif
// r = r - q[0:k-1] dH(1:k,k)
magmablas_cgemv(MagmaNoTrans, dofs, k, c_mone, q(0),
dofs, &dH(1,k), 1, c_one, r.dval, 1);
#ifdef SCNRM2SCALE
magma_ccopy(dofs, r.dval, 1, q(k), 1);
// q[k] = r / H(k,k-1)
magma_scnrm2scale(dofs, q(k), dofs, &dH(k+1,k) );
// dH(k+1,k) = sqrt(r . r) and r = r / dH(k+1,k)
magma_event_record( event[0], stream[0] );
// start sending dH(1:k,k) to H(1:k,k)
magma_queue_wait_event( stream[1], event[0] );
// can we keep H(k+1,k) on GPU and combine?
magma_cgetvector_async(k+1, &dH(1,k), 1, &H(1,k), 1, stream[1]);
#else
H(k+1,k) = MAGMA_C_MAKE( magma_scnrm2(dofs, r.dval, 1), 0. );
// H(k+1,k) = sqrt(r . r)
if ( k<solver_par->restart ) {
magmablasSetKernelStream(stream[0]);
magma_ccopy(dofs, r.dval, 1, q(k), 1);
// q[k] = 1.0/H[k][k-1] r
magma_cscal(dofs, 1./H(k+1,k), q(k), 1);
// (to be fused)
}
#endif
}*/
/* Minimization of || b-Ax || in H_k */
for (i=1; i<=k; i++) {
HH(k,i) = magma_cblas_cdotc( i+1, &H(1,k), 1, &H(1,i), 1 );
}
h1[k] = H(1,k)*H(1,0);
if (k != 1) {
for (i=1; i<k; i++) {
HH(k,i) = HH(k,i)/HH(i,i);//
for (m=i+1; m<=k; m++) {
HH(k,m) -= HH(k,i) * HH(m,i) * HH(i,i);
}
h1[k] -= h1[i] * HH(k,i);
}
}
y[k] = h1[k]/HH(k,k);
if (k != 1)
for (i=k-1; i>=1; i--) {
y[i] = h1[i]/HH(i,i);
for (j=i+1; j<=k; j++)
y[i] -= y[j] * HH(j,i);
}
m = k;
rNorm = fabs(MAGMA_C_REAL(H(k+1,k)));
}/* Minimization done */
// compute solution approximation
magma_csetmatrix(m, 1, y+1, m, dy, m );
magma_cgemv(MagmaNoTrans, dofs, m, c_one, q(0), dofs, dy, 1,
c_one, x->dval, 1);
// compute residual
magma_c_spmv( c_mone, A, *x, c_zero, r, queue ); // r = - A * x
magma_caxpy(dofs, c_one, b.dval, 1, r.dval, 1); // r = r + b
H(1,0) = MAGMA_C_MAKE( magma_scnrm2(dofs, r.dval, 1), 0. );
// RNorm = H[1][0] = || r ||
RNorm = MAGMA_C_REAL( H(1,0) );
betanom = fabs(RNorm);
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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( betanom < r0 ) {
break;
}
}
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
float residual;
magma_cresidual( A, b, *x, &residual, queue );
solver_par->iter_res = betanom;
solver_par->final_res = residual;
if ( solver_par->numiter < solver_par->maxiter) {
solver_par->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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
solver_par->info = MAGMA_SLOW_CONVERGENCE;
}
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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
solver_par->info = MAGMA_DIVERGENCE;
}
// free pinned memory
magma_free_pinned( H );
magma_free_pinned( y );
magma_free_pinned( HH );
magma_free_pinned( h1 );
// free GPU memory
magma_free(dy);
if (dH != NULL ) magma_free(dH);
magma_c_vfree(&r, queue );
magma_c_vfree(&q, queue );
// free GPU streams and events
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_event_destroy( event[0] );
//magmablasSetKernelStream(NULL);
magmablasSetKernelStream( orig_queue );
return MAGMA_SUCCESS;
} /* magma_cgmres */
extern "C" magma_int_t
magma_cidr(
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;
// prepare solver feedback
solver_par->solver = Magma_IDR;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
solver_par->init_res = 0.0;
solver_par->final_res = 0.0;
solver_par->iter_res = 0.0;
solver_par->runtime = 0.0;
// constants
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_n_one = MAGMA_C_NEG_ONE;
// internal user parameters
const magma_int_t smoothing = 1; // 0 = disable, 1 = enable
const float angle = 0.7; // [0-1]
// local variables
magma_int_t iseed[4] = {0, 0, 0, 1};
magma_int_t dof;
magma_int_t s;
magma_int_t distr;
magma_int_t k, i, sk;
magma_int_t innerflag;
float residual;
float nrm;
float nrmb;
float nrmr;
float nrmt;
float rho;
magmaFloatComplex om;
magmaFloatComplex tt;
magmaFloatComplex tr;
magmaFloatComplex gamma;
magmaFloatComplex alpha;
magmaFloatComplex mkk;
magmaFloatComplex fk;
// matrices and vectors
magma_c_matrix dxs = {Magma_CSR};
magma_c_matrix dr = {Magma_CSR}, drs = {Magma_CSR};
magma_c_matrix dP = {Magma_CSR}, dP1 = {Magma_CSR};
magma_c_matrix dG = {Magma_CSR};
magma_c_matrix dU = {Magma_CSR};
magma_c_matrix dM = {Magma_CSR};
magma_c_matrix df = {Magma_CSR};
magma_c_matrix dt = {Magma_CSR};
magma_c_matrix dc = {Magma_CSR};
magma_c_matrix dv = {Magma_CSR};
magma_c_matrix dbeta = {Magma_CSR}, hbeta = {Magma_CSR};
// chronometry
real_Double_t tempo1, tempo2;
// initial s space
// TODO: add option for 's' (shadow space number)
// Hack: uses '--restart' option as the shadow space number.
// This is not a good idea because the default value of restart option is used to detect
// if the user provided a custom restart. This means that if the default restart value
// is changed then the code will think it was the user (unless the default value is
// also updated in the 'if' statement below.
s = 1;
if ( solver_par->restart != 50 ) {
if ( solver_par->restart > A.num_cols ) {
s = A.num_cols;
} else {
s = solver_par->restart;
}
}
solver_par->restart = s;
// set max iterations
solver_par->maxiter = min( 2 * A.num_cols, solver_par->maxiter );
// check if matrix A is square
if ( A.num_rows != A.num_cols ) {
//printf("Matrix A is not square.\n");
info = MAGMA_ERR_NOT_SUPPORTED;
goto cleanup;
}
// |b|
nrmb = magma_scnrm2( b.num_rows, b.dval, 1, queue );
if ( nrmb == 0.0 ) {
magma_cscal( x->num_rows, MAGMA_C_ZERO, x->dval, 1, queue );
info = MAGMA_SUCCESS;
goto cleanup;
}
// r = b - A x
CHECK( magma_cvinit( &dr, Magma_DEV, b.num_rows, 1, c_zero, queue ));
CHECK( magma_cresidualvec( A, b, *x, &dr, &nrmr, queue ));
// |r|
solver_par->init_res = nrmr;
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)nrmr;
}
// check if initial is guess good enough
if ( nrmr <= solver_par->atol ||
nrmr/nrmb <= solver_par->rtol ) {
info = MAGMA_SUCCESS;
goto cleanup;
}
// P = randn(n, s)
// P = ortho(P)
//---------------------------------------
// P = 0.0
CHECK( magma_cvinit( &dP, Magma_CPU, A.num_cols, s, c_zero, queue ));
// P = randn(n, s)
distr = 3; // 1 = unif (0,1), 2 = unif (-1,1), 3 = normal (0,1)
dof = dP.num_rows * dP.num_cols;
lapackf77_clarnv( &distr, iseed, &dof, dP.val );
// transfer P to device
CHECK( magma_cmtransfer( dP, &dP1, Magma_CPU, Magma_DEV, queue ));
magma_cmfree( &dP, queue );
// P = ortho(P1)
if ( dP1.num_cols > 1 ) {
// P = magma_cqr(P1), QR factorization
CHECK( magma_cqr( dP1.num_rows, dP1.num_cols, dP1, dP1.ld, &dP, NULL, queue ));
} else {
// P = P1 / |P1|
nrm = magma_scnrm2( dof, dP1.dval, 1, queue );
nrm = 1.0 / nrm;
magma_csscal( dof, nrm, dP1.dval, 1, queue );
CHECK( magma_cmtransfer( dP1, &dP, Magma_DEV, Magma_DEV, queue ));
}
magma_cmfree( &dP1, queue );
//---------------------------------------
// allocate memory for the scalar products
CHECK( magma_cvinit( &hbeta, Magma_CPU, s, 1, c_zero, queue ));
CHECK( magma_cvinit( &dbeta, Magma_DEV, s, 1, c_zero, queue ));
// smoothing enabled
if ( smoothing > 0 ) {
// set smoothing solution vector
CHECK( magma_cmtransfer( *x, &dxs, Magma_DEV, Magma_DEV, queue ));
// set smoothing residual vector
CHECK( magma_cmtransfer( dr, &drs, Magma_DEV, Magma_DEV, queue ));
}
// G(n,s) = 0
CHECK( magma_cvinit( &dG, Magma_DEV, A.num_cols, s, c_zero, queue ));
// U(n,s) = 0
CHECK( magma_cvinit( &dU, Magma_DEV, A.num_cols, s, c_zero, queue ));
// M(s,s) = I
CHECK( magma_cvinit( &dM, Magma_DEV, s, s, c_zero, queue ));
magmablas_claset( MagmaFull, s, s, c_zero, c_one, dM.dval, s, queue );
// f = 0
CHECK( magma_cvinit( &df, Magma_DEV, dP.num_cols, 1, c_zero, queue ));
// t = 0
CHECK( magma_cvinit( &dt, Magma_DEV, dr.num_rows, 1, c_zero, queue ));
// c = 0
CHECK( magma_cvinit( &dc, Magma_DEV, dM.num_cols, 1, c_zero, queue ));
// v = 0
CHECK( magma_cvinit( &dv, Magma_DEV, dr.num_rows, 1, c_zero, queue ));
//--------------START TIME---------------
// chronometry
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->timing[0] = 0.0;
}
om = MAGMA_C_ONE;
innerflag = 0;
// start iteration
do
{
solver_par->numiter++;
// new RHS for small systems
// f = P' r
magmablas_cgemv( MagmaConjTrans, dP.num_rows, dP.num_cols, c_one, dP.dval, dP.ld, dr.dval, 1, c_zero, df.dval, 1, queue );
// shadow space loop
for ( k = 0; k < s; ++k ) {
sk = s - k;
// f(k:s) = M(k:s,k:s) c(k:s)
magma_ccopyvector( sk, &df.dval[k], 1, &dc.dval[k], 1, queue );
