extern "C" magma_int_t
magma_dqmr_merge(
magma_d_matrix A, magma_d_matrix b, magma_d_matrix *x,
magma_d_solver_par *solver_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// prepare solver feedback
solver_par->solver = Magma_QMRMERGE;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// local variables
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE;
// solver variables
double nom0, r0, res=0, nomb;
double 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_d_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR};
// GPU workspace
magma_d_matrix r={Magma_CSR}, r_tld={Magma_CSR},
v={Magma_CSR}, w={Magma_CSR}, wt={Magma_CSR},
d={Magma_CSR}, s={Magma_CSR}, z={Magma_CSR}, q={Magma_CSR},
p={Magma_CSR}, pt={Magma_CSR}, y={Magma_CSR};
CHECK( magma_dvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &r_tld, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &w, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &wt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &d, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver setup
CHECK( magma_dresidualvec( A, b, *x, &r, &nom0, queue));
solver_par->init_res = nom0;
magma_dcopy( dofs, r.dval, 1, r_tld.dval, 1, queue );
magma_dcopy( dofs, r.dval, 1, y.dval, 1, queue );
magma_dcopy( dofs, r.dval, 1, v.dval, 1, queue );
magma_dcopy( dofs, r.dval, 1, wt.dval, 1, queue );
magma_dcopy( dofs, r.dval, 1, z.dval, 1, queue );
// transpose the matrix
magma_dmtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue );
magma_dmconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue );
magma_dmfree(&Ah1, queue );
magma_dmtransposeconjugate( Ah2, &Ah1, queue );
magma_dmfree(&Ah2, queue );
Ah2.blocksize = A.blocksize;
Ah2.alignment = A.alignment;
magma_dmconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue );
magma_dmfree(&Ah1, queue );
magma_dmtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue );
magma_dmfree(&Ah2, queue );
nomb = magma_dnrm2( dofs, b.dval, 1, queue );
if ( nomb == 0.0 ){
nomb=1.0;
}
if ( (r0 = nomb * solver_par->rtol) < ATOLERANCE ){
r0 = ATOLERANCE;
}
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = (real_Double_t)nom0;
solver_par->timing[0] = 0.0;
}
if ( nom0 < r0 ) {
info = MAGMA_SUCCESS;
goto cleanup;
}
psi = magma_dsqrt( magma_ddot( dofs, z.dval, 1, z.dval, 1, queue ));
rho = magma_dsqrt( magma_ddot( dofs, y.dval, 1, y.dval, 1, queue ));
// v = y / rho
// y = y / rho
// w = wt / psi
// z = z / psi
magma_dqmr_1(
r.num_rows,
r.num_cols,
rho,
psi,
y.dval,
z.dval,
v.dval,
w.dval,
queue );
//Chronometry
real_Double_t tempo1, tempo2;
tempo1 = magma_sync_wtime( queue );
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// start iteration
do
{
solver_par->numiter++;
if( magma_d_isnan_inf( rho ) || magma_d_isnan_inf( psi ) ){
info = MAGMA_DIVERGENCE;
break;
}
// delta = z' * y;
delta = magma_ddot( dofs, z.dval, 1, y.dval, 1, queue );
if( magma_d_isnan_inf( delta ) ){
info = MAGMA_DIVERGENCE;
break;
}
// no precond: yt = y, zt = z
//magma_dcopy( dofs, y.dval, 1, yt.dval, 1 );
//magma_dcopy( dofs, z.dval, 1, zt.dval, 1 );
if( solver_par->numiter == 1 ){
// p = y;
// q = z;
