void magma_smake_hpd( magma_int_t N, float* A, magma_int_t lda )
{
magma_int_t i, j;
for( i=0; i < N; ++i ) {
A(i,i) = MAGMA_S_MAKE( MAGMA_S_REAL( A(i,i) ) + N, 0. );
for( j=0; j < i; ++j ) {
A(j,i) = MAGMA_S_CONJ( A(i,j) );
}
}
}
extern "C" void
magmablas_ssyr2k_vbatched_max_nocheck(
magma_uplo_t uplo, magma_trans_t trans, magma_int_t* n, magma_int_t* k,
float alpha,
float const * const * dA_array, magma_int_t* ldda,
float const * const * dB_array, magma_int_t* lddb,
float beta, float **dC_array, magma_int_t* lddc,
magma_int_t batchCount,
magma_int_t max_n, magma_int_t max_k, magma_queue_t queue )
{
float cbeta = MAGMA_S_MAKE(beta, 0.);
float c_one = MAGMA_S_MAKE(1., 0.);
if( trans == MagmaNoTrans){
magmablas_ssyrk_internal_vbatched(uplo, MagmaNoTrans, n, k, alpha, dA_array, ldda, dB_array, lddb, cbeta, dC_array, lddc, max_n, max_k, batchCount, queue );
magmablas_ssyrk_internal_vbatched(uplo, MagmaNoTrans, n, k, MAGMA_S_CONJ(alpha), dB_array, lddb, dA_array, ldda, c_one, dC_array, lddc, max_n, max_k, batchCount, queue );
}else{
magmablas_ssyrk_internal_vbatched(uplo, MagmaTrans, n, k, alpha, dA_array, ldda, dB_array, lddb, cbeta, dC_array, lddc, max_n, max_k, batchCount, queue );
magmablas_ssyrk_internal_vbatched(uplo, MagmaTrans, n, k, MAGMA_S_CONJ(alpha), dB_array, lddb, dA_array, ldda, c_one, dC_array, lddc, max_n, max_k, batchCount, queue );
}
}
/* ////////////////////////////////////////////////////////////////////////////
-- Testing ssymmetrize
Code is very similar to testing_stranspose.cpp
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gbytes, gpu_perf, gpu_time, cpu_perf, cpu_time;
float error, work[1];
float c_neg_one = MAGMA_S_NEG_ONE;
float *h_A, *h_R;
magmaFloat_ptr d_A;
magma_int_t N, size, lda, ldda;
magma_int_t ione = 1;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
printf("%% uplo = %s\n", lapack_uplo_const(opts.uplo) );
printf("%% N CPU GByte/s (ms) GPU GByte/s (ms) check\n");
printf("%%====================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
N = opts.nsize[itest];
lda = N;
ldda = magma_roundup( N, opts.align ); // multiple of 32 by default
size = lda*N;
// load strictly lower triangle, save strictly upper triangle
gbytes = sizeof(float) * 1.*N*(N-1) / 1e9;
TESTING_MALLOC_CPU( h_A, float, size );
TESTING_MALLOC_CPU( h_R, float, size );
TESTING_MALLOC_DEV( d_A, float, ldda*N );
/* Initialize the matrix */
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < N; ++i ) {
h_A[i + j*lda] = MAGMA_S_MAKE( i + j/10000., j );
}
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_ssetmatrix( N, N, h_A, lda, d_A, ldda );
magmablasSetKernelStream( opts.queue );
gpu_time = magma_sync_wtime( opts.queue );
//magmablas_ssymmetrize( opts.uplo, N-2, d_A+1+ldda, ldda ); // inset by 1 row & col
magmablas_ssymmetrize( opts.uplo, N, d_A, ldda );
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gbytes / gpu_time;
/* =====================================================================
Performs operation using naive in-place algorithm
(LAPACK doesn't implement symmetrize)
=================================================================== */
cpu_time = magma_wtime();
//for( int j = 1; j < N-1; ++j ) { // inset by 1 row & col
// for( int i = 1; i < j; ++i ) {
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < j; ++i ) {
if ( opts.uplo == MagmaLower ) {
h_A[i + j*lda] = MAGMA_S_CONJ( h_A[j + i*lda] );
}
else {
h_A[j + i*lda] = MAGMA_S_CONJ( h_A[i + j*lda] );
}
}
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
/* =====================================================================
Check the result
=================================================================== */
magma_sgetmatrix( N, N, d_A, ldda, h_R, lda );
blasf77_saxpy(&size, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_slange("f", &N, &N, h_R, &lda, work);
