magma_int_t
magma_dcg_merge( magma_d_sparse_matrix A, magma_d_vector b, magma_d_vector *x,
magma_d_solver_par *solver_par ){
// prepare solver feedback
solver_par->solver = Magma_CGMERGE;
solver_par->numiter = 0;
solver_par->info = 0;
// some useful variables
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE;
magma_int_t dofs = A.num_rows;
// 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] );
// GPU workspace
magma_d_vector r, d, z;
magma_d_vinit( &r, Magma_DEV, dofs, c_zero );
magma_d_vinit( &d, Magma_DEV, dofs, c_zero );
magma_d_vinit( &z, Magma_DEV, dofs, c_zero );
double *d1, *d2, *skp;
magma_dmalloc( &d1, dofs*(1) );
magma_dmalloc( &d2, dofs*(1) );
// array for the parameters
magma_dmalloc( &skp, 6 ); // skp = [alpha|beta|gamma|rho|tmp1|tmp2]
// solver variables
double alpha, beta, gamma, rho, tmp1, *skp_h;
double nom, nom0, r0, betanom, den;
// solver setup
magma_dscal( dofs, c_zero, x->val, 1) ; // x = 0
magma_dcopy( dofs, b.val, 1, r.val, 1 ); // r = b
magma_dcopy( dofs, b.val, 1, d.val, 1 ); // d = b
nom0 = betanom = magma_dnrm2( dofs, r.val, 1 );
nom = nom0 * nom0; // nom = r' * r
magma_d_spmv( c_one, A, d, c_zero, z ); // z = A d
den = MAGMA_D_REAL( magma_ddot(dofs, d.val, 1, z.val, 1) ); // den = d'* z
solver_par->init_res = nom0;
// array on host for the parameters
magma_dmalloc_cpu( &skp_h, 6 );
alpha = rho = gamma = tmp1 = c_one;
beta = magma_ddot(dofs, r.val, 1, r.val, 1);
skp_h[0]=alpha;
skp_h[1]=beta;
skp_h[2]=gamma;
skp_h[3]=rho;
skp_h[4]=tmp1;
skp_h[5]=MAGMA_D_MAKE(nom, 0.0);
magma_dsetvector( 6, skp_h, 1, skp, 1 );
if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE )
r0 = ATOLERANCE;
if ( nom < r0 )
return MAGMA_SUCCESS;
// check positive definite
if (den <= 0.0) {
printf("Operator A is not postive definite. (Ar,r) = %f\n", den);
return -100;
}
//Chronometry
real_Double_t tempo1, tempo2;
magma_device_sync(); tempo1=magma_wtime();
if( solver_par->verbose > 0 ){
solver_par->res_vec[0] = (real_Double_t) nom0;
solver_par->timing[0] = 0.0;
}
// start iteration
for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter;
solver_par->numiter++ ){
magmablasSetKernelStream(stream[0]);
// computes SpMV and dot product
magma_dcgmerge_spmv1( A, d1, d2, d.val, z.val, skp );
// updates x, r, computes scalars and updates d
magma_dcgmerge_xrbeta( dofs, d1, d2, x->val, r.val, d.val, z.val, skp );
// check stopping criterion (asynchronous copy)
magma_dgetvector_async( 1 , skp+1, 1,
skp_h+1, 1, stream[1] );
betanom = sqrt(MAGMA_D_REAL(skp_h[1]));
if( solver_par->verbose > 0 ){
magma_device_sync(); tempo2=magma_wtime();
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;
}
}
magma_device_sync(); tempo2=magma_wtime();
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
magma_dresidual( A, b, *x, &residual );
solver_par->iter_res = betanom;
solver_par->final_res = residual;
if( solver_par->numiter < solver_par->maxiter){
solver_par->info = 0;
}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 = -2;
}
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 = -1;
}
magma_d_vfree(&r);
magma_d_vfree(&z);
magma_d_vfree(&d);
magma_free( d1 );
magma_free( d2 );
magma_free( skp );
magma_free_cpu( skp_h );
return MAGMA_SUCCESS;
} /* magma_dcg_merge */
magma_int_t
magma_dpgmres( magma_d_sparse_matrix A, magma_d_vector b, magma_d_vector *x,
magma_d_solver_par *solver_par,
magma_d_preconditioner *precond_par ){
// prepare solver feedback
solver_par->solver = Magma_PGMRES;
solver_par->numiter = 0;
solver_par->info = 0;
// local variables
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE,
c_mone = MAGMA_D_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;
double nom, rNorm, RNorm, nom0, betanom, r0 = 0.;
// CPU workspace
magma_setdevice(0);
double *H, *HH, *y, *h1;
magma_dmalloc_pinned( &H, (ldh+1)*ldh );
magma_dmalloc_pinned( &y, ldh );
magma_dmalloc_pinned( &HH, ldh*ldh );
magma_dmalloc_pinned( &h1, ldh );
// GPU workspace
magma_d_vector r, q, q_t, z, z_t, t;
magma_d_vinit( &t, Magma_DEV, dofs, c_zero );
magma_d_vinit( &r, Magma_DEV, dofs, c_zero );