magma_ctrsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, sk, &dM.dval[k*dM.ld+k], dM.ld, &dc.dval[k], 1, queue );
// v = r - G(:,k:s) c(k:s)
magma_ccopyvector( dr.num_rows, dr.dval, 1, dv.dval, 1, queue );
magmablas_cgemv( MagmaNoTrans, dG.num_rows, sk, c_n_one, &dG.dval[k*dG.ld], dG.ld, &dc.dval[k], 1, c_one, dv.dval, 1, queue );
// U(:,k) = om * v + U(:,k:s) c(k:s)
magmablas_cgemv( MagmaNoTrans, dU.num_rows, sk, c_one, &dU.dval[k*dU.ld], dU.ld, &dc.dval[k], 1, om, dv.dval, 1, queue );
magma_ccopyvector( dU.num_rows, dv.dval, 1, &dU.dval[k*dU.ld], 1, queue );
// G(:,k) = A U(:,k)
CHECK( magma_c_spmv( c_one, A, dv, c_zero, dv, queue ));
solver_par->spmv_count++;
magma_ccopyvector( dG.num_rows, dv.dval, 1, &dG.dval[k*dG.ld], 1, queue );
// bi-orthogonalize the new basis vectors
for ( i = 0; i < k; ++i ) {
// alpha = P(:,i)' G(:,k)
alpha = magma_cdotc( dP.num_rows, &dP.dval[i*dP.ld], 1, &dG.dval[k*dG.ld], 1, queue );
// alpha = alpha / M(i,i)
magma_cgetvector( 1, &dM.dval[i*dM.ld+i], 1, &mkk, 1, queue );
alpha = alpha / mkk;
// G(:,k) = G(:,k) - alpha * G(:,i)
magma_caxpy( dG.num_rows, -alpha, &dG.dval[i*dG.ld], 1, &dG.dval[k*dG.ld], 1, queue );
// U(:,k) = U(:,k) - alpha * U(:,i)
magma_caxpy( dU.num_rows, -alpha, &dU.dval[i*dU.ld], 1, &dU.dval[k*dU.ld], 1, queue );
}
// new column of M = P'G, first k-1 entries are zero
// M(k:s,k) = P(:,k:s)' G(:,k)
magmablas_cgemv( MagmaConjTrans, dP.num_rows, sk, c_one, &dP.dval[k*dP.ld], dP.ld, &dG.dval[k*dG.ld], 1, c_zero, &dM.dval[k*dM.ld+k], 1, queue );
// check M(k,k) == 0
magma_cgetvector( 1, &dM.dval[k*dM.ld+k], 1, &mkk, 1, queue );
if ( MAGMA_C_EQUAL(mkk, MAGMA_C_ZERO) ) {
innerflag = 1;
info = MAGMA_DIVERGENCE;
break;
}
// beta = f(k) / M(k,k)
magma_cgetvector( 1, &df.dval[k], 1, &fk, 1, queue );
hbeta.val[k] = fk / mkk;
// check for nan
if ( magma_c_isnan( hbeta.val[k] ) || magma_c_isinf( hbeta.val[k] )) {
innerflag = 1;
info = MAGMA_DIVERGENCE;
break;
}
// r = r - beta * G(:,k)
magma_caxpy( dr.num_rows, -hbeta.val[k], &dG.dval[k*dG.ld], 1, dr.dval, 1, queue );
// smoothing disabled
if ( smoothing <= 0 ) {
// |r|
nrmr = magma_scnrm2( dr.num_rows, dr.dval, 1, queue );
// smoothing enabled
} else {
// x = x + beta * U(:,k)
magma_caxpy( x->num_rows, hbeta.val[k], &dU.dval[k*dU.ld], 1, x->dval, 1, queue );
// smoothing operation
//---------------------------------------
// t = rs - r
magma_ccopyvector( drs.num_rows, drs.dval, 1, dt.dval, 1, queue );
magma_caxpy( dt.num_rows, c_n_one, dr.dval, 1, dt.dval, 1, queue );
// t't
// t'rs
tt = magma_cdotc( dt.num_rows, dt.dval, 1, dt.dval, 1, queue );
tr = magma_cdotc( dt.num_rows, dt.dval, 1, drs.dval, 1, queue );
// gamma = (t' * rs) / (t' * t)
gamma = tr / tt;
// rs = rs - gamma * (rs - r)
magma_caxpy( drs.num_rows, -gamma, dt.dval, 1, drs.dval, 1, queue );
// xs = xs - gamma * (xs - x)
magma_ccopyvector( dxs.num_rows, dxs.dval, 1, dt.dval, 1, queue );
magma_caxpy( dt.num_rows, c_n_one, x->dval, 1, dt.dval, 1, queue );
magma_caxpy( dxs.num_rows, -gamma, dt.dval, 1, dxs.dval, 1, queue );
// |rs|
nrmr = magma_scnrm2( drs.num_rows, drs.dval, 1, queue );
//---------------------------------------
}
// store current timing and residual
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)nrmr;
solver_par->timing[(solver_par->numiter) / solver_par->verbose]
= (real_Double_t)tempo2 - tempo1;
}
}
// check convergence
if ( nrmr <= solver_par->atol ||
nrmr/nrmb <= solver_par->rtol ) {
s = k + 1; // for the x-update outside the loop
innerflag = 2;
info = MAGMA_SUCCESS;
break;
}
// non-last s iteration
if ( (k + 1) < s ) {
// f(k+1:s) = f(k+1:s) - beta * M(k+1:s,k)
magma_caxpy( sk-1, -hbeta.val[k], &dM.dval[k*dM.ld+(k+1)], 1, &df.dval[k+1], 1, queue );
}
}
// smoothing disabled
if ( smoothing <= 0 && innerflag != 1 ) {
// update solution approximation x
// x = x + U(:,1:s) * beta(1:s)
magma_csetvector( s, hbeta.val, 1, dbeta.dval, 1, queue );
magmablas_cgemv( MagmaNoTrans, dU.num_rows, s, c_one, dU.dval, dU.ld, dbeta.dval, 1, c_one, x->dval, 1, queue );
}
// check convergence or iteration limit or invalid result of inner loop
if ( innerflag > 0 ) {
break;
}
// t = A v
// t = A r
CHECK( magma_c_spmv( c_one, A, dr, c_zero, dt, queue ));
solver_par->spmv_count++;
// computation of a new omega
//---------------------------------------
// |t|
nrmt = magma_scnrm2( dt.num_rows, dt.dval, 1, queue );
// t'r
tr = magma_cdotc( dt.num_rows, dt.dval, 1, dr.dval, 1, queue );
// rho = abs(t' * r) / (|t| * |r|))
rho = MAGMA_D_ABS( MAGMA_C_REAL(tr) / (nrmt * nrmr) );
// om = (t' * r) / (|t| * |t|)
om = tr / (nrmt * nrmt);
if ( rho < angle ) {
om = (om * angle) / rho;
}
//---------------------------------------
if ( MAGMA_C_EQUAL(om, MAGMA_C_ZERO) ) {
info = MAGMA_DIVERGENCE;
break;
}
// update approximation vector
// x = x + om * v
// x = x + om * r
magma_caxpy( x->num_rows, om, dr.dval, 1, x->dval, 1, queue );
// update residual vector
// r = r - om * t
magma_caxpy( dr.num_rows, -om, dt.dval, 1, dr.dval, 1, queue );
// smoothing disabled
if ( smoothing <= 0 ) {
// residual norm
nrmr = magma_scnrm2( b.num_rows, dr.dval, 1, queue );
// smoothing enabled
} else {
// smoothing operation
//---------------------------------------
// t = rs - r
magma_ccopyvector( drs.num_rows, drs.dval, 1, dt.dval, 1, queue );
magma_caxpy( dt.num_rows, c_n_one, dr.dval, 1, dt.dval, 1, queue );
// t't
// t'rs
tt = magma_cdotc( dt.num_rows, dt.dval, 1, dt.dval, 1, queue );
tr = magma_cdotc( dt.num_rows, dt.dval, 1, drs.dval, 1, queue );
// gamma = (t' * rs) / (|t| * |t|)
gamma = tr / tt;
// rs = rs - gamma * (rs - r)
magma_caxpy( drs.num_rows, -gamma, dt.dval, 1, drs.dval, 1, queue );
// xs = xs - gamma * (xs - x)
magma_ccopyvector( dxs.num_rows, dxs.dval, 1, dt.dval, 1, queue );
magma_caxpy( dt.num_rows, c_n_one, x->dval, 1, dt.dval, 1, queue );
magma_caxpy( dxs.num_rows, -gamma, dt.dval, 1, dxs.dval, 1, queue );
// |rs|
nrmr = magma_scnrm2( b.num_rows, drs.dval, 1, queue );
//---------------------------------------
}
// store current timing and residual
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)nrmr;
solver_par->timing[(solver_par->numiter) / solver_par->verbose]
= (real_Double_t)tempo2 - tempo1;
}
}
// check convergence
if ( nrmr <= solver_par->atol ||
nrmr/nrmb <= solver_par->rtol ) {
info = MAGMA_SUCCESS;
break;
}
}
while ( solver_par->numiter + 1 <= solver_par->maxiter );
// smoothing enabled
if ( smoothing > 0 ) {
// x = xs
magma_ccopyvector( x->num_rows, dxs.dval, 1, x->dval, 1, queue );
// r = rs
magma_ccopyvector( dr.num_rows, drs.dval, 1, dr.dval, 1, queue );
}
// get last iteration timing
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t)tempo2 - tempo1;
//--------------STOP TIME----------------
// get final stats
solver_par->iter_res = nrmr;
CHECK( magma_cresidualvec( A, b, *x, &dr, &residual, queue ));
solver_par->final_res = residual;
// set solver conclusion
if ( info != MAGMA_SUCCESS && info != MAGMA_DIVERGENCE ) {
if ( solver_par->init_res > solver_par->final_res ) {
info = MAGMA_SLOW_CONVERGENCE;
}
}
cleanup:
// free resources
// smoothing enabled
if ( smoothing > 0 ) {
magma_cmfree( &dxs, queue );
magma_cmfree( &drs, queue );
}
magma_cmfree( &dr, queue );
magma_cmfree( &dP, queue );
magma_cmfree( &dP1, queue );
magma_cmfree( &dG, queue );
magma_cmfree( &dU, queue );
magma_cmfree( &dM, queue );
magma_cmfree( &df, queue );
magma_cmfree( &dt, queue );
magma_cmfree( &dc, queue );
magma_cmfree( &dv, queue );
magma_cmfree( &dbeta, queue );
magma_cmfree( &hbeta, queue );
solver_par->info = info;
return info;
/* magma_cidr */
}
/**
Purpose
-------
CGEGQR orthogonalizes the N vectors given by a complex M-by-N matrix A:
A = Q * R.
On exit, if successful, the orthogonal vectors Q overwrite A
and R is given in work (on the CPU memory).
The routine is designed for tall-and-skinny matrices: M >> N, N <= 128.
This version uses normal equations and SVD in an iterative process that
makes the computation numerically accurate.
Arguments
---------
@param[in]
ikind INTEGER
Several versions are implemented indiceted by the ikind value:
1: This version uses normal equations and SVD in an iterative process
that makes the computation numerically accurate.
