/**
Purpose
-------
SORMQL overwrites the general real M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaTrans: Q**H * C C * Q**H
@endverbatim
where Q is a real unitary matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by SGEQLF. Q is of order M if SIDE = MagmaLeft and of order N
if SIDE = MagmaRight.
Arguments
---------
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = MagmaTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = MagmaLeft, M >= K >= 0;
if SIDE = MagmaRight, N >= K >= 0.
@param[in]
dA REAL array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
SGEQLF in the last k columns of its array argument A.
The diagonal and the lower part
are destroyed, the reflectors are not modified.
@param[in]
ldda INTEGER
The leading dimension of the array DA.
LDDA >= max(1,M) if SIDE = MagmaLeft;
LDDA >= max(1,N) if SIDE = MagmaRight.
@param[in]
tau REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEQLF.
@param[in,out]
dC REAL array, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
@param[in]
lddc INTEGER
The leading dimension of the array C. LDDC >= max(1,M).
@param[in]
wA (workspace) REAL array, dimension
(LDWA,M) if SIDE = MagmaLeft
(LDWA,N) if SIDE = MagmaRight
The vectors which define the elementary reflectors, as
returned by SSYTRD_GPU.
@param[in]
ldwa INTEGER
The leading dimension of the array wA.
LDWA >= max(1,M) if SIDE = MagmaLeft; LDWA >= max(1,N) if SIDE = MagmaRight.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_sgeqlf_comp
********************************************************************/
extern "C" magma_int_t
magma_sormql2_gpu(
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
magmaFloat_ptr dA, magma_int_t ldda,
float *tau,
magmaFloat_ptr dC, magma_int_t lddc,
float *wA, magma_int_t ldwa,
magma_int_t *info)
{
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dC(i_,j_) (dC + (i_) + (j_)*lddc)
#define wA(i_,j_) (wA + (i_) + (j_)*ldwa)
/* Allocate work space on the GPU */
magmaFloat_ptr dwork;
magma_smalloc( &dwork, 2*(m + 64)*64 );
float c_zero = MAGMA_S_ZERO;
float c_one = MAGMA_S_ONE;
magma_int_t i, i__4;
float T[2*4160] /* was [65][64] */;
magma_int_t i1, i2, step, ib, nb, mi, ni, nq, nw;
magma_int_t ldwork;
int left, notran;
wA -= 1 + ldwa;
dC -= 1 + lddc;
--tau;
*info = 0;
left = (side == MagmaLeft);
notran = (trans == MagmaNoTrans);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = max(1,n);
} else {
nq = n;
nw = max(1,m);
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != MagmaTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
} else if (ldwa < max(1,nq)) {
*info = -12;
}
// size of the block
nb = 64;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0) {
return *info;
}
ldwork = nw;
/* Use hybrid CPU-GPU code */
if ((left && notran) || (! left && ! notran)) {
i1 = 1;
i2 = k;
step = nb;
} else {
i1 = (k - 1) / nb * nb + 1;
i2 = 1;
step = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
} else {
mi = m;
}
// set nb-1 sub-diagonals to 0, and diagonal to 1.
// This way we can copy V directly to the GPU,
// already with the lower triangle parts already set to identity.