magma_d_vinit( &q, Magma_DEV, dofs*(ldh+1), c_zero );
magma_d_vinit( &z, Magma_DEV, dofs*(ldh+1), c_zero );
magma_d_vinit( &z_t, Magma_DEV, dofs, c_zero );
q_t.memory_location = Magma_DEV;
q_t.val = NULL;
q_t.num_rows = q_t.nnz = dofs;
double *dy, *dH = NULL;
if (MAGMA_SUCCESS != magma_dmalloc( &dy, ldh ))
return MAGMA_ERR_DEVICE_ALLOC;
if (MAGMA_SUCCESS != magma_dmalloc( &dH, (ldh+1)*ldh ))
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_dscal( dofs, c_zero, x->val, 1 ); // x = 0
magma_dcopy( dofs, b.val, 1, r.val, 1 ); // r = b
nom0 = betanom = magma_dnrm2( dofs, r.val, 1 ); // nom0= || r||
nom = nom0 * nom0;
solver_par->init_res = nom0;
H(1,0) = MAGMA_D_MAKE( nom0, 0. );
magma_dsetvector(1, &H(1,0), 1, &dH(1,0), 1);
if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE )
r0 = ATOLERANCE;
if ( nom < r0 )
return MAGMA_SUCCESS;
//Chronometry
real_Double_t tempo1, tempo2;
magma_device_sync(); tempo1=magma_wtime();
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_dcopy(dofs, r.val, 1, q(0), 1); // q[0] = 1.0/H(1,0) r
magma_dscal(dofs, 1./H(1,0), q(0), 1); // (to be fused)
for(k=1; k<=restart; k++) {
q_t.val = q(k-1);
magmablasSetKernelStream(stream[0]);
// preconditioner
// z[k] = M^(-1) q(k)
magma_d_applyprecond_left( A, q_t, &t, precond_par );
magma_d_applyprecond_right( A, t, &z_t, precond_par );
magma_dcopy(dofs, z_t.val, 1, z(k-1), 1);
// r = A q[k]
magma_d_spmv( c_one, A, z_t, c_zero, r );
if (solver_par->ortho == Magma_MGS ) {
// modified Gram-Schmidt
magmablasSetKernelStream(stream[0]);
for (i=1; i<=k; i++) {
H(i,k) =magma_ddot(dofs, q(i-1), 1, r.val, 1);
// H(i,k) = q[i] . r
magma_daxpy(dofs,-H(i,k), q(i-1), 1, r.val, 1);
// r = r - H(i,k) q[i]
}
H(k+1,k) = MAGMA_D_MAKE( magma_dnrm2(dofs, r.val, 1), 0. );
// H(k+1,k) = sqrt(r . r)
if (k < restart) {
magma_dcopy(dofs, r.val, 1, q(k), 1);
// q[k] = 1.0/H[k][k-1] r
magma_dscal(dofs, 1./H(k+1,k), q(k), 1);
// (to be fused)
}
} else if (solver_par->ortho == Magma_FUSED_CGS ) {
// fusing dgemv with dnrm2 in classical Gram-Schmidt
magmablasSetKernelStream(stream[0]);
magma_dcopy(dofs, r.val, 1, q(k), 1);
// dH(1:k+1,k) = q[0:k] . r
magmablas_dgemv(MagmaTrans, dofs, k+1, c_one, q(0),
dofs, r.val, 1, c_zero, &dH(1,k), 1);
// r = r - q[0:k-1] dH(1:k,k)
magmablas_dgemv(MagmaNoTrans, dofs, k, c_mone, q(0),
dofs, &dH(1,k), 1, c_one, r.val, 1);
// 1) dH(k+1,k) = sqrt( dH(k+1,k) - dH(1:k,k) )
magma_dcopyscale( dofs, k, r.val, 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_dgetvector_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_dgemv(MagmaTrans, dofs, k, c_one, q(0),
dofs, r.val, 1, c_zero, &dH(1,k), 1);
// dH(1:k,k) = q[0:k-1] . r
#ifndef DNRM2SCALE
// 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_dgetvector_async(k, &dH(1,k), 1, &H(1,k),
1, stream[1]);
#endif
// r = r - q[0:k-1] dH(1:k,k)
magmablas_dgemv(MagmaNoTrans, dofs, k, c_mone, q(0),
dofs, &dH(1,k), 1, c_one, r.val, 1);
#ifdef DNRM2SCALE
magma_dcopy(dofs, r.val, 1, q(k), 1);
// q[k] = r / H(k,k-1)
magma_dnrm2scale(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_dgetvector_async(k+1, &dH(1,k), 1, &H(1,k), 1, stream[1]);
#else
H(k+1,k) = MAGMA_D_MAKE( magma_dnrm2(dofs, r.val, 1), 0. );
// H(k+1,k) = sqrt(r . r)
if( k<solver_par->restart ){
magmablasSetKernelStream(stream[0]);
magma_dcopy(dofs, r.val, 1, q(k), 1);
// q[k] = 1.0/H[k][k-1] r
magma_dscal(dofs, 1./H(k+1,k), q(k), 1);
// (to be fused)
}
#endif
}
}
magma_queue_sync( stream[1] );
for( k=1; k<=restart; k++ ){
/* Minimization of || b-Ax || in H_k */
for (i=1; i<=k; i++) {
#if defined(PRECISION_z) || defined(PRECISION_c)
cblas_ddot_sub( i+1, &H(1,k), 1, &H(1,i), 1, &HH(k,i) );
#else
HH(k,i) = cblas_ddot(i+1, &H(1,k), 1, &H(1,i), 1);
#endif
}
h1[k] = H(1,k)*H(1,0);
if (k != 1)
for (i=1; i<k; i++) {
for (m=i+1; m<k; m++){
HH(k,m) -= HH(k,i) * HH(m,i);
}
HH(k,k) -= HH(k,i) * HH(k,i) / HH(i,i);
HH(k,i) = HH(k,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_D_REAL(H(k+1,k)));
}
magma_dsetmatrix_async(m, 1, y+1, m, dy, m, stream[0]);