2: This version uses a standard LAPACK-based orthogonalization through
MAGMA's QR panel factorization (magma_cgeqr2x3_gpu) and magma_cungqr
3: MGS
4. Cholesky QR
@param[in]
m INTEGER
The number of rows of the matrix A. m >= n >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. 128 >= n >= 0.
@param[in,out]
dA COMPLEX array on the GPU, dimension (ldda,n)
On entry, the m-by-n matrix A.
On exit, the m-by-n matrix Q with orthogonal columns.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,m).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param
dwork (GPU workspace) COMPLEX array, dimension:
n^2 for ikind = 1
3 n^2 + min(m, n) for ikind = 2
0 (not used) for ikind = 3
n^2 for ikind = 4
@param[out]
work (CPU workspace) COMPLEX array, dimension 3 n^2.
On exit, work(1:n^2) holds the rectangular matrix R.
Preferably, for higher performance, work should be in pinned memory.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
@ingroup magma_cgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgegqr_gpu( magma_int_t ikind, magma_int_t m, magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
magmaFloatComplex *dwork, magmaFloatComplex *work,
magma_int_t *info )
{
#define work(i_,j_) (work + (i_) + (j_)*n)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
magma_int_t i = 0, j, k, n2 = n*n;
magma_int_t ione = 1;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magmaFloatComplex c_one = MAGMA_C_ONE;
float cn = 200., mins, maxs;
/* check arguments */
*info = 0;
if (ikind < 1 || ikind > 4) {
*info = -1;
} else if (m < 0 || m < n) {
*info = -2;
} else if (n < 0 || n > 128) {
*info = -3;
} else if (ldda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (ikind == 1) {
// === Iterative, based on SVD ============================================================
magmaFloatComplex *U, *VT, *vt, *R, *G, *hwork, *tau;
float *S;
R = work; // Size n * n
G = R + n*n; // Size n * n
VT = G + n*n; // Size n * n
magma_cmalloc_cpu( &hwork, 32 + 2*n*n + 2*n);
if ( hwork == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_int_t lwork=n*n+32; // First part f hwork; used as workspace in svd
U = hwork + n*n + 32; // Size n*n
S = (float *)(U+n*n); // Size n
tau = U + n*n + n; // Size n
#if defined(PRECISION_c) || defined(PRECISION_z)
float *rwork;
magma_smalloc_cpu( &rwork, 5*n);
if ( rwork == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
#endif
do {
i++;
magma_cgemm(MagmaConjTrans, MagmaNoTrans, n, n, m, c_one, dA, ldda, dA, ldda, c_zero, dwork, n );
magma_cgetmatrix(n, n, dwork, n, G, n);
#if defined(PRECISION_s) || defined(PRECISION_d)
lapackf77_cgesvd("n", "a", &n, &n, G, &n, S, U, &n, VT, &n,
hwork, &lwork, info);
#else
lapackf77_cgesvd("n", "a", &n, &n, G, &n, S, U, &n, VT, &n,
hwork, &lwork, rwork, info);
#endif
mins = 100.f, maxs = 0.f;
for (k=0; k < n; k++) {
S[k] = magma_ssqrt( S[k] );
if (S[k] < mins) mins = S[k];
if (S[k] > maxs) maxs = S[k];
}
for (k=0; k < n; k++) {
vt = VT + k*n;
for (j=0; j < n; j++)
vt[j] *= S[j];
}
lapackf77_cgeqrf(&n, &n, VT, &n, tau, hwork, &lwork, info);
if (i == 1)
blasf77_ccopy(&n2, VT, &ione, R, &ione);
else
blasf77_ctrmm("l", "u", "n", "n", &n, &n, &c_one, VT, &n, R, &n);
magma_csetmatrix(n, n, VT, n, dwork, n);
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m, n, c_one, dwork, n, dA, ldda);
if (mins > 0.00001f)
cn = maxs/mins;
//fprintf(stderr, "Iteration %d, cond num = %f \n", i, cn);
} while (cn > 10.f);
magma_free_cpu( hwork );
#if defined(PRECISION_c) || defined(PRECISION_z)
magma_free_cpu( rwork );
#endif
// ================== end of ikind == 1 ===================================================
}
else if (ikind == 2) {
// ================== LAPACK based ===================================================
magma_int_t min_mn = min(m, n);
magma_int_t nb = n;
magmaFloatComplex *dtau = dwork + 2*n*n, *d_T = dwork, *ddA = dwork + n*n;
magmaFloatComplex *tau = work+n*n;
magmablas_claset( MagmaFull, n, n, c_zero, c_zero, d_T, n );
magma_cgeqr2x3_gpu(&m, &n, dA, &ldda, dtau, d_T, ddA,
(float *)(dwork+min_mn+2*n*n), info);
magma_cgetmatrix( min_mn, 1, dtau, min_mn, tau, min_mn);
magma_cgetmatrix( n, n, ddA, n, work, n);
magma_cungqr_gpu( m, n, n, dA, ldda, tau, d_T, nb, info );
// ================== end of ikind == 2 ===================================================
}
else if (ikind == 3) {
// ================== MGS ===================================================
for(magma_int_t j = 0; j<n; j++){
for(magma_int_t i = 0; i<j; i++){
*work(i, j) = magma_cdotc(m, dA(0,i), 1, dA(0,j), 1);
magma_caxpy(m, -(*work(i,j)), dA(0,i), 1, dA(0,j), 1);
}
for(magma_int_t i = j; i<n; i++)
*work(i, j) = MAGMA_C_ZERO;
//*work(j,j) = MAGMA_C_MAKE( magma_scnrm2(m, dA(0,j), 1), 0. );
*work(j,j) = magma_cdotc(m, dA(0,j), 1, dA(0,j), 1);
*work(j,j) = MAGMA_C_MAKE( sqrt(MAGMA_C_REAL( *work(j,j) )), 0.);
magma_cscal(m, 1./ *work(j,j), dA(0,j), 1);
}
// ================== end of ikind == 3 ===================================================
}
else if (ikind == 4) {
// ================== Cholesky QR ===================================================
magma_cgemm(MagmaConjTrans, MagmaNoTrans, n, n, m, c_one, dA, ldda, dA, ldda, c_zero, dwork, n );
magma_cgetmatrix(n, n, dwork, n, work, n);
lapackf77_cpotrf("u", &n, work, &n, info);
magma_csetmatrix(n, n, work, n, dwork, n);
magma_ctrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit, m, n, c_one, dwork, n, dA, ldda);
// ================== end of ikind == 4 ===================================================
}
return *info;
} /* magma_cgegqr_gpu */
extern "C" magma_int_t
magma_clsqr(
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_LSQR;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
magma_int_t m = A.num_rows * b.num_cols;
magma_int_t n = A.num_cols * b.num_cols;
// local variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE;
// solver variables
float s, nom0, r0, res=0, nomb, phibar, beta, alpha, c, rho, rhot, phi, thet, normr, normar, norma, sumnormd2, normd;
// need to transpose the matrix
magma_c_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR};
// GPU workspace
magma_c_matrix r={Magma_CSR},
v={Magma_CSR}, z={Magma_CSR}, zt={Magma_CSR},
d={Magma_CSR}, vt={Magma_CSR}, q={Magma_CSR},
w={Magma_CSR}, u={Magma_CSR};
CHECK( magma_cvinit( &r, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &v, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &z, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &d, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &vt,Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &q, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &w, Magma_DEV, A.num_cols, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &zt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// 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 );
// solver setup
CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue));
solver_par->init_res = nom0;
nomb = magma_scnrm2( m, 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;
}
magma_ccopy( m, b.dval, 1, u.dval, 1, queue );
beta = magma_scnrm2( m, u.dval, 1, queue );
magma_cscal( m, MAGMA_C_MAKE(1./beta, 0.0 ), u.dval, 1, queue );
normr = beta;
c = 1.0;
s = 0.0;
phibar = beta;
CHECK( magma_c_spmv( c_one, AT, u, c_zero, v, queue ));
if( precond_par->solver == Magma_NONE ){
;
} else {
CHECK( magma_c_applyprecond_right( MagmaTrans, A, v, &zt, precond_par, queue ));
CHECK( magma_c_applyprecond_left( MagmaTrans, A, zt, &v, precond_par, queue ));
}
alpha = magma_scnrm2( n, v.dval, 1, queue );
magma_cscal( n, MAGMA_C_MAKE(1./alpha, 0.0 ), v.dval, 1, queue );
normar = alpha * beta;
norma = 0;
sumnormd2 = 0;
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
solver_par->numiter = 0;
// start iteration
do
{
solver_par->numiter++;
if( precond_par->solver == Magma_NONE || A.num_rows != A.num_cols ) {
magma_ccopy( n, v.dval, 1 , z.dval, 1, queue );
} else {
CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, v, &zt, precond_par, queue ));
CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, zt, &z, precond_par, queue ));
}
//CHECK( magma_c_spmv( c_one, A, z, MAGMA_C_MAKE(-alpha,0.0), u, queue ));
CHECK( magma_c_spmv( c_one, A, z, c_zero, zt, queue ));
magma_cscal( m, MAGMA_C_MAKE(-alpha, 0.0 ), u.dval, 1, queue );
magma_caxpy( m, c_one, zt.dval, 1, u.dval, 1, queue );
solver_par->spmv_count++;
beta = magma_scnrm2( m, u.dval, 1, queue );
magma_cscal( m, MAGMA_C_MAKE(1./beta, 0.0 ), u.dval, 1, queue );
// norma = norm([norma alpha beta]);
norma = sqrt(norma*norma + alpha*alpha + beta*beta );