magma_dcopy( dofs, y.dval, 1, p.dval, 1, queue );
magma_dcopy( dofs, z.dval, 1, q.dval, 1, queue );
}
else{
pde = psi * delta / epsilon;
rde = rho * MAGMA_D_CONJ(delta/epsilon);
// p = y - pde * p
// q = z - rde * q
magma_dqmr_2(
r.num_rows,
r.num_cols,
pde,
rde,
y.dval,
z.dval,
p.dval,
q.dval,
queue );
}
if( magma_d_isnan_inf( rho ) || magma_d_isnan_inf( psi ) ){
info = MAGMA_DIVERGENCE;
break;
}
CHECK( magma_d_spmv( c_one, A, p, c_zero, pt, queue ));
solver_par->spmv_count++;
// epsilon = q' * pt;
epsilon = magma_ddot( dofs, q.dval, 1, pt.dval, 1, queue );
beta = epsilon / delta;
if( magma_d_isnan_inf( epsilon ) || magma_d_isnan_inf( beta ) ){
info = MAGMA_DIVERGENCE;
break;
}
// v = pt - beta * v
// y = v
magma_dqmr_3(
r.num_rows,
r.num_cols,
beta,
pt.dval,
v.dval,
y.dval,
queue );
rho1 = rho;
// rho = norm(y);
rho = magma_dsqrt( magma_ddot( dofs, y.dval, 1, y.dval, 1, queue ));
// wt = A' * q - beta' * w;
CHECK( magma_d_spmv( c_one, AT, q, c_zero, wt, queue ));
solver_par->spmv_count++;
magma_daxpy( dofs, - MAGMA_D_CONJ( beta ), w.dval, 1, wt.dval, 1, queue );
// no precond: z = wt
magma_dcopy( dofs, wt.dval, 1, z.dval, 1, queue );
thet1 = thet;
thet = rho / (gamm * MAGMA_D_MAKE( MAGMA_D_ABS(beta), 0.0 ));
gamm1 = gamm;
gamm = c_one / magma_dsqrt(c_one + thet*thet);
eta = - eta * rho1 * gamm * gamm / (beta * gamm1 * gamm1);
if( magma_d_isnan_inf( thet ) || magma_d_isnan_inf( gamm ) || magma_d_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_dqmr_4(
r.num_rows,
r.num_cols,
eta,
p.dval,
pt.dval,
d.dval,
s.dval,
x->dval,
r.dval,
queue );
}
else{
pds = (thet1 * gamm) * (thet1 * gamm);
// d = eta * p + pds * d;
// s = eta * pt + pds * d;
// x = x + d;
// r = r - s;
magma_dqmr_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_dsqrt( magma_ddot( dofs, z.dval, 1, z.dval, 1, queue ) );
res = magma_dnrm2( dofs, r.dval, 1, queue );
if ( solver_par->verbose > 0 ) {
tempo2 = magma_sync_wtime( queue );
if ( (solver_par->numiter)%solver_par->verbose == c_zero ) {
solver_par->res_vec[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) res;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
// v = y / rho
// y = y / rho
// w = wt / psi
// z = z / psi
magma_dqmr_1(
r.num_rows,
r.num_cols,
rho,
psi,
y.dval,
z.dval,
v.dval,
w.dval,
queue );
if ( res/nomb <= solver_par->rtol || res <= solver_par->atol ){
break;
}
}
while ( solver_par->numiter+1 <= solver_par->maxiter );
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
CHECK( magma_dresidualvec( 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_dmfree(&r, queue );
magma_dmfree(&r_tld, queue );
magma_dmfree(&v, queue );
magma_dmfree(&w, queue );
magma_dmfree(&wt, queue );
magma_dmfree(&d, queue );
magma_dmfree(&s, queue );
magma_dmfree(&z, queue );
magma_dmfree(&q, queue );
magma_dmfree(&p, queue );
magma_dmfree(&pt, queue );
magma_dmfree(&y, queue );
magma_dmfree(&AT, queue );
magma_dmfree(&Ah1, queue );
magma_dmfree(&Ah2, queue );
solver_par->info = info;
return info;
} /* magma_dqmr_merge */
extern "C" magma_int_t
magma_dbicgstab_merge(
magma_d_matrix A, magma_d_matrix b, magma_d_matrix *x,