magmablasSetKernelStream(stream[0]);
magma_dgemv(MagmaNoTrans, dofs, m, c_one, z(0), dofs, dy, 1,
c_one, x->val, 1);
magma_d_spmv( c_mone, A, *x, c_zero, r ); // r = - A * x
magma_daxpy(dofs, c_one, b.val, 1, r.val, 1); // r = r + b
H(1,0) = MAGMA_D_MAKE( magma_dnrm2(dofs, r.val, 1), 0. );
// RNorm = H[1][0] = || r ||
RNorm = MAGMA_D_REAL( H(1,0) );
betanom = fabs(RNorm);
if( solver_par->verbose > 0 ){
magma_device_sync(); tempo2=magma_wtime();
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;
}
}
magma_device_sync(); tempo2=magma_wtime();
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
magma_dresidual( A, b, *x, &residual );
solver_par->iter_res = betanom;
solver_par->final_res = residual;
if( solver_par->numiter < solver_par->maxiter){
solver_par->info = 0;
}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 = -2;
}
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 = -1;
}
// 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_d_vfree(&t);
magma_d_vfree(&r);
magma_d_vfree(&q);
magma_d_vfree(&z);
magma_d_vfree(&z_t);
// free GPU streams and events
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_event_destroy( event[0] );
magmablasSetKernelStream(NULL);
return MAGMA_SUCCESS;
} /* magma_dgmres */
extern "C" magma_int_t
magma_diterref(
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;
// some useful variables
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
// prepare solver feedback
solver_par->solver = Magma_ITERREF;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
magma_int_t dofs = A.num_rows*b.num_cols;
// solver variables
double nom, nom0;
// workspace
magma_d_matrix r={Magma_CSR}, z={Magma_CSR};
CHECK( magma_dvinit( &r, 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 ));
double residual;
CHECK( magma_dresidual( A, b, *x, &residual, queue ));
solver_par->init_res = residual;
// solver setup
magma_dscal( dofs, c_zero, x->dval, 1, queue ); // x = 0
//CHECK( magma_dresidualvec( A, b, *x, &r, nom, queue));
magma_dcopy( dofs, b.dval, 1, r.dval, 1, queue ); // r = b
nom0 = magma_dnrm2( dofs, r.dval, 1, queue ); // nom0 = || r ||
nom = nom0 * nom0;
solver_par->init_res = nom0;
if( nom0 < solver_par->atol ||
nom0/solver_par->init_res < solver_par->rtol ){
solver_par->final_res = solver_par->init_res;
solver_par->iter_res = solver_par->init_res;
info = MAGMA_SUCCESS;
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_dscal( dofs, MAGMA_D_MAKE(1./nom, 0.), r.dval, 1, queue ); // scale it
CHECK( magma_d_precond( A, r, &z, precond_par, queue )); // inner solver: A * z = r
magma_dscal( dofs, MAGMA_D_MAKE(nom, 0.), z.dval, 1, queue ); // scale it
magma_daxpy( dofs, c_one, z.dval, 1, x->dval, 1, queue ); // x = x + z
CHECK( magma_d_spmv( c_neg_one, A, *x, c_zero, r, queue )); // r = - A x
solver_par->spmv_count++;
magma_daxpy( dofs, c_one, b.dval, 1, r.dval, 1, queue ); // r = r + b
nom = magma_dnrm2( dofs, r.dval, 1, queue ); // 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 < solver_par->atol ||
nom/solver_par->init_res < solver_par->rtol ){
break;
}
}
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
CHECK( magma_dresidualvec( A, b, *x, &r, &residual, queue));
solver_par->final_res = residual;
solver_par->iter_res = nom;
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) 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->atol ||
solver_par->iter_res/solver_par->init_res < solver_par->rtol ){
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_dmfree(&r, queue );
magma_dmfree(&z, queue );
solver_par->info = info;
return info;
} /* magma_diterref */
extern "C" magma_int_t
magma_dpbicgstab(
magma_d_sparse_matrix A, magma_d_vector b, magma_d_vector *x,
magma_d_solver_par *solver_par,
magma_d_preconditioner *precond_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_PBICGSTAB;
solver_par->numiter = 0;
solver_par->info = MAGMA_SUCCESS;
// some useful variables
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE,
c_mone = MAGMA_D_NEG_ONE;
magma_int_t dofs = A.num_rows;
// workspace
