extern "C" magma_int_t
magma_sgeqrf2_mgpu( magma_int_t num_gpus, magma_int_t m, magma_int_t n,
float **dlA, magma_int_t ldda,
float *tau,
magma_int_t *info )
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2012
Purpose
=======
SGEQRF2_MGPU computes a QR factorization of a real M-by-N matrix A:
A = Q * R. This is a GPU interface of the routine.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
dA (input/output) REAL array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix dA.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
TAU (output) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
===================================================================== */
#define dlA(gpu,a_1,a_2) ( dlA[gpu]+(a_2)*(ldda) + (a_1))
#define work_ref(a_1) ( work + (a_1))
#define hwork ( work + (nb)*(m))
#define hwrk_ref(a_1) ( local_work + (a_1))
#define lhwrk ( local_work + (nb)*(m))
float *dwork[4], *panel[4], *local_work;
magma_int_t i, j, k, ldwork, lddwork, old_i, old_ib, rows;
magma_int_t nbmin, nx, ib, nb;
magma_int_t lhwork, lwork;
magma_device_t cdevice;
magma_getdevice(&cdevice);
int panel_gpunum, i_local, n_local[4], la_gpu, displacement;
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
k = min(m,n);
if (k == 0)
return *info;
nb = magma_get_sgeqrf_nb(m);
displacement = n * nb;
lwork = (m+n+64) * nb;
lhwork = lwork - (m)*nb;
for(i=0; i<num_gpus; i++){
#ifdef MultiGPUs
magma_setdevice(i);
#endif
if (MAGMA_SUCCESS != magma_smalloc( &(dwork[i]), (n + ldda)*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
/* Set the number of local n for each GPU */
for(i=0; i<num_gpus; i++){
n_local[i] = ((n/nb)/num_gpus)*nb;
if (i < (n/nb)%num_gpus)
n_local[i] += nb;
else if (i == (n/nb)%num_gpus)
n_local[i] += n%nb;
}
if (MAGMA_SUCCESS != magma_smalloc_pinned( &local_work, lwork )) {
*info = -9;
for(i=0; i<num_gpus; i++){
#ifdef MultiGPUs
magma_setdevice(i);
#endif
magma_free( dwork[i] );
}
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
cudaStream_t streaml[4][2];
for(i=0; i<num_gpus; i++){
#ifdef MultiGPUs
magma_setdevice(i);
#endif
magma_queue_create( &streaml[i][0] );
magma_queue_create( &streaml[i][1] );
}
nbmin = 2;
nx = nb;
ldwork = m;
lddwork= n;
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
old_i = 0; old_ib = nb;
for (i = 0; i < k-nx; i += nb)
{
/* Set the GPU number that holds the current panel */
panel_gpunum = (i/nb)%num_gpus;
/* Set the local index where the current panel is */
i_local = i/(nb*num_gpus)*nb;
ib = min(k-i, nb);
rows = m -i;
/* Send current panel to the CPU */
#ifdef MultiGPUs
magma_setdevice(panel_gpunum);
#endif
magma_sgetmatrix_async( rows, ib,
dlA(panel_gpunum, i, i_local), ldda,
hwrk_ref(i), ldwork, streaml[panel_gpunum][1] );
if (i>0){
/* Apply H' to A(i:m,i+2*ib:n) from the left; this is the look-ahead
application to the trailing matrix */
la_gpu = panel_gpunum;
/* only the GPU that has next panel is done look-ahead */
#ifdef MultiGPUs
magma_setdevice(la_gpu);
#endif
magma_slarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
m-old_i, n_local[la_gpu]-i_local-old_ib, old_ib,
panel[la_gpu], ldda, dwork[la_gpu], lddwork,
dlA(la_gpu, old_i, i_local+old_ib), ldda,
dwork[la_gpu]+old_ib, lddwork);
la_gpu = ((i-nb)/nb)%num_gpus;
#ifdef MultiGPUs
magma_setdevice(la_gpu);
#endif
magma_ssetmatrix_async( old_ib, old_ib,
hwrk_ref(old_i), ldwork,
panel[la_gpu], ldda, streaml[la_gpu][0] );
}
#ifdef MultiGPUs
magma_setdevice(panel_gpunum);
#endif
magma_queue_sync( streaml[panel_gpunum][1] );
lapackf77_sgeqrf(&rows, &ib, hwrk_ref(i), &ldwork, tau+i, lhwrk, &lhwork, info);
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
lapackf77_slarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
hwrk_ref(i), &ldwork, tau+i, lhwrk, &ib);
spanel_to_q( MagmaUpper, ib, hwrk_ref(i), ldwork, lhwrk+ib*ib );
// Send the current panel back to the GPUs
// Has to be done with asynchronous copies
for(j=0; j<num_gpus; j++)
{
#ifdef MultiGPUs
magma_setdevice(j);
#endif
if (j == panel_gpunum)
panel[j] = dlA(j, i, i_local);
else
panel[j] = dwork[j]+displacement;
magma_ssetmatrix_async( rows, ib,
hwrk_ref(i), ldwork,
panel[j], ldda, streaml[j][0] );
}
for(j=0; j<num_gpus; j++)
{
#ifdef MultiGPUs
magma_setdevice(j);
#endif
magma_queue_sync( streaml[j][0] );
}
/* Restore the panel */
sq_to_panel( MagmaUpper, ib, hwrk_ref(i), ldwork, lhwrk+ib*ib );
if (i + ib < n)
{
/* Send the T matrix to the GPU.
Has to be done with asynchronous copies */
for(j=0; j<num_gpus; j++)
{
#ifdef MultiGPUs
magma_setdevice(j);
#endif
magma_ssetmatrix_async( ib, ib,
lhwrk, ib,
dwork[j], lddwork, streaml[j][0] );
}
if (i+nb < k-nx)
{
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left;
This is update for the next panel; part of the look-ahead */
la_gpu = (panel_gpunum+1)%num_gpus;
int i_loc = (i+nb)/(nb*num_gpus)*nb;
for(j=0; j<num_gpus; j++){
#ifdef MultiGPUs
magma_setdevice(j);
#endif
//magma_queue_sync( streaml[j][0] );
if (j==la_gpu)
magma_slarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
panel[j], ldda, dwork[j], lddwork,
dlA(j, i, i_loc), ldda, dwork[j]+ib, lddwork);
else if (j<=panel_gpunum)
magma_slarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, n_local[j]-i_local-ib, ib,
panel[j], ldda, dwork[j], lddwork,
dlA(j, i, i_local+ib), ldda, dwork[j]+ib, lddwork);
else
magma_slarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, n_local[j]-i_local, ib,
panel[j], ldda, dwork[j], lddwork,
dlA(j, i, i_local), ldda, dwork[j]+ib, lddwork);
}
}
else {
/* do the entire update as we exit and there would be no lookahead */
la_gpu = (panel_gpunum+1)%num_gpus;
int i_loc = (i+nb)/(nb*num_gpus)*nb;
#ifdef MultiGPUs
magma_setdevice(la_gpu);
#endif
magma_slarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, n_local[la_gpu]-i_loc, ib,
panel[la_gpu], ldda, dwork[la_gpu], lddwork,
dlA(la_gpu, i, i_loc), ldda, dwork[la_gpu]+ib, lddwork);
#ifdef MultiGPUs
magma_setdevice(panel_gpunum);
#endif
magma_ssetmatrix( ib, ib,
hwrk_ref(i), ldwork,
dlA(panel_gpunum, i, i_local), ldda );
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
for(j=0; j<num_gpus; j++){
#ifdef MultiGPUs
magma_setdevice(j);
#endif
magma_free( dwork[j] );
}
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
rows = m-i;
lhwork = lwork - rows*ib;
panel_gpunum = (panel_gpunum+1)%num_gpus;
int i_loc = (i)/(nb*num_gpus)*nb;
#ifdef MultiGPUs
magma_setdevice(panel_gpunum);
#endif
magma_sgetmatrix( rows, ib,
dlA(panel_gpunum, i, i_loc), ldda,
lhwrk, rows );
lhwork = lwork - rows*ib;
lapackf77_sgeqrf(&rows, &ib, lhwrk, &rows, tau+i, lhwrk+ib*rows, &lhwork, info);
magma_ssetmatrix( rows, ib,
lhwrk, rows,
dlA(panel_gpunum, i, i_loc), ldda );
}
for(i=0; i<num_gpus; i++){
#ifdef MultiGPUs
magma_setdevice(i);
#endif
magma_queue_destroy( streaml[i][0] );
magma_queue_destroy( streaml[i][1] );
}
magma_setdevice(cdevice);
magma_free_pinned( local_work );
return *info;
} /* magma_sgeqrf2_mgpu */
extern "C" magma_int_t
magma_sgeqrf_msub(
magma_int_t num_subs, magma_int_t num_gpus,
magma_int_t m, magma_int_t n,
magmaFloat_ptr *dlA, magma_int_t ldda,
float *tau,
magma_queue_t *queues,
magma_int_t *info)
{
/* -- clMAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date November 2014
Purpose
=======
SGEQRF2_MGPU computes a QR factorization of a real M-by-N matrix A:
A = Q * R. This is a GPU interface of the routine.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
dA (input/output) REAL array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix dA.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
TAU (output) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
===================================================================== */
#define dlA(gpu,a_1,a_2) dlA[gpu], ((a_2)*(ldda) + (a_1))
#define dlA_offset(a_1, a_2) ((a_2)*(ldda) + (a_1))
#define work_ref(a_1) ( work + (a_1))
#define hwork ( work + (nb)*(m))
#define hwrk(a_1) ( local_work + (a_1))
#define lhwrk ( local_work + (nb)*(m))
magmaFloat_ptr dwork[MagmaMaxGPUs], panel[MagmaMaxGPUs];
size_t panel_offset[MagmaMaxGPUs];
float *local_work = NULL;
magma_int_t i, j, k, ldwork, lddwork, old_i, old_ib, rows;
magma_int_t nbmin, nx, ib, nb;
magma_int_t lhwork, lwork;
int panel_id = -1, i_local, n_local[MagmaMaxGPUs * MagmaMaxSubs], la_id, displacement,
tot_subs = num_gpus * num_subs;
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
k = min(m,n);
if (k == 0)
return *info;
nb = magma_get_sgeqrf_nb(m);
displacement = n * nb;
lwork = (m+n+64) * nb;
lhwork = lwork - (m)*nb;
for (i=0; i<num_gpus; i++) {
if (MAGMA_SUCCESS != magma_smalloc( &(dwork[i]), (n + ldda)*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
/* Set the number of local n for each GPU */
for (i=0; i<tot_subs; i++) {
n_local[i] = ((n/nb)/tot_subs)*nb;
if (i < (n/nb)%tot_subs)
n_local[i] += nb;
else if (i == (n/nb)%tot_subs)
n_local[i] += n%nb;
}
#ifdef USE_PINNED_CLMEMORY
cl_mem buffer = clCreateBuffer(gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, sizeof(float)*lwork, NULL, NULL);
for (j=0; j<num_gpus; j++) {
local_work = (float*)clEnqueueMapBuffer(queues[2*j], buffer, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0,
sizeof(float)*lwork, 0, NULL, NULL, NULL);
}
#else
if (MAGMA_SUCCESS != magma_smalloc_cpu( (&local_work), lwork )) {
*info = -9;
for (i=0; i<num_gpus; i++) {
magma_free( dwork[i] );
}
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
#endif
nbmin = 2;
nx = nb;
ldwork = m;
lddwork= n;
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
old_i = 0; old_ib = nb;
for (i = 0; i < k-nx; i += nb) {
/* Set the GPU number that holds the current panel */
panel_id = (i/nb)%tot_subs;
/* Set the local index where the current panel is */
i_local = i/(nb*tot_subs)*nb;
ib = min(k-i, nb);
rows = m -i;
/* Send current panel to the CPU */
magma_queue_sync(queues[2*(panel_id%num_gpus)]);
magma_sgetmatrix_async( rows, ib,
dlA(panel_id, i, i_local), ldda,
hwrk(i), ldwork,
queues[2*(panel_id%num_gpus)+1], NULL );
if (i > 0) {
/* Apply H' to A(i:m,i+2*ib:n) from the left; this is the look-ahead
application to the trailing matrix */
la_id = panel_id;
/* only the GPU that has next panel is done look-ahead */
magma_slarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, n_local[la_id]-i_local-old_ib, old_ib,
panel[la_id%num_gpus], panel_offset[la_id%num_gpus], ldda,
dwork[la_id%num_gpus], 0, lddwork,
dlA(la_id, old_i, i_local+old_ib), ldda,
dwork[la_id%num_gpus], old_ib, lddwork,
queues[2*(la_id%num_gpus)]);
la_id = ((i-nb)/nb)%tot_subs;
magma_ssetmatrix_async( old_ib, old_ib,
hwrk(old_i), ldwork,
panel[la_id%num_gpus], panel_offset[la_id%num_gpus], ldda,
queues[2*(la_id%num_gpus)], NULL );
}
magma_queue_sync( queues[2*(panel_id%num_gpus)+1] );
lapackf77_sgeqrf(&rows, &ib, hwrk(i), &ldwork, tau+i, lhwrk, &lhwork, info);
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
lapackf77_slarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
hwrk(i), &ldwork, tau+i, lhwrk, &ib);
spanel_to_q( MagmaUpper, ib, hwrk(i), ldwork, lhwrk+ib*ib );
// Send the current panel back to the GPUs
// Has to be done with asynchronous copies
for (j=0; j<num_gpus; j++) {
if (j == panel_id%num_gpus){
panel[j] = dlA(panel_id, i, i_local);
panel_offset[j] = dlA_offset(i, i_local);
} else {
panel[j] = dwork[j];
panel_offset[j] = displacement;
}
magma_queue_sync( queues[2*j] );
magma_ssetmatrix_async( rows, ib,
hwrk(i), ldwork,
panel[j], panel_offset[j], ldda,
queues[2*j+1], NULL );
/* Send the T matrix to the GPU.
Has to be done with asynchronous copies */
magma_ssetmatrix_async( ib, ib, lhwrk, ib,
dwork[j], 0, lddwork,
queues[2*j+1], NULL );
}
for(j=0; j<num_gpus; j++) {
magma_queue_sync( queues[2*j+1] );
}
if (i + ib < n) {
if (i+nb < k-nx) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left;
This is update for the next panel; part of the look-ahead */
la_id = (panel_id+1)%tot_subs;
int i_loc = (i+nb)/(nb*tot_subs)*nb;
for (j=0; j<tot_subs; j++) {
if (j == la_id)
magma_slarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
panel[j%num_gpus], panel_offset[j%num_gpus], ldda,
dwork[j%num_gpus], 0, lddwork,
dlA(j, i, i_loc), ldda,
dwork[j%num_gpus], ib, lddwork,
queues[2*(j%num_gpus)]);
else if (j <= panel_id)
magma_slarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[j]-i_local-ib, ib,
panel[j%num_gpus], panel_offset[j%num_gpus], ldda,
dwork[j%num_gpus], 0, lddwork,
dlA(j, i, i_local+ib), ldda,
dwork[j%num_gpus], ib, lddwork,
queues[2*(j%num_gpus)]);
else
magma_slarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[j]-i_local, ib,
panel[j%num_gpus], panel_offset[j%num_gpus], ldda,
dwork[j%num_gpus], 0, lddwork,
dlA(j, i, i_local), ldda,
dwork[j%num_gpus], ib, lddwork,
queues[2*(j%num_gpus)]);
}
/* Restore the panel */
sq_to_panel( MagmaUpper, ib, hwrk(i), ldwork, lhwrk+ib*ib );
} else {
/* do the entire update as we exit and there would be no lookahead */
la_id = (panel_id+1)%tot_subs;
int i_loc = (i+nb)/(nb*tot_subs)*nb;
magma_slarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[la_id]-i_loc, ib,
panel[la_id%num_gpus], panel_offset[la_id%num_gpus], ldda,
dwork[la_id%num_gpus], 0, lddwork,
dlA(la_id, i, i_loc), ldda,
dwork[la_id%num_gpus], ib, lddwork,
queues[2*(la_id%num_gpus)]);
/* Restore the panel */
sq_to_panel( MagmaUpper, ib, hwrk(i), ldwork, lhwrk+ib*ib );
magma_ssetmatrix( ib, ib,
hwrk(i), ldwork,
dlA(panel_id, i, i_local), ldda,
queues[2*(panel_id%num_gpus)]);
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
for (j=0; j<num_gpus; j++) {
magma_free( dwork[j] );
}
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
rows = m-i;
lhwork = lwork - rows*ib;
panel_id = (panel_id+1)%tot_subs;
int i_loc = (i)/(nb*tot_subs)*nb;
magma_sgetmatrix( rows, ib,
dlA(panel_id, i, i_loc), ldda,
lhwrk, rows,
queues[2*(panel_id%num_gpus)]);
lhwork = lwork - rows*ib;
lapackf77_sgeqrf(&rows, &ib, lhwrk, &rows, tau+i, lhwrk+ib*rows, &lhwork, info);
magma_ssetmatrix( rows, ib,
lhwrk, rows,
dlA(panel_id, i, i_loc), ldda,
queues[2*(panel_id%num_gpus)]);
}
#ifdef USE_PINNED_CLMEMORY
#else
magma_free_cpu( local_work );
#endif
return *info;
} /* magma_sgeqrf_msub */
/**
Purpose
-------
SPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix dA.