magmablas_slaset_band( MagmaLower, k, k, nb, c_zero, c_one, dA, ldda );
for (i = i1; (step < 0 ? i >= i2 : i <= i2); i += step) {
ib = min(nb, k - i + 1);
/* Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i) */
i__4 = nq - k + i + ib - 1;
lapackf77_slarft("Backward", "Columnwise", &i__4, &ib,
wA(1,i), &ldwa, &tau[i], T, &ib);
if (left) {
/* H or H' is applied to C(1:m-k+i+ib-1,1:n) */
mi = m - k + i + ib - 1;
}
else {
/* H or H' is applied to C(1:m,1:n-k+i+ib-1) */
ni = n - k + i + ib - 1;
}
/* Apply H or H'; First copy T to the GPU */
magma_ssetmatrix( ib, ib, T, ib, dwork+i__4*ib, ib );
magma_slarfb_gpu(side, trans, MagmaBackward, MagmaColumnwise,
mi, ni, ib,
dA(0,i-1), ldda, dwork+i__4*ib, ib, // dA using 0-based indices here
dC(1,1), lddc,
dwork+i__4*ib + ib*ib, ldwork);
}
magma_free( dwork );
return *info;
} /* magma_sormql */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing slaset_band
Code is very similar to testing_slacpy.cpp
*/
int main( int argc, char** argv)
{
TESTING_INIT();
#define h_A(i_,j_) (h_A + (i_) + (j_)*lda)
#define d_A(i_,j_) (d_A + (i_) + (j_)*ldda)
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;
float *d_A;
float offdiag = MAGMA_S_MAKE( 1.2000, 6.7000 );
float diag = MAGMA_S_MAKE( 3.1415, 2.7183 );
magma_int_t M, N, nb, cnt, size, lda, ldb, ldda;
magma_int_t ione = 1;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
nb = (opts.nb == 0 ? 32 : opts.nb);
magma_uplo_t uplo[] = { MagmaLower, MagmaUpper, MagmaFull };
printf("K = nb = %d\n", (int) nb );
printf("uplo M N CPU GByte/s (ms) GPU GByte/s (ms) check\n");
printf("==================================================================\n");
for( int iuplo = 0; iuplo < 2; ++iuplo ) {
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
int inset = 0;
M = opts.msize[itest] + 2*inset;
N = opts.nsize[itest] + 2*inset;
lda = M;
ldb = lda;
ldda = ((M+31)/32)*32;
size = lda*N;
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 < M; ++i ) {
h_A[i + j*lda] = MAGMA_S_MAKE( i + j/10000., j );
}
}
magma_ssetmatrix( M, N, h_A, lda, d_A, ldda );
/* =====================================================================
Performs operation on CPU
Also count number of elements touched.
=================================================================== */
cpu_time = magma_wtime();
cnt = 0;
for( int j=inset; j < N-inset; ++j ) {
for( int k=0; k < nb; ++k ) { // set k-th sub- or super-diagonal
if ( k == 0 && j < M-inset ) {
*h_A(j,j) = diag;
cnt += 1;
}
else if ( uplo[iuplo] == MagmaLower && j+k < M-inset ) {
*h_A(j+k,j) = offdiag;
cnt += 1;
}
else if ( uplo[iuplo] == MagmaUpper && j-k >= inset && j-k < M-inset ) {
*h_A(j-k,j) = offdiag;
cnt += 1;
}
}
}
gbytes = cnt / 1e9;
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
gpu_time = magma_sync_wtime( 0 );
int mm = M - 2*inset;
int nn = N - 2*inset;
magmablas_slaset_band( uplo[iuplo], mm, nn, nb, offdiag, diag, d_A(inset,inset), ldda );
gpu_time = magma_sync_wtime( 0 ) - gpu_time;
gpu_perf = gbytes / gpu_time;
/* =====================================================================
Check the result
=================================================================== */
magma_sgetmatrix( M, N, d_A, ldda, h_R, lda );
//printf( "h_R=" ); magma_sprint( M, N, h_R, lda );
//printf( "h_A=" ); magma_sprint( M, N, h_A, lda );
blasf77_saxpy(&size, &c_neg_one, h_A, &ione, h_R, &ione);
error = lapackf77_slange("f", &M, &N, h_R, &lda, work);
printf("%4c %5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %s\n",
lapacke_uplo_const( uplo[iuplo] ), (int) M, (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" );
}
}
printf( "\n" );
}
TESTING_FINALIZE();
return status;
}
/***************************************************************************//**
Purpose
-------
SORMQR overwrites the general real M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaTrans: Q**H * C C * Q**H
@endverbatim
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by SGEQRF. Q is of order M if SIDE = MagmaLeft and of order N
if SIDE = MagmaRight.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = MagmaTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = MagmaLeft, M >= K >= 0;
if SIDE = MagmaRight, N >= K >= 0.
@param[in]
A REAL array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
SGEQRF in the first k columns of its array argument A.
@param[in]
lda INTEGER
The leading dimension of the array A.