magma_d_vector r,rr,p,v,s,t,ms,mt,y,z;
magma_d_vinit( &r, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &rr, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &p, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &v, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &s, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &t, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &ms, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &mt, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &y, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &z, Magma_DEV, dofs, c_zero, queue );
// solver variables
double alpha, beta, omega, rho_old, rho_new;
double nom, betanom, nom0, r0, den, res;
// solver setup
magma_dscal( dofs, c_zero, x->dval, 1) ; // x = 0
magma_dcopy( dofs, b.dval, 1, r.dval, 1 ); // r = b
magma_dcopy( dofs, b.dval, 1, rr.dval, 1 ); // rr = b
nom0 = betanom = magma_dnrm2( dofs, r.dval, 1 ); // nom = || r ||
nom = nom0*nom0;
rho_new = omega = alpha = MAGMA_D_MAKE( 1.0, 0. );
solver_par->init_res = nom0;
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) ); // 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;
}
//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_old = rho_new; // rho_old=rho
rho_new = magma_ddot( dofs, rr.dval, 1, r.dval, 1 ); // rho=<rr,r>
beta = rho_new/rho_old * alpha/omega; // beta=rho/rho_old *alpha/omega
magma_dscal( dofs, beta, p.dval, 1 ); // p = beta*p
magma_daxpy( dofs, c_mone * omega * beta, v.dval, 1 , p.dval, 1 );
// p = p-omega*beta*v
magma_daxpy( dofs, c_one, r.dval, 1, p.dval, 1 ); // p = p+r
// preconditioner
magma_d_applyprecond_left( A, p, &mt, precond_par, queue );
magma_d_applyprecond_right( A, mt, &y, precond_par, queue );
magma_d_spmv( c_one, A, y, c_zero, v, queue ); // v = Ap
alpha = rho_new / magma_ddot( dofs, rr.dval, 1, v.dval, 1 );
magma_dcopy( dofs, r.dval, 1 , s.dval, 1 ); // s=r
magma_daxpy( dofs, c_mone * alpha, v.dval, 1 , s.dval, 1 ); // s=s-alpha*v
// preconditioner
magma_d_applyprecond_left( A, s, &ms, precond_par, queue );
magma_d_applyprecond_right( A, ms, &z, precond_par, queue );
magma_d_spmv( c_one, A, z, c_zero, t, queue ); // t=As
// preconditioner
magma_d_applyprecond_left( A, s, &ms, precond_par, queue );
magma_d_applyprecond_left( A, t, &mt, precond_par, queue );
// omega = <ms,mt>/<mt,mt>
omega = magma_ddot( dofs, mt.dval, 1, ms.dval, 1 )
/ magma_ddot( dofs, mt.dval, 1, mt.dval, 1 );
magma_daxpy( dofs, alpha, y.dval, 1 , x->dval, 1 ); // x=x+alpha*p
magma_daxpy( dofs, omega, z.dval, 1 , x->dval, 1 ); // x=x+omega*s
magma_dcopy( dofs, s.dval, 1 , r.dval, 1 ); // r=s
magma_daxpy( dofs, c_mone * omega, t.dval, 1 , r.dval, 1 ); // r=r-omega*t
res = betanom = magma_dnrm2( 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;
}
}
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
magma_dresidual( A, b, *x, &residual, queue );
solver_par->final_res = residual;
solver_par->iter_res = res;
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_d_vfree(&r, queue );
magma_d_vfree(&rr, queue );
magma_d_vfree(&p, queue );
magma_d_vfree(&v, queue );
magma_d_vfree(&s, queue );
magma_d_vfree(&t, queue );
magma_d_vfree(&ms, queue );
magma_d_vfree(&mt, queue );
magma_d_vfree(&y, queue );
magma_d_vfree(&z, queue );
magmablasSetKernelStream( orig_queue );
return MAGMA_SUCCESS;
} /* magma_dbicgstab */
magma_int_t
magma_dbicgstab_merge2( magma_d_sparse_matrix A, magma_d_vector b,
magma_d_vector *x, magma_d_solver_par *solver_par ){
// prepare solver feedback
solver_par->solver = Magma_BICGSTABMERGE2;
solver_par->numiter = 0;
solver_par->info = 0;
// some useful variables
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE;
magma_int_t dofs = A.num_rows;
// 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] );
// workspace
magma_d_vector q, r,rr,p,v,s,t;
double *d1, *d2, *skp;
magma_dmalloc( &d1, dofs*(2) );
magma_dmalloc( &d2, dofs*(2) );
// array for the parameters
magma_dmalloc( &skp, 8 );
// skp = [alpha|beta|omega|rho_old|rho|nom|tmp1|tmp2]
magma_d_vinit( &q, Magma_DEV, dofs*6, c_zero );