magma_d_solver_par *solver_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// prepare solver feedback
solver_par->solver = Magma_BICGSTAB;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// some useful variables
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t dofs = A.num_rows * b.num_cols;
// workspace
magma_d_matrix r={Magma_CSR}, rr={Magma_CSR}, p={Magma_CSR}, v={Magma_CSR},
s={Magma_CSR}, t={Magma_CSR}, d1={Magma_CSR}, d2={Magma_CSR};
CHECK( magma_dvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &rr,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &s, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &d1, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &d2, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver variables
double alpha, beta, omega, rho_old, rho_new;
double nom, betanom, nom0, r0, res, nomb;
res=0;
//double den;
// solver setup
CHECK( magma_dresidualvec( A, b, *x, &r, &nom0, queue));
magma_dcopy( dofs, r.dval, 1, rr.dval, 1, queue ); // rr = r
betanom = nom0;
nom = nom0*nom0;
rho_new = magma_ddot( dofs, r.dval, 1, r.dval, 1, queue ); // rho=<rr,r>
rho_old = omega = alpha = MAGMA_D_MAKE( 1.0, 0. );
solver_par->init_res = nom0;
CHECK( magma_d_spmv( c_one, A, r, c_zero, v, queue )); // z = A r
//den = MAGMA_D_REAL( magma_ddot( dofs, v.dval, 1, r.dval, 1), queue ); // den = z' * r
nomb = magma_dnrm2( 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] = nom0;
solver_par->timing[0] = 0.0;
}
if ( nom < 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_old = rho_new; // rho_old=rho
rho_new = magma_ddot( dofs, rr.dval, 1, r.dval, 1, queue ); // rho=<rr,r>
beta = rho_new/rho_old * alpha/omega; // beta=rho/rho_old *alpha/omega
if( magma_d_isnan_inf( beta ) ){
info = MAGMA_DIVERGENCE;
break;
}
// p = r + beta * ( p - omega * v )
magma_dbicgstab_1(
r.num_rows,
r.num_cols,
beta,
omega,
r.dval,
v.dval,
p.dval,
queue );
CHECK( magma_d_spmv( c_one, A, p, c_zero, v, queue )); // v = Ap
solver_par->spmv_count++;
//alpha = rho_new / tmpval;
alpha = rho_new /magma_ddot( dofs, rr.dval, 1, v.dval, 1, queue );
if( magma_d_isnan_inf( alpha ) ){
info = MAGMA_DIVERGENCE;
break;
}
// s = r - alpha v
magma_dbicgstab_2(
r.num_rows,
r.num_cols,
alpha,
r.dval,
v.dval,
s.dval,
queue );
CHECK( magma_d_spmv( c_one, A, s, c_zero, t, queue )); // t=As
solver_par->spmv_count++;
omega = magma_ddot( dofs, t.dval, 1, s.dval, 1, queue ) // omega = <s,t>/<t,t>
/ magma_ddot( dofs, t.dval, 1, t.dval, 1, queue );
// x = x + alpha * p + omega * s
// r = s - omega * t
magma_dbicgstab_3(
r.num_rows,
r.num_cols,
alpha,
omega,
p.dval,
s.dval,
t.dval,
x->dval,
r.dval,
queue );
res = betanom = magma_dnrm2( dofs, r.dval, 1, queue );
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/nomb <= solver_par->rtol || res <= solver_par->atol ){
break;
}
}
while ( solver_par->numiter+1 <= solver_par->maxiter );
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
CHECK( magma_dresidualvec( 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) 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->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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