printf("%5d %7.2f (%7.2f) %7.2f (%7.2f) %s\n",
(int) N, cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
(error == 0. ? "ok" : "failed") );
status += ! (error == 0.);
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
extern "C" magma_int_t
magma_sbicg(
magma_s_matrix A, magma_s_matrix b, magma_s_matrix *x,
magma_s_solver_par *solver_par,
magma_queue_t queue )
{
magma_int_t info = MAGMA_NOTCONVERGED;
// prepare solver feedback
solver_par->solver = Magma_BICG;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
// some useful variables
float c_zero = MAGMA_S_ZERO;
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
magma_int_t dofs = A.num_rows * b.num_cols;
// workspace
magma_s_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_s_matrix AT={Magma_CSR}, Ah1={Magma_CSR}, Ah2={Magma_CSR};
CHECK( magma_svinit( &r, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_svinit( &rt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_svinit( &p, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_svinit( &pt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_svinit( &q, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_svinit( &qt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_svinit( &y, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_svinit( &yt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_svinit( &z, Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
CHECK( magma_svinit( &zt,Magma_DEV, A.num_rows, b.num_cols, c_zero, queue ));
// solver variables
float alpha, rho, beta, rho_new, ptq;
float res, nomb, nom0, r0;
// transpose the matrix
magma_smtransfer( A, &Ah1, Magma_DEV, Magma_CPU, queue );
magma_smconvert( Ah1, &Ah2, A.storage_type, Magma_CSR, queue );
magma_smfree(&Ah1, queue );
magma_smtransposeconjugate( Ah2, &Ah1, queue );
magma_smfree(&Ah2, queue );
Ah2.blocksize = A.blocksize;
Ah2.alignment = A.alignment;
magma_smconvert( Ah1, &Ah2, Magma_CSR, A.storage_type, queue );
magma_smfree(&Ah1, queue );
magma_smtransfer( Ah2, &AT, Magma_CPU, Magma_DEV, queue );
magma_smfree(&Ah2, queue );
// solver setup
CHECK( magma_sresidualvec( A, b, *x, &r, &nom0, queue));
res = nom0;
solver_par->init_res = nom0;
magma_scopy( dofs, r.dval, 1, rt.dval, 1, queue ); // rr = r
rho_new = magma_sdot( dofs, rt.dval, 1, r.dval, 1, queue ); // rho=<rr,r>
rho = alpha = MAGMA_S_MAKE( 1.0, 0. );
nomb = magma_snrm2( 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++;
magma_scopy( dofs, r.dval, 1 , y.dval, 1, queue ); // y=r
magma_scopy( dofs, y.dval, 1 , z.dval, 1, queue ); // z=y
magma_scopy( dofs, rt.dval, 1 , yt.dval, 1, queue ); // yt=rt
magma_scopy( dofs, yt.dval, 1 , zt.dval, 1, queue ); // zt=yt
rho= rho_new;
rho_new = magma_sdot( dofs, rt.dval, 1, z.dval, 1, queue ); // rho=<rt,z>
if( magma_s_isnan_inf( rho_new ) ){
info = MAGMA_DIVERGENCE;
break;
}
if( solver_par->numiter==1 ){
magma_scopy( dofs, z.dval, 1 , p.dval, 1, queue ); // yt=rt
magma_scopy( dofs, zt.dval, 1 , pt.dval, 1, queue ); // zt=yt
} else {
beta = rho_new/rho;
magma_sscal( dofs, beta, p.dval, 1, queue ); // p = beta*p
magma_saxpy( dofs, c_one , z.dval, 1 , p.dval, 1, queue ); // p = z+beta*p
magma_sscal( dofs, MAGMA_S_CONJ(beta), pt.dval, 1, queue ); // pt = beta*pt
magma_saxpy( dofs, c_one , zt.dval, 1 , pt.dval, 1, queue ); // pt = zt+beta*pt
}
CHECK( magma_s_spmv( c_one, A, p, c_zero, q, queue )); // v = Ap
CHECK( magma_s_spmv( c_one, AT, pt, c_zero, qt, queue )); // v = Ap
solver_par->spmv_count++;
solver_par->spmv_count++;
ptq = magma_sdot( dofs, pt.dval, 1, q.dval, 1, queue );
alpha = rho_new /ptq;
magma_saxpy( dofs, alpha, p.dval, 1 , x->dval, 1, queue ); // x=x+alpha*p
magma_saxpy( dofs, c_neg_one * alpha, q.dval, 1 , r.dval, 1, queue ); // r=r+alpha*q
magma_saxpy( dofs, c_neg_one * MAGMA_S_CONJ(alpha), qt.dval, 1 , rt.dval, 1, queue ); // r=r+alpha*q