// q = rr|r|p|v|s|t
rr.memory_location = Magma_DEV; rr.val = NULL; rr.num_rows = rr.nnz = dofs;
r.memory_location = Magma_DEV; r.val = NULL; r.num_rows = r.nnz = dofs;
p.memory_location = Magma_DEV; p.val = NULL; p.num_rows = p.nnz = dofs;
v.memory_location = Magma_DEV; v.val = NULL; v.num_rows = v.nnz = dofs;
s.memory_location = Magma_DEV; s.val = NULL; s.num_rows = s.nnz = dofs;
t.memory_location = Magma_DEV; t.val = NULL; t.num_rows = t.nnz = dofs;
rr.val = q(0);
r.val = q(1);
p.val = q(2);
v.val = q(3);
s.val = q(4);
t.val = q(5);
// solver variables
double alpha, beta, omega, rho_old, rho_new, *skp_h;
double nom, nom0, betanom, r0, den;
// solver setup
magma_dscal( dofs, c_zero, x->val, 1) ; // x = 0
magma_dcopy( dofs, b.val, 1, q(0), 1 ); // rr = b
magma_dcopy( dofs, b.val, 1, q(1), 1 ); // r = b
rho_new = magma_ddot( dofs, r.val, 1, r.val, 1 ); // rho=<rr,r>
nom = MAGMA_D_REAL(magma_ddot( dofs, r.val, 1, r.val, 1 ));
nom0 = betanom = sqrt(nom); // nom = || r ||
rho_old = omega = alpha = MAGMA_D_MAKE( 1.0, 0. );
beta = rho_new;
solver_par->init_res = nom0;
// array on host for the parameters
magma_dmalloc_cpu( &skp_h, 8 );
skp_h[0]=alpha;
skp_h[1]=beta;
skp_h[2]=omega;
skp_h[3]=rho_old;
skp_h[4]=rho_new;
skp_h[5]=MAGMA_D_MAKE(nom, 0.0);
magma_dsetvector( 8, skp_h, 1, skp, 1 );
magma_d_spmv( c_one, A, r, c_zero, v ); // z = A r
den = MAGMA_D_REAL( magma_ddot(dofs, v.val, 1, r.val, 1) );// den = z dot r
if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE )
r0 = ATOLERANCE;
if ( nom < r0 )
return MAGMA_SUCCESS;
// check positive definite
if (den <= 0.0) {
printf("Operator A is not postive definite. (Ar,r) = %f\n", den);
return -100;
}
//Chronometry
real_Double_t tempo1, tempo2;
magma_device_sync(); tempo1=magma_wtime();
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++ ){
magmablasSetKernelStream(stream[0]);
// computes p=r+beta*(p-omega*v)
magma_dbicgmerge1( dofs, skp, v.val, r.val, p.val );
magma_dbicgmerge_spmv1( A, d1, d2, q(2), q(0), q(3), skp );
magma_dbicgmerge2( dofs, skp, r.val, v.val, s.val ); // s=r-alpha*v
magma_dbicgmerge_spmv2( A, d1, d2, q(4), q(5), skp);
magma_dbicgmerge_xrbeta( dofs, d1, d2, q(0), q(1), q(2),
q(4), q(5), x->val, skp);
// check stopping criterion (asynchronous copy)
magma_dgetvector_async( 1 , skp+5, 1,
skp_h+5, 1, stream[1] );
betanom = sqrt(MAGMA_D_REAL(skp_h[5]));
if( solver_par->verbose > 0 ){
magma_device_sync(); tempo2=magma_wtime();
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;
}
}
magma_device_sync(); tempo2=magma_wtime();
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
magma_dresidual( A, b, *x, &residual );
solver_par->iter_res = betanom;
solver_par->final_res = residual;
if( solver_par->numiter < solver_par->maxiter){
solver_par->info = 0;
}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 = -2;
}
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 = -1;
}
magma_d_vfree(&q); // frees all vectors
magma_free(d1);
magma_free(d2);
magma_free( skp );
magma_free_cpu( skp_h );
return MAGMA_SUCCESS;
} /* dbicgstab_merge2 */
magma_int_t
magma_dpcg( magma_d_sparse_matrix A, magma_d_vector b, magma_d_vector *x,
magma_d_solver_par *solver_par,
magma_d_preconditioner *precond_par ){
// prepare solver feedback
solver_par->solver = Magma_PCG;
solver_par->numiter = 0;
solver_par->info = 0;
// local variables
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE;
magma_int_t dofs = A.num_rows;
// GPU workspace
magma_d_vector r, rt, p, q, h;
magma_d_vinit( &r, Magma_DEV, dofs, c_zero );
magma_d_vinit( &rt, Magma_DEV, dofs, c_zero );
magma_d_vinit( &p, Magma_DEV, dofs, c_zero );
magma_d_vinit( &q, Magma_DEV, dofs, c_zero );
magma_d_vinit( &h, Magma_DEV, dofs, c_zero );
// solver variables
double alpha, beta;
double nom, nom0, r0, gammaold, gammanew, den, res;
// solver setup
magma_dscal( dofs, c_zero, x->val, 1) ; // x = 0
magma_dcopy( dofs, b.val, 1, r.val, 1 ); // r = b
// preconditioner
magma_d_applyprecond_left( A, r, &rt, precond_par );
magma_d_applyprecond_right( A, rt, &h, precond_par );