//lsvec( solver_par->numiter-1 ) = normar / norma;
thet = -s * alpha;
rhot = c * alpha;
rho = sqrt( rhot * rhot + beta * beta );
c = rhot / rho;
s = - beta / rho;
phi = c * phibar;
phibar = s * phibar;
// d = (z - thet * d) / rho;
magma_cscal( n, MAGMA_C_MAKE(-thet, 0.0 ), d.dval, 1, queue );
magma_caxpy( n, c_one, z.dval, 1, d.dval, 1, queue );
magma_cscal( n, MAGMA_C_MAKE(1./rho, 0.0 ), d.dval, 1, queue );
normd = magma_scnrm2( n, d.dval, 1, queue );
sumnormd2 = sumnormd2 + normd*normd;
// convergence check
res = normr;
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;
}
}
// check for convergence in A*x=b
if ( res/nomb <= solver_par->rtol || res <= solver_par->atol ){
info = MAGMA_SUCCESS;
break;
}
// check for convergence in min{|b-A*x|}
if ( A.num_rows != A.num_cols &&
( normar/(norma*normr) <= solver_par->rtol || normar <= solver_par->atol ) ){
printf("%% warning: quit from minimization convergence check.\n");
info = MAGMA_SUCCESS;
break;
}
magma_caxpy( n, MAGMA_C_MAKE( phi, 0.0 ), d.dval, 1, x->dval, 1, queue );
normr = fabs(s) * normr;
CHECK( magma_c_spmv( c_one, AT, u, c_zero, vt, queue ));
solver_par->spmv_count++;
if( precond_par->solver == Magma_NONE ){
;
} else {
CHECK( magma_c_applyprecond_right( MagmaTrans, A, vt, &zt, precond_par, queue ));
CHECK( magma_c_applyprecond_left( MagmaTrans, A, zt, &vt, precond_par, queue ));
}
magma_cscal( n, MAGMA_C_MAKE(-beta, 0.0 ), v.dval, 1, queue );
magma_caxpy( n, c_one, vt.dval, 1, v.dval, 1, queue );
alpha = magma_scnrm2( n, v.dval, 1, queue );
magma_cscal( n, MAGMA_C_MAKE(1./alpha, 0.0 ), v.dval, 1, queue );
normar = alpha * fabs(s*phi);
}
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 ) {
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, queue );
magma_cmfree(&v, queue );
magma_cmfree(&z, queue );
magma_cmfree(&zt, queue );
magma_cmfree(&d, queue );
magma_cmfree(&vt, queue );
magma_cmfree(&q, queue );
magma_cmfree(&u, queue );
magma_cmfree(&w, queue );
magma_cmfree(&AT, queue );
magma_cmfree(&Ah1, queue );
magma_cmfree(&Ah2, queue );
solver_par->info = info;
return info;
} /* magma_cqmr */
extern "C" magma_int_t
magma_cbicgstab(
magma_c_sparse_matrix A, magma_c_vector b, magma_c_vector *x,
magma_c_solver_par *solver_par,
magma_queue_t queue )
{
// set queue for old dense routines
magma_queue_t orig_queue;
magmablasGetKernelStream( &orig_queue );
// prepare solver feedback
solver_par->solver = Magma_BICGSTAB;
solver_par->numiter = 0;
solver_par->info = MAGMA_SUCCESS;
// some useful variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE,
c_mone = MAGMA_C_NEG_ONE;
magma_int_t dofs = A.num_rows;
// workspace
magma_c_vector r,rr,p,v,s,t;
magma_c_vinit( &r, Magma_DEV, dofs, c_zero, queue );
magma_c_vinit( &rr, Magma_DEV, dofs, c_zero, queue );
magma_c_vinit( &p, Magma_DEV, dofs, c_zero, queue );
magma_c_vinit( &v, Magma_DEV, dofs, c_zero, queue );
magma_c_vinit( &s, Magma_DEV, dofs, c_zero, queue );
magma_c_vinit( &t, Magma_DEV, dofs, c_zero, queue );
// solver variables
magmaFloatComplex alpha, beta, omega, rho_old, rho_new;
float nom, betanom, nom0, r0, den, res;
// solver setup
magma_cscal( dofs, c_zero, x->dval, 1) ; // x = 0
magma_ccopy( dofs, b.dval, 1, r.dval, 1 ); // r = b
magma_ccopy( dofs, b.dval, 1, rr.dval, 1 ); // rr = b
nom0 = betanom = magma_scnrm2( dofs, r.dval, 1 ); // nom = || r ||
nom = nom0*nom0;
rho_old = omega = alpha = MAGMA_C_MAKE( 1.0, 0. );
solver_par->init_res = nom0;
magma_c_spmv( c_one, A, r, c_zero, v, queue ); // z = A r
den = MAGMA_C_REAL( magma_cdotc(dofs, v.dval, 1, r.dval, 1) ); // den = z' * r
if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE )
r0 = ATOLERANCE;
if ( nom < r0 ) {
magmablasSetKernelStream( orig_queue );
return MAGMA_SUCCESS;
}
// check positive definite
if (den <= 0.0) {
printf("Operator A is not postive definite. (Ar,r) = %f\n", den);
magmablasSetKernelStream( orig_queue );
return MAGMA_NONSPD;
solver_par->info = MAGMA_NONSPD;;
}
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = nom0;
solver_par->timing[0] = 0.0;
}
// start iteration
for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter;
solver_par->numiter++ ) {
rho_new = magma_cdotc( dofs, rr.dval, 1, r.dval, 1 ); // rho=<rr,r>
beta = rho_new/rho_old * alpha/omega; // beta=rho/rho_old *alpha/omega
magma_cscal( dofs, beta, p.dval, 1 ); // p = beta*p
magma_caxpy( dofs, c_mone * omega * beta, v.dval, 1 , p.dval, 1 );
// p = p-omega*beta*v
magma_caxpy( dofs, c_one, r.dval, 1, p.dval, 1 ); // p = p+r
magma_c_spmv( c_one, A, p, c_zero, v, queue ); // v = Ap
alpha = rho_new / magma_cdotc( dofs, rr.dval, 1, v.dval, 1 );
magma_ccopy( dofs, r.dval, 1 , s.dval, 1 ); // s=r
magma_caxpy( dofs, c_mone * alpha, v.dval, 1 , s.dval, 1 ); // s=s-alpha*v
magma_c_spmv( c_one, A, s, c_zero, t, queue ); // t=As
omega = magma_cdotc( dofs, t.dval, 1, s.dval, 1 ) // omega = <s,t>/<t,t>
/ magma_cdotc( dofs, t.dval, 1, t.dval, 1 );
magma_caxpy( dofs, alpha, p.dval, 1 , x->dval, 1 ); // x=x+alpha*p
magma_caxpy( dofs, omega, s.dval, 1 , x->dval, 1 ); // x=x+omega*s
magma_ccopy( dofs, s.dval, 1 , r.dval, 1 ); // r=s
magma_caxpy( dofs, c_mone * omega, t.dval, 1 , r.dval, 1 ); // r=r-omega*t
res = betanom = magma_scnrm2( dofs, r.dval, 1 );
nom = betanom*betanom;
rho_old = rho_new; // rho_old=rho
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/nom0 < solver_par->epsilon ) {
break;
}
}
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
float residual;
magma_cresidual( A, b, *x, &residual, queue );
solver_par->iter_res = res;
solver_par->final_res = residual;
if ( solver_par->numiter < solver_par->maxiter) {
solver_par->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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
solver_par->info = MAGMA_SLOW_CONVERGENCE;
}
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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
solver_par->info = MAGMA_DIVERGENCE;
}
magma_c_vfree(&r, queue );
magma_c_vfree(&rr, queue );
magma_c_vfree(&p, queue );
magma_c_vfree(&v, queue );
magma_c_vfree(&s, queue );
magma_c_vfree(&t, queue );
magmablasSetKernelStream( orig_queue );
return MAGMA_SUCCESS;
} /* magma_cbicgstab */
extern "C" magma_int_t
magma_ccg(
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 = 0;
// set queue for old dense routines
magma_queue_t orig_queue=NULL;
magmablasGetKernelStream( &orig_queue );
// prepare solver feedback
solver_par->solver = Magma_CG;
solver_par->numiter = 0;
solver_par->info = MAGMA_SUCCESS;
// local variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE;
magma_int_t dofs = A.num_rows * b.num_cols;
// GPU workspace
magma_c_matrix r={Magma_CSR}, p={Magma_CSR}, q={Magma_CSR};
CHECK( magma_cvinit( &r, 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( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver variables
magmaFloatComplex alpha, beta;
float nom, nom0, r0, betanom, betanomsq, den;
// solver setup
CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue));
magma_ccopy( dofs, r.dval, 1, p.dval, 1 ); // p = r
betanom = nom0;
nom = nom0 * nom0; // nom = r' * r
CHECK( magma_c_spmv( c_one, A, p, c_zero, q, queue )); // q = A p
den = MAGMA_C_REAL( magma_cdotc(dofs, p.dval, 1, q.dval, 1) );// den = p dot q
solver_par->init_res = nom0;
if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE )
r0 = ATOLERANCE;
if ( nom < r0 ) {
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
goto cleanup;
}
// check positive definite
if (den <= 0.0) {
printf("Operator A is not postive definite. (Ar,r) = %f\n", den);
magmablasSetKernelStream( orig_queue );
info = MAGMA_NONSPD;
goto cleanup;
}
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = (real_Double_t)nom0;
solver_par->timing[0] = 0.0;
}
solver_par->numiter = 0;
// start iteration
do
{
solver_par->numiter++;
alpha = MAGMA_C_MAKE(nom/den, 0.);
magma_caxpy(dofs, alpha, p.dval, 1, x->dval, 1); // x = x + alpha p
magma_caxpy(dofs, -alpha, q.dval, 1, r.dval, 1); // r = r - alpha q
betanom = magma_scnrm2(dofs, r.dval, 1); // betanom = || r ||
betanomsq = betanom * betanom; // betanoms = r' * r
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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( betanom < r0 ) {
break;
}
beta = MAGMA_C_MAKE(betanomsq/nom, 0.); // beta = betanoms/nom
magma_cscal(dofs, beta, p.dval, 1); // p = beta*p
magma_caxpy(dofs, c_one, r.dval, 1, p.dval, 1); // p = p + r
CHECK( magma_c_spmv( c_one, A, p, c_zero, q, queue )); // q = A p
den = MAGMA_C_REAL(magma_cdotc(dofs, p.dval, 1, q.dval, 1));
// den = p dot q
nom = betanomsq;
}
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->final_res = residual;