cleanup:
magma_dmfree(&r, queue );
magma_dmfree(&rr, queue );
magma_dmfree(&p, queue );
magma_dmfree(&v, queue );
magma_dmfree(&s, queue );
magma_dmfree(&t, queue );
magma_dmfree(&d1, queue );
magma_dmfree(&d2, queue );
solver_par->info = info;
return info;
} /* magma_dbicgstab_merge */
magma_int_t
magma_dorderstatistics(
double *val,
magma_int_t length,
magma_int_t k,
magma_int_t r,
double *element,
magma_queue_t queue )
{
magma_int_t info = 0;
magma_int_t i, st;
double tmp;
if( r == 0 ){
for ( st = i = 0; i < length - 1; i++ ) {
if ( magma_d_isnan_inf( val[i]) ) {
printf("error: array contains %f + %fi.\n", MAGMA_D_REAL(val[i]), MAGMA_D_IMAG(val[i]) );
info = MAGMA_ERR_NAN;
goto cleanup;
}
if ( MAGMA_D_ABS(val[i]) > MAGMA_D_ABS(val[length-1]) ){
continue;
}
SWAP(i, st);
st++;
}
SWAP(length-1, st);
if ( k == st ){
*element = val[st];
}
else if ( st > k ) {
CHECK( magma_dorderstatistics( val, st, k, r, element, queue ));
}
else {
CHECK( magma_dorderstatistics( val+st, length-st, k-st, r, element, queue ));
}
} else {
for ( st = i = 0; i < length - 1; i++ ) {
if ( magma_d_isnan_inf( val[i]) ) {
printf("error: array contains %f + %fi.\n", MAGMA_D_REAL(val[i]), MAGMA_D_IMAG(val[i]) );
info = MAGMA_ERR_NAN;
goto cleanup;
}
if ( MAGMA_D_ABS(val[i]) < MAGMA_D_ABS(val[length-1]) ){
continue;
}
SWAP(i, st);
st++;
}
SWAP(length-1, st);
if ( k == st ){
*element = val[st];
}
else if ( st > k ) {
CHECK( magma_dorderstatistics( val, st, k, r, element, queue ));
}
else {
CHECK( magma_dorderstatistics( val+st, length-st, k-st, r, element, queue ));
}
}
cleanup:
return info;
}
extern "C" magma_int_t
magma_dfgmres(
magma_d_matrix A, magma_d_matrix b, magma_d_matrix *x,
magma_d_solver_par *solver_par,
magma_d_preconditioner *precond_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
magma_int_t dofs = A.num_rows;
// prepare solver feedback
solver_par->solver = Magma_PGMRES;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
//Chronometry
real_Double_t tempo1, tempo2;
magma_int_t dim = solver_par->restart;
magma_int_t m1 = dim+1; // used inside H macro
magma_int_t i, j, k;
double beta;
double rel_resid, resid0=1, r0=0.0, betanom = 0.0, nom;
magma_d_matrix v_t={Magma_CSR}, w_t={Magma_CSR}, t={Magma_CSR}, t2={Magma_CSR}, V={Magma_CSR}, W={Magma_CSR};
v_t.memory_location = Magma_DEV;
v_t.num_rows = dofs;
v_t.num_cols = 1;
v_t.dval = NULL;
v_t.storage_type = Magma_DENSE;
w_t.memory_location = Magma_DEV;
w_t.num_rows = dofs;
w_t.num_cols = 1;
w_t.dval = NULL;
w_t.storage_type = Magma_DENSE;
double temp;
double *H={0}, *s={0}, *cs={0}, *sn={0};
CHECK( magma_dvinit( &t, Magma_DEV, dofs, 1, MAGMA_D_ZERO, queue ));
CHECK( magma_dvinit( &t2, Magma_DEV, dofs, 1, MAGMA_D_ZERO, queue ));
CHECK( magma_dmalloc_pinned( &H, (dim+1)*dim ));
CHECK( magma_dmalloc_pinned( &s, dim+1 ));
CHECK( magma_dmalloc_pinned( &cs, dim ));
CHECK( magma_dmalloc_pinned( &sn, dim ));
CHECK( magma_dvinit( &V, Magma_DEV, dofs*(dim+1), 1, MAGMA_D_ZERO, queue ));
CHECK( magma_dvinit( &W, Magma_DEV, dofs*dim, 1, MAGMA_D_ZERO, queue ));
CHECK( magma_dresidual( A, b, *x, &nom, queue));