The factorization has the form
dA = U**T * U, if UPLO = MagmaUpper, or
dA = L * L**T, if UPLO = MagmaLower,
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of dA is stored;
- = MagmaLower: Lower triangle of dA is stored.
@param[in]
n INTEGER
The order of the matrix dA. N >= 0.
@param[in,out]
dA REAL array on the GPU, dimension (LDDA,N)
On entry, the symmetric matrix dA. If UPLO = MagmaUpper, the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**T * U or dA = L * L**T.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
@ingroup magma_sposv_comp
********************************************************************/
extern "C" magma_int_t
magma_spotrf2_mgpu(int num_gpus, magma_uplo_t uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
float **d_lA, magma_int_t ldda,
float **d_lP, magma_int_t lddp,
float *A, magma_int_t lda, magma_int_t h,
magma_queue_t stream[][3], magma_event_t event[][5],
magma_int_t *info )
{
#define Alo(i, j) (A + ((j)+off_j)*lda + (nb*(((i)/nb)%h)+off_i))
#define Aup(i, j) (A + (nb*(((j)/nb)%h)+off_j)*lda + (i+off_i))
#define dlA(id, i, j) (d_lA[(id)] + (j)*ldda + (i))
#define dlP(id, i, j, k) (d_lP[(id)] + (k)*nb*lddp + (j)*lddp + (i))
#define dlPT(id, i, j, k) (d_lP[(id)] + (k)*nb*lddp + (j)*nb + (i))
magma_int_t j, jb, nb0, nb2, dd, d, id, j_local, j_local2, buf;
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
float d_one = 1.0;
float d_neg_one = -1.0;
int upper = (uplo == MagmaUpper);
float *dlpanel;
//magma_event_t event0[MagmaMaxGPUs], // syrk
// event1[MagmaMaxGPUs], // send off-diagonal
// event2[MagmaMaxGPUs], // send diagonal
// event3[MagmaMaxGPUs]; // trsm
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
int stream0 = 0, stream1 = 1;
#ifdef STRSM_WORK
float *d_dinvA[MagmaMaxGPUs][2], *d_x[MagmaMaxGPUs][2]; /* used by strsm_work */
#endif
*info = 0;
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (!upper && num_gpus*ldda < max(1,n)) {
*info = -4;
} else if (upper && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
for( d=0; d < num_gpus; d++ ) {
/* local-n and local-ld */
if (upper) {
n_local[d] = ((n/nb)/num_gpus)*nb;
if (d < (n/nb)%num_gpus)
n_local[d] += nb;
else if (d == (n/nb)%num_gpus)
n_local[d] += n%nb;
} else {
n_local[d] = ((m/nb)/num_gpus)*nb;
if (d < (m/nb)%num_gpus)
n_local[d] += nb;
else if (d == (m/nb)%num_gpus)
n_local[d] += m%nb;
}
//magma_setdevice(d);
//magma_event_create( &event0[d] );
//magma_event_create( &event1[d] );
//magma_event_create( &event2[d] );
//magma_event_create( &event3[d] );
}
magma_setdevice(0);
/* == initialize the trace */
trace_init( 1, num_gpus, 3, (magma_queue_t*)stream );
/* Use blocked code. */
if (upper) {
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
#if defined(PRECISION_d) && defined(STRSM_WORK)
/* invert the diagonals
* Allocate device memory for the inversed diagonal blocks, size=m*NB
*/
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j < 2; j++ ) {
magma_smalloc( &d_dinvA[d][j], nb*nb );
magma_smalloc( &d_x[d][j], n*nb );
cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(float));
cudaMemset(d_x[d][j], 0, n*nb*sizeof(float));
}
}
magma_setdevice(0);
#endif
for (j=0; j < m; j += nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (m-j));
if ( j > 0 ) {
/* needed on pluto... */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] ); // wait for the column on CPU
/* broadcast off-diagonal column to all gpus */
d = (j/nb+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
if ( d != id ) {
magma_setdevice(d);
/* wait for it on CPU */
magma_queue_wait_event( stream[d][stream0], event[id][1] );
/* send it to GPU */
trace_gpu_start( d, stream0, "comm", "rows to GPUs" );
magma_ssetmatrix_async( j, jb,
Aup(0,j), lda,
dlP(d,jb,0,buf), lddp,
stream[d][stream0] );
trace_gpu_end( d, stream0 );
magma_event_record( event[d][1], stream[d][stream0] );
}
d = (d+1)%num_gpus;
}
}
/* Update the current diagonal block */
magma_setdevice(id);
if ( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
trace_gpu_start( id, stream1, "syrk", "syrk" );
magma_ssyrk(MagmaUpper, MagmaTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda);
trace_gpu_end( id, stream1 );
magma_event_record( event[id][0], stream[id][stream1] );
}
/* send the diagonal to cpu */
magma_queue_wait_event( stream[id][stream0], event[id][0] ); // wait for syrk
trace_gpu_start( id, stream0, "comm", "D to CPU" );
magma_sgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
stream[id][stream0] );
trace_gpu_end( id, stream0 );
if ( j > 0 ) {
/* Compute the local block column of the panel. */
d = (j/nb+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
j_local2 = j_local+1;
if ( d > id ) j_local2 --;
nb0 = nb*j_local2;
if ( n_local[d] > nb0 ) {
/* wait for the off-diagonal */
if ( d != id ) {
//magma_queue_sync( stream[id][3] );
dlpanel = dlP(d, jb, 0, buf);
ldpanel = lddp;
/* wait for the offdiagonal column */
magma_queue_wait_event( stream[d][stream1], event[d][1] );
} else {
dlpanel = dlA(d, 0, nb*j_local);
ldpanel = ldda;
}
/* update the panel */
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
trace_gpu_start( d, stream1, "gemm", "gemm" );
magma_sgemm(MagmaTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda);
trace_gpu_end( d, stream1 );
}
d = (d+1)%num_gpus;
}
}
/* factor the diagonal */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] ); // wait for the diagonal
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_spotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
magma_setdevice(d);
if ( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, 0, 0, buf);
ldpanel = lddp;
}
trace_gpu_start( d, stream0, "comm", "D to GPUs" );
magma_ssetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, ldpanel,
stream[d][stream0] );
trace_gpu_end( d, stream0 );
magma_event_record( event[d][2], stream[d][stream0] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
trace_gpu_start( id, stream0, "comm", "D to GPUs" );
magma_ssetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
stream[id][stream0] );
trace_gpu_end( id, stream0 );
}
/* panel-factorize the off-diagonal */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if ( d > id ) j_local2--;
if ( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, 0, 0, buf);
ldpanel = lddp;
}
nb2 = n_local[d]-nb*j_local2;
nb0 = min(nb, nb2 );
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for the diagonal
if ( j+jb < m && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead the column */
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if defined(PRECISION_d) && defined(STRSM_WORK)
magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d][0], d_x[d][0] );
/*nb2 = n_local[d] - j_local2*nb;
magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d], d_x[d] ); */
#else
/*nb2 = n_local[d] - j_local2*nb;
magma_strsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldda,
dlA(d, j, nb*j_local2), ldda);
*/
magma_strsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream1 );
magma_event_record( event[d][3], stream[d][stream1] );
/* send the column to cpu */
if ( j+jb < m ) {
trace_gpu_start( d, stream0, "comm", "rows to CPU" );
magma_queue_wait_event( stream[d][stream0], event[d][3] ); // wait for lookahead
magma_sgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
stream[d][stream0] );
trace_gpu_end( d, stream0 );
magma_event_record( event[d][1], stream[d][stream0] );
}
/* update the remaining blocks */
nb2 = nb2 - nb0;
#if defined(PRECISION_d) && defined(STRSM_WORK)
magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_strsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda);
#endif
} else if ( nb2 > 0 ) {
/* update the entire trailing matrix */
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if defined(PRECISION_d) && defined(STRSM_WORK)
magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_strsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream1 );
}
d = (d+1)%num_gpus;
}
} /* end of strsm */
} /* end of for j=1, .., n */
} else {
/* -------------------------------------------- */
/* Lower-triangular case */
/* Compute the Cholesky factorization A = L*L'. */
/* -------------------------------------------- */
#if defined(PRECISION_d) && defined(STRSM_WORK)
/*
* Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
*/
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j < 2; j++ ) {
magma_smalloc( &d_dinvA[d][j], nb*nb );
magma_smalloc( &d_x[d][j], nb*m );
cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(float));
cudaMemset(d_x[d][j], 0, nb* m*sizeof(float));
}
}
magma_setdevice(0);
#endif
for (j=0; j < n; j += nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (n-j));
if ( j > 0 ) {
/* needed on pluto... */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] ); // wait for the column on CPU
/* broadcast offdiagonal row to all gpus */
d = (j/nb+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
if ( d != id ) {
magma_setdevice(d);
/* wait for it on CPU */
magma_queue_wait_event( stream[d][stream0], event[id][1] );
/* send it to GPU */
magma_ssetmatrix_async( jb, j,
Alo(j,0), lda,
dlPT(d,0,jb,buf), nb,
stream[d][stream0] );
magma_event_record( event[d][1], stream[d][stream0] );
}
d = (d+1)%num_gpus;
}
}
/* Update the current diagonal block */
magma_setdevice(id);
if ( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
magma_ssyrk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda);
magma_event_record( event[id][0], stream[id][stream1] );
}
/* send the diagonal to cpu */
magma_queue_wait_event( stream[id][stream0], event[id][0] ); // wait for syrk
magma_sgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
stream[id][stream0] );
/* update the offdiagonal blocks */
if ( j > 0 ) {
/* compute the block-rows of the panel */
d = (j/nb+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
j_local2 = j_local+1;
if ( d > id ) j_local2 --;
nb0 = nb*j_local2;
if ( nb0 < n_local[d] ) {
if ( d != id ) {
dlpanel = dlPT(d, 0, jb, buf);
ldpanel = nb;
/* wait for offdiagonal row */
magma_queue_wait_event( stream[d][stream1], event[d][1] );
} else {
dlpanel = dlA(d, nb*j_local, 0);
ldpanel = ldda;
}
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
magma_sgemm( MagmaNoTrans, MagmaTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, ldpanel,
c_one, dlA(d, nb0, j), ldda);
}
d = (d+1)%num_gpus;
}
}
/* factor the diagonal */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] );
lapackf77_spotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ( (j+jb) < m ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
magma_setdevice(d);
if ( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
magma_ssetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, ldpanel,
stream[d][stream0] );
magma_event_record( event[d][2], stream[d][stream0] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
magma_ssetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
stream[id][stream0] );
}
/* factorize off-diagonal blocks */
if ( (j+jb) < m ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if ( d > id ) j_local2--;
if ( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2 );
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for the diagonal
if ( j+jb < n && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead the column */
#if defined(PRECISION_d) && defined(STRSM_WORK)
magmablas_strsm_work( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
d_dinvA[d][0], d_x[d][0]);
#else
magma_strsm( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
magma_event_record( event[d][3], stream[d][stream1] );
/* send the column to cpu */
if ( j+jb < n ) {
magma_queue_wait_event( stream[d][stream0], event[d][3] ); // wait for lookahead
magma_sgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream0] );
magma_event_record( event[d][1], stream[d][stream0] );
}
/* update the remaining blocks */
nb2 = nb2 - nb0;
#if defined(PRECISION_d) && defined(STRSM_WORK)
magmablas_strsm_work( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_strsm( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda);
#endif
} else if ( nb2 > 0 ) {
/* update the entire trailing matrix */
#if defined(PRECISION_d) && defined(STRSM_WORK)
magmablas_strsm_work( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_strsm( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
}
d = (d+1)%num_gpus;
}
}
}
} /* end of else not upper */
/* == finalize the trace == */
trace_finalize( "spotrf.svg", "trace.css" );
/* clean up */
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magmablasSetKernelStream(NULL);
//magma_event_destroy( event0[d] );
//magma_event_destroy( event1[d] );
//magma_event_destroy( event2[d] );
//magma_event_destroy( event3[d] );
}
magma_setdevice(0);
return *info;
} /* magma_spotrf_mgpu */
/**
Purpose
-------
SPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = MagmaUpper, or
dA = L * L**H, if UPLO = MagmaLower,
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of dA is stored;
- = MagmaLower: Lower triangle of dA is stored.
@param[in]
n INTEGER
The order of the matrix dA. N >= 0.
@param[in,out]
d_lA REAL array of pointers on the GPU, dimension (ngpu)
On entry, the symmetric matrix dA distributed over GPUs
(dl_A[d] points to the local matrix on the d-th GPU).
It is distributed in 1D block column or row cyclic (with the
block size of nb) if UPLO = MagmaUpper or MagmaLower, respectively.
If UPLO = MagmaUpper, the leading N-by-N upper triangular
part of dA contains the upper triangular part of the matrix dA,
and the strictly lower triangular part of dA is not referenced.