If SIDE = MagmaLeft, LDA >= max(1,M);
if SIDE = MagmaRight, LDA >= max(1,N).
@param[in]
tau REAL array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SGEQRF.
@param[in,out]
C REAL array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
@param[in]
ldc INTEGER
The leading dimension of the array C. LDC >= max(1,M).
@param[out]
work (workspace) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK.
If SIDE = MagmaLeft, LWORK >= max(1,N);
if SIDE = MagmaRight, LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and
LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal
blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_unmqr
*******************************************************************************/
extern "C" magma_int_t
magma_sormqr_m(
magma_int_t ngpu,
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
float *A, magma_int_t lda,
float *tau,
float *C, magma_int_t ldc,
float *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define C(i, j) (C + (j)*ldc + (i))
#define dC(gpui, i, j) (dw[gpui] + (j)*lddc + (i))
#define dA_c(gpui, ind, i, j) (dw[gpui] + maxnlocal*lddc + (ind)*lddar*lddac + (i) + (j)*lddac)
#define dA_r(gpui, ind, i, j) (dw[gpui] + maxnlocal*lddc + (ind)*lddar*lddac + (i) + (j)*lddar)
#define dT(gpui, ind) (dw[gpui] + maxnlocal*lddc + 2*lddac*lddar + (ind)*((nb+1)*nb))
#define dwork(gpui, ind) (dw[gpui] + maxnlocal*lddc + 2*lddac*lddar + 2*((nb+1)*nb) + (ind)*(lddwork*nb))
/* Constants */
float c_zero = MAGMA_S_ZERO;
float c_one = MAGMA_S_ONE;
/* Local variables */
const char* side_ = lapack_side_const( side );
const char* trans_ = lapack_trans_const( trans );
magma_int_t nb = 128;
float *T = NULL;
magmaFloat_ptr dw[MagmaMaxGPUs] = { NULL };
magma_queue_t queues[MagmaMaxGPUs][2] = {{ NULL }};
magma_event_t events[MagmaMaxGPUs][2] = {{ NULL }};
magma_int_t ind_c;
magma_device_t dev;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
*info = 0;
magma_int_t left = (side == MagmaLeft);
magma_int_t notran = (trans == MagmaNoTrans);
magma_int_t lquery = (lwork == -1);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
magma_int_t nq, nw;
if (left) {
nq = m;
nw = n;
} else {
nq = n;
nw = m;
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != MagmaTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (lda < max(1,nq)) {
*info = -7;
} else if (ldc < max(1,m)) {
*info = -10;
} else if (lwork < max(1,nw) && ! lquery) {
*info = -12;
}
magma_int_t lwkopt = max(1,nw) * nb;
if (*info == 0) {
work[0] = magma_smake_lwork( lwkopt );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
work[0] = c_one;
return *info;
}
if (nb >= k) {
/* Use CPU code */
lapackf77_sormqr(side_, trans_, &m, &n, &k, A, &lda, tau,
C, &ldc, work, &lwork, info);
return *info;
}
magma_int_t lddc = magma_roundup( m, 64 ); // TODO why 64 instead of 32 ?
magma_int_t lddac = nq;
magma_int_t lddar = nb;
magma_int_t lddwork = nw;
magma_int_t nlocal[ MagmaMaxGPUs ] = { 0 };
magma_int_t nb_l=256;
magma_int_t nbl = magma_ceildiv( n, nb_l ); // number of blocks
magma_int_t maxnlocal = magma_ceildiv( nbl, ngpu )*nb_l;
ngpu = min( ngpu, magma_ceildiv( n, nb_l )); // Don't use GPU that will not have data.