magma_dcopy( dofs, h.val, 1, p.val, 1 ); // p = h
nom = MAGMA_D_REAL( magma_ddot(dofs, r.val, 1, h.val, 1) );
nom0 = magma_dnrm2( dofs, r.val, 1 );
magma_d_spmv( c_one, A, p, c_zero, q ); // q = A p
den = MAGMA_D_REAL( magma_ddot(dofs, p.val, 1, q.val, 1) );// den = p dot q
solver_par->init_res = nom0;
if ( (r0 = nom * solver_par->epsilon) < ATOLERANCE )
r0 = ATOLERANCE;
if ( nom < r0 )
return MAGMA_SUCCESS;
// check positive definite
if (den <= 0.0) {
printf("Operator A is not postive definite. (Ar,r) = %f\n", den);
return -100;
}
//Chronometry
real_Double_t tempo1, tempo2;
magma_device_sync(); tempo1=magma_wtime();
if( solver_par->verbose > 0 ){
solver_par->res_vec[0] = (real_Double_t)nom0;
solver_par->timing[0] = 0.0;
}
// start iteration
for( solver_par->numiter= 1; solver_par->numiter<solver_par->maxiter;
solver_par->numiter++ ){
// preconditioner
magma_d_applyprecond_left( A, r, &rt, precond_par );
magma_d_applyprecond_right( A, rt, &h, precond_par );
gammanew = MAGMA_D_REAL( magma_ddot(dofs, r.val, 1, h.val, 1) );
// gn = < r,h>
if( solver_par->numiter==1 ){
magma_dcopy( dofs, h.val, 1, p.val, 1 ); // p = h
}else{
beta = MAGMA_D_MAKE(gammanew/gammaold, 0.); // beta = gn/go
magma_dscal(dofs, beta, p.val, 1); // p = beta*p
magma_daxpy(dofs, c_one, h.val, 1, p.val, 1); // p = p + h
}
magma_d_spmv( c_one, A, p, c_zero, q ); // q = A p
den = MAGMA_D_REAL(magma_ddot(dofs, p.val, 1, q.val, 1));
// den = p dot q
alpha = MAGMA_D_MAKE(gammanew/den, 0.);
magma_daxpy(dofs, alpha, p.val, 1, x->val, 1); // x = x + alpha p
magma_daxpy(dofs, -alpha, q.val, 1, r.val, 1); // r = r - alpha q
gammaold = gammanew;
res = magma_dnrm2( dofs, r.val, 1 );
if( solver_par->verbose > 0 ){
magma_device_sync(); tempo2=magma_wtime();
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;
}
}
magma_device_sync(); tempo2=magma_wtime();
solver_par->runtime = (real_Double_t) tempo2-tempo1;
double residual;
magma_dresidual( A, b, *x, &residual );
solver_par->iter_res = res;
solver_par->final_res = residual;
if( solver_par->numiter < solver_par->maxiter){
solver_par->info = 0;
}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;
}
}
solver_par->info = -2;
}
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;
}
}
solver_par->info = -1;
}
magma_d_vfree(&r);
magma_d_vfree(&rt);
magma_d_vfree(&p);
magma_d_vfree(&q);
magma_d_vfree(&h);
return MAGMA_SUCCESS;
} /* magma_dcg */
extern "C" magma_int_t
magma_dbpcg(
magma_d_sparse_matrix A, magma_d_vector b, magma_d_vector *x,
magma_d_solver_par *solver_par,
magma_d_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
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE;
magma_int_t dofs = A.num_rows;
// GPU workspace
magma_d_vector r, rt, p, q, h;
magma_d_vinit( &r, Magma_DEV, dofs*num_vecs, c_zero, queue );
magma_d_vinit( &rt, Magma_DEV, dofs*num_vecs, c_zero, queue );
magma_d_vinit( &p, Magma_DEV, dofs*num_vecs, c_zero, queue );
magma_d_vinit( &q, Magma_DEV, dofs*num_vecs, c_zero, queue );
magma_d_vinit( &h, Magma_DEV, dofs*num_vecs, c_zero, queue );
// solver variables
double *alpha, *beta;
alpha = NULL;
beta = NULL;
stat_cpu += magma_dmalloc_cpu(&alpha, num_vecs);
stat_cpu += magma_dmalloc_cpu(&beta, num_vecs);
double *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_dmalloc_cpu(&residual, num_vecs);
stat_cpu += magma_dmalloc_cpu(&nom, num_vecs);
stat_cpu += magma_dmalloc_cpu(&nom0, num_vecs);
stat_cpu += magma_dmalloc_cpu(&r0, num_vecs);
stat_cpu += magma_dmalloc_cpu(&gammaold, num_vecs);
stat_cpu += magma_dmalloc_cpu(&gammanew, num_vecs);
stat_cpu += magma_dmalloc_cpu(&den, num_vecs);
stat_cpu += magma_dmalloc_cpu(&res, num_vecs);
stat_cpu += magma_dmalloc_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_dscal( dofs*num_vecs, c_zero, x->dval, 1) ; // x = 0
magma_dcopy( dofs*num_vecs, b.dval, 1, r.dval, 1 ); // r = b
// preconditioner
magma_d_applyprecond_left( A, r, &rt, precond_par, queue );
magma_d_applyprecond_right( A, rt, &h, precond_par, queue );
magma_dcopy( dofs*num_vecs, h.dval, 1, p.dval, 1 ); // p = h