solver_par->init_res = nom;
if ( ( nom * solver_par->rtol) < ATOLERANCE )
r0 = ATOLERANCE;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
tempo1 = magma_sync_wtime( queue );
do
{
solver_par->numiter++;
// compute initial residual and its norm
// A.mult(n, 1, x, n, V(0), n); // V(0) = A*x
CHECK( magma_d_spmv( MAGMA_D_ONE, A, *x, MAGMA_D_ZERO, t, queue ));
solver_par->spmv_count++;
magma_dcopy( dofs, t.dval, 1, V(0), 1, queue );
temp = MAGMA_D_MAKE(-1.0, 0.0);
magma_daxpy( dofs,temp, b.dval, 1, V(0), 1, queue ); // V(0) = V(0) - b
beta = MAGMA_D_MAKE( magma_dnrm2( dofs, V(0), 1, queue ), 0.0 ); // beta = norm(V(0))
if( magma_d_isnan_inf( beta ) ){
info = MAGMA_DIVERGENCE;
break;
}
if (solver_par->numiter == 0){
solver_par->init_res = MAGMA_D_REAL( beta );
resid0 = MAGMA_D_REAL( beta );
r0 = resid0 * solver_par->rtol;
if ( r0 < ATOLERANCE )
r0 = ATOLERANCE;
if ( resid0 < r0 ) {
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
info = MAGMA_SUCCESS;
goto cleanup;
}
}
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = resid0;
solver_par->timing[0] = 0.0;
}
temp = -1.0/beta;
magma_dscal( dofs, temp, V(0), 1, queue ); // V(0) = -V(0)/beta
// save very first residual norm
if (solver_par->numiter == 0)
solver_par->init_res = MAGMA_D_REAL( beta );
for (i = 1; i < dim+1; i++)
s[i] = MAGMA_D_ZERO;
s[0] = beta;
i = -1;
do {
i++;
// M.apply(n, 1, V(i), n, W(i), n);
v_t.dval = V(i);
CHECK( magma_d_applyprecond_left( MagmaNoTrans, A, v_t, &t, precond_par, queue ));
CHECK( magma_d_applyprecond_right( MagmaNoTrans, A, t, &t2, precond_par, queue ));
magma_dcopy( dofs, t2.dval, 1, W(i), 1, queue );
// A.mult(n, 1, W(i), n, V(i+1), n);
w_t.dval = W(i);
CHECK( magma_d_spmv( MAGMA_D_ONE, A, w_t, MAGMA_D_ZERO, t, queue ));
solver_par->spmv_count++;
magma_dcopy( dofs, t.dval, 1, V(i+1), 1, queue );
for (k = 0; k <= i; k++)
{
H(k, i) = magma_ddot( dofs, V(k), 1, V(i+1), 1, queue );
temp = -H(k,i);
// V(i+1) -= H(k, i) * V(k);
magma_daxpy( dofs,-H(k,i), V(k), 1, V(i+1), 1, queue );
}
H(i+1, i) = MAGMA_D_MAKE( magma_dnrm2( dofs, V(i+1), 1, queue), 0. ); // H(i+1,i) = ||r||
temp = 1.0 / H(i+1, i);
// V(i+1) = V(i+1) / H(i+1, i)
magma_dscal( dofs, temp, V(i+1), 1, queue ); // (to be fused)
for (k = 0; k < i; k++)
ApplyPlaneRotation(&H(k,i), &H(k+1,i), cs[k], sn[k]);
GeneratePlaneRotation(H(i,i), H(i+1,i), &cs[i], &sn[i]);
ApplyPlaneRotation(&H(i,i), &H(i+1,i), cs[i], sn[i]);
ApplyPlaneRotation(&s[i], &s[i+1], cs[i], sn[i]);
betanom = MAGMA_D_ABS( s[i+1] );
rel_resid = betanom / resid0;
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 (rel_resid <= solver_par->rtol || betanom <= solver_par->atol ){
info = MAGMA_SUCCESS;
break;
}
}
while (i+1 < dim && solver_par->numiter+1 <= solver_par->maxiter);
// solve upper triangular system in place
for (j = i; j >= 0; j--)
{
s[j] /= H(j,j);
for (k = j-1; k >= 0; k--)
s[k] -= H(k,j) * s[j];
}
// update the solution
for (j = 0; j <= i; j++)
{
// x = x + s[j] * W(j)
magma_daxpy( dofs, s[j], W(j), 1, x->dval, 1, queue );
}
}
while (rel_resid > solver_par->rtol
&& solver_par->numiter+1 <= solver_par->maxiter);