magma_int_t ldw = maxnlocal*lddc // dC
+ 2*lddac*lddar // 2*dA
+ 2*(nb + 1 + lddwork)*nb; // 2*(dT and dwork)
if (MAGMA_SUCCESS != magma_smalloc_pinned( &T, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
goto cleanup;
}
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
if (MAGMA_SUCCESS != magma_smalloc( &dw[dev], ldw )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
magma_queue_create( dev, &queues[dev][0] );
magma_queue_create( dev, &queues[dev][1] );
magma_event_create( &events[dev][0] );
magma_event_create( &events[dev][1] );
}
/* Use hybrid CPU-MGPU code */
if (left) {
//copy C to mgpus
for (magma_int_t i = 0; i < nbl; ++i) {
dev = i % ngpu;
magma_setdevice( dev );
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_ssetmatrix_async( m, kb,
C(0, i*nb_l), ldc,
dC(dev, 0, i/ngpu*nb_l), lddc, queues[dev][0] );
nlocal[dev] += kb;
}
magma_int_t i1, i2, i3;
if ( !notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
ind_c = 0;
for (magma_int_t i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3) {
// start the copy of A panel
magma_int_t kb = min(nb, k - i);
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_event_sync( events[dev][ind_c] ); // check if the new data can be copied
magma_ssetmatrix_async(nq-i, kb,
A(i, i), lda,
dA_c(dev, ind_c, i, 0), lddac, queues[dev][0] );
// set upper triangular part of dA to identity
magmablas_slaset_band( MagmaUpper, kb, kb, kb, c_zero, c_one, dA_c(dev, ind_c, i, 0), lddac, queues[dev][0] );
}
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
magma_int_t nqi = nq - i;
lapackf77_slarft("F", "C", &nqi, &kb, A(i, i), &lda,
&tau[i], T, &kb);
/* H or H' is applied to C(1:m,i:n) */
/* Apply H or H'; First copy T to the GPU */
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_ssetmatrix_async(kb, kb,
T, kb,
dT(dev, ind_c), kb, queues[dev][0] );
}
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] ); // check if the data was copied
magma_slarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
m-i, nlocal[dev], kb,
dA_c(dev, ind_c, i, 0), lddac, dT(dev, ind_c), kb,
dC(dev, i, 0), lddc,
dwork(dev, ind_c), lddwork, queues[dev][1] );
magma_event_record(events[dev][ind_c], queues[dev][1] );
}
ind_c = (ind_c+1)%2;
}
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][1] );
}
//copy C from mgpus
for (magma_int_t i = 0; i < nbl; ++i) {
dev = i % ngpu;
magma_setdevice( dev );
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_sgetmatrix( m, kb,
dC(dev, 0, i/ngpu*nb_l), lddc,
C(0, i*nb_l), ldc, queues[dev][1] );
// magma_sgetmatrix_async( m, kb,
// dC(dev, 0, i/ngpu*nb_l), lddc,
// C(0, i*nb_l), ldc, queues[dev][0] );
}
} else {
*info = MAGMA_ERR_NOT_IMPLEMENTED;
magma_xerbla( __func__, -(*info) );
goto cleanup;
/*
if ( notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
mi = m;
ic = 0;
for (i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3) {
ib = min(nb, k - i);
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
i__4 = nq - i;
lapackf77_slarft("F", "C", &i__4, &ib, A(i, i), &lda,
&tau[i], T, &ib);
// 1) copy the panel from A to the GPU, and
// 2) set upper triangular part of dA to identity
magma_ssetmatrix( i__4, ib, A(i, i), lda, dA(i, 0), ldda, queues[dev][1] );
magmablas_slaset_band( MagmaUpper, ib, ib, ib, c_zero, c_one, dA(i, 0), ldda, queues[dev][1] );
// H or H' is applied to C(1:m,i:n)
ni = n - i;
jc = i;
// Apply H or H'; First copy T to the GPU
magma_ssetmatrix( ib, ib, T, ib, dT, ib, queues[dev][1] );
magma_slarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dA(i, 0), ldda, dT, ib,
dC(ic, jc), lddc,
dwork, lddwork, queues[dev][1] );
}
*/
}
cleanup:
work[0] = magma_smake_lwork( lwkopt );
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_event_destroy( events[dev][0] );
magma_event_destroy( events[dev][1] );
magma_queue_destroy( queues[dev][0] );
magma_queue_destroy( queues[dev][1] );
magma_free( dw[dev] );
}
magma_setdevice( orig_dev );
magma_free_pinned( T );
return *info;
} /* magma_sormqr */