for( i=0; i<num_vecs; i++) {
nom[i] = MAGMA_D_REAL( magma_ddot(dofs, r(i), 1, h(i), 1) );
nom0[i] = magma_dnrm2( dofs, r(i), 1 );
}
magma_d_spmv( c_one, A, p, c_zero, q, queue ); // q = A p
for( i=0; i<num_vecs; i++)
den[i] = MAGMA_D_REAL( magma_ddot(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_d_applyprecond_left( A, r, &rt, precond_par, queue );
magma_d_applyprecond_right( A, rt, &h, precond_par, queue );
for( i=0; i<num_vecs; i++)
gammanew[i] = MAGMA_D_REAL( magma_ddot(dofs, r(i), 1, h(i), 1) ); // gn = < r,h>
if ( solver_par->numiter==1 ) {
magma_dcopy( dofs*num_vecs, h.dval, 1, p.dval, 1 ); // p = h
} else {
for( i=0; i<num_vecs; i++) {
beta[i] = MAGMA_D_MAKE(gammanew[i]/gammaold[i], 0.); // beta = gn/go
magma_dscal(dofs, beta[i], p(i), 1); // p = beta*p
magma_daxpy(dofs, c_one, h(i), 1, p(i), 1); // p = p + h
}
}
magma_d_spmv( c_one, A, p, c_zero, q, queue ); // q = A p
// magma_d_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_D_REAL(magma_ddot(dofs, p(i), 1, q(i), 1));
// den = p dot q
alpha[i] = MAGMA_D_MAKE(gammanew[i]/den[i], 0.);
magma_daxpy(dofs, alpha[i], p(i), 1, x->dval+dofs*i, 1); // x = x + alpha p
magma_daxpy(dofs, -alpha[i], q(i), 1, r(i), 1); // r = r - alpha q
gammaold[i] = gammanew[i];
res[i] = magma_dnrm2( 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_dresidual( 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_d_vfree(&r, queue );
magma_d_vfree(&rt, queue );
magma_d_vfree(&p, queue );
magma_d_vfree(&q, queue );
magma_d_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_dbpcg */
extern "C" magma_int_t
magma_diterref(
magma_d_sparse_matrix A, magma_d_vector b, magma_d_vector *x,
magma_d_solver_par *solver_par, magma_d_preconditioner *precond_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_ITERREF;
solver_par->numiter = 0;
solver_par->info = MAGMA_SUCCESS;
double residual;
magma_dresidual( A, b, *x, &residual, queue );
solver_par->init_res = residual;
// some useful variables
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE,
c_mone = MAGMA_D_NEG_ONE;
magma_int_t dofs = A.num_rows;
// workspace
magma_d_vector r,z;
magma_d_vinit( &r, Magma_DEV, dofs, c_zero, queue );
magma_d_vinit( &z, Magma_DEV, dofs, c_zero, queue );
// solver variables
double nom, nom0, r0;
// solver setup
magma_dscal( dofs, c_zero, x->dval, 1) ; // x = 0
magma_dcopy( dofs, b.dval, 1, r.dval, 1 ); // r = b
nom0 = magma_dnrm2(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 ) {
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++ ) {
magma_dscal( dofs, MAGMA_D_MAKE(1./nom, 0.), r.dval, 1) ; // scale it
magma_d_precond( A, r, &z, precond_par, queue ); // inner solver: A * z = r
magma_dscal( dofs, MAGMA_D_MAKE(nom, 0.), z.dval, 1) ; // scale it
magma_daxpy(dofs, c_one, z.dval, 1, x->dval, 1); // x = x + z
magma_d_spmv( c_mone, A, *x, c_zero, r, queue ); // r = - A x
magma_daxpy(dofs, c_one, b.dval, 1, r.dval, 1); // r = r + b
nom = magma_dnrm2(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;
magma_dresidual( A, b, *x, &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;
}
}
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) nom;
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
solver_par->info = MAGMA_DIVERGENCE;
}
magma_d_vfree(&r, queue );
magma_d_vfree(&z, queue );
magmablasSetKernelStream( orig_queue );
return MAGMA_SUCCESS;
} /* magma_diterref */
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_dbpcg(
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 = 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->spmv_count = 0;
solver_par->info = MAGMA_SUCCESS;
// local variables
double c_zero = MAGMA_D_ZERO, c_one = MAGMA_D_ONE;
magma_int_t dofs = A.num_rows;
// GPU workspace
magma_d_matrix r={Magma_CSR}, rt={Magma_CSR}, p={Magma_CSR}, q={Magma_CSR}, h={Magma_CSR};
// solver variables
double *alpha={0}, *beta={0};
alpha = NULL;
beta = NULL;
double *nom={0}, *nom0={0}, *r0={0}, *gammaold={0}, *gammanew={0}, *den={0}, *res={0}, *residual={0};
nom = NULL;
nom0 = NULL;
r0 = NULL;