If UPLO = MagmaLower, the leading N-by-N lower triangular part
of dA contains the lower triangular part of the matrix dA, and
the strictly upper triangular part of dA is not referenced.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
@ingroup magma_sposv_comp
********************************************************************/
extern "C" magma_int_t
magma_spotrf_mgpu_right(
magma_int_t ngpu,
magma_uplo_t uplo, magma_int_t n,
magmaFloat_ptr d_lA[], magma_int_t ldda,
magma_int_t *info )
{
#define dlA(id, i, j) (d_lA[(id)] + (j) * ldda + (i))
#define dlP(id, i, j) (d_lP[(id)] + (j) * ldda + (i))
#define panel(j) (panel + (j))
#define tmppanel(j) (tmppanel + (j))
#define tmpprevpanel(j) (tmpprevpanel + (j))
#define STREAM_ID(i) (nqueue > 1 ? 1+((i)/nb)%(nqueue-1) : 0)
float z_one = MAGMA_S_MAKE( 1.0, 0.0 );
float mz_one = MAGMA_S_MAKE( -1.0, 0.0 );
float one = 1.0;
float m_one = -1.0;
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t j, nb, d, id, j_local, blkid, crosspoint, prevtrsmrows=0, nqueue = 5;
float *panel, *tmppanel0, *tmppanel1, *tmppanel, *tmpprevpanel;
float *d_lP[MagmaMaxGPUs], *dlpanel, *dlpanels[MagmaMaxGPUs];
magma_int_t rows, trsmrows, igpu, n_local[MagmaMaxGPUs], ldpanel;
magma_queue_t queues[MagmaMaxGPUs][10];
*info = 0;
if ( uplo != MagmaUpper && uplo != MagmaLower ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
nb = magma_get_spotrf_nb(n);
ldpanel = ldda;
magma_setdevice(0);
if (MAGMA_SUCCESS != magma_smalloc_pinned( &panel, 2 * nb * ldpanel )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
tmppanel0 = panel;
tmppanel1 = tmppanel0 + nb * ldpanel;
if ((nb <= 1) || (nb >= n)) {
// Use unblocked code.
magma_sgetmatrix( n, n, dlA(0, 0, 0), ldda, panel, ldpanel);
lapackf77_spotrf( uplo_, &n, panel, &ldpanel, info);
magma_ssetmatrix( n, n, panel, ldpanel, dlA(0, 0, 0), ldda );
} else {
for( d = 0; d < ngpu; d++ ) {
// local-n and local-ld
n_local[d] = ((n / nb) / ngpu) * nb;
if (d < (n / nb) % ngpu)
n_local[d] += nb;
else if (d == (n / nb) % ngpu)
n_local[d] += n % nb;
magma_setdevice(d);
magma_device_sync();
if (MAGMA_SUCCESS != magma_smalloc( &d_lP[d], nb * ldda )) {
for( j = 0; j < d; j++ ) {
magma_setdevice(j);
magma_free( d_lP[d] );
}
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
for( j=0; j < nqueue; j++ ) {
magma_queue_create( &queues[d][j] );
}
}
//#define ENABLE_TIMER
#if defined (ENABLE_TIMER)
real_Double_t therk[4], tmtc, tcchol, tctrsm, tctm, tmnp, tcnp;
real_Double_t ttot_herk[4] = {0,0,0,0}, ttot_mtc = 0, ttot_cchol = 0, ttot_ctrsm = 0, ttot_ctm = 0, ttot_mnp = 0, ttot_cnp = 0;
printf("\n\n %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s %10s\n",
"j", "nb", "row", "mtc", "CPU_np", "panel", "ctrsm", "CH+TRSM", "CPU", "dsyrk[0]", "dsyrk[1]", "dsyrk[2]", "dsyrk[3]", "ctm P", "gpu_np");
printf(" ====================================================================================================\n");
#endif
// Use blocked code.
if (uplo == MagmaUpper) {
printf( " === not supported, yet ===\n" );
} else {
blkid = -1;
if (ngpu == 4)
crosspoint = n;
else if (ngpu == 3)
crosspoint = n;
else if (ngpu == 2)
crosspoint = 20160;
else
crosspoint = 0;
crosspoint = 0; //n; //n -- > gpu always does next panel, 0 --> cpu always does next panel
crosspoint = n;
#if defined (ENABLE_TIMER)
real_Double_t tget = magma_wtime(), tset = 0.0, ttot = 0.0;
#endif
if ( n > nb ) {
// send first panel to cpu
magma_setdevice(0);
tmppanel = tmppanel0;
magma_sgetmatrix_async(n, nb,
dlA(0, 0, 0), ldda,
tmppanel(0), ldpanel,
queues[0][0] );
}
#if defined (ENABLE_TIMER)
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magma_device_sync();
}
tget = magma_wtime()-tget;
#endif
// Compute the Cholesky factorization A = L*L'
for (j = 0; (j + nb) < n; j += nb) {
#if defined (ENABLE_TIMER)
therk[0] = therk[1] = therk[2] = therk[3] = tmtc = tcchol = tctrsm = tctm = tmnp = tcnp = 0.0;
#endif
blkid += 1;
tmppanel = (blkid % 2 == 0) ? tmppanel0 : tmppanel1;
// Set the gpu number that holds the current panel
id = (j / nb) % ngpu;
magma_setdevice(id);
// Set the local index where the current panel is
j_local = j / (nb * ngpu) * nb;
rows = n - j;
// Wait for the panel on cpu
magma_queue_sync( queues[id][0] );
if (j > 0 && prevtrsmrows > crosspoint) {
#if defined (ENABLE_TIMER)
tcnp = magma_wtime();
#endif
tmpprevpanel = ((blkid - 1) % 2) == 0 ? tmppanel0 : tmppanel1;
blasf77_sgemm( MagmaNoTransStr, MagmaConjTransStr,
&rows, &nb, &nb,
&mz_one, tmpprevpanel(j), &ldpanel,
tmpprevpanel(j), &ldpanel,
&z_one, tmppanel(j), &ldpanel );
#if defined (ENABLE_TIMER)
tcnp = magma_wtime() - tcnp;
ttot_cnp += tcnp;
#endif
}
#if defined (ENABLE_TIMER)
tcchol = magma_wtime();
#endif
lapackf77_spotrf(MagmaLowerStr, &nb, tmppanel(j), &ldpanel, info);
if (*info != 0) {
*info = *info + j;
break;
}
#if defined (ENABLE_TIMER)
tcchol = magma_wtime() - tcchol;
ttot_cchol += tcchol;
tctrsm = magma_wtime();
#endif
trsmrows = rows - nb;
if (trsmrows > 0) {
blasf77_strsm(MagmaRightStr, MagmaLowerStr, MagmaConjTransStr, MagmaNonUnitStr,
&trsmrows, &nb,
&z_one, tmppanel(j), &ldpanel,
tmppanel(j + nb), &ldpanel);
}
#if defined (ENABLE_TIMER)
tctrsm = magma_wtime() - tctrsm;
ttot_ctrsm += tctrsm;
tctm = magma_wtime();
#endif
d = (id + 1) % ngpu;
// send current panel to gpus
for (igpu = 0; igpu < ngpu; igpu++, d = (d + 1) % ngpu ) {
magma_int_t myrows = 0;
magma_int_t row_offset = 0;
if ( d == id ) {
dlpanel = dlA(d, j, j_local);
myrows = rows;
row_offset = 0;
} else {
dlpanel = dlP(d, 0, 0);
myrows = trsmrows;
row_offset = nb;
}
if (myrows > 0) {
magma_setdevice(d);
magma_ssetmatrix_async(myrows, nb,
tmppanel(j + row_offset), ldpanel,
dlpanel, ldda, queues[d][0] );
}
}
/* make sure panel is on GPUs */
d = (id + 1) % ngpu;
for (igpu = 0; igpu < ngpu; igpu++, d = (d + 1) % ngpu ) {
magma_setdevice(d);
magma_queue_sync( queues[d][0] );
}
#if defined (ENABLE_TIMER)
tctm = magma_wtime() - tctm;
ttot_ctm += tctm;
#endif
if ( (j + nb) < n) {
magma_int_t offset = 0;
magma_int_t row_offset = 0;
if (j + nb + nb < n) {
d = (id + 1) % ngpu;
magma_setdevice(d);
magma_int_t j_local2 = (j + nb) / (nb * ngpu) * nb;
if (trsmrows <= crosspoint) {
#if defined (ENABLE_TIMER)
tmnp = magma_wtime();
#endif
// do gemm on look ahead panel
if ( d == id ) {
dlpanel = dlA(d, j + nb, j_local);
} else {
dlpanel = dlP(d, 0, 0);
}
magmablasSetKernelStream( queues[d][STREAM_ID(j_local2)] );
#define SSYRK_ON_DIAG
#ifdef SSYRK_ON_DIAG
magma_ssyrk( MagmaLower, MagmaNoTrans,
nb, nb,
m_one, dlpanel, ldda,
one, dlA(d, j + nb, j_local2), ldda);
magma_sgemm( MagmaNoTrans, MagmaConjTrans,
trsmrows-nb, nb, nb,
mz_one, dlpanel+nb, ldda,
dlpanel, ldda,
z_one, dlA(d, j + nb +nb, j_local2), ldda);
#else
magma_sgemm( MagmaNoTrans, MagmaConjTrans,
trsmrows, nb, nb,
mz_one, dlpanel, ldda,
dlpanel, ldda,
z_one, dlA(d, j + nb, j_local2), ldda);
#endif
#if defined (ENABLE_TIMER)
magma_device_sync();
tmnp = magma_wtime() - tmnp;
ttot_mnp += tmnp;
#endif
}
// send next panel to cpu
magma_queue_sync( queues[d][STREAM_ID(j_local2)] ); // make sure lookahead is done
tmppanel = ((blkid+1) % 2 == 0) ? tmppanel0 : tmppanel1;
magma_sgetmatrix_async(rows-nb, nb,
dlA(d, j+nb, j_local2), ldda,
tmppanel(j+nb), ldpanel,
queues[d][0] );
tmppanel = (blkid % 2 == 0) ? tmppanel0 : tmppanel1;
offset = j + nb + nb;
row_offset = nb;
} else {
offset = j + nb;
row_offset = 0;
}
if (n - offset > 0) {
// syrk on multiple gpu
for (d = 0; d < ngpu; d++ ) {
if ( d == id ) {
dlpanels[d] = dlA(d, j + nb + row_offset, j_local);
} else {
dlpanels[d] = dlP(d, row_offset, 0);
}
}
#if defined (ENABLE_TIMER)
for( d=0; d < ngpu; d++ ) therk[d] = magma_wtime();
#endif
//magmablasSetKernelStream( queues[d] );
//magma_ssyrk(MagmaLower, MagmaNoTrans, n - offset, nb,
// m_one, dlpanel, ldda,
// one, &d_lA[d][offset + offset*ldda], ldda );
#ifdef SSYRK_ON_DIAG
magma_ssyrk_mgpu
#else
magma_ssyrk_mgpu2
#endif
(ngpu, MagmaLower, MagmaNoTrans,
nb, n - offset, nb,
m_one, dlpanels, ldda, 0,
one, d_lA, ldda, offset,
nqueue, queues );
#if defined (ENABLE_TIMER)
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magma_device_sync();
therk[d] = magma_wtime() - therk[d];
ttot_herk[d] += therk[d];
}
#endif
}
prevtrsmrows = trsmrows;
#if defined (ENABLE_TIMER)
ttot += (tcnp+tcchol+tctrsm+therk[0]+therk[1]+therk[2]+tctm+tmnp);
printf("%10d %10d %10d %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf(%d) %10.3lf\n",
j, nb, rows, tmtc,
tcnp, // gemm
tcchol, // potrf
tctrsm, // trsm
(tcchol + tctrsm),
(tmtc+tcnp+tcchol+tctrsm),
therk[0], therk[1], therk[2], therk[3], // syrk
tctm, // copy panel to GPU
tmnp, // lookahead on GPU
(id + 1) % ngpu,
(tcnp+tcchol+tctrsm+therk[0]+therk[1]+therk[2]+tctm+tmnp));
fflush(0);
#endif
}
}
for( d = 0; d < ngpu; d++ ) {
magma_setdevice(d);
for( id=0; id < nqueue; id++ ) {
magma_queue_sync( queues[d][id] );
}
}
#if defined (ENABLE_TIMER)
printf("\n%10d %10d %10d %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf(-) %10.3lf\n",
n, n, 0, ttot_mtc,
ttot_cnp, // gemm
ttot_cchol, // potrf
ttot_ctrsm, // trsm
(ttot_cchol + ttot_ctrsm),
(ttot_mtc+ttot_cnp+ttot_cchol+ttot_ctrsm),
ttot_herk[0], ttot_herk[1], ttot_herk[2], ttot_herk[3], // syrk
ttot_ctm, // copy panel to GPU
ttot_mnp, // lookahead on GPU
(ttot_cnp+ttot_cchol+ttot_ctrsm+ttot_herk[0]+ttot_herk[1]+ttot_herk[2]+ttot_ctm+ttot_mnp));
printf("%10d %10d %10d %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf %10.3lf(-) %10.3lf (ratio)\n",
n, n, 0, ttot_mtc/ttot,
ttot_cnp/ttot, // gemm
ttot_cchol/ttot, // potrf
ttot_ctrsm/ttot, // trsm
(ttot_cchol + ttot_ctrsm)/ttot,
(ttot_mtc+ttot_cnp+ttot_cchol+ttot_ctrsm)/ttot,
ttot_herk[0]/ttot, ttot_herk[1]/ttot, ttot_herk[2]/ttot, ttot_herk[3]/ttot, // syrk
ttot_ctm/ttot, // copy panel to GPU
ttot_mnp/ttot, // lookahead on GPU
(ttot_cnp+ttot_cchol+ttot_ctrsm+ttot_herk[0]+ttot_herk[1]+ttot_herk[2]+ttot_ctm+ttot_mnp)/ttot);
#endif
// cholesky for the last block
if (j < n && *info == 0) {
rows = n - j;
id = (j / nb) % ngpu;
// Set the local index where the current panel is
j_local = j / (nb * ngpu) * nb;
magma_setdevice(id);
#if defined (ENABLE_TIMER)
tset = magma_wtime();
#endif
magma_sgetmatrix(rows, rows, dlA(id, j, j_local), ldda, panel(j), ldpanel);
lapackf77_spotrf(MagmaLowerStr, &rows, panel(j), &ldpanel, info);
magma_ssetmatrix(rows, rows, panel(j), ldpanel, dlA(id, j, j_local), ldda);
#if defined (ENABLE_TIMER)
tset = magma_wtime() - tset;
#endif
}
#if defined (ENABLE_TIMER)
printf( " matrix_get,set: %10.3lf %10.3lf -> %10.3lf\n",tget,tset,ttot+tget+tset );
#endif
} // end of else not upper
// clean up
for( d = 0; d < ngpu; d++ ) {
magma_setdevice(d);
for( j=0; j < nqueue; j++ ) {
magma_queue_destroy( queues[d][j] );
}
magma_free( d_lP[d] );
}
} // end of not lapack
// free workspace
magma_free_pinned( panel );
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
return *info;
} /* magma_spotrf_mgpu_right */
extern "C" magma_int_t
magma_cgeqrf2_mgpu( magma_int_t num_gpus, magma_int_t m, magma_int_t n,
magmaFloatComplex **dlA, magma_int_t ldda,
magmaFloatComplex *tau,
magma_int_t *info )
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
CGEQRF2_MGPU computes a QR factorization of a complex M-by-N matrix A:
A = Q * R. This is a GPU interface of the routine.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
dA (input/output) COMPLEX array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix dA.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
TAU (output) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
===============
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
===================================================================== */
#define dlA(dev, i, j) (dlA[dev] + (i) + (j)*(ldda))
#define hpanel(i) (hpanel + (i))
// set to NULL to make cleanup easy: free(NULL) does nothing.
magmaFloatComplex *dwork[MagmaMaxGPUs]={NULL}, *dpanel[MagmaMaxGPUs]={NULL};
magmaFloatComplex *hwork=NULL, *hpanel=NULL;
magma_queue_t stream[MagmaMaxGPUs][2]={{NULL}};
magma_event_t panel_event[MagmaMaxGPUs]={NULL};
magma_int_t i, j, min_mn, dev, ldhpanel, lddwork, rows;
magma_int_t ib, nb;
magma_int_t lhwork, lwork;
magma_int_t panel_dev, i_local, i_nb_local, n_local[MagmaMaxGPUs], la_dev, dpanel_offset;
magma_queue_t cqueue;
magmablasGetKernelStream( &cqueue );
magma_device_t cdevice;
magma_getdevice( &cdevice );
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
min_mn = min(m,n);
if (min_mn == 0)
return *info;
nb = magma_get_cgeqrf_nb( m );
/* dwork is (n*nb) --- for T (nb*nb) and clarfb work ((n-nb)*nb) ---
* + dpanel (ldda*nb), on each GPU.
* I think clarfb work could be smaller, max(n_local[:]).
* Oddly, T and clarfb work get stacked on top of each other, both with lddwork=n.
* on GPU that owns panel, set dpanel = dlA(dev,i,i_local).
* on other GPUs, set dpanel = dwork[dev] + dpanel_offset. */
lddwork = n;
dpanel_offset = lddwork*nb;
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
if ( MAGMA_SUCCESS != magma_cmalloc( &(dwork[dev]), (lddwork + ldda)*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
}
/* hwork is MAX( workspace for cgeqrf (n*nb), two copies of T (2*nb*nb) )
* + hpanel (m*nb).