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
CHECK( magma_dresidual( A, b, *x, &residual, queue ));
solver_par->iter_res = betanom;
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) 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->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) betanom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
info = MAGMA_DIVERGENCE;
}
cleanup:
// free pinned memory
magma_free_pinned(s);
magma_free_pinned(cs);
magma_free_pinned(sn);
magma_free_pinned(H);
//free DEV memory
magma_dmfree( &V, queue);
magma_dmfree( &W, queue);
magma_dmfree( &t, queue);
magma_dmfree( &t2, queue);
solver_par->info = info;
return info;
} /* magma_dfgmres */
extern "C" magma_int_t
magma_dpcgs(
magma_d_matrix A, magma_d_matrix b, magma_d_matrix *x,
magma_d_solver_par *solver_par,
magma_d_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 double c_zero = MAGMA_D_ZERO;
const double c_one = MAGMA_D_ONE;
const double c_neg_one = MAGMA_D_NEG_ONE;
// solver variables
double nom0, r0, res=0, nomb;
double rho, rho_l = c_one, alpha, beta;
magma_int_t dofs = A.num_rows* b.num_cols;
// GPU workspace
magma_d_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_dvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &r_tld,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &p_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &q_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &u, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &u_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &v, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &v_hat, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &t, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver setup
CHECK( magma_dresidualvec( A, b, *x, &r, &nom0, queue));
magma_dcopy( dofs, r.dval, 1, r_tld.dval, 1, queue );
solver_par->init_res = nom0;
nomb = magma_dnrm2( dofs, b.dval, 1, queue );
if ( nomb == 0.0 ){
nomb=1.0;
}
if ( (r0 = nomb * solver_par->rtol) < ATOLERANCE ){
r0 = ATOLERANCE;
}
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
if ( solver_par->verbose > 0 ) {
solver_par->res_vec[0] = (real_Double_t)nom0;
solver_par->timing[0] = 0.0;
}
if ( nom0 < r0 ) {
info = MAGMA_SUCCESS;
goto cleanup;
}
//Chronometry
real_Double_t tempo1, tempo2, tempop1, tempop2;
tempo1 = magma_sync_wtime( queue );
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// start iteration
do
{
solver_par->numiter++;
rho = magma_ddot( dofs, r.dval, 1, r_tld.dval, 1, queue );
// rho = < r,r_tld>
if( magma_d_isnan_inf( rho ) ){
info = MAGMA_DIVERGENCE;
break;
}
if ( solver_par->numiter > 1 ) { // direction vectors
beta = rho / rho_l;
magma_dcopy( dofs, r.dval, 1, u.dval, 1, queue ); // u = r
magma_daxpy( dofs, beta, q.dval, 1, u.dval, 1, queue ); // u = r + beta q
magma_dscal( dofs, beta, p.dval, 1, queue ); // p = beta*p
magma_daxpy( dofs, c_one, q.dval, 1, p.dval, 1, queue ); // p = q + beta*p
magma_dscal( dofs, beta, p.dval, 1, queue ); // p = beta*(q + beta*p)
magma_daxpy( 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_dcopy( dofs, r.dval, 1, u.dval, 1, queue ); // u = r