if ( solver_par->numiter < solver_par->maxiter ) {
solver_par->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) betanom;
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->epsilon*solver_par->init_res ){
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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
cleanup:
magma_cmfree(&r, queue );
magma_cmfree(&p, queue );
magma_cmfree(&q, queue );
magmablasSetKernelStream( orig_queue );
solver_par->info = info;
return info;
} /* magma_ccg */
extern "C" magma_int_t
magma_cbpcg(
magma_c_sparse_matrix A, magma_c_vector b, magma_c_vector *x,
magma_c_solver_par *solver_par,
magma_c_preconditioner *precond_par,
magma_queue_t queue )
{
// set queue for old dense routines
magma_queue_t orig_queue;
magmablasGetKernelStream( &orig_queue );
magma_int_t stat_dev = 0, stat_cpu = 0;
magma_int_t i, num_vecs = b.num_rows/A.num_rows;
// prepare solver feedback
solver_par->solver = Magma_PCG;
solver_par->numiter = 0;
solver_par->info = MAGMA_SUCCESS;
// local variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE;
magma_int_t dofs = A.num_rows;
// GPU workspace
magma_c_vector r, rt, p, q, h;
magma_c_vinit( &r, Magma_DEV, dofs*num_vecs, c_zero, queue );
magma_c_vinit( &rt, Magma_DEV, dofs*num_vecs, c_zero, queue );
magma_c_vinit( &p, Magma_DEV, dofs*num_vecs, c_zero, queue );
magma_c_vinit( &q, Magma_DEV, dofs*num_vecs, c_zero, queue );
magma_c_vinit( &h, Magma_DEV, dofs*num_vecs, c_zero, queue );
// solver variables
magmaFloatComplex *alpha, *beta;
alpha = NULL;
beta = NULL;
stat_cpu += magma_cmalloc_cpu(&alpha, num_vecs);
stat_cpu += magma_cmalloc_cpu(&beta, num_vecs);
float *nom, *nom0, *r0, *gammaold, *gammanew, *den, *res, *residual;
nom = NULL;
nom0 = NULL;
r0 = NULL;
gammaold = NULL;
gammanew = NULL;
den = NULL;
res = NULL;
residual = NULL;
stat_cpu += magma_smalloc_cpu(&residual, num_vecs);
stat_cpu += magma_smalloc_cpu(&nom, num_vecs);
stat_cpu += magma_smalloc_cpu(&nom0, num_vecs);
stat_cpu += magma_smalloc_cpu(&r0, num_vecs);
stat_cpu += magma_smalloc_cpu(&gammaold, num_vecs);
stat_cpu += magma_smalloc_cpu(&gammanew, num_vecs);
stat_cpu += magma_smalloc_cpu(&den, num_vecs);
stat_cpu += magma_smalloc_cpu(&res, num_vecs);
stat_cpu += magma_smalloc_cpu(&residual, num_vecs);
if( stat_cpu != 0 ){
magma_free_cpu( nom );
magma_free_cpu( nom0 );
magma_free_cpu( r0 );
magma_free_cpu( gammaold );
magma_free_cpu( gammanew );
magma_free_cpu( den );
magma_free_cpu( res );
magma_free_cpu( alpha );
magma_free_cpu( beta );
magma_free_cpu( residual );
magmablasSetKernelStream( orig_queue );
printf("error: memory allocation.\n");
return MAGMA_ERR_HOST_ALLOC;
}
// solver setup
magma_cscal( dofs*num_vecs, c_zero, x->dval, 1) ; // x = 0
magma_ccopy( dofs*num_vecs, b.dval, 1, r.dval, 1 ); // r = b
// preconditioner
magma_c_applyprecond_left( A, r, &rt, precond_par, queue );
magma_c_applyprecond_right( A, rt, &h, precond_par, queue );
magma_ccopy( dofs*num_vecs, h.dval, 1, p.dval, 1 ); // p = h
for( i=0; i<num_vecs; i++) {
nom[i] = MAGMA_C_REAL( magma_cdotc(dofs, r(i), 1, h(i), 1) );
nom0[i] = magma_scnrm2( dofs, r(i), 1 );
}
magma_c_spmv( c_one, A, p, c_zero, q, queue ); // q = A p
for( i=0; i<num_vecs; i++)
den[i] = MAGMA_C_REAL( magma_cdotc(dofs, p(i), 1, q(i), 1) ); // den = p dot q
solver_par->init_res = nom0[0];
if ( (r0[0] = nom[0] * solver_par->epsilon) < ATOLERANCE )
r0[0] = ATOLERANCE;
// check positive definite
if (den[0] <= 0.0) {
printf("Operator A is not postive definite. (Ar,r) = %f\n", den[0]);
magmablasSetKernelStream( orig_queue );
return MAGMA_NONSPD;
solver_par->info = MAGMA_NONSPD;;
}
if ( nom[0] < r0[0] ) {
magmablasSetKernelStream( orig_queue );
return MAGMA_SUCCESS;
}
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = (real_Double_t)nom0[0];
solver_par->timing[0] = 0.0;
}
// start iteration
for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter;
solver_par->numiter++ ) {
// preconditioner
magma_c_applyprecond_left( A, r, &rt, precond_par, queue );
magma_c_applyprecond_right( A, rt, &h, precond_par, queue );
for( i=0; i<num_vecs; i++)
gammanew[i] = MAGMA_C_REAL( magma_cdotc(dofs, r(i), 1, h(i), 1) ); // gn = < r,h>
if ( solver_par->numiter==1 ) {
magma_ccopy( dofs*num_vecs, h.dval, 1, p.dval, 1 ); // p = h
} else {
for( i=0; i<num_vecs; i++) {
beta[i] = MAGMA_C_MAKE(gammanew[i]/gammaold[i], 0.); // beta = gn/go
magma_cscal(dofs, beta[i], p(i), 1); // p = beta*p
magma_caxpy(dofs, c_one, h(i), 1, p(i), 1); // p = p + h
}
}
magma_c_spmv( c_one, A, p, c_zero, q, queue ); // q = A p
// magma_c_bspmv_tuned( dofs, num_vecs, c_one, A, p.dval, c_zero, q.dval, queue );
for( i=0; i<num_vecs; i++) {
den[i] = MAGMA_C_REAL(magma_cdotc(dofs, p(i), 1, q(i), 1));
// den = p dot q
alpha[i] = MAGMA_C_MAKE(gammanew[i]/den[i], 0.);
magma_caxpy(dofs, alpha[i], p(i), 1, x->dval+dofs*i, 1); // x = x + alpha p
magma_caxpy(dofs, -alpha[i], q(i), 1, r(i), 1); // r = r - alpha q
gammaold[i] = gammanew[i];
res[i] = magma_scnrm2( dofs, r(i), 1 );
}
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[0];
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( res[0]/nom0[0] < solver_par->epsilon ) {
break;
}
}
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
magma_cresidual( A, b, *x, residual, queue );
solver_par->iter_res = res[0];
solver_par->final_res = residual[0];
if ( solver_par->numiter < solver_par->maxiter) {
solver_par->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[0];
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
solver_par->info = MAGMA_SLOW_CONVERGENCE;
}
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[0];
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
solver_par->info = MAGMA_DIVERGENCE;
}
for( i=0; i<num_vecs; i++) {
printf("%.4e ",res[i]);
}
printf("\n");
for( i=0; i<num_vecs; i++) {
printf("%.4e ",residual[i]);
}
printf("\n");
magma_c_vfree(&r, queue );
magma_c_vfree(&rt, queue );
magma_c_vfree(&p, queue );
magma_c_vfree(&q, queue );
magma_c_vfree(&h, queue );
magma_free_cpu(alpha);
magma_free_cpu(beta);
magma_free_cpu(nom);
magma_free_cpu(nom0);
magma_free_cpu(r0);
magma_free_cpu(gammaold);
magma_free_cpu(gammanew);
magma_free_cpu(den);
magma_free_cpu(res);
magmablasSetKernelStream( orig_queue );
return MAGMA_SUCCESS;
} /* magma_cbpcg */
extern "C" magma_int_t
magma_cpidr_strms(
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_PIDRMERGE;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
solver_par->init_res = 0.0;
solver_par->final_res = 0.0;
solver_par->iter_res = 0.0;
solver_par->runtime = 0.0;
// constants
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_n_one = MAGMA_C_NEG_ONE;
// internal user options
const magma_int_t smoothing = 1; // 0 = disable, 1 = enable
const float angle = 0.7; // [0-1]
// local variables
magma_int_t iseed[4] = {0, 0, 0, 1};
magma_int_t dof;
magma_int_t s;
magma_int_t distr;
magma_int_t k, i, sk;
magma_int_t innerflag;
magma_int_t ldd;
magma_int_t q;
float residual;
float nrm;
float nrmb;
float nrmr;
float nrmt;
float rho;
magmaFloatComplex om;
magmaFloatComplex gamma;
// matrices and vectors
magma_c_matrix dxs = {Magma_CSR};
magma_c_matrix dr = {Magma_CSR}, drs = {Magma_CSR};
magma_c_matrix dP = {Magma_CSR}, dP1 = {Magma_CSR};
magma_c_matrix dG = {Magma_CSR}, dGcol = {Magma_CSR};
magma_c_matrix dU = {Magma_CSR};
magma_c_matrix dM = {Magma_CSR};
magma_c_matrix df = {Magma_CSR};
magma_c_matrix dt = {Magma_CSR}, dtt = {Magma_CSR};
magma_c_matrix dc = {Magma_CSR};
magma_c_matrix dv = {Magma_CSR};
magma_c_matrix dlu = {Magma_CSR};
magma_c_matrix dskp = {Magma_CSR};
magma_c_matrix dalpha = {Magma_CSR};
magma_c_matrix dbeta = {Magma_CSR};
magmaFloatComplex *hMdiag = NULL;
magmaFloatComplex *hskp = NULL;
magmaFloatComplex *halpha = NULL;
magmaFloatComplex *hbeta = NULL;
magmaFloatComplex *d1 = NULL, *d2 = NULL;
// queue variables
const magma_int_t nqueues = 3; // number of queues
magma_queue_t queues[nqueues];
// chronometry
real_Double_t tempo1, tempo2;
// create additional queues
queues[0] = queue;
for ( q = 1; q < nqueues; q++ ) {
magma_queue_create( queue->device(), &(queues[q]) );
}
// initial s space
// TODO: add option for 's' (shadow space number)
// Hack: uses '--restart' option as the shadow space number.
// This is not a good idea because the default value of restart option is used to detect
// if the user provided a custom restart. This means that if the default restart value
// is changed then the code will think it was the user (unless the default value is
// also updated in the 'if' statement below.