* for last block, need 2*n*nb total. */
ldhpanel = m;
lhwork = max( n*nb, 2*nb*nb );
lwork = max( lhwork + ldhpanel*nb, 2*n*nb );
if ( MAGMA_SUCCESS != magma_cmalloc_pinned( &hwork, lwork )) {
*info = MAGMA_ERR_HOST_ALLOC;
goto CLEANUP;
}
hpanel = hwork + lhwork;
/* Set the number of local n for each GPU */
for( dev=0; dev < num_gpus; dev++ ) {
n_local[dev] = ((n/nb)/num_gpus)*nb;
if (dev < (n/nb) % num_gpus)
n_local[dev] += nb;
else if (dev == (n/nb) % num_gpus)
n_local[dev] += n % nb;
}
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_queue_create( &stream[dev][0] );
magma_queue_create( &stream[dev][1] );
magma_event_create( &panel_event[dev] );
}
if ( nb < min_mn ) {
/* Use blocked code initially */
// Note: as written, ib cannot be < nb.
for( i = 0; i < min_mn-nb; i += nb ) {
/* Set the GPU number that holds the current panel */
panel_dev = (i/nb) % num_gpus;
/* Set the local index where the current panel is (j==i) */
i_local = i/(nb*num_gpus)*nb;
ib = min(min_mn-i, nb);
rows = m-i;
/* Send current panel to the CPU, after panel_event indicates it has been updated */
magma_setdevice( panel_dev );
magma_queue_wait_event( stream[panel_dev][1], panel_event[panel_dev] );
magma_cgetmatrix_async( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hpanel(i), ldhpanel, stream[panel_dev][1] );
magma_queue_sync( stream[panel_dev][1] );
// Factor panel
lapackf77_cgeqrf( &rows, &ib, hpanel(i), &ldhpanel, tau+i,
hwork, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %d\n", (int) *info );
}
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
hpanel(i), &ldhpanel, tau+i, hwork, &ib );
cpanel_to_q( MagmaUpper, ib, hpanel(i), ldhpanel, hwork + ib*ib );
// Send the current panel back to the GPUs
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
if (dev == panel_dev)
dpanel[dev] = dlA(dev, i, i_local);
else
dpanel[dev] = dwork[dev] + dpanel_offset;
magma_csetmatrix_async( rows, ib,
hpanel(i), ldhpanel,
dpanel[dev], ldda, stream[dev][0] );
}
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( stream[dev][0] );
}
// TODO: if cpanel_to_q copied whole block, wouldn't need to restore
// -- just send the copy to the GPUs.
// TODO: also, could zero out the lower triangle and use Azzam's larfb w/ gemm.
/* Restore the panel */
cq_to_panel( MagmaUpper, ib, hpanel(i), ldhpanel, hwork + ib*ib );
if (i + ib < n) {
/* Send the T matrix to the GPU. */
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_csetmatrix_async( ib, ib,
hwork, ib,
dwork[dev], lddwork, stream[dev][0] );
}
la_dev = (panel_dev+1) % num_gpus;
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magmablasSetKernelStream( stream[dev][0] );
if (dev == la_dev && i+nb < min_mn-nb) {
// If not last panel,
// for look-ahead panel, apply H' to A(i:m,i+ib:i+2*ib)
i_nb_local = (i+nb)/(nb*num_gpus)*nb;
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local), ldda, // C
dwork[dev]+ib, lddwork ); // work
magma_event_record( panel_event[dev], stream[dev][0] );
// for trailing matrix, apply H' to A(i:m,i+2*ib:n)
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[dev]-(i_nb_local+ib), ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local+ib), ldda, // C
dwork[dev]+ib, lddwork ); // work
}
else {
// for trailing matrix, apply H' to A(i:m,i+ib:n)
i_nb_local = i_local;
if (dev <= panel_dev) {
i_nb_local += ib;
}
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[dev]-i_nb_local, ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local), ldda, // C
dwork[dev]+ib, lddwork ); // work
}
}
// Restore top of panel (after larfb is done)
magma_setdevice( panel_dev );
magma_csetmatrix_async( ib, ib,
hpanel(i), ldhpanel,
dlA(panel_dev, i, i_local), ldda, stream[panel_dev][0] );
}
}
}
else {
i = 0;
}
/* Use unblocked code to factor the last or only block row. */
if (i < min_mn) {
rows = m-i;
for( j=i; j < n; j += nb ) {
panel_dev = (j/nb) % num_gpus;
i_local = j/(nb*num_gpus)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_cgetmatrix( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hwork + (j-i)*rows, rows );
}
// needs lwork >= 2*n*nb:
// needs (m-i)*(n-i) for last block row, bounded by nb*n.
// needs (n-i)*nb for cgeqrf work, bounded by n*nb.
ib = n-i; // total columns in block row
lhwork = lwork - ib*rows;
lapackf77_cgeqrf( &rows, &ib, hwork, &rows, tau+i, hwork + ib*rows, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %d\n", (int) *info );
}
for( j=i; j < n; j += nb ) {
panel_dev = (j/nb) % num_gpus;
i_local = j/(nb*num_gpus)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_csetmatrix( rows, ib,
hwork + (j-i)*rows, rows,
dlA(panel_dev, i, i_local), ldda );
}
}
CLEANUP:
// free(NULL) does nothing.
// check that queues and events are non-zero before destroying them, though.
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
if ( stream[dev][0] ) { magma_queue_destroy( stream[dev][0] ); }
if ( stream[dev][1] ) { magma_queue_destroy( stream[dev][1] ); }
if ( panel_event[dev] ) { magma_event_destroy( panel_event[dev] ); }
magma_free( dwork[dev] );
}
magma_free_pinned( hwork );
magma_setdevice( cdevice );
magmablasSetKernelStream( cqueue );
return *info;
} /* magma_cgeqrf2_mgpu */
extern "C" magma_int_t
magma_zpotrf2_mgpu(int num_gpus, char uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaDoubleComplex **d_lA, magma_int_t ldda,
magmaDoubleComplex **d_lP, magma_int_t lddp,
magmaDoubleComplex *a, magma_int_t lda, magma_int_t h,
magma_queue_t stream[][3], magma_event_t event[][5],
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
magma_int_t j, jb, nb0, nb2, dd, d, id, j_local, j_local2, buf;
char uplo_[2] = {uplo, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
double d_one = 1.0;
double d_neg_one = -1.0;
int upper = lapackf77_lsame(uplo_, "U");
magmaDoubleComplex *dlpanel;
//magma_event_t event0[MagmaMaxGPUs], // syrk
// event1[MagmaMaxGPUs], // send off-diagonal
// event2[MagmaMaxGPUs], // send diagonal
// event3[MagmaMaxGPUs]; // trsm
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
int stream0 = 0, stream1 = 1;
#ifdef ZTRSM_WORK
magmaDoubleComplex *d_dinvA[MagmaMaxGPUs][2], *d_x[MagmaMaxGPUs][2]; /* used by ztrsm_work */
#endif
*info = 0;
if ( (! upper) && (! lapackf77_lsame(uplo_, "L")) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (!upper && num_gpus*ldda < max(1,n)) {
*info = -4;
} else if (upper && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
for( d=0; d<num_gpus; d++ ) {
/* local-n and local-ld */
if (upper) {
n_local[d] = ((n/nb)/num_gpus)*nb;
if (d < (n/nb)%num_gpus)
n_local[d] += nb;
else if (d == (n/nb)%num_gpus)
n_local[d] += n%nb;
} else {
n_local[d] = ((m/nb)/num_gpus)*nb;
if (d < (m/nb)%num_gpus)
n_local[d] += nb;
else if (d == (m/nb)%num_gpus)
n_local[d] += m%nb;
}
//magma_setdevice(d);
//magma_event_create( &event0[d] );
//magma_event_create( &event1[d] );
//magma_event_create( &event2[d] );
//magma_event_create( &event3[d] );
}
magma_setdevice(0);
/* == initialize the trace */
trace_init( 1, num_gpus, 3, stream );
/* Use blocked code. */
if (upper) {
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
/* invert the diagonals
* Allocate device memory for the inversed diagonal blocks, size=m*NB
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<2; j++ ) {
magma_zmalloc( &d_dinvA[d][j], nb*nb );
magma_zmalloc( &d_x[d][j], n*nb );
cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(magmaDoubleComplex));
cudaMemset(d_x[d][j], 0, n*nb*sizeof(magmaDoubleComplex));
}
}
magma_setdevice(0);
#endif
for (j=0; j<m; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (m-j));
if( j > 0 ) {
/* needed on pluto... */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] ); // wait for the column on CPU
/* broadcast off-diagonal column to all gpus */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d != id ) {
magma_setdevice(d);
/* wait for it on CPU */
magma_queue_wait_event( stream[d][stream0], event[id][1] );
/* send it to GPU */
trace_gpu_start( d, stream0, "comm", "rows to GPUs" );
magma_zsetmatrix_async( j, jb,
Aup(0,j), lda,
dlP(d,jb,0,buf), lddp,
stream[d][stream0] );
trace_gpu_end( d, stream0 );
magma_event_record( event[d][1], stream[d][stream0] );
}
d = (d+1)%num_gpus;
}
}
/* Update the current diagonal block */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
trace_gpu_start( id, stream1, "syrk", "syrk" );
magma_zherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda);
trace_gpu_end( id, stream1 );
magma_event_record( event[id][0], stream[id][stream1] );
}
/* send the diagonal to cpu */
magma_queue_wait_event( stream[id][stream0], event[id][0] ); // wait for syrk
trace_gpu_start( id, stream0, "comm", "D to CPU" );
magma_zgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
stream[id][stream0] );
trace_gpu_end( id, stream0 );
if ( j > 0 ) {
/* Compute the local block column of the panel. */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( n_local[d] > nb0 ) {
/* wait for the off-diagonal */
if( d != id ) {
//magma_queue_sync( stream[id][3] );
dlpanel = dlP(d, jb, 0, buf);
ldpanel = lddp;
/* wait for the offdiagonal column */
magma_queue_wait_event( stream[d][stream1], event[d][1] );
} else {
dlpanel = dlA(d, 0, nb*j_local);
ldpanel = ldda;
}
/* update the panel */
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
trace_gpu_start( d, stream1, "gemm", "gemm" );
magma_zgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda);
trace_gpu_end( d, stream1 );
}
d = (d+1)%num_gpus;
}
}
/* factor the diagonal */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] ); // wait for the diagonal
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_zpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
magma_setdevice(d);
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, 0, 0, buf);
ldpanel = lddp;
}
trace_gpu_start( d, stream0, "comm", "D to GPUs" );
magma_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, ldpanel,
stream[d][stream0] );
trace_gpu_end( d, stream0 );
magma_event_record( event[d][2], stream[d][stream0] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
trace_gpu_start( id, stream0, "comm", "D to GPUs" );
magma_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
stream[id][stream0] );
trace_gpu_end( id, stream0 );
}
/* panel-factorize the off-diagonal */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, 0, 0, buf);
ldpanel = lddp;
}
nb2 = n_local[d]-nb*j_local2;
nb0 = min(nb, nb2 );
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for the diagonal
if( j+jb < m && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead the column */
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d][0], d_x[d][0] );
/*nb2 = n_local[d] - j_local2*nb;
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d], d_x[d] );*/
#else
/*nb2 = n_local[d] - j_local2*nb;
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldda,
dlA(d, j, nb*j_local2), ldda);
*/
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream1 );
magma_event_record( event[d][3], stream[d][stream1] );
/* send the column to cpu */
if( j+jb < m ) {
trace_gpu_start( d, stream0, "comm", "rows to CPU" );
magma_queue_wait_event( stream[d][stream0], event[d][3] ); // wait for lookahead
magma_zgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
stream[d][stream0] );
trace_gpu_end( d, stream0 );
magma_event_record( event[d][1], stream[d][stream0] );
}
/* update the remaining blocks */
nb2 = nb2 - nb0;
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda);
#endif
} else if( nb2 > 0 ) {
/* update the entire trailing matrix */
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream1 );
}
d = (d+1)%num_gpus;
}
} /* end of ztrsm */
} /* end of for j=1, .., n */
} else {
/* -------------------------------------------- */
/* Lower-triangular case */
/* Compute the Cholesky factorization A = L*L'. */
/* -------------------------------------------- */
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
/*
* Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<2; j++ ) {
magma_zmalloc( &d_dinvA[d][j], nb*nb );
magma_zmalloc( &d_x[d][j], nb*m );
cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(magmaDoubleComplex));
cudaMemset(d_x[d][j], 0, nb* m*sizeof(magmaDoubleComplex));
}
}
magma_setdevice(0);
#endif
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (n-j));
if( j > 0 ) {
/* needed on pluto... */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] ); // wait for the column on CPU
/* broadcast offdiagonal row to all gpus */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d != id ) {
magma_setdevice(d);
/* wait for it on CPU */
magma_queue_wait_event( stream[d][stream0], event[id][1] );
/* send it to GPU */
magma_zsetmatrix_async( jb, j,
Alo(j,0), lda,
dlPT(d,0,jb,buf), nb,
stream[d][stream0] );
magma_event_record( event[d][1], stream[d][stream0] );
}
d = (d+1)%num_gpus;
}
}
/* Update the current diagonal block */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
magma_zherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda);
magma_event_record( event[id][0], stream[id][stream1] );
}
/* send the diagonal to cpu */
magma_queue_wait_event( stream[id][stream0], event[id][0] ); // wait for syrk
magma_zgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
stream[id][stream0] );
/* update the offdiagonal blocks */
if ( j > 0 ) {
/* compute the block-rows of the panel */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( nb0 < n_local[d] ) {
if( d != id ) {
dlpanel = dlPT(d, 0, jb, buf);
ldpanel = nb;
/* wait for offdiagonal row */
magma_queue_wait_event( stream[d][stream1], event[d][1] );
} else {
dlpanel = dlA(d, nb*j_local, 0);
ldpanel = ldda;
}
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
magma_zgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, ldpanel,
c_one, dlA(d, nb0, j), ldda);
}
d = (d+1)%num_gpus;
}
}
/* factor the diagonal */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] );
lapackf77_zpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ( (j+jb) < m ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
magma_setdevice(d);
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
magma_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, ldpanel,
stream[d][stream0] );
magma_event_record( event[d][2], stream[d][stream0] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
magma_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
stream[id][stream0] );
}
/* factorize off-diagonal blocks */
if ( (j+jb) < m ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2 );
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for the diagonal
if( j+jb < n && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead the column */
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
d_dinvA[d][0], d_x[d][0]);
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
magma_event_record( event[d][3], stream[d][stream1] );
/* send the column to cpu */
if( j+jb < n ) {
magma_queue_wait_event( stream[d][stream0], event[d][3] ); // wait for lookahead
magma_zgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream0] );
magma_event_record( event[d][1], stream[d][stream0] );
}
/* update the remaining blocks */
nb2 = nb2 - nb0;
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda);
#endif
} else if( nb2 > 0 ) {
/* update the entire trailing matrix */
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
}
d = (d+1)%num_gpus;
}
}
}
} /* end of else not upper */
/* == finalize the trace == */
trace_finalize( "zpotrf.svg","trace.css" );
/* clean up */
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magmablasSetKernelStream(NULL);
//magma_event_destroy( event0[d] );
//magma_event_destroy( event1[d] );
//magma_event_destroy( event2[d] );
//magma_event_destroy( event3[d] );
}
magma_setdevice(0);
return *info;
} /* magma_zpotrf_mgpu */
extern "C" magma_int_t
magma_zpotrf3_mgpu(magma_int_t num_gpus, char uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaDoubleComplex *d_lA[], magma_int_t ldda,
magmaDoubleComplex *d_lP[], magma_int_t lddp,
magmaDoubleComplex *a, magma_int_t lda, magma_int_t h,
magma_queue_t stream[][3], magma_event_t event[][5],
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
Auxiliary subroutine for zpotrf2_ooc. It is multiple gpu interface to compute
Cholesky of a "rectangular" matrix.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
magma_int_t j, jb, nb0, nb2, d, dd, id, j_local, j_local2, buf;
char uplo_[2] = {uplo, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
double d_one = 1.0;
double d_neg_one = -1.0;
int upper = lapackf77_lsame(uplo_, "U");
magmaDoubleComplex *dlpanel;
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
const magma_int_t stream1 = 0, stream2 = 1, stream3 = 2;
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
/* used by ztrsm_work */
int trsm_nb = 128;
int trsm_n = trsm_nb*((nb+trsm_nb-1)/trsm_nb);
magmaDoubleComplex *d_dinvA[MagmaMaxGPUs];
magmaDoubleComplex *d_x[MagmaMaxGPUs];
#define dinvA(d,j) &(d_dinvA[(d)][(j)*trsm_nb*trsm_n])
#define dx(d,j) &(d_x[(d)][(j)*nb*m])
/*
* Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
if ( (MAGMA_SUCCESS != magma_zmalloc( &d_dinvA[d], 2*trsm_nb*trsm_n )) ||
(MAGMA_SUCCESS != magma_zmalloc( &d_x[d], 2*nb*(upper ? n : m) )) ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
magma_setdevice(0);
#endif
*info = 0;
if ( (! upper) && (! lapackf77_lsame(uplo_, "L")) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (!upper && num_gpus*ldda < max(1,n)) {
*info = -4;
} else if (upper && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* initialization */
for( d=0; d<num_gpus; d++ ) {
/* local-n and local-ld */
if (upper) {
n_local[d] = (n/(nb*num_gpus))*nb;
if (d < (n/nb)%num_gpus)
n_local[d] += nb;
else if (d == (n/nb)%num_gpus)
n_local[d] += n%nb;
} else {
n_local[d] = (m/(nb*num_gpus))*nb;
if (d < (m/nb)%num_gpus)
n_local[d] += nb;
else if (d == (m/nb)%num_gpus)
n_local[d] += m%nb;
}
}
/* == initialize the trace */
trace_init( 1, num_gpus, 3, (CUstream_st**)stream );
if (upper)
{
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
for (j=0; j<m; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus; // right now, we have num_gpu buffers, so id and buf are the same..