gammaold = NULL;
gammanew = NULL;
den = NULL;
res = NULL;
residual = NULL;
CHECK( magma_dmalloc_cpu(&alpha, num_vecs));
CHECK( magma_dmalloc_cpu(&beta, num_vecs));
CHECK( magma_dmalloc_cpu(&residual, num_vecs));
CHECK( magma_dmalloc_cpu(&nom, num_vecs));
CHECK( magma_dmalloc_cpu(&nom0, num_vecs));
CHECK( magma_dmalloc_cpu(&r0, num_vecs));
CHECK( magma_dmalloc_cpu(&gammaold, num_vecs));
CHECK( magma_dmalloc_cpu(&gammanew, num_vecs));
CHECK( magma_dmalloc_cpu(&den, num_vecs));
CHECK( magma_dmalloc_cpu(&res, num_vecs));
CHECK( magma_dmalloc_cpu(&residual, num_vecs));
CHECK( magma_dvinit( &r, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
CHECK( magma_dvinit( &rt, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
CHECK( magma_dvinit( &p, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
CHECK( magma_dvinit( &q, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
CHECK( magma_dvinit( &h, Magma_DEV, dofs*num_vecs, 1, c_zero, queue ));
// solver setup
CHECK( magma_dresidualvec( A, b, *x, &r, nom0, queue));
// preconditioner
CHECK( magma_d_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue ));
CHECK( magma_d_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue ));
magma_dcopy( dofs*num_vecs, h.dval, 1, p.dval, 1, queue ); // p = h
for( i=0; i<num_vecs; i++) {
nom[i] = MAGMA_D_REAL( magma_ddot( dofs, r(i), 1, h(i), 1, queue ) );
nom0[i] = magma_dnrm2( dofs, r(i), 1, queue );
}
CHECK( magma_d_spmv( c_one, A, p, c_zero, q, queue )); // q = A p
for( i=0; i<num_vecs; i++)
den[i] = MAGMA_D_REAL( magma_ddot( dofs, p(i), 1, q(i), 1, queue ) ); // den = p dot q
solver_par->init_res = nom0[0];
if ( (r0[0] = nom[0] * solver_par->rtol) < 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]);
info = MAGMA_NONSPD;
goto cleanup;
}
if ( nom[0] < r0[0] ) {
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] = (real_Double_t)nom0[0];
solver_par->timing[0] = 0.0;
}
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// start iteration
do
{
solver_par->numiter++;
// preconditioner
CHECK( magma_d_applyprecond_left( MagmaNoTrans, A, r, &rt, precond_par, queue ));
CHECK( magma_d_applyprecond_right( MagmaNoTrans, A, rt, &h, precond_par, queue ));
for( i=0; i<num_vecs; i++)
gammanew[i] = MAGMA_D_REAL( magma_ddot( dofs, r(i), 1, h(i), 1, queue ) ); // gn = < r,h>
if ( solver_par->numiter==1 ) {
magma_dcopy( dofs*num_vecs, h.dval, 1, p.dval, 1, queue ); // p = h
} else {
for( i=0; i<num_vecs; i++) {
beta[i] = MAGMA_D_MAKE(gammanew[i]/gammaold[i], 0.); // beta = gn/go
magma_dscal( dofs, beta[i], p(i), 1, queue ); // p = beta*p
magma_daxpy( dofs, c_one, h(i), 1, p(i), 1, queue ); // p = p + h
}
}
CHECK( magma_d_spmv( c_one, A, p, c_zero, q, queue )); // q = A p
solver_par->spmv_count++;
// magma_d_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_D_REAL(magma_ddot( dofs, p(i), 1, q(i), 1, queue) );
// den = p dot q
alpha[i] = MAGMA_D_MAKE(gammanew[i]/den[i], 0.);
magma_daxpy( dofs, alpha[i], p(i), 1, x->dval+dofs*i, 1, queue ); // x = x + alpha p
magma_daxpy( dofs, -alpha[i], q(i), 1, r(i), 1, queue ); // r = r - alpha q
gammaold[i] = gammanew[i];
res[i] = magma_dnrm2( dofs, r(i), 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[0];
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
if ( res[0]/nom0[0] < solver_par->rtol ) {
break;
}
}
while ( solver_par->numiter+1 <= solver_par->maxiter );
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
CHECK( magma_dresidual( 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;
}
}
info = MAGMA_SLOW_CONVERGENCE;
if( solver_par->iter_res < solver_par->rtol*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) res[0];
solver_par->timing[(solver_par->numiter)/solver_par->verbose]
= (real_Double_t) tempo2-tempo1;
}
}
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");
cleanup:
magma_dmfree(&r, queue );
magma_dmfree(&rt, queue );
magma_dmfree(&p, queue );
magma_dmfree(&q, queue );
magma_dmfree(&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);
solver_par->info = info;
return info;
} /* magma_dbpcg */