magma_dcopy( dofs, r.dval, 1, p.dval, 1, queue ); // p = r
}
// preconditioner
tempop1 = magma_sync_wtime( queue );
CHECK( magma_d_applyprecond_left( MagmaNoTrans, A, p, &rt, precond_par, queue ));
CHECK( magma_d_applyprecond_right( MagmaNoTrans, A, rt, &p_hat, precond_par, queue ));
tempop2 = magma_sync_wtime( queue );
precond_par->runtime += tempop2-tempop1;
// SpMV
CHECK( magma_d_spmv( c_one, A, p_hat, c_zero, v_hat, queue )); // v = A p
solver_par->spmv_count++;
alpha = rho / magma_ddot( dofs, r_tld.dval, 1, v_hat.dval, 1, queue );
magma_dcopy( dofs, u.dval, 1, q.dval, 1, queue ); // q = u
magma_daxpy( dofs, -alpha, v_hat.dval, 1, q.dval, 1, queue ); // q = u - alpha v_hat
magma_dcopy( dofs, u.dval, 1, t.dval, 1, queue ); // t = q
magma_daxpy( dofs, c_one, q.dval, 1, t.dval, 1, queue ); // t = u + q
// preconditioner
tempop1 = magma_sync_wtime( queue );
CHECK( magma_d_applyprecond_left( MagmaNoTrans, A, t, &rt, precond_par, queue ));
CHECK( magma_d_applyprecond_right( MagmaNoTrans, A, rt, &u_hat, precond_par, queue ));
tempop2 = magma_sync_wtime( queue );
precond_par->runtime += tempop2-tempop1;
// SpMV
CHECK( magma_d_spmv( c_one, A, u_hat, c_zero, t, queue )); // t = A u_hat
solver_par->spmv_count++;
magma_daxpy( dofs, alpha, u_hat.dval, 1, x->dval, 1, queue ); // x = x + alpha u_hat
magma_daxpy( dofs, c_neg_one*alpha, t.dval, 1, r.dval, 1, queue ); // r = r -alpha*A u_hat
res = magma_dnrm2( 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;
double residual;
CHECK( magma_dresidualvec( 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_dmfree(&r, queue );
magma_dmfree(&rt, queue );
magma_dmfree(&r_tld, queue );
magma_dmfree(&p, queue );
magma_dmfree(&q, queue );
magma_dmfree(&u, queue );
magma_dmfree(&v, queue );
magma_dmfree(&t, queue );
magma_dmfree(&p_hat, queue );
magma_dmfree(&q_hat, queue );
magma_dmfree(&u_hat, queue );
magma_dmfree(&v_hat, queue );
solver_par->info = info;
return info;
} /* magma_dpcgs */
extern "C" magma_int_t
magma_dpbicg(
magma_d_matrix A, magma_d_matrix b, magma_d_matrix *x,
magma_d_solver_par *solver_par,
magma_d_preconditioner *precond_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// prepare solver feedback
solver_par->solver = Magma_PBICG;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// some useful variables
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t dofs = A.num_rows * b.num_cols;
// workspace
magma_d_matrix r={Magma_CSR}, rt={Magma_CSR}, p={Magma_CSR}, pt={Magma_CSR},
z={Magma_CSR}, zt={Magma_CSR}, q={Magma_CSR}, y={Magma_CSR},
yt={Magma_CSR}, qt={Magma_CSR};
// need to transpose the matrix
magma_d_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR};
CHECK( magma_dvinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &qt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &yt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_dvinit( &zt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver variables
double alpha, rho, beta, rho_new, ptq;
double res, nomb, nom0, r0;
// transpose the matrix
magma_dmtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue );
magma_dmconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue );
magma_dmfree(&Ah1, queue );
magma_dmtransposeconjugate( Ah2, &Ah1, queue );
magma_dmfree(&Ah2, queue );
Ah2.blocksize = A.blocksize;
Ah2.alignment = A.alignment;
magma_dmconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue );
magma_dmfree(&Ah1, queue );
magma_dmtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue );
magma_dmfree(&Ah2, queue );
// solver setup
CHECK( magma_dresidualvec( A, b, *x, &r, &nom0, queue));
res = nom0;
solver_par->init_res = nom0;
magma_dcopy( dofs, r.dval, 1, rt.dval, 1, queue ); // rr = r
rho_new = magma_ddot( dofs, rt.dval, 1, r.dval, 1, queue ); // rho=<rr,r>
rho = alpha = MAGMA_D_MAKE( 1.0, 0. );
nomb = magma_dnrm2( 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] = 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++;
CHECK( magma_d_applyprecond_left( MagmaNoTrans, A, r, &y, precond_par, queue ));
CHECK( magma_d_applyprecond_right( MagmaNoTrans, A, y, &z, precond_par, queue ));
CHECK( magma_d_applyprecond_right( MagmaTrans, A, rt, &yt, precond_par, queue ));
CHECK( magma_d_applyprecond_left( MagmaTrans, A, yt, &zt, precond_par, queue ));
//magma_dcopy( dofs, r.dval, 1 , y.dval, 1, queue ); // y=r
//magma_dcopy( dofs, y.dval, 1 , z.dval, 1, queue ); // z=y
//magma_dcopy( dofs, rt.dval, 1 , yt.dval, 1, queue ); // yt=rt
//magma_dcopy( dofs, yt.dval, 1 , zt.dval, 1, queue ); // yt=rt
rho= rho_new;
rho_new = magma_ddot( dofs, rt.dval, 1, z.dval, 1, queue ); // rho=<rt,z>
if( magma_d_isnan_inf( rho_new ) ){
info = MAGMA_DIVERGENCE;
break;
}
if( solver_par->numiter==1 ){
magma_dcopy( dofs, z.dval, 1 , p.dval, 1, queue ); // yt=rt
magma_dcopy( dofs, zt.dval, 1 , pt.dval, 1, queue ); // zt=yt
} else {
beta = rho_new/rho;
magma_dscal( dofs, beta, p.dval, 1, queue ); // p = beta*p
magma_daxpy( dofs, c_one , z.dval, 1 , p.dval, 1, queue ); // p = z+beta*p
magma_dscal( dofs, MAGMA_D_CONJ(beta), pt.dval, 1, queue ); // pt = beta*pt
magma_daxpy( dofs, c_one , zt.dval, 1 , pt.dval, 1, queue ); // pt = zt+beta*pt
}
CHECK( magma_d_spmv( c_one, A, p, c_zero, q, queue )); // v = Ap
CHECK( magma_d_spmv( c_one, AT, pt, c_zero, qt, queue )); // v = Ap
solver_par->spmv_count++;
solver_par->spmv_count++;
ptq = magma_ddot( dofs, pt.dval, 1, q.dval, 1, queue );
alpha = rho_new /ptq;
magma_daxpy( dofs, alpha, p.dval, 1 , x->dval, 1, queue ); // x=x+alpha*p
magma_daxpy( dofs, c_neg_one * alpha, q.dval, 1 , r.dval, 1, queue ); // r=r+alpha*q
magma_daxpy( dofs, c_neg_one * MAGMA_D_CONJ(alpha), qt.dval, 1 , rt.dval, 1, queue ); // r=r+alpha*q
res = magma_dnrm2( 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;
double residual;
CHECK( magma_dresidualvec( 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_dmfree(&r, queue );
magma_dmfree(&rt, queue );
magma_dmfree(&p, queue );
magma_dmfree(&pt, queue );
magma_dmfree(&q, queue );
magma_dmfree(&qt, queue );
magma_dmfree(&y, queue );
magma_dmfree(&yt, queue );
magma_dmfree(&z, queue );
magma_dmfree(&zt, queue );
magma_dmfree(&AT, queue );
magma_dmfree(&Ah1, queue );
magma_dmfree(&Ah2, queue );
solver_par->info = info;
return info;
} /* magma_dpbicg */