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (m-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
trace_gpu_start( id, stream1, "syrk", "syrk" );
magma_zherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda);
trace_gpu_end( id, stream1 );
}
/* send the diagonal to cpu on stream1 */
trace_gpu_start( id, stream1, "comm", "D to CPU" );
magma_zgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
/* update off-diagonal blocks in the panel */
if( j > 0 ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2; // number of local columns in the panel, while jb is panel-size (number of rows)
if( n_local[d] > nb0 ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
if( d == id ) {
dlpanel = dlA(d,0,nb*j_local);
ldpanel = ldda;
// the GPU owns the row from start, and no need of synch.
//magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
} else {
dlpanel = dlP(d,nb,0,buf);
ldpanel = lddp;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
trace_gpu_start( d, stream2, "gemm", "gemm" );
magma_zgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda);
trace_gpu_end( d, stream2 );
magma_event_record( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for panel and factorize it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_zpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
magma_setdevice(d);
trace_gpu_start( d, stream1, "comm", "comm" );
magma_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
trace_gpu_end( d, stream1 );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
trace_gpu_start( id, stream1, "comm", "comm" );
magma_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
}
/* panel-factorize the off-diagonal */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d,j,nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
nb2 = n_local[d] - j_local2*nb;
magma_setdevice(d);
if( j+jb < m && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead next block on stream1 */
nb0 = min(nb, nb2);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb, trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb0,jb, dx(d,0),nb0 );
magmablas_ztrsm_work( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ztrsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
trace_gpu_end( d, stream1 );
} else if( nb2 > 0 ) {
/* update all the blocks on stream2 */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for cholesky factor
trace_gpu_start( d, stream2, "trsm", "trsm" );
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,0),nb2 );
magmablas_ztrsm_work( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ztrsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream2 );
}
d = (d+1)%num_gpus;
} /* end of for */
/* ========================================================== */
if( j+jb < m ) {
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, off-diagonals are copied to cpu (synchronize at the end). *
* so we have the Cholesky factor, but only diagonal submatrix of the big panel, *
* on cpu at the end. */
int d2, buf2;
magma_setdevice(d);
/* lookahead done */
magma_queue_wait_event( stream[d][stream3], event[d][4] );
trace_gpu_start( d, stream3, "comm", "row to CPU" );
magma_zgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
stream[d][stream3] );
trace_gpu_end( d, stream3 );
magma_event_record( event[d][3], stream[d][stream3] );
/* needed on pluto */
//magma_queue_sync( stream[d][stream3] );
/* broadcast rows to gpus on stream2 */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
trace_gpu_start( d2, stream3, "comm", "row to GPUs" );
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // rows arrived at cpu on stream3
magma_zsetmatrix_async( j+jb, nb0,
Aup(0,j+jb), lda,
dlP(d2,nb,0,buf2), lddp,
stream[d2][stream3] );
trace_gpu_end( d2, stream3 );
magma_event_record( event[d2][0], stream[d2][stream3] );
}
}
/* =========================== */
/* update the remaining blocks */
nb2 = n_local[d]-(nb*j_local2 + nb0);
if( nb2 > 0 ) {
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
trace_gpu_start( d, stream2, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( stream[d][stream2], event[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,flag),trsm_nb );
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
}
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,1),nb2 );
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
flag, dinvA(d,flag), dx(d,1) );
#else
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for cholesky factor
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda);
#endif
trace_gpu_end( d, stream2 );
}
}
} /* end of ztrsm */
} /* end of for j=1, .., n */
} else {
/* ---------------------------------------------- */
/* Lower-triangular case */
/* > Compute the Cholesky factorization A = L*L'. */
/* ---------------------------------------------- */
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (n-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
magma_zherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda);
}
/* send the diagonal to cpu on stream1 */
magma_zgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
stream[id][stream1] );
/* update off-diagonal blocks of the panel */
if( j > 0 ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( nb0 < n_local[d] ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
if( d == id ) {
dlpanel = dlA(d, nb*j_local, 0);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,nb,buf);
ldpanel = nb;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
magma_zgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, ldpanel,
c_one, dlA(d, nb0, j), ldda);
magma_event_record( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for the panel and factorized it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
lapackf77_zpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < m) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
magma_setdevice(d);
magma_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
magma_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
stream[id][stream1] );
}
/* panel factorize the off-diagonal */
if ( (j+jb) < m) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2);
magma_setdevice(d);
if( j+nb < n && d == (j/nb+1)%num_gpus ) { /* owns next column, look-ahead next block on stream1 */
if ( j > 0 ) magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
magmablasSetKernelStream(stream[d][stream1]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb, trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb0,jb, dx(d,0),nb0 );
magmablas_ztrsm_work( MagmaRight, MagmaLower,
MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ztrsm( MagmaRight, MagmaLower,
MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
} else if( nb2 > 0 ) { /* other gpus updating all the blocks on stream2 */
/* update the entire column */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for the cholesky factor
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,0),nb2 );
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
}
d = (d+1)%num_gpus;
} /* end for d */
/* ========================================================== */
if( j+jb < n ) {
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, we copy off-diagonal to cpu (but don't synchronize). */
/* so we have the Cholesky factor on cpu at the end. */
int d2, buf2;
//#define ZPOTRF_DEVICE_TO_DEVICE
#ifdef ZPOTRF_DEVICE_TO_DEVICE
// lookahead done
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
magma_setdevice(d2);
magma_queue_wait_event( stream[d2][stream3], event[d][4] );
if( d2 != d ) {
magma_zcopymatrix_async( nb0, j+jb,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
dlA(d, nb*j_local2, 0), ldda,
stream[d2][stream3] );
magma_event_record( event[d2][0], stream[d2][stream3] );
} else {
magma_zgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream3] );
}
}
#else
// lookahead done
magma_setdevice(d);
magma_queue_wait_event( stream[d][stream3], event[d][4] );
magma_zgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream3] );
magma_event_record( event[d][3], stream[d][stream3] );
/* syn on rows on CPU, seem to be needed on Pluto */
//magma_queue_sync( stream[d][stream3] );
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // getmatrix done
magma_zsetmatrix_async( nb0, j+jb,
Alo(j+jb,0), lda,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
stream[d2][stream3] );
magma_event_record( event[d2][0], stream[d2][stream3] );
}
}
#endif
/* =================================== */
/* updates remaining blocks on stream2 */
nb2 = n_local[d] - (j_local2*nb + nb0);
if( nb2 > 0 ) {
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,0,buf);
ldpanel = nb;
}
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
/* update the remaining blocks in the column */
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( stream[d][stream2], event[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,flag),trsm_nb );
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
}
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,1),nb2 );
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
flag, dinvA(d,flag), dx(d,1) );
#else
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda);
#endif
}
}
}
}
} /* end of else not upper */
/* == finalize the trace == */
trace_finalize( "zpotrf.svg","trace.css" );
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<3; j++ ) {
magma_queue_sync( stream[d][j] );
}
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magma_free( d_dinvA[d] );
magma_free( d_x[d] );
#endif
magmablasSetKernelStream(NULL);
}
magma_setdevice(0);
return *info;
} /* magma_zpotrf_mgpu */
extern "C" magma_int_t
magma_cpotrf2_msub(
magma_int_t num_subs, magma_int_t num_gpus, magma_uplo_t uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaFloatComplex_ptr *d_lA, size_t d_lA_offset, magma_int_t ldda,
magmaFloatComplex_ptr *d_lP, magma_int_t lddp,
magmaFloatComplex *a, magma_int_t lda, magma_int_t h,
magma_queue_t *queues,
magma_int_t *info )
{
/* -- clMAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date November 2014
Purpose
=======
CPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) COMPLEX array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
int tot_subs = num_subs*num_gpus;
magma_int_t j, jb, nb0, nb2, dd, d, id, j_local, j_local2;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
float d_one = 1.0;
float d_neg_one = -1.0;
magmaFloatComplex_ptr dlpanel;
size_t dlpanel_offset;
magma_int_t n_local[MagmaMaxSubs * MagmaMaxGPUs], ldpanel;
// initialize trace
trace_init(1, num_gpus, 2, queues);
*info = 0;
if ( (uplo != MagmaUpper) && (uplo != MagmaLower) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if ((uplo != MagmaUpper) && tot_subs*ldda < max(1,n)) {
*info = -4;
} else if ((uplo == MagmaUpper) && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
for (d=0; d<tot_subs; d++) {
/* local-n and local-ld */
if (uplo == MagmaUpper) {
n_local[d] = ((n/nb)/tot_subs)*nb;
if (d < (n/nb)%tot_subs)
n_local[d] += nb;
else if (d == (n/nb)%tot_subs)
n_local[d] += n%nb;
} else {
n_local[d] = ((m/nb)/tot_subs)*nb;
if (d < (m/nb)%tot_subs)
n_local[d] += nb;
else if (d == (m/nb)%tot_subs)
n_local[d] += m%nb;
}
}
/* Use blocked code. */
if (uplo == MagmaUpper) {
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
for (j=0; j<m; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%tot_subs;
/* Set the local index where the current panel is */
j_local = j/(nb*tot_subs);
jb = min(nb, (m-j));
if (j > 0) {
// Wait for the column on CPU
magma_queue_sync(queues[2*(id%num_gpus)]);
/* broadcast off-diagonal column to all gpus */
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d != id%num_gpus) {
magma_csetmatrix_async( j, jb,
Aup(0,j), lda,
dlP(d,jb,0,id%num_gpus), lddp,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-col") );
}
d = (d+1)%num_gpus;
}
/* Update the current diagonal block */
trace_gpu_start(id%num_gpus, 1, "herk", "herk");
magma_cherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda,
queues[2*(id%num_gpus)+1]);
magma_queue_sync(queues[2*(id%num_gpus)+1]); // Wait for syrk
}
/* Send the diagonal to cpu */
magma_cgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "get", "get-diag") );
if (j > 0) {
/* Compute the local block column of the panel. */
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
j_local2 = j_local+1;
if (d > id) j_local2 --;
nb0 = nb*j_local2;
if (n_local[d] > nb0) {
if (d%num_gpus != id%num_gpus) {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlP_offset(jb, 0, id%num_gpus);
ldpanel = lddp;
/* Wait for the offdiagonal column */
if (dd < num_gpus) magma_queue_sync(queues[2*(d%num_gpus)]);
} else {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(0, nb*j_local);
ldpanel = ldda;
}
/* update the panel */
trace_gpu_start(d%num_gpus, 1, "gemm", "gemm");
magma_cgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, dlpanel_offset, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda,
queues[2*(d%num_gpus)+1]);
}
d = (d+1)%tot_subs;
}
}
/* factor the diagonal */
magma_queue_sync( queues[2*(id%num_gpus)] ); // wait for the diagonal
trace_cpu_start(0, "potrf", "potrf");
lapackf77_cpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end(0);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ((j+jb) < n) {
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = d_lP[d];
dlpanel_offset = dlP_offset(0, 0, id%num_gpus);
ldpanel = lddp;
}
magma_csetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, dlpanel_offset, ldpanel,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-diag"));
d = (d+1)%num_gpus;
}
} else {
magma_csetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "set", "set-diag") );
}
/* panel-factorize the off-diagonal */
if ((j+jb) < n) {
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
/* next column */
j_local2 = j_local+1;
if (d > id) j_local2--;
if (d%num_gpus == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlP_offset(0, 0, id%num_gpus);
ldpanel = lddp;
}
nb2 = n_local[d]-nb*j_local2;
nb0 = min(nb, nb2);
if (dd < num_gpus) magma_queue_sync( queues[2*(d%num_gpus)] ); // wait for the diagonal
if (j+jb < m && d == (j/nb+1)%tot_subs) {
/* owns the next column, look-ahead the column */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2), ldda,
queues[2*(d%num_gpus)+1] );
/* send the column to cpu */
magma_queue_sync(queues[2*(d%num_gpus)+1]); // wait for lookahead
magma_cgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
queues[2*(d%num_gpus)],
trace_gpu_event(d%num_gpus, 0, "get", "get-col") );
/* update the remaining blocks */
nb2 = nb2 - nb0;
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
queues[2*(d%num_gpus)+1] );
} else if (nb2 > 0) {
/* update the entire trailing matrix */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2), ldda,
queues[2*(d%num_gpus)+1] );
}
d = (d+1)%tot_subs;
}
}
}
} else {
/* -------------------------------------------- */
/* Lower-triangular case */
/* Compute the Cholesky factorization A = L*L'. */
/* -------------------------------------------- */
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%tot_subs;
/* Set the local index where the current panel is */
j_local = j/(nb*tot_subs);
jb = min(nb, (n-j));
if (j > 0) {
if (num_gpus > 1) {
// Wait for the row on CPU to broadcast
magma_queue_sync(queues[2*(id%num_gpus)]);
}
/* broadcast off-diagonal row to all the GPUs */
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d != id%num_gpus) {
/* send it to GPU-d */
magma_csetmatrix_async( jb, j,
Alo(j,0), lda,
dlPT(d,0,jb,id%num_gpus), nb,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-row") );
}
d = (d+1)%num_gpus;
}
/* Update the current diagonal block */
trace_gpu_start(id%num_gpus, 1, "herk", "herk");
magma_cherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda,
queues[2*(id%num_gpus)+1]);
magma_queue_sync(queues[2*(id%num_gpus)+1]); // wait for syrk
}
/* send the diagonal to cpu */
magma_cgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "get", "get") );