res = magma_snrm2( 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_sresidualvec( 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_smfree(&r, queue );
magma_smfree(&rt, queue );
magma_smfree(&p, queue );
magma_smfree(&pt, queue );
magma_smfree(&q, queue );
magma_smfree(&qt, queue );
magma_smfree(&y, queue );
magma_smfree(&yt, queue );
magma_smfree(&z, queue );
magma_smfree(&zt, queue );
magma_smfree(&AT, queue );
magma_smfree(&Ah1, queue );
magma_smfree(&Ah2, queue );
solver_par->info = info;
return info;
} /* magma_sbicg */
void magmablas_ssyr2k_mgpu2(
magma_uplo_t uplo, magma_trans_t trans, magma_int_t n, magma_int_t k,
float alpha,
magmaFloat_ptr dA[], magma_int_t ldda, magma_int_t a_offset,
magmaFloat_ptr dB[], magma_int_t lddb, magma_int_t b_offset,
float beta,
magmaFloat_ptr dC[], magma_int_t lddc, magma_int_t c_offset,
magma_int_t ngpu, magma_int_t nb, magma_queue_t queues[][20], magma_int_t nqueue )
{
#define dA(dev, i, j) (dA[dev] + (i) + (j)*ldda + (a_offset) )
#define dB(dev, i, j) (dB[dev] + (i) + (j)*lddb + (b_offset) )
#define dC(dev, i, j) (dC[dev] + (i) + (j)*lddc)
/* Check arguments */
magma_int_t info = 0;
if ( uplo != MagmaLower ) {
info = -1; // upper not yet handled
} else if ( trans != MagmaNoTrans ) {
info = -2; // conj not yet handled
} else if ( n < 0 ) {
info = -3;
} else if ( k < 0 ) {
info = -4;
} else if ( ((trans == MagmaNoTrans) && ldda < max(1,n)) ||
((trans == MagmaTrans) && ldda < max(1,k)) ) {
info = -7;
} else if ( a_offset < 0 || a_offset > ldda ) {
info = -8;
} else if ( ((trans == MagmaNoTrans) && lddb < max(1,n)) ||
((trans == MagmaTrans) && lddb < max(1,k)) ) {
info = -10;
} else if ( b_offset < 0 || b_offset > lddb ) {
info = -11;
} else if ( lddc < max(1,n) ) {
info = -13;
} else if ( c_offset < 0 || c_offset > lddc ) {
info = -14;
} else if ( ngpu <= 0 ) {
info = -15;
} else if ( nb <= 0 ) {
info = -16;
} else if ( nqueue <= 0 ) {
info = -18;
}
if ( info != 0 ) {
magma_xerbla( __func__, -(info) );
return;
}
const float c_one = MAGMA_S_ONE;
float cbeta = MAGMA_S_MAKE( beta, 0. );
magma_int_t ib, ioff, iblock, idev, di, s;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
// loop over all blocks
// Faster to have two loops: first loop does C_hat = alpha*A*B**H + beta*C
// blockoffset is offset within first block; for subsequent blocks it is 0
magma_int_t blockoffset = c_offset % nb;
for( magma_int_t i = 0; i < n; i += ib ) {
ib = min( nb-blockoffset, n-i ); // block size
ioff = i + c_offset; // global index in parent matrix
iblock = (ioff / nb) / ngpu; // local block id
idev = (ioff / nb) % ngpu; // device with this block
di = iblock*nb + blockoffset; // local index in parent matrix
magma_setdevice( idev );
s = iblock % nqueue;
// C[i:n,i] = alpha * A[i:n,0] * B[i,0]' + beta*C[i:n,i]
//printf( "sgemm n=%4d, ib=%4d, k=%4d, i=%4d\n", n-i, ib, k, i );
magma_sgemm( MagmaNoTrans, MagmaTrans, n-i, ib, k,
alpha, dA(idev,i,0), ldda,
dB(idev,i,0), lddb,
cbeta, dC(idev,ioff,di), lddc, queues[idev][s] );
blockoffset = 0;
}
// second loop does C = conj(alpha)*B*A**H + C_hat
alpha = MAGMA_S_CONJ( alpha );
blockoffset = c_offset % nb;
for( magma_int_t i = 0; i < n; i += ib ) {
ib = min( nb-blockoffset, n-i ); // block size
ioff = i + c_offset; // global index in parent matrix
iblock = (ioff / nb) / ngpu; // local block id
idev = (ioff / nb) % ngpu; // device with this block
di = iblock*nb + blockoffset; // local index in parent matrix
magma_setdevice( idev );
s = iblock % nqueue;
// C[i:n,i] += conj(alpha) * B[i:n,0] * A[i,0]'
//printf( "sgemm n=%4d, ib=%4d, k=%4d, i=%4d\n", n-i, ib, k, i );
magma_sgemm( MagmaNoTrans, MagmaTrans, n-i, ib, k,
alpha, dB(idev,i,0), lddb,
dA(idev,i,0), ldda,
c_one, dC(idev,ioff,di), lddc, queues[idev][s] );
blockoffset = 0;
}
magma_setdevice( orig_dev );
}