s = 1;
if ( solver_par->restart != 50 ) {
if ( solver_par->restart > A.num_cols ) {
s = A.num_cols;
} else {
s = solver_par->restart;
}
}
solver_par->restart = s;
// set max iterations
solver_par->maxiter = min( 2 * A.num_cols, solver_par->maxiter );
// check if matrix A is square
if ( A.num_rows != A.num_cols ) {
//printf("Matrix A is not square.\n");
info = MAGMA_ERR_NOT_SUPPORTED;
goto cleanup;
}
// |b|
nrmb = magma_scnrm2( b.num_rows, b.dval, 1, queue );
if ( nrmb == 0.0 ) {
magma_cscal( x->num_rows, MAGMA_C_ZERO, x->dval, 1, queue );
info = MAGMA_SUCCESS;
goto cleanup;
}
// t = 0
// make t twice as large to contain both, dt and dr
ldd = magma_roundup( b.num_rows, 32 );
CHECK( magma_cvinit( &dt, Magma_DEV, ldd, 2, c_zero, queue ));
dt.num_rows = b.num_rows;
dt.num_cols = 1;
dt.nnz = dt.num_rows;
// redirect the dr.dval to the second part of dt
CHECK( magma_cvinit( &dr, Magma_DEV, b.num_rows, 1, c_zero, queue ));
magma_free( dr.dval );
dr.dval = dt.dval + ldd;
// r = b - A x
CHECK( magma_cresidualvec( A, b, *x, &dr, &nrmr, queue ));
// |r|
solver_par->init_res = nrmr;
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)nrmr;
}
// check if initial is guess good enough
if ( nrmr <= solver_par->atol ||
nrmr/nrmb <= solver_par->rtol ) {
info = MAGMA_SUCCESS;
goto cleanup;
}
// P = randn(n, s)
// P = ortho(P)
//---------------------------------------
// P = 0.0
CHECK( magma_cvinit( &dP, Magma_CPU, A.num_cols, s, c_zero, queue ));
// P = randn(n, s)
distr = 3; // 1 = unif (0,1), 2 = unif (-1,1), 3 = normal (0,1)
dof = dP.num_rows * dP.num_cols;
lapackf77_clarnv( &distr, iseed, &dof, dP.val );
// transfer P to device
CHECK( magma_cmtransfer( dP, &dP1, Magma_CPU, Magma_DEV, queue ));
magma_cmfree( &dP, queue );
// P = ortho(P1)
if ( dP1.num_cols > 1 ) {
// P = magma_cqr(P1), QR factorization
CHECK( magma_cqr( dP1.num_rows, dP1.num_cols, dP1, dP1.ld, &dP, NULL, queue ));
} else {
// P = P1 / |P1|
nrm = magma_scnrm2( dof, dP1.dval, 1, queue );
nrm = 1.0 / nrm;
magma_csscal( dof, nrm, dP1.dval, 1, queue );
CHECK( magma_cmtransfer( dP1, &dP, Magma_DEV, Magma_DEV, queue ));
}
magma_cmfree( &dP1, queue );
//---------------------------------------
// allocate memory for the scalar products
CHECK( magma_cmalloc_pinned( &hskp, 5 ));
CHECK( magma_cvinit( &dskp, Magma_DEV, 4, 1, c_zero, queue ));
CHECK( magma_cmalloc_pinned( &halpha, s ));
CHECK( magma_cvinit( &dalpha, Magma_DEV, s, 1, c_zero, queue ));
CHECK( magma_cmalloc_pinned( &hbeta, s ));
CHECK( magma_cvinit( &dbeta, Magma_DEV, s, 1, c_zero, queue ));
// workspace for merged dot product
CHECK( magma_cmalloc( &d1, max(2, s) * b.num_rows ));
CHECK( magma_cmalloc( &d2, max(2, s) * b.num_rows ));
// smoothing enabled
if ( smoothing > 0 ) {
// set smoothing solution vector
CHECK( magma_cmtransfer( *x, &dxs, Magma_DEV, Magma_DEV, queue ));
// tt = 0
// make tt twice as large to contain both, dtt and drs
ldd = magma_roundup( b.num_rows, 32 );
CHECK( magma_cvinit( &dtt, Magma_DEV, ldd, 2, c_zero, queue ));
dtt.num_rows = dr.num_rows;
dtt.num_cols = 1;
dtt.nnz = dtt.num_rows;
// redirect the drs.dval to the second part of dtt
CHECK( magma_cvinit( &drs, Magma_DEV, dr.num_rows, 1, c_zero, queue ));
magma_free( drs.dval );
drs.dval = dtt.dval + ldd;
// set smoothing residual vector
magma_ccopyvector( dr.num_rows, dr.dval, 1, drs.dval, 1, queue );
}
// G(n,s) = 0
if ( s > 1 ) {
ldd = magma_roundup( A.num_rows, 32 );
CHECK( magma_cvinit( &dG, Magma_DEV, ldd, s, c_zero, queue ));
dG.num_rows = A.num_rows;
} else {
CHECK( magma_cvinit( &dG, Magma_DEV, A.num_rows, s, c_zero, queue ));
}
// dGcol represents a single column of dG, array pointer is set inside loop
CHECK( magma_cvinit( &dGcol, Magma_DEV, dG.num_rows, 1, c_zero, queue ));
magma_free( dGcol.dval );
// U(n,s) = 0
if ( s > 1 ) {
ldd = magma_roundup( A.num_cols, 32 );
CHECK( magma_cvinit( &dU, Magma_DEV, ldd, s, c_zero, queue ));
dU.num_rows = A.num_cols;
} else {
CHECK( magma_cvinit( &dU, Magma_DEV, A.num_cols, s, c_zero, queue ));
}
// M(s,s) = I
CHECK( magma_cvinit( &dM, Magma_DEV, s, s, c_zero, queue ));
CHECK( magma_cmalloc_pinned( &hMdiag, s ));
magmablas_claset( MagmaFull, dM.num_rows, dM.num_cols, c_zero, c_one, dM.dval, dM.ld, queue );
// f = 0
CHECK( magma_cvinit( &df, Magma_DEV, dP.num_cols, 1, c_zero, queue ));
// c = 0
CHECK( magma_cvinit( &dc, Magma_DEV, dM.num_cols, 1, c_zero, queue ));
// v = r
CHECK( magma_cmtransfer( dr, &dv, Magma_DEV, Magma_DEV, queue ));
// lu = 0
CHECK( magma_cvinit( &dlu, Magma_DEV, dr.num_rows, 1, c_zero, queue ));
//--------------START TIME---------------
// chronometry
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->timing[0] = 0.0;
}
om = MAGMA_C_ONE;
gamma = MAGMA_C_ZERO;
innerflag = 0;
// start iteration
do
{
solver_par->numiter++;
// new RHS for small systems
// f = P' r
// Q1
magma_cgemvmdot_shfl( dP.num_rows, dP.num_cols, dP.dval, dr.dval, d1, d2, df.dval, queues[1] );
// skp[4] = f(k)
// Q1
magma_cgetvector_async( 1, df.dval, 1, &hskp[4], 1, queues[1] );
// c(k:s) = f(k:s)
// Q1
magma_ccopyvector_async( s, df.dval, 1, dc.dval, 1, queues[1] );
// c(k:s) = M(k:s,k:s) \ f(k:s)
// Q1
magma_ctrsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, s, dM.dval, dM.ld, dc.dval, 1, queues[1] );
// shadow space loop
for ( k = 0; k < s; ++k ) {
sk = s - k;
dGcol.dval = dG.dval + k * dG.ld;
// v = r - G(:,k:s) c(k:s)
// Q1
magmablas_cgemv( MagmaNoTrans, dG.num_rows, sk, c_n_one, dGcol.dval, dG.ld, &dc.dval[k], 1, c_one, dv.dval, 1, queues[1] );
// preconditioning operation
// v = L \ v;
// v = U \ v;
// Q1
CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, dv, &dlu, precond_par, queues[1] ));
CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, dlu, &dv, precond_par, queues[1] ));
// sync Q0 --> U(:,k) = U(:,k) - U(:,1:k) * alpha(1:k)
magma_queue_sync( queues[0] );
// U(:,k) = om * v + U(:,k:s) c(k:s)
// Q1
magmablas_cgemv( MagmaNoTrans, dU.num_rows, sk, c_one, &dU.dval[k*dU.ld], dU.ld, &dc.dval[k], 1, om, dv.dval, 1, queues[1] );
// G(:,k) = A U(:,k)
// Q1
CHECK( magma_c_spmv( c_one, A, dv, c_zero, dGcol, queues[1] ));
solver_par->spmv_count++;
// bi-orthogonalize the new basis vectors
for ( i = 0; i < k; ++i ) {
// alpha = P(:,i)' G(:,k)
// Q1
halpha[i] = magma_cdotc( dP.num_rows, &dP.dval[i*dP.ld], 1, dGcol.dval, 1, queues[1] );
// implicit sync Q1 --> alpha = P(:,i)' G(:,k)
// alpha = alpha / M(i,i)
halpha[i] = halpha[i] / hMdiag[i];
// G(:,k) = G(:,k) - alpha * G(:,i)
// Q1
magma_caxpy( dG.num_rows, -halpha[i], &dG.dval[i*dG.ld], 1, dGcol.dval, 1, queues[1] );
}
// sync Q1 --> compute new G, skp[4] = f(k
magma_queue_sync( queues[1] );
// new column of M = P'G, first k-1 entries are zero
// M(k:s,k) = P(:,k:s)' G(:,k)
// Q2
magma_cgemvmdot_shfl( dP.num_rows, sk, &dP.dval[k*dP.ld], dGcol.dval, d1, d2, &dM.dval[k*dM.ld+k], queues[2] );
// U(:,k) = v
// Q0
magma_ccopyvector_async( dU.num_rows, dv.dval, 1, &dU.dval[k*dU.ld], 1, queues[0] );
// non-first s iteration
if ( k > 0 ) {
// alpha = dalpha
// Q0
magma_csetvector_async( k, halpha, 1, dalpha.dval, 1, queues[0] );
// U update outside of loop using GEMV
// U(:,k) = U(:,k) - U(:,1:k) * alpha(1:k)
// Q0
magmablas_cgemv( MagmaNoTrans, dU.num_rows, k, c_n_one, dU.dval, dU.ld, dalpha.dval, 1, c_one, &dU.dval[k*dU.ld], 1, queues[0] );
}
// Mdiag(k) = M(k,k)
// Q2
magma_cgetvector( 1, &dM.dval[k*dM.ld+k], 1, &hMdiag[k], 1, queues[2] );
// implicit sync Q2 --> Mdiag(k) = M(k,k)
// check M(k,k) == 0
if ( MAGMA_C_EQUAL(hMdiag[k], MAGMA_C_ZERO) ) {
innerflag = 1;
info = MAGMA_DIVERGENCE;
break;
}
// beta = f(k) / M(k,k)
hbeta[k] = hskp[4] / hMdiag[k];
// check for nan
if ( magma_c_isnan( hbeta[k] ) || magma_c_isinf( hbeta[k] )) {
innerflag = 1;
info = MAGMA_DIVERGENCE;
break;
}
// non-last s iteration
if ( (k + 1) < s ) {
// f(k+1:s) = f(k+1:s) - beta * M(k+1:s,k)
// Q1
magma_caxpy( sk-1, -hbeta[k], &dM.dval[k*dM.ld+(k+1)], 1, &df.dval[k+1], 1, queues[1] );
// c(k+1:s) = f(k+1:s)
// Q1
magma_ccopyvector_async( sk-1, &df.dval[k+1], 1, &dc.dval[k+1], 1, queues[1] );
// c(k+1:s) = M(k+1:s,k+1:s) \ f(k+1:s)
// Q1
magma_ctrsv( MagmaLower, MagmaNoTrans, MagmaNonUnit, sk-1, &dM.dval[(k+1)*dM.ld+(k+1)], dM.ld, &dc.dval[k+1], 1, queues[1] );
// skp[4] = f(k+1)
// Q1
magma_cgetvector_async( 1, &df.dval[k+1], 1, &hskp[4], 1, queues[1] );
}
// r = r - beta * G(:,k)
// Q2
magma_caxpy( dr.num_rows, -hbeta[k], dGcol.dval, 1, dr.dval, 1, queues[2] );
// smoothing disabled
if ( smoothing <= 0 ) {
// |r|
// Q2
nrmr = magma_scnrm2( dr.num_rows, dr.dval, 1, queues[2] );
// implicit sync Q2 --> |r|
// v = r
// Q1
magma_ccopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[1] );
// smoothing enabled
} else {
// x = x + beta * U(:,k)
// Q0
magma_caxpy( x->num_rows, hbeta[k], &dU.dval[k*dU.ld], 1, x->dval, 1, queues[0] );
// smoothing operation
//---------------------------------------
// t = rs - r
// Q2
magma_cidr_smoothing_1( drs.num_rows, drs.num_cols, drs.dval, dr.dval, dtt.dval, queues[2] );
// t't
// t'rs
// Q2
CHECK( magma_cgemvmdot_shfl( dt.ld, 2, dtt.dval, dtt.dval, d1, d2, &dskp.dval[2], queues[2] ));
// skp[2-3] = dskp[2-3]
// Q2