/* update the offdiagonal blocks */
if (j > 0) {
/* compute the block-rows of the panel */
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
j_local2 = j_local+1;
if (d > id) j_local2 --;
nb0 = nb*j_local2;
if (nb0 < n_local[d]) {
if (d%num_gpus != id%num_gpus) {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlPT_offset(0, jb, id%num_gpus);
ldpanel = nb;
/* Wait for offdiagonal row */
if (dd < num_gpus) magma_queue_sync(queues[2*(d%num_gpus)]);
} else {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(nb*j_local, 0);
ldpanel = ldda;
}
/* Update the panel */
trace_gpu_start(d%num_gpus, 1, "gemm", "gemm");
magma_cgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, dlpanel_offset, ldpanel,
c_one, dlA(d, nb0, j), ldda,
queues[2*(d%num_gpus)+1]);
}
d = (d+1)%tot_subs;
}
}
/* factor the diagonal */
magma_queue_sync( queues[2*(id%num_gpus)] );
trace_cpu_start(0, "potrf", "potrf");
lapackf77_cpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
trace_cpu_end(0);
if (*info != 0) {
printf( " cpotrf returned %d (id=%d,j=%d,j_local=%d,jb=%d)\n",*info,id,j,j_local,jb );
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ((j+jb) < m) {
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = d_lP[d];
dlpanel_offset = dlPT_offset(0, 0, id%num_gpus);
ldpanel = nb;
}
magma_csetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, dlpanel_offset, ldpanel,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-diag") );
d = (d+1)%num_gpus;
}
} else {
magma_csetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "set", "set-diag") );
}
/* factorize off-diagonal blocks */
if ((j+jb) < m) {
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
/* next column */
j_local2 = j_local+1;
if (d > id) j_local2--;
if (d%num_gpus == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlPT_offset(0, 0, id%num_gpus);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2 );
// wait for the diagonal
if (dd < num_gpus) magma_queue_sync(queues[2*(d%num_gpus)]);
if (j+jb < n && d == (j/nb+1)%tot_subs) {
/* owns the next column, look-ahead the column */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2, j), ldda,
queues[2*(d%num_gpus)+1]);
/* send the column to cpu */
magma_queue_sync( queues[2*(d%num_gpus)+1] ); // wait for lookahead
magma_cgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
queues[2*(d%num_gpus)],
trace_gpu_event(d%num_gpus, 0, "get", "get") );
/* update the remaining blocks */
nb2 = nb2 - nb0;
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
queues[2*(d%num_gpus)+1]);
} else if (nb2 > 0) {
/* update the entire trailing matrix */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ctrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2, j), ldda,
queues[2*(d%num_gpus)+1]);
}
d = (d+1)%tot_subs;
}
}
}
} /* end of else not upper */
/* clean up */
for( d=0; d<num_gpus; d++ ) {
magma_queue_sync( queues[2*d] );
magma_queue_sync( queues[2*d+1] );
}
trace_finalize("cpotrf_msub.svg", "trace.css");
return *info;
} /* magma_cpotrf2_msub */
extern "C" magma_int_t
magma_dpotrf2_mgpu(
magma_int_t num_gpus, magma_uplo_t uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaDouble_ptr *d_lA, size_t d_lA_offset, magma_int_t ldda,
magmaDouble_ptr *d_lP, magma_int_t lddp,
double *a, magma_int_t lda, magma_int_t h,
magma_queue_t *queues,
magma_int_t *info )
{
/* -- clMAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date November 2014
Purpose
=======
DPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) DOUBLE_PRECISION array on the GPU, dimension (LDDA,N)
On entry, the symmetric matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
magma_int_t j, jb, nb0, nb2, dd, d, id, j_local, j_local2, buf;
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
double d_one = 1.0;
double d_neg_one = -1.0;
magmaDouble_ptr dlpanel;
size_t dlpanel_offset;
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
magma_event_t events[MagmaMaxGPUs];
*info = 0;
if ( (uplo != MagmaUpper) && (uplo != MagmaLower) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if ((uplo != MagmaUpper) && num_gpus*ldda < max(1,n)) {
*info = -4;
} else if ((uplo == MagmaUpper) && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
{
for( d=0; d<num_gpus; d++ ) {
/* local-n and local-ld */
if (uplo == MagmaUpper) {
n_local[d] = ((n/nb)/num_gpus)*nb;
if (d < (n/nb)%num_gpus)
n_local[d] += nb;
else if (d == (n/nb)%num_gpus)
n_local[d] += n%nb;
} else {
n_local[d] = ((m/nb)/num_gpus)*nb;
if (d < (m/nb)%num_gpus)
n_local[d] += nb;
else if (d == (m/nb)%num_gpus)
n_local[d] += m%nb;
}
}
/* Use blocked code. */
if (uplo == MagmaUpper)
{
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
for(j=0;j<m;j+=nb){
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (m-j));
if(j>0){
magma_queue_sync(queues[id*2]); // wait for the column on CPU
/* broadcast off-diagonal column to all gpus */
d = (j/nb+1)%num_gpus;
for(dd=0;dd<num_gpus;dd++){
if(d != id){
//magma_queue_sync(queues[2*d]);
magma_dsetmatrix_async( j, jb,
Aup(0,j), lda,
dlP(d,jb,0,buf), lddp,
queues[d*2], NULL );
}
d = (d+1)%num_gpus;
}
}
/* Update the current diagonal block */
if( j > 0 ) {
magma_dsyrk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda,
queues[2*id+1]);
}
/* send the diagonal to cpu */
magma_queue_sync(queues[2*id+1]);// wait for syrk
magma_dgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
queues[2*id], NULL);
if(j>0){
/* Compute the local block column of the panel. */
d = (j/nb+1)%num_gpus;
for(dd=0;dd<num_gpus;dd++){
j_local2 = j_local+1;
if(d>id) j_local2 --;
nb0 = nb*j_local2;
if(n_local[d]>nb0){
/* wait for the off-diagonal */
if(d!=id){
dlpanel = d_lP[d];
dlpanel_offset = dlP_offset(jb, 0, buf);
ldpanel = lddp;
/* wait for the offdiagonal column */
magma_queue_sync(queues[d*2]);
}else{
dlpanel = d_lA[d];
dlpanel_offset = dlA_offset(0, nb*j_local);
ldpanel = ldda;
}
/* update the panel */
magma_dgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, dlpanel_offset, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda,
queues[2*d+1]);
}
d = (d+1)%num_gpus;
}
}
/* factor the diagonal */
magma_queue_sync( queues[id*2] ); // wait for the diagonal
lapackf77_dpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = d_lA[d];
dlpanel_offset = dlA_offset(j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = d_lP[d];
dlpanel_offset = dlP_offset(0, 0, buf);
ldpanel = lddp;
}
magma_dsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, dlpanel_offset, ldpanel,
queues[d*2], NULL);
d = (d+1)%num_gpus;
}
} else {
magma_dsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
queues[id*2], NULL );
}
/* panel-factorize the off-diagonal */
if((j+jb)<n){
d = (j/nb+1)%num_gpus;
for(dd=0;dd<num_gpus;dd++){
/* next column */
j_local2 = j_local+1;
if(d>id) j_local2--;
if( d == id ) {
dlpanel = d_lA[d];
dlpanel_offset = dlA_offset(j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = d_lP[d];
dlpanel_offset = dlP_offset(0, 0, buf);
ldpanel = lddp;
}
nb2 = n_local[d]-nb*j_local2;
nb0 = min(nb, nb2 );
magma_queue_sync( queues[2*d]); // wait for the diagonal
if(j+jb < m && d == (j/nb+1)%num_gpus){
/* owns the next column, look-ahead the column */
magma_dtrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2), ldda,
queues[2*d+1]);
/* send the column to cpu */
if(j+jb < m){
magma_queue_sync(queues[2*d+1]); // wait for lookahead
magma_dgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
queues[2*d], NULL);
}
/* update the remaining blocks */
nb2 = nb2 - nb0;
magma_dtrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
queues[2*d+1]);
}else if(nb2 > 0){
/* update the entire trailing matrix */
magma_dtrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2), ldda,
queues[d*2+1]);
}
d = (d+1)%num_gpus;
}
}
}
} else {
/* -------------------------------------------- */
/* Lower-triangular case */
/* Compute the Cholesky factorization A = L*L'. */
/* -------------------------------------------- */
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (n-j));
if( j > 0 ) {
/* needed on pluto... */
//magma_setdevice(id);
magma_queue_sync( queues[id*2] ); // wait for the column on CPU
/* broadcast offdiagonal row to all gpus */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d != id ) {
/* wait for it on CPU */
//magma_queue_sync( queues[d*2] );
/* send it to GPU */
magma_dsetmatrix_async( jb, j,
Alo(j,0), lda,
dlPT(d,0,jb,buf), nb,
queues[d*2], NULL );
clFlush(queues[d*2]);
}
d = (d+1)%num_gpus;
}
}
/* Update the current diagonal block */
if( j > 0 ) {
magma_dsyrk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda,
queues[id*2+1]);
magma_queue_sync( queues[id*2+1] ); // wait for syrk
}
/* update the offdiagonal blocks */
if ( j > 0 ) {
/* compute the block-rows of the panel */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( nb0 < n_local[d] ) {
if( d != id ) {
//dlpanel = dlPT(d);
dlpanel = d_lP[d];
dlpanel_offset = dlPT_offset(0, jb, buf);
ldpanel = nb;
/* wait for offdiagonal row */
magma_queue_sync(queues[d*2]);
} else {
dlpanel = d_lA[d];
dlpanel_offset = dlA_offset(nb*j_local, 0);
ldpanel = ldda;
}
magma_dgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, dlpanel_offset, ldpanel,
c_one, dlA(d, nb0, j), ldda,
queues[d*2+1]);
}
d = (d+1)%num_gpus;
}
}
/* send the diagonal to cpu */
magma_dgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
queues[id*2], &events[id] );
clFlush(queues[id*2]);
/* factor the diagonal */
magma_queue_sync( queues[id*2] );
lapackf77_dpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
if (*info != 0) {
printf("row number: %d\n", (int) j);
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ( (j+jb) < m ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = d_lA[d];
dlpanel_offset = dlA_offset(nb*j_local, j);
ldpanel = ldda;
} else {
//dlpanel = dlPT(d);
dlpanel = d_lP[d];
dlpanel_offset = dlPT_offset(0, 0, buf);
ldpanel = nb;
}
magma_dsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, dlpanel_offset, ldpanel,
queues[d*2], NULL );
clFlush(queues[d*2]);
d = (d+1)%num_gpus;
}
} else {
magma_dsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
queues[id*2], NULL );
clFlush(queues[id*2]);
}
/* factorize off-diagonal blocks */
if ( (j+jb) < m ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = d_lA[d];
dlpanel_offset = dlA_offset(nb*j_local, j);
ldpanel = ldda;
} else {
//dlpanel = dlPT(d);
dlpanel = d_lP[d];
dlpanel_offset = dlPT_offset(0, 0, buf);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2 );
magma_queue_sync(queues[d*2]);
// wait for the diagonal
if( j+jb < n && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead the column */
magma_dtrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2, j), ldda,
queues[d*2+1]);
/* send the column to cpu */
if( j+jb < n ) {
magma_queue_sync( queues[d*2+1] ); // wait for lookahead
magma_dgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
queues[d*2], NULL);
clFlush(queues[d*2]);
}
/* update the remaining blocks */
nb2 = nb2 - nb0;
magma_dtrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
queues[d*2+1]);
} else if( nb2 > 0 ) {
/* update the entire trailing matrix */
magma_dtrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2, j), ldda,
queues[d*2+1]);
}
d = (d+1)%num_gpus;
}
}
}
} /* end of else not upper */
/* clean up */
for( d=0; d<num_gpus; d++ ) {
magma_queue_sync( queues[d*2] );
magma_queue_sync( queues[d*2+1] );
}
} /* end of not lapack */
return *info;
} /* magma_dpotrf_mgpu */
/***************************************************************************//**
Purpose
-------
CGEQRF computes a QR factorization of a complex M-by-N matrix A:
A = Q * R. This is a GPU interface of the routine.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
dlA COMPLEX array of pointers on the GPU, dimension (ngpu).
On entry, the M-by-N matrix A distributed over GPUs
(d_lA[d] points to the local matrix on d-th GPU).
It uses 1D block column cyclic format with the block size of nb,
and each local matrix is stored by column.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
tau COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_geqrf
*******************************************************************************/
extern "C" magma_int_t
magma_cgeqrf2_mgpu(
magma_int_t ngpu,
magma_int_t m, magma_int_t n,
magmaFloatComplex_ptr dlA[], magma_int_t ldda,
magmaFloatComplex *tau,
magma_int_t *info )
{
#define dlA(dev, i, j) (dlA[dev] + (i) + (j)*(ldda))
#define hpanel(i) (hpanel + (i))
// set to NULL to make cleanup easy: free(NULL) does nothing.
magmaFloatComplex *dwork[MagmaMaxGPUs]={NULL}, *dpanel[MagmaMaxGPUs]={NULL};
magmaFloatComplex *hwork=NULL, *hpanel=NULL;
magma_queue_t queues[MagmaMaxGPUs][2]={{NULL}};
magma_event_t panel_event[MagmaMaxGPUs]={NULL};
magma_int_t i, j, min_mn, dev, ldhpanel, lddwork, rows;
magma_int_t ib, nb;
magma_int_t lhwork, lwork;
magma_int_t panel_dev, i_local, i_nb_local, n_local[MagmaMaxGPUs], la_dev, dpanel_offset;
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
min_mn = min(m,n);
if (min_mn == 0)
return *info;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
nb = magma_get_cgeqrf_nb( m, n );
/* dwork is (n*nb) --- for T (nb*nb) and clarfb work ((n-nb)*nb) ---
* + dpanel (ldda*nb), on each GPU.
* I think clarfb work could be smaller, max(n_local[:]).
* Oddly, T and clarfb work get stacked on top of each other, both with lddwork=n.
* on GPU that owns panel, set dpanel = dlA(dev,i,i_local).
* on other GPUs, set dpanel = dwork[dev] + dpanel_offset. */
lddwork = n;
dpanel_offset = lddwork*nb;
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
if ( MAGMA_SUCCESS != magma_cmalloc( &(dwork[dev]), (lddwork + ldda)*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
}
/* hwork is MAX( workspace for cgeqrf (n*nb), two copies of T (2*nb*nb) )
* + hpanel (m*nb).
* for last block, need 2*n*nb total. */
ldhpanel = m;
lhwork = max( n*nb, 2*nb*nb );
lwork = max( lhwork + ldhpanel*nb, 2*n*nb );
if ( MAGMA_SUCCESS != magma_cmalloc_pinned( &hwork, lwork )) {
*info = MAGMA_ERR_HOST_ALLOC;
goto CLEANUP;
}
hpanel = hwork + lhwork;
/* Set the number of local n for each GPU */
for( dev=0; dev < ngpu; dev++ ) {
n_local[dev] = ((n/nb)/ngpu)*nb;
if (dev < (n/nb) % ngpu)
n_local[dev] += nb;
else if (dev == (n/nb) % ngpu)
n_local[dev] += n % nb;
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_create( dev, &queues[dev][0] );
magma_queue_create( dev, &queues[dev][1] );
magma_event_create( &panel_event[dev] );
}
if ( nb < min_mn ) {
/* Use blocked code initially */
// Note: as written, ib cannot be < nb.
for( i = 0; i < min_mn-nb; i += nb ) {
/* Set the GPU number that holds the current panel */
panel_dev = (i/nb) % ngpu;
/* Set the local index where the current panel is (j == i) */
i_local = i/(nb*ngpu)*nb;
ib = min(min_mn-i, nb);
rows = m-i;
/* Send current panel to the CPU, after panel_event indicates it has been updated */
magma_setdevice( panel_dev );
magma_queue_wait_event( queues[panel_dev][1], panel_event[panel_dev] );
magma_cgetmatrix_async( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hpanel(i), ldhpanel,
queues[panel_dev][1] );
magma_queue_sync( queues[panel_dev][1] );
// Factor panel
lapackf77_cgeqrf( &rows, &ib, hpanel(i), &ldhpanel, tau+i,
hwork, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %lld\n", (long long) *info );
}
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
hpanel(i), &ldhpanel, tau+i, hwork, &ib );
magma_cpanel_to_q( MagmaUpper, ib, hpanel(i), ldhpanel, hwork + ib*ib );
// Send the current panel back to the GPUs
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
if (dev == panel_dev)
dpanel[dev] = dlA(dev, i, i_local);
else
dpanel[dev] = dwork[dev] + dpanel_offset;
magma_csetmatrix_async( rows, ib,
hpanel(i), ldhpanel,
dpanel[dev], ldda,
queues[dev][0] );
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] );
}
// TODO: if magma_cpanel_to_q copied whole block, wouldn't need to restore
// -- just send the copy to the GPUs.
// TODO: also, could zero out the lower triangle and use Azzam's larfb w/ gemm.
/* Restore the panel */
magma_cq_to_panel( MagmaUpper, ib, hpanel(i), ldhpanel, hwork + ib*ib );
if (i + ib < n) {
/* Send the T matrix to the GPU. */
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_csetmatrix_async( ib, ib,
hwork, ib,
dwork[dev], lddwork,
queues[dev][0] );
}
la_dev = (panel_dev+1) % ngpu;
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
if (dev == la_dev && i+nb < min_mn-nb) {
// If not last panel,
// for look-ahead panel, apply H' to A(i:m,i+ib:i+2*ib)
i_nb_local = (i+nb)/(nb*ngpu)*nb;
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local), ldda, // C
dwork[dev]+ib, lddwork, // work
queues[dev][0] );
magma_event_record( panel_event[dev], queues[dev][0] );
// for trailing matrix, apply H' to A(i:m,i+2*ib:n)
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[dev]-(i_nb_local+ib), ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local+ib), ldda, // C
dwork[dev]+ib, lddwork, // work
queues[dev][0] );
}
else {
// for trailing matrix, apply H' to A(i:m,i+ib:n)
i_nb_local = i_local;
if (dev <= panel_dev) {
i_nb_local += ib;
}
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[dev]-i_nb_local, ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local), ldda, // C
dwork[dev]+ib, lddwork, // work
queues[dev][0] );
}
}
// Restore top of panel (after larfb is done)
magma_setdevice( panel_dev );
magma_csetmatrix_async( ib, ib,
hpanel(i), ldhpanel,
dlA(panel_dev, i, i_local), ldda,
queues[panel_dev][0] );
}
}
}
else {
i = 0;
}
/* Use unblocked code to factor the last or only block row. */
if (i < min_mn) {
rows = m-i;
for( j=i; j < n; j += nb ) {
panel_dev = (j/nb) % ngpu;
i_local = j/(nb*ngpu)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_cgetmatrix( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hwork + (j-i)*rows, rows,
queues[panel_dev][0] );
}
// needs lwork >= 2*n*nb:
// needs (m-i)*(n-i) for last block row, bounded by nb*n.
// needs (n-i)*nb for cgeqrf work, bounded by n*nb.
ib = n-i; // total columns in block row
lhwork = lwork - ib*rows;
lapackf77_cgeqrf( &rows, &ib, hwork, &rows, tau+i, hwork + ib*rows, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %lld\n", (long long) *info );
}
for( j=i; j < n; j += nb ) {
panel_dev = (j/nb) % ngpu;
i_local = j/(nb*ngpu)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_csetmatrix( rows, ib,
hwork + (j-i)*rows, rows,
dlA(panel_dev, i, i_local), ldda,
queues[panel_dev][0] );
}
}
CLEANUP:
// free(NULL) does nothing.
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_destroy( queues[dev][0] );
magma_queue_destroy( queues[dev][1] );
magma_event_destroy( panel_event[dev] );
magma_free( dwork[dev] );
}
magma_free_pinned( hwork );
magma_setdevice( orig_dev );
return *info;
} /* magma_cgeqrf2_mgpu */
extern "C" magma_int_t
magma_dpotrf3_mgpu(int num_gpus, char uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
double **d_lA, magma_int_t ldda,
double **d_lP, magma_int_t lddp,
double *a, magma_int_t lda, magma_int_t h,
cudaStream_t stream[][3], cudaEvent_t event[][5],
magma_int_t *info )
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2012
Purpose
=======
DPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix dA.
Auxiliary subroutine for dpotrf2_ooc. It is multiple gpu interface to compute
Cholesky of a "rectangular" matrix.
The factorization has the form
dA = U**T * U, if UPLO = 'U', or
dA = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) DOUBLE_PRECISION array on the GPU, dimension (LDDA,N)
On entry, the symmetric matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**T * U or dA = L * L**T.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
magma_int_t j, jb, nb0, nb2, d, dd, id, j_local, j_local2, buf;
char uplo_[2] = {uplo, 0};
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
double d_one = 1.0;
double d_neg_one = -1.0;
int upper = lapackf77_lsame(uplo_, "U");
double *dlpanel;
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
//cudaEvent_t event0[MagmaMaxGPUs], /* send row to CPU */
// event1[MagmaMaxGPUs], /* send diag to GPU */
// event2[MagmaMaxGPUs], /* offdiagonal update */
// event3[MagmaMaxGPUs], /* send row to GPU */
// event4[MagmaMaxGPUs]; /* lookahead */
const magma_int_t stream1 = 0, stream2 = 1, stream3 = 2;
double *d_dinvA[MagmaMaxGPUs][2], *d_x[MagmaMaxGPUs][2]; /* used by dtrsm_work */
*info = 0;
if ( (! upper) && (! lapackf77_lsame(uplo_, "L")) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (!upper && num_gpus*ldda < max(1,n)) {
*info = -4;
} else if (upper && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* initialization */
for( d=0; d<num_gpus; d++ ) {
/* local-n and local-ld */
if (upper) {
n_local[d] = ((n/nb)/num_gpus)*nb;
if (d < (n/nb)%num_gpus)
n_local[d] += nb;
else if (d == (n/nb)%num_gpus)
n_local[d] += n%nb;
} else {
n_local[d] = ((m/nb)/num_gpus)*nb;
if (d < (m/nb)%num_gpus)
n_local[d] += nb;
else if (d == (m/nb)%num_gpus)
n_local[d] += m%nb;
}
//magma_setdevice(d);
//magma_event_create( &event0[d] );
//magma_event_create( &event1[d] );
//magma_event_create( &event2[d] );
//magma_event_create( &event3[d] );
//magma_event_create( &event4[d] );
}
/* == initialize the trace */
trace_init( 1, num_gpus, 3, (CUstream_st**)stream );
if (upper)
{
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(DTRSM_WORK)
/* invert the diagonals
* Allocate device memory for the inversed diagonal blocks, size=m*NB
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<2; j++ ) {
cudaMalloc((void**)&d_dinvA[d][j], nb*nb*sizeof(double));
cudaMalloc((void**)&d_x[d][j], n*nb*sizeof(double));
cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(double));
cudaMemset(d_x[d][j], 0, n*nb*sizeof(double));
}
}
magma_setdevice(0);
#endif
for (j=0; j<m; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (m-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
trace_gpu_start( id, stream1, "syrk", "syrk" );
magma_dsyrk(MagmaUpper, MagmaTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda);
trace_gpu_end( id, stream1 );
}
/* send the diagonal to cpu on stream1 */
trace_gpu_start( id, stream1, "comm", "D to CPU" );
magma_dgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
/* update off-diagonal blocks in the panel */
if( j > 0 ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( n_local[d] > nb0 ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
if( d == id ) {
dlpanel = dlA(d, 0, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, jb, 0, buf);
ldpanel = lddp;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
trace_gpu_start( d, stream2, "gemm", "gemm" );
magma_dgemm(MagmaTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda);
trace_gpu_end( d, stream2 );
magma_event_record( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for panel and factorize it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_dpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, 0, 0, buf);
ldpanel = lddp;
}
magma_setdevice(d);
trace_gpu_start( d, stream1, "comm", "comm" );
magma_dsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
trace_gpu_end( d, stream1 );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
trace_gpu_start( id, stream1, "comm", "comm" );
magma_dsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
}
/* panel-factorize the off-diagonal */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d,j,nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, 0, 0, buf);
ldpanel = lddp;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2);
magma_setdevice(d);
//magma_queue_sync( stream[d][stream1] ); // synch on chol for remaining update
//magma_queue_sync( stream[d][stream2] );
if( j+jb < m && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead next block on stream1 */
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
magmablasSetKernelStream(stream[d][stream1]);
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(DTRSM_WORK)
magmablas_dtrsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d][0], d_x[d][0] );
#else
magma_dtrsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
trace_gpu_end( d, stream1 );
} else if( nb2 > 0 ) {
/* update all the blocks on stream2 */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for cholesky factor
trace_gpu_start( d, stream2, "trsm", "trsm" );
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(DTRSM_WORK)
magmablas_dtrsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_dtrsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream2 );
}
d = (d+1)%num_gpus;
} /* end of for */
/* ======================================================================================== */
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, off-diagonals are copied to cpu (synchronize at the end). *
* so we have the Cholesky factor, but only diagonal submatrix of the big panel, *
* on cpu at the end. */
if( j+jb < m ) {
int d2, id2, j2, buf2;
magma_setdevice(d);
/* make sure all the previous sets are done */
if( h < num_gpus ) {
/* > offdiagonal */
for( d2=0; d2<num_gpus; d2++ ) {
j2 = j - (1+d2)*nb;
if( j2 < 0 ) break;
id2 = (j2/nb)%num_gpus;
magma_queue_wait_event( stream[d][stream3], event[id2][0] );
}
/* > diagonal */
for( d2=0; d2<num_gpus; d2++ ) {
j2 = j - d2*nb;
if( j2 < 0 ) break;
id2 = (j2/nb)%num_gpus;
magma_queue_wait_event( stream[d][stream3], event[id2][1] );
}
}
/* lookahead */
magma_queue_wait_event( stream[d][stream3], event[d][4] );
trace_gpu_start( d, stream3, "comm", "row to CPU" );
magma_dgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
stream[d][stream3] );
trace_gpu_end( d, stream3 );
magma_event_record( event[d][3], stream[d][stream3] );
/* needed on pluto */
magma_queue_sync( stream[d][stream3] );
/* wait for the off-diagonal on cpu */
//magma_setdevice(id);
//magma_queue_sync( stream[id][stream3] );
/* broadcast rows to gpus on stream2 */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
trace_gpu_start( d2, stream3, "comm", "row to GPUs" );
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // rows arrived at cpu on stream3
magma_dsetmatrix_async( j+jb, nb0,
Aup(0,j+jb), lda,
dlP(d2,nb0,0,buf2), lddp,
stream[d2][stream3] );
trace_gpu_end( d2, stream3 );
magma_event_record( event[d2][0], stream[d2][stream3] );
}
}
}
/* ======================================================================================== */
/* gpu owning the next column */
/* after look ahead, update the remaining blocks */
if( j+jb < m ) /* no update on the last block column */
{
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, 0, 0, buf);
ldpanel = lddp;
}
nb0 = min(nb, n_local[d]-nb*j_local2 );
nb2 = n_local[d]-nb*j_local2 - nb0;
/* update the remaining blocks */
if( nb2 > 0 ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for cholesky factor
trace_gpu_start( d, stream2, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(DTRSM_WORK)
magmablas_dtrsm_work( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_dtrsm( MagmaLeft, MagmaUpper, MagmaTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda);
#endif
trace_gpu_end( d, stream2 );
}
}
} /* end of dtrsm */
} /* end of for j=1, .., n */
} else {
/* ---------------------------------------------- */
/* Lower-triangular case */
/* > Compute the Cholesky factorization A = L*L'. */
/* ---------------------------------------------- */
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(DTRSM_WORK)
/*
* Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<2; j++ ) {
cudaMalloc((void**)&d_dinvA[d][j], nb*nb*sizeof(double));
cudaMalloc((void**)&d_x[d][j], nb*m *sizeof(double));
cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(double));
cudaMemset(d_x[d][j], 0, nb* m*sizeof(double));
}
}
magma_setdevice(0);
#endif
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (n-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
magma_dsyrk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda);
}
/* send the diagonal to cpu on stream1 */
magma_dgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
stream[id][stream1] );
/* update off-diagonal blocks of the panel */
if( j > 0 ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( nb0 < n_local[d] ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
if( d == id ) {
dlpanel = dlA(d, nb*j_local, 0);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,jb,buf);
ldpanel = nb;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
magma_dgemm( MagmaNoTrans, MagmaTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, ldpanel,
c_one, dlA(d, nb0, j), ldda);
magma_event_record( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for the panel and factorized it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
lapackf77_dpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < m) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
magma_setdevice(d);
magma_dsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
magma_dsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
stream[id][stream1] );
}
/* panel factorize the off-diagonal */
if ( (j+jb) < m) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2 );
magma_setdevice(d);
if( j+nb < n && d == (j/nb+1)%num_gpus ) { /* owns next column, look-ahead next block on stream1 */
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
magmablasSetKernelStream(stream[d][stream1]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(DTRSM_WORK)
magmablas_dtrsm_work( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
d_dinvA[d][0], d_x[d][0] );
#else
magma_dtrsm( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
} else if( nb2 > 0 ) { /* other gpus updating all the blocks on stream2 */
/* update the entire column */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for the cholesky factor
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(DTRSM_WORK)
magmablas_dtrsm_work( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_dtrsm( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
}
d = (d+1)%num_gpus;
} /* end for d */
/* ======================================================================================== */
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, we copy off-diagonal to cpu (but don't synchronize). */
/* so we have the Cholesky factor on cpu at the end. */
if( j+jb < n ) {
int d2, id2, j2, buf2;
magma_setdevice(d);
/* make sure all the previous sets are done */
if( h < num_gpus ) {
/* > offdiagonal */
for( d2=0; d2<num_gpus; d2++ ) {
j2 = j - (1+d2)*nb;
if( j2 < 0 ) break;
id2 = (j2/nb)%num_gpus;
magma_queue_wait_event( stream[d][stream3], event[id2][0] );
}
/* > diagonal */
for( d2=0; d2<num_gpus; d2++ ) {
j2 = j - d2*nb;
if( j2 < 0 ) break;
id2 = (j2/nb)%num_gpus;
magma_queue_wait_event( stream[d][stream3], event[id2][1] );
}
}
// lookahead done
magma_queue_wait_event( stream[d][stream3], event[d][4] );
magma_dgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream3] );
magma_event_record( event[d][3], stream[d][stream3] );
/* syn on rows on CPU, seem to be needed on Pluto */
magma_queue_sync( stream[d][stream3] );
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // getmatrix done
magma_dsetmatrix_async( nb0, j+jb,
Alo(j+jb,0), lda,
dlPT(d2,0,nb0,buf2), nb,
stream[d2][stream3] );
magma_event_record( event[d2][0], stream[d2][stream3] );
}
}
}
/* ======================================================================================== */
/* gpu owing the next column updates remaining blocks on stream2 */
if( j+nb < n ) { // no lookahead on the last block column
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,0,buf);
ldpanel = nb;
}
nb0 = min(nb, n_local[d]-nb*j_local2 );
nb2 = n_local[d] - j_local2*nb - nb0;
if( nb2 > 0 ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
/* update the remaining blocks in the column */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(DTRSM_WORK)
magmablas_dtrsm_work( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_dtrsm( MagmaRight, MagmaLower, MagmaTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda);
#endif
}
}
}
}
} /* end of else not upper */
/* == finalize the trace == */
trace_finalize( "dpotrf.svg","trace.css" );
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magma_queue_sync( stream[d][2] );
magmablasSetKernelStream(NULL);
//magma_event_destroy( event0[d] );
//magma_event_destroy( event1[d] );
//magma_event_destroy( event2[d] );
//magma_event_destroy( event3[d] );
//magma_event_destroy( event4[d] );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(DTRSM_WORK)
for( j=0; j<2; j++ ) {
magma_free( d_dinvA[d][j] );
magma_free( d_x[d][j] );
}
#endif
}
magma_setdevice(0);
return *info;
} /* magma_dpotrf_mgpu */
/**
Purpose
-------
SPOTRF computes the Cholesky factorization of a real symmetric
positive definite matrix dA.
Auxiliary subroutine for spotrf2_ooc. It is multiple gpu interface to compute
Cholesky of a "rectangular" matrix.
The factorization has the form
dA = U**H * U, if UPLO = MagmaUpper, or
dA = L * L**H, if UPLO = MagmaLower,
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of dA is stored;
- = MagmaLower: Lower triangle of dA is stored.
@param[in]
n INTEGER
The order of the matrix dA. N >= 0.