magma_cgetvector( 2, &dskp.dval[2], 1, &hskp[2], 1, queues[2] );
// implicit sync Q2 --> skp = dskp
// gamma = (t' * rs) / (t' * t)
gamma = hskp[3] / hskp[2];
// xs = xs - gamma * (xs - x)
// Q0
magma_cidr_smoothing_2( dxs.num_rows, dxs.num_cols, -gamma, x->dval, dxs.dval, queues[0] );
// v = r
// Q1
magma_ccopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[1] );
// rs = rs - gamma * t
// Q2
magma_caxpy( drs.num_rows, -gamma, dtt.dval, 1, drs.dval, 1, queues[2] );
// |rs|
// Q2
nrmr = magma_scnrm2( drs.num_rows, drs.dval, 1, queues[2] );
// implicit sync Q2 --> |r|
//---------------------------------------
}
// store current timing and residual
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)nrmr;
solver_par->timing[(solver_par->numiter) / solver_par->verbose]
= (real_Double_t)tempo2 - tempo1;
}
}
// check convergence or iteration limit
if ( nrmr <= solver_par->atol ||
nrmr/nrmb <= solver_par->rtol ) {
s = k + 1; // for the x-update outside the loop
innerflag = 2;
info = MAGMA_SUCCESS;
break;
}
}
// smoothing disabled
if ( smoothing <= 0 && innerflag != 1 ) {
// dbeta(1:s) = beta(1:s)
// Q0
magma_csetvector_async( s, hbeta, 1, dbeta.dval, 1, queues[0] );
// x = x + U(:,1:s) * beta(1:s)
// Q0
magmablas_cgemv( MagmaNoTrans, dU.num_rows, s, c_one, dU.dval, dU.ld, dbeta.dval, 1, c_one, x->dval, 1, queues[0] );
}
// check convergence or iteration limit or invalid result of inner loop
if ( innerflag > 0 ) {
break;
}
// preconditioning operation
// v = L \ v;
// v = U \ v;
// Q2
CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, dv, &dlu, precond_par, queues[2] ));
CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, dlu, &dv, precond_par, queues[2] ));
// t = A v
// Q2
CHECK( magma_c_spmv( c_one, A, dv, c_zero, dt, queues[2] ));
solver_par->spmv_count++;
// computation of a new omega
//---------------------------------------
// t't
// t'r
// Q2
CHECK( magma_cgemvmdot_shfl( dt.ld, 2, dt.dval, dt.dval, d1, d2, dskp.dval, queues[2] ));
// skp[0-2] = dskp[0-2]
// Q2
magma_cgetvector( 2, dskp.dval, 1, hskp, 1, queues[2] );
// implicit sync Q2 --> skp = dskp
// |t|
nrmt = magma_ssqrt( MAGMA_C_REAL(hskp[0]) );
// rho = abs((t' * r) / (|t| * |r|))
rho = MAGMA_D_ABS( MAGMA_C_REAL(hskp[1]) / (nrmt * nrmr) );
// om = (t' * r) / (|t| * |t|)
om = hskp[1] / hskp[0];
if ( rho < angle ) {
om = (om * angle) / rho;
}
//---------------------------------------
if ( MAGMA_C_EQUAL(om, MAGMA_C_ZERO) ) {
info = MAGMA_DIVERGENCE;
break;
}
// sync Q1 --> v = r
magma_queue_sync( queues[1] );
// r = r - om * t
// Q2
magma_caxpy( dr.num_rows, -om, dt.dval, 1, dr.dval, 1, queues[2] );
// x = x + om * v
// Q0
magma_caxpy( x->num_rows, om, dv.dval, 1, x->dval, 1, queues[0] );
// smoothing disabled
if ( smoothing <= 0 ) {
// |r|
// Q2
nrmr = magma_scnrm2( dr.num_rows, dr.dval, 1, queues[2] );
// implicit sync Q2 --> |r|
// v = r
// Q1
magma_ccopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[1] );
// smoothing enabled
} else {
// smoothing operation
//---------------------------------------
// t = rs - r
// Q2
magma_cidr_smoothing_1( drs.num_rows, drs.num_cols, drs.dval, dr.dval, dtt.dval, queues[2] );
// t't
// t'rs
// Q2
CHECK( magma_cgemvmdot_shfl( dt.ld, 2, dtt.dval, dtt.dval, d1, d2, &dskp.dval[2], queues[2] ));
// skp[2-3] = dskp[2-3]
// Q2
magma_cgetvector( 2, &dskp.dval[2], 1, &hskp[2], 1, queues[2] );
// implicit sync Q2 --> skp = dskp
// gamma = (t' * rs) / (t' * t)
gamma = hskp[3] / hskp[2];
// xs = xs - gamma * (xs - x)
// Q0
magma_cidr_smoothing_2( dxs.num_rows, dxs.num_cols, -gamma, x->dval, dxs.dval, queues[0] );
// v = r
// Q1
magma_ccopyvector_async( dr.num_rows, dr.dval, 1, dv.dval, 1, queues[1] );
// rs = rs - gamma * (rs - r)
// Q2
magma_caxpy( drs.num_rows, -gamma, dtt.dval, 1, drs.dval, 1, queues[2] );
// |rs|
// Q2
nrmr = magma_scnrm2( drs.num_rows, drs.dval, 1, queues[2] );
// implicit sync Q2 --> |r|
//---------------------------------------
}
// store current timing and residual
if ( solver_par->verbose > 0 ) {
tempo2 = magma_sync_wtime( queue );
magma_queue_sync( queue );
if ( (solver_par->numiter) % solver_par->verbose == 0 ) {
solver_par->res_vec[(solver_par->numiter) / solver_par->verbose]
= (real_Double_t)nrmr;
solver_par->timing[(solver_par->numiter) / solver_par->verbose]
= (real_Double_t)tempo2 - tempo1;
}
}
// check convergence or iteration limit
if ( nrmr <= solver_par->atol ||
nrmr/nrmb <= solver_par->rtol ) {
info = MAGMA_SUCCESS;
break;
}
}
while ( solver_par->numiter + 1 <= solver_par->maxiter );
// sync all queues
for ( q = 0; q < nqueues; q++ ) {
magma_queue_sync( queues[q] );
}
// smoothing enabled
if ( smoothing > 0 ) {
// x = xs
magma_ccopyvector_async( x->num_rows, dxs.dval, 1, x->dval, 1, queue );
// r = rs
magma_ccopyvector_async( dr.num_rows, drs.dval, 1, dr.dval, 1, queue );
}
// get last iteration timing
tempo2 = magma_sync_wtime( queue );
magma_queue_sync( queue );
solver_par->runtime = (real_Double_t)tempo2 - tempo1;
//--------------STOP TIME----------------
// get final stats
solver_par->iter_res = nrmr;
CHECK( magma_cresidualvec( A, b, *x, &dr, &residual, queue ));
solver_par->final_res = residual;
// set solver conclusion
if ( info != MAGMA_SUCCESS && info != MAGMA_DIVERGENCE ) {
if ( solver_par->init_res > solver_par->final_res ) {
info = MAGMA_SLOW_CONVERGENCE;
}
}
cleanup:
// free resources
// sync all queues, destory additional queues
magma_queue_sync( queues[0] );
for ( q = 1; q < nqueues; q++ ) {
magma_queue_sync( queues[q] );
magma_queue_destroy( queues[q] );
}
// smoothing enabled
if ( smoothing > 0 ) {
drs.dval = NULL; // needed because its pointer is redirected to dtt
magma_cmfree( &dxs, queue );
magma_cmfree( &drs, queue );
magma_cmfree( &dtt, queue );
}
dr.dval = NULL; // needed because its pointer is redirected to dt
dGcol.dval = NULL; // needed because its pointer is redirected to dG
magma_cmfree( &dr, queue );
magma_cmfree( &dP, queue );
magma_cmfree( &dP1, queue );
magma_cmfree( &dG, queue );
magma_cmfree( &dGcol, queue );
magma_cmfree( &dU, queue );
magma_cmfree( &dM, queue );
magma_cmfree( &df, queue );
magma_cmfree( &dt, queue );
magma_cmfree( &dc, queue );
magma_cmfree( &dv, queue );
magma_cmfree( &dlu, queue );
magma_cmfree( &dskp, queue );
magma_cmfree( &dalpha, queue );
magma_cmfree( &dbeta, queue );
magma_free_pinned( hMdiag );
magma_free_pinned( hskp );
magma_free_pinned( halpha );
magma_free_pinned( hbeta );
magma_free( d1 );
magma_free( d2 );
solver_par->info = info;
return info;
/* magma_cpidr_strms */
}
extern "C" magma_int_t
magma_cpcgs(
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;
// constants
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
// solver variables
float nom0, r0, res=0, 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;
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_isnan_inf( rho ) ){
info = MAGMA_DIVERGENCE;
break;
}
if ( solver_par->numiter > 1 ) { // direction vectors
beta = rho / rho_l;
magma_ccopy( dofs, r.dval, 1, u.dval, 1, queue ); // u = r
magma_caxpy( dofs, beta, q.dval, 1, u.dval, 1, queue ); // u = r + beta q
magma_cscal( dofs, beta, p.dval, 1, queue ); // p = beta*p
magma_caxpy( dofs, c_one, q.dval, 1, p.dval, 1, queue ); // p = q + beta*p
magma_cscal( dofs, beta, p.dval, 1, queue ); // p = beta*(q + beta*p)
magma_caxpy( dofs, c_one, u.dval, 1, p.dval, 1, queue ); // p = u + beta*(q + beta*p)
//u = r + beta*q;
//p = u + beta*( q + beta*p );
}
else{
magma_ccopy( dofs, r.dval, 1, u.dval, 1, queue ); // u = r
magma_ccopy( dofs, r.dval, 1, p.dval, 1, queue ); // p = r
}
// preconditioner
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 ));
// SpMV
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_ccopy( dofs, u.dval, 1, q.dval, 1, queue ); // q = u
magma_caxpy( dofs, -alpha, v_hat.dval, 1, q.dval, 1, queue ); // q = u - alpha v_hat
magma_ccopy( dofs, u.dval, 1, t.dval, 1, queue ); // t = q
magma_caxpy( dofs, c_one, q.dval, 1, t.dval, 1, queue ); // t = u + q
// preconditioner
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 ));
// SpMV
CHECK( magma_c_spmv( c_one, A, u_hat, c_zero, t, queue )); // t = A u_hat
solver_par->spmv_count++;
magma_caxpy( dofs, alpha, u_hat.dval, 1, x->dval, 1, queue ); // x = x + alpha u_hat
magma_caxpy( dofs, c_neg_one*alpha, t.dval, 1, r.dval, 1, queue ); // r = r -alpha*A 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 ) {
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 */
extern "C" magma_int_t
magma_ctfqmr(
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;
// prepare solver feedback
solver_par->solver = Magma_TFQMR;
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; //, normx, normd, normr_act;
magmaFloatComplex rho = c_one, rho_l = c_one, eta = c_zero , c = c_zero ,
theta = c_zero , tau = c_zero, alpha = c_one, beta = c_zero,
sigma = c_zero;
magma_int_t dofs = A.num_rows* b.num_cols;
// magma_int_t stag = 0;
// GPU workspace
magma_c_matrix r={Magma_CSR}, r_tld={Magma_CSR}, pu_m={Magma_CSR},
d={Magma_CSR}, w={Magma_CSR}, v={Magma_CSR},
u_mp1={Magma_CSR}, u_m={Magma_CSR}, Au={Magma_CSR},
Ad={Magma_CSR}, Au_new={Magma_CSR};
CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &u_mp1,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( &u_m, Magma_DEV, A.num_rows, b.num_cols, c_one, queue ));
CHECK( magma_cvinit( &pu_m, Magma_DEV, A.num_rows, b.num_cols, c_one, queue ));
CHECK( magma_cvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &w, Magma_DEV, A.num_rows, b.num_cols, c_one, queue ));
CHECK( magma_cvinit( &Ad, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Au_new, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &Au, Magma_DEV, A.num_rows, b.num_cols, c_one, queue ));
// solver setup
CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue));
solver_par->init_res = nom0;
magma_ccopy( dofs, r.dval, 1, r_tld.dval, 1, queue );
magma_ccopy( dofs, r.dval, 1, w.dval, 1, queue );
magma_ccopy( dofs, r.dval, 1, u_m.dval, 1, queue );
magma_ccopy( dofs, u_m.dval, 1, pu_m.dval, 1, queue );
CHECK( magma_c_spmv( c_one, A, pu_m, c_zero, v, queue )); // v = A u
magma_ccopy( dofs, v.dval, 1, Au.dval, 1, 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;
}
tau = magma_csqrt( magma_cdotc( dofs, r.dval, 1, r_tld.dval, 1, queue ));
rho = magma_cdotc( dofs, r.dval, 1, r_tld.dval, 1, queue );
rho_l = rho;
//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( solver_par->numiter%2 == 1 ){
alpha = rho / magma_cdotc( dofs, v.dval, 1, r_tld.dval, 1, queue );
magma_ccopy( dofs, u_m.dval, 1, u_mp1.dval, 1, queue );
magma_caxpy( dofs, -alpha, v.dval, 1, u_mp1.dval, 1, queue ); // u_mp1 = u_m - alpha*v;
}
magma_caxpy( dofs, -alpha, Au.dval, 1, w.dval, 1, queue ); // w = w - alpha*Au;
sigma = theta * theta / alpha * eta;
magma_cscal( dofs, sigma, d.dval, 1, queue );
magma_caxpy( dofs, c_one, pu_m.dval, 1, d.dval, 1, queue ); // d = pu_m + sigma*d;
magma_cscal( dofs, sigma, Ad.dval, 1, queue );
magma_caxpy( dofs, c_one, Au.dval, 1, Ad.dval, 1, queue ); // Ad = Au + sigma*Ad;
theta = magma_csqrt( magma_cdotc(dofs, w.dval, 1, w.dval, 1, queue) ) / tau;
c = c_one / magma_csqrt( c_one + theta*theta );
tau = tau * theta *c;
eta = c * c * alpha;
// normd = magma_scnrm2( dofs, d.dval, 1, queue );
// normx = magma_scnrm2( dofs, x->dval, 1, queue );
//
//
// if ( MAGMA_C_ABS(eta)*normd < 1e-15*normx ){
// stag = stag + 1;
// } else {
// stag = 0;
// }
magma_caxpy( dofs, eta, d.dval, 1, x->dval, 1, queue ); // x = x + eta * d
magma_caxpy( dofs, -eta, Ad.dval, 1, r.dval, 1, queue ); // r = r - eta * Ad
res = magma_scnrm2( dofs, r.dval, 1, queue );
// normr_act = res;
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 ){
info = MAGMA_SUCCESS;
break;
}
// if (normr_act < normrmin){ //update minimal norm quantities
// normrmin = normr_act;
// //xmin = x;
// }
// if ( stag >= maxstagsteps ){ // 3 iterates are the same
// break;
// }
if( solver_par->numiter%2 == 0 ){
rho = magma_cdotc( dofs, w.dval, 1, r_tld.dval, 1, queue );
beta = rho / rho_l;
rho_l = rho;
magma_ccopy( dofs, w.dval, 1, u_mp1.dval, 1, queue );
magma_caxpy( dofs, beta, u_m.dval, 1, u_mp1.dval, 1, queue ); // u_mp1 = w + beta*u_m;
}
magma_ccopy( dofs, u_mp1.dval, 1, pu_m.dval, 1, queue );
CHECK( magma_c_spmv( c_one, A, pu_m, c_zero, Au_new, queue )); // Au_new = A pu_m
solver_par->spmv_count++;
if( solver_par->numiter%2 == 0 ){
magma_cscal( dofs, beta*beta, v.dval, 1, queue );
magma_caxpy( dofs, beta, Au.dval, 1, v.dval, 1, queue );
magma_caxpy( dofs, c_one, Au_new.dval, 1, v.dval, 1, queue ); // v = Au_new + beta*(Au+beta*v);
}
magma_ccopy( dofs, Au_new.dval, 1, Au.dval, 1, queue );
magma_ccopy( dofs, u_mp1.dval, 1, u_m.dval, 1, queue );
}
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(&r_tld, queue );
magma_cmfree(&d, queue );
magma_cmfree(&w, queue );
magma_cmfree(&v, queue );
magma_cmfree(&pu_m, queue );
magma_cmfree(&u_m, queue );
magma_cmfree(&u_mp1, queue );
magma_cmfree(&d, queue );
magma_cmfree(&Au, queue );
magma_cmfree(&Au_new, queue );
magma_cmfree(&Ad, queue );
solver_par->info = info;
return info;
} /* magma_ctfqmr */
extern "C" magma_int_t
magma_citerref(
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 = 0;
// set queue for old dense routines
magma_queue_t orig_queue=NULL;
magmablasGetKernelStream( &orig_queue );
// some useful variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE,
c_mone = MAGMA_C_NEG_ONE;
// prepare solver feedback
solver_par->solver = Magma_ITERREF;
solver_par->numiter = 0;
solver_par->info = MAGMA_SUCCESS;
magma_int_t dofs = A.num_rows*b.num_cols;
// solver variables
float nom, nom0, r0;
// workspace
magma_c_matrix r={Magma_CSR}, z={Magma_CSR};
CHECK( magma_cvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_cvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
float residual;
CHECK( magma_cresidual( A, b, *x, &residual, queue ));
solver_par->init_res = residual;
// solver setup
magma_cscal( dofs, c_zero, x->dval, 1) ; // x = 0
//CHECK( magma_cresidualvec( A, b, *x, &r, nom, queue));
magma_ccopy( dofs, b.dval, 1, r.dval, 1 ); // r = b
nom0 = magma_scnrm2(dofs, r.dval, 1); // nom0 = || r ||
nom = nom0 * nom0;
solver_par->init_res = nom0;
if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE )
r0 = ATOLERANCE;
if ( nom < r0 ) {
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
goto cleanup;
}
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = nom0;
solver_par->timing[0] = 0.0;
}
// start iteration
for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter;
solver_par->numiter++ ) {
magma_cscal( dofs, MAGMA_C_MAKE(1./nom, 0.), r.dval, 1) ; // scale it
CHECK( magma_c_precond( A, r, &z, precond_par, queue )); // inner solver: A * z = r
magma_cscal( dofs, MAGMA_C_MAKE(nom, 0.), z.dval, 1) ; // scale it
magma_caxpy(dofs, c_one, z.dval, 1, x->dval, 1); // x = x + z
CHECK( magma_c_spmv( c_mone, A, *x, c_zero, r, queue )); // r = - A x
magma_caxpy(dofs, c_one, b.dval, 1, r.dval, 1); // r = r + b
nom = magma_scnrm2(dofs, r.dval, 1); // nom = || r ||
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) nom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( nom < r0 ) {
break;
}
}
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
CHECK( magma_cresidualvec( A, b, *x, &r, &residual, queue));
solver_par->final_res = residual;
solver_par->iter_res = nom;
if ( solver_par->numiter < solver_par->maxiter ) {
solver_par->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) nom;
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->epsilon*solver_par->init_res ){
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) nom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
cleanup:
magma_cmfree(&r, queue );
magma_cmfree(&z, queue );
magmablasSetKernelStream( orig_queue );
solver_par->info = info;
return info;
} /* magma_citerref */
extern "C" magma_int_t
magma_cpcg(
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_PCG;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// solver variables
magmaFloatComplex alpha, beta;
float nom0, r0, res, nomb;
magmaFloatComplex den, gammanew, gammaold = MAGMA_C_MAKE(1.0,0.0);
// local variables
magmaFloatComplex c_zero = MAGMA_C_ZERO, c_one = MAGMA_C_ONE;
magma_int_t dofs = A.num_rows* b.num_cols;
// GPU workspace
magma_c_matrix r={Magma_CSR}, rt={Magma_CSR}, p={Magma_CSR}, q={Magma_CSR}, h={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( &p, 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( &h, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver setup
CHECK( magma_cresidualvec( A, b, *x, &r, &nom0, queue));
// preconditioner
CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue ));
CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue ));
magma_ccopy( dofs, h.dval, 1, p.dval, 1, queue ); // p = h
CHECK( magma_c_spmv( c_one, A, p, c_zero, q, queue )); // q = A p
den = magma_cdotc( dofs, p.dval, 1, q.dval, 1, queue ); // den = p dot q
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 ( nomb < r0 ) {
info = MAGMA_SUCCESS;
goto cleanup;
}
// check positive definite
if ( MAGMA_C_ABS(den) <= 0.0 ) {
info = MAGMA_NONSPD;
goto cleanup;
}
//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++;
// preconditioner
CHECK( magma_c_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue ));
CHECK( magma_c_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue ));
gammanew = magma_cdotc( dofs, r.dval, 1, h.dval, 1, queue );
// gn = < r,h>
if ( solver_par->numiter == 1 ) {
magma_ccopy( dofs, h.dval, 1, p.dval, 1, queue ); // p = h
} else {
beta = (gammanew/gammaold); // beta = gn/go
magma_cscal( dofs, beta, p.dval, 1, queue ); // p = beta*p
magma_caxpy( dofs, c_one, h.dval, 1, p.dval, 1, queue ); // p = p + h
}
CHECK( magma_c_spmv( c_one, A, p, c_zero, q, queue )); // q = A p
den = magma_cdotc( dofs, p.dval, 1, q.dval, 1, queue );
// den = p dot q
alpha = gammanew / den;
magma_caxpy( dofs, alpha, p.dval, 1, x->dval, 1, queue ); // x = x + alpha p
magma_caxpy( dofs, -alpha, q.dval, 1, r.dval, 1, queue ); // r = r - alpha q
gammaold = gammanew;
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;
}
}
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(&p, queue );
magma_cmfree(&q, queue );
magma_cmfree(&h, queue );
solver_par->info = info;
return info;
} /* magma_ccg */