@param[in,out]
dA REAL array on the GPU, dimension (LDDA,N)
On entry, the symmetric matrix dA. If UPLO = MagmaUpper, the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
@ingroup magma_sposv_comp
********************************************************************/
extern "C" magma_int_t
magma_spotrf3_mgpu(
magma_int_t ngpu,
magma_uplo_t uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaFloat_ptr d_lA[], magma_int_t ldda,
magmaFloat_ptr d_lP[], magma_int_t lddp,
float *A, magma_int_t lda, magma_int_t h,
magma_queue_t queues[][3], magma_event_t events[][5],
magma_int_t *info )
{
#define Alo(i, j) (A + ((j)+off_j)*lda + (nb*(((i)/nb)%h)+off_i))
#define Aup(i, j) (A + (nb*(((j)/nb)%h)+off_j)*lda + (i+off_i))
#define dlA(id, i, j) (d_lA[(id)] + (j)*ldda + (i))
#define dlP(id, i, j, k) (d_lP[(id)] + (k)*nb*lddp + (j)*lddp + (i))
#define dlPT(id, i, j, k) (d_lP[(id)] + (k)*nb*lddp + (j)*nb + (i))
magma_int_t j, jb, nb0, nb2, d, dd, id, j_local, j_local2, buf;
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
float d_one = 1.0;
float d_neg_one = -1.0;
int upper = (uplo == MagmaUpper);
float *dlpanel;
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
const magma_int_t stream1 = 0, stream2 = 1, stream3 = 2;
*info = 0;
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (!upper && ngpu*ldda < max(1,n)) {
*info = -4;
} else if (upper && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
/* used by strsm_work */
float c_zero = MAGMA_S_ZERO;
int trsm_nb = 128;
int trsm_n = trsm_nb*((nb+trsm_nb-1)/trsm_nb);
float *d_dinvA[MagmaMaxGPUs];
float *d_x[MagmaMaxGPUs];
#define dinvA(d,j) &(d_dinvA[(d)][(j)*trsm_nb*trsm_n])
#define dx(d,j) &(d_x[(d)][(j)*nb*m])
/*
* Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
*/
// TODO free memory on failure.
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
if ( (MAGMA_SUCCESS != magma_smalloc( &d_dinvA[d], 2*trsm_nb*trsm_n )) ||
(MAGMA_SUCCESS != magma_smalloc( &d_x[d], 2*nb*(upper ? n : m) )) ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
magma_setdevice(0);
#endif
/* initialization */
for( d=0; d < ngpu; d++ ) {
/* local-n and local-ld */
if (upper) {
n_local[d] = (n/(nb*ngpu))*nb;
if (d < (n/nb)%ngpu)
n_local[d] += nb;
else if (d == (n/nb)%ngpu)
n_local[d] += n%nb;
} else {
n_local[d] = (m/(nb*ngpu))*nb;
if (d < (m/nb)%ngpu)
n_local[d] += nb;
else if (d == (m/nb)%ngpu)
n_local[d] += m%nb;
}
}
/* == initialize the trace */
trace_init( 1, ngpu, 3, (CUstream_st**)queues );
if (upper) {
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
for (j=0; j < m; j += nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%ngpu;
buf = (j/nb)%ngpu; // right now, we have ngpu buffers, so id and buf are the same..
/* Set the local index where the current panel is */
j_local = j/(nb*ngpu);
jb = min(nb, (m-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if ( j > 0 ) {
magmablasSetKernelStream( queues[id][stream1] );
trace_gpu_start( id, stream1, "syrk", "syrk" );
magma_ssyrk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda);
trace_gpu_end( id, stream1 );
}
/* send the diagonal to cpu on stream1 */
trace_gpu_start( id, stream1, "comm", "D to CPU" );
magma_sgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
queues[id][stream1] );
trace_gpu_end( id, stream1 );
/* update off-diagonal blocks in the panel */
if ( j > 0 ) {
d = (j/nb+1)%ngpu;
for( dd=0; dd < ngpu; dd++ ) {
j_local2 = j_local+1;
if ( d > id ) j_local2 --;
nb0 = nb*j_local2; // number of local columns in the panel, while jb is panel-size (number of rows)
if ( n_local[d] > nb0 ) {
magma_setdevice(d);
magmablasSetKernelStream( queues[d][stream2] );
if ( d == id ) {
dlpanel = dlA(d,0,nb*j_local);
ldpanel = ldda;
// the GPU owns the row from start, and no need of synch.
//magma_queue_wait_event( queues[d][stream2], events[d][0] ); // rows arrived at gpu
magma_queue_wait_event( queues[d][stream2], events[d][4] ); // wait for look-ahead trsm to finish
} else {
dlpanel = dlP(d,nb,0,buf);
ldpanel = lddp;
magma_queue_wait_event( queues[d][stream2], events[d][0] ); // rows arrived at gpu
}
trace_gpu_start( d, stream2, "gemm", "gemm" );
magma_sgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda);
trace_gpu_end( d, stream2 );
magma_event_record( events[d][2], queues[d][stream2] );
}
d = (d+1)%ngpu;
}
}
/* wait for panel and factorize it on cpu */
magma_setdevice(id);
magma_queue_sync( queues[id][stream1] );
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_spotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < n) {
d = (j/nb+1)%ngpu;
for( dd=0; dd < ngpu; dd++ ) {
if ( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
magma_setdevice(d);
trace_gpu_start( d, stream1, "comm", "comm" );
magma_ssetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, ldpanel,
queues[d][stream1] );
trace_gpu_end( d, stream1 );
magma_event_record( events[d][1], queues[d][stream1] );
d = (d+1)%ngpu;
}
} else {
magma_setdevice(id);
trace_gpu_start( id, stream1, "comm", "comm" );
magma_ssetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
queues[id][stream1] );
trace_gpu_end( id, stream1 );
}
/* panel-factorize the off-diagonal */
if ( (j+jb) < n) {
d = (j/nb+1)%ngpu;
for( dd=0; dd < ngpu; dd++ ) {
/* next column */
j_local2 = j_local+1;
if ( d > id ) j_local2--;
if ( d == id ) {
dlpanel = dlA(d,j,nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
nb2 = n_local[d] - j_local2*nb;
magma_setdevice(d);
if ( j+jb < m && d == (j/nb+1)%ngpu ) {
/* owns the next column, look-ahead next block on stream1 */
nb0 = min(nb, nb2);
magmablasSetKernelStream( queues[d][stream1] );
magma_queue_wait_event( queues[d][stream1], events[d][2] ); // wait for gemm update
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,0), trsm_nb );
magmablas_slaset( MagmaFull, nb0, jb, c_zero, c_zero, dx(d,0), nb0 );
magmablas_strsm_work( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_strsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
magma_event_record( events[d][4], queues[d][stream1] );
trace_gpu_end( d, stream1 );
} else if ( nb2 > 0 ) {
/* update all the blocks on stream2 */
magma_queue_wait_event( queues[d][stream2], events[d][1] ); // wait for cholesky factor
trace_gpu_start( d, stream2, "trsm", "trsm" );
magmablasSetKernelStream( queues[d][stream2] );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,0), trsm_nb );
magmablas_slaset( MagmaFull, nb2, jb, c_zero, c_zero, dx(d,0), nb2 );
magmablas_strsm_work( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_strsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream2 );
}
d = (d+1)%ngpu;
} /* end of for */
/* ========================================================== */
if ( j+jb < m ) {
d = (j/nb+1)%ngpu;
/* next column */
j_local2 = j_local+1;
if ( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, off-diagonals are copied to cpu (synchronize at the end). *
* so we have the Cholesky factor, but only diagonal submatrix of the big panel, *
* on cpu at the end. */
int d2, buf2;
magma_setdevice(d);
/* lookahead done */
magma_queue_wait_event( queues[d][stream3], events[d][4] );
trace_gpu_start( d, stream3, "comm", "row to CPU" );
magma_sgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
queues[d][stream3] );
trace_gpu_end( d, stream3 );
magma_event_record( events[d][3], queues[d][stream3] );
/* needed on pluto */
//magma_queue_sync( queues[d][stream3] );
/* broadcast rows to gpus on stream2 */
buf2 = ((j+jb)/nb)%ngpu;
for( d2=0; d2 < ngpu; d2++ ) {
if ( d2 != d ) {
magma_setdevice(d2);
trace_gpu_start( d2, stream3, "comm", "row to GPUs" );
magma_queue_wait_event( queues[d2][stream3], events[d][3] ); // rows arrived at cpu on stream3
magma_ssetmatrix_async( j+jb, nb0,
Aup(0,j+jb), lda,
dlP(d2,nb,0,buf2), lddp,
queues[d2][stream3] );
trace_gpu_end( d2, stream3 );
magma_event_record( events[d2][0], queues[d2][stream3] );
}
}
/* =========================== */
/* update the remaining blocks */
nb2 = n_local[d]-(nb*j_local2 + nb0);
if ( nb2 > 0 ) {
if ( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
magma_setdevice(d);
magmablasSetKernelStream( queues[d][stream2] );
trace_gpu_start( d, stream2, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( queues[d][stream2], events[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,flag), trsm_nb );
magma_queue_wait_event( queues[d][stream2], events[d][1] ); // panel received
}
magmablas_slaset( MagmaFull, nb2, jb, c_zero, c_zero, dx(d,1), nb2 );
magmablas_strsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
flag, dinvA(d,flag), dx(d,1) );
#else
magma_queue_wait_event( queues[d][stream2], events[d][1] ); // wait for cholesky factor
magma_strsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda);
#endif
trace_gpu_end( d, stream2 );
}
}
} /* end of strsm */
} /* end of for j=1, .., n */
} else {
/* ---------------------------------------------- */
/* Lower-triangular case */
/* > Compute the Cholesky factorization A = L*L'. */
/* ---------------------------------------------- */
for (j=0; j < n; j += nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%ngpu;
buf = (j/nb)%ngpu;
/* Set the local index where the current panel is */
j_local = j/(nb*ngpu);
jb = min(nb, (n-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if ( j > 0 ) {
magmablasSetKernelStream( queues[id][stream1] );
magma_ssyrk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda);
}
/* send the diagonal to cpu on stream1 */
magma_sgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
queues[id][stream1] );
/* update off-diagonal blocks of the panel */
if ( j > 0 ) {
d = (j/nb+1)%ngpu;
for( dd=0; dd < ngpu; dd++ ) {
j_local2 = j_local+1;
if ( d > id ) j_local2 --;
nb0 = nb*j_local2;
if ( nb0 < n_local[d] ) {
magma_setdevice(d);
magmablasSetKernelStream( queues[d][stream2] );
if ( d == id ) {
dlpanel = dlA(d, nb*j_local, 0);
ldpanel = ldda;
magma_queue_wait_event( queues[d][stream2], events[d][4] ); // wait for look-ahead trsm to finish
} else {
dlpanel = dlPT(d,0,nb,buf);
ldpanel = nb;
magma_queue_wait_event( queues[d][stream2], events[d][0] ); // rows arrived at gpu
}
magma_sgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, ldpanel,
c_one, dlA(d, nb0, j), ldda);
magma_event_record( events[d][2], queues[d][stream2] );
}
d = (d+1)%ngpu;
}
}
/* wait for the panel and factorized it on cpu */
magma_setdevice(id);
magma_queue_sync( queues[id][stream1] );
lapackf77_spotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < m) {
d = (j/nb+1)%ngpu;
for( dd=0; dd < ngpu; dd++ ) {
if ( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
magma_setdevice(d);
magma_ssetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, ldpanel,
queues[d][stream1] );
magma_event_record( events[d][1], queues[d][stream1] );
d = (d+1)%ngpu;
}
} else {
magma_setdevice(id);
magma_ssetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
queues[id][stream1] );
}
/* panel factorize the off-diagonal */
if ( (j+jb) < m) {
d = (j/nb+1)%ngpu;
for( dd=0; dd < ngpu; dd++ ) {
/* next column */
j_local2 = j_local+1;
if ( d > id ) j_local2--;
if ( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2);
magma_setdevice(d);
if ( j+nb < n && d == (j/nb+1)%ngpu ) { /* owns next column, look-ahead next block on stream1 */
if ( j > 0 ) magma_queue_wait_event( queues[d][stream1], events[d][2] ); // wait for gemm update
magmablasSetKernelStream( queues[d][stream1] );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,0), trsm_nb );
magmablas_slaset( MagmaFull, nb0, jb, c_zero, c_zero, dx(d,0), nb0 );
magmablas_strsm_work( MagmaRight, MagmaLower,
MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_strsm( MagmaRight, MagmaLower,
MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
magma_event_record( events[d][4], queues[d][stream1] );
} else if ( nb2 > 0 ) { /* other gpus updating all the blocks on stream2 */
/* update the entire column */
magma_queue_wait_event( queues[d][stream2], events[d][1] ); // wait for the cholesky factor
magmablasSetKernelStream( queues[d][stream2] );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,0), trsm_nb );
magmablas_slaset( MagmaFull, nb2, jb, c_zero, c_zero, dx(d,0), nb2 );
magmablas_strsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_strsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
}
d = (d+1)%ngpu;
} /* end for d */
/* ========================================================== */
if ( j+jb < n ) {
d = (j/nb+1)%ngpu;
/* next column */
j_local2 = j_local+1;
if ( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, we copy off-diagonal to cpu (but don't synchronize). */
/* so we have the Cholesky factor on cpu at the end. */
int d2, buf2;
//#define SPOTRF_DEVICE_TO_DEVICE
#ifdef SPOTRF_DEVICE_TO_DEVICE
// lookahead done
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%ngpu;
for( d2=0; d2 < ngpu; d2++ ) {
magma_setdevice(d2);
magma_queue_wait_event( queues[d2][stream3], events[d][4] );
if ( d2 != d ) {
magma_scopymatrix_async( nb0, j+jb,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
dlA(d, nb*j_local2, 0), ldda,
queues[d2][stream3] );
magma_event_record( events[d2][0], queues[d2][stream3] );
} else {
magma_sgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
queues[d][stream3] );
}
}
#else
// lookahead done
magma_setdevice(d);
magma_queue_wait_event( queues[d][stream3], events[d][4] );
magma_sgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
queues[d][stream3] );
magma_event_record( events[d][3], queues[d][stream3] );
/* syn on rows on CPU, seem to be needed on Pluto */
//magma_queue_sync( queues[d][stream3] );
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%ngpu;
for( d2=0; d2 < ngpu; d2++ ) {
if ( d2 != d ) {
magma_setdevice(d2);
magma_queue_wait_event( queues[d2][stream3], events[d][3] ); // getmatrix done
magma_ssetmatrix_async( nb0, j+jb,
Alo(j+jb,0), lda,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
queues[d2][stream3] );
magma_event_record( events[d2][0], queues[d2][stream3] );
}
}
#endif
/* =================================== */
/* updates remaining blocks on stream2 */
nb2 = n_local[d] - (j_local2*nb + nb0);
if ( nb2 > 0 ) {
if ( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,0,buf);
ldpanel = nb;
}
magma_setdevice(d);
magmablasSetKernelStream( queues[d][stream2] );
/* update the remaining blocks in the column */
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( queues[d][stream2], events[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_slaset( MagmaFull, trsm_nb, trsm_n, c_zero, c_zero, dinvA(d,flag), trsm_nb );
magma_queue_wait_event( queues[d][stream2], events[d][1] ); // panel received
}
magmablas_slaset( MagmaFull, nb2, jb, c_zero, c_zero, dx(d,1), nb2 );
magmablas_strsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
flag, dinvA(d,flag), dx(d,1) );
#else
magma_queue_wait_event( queues[d][stream2], events[d][1] ); // panel received
magma_strsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda);
#endif
}
}
}
}
} /* end of else not upper */
/* == finalize the trace == */
trace_finalize( "spotrf.svg", "trace.css" );
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
for( j=0; j < 3; j++ ) {
magma_queue_sync( queues[d][j] );
}
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(STRSM_WORK)
magma_free( d_dinvA[d] );
magma_free( d_x[d] );
#endif
}
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
return *info;
} /* magma_spotrf_mgpu */
