/**
Purpose
-------
DPOTRS solves a system of linear equations A*X = B with a symmetric
positive definite matrix A using the Cholesky factorization
A = U**H*U or A = L*L**H computed by DPOTRF.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored;
- = MagmaLower: Lower triangle of A is stored.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
nrhs INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
@param[in]
dA_array Array of pointers, dimension (batchCount).
Each is a DOUBLE PRECISION array on the GPU, dimension (LDDA,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H, as computed by DPOTRF.
@param[in]
ldda INTEGER
The leading dimension of each array A. LDDA >= max(1,N).
@param[in,out]
dB_array Array of pointers, dimension (batchCount).
Each is a DOUBLE PRECISION array on the GPU, dimension (LDDB,NRHS)
On entry, each pointer is a right hand side matrix B.
On exit, the corresponding solution matrix X.
@param[in]
lddb INTEGER
The leading dimension of each array B. LDDB >= max(1,N).
@param[in]
batchCount INTEGER
The number of matrices to operate on.
@param[in]
queue magma_queue_t
Queue to execute in.
@ingroup magma_dposv_comp
********************************************************************/
extern "C" magma_int_t
magma_dpotrs_batched(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs,
double **dA_array, magma_int_t ldda,
double **dB_array, magma_int_t lddb,
magma_int_t batchCount, magma_queue_t queue)
{
double c_one = MAGMA_D_ONE;
magma_int_t info = 0;
if ( uplo != MagmaUpper && uplo != MagmaLower )
info = -1;
if ( n < 0 )
info = -2;
if ( nrhs < 0)
info = -3;
if ( ldda < max(1, n) )
info = -5;
if ( lddb < max(1, n) )
info = -7;
if (info != 0) {
magma_xerbla( __func__, -(info) );
return info;
}
/* Quick return if possible */
if ( (n == 0) || (nrhs == 0) ) {
return info;
}
double **dW1_displ = NULL;
double **dW2_displ = NULL;
double **dW3_displ = NULL;
double **dW4_displ = NULL;
double **dinvA_array = NULL;
double **dwork_array = NULL;
magma_malloc((void**)&dW1_displ, batchCount * sizeof(*dW1_displ));
magma_malloc((void**)&dW2_displ, batchCount * sizeof(*dW2_displ));
magma_malloc((void**)&dW3_displ, batchCount * sizeof(*dW3_displ));
magma_malloc((void**)&dW4_displ, batchCount * sizeof(*dW4_displ));
magma_malloc((void**)&dinvA_array, batchCount * sizeof(*dinvA_array));
magma_malloc((void**)&dwork_array, batchCount * sizeof(*dwork_array));
magma_int_t invA_msize = magma_roundup( n, TRI_NB )*TRI_NB;
magma_int_t dwork_msize = n*nrhs;
double* dinvA = NULL;
double* dwork = NULL; // dinvA and dwork are workspace in dtrsm
magma_dmalloc( &dinvA, invA_msize * batchCount);
magma_dmalloc( &dwork, dwork_msize * batchCount );
/* check allocation */
if ( dW1_displ == NULL || dW2_displ == NULL || dW3_displ == NULL || dW4_displ == NULL ||
dinvA_array == NULL || dwork_array == NULL || dinvA == NULL || dwork == NULL ) {
magma_free(dW1_displ);
magma_free(dW2_displ);
magma_free(dW3_displ);
magma_free(dW4_displ);
magma_free(dinvA_array);
magma_free(dwork_array);
magma_free( dinvA );
magma_free( dwork );
info = MAGMA_ERR_DEVICE_ALLOC;
magma_xerbla( __func__, -(info) );
return info;
}
magmablas_dlaset_q( MagmaFull, invA_msize, batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dinvA, invA_msize, queue );
magmablas_dlaset_q( MagmaFull, dwork_msize, batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dwork, dwork_msize, queue );
magma_dset_pointer( dwork_array, dwork, n, 0, 0, dwork_msize, batchCount, queue );
magma_dset_pointer( dinvA_array, dinvA, TRI_NB, 0, 0, invA_msize, batchCount, queue );
if ( uplo == MagmaUpper) {
if (nrhs > 1)
{
// A = U^T U
// solve U^{T}X = B ==> dworkX = U^-T * B
magmablas_dtrsm_outofplace_batched( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit, 1,
n, nrhs,
c_one,
dA_array, ldda, // dA
dB_array, lddb, // dB
dwork_array, n, // dX //output
dinvA_array, invA_msize,
dW1_displ, dW2_displ,
dW3_displ, dW4_displ,
1, batchCount, queue );
// solve U X = dwork ==> X = U^-1 * dwork
magmablas_dtrsm_outofplace_batched( MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit, 1,
n, nrhs,
c_one,
dA_array, ldda, // dA
dwork_array, n, // dB
dB_array, lddb, // dX //output
dinvA_array, invA_msize,
dW1_displ, dW2_displ,
dW3_displ, dW4_displ,
1, batchCount, queue );
}
else
{
// A = U^T U
// solve U^{T}X = B ==> dworkX = U^-T * B
magmablas_dtrsv_outofplace_batched( MagmaUpper, MagmaConjTrans, MagmaNonUnit,
n,
dA_array, ldda, // dA
dB_array, 1, // dB
dwork_array, // dX //output
batchCount, queue, 0 );
// solve U X = dwork ==> X = U^-1 * dwork
magmablas_dtrsv_outofplace_batched( MagmaUpper, MagmaNoTrans, MagmaNonUnit,
n,
dA_array, ldda, // dA
dwork_array, 1, // dB
dB_array, // dX //output
batchCount, queue, 0 );
}
}
else {
if (nrhs > 1)
{
// A = L L^T
// solve LX= B ==> dwork = L^{-1} B
magmablas_dtrsm_outofplace_batched( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaNonUnit, 1,
n, nrhs,
c_one,
dA_array, ldda, // dA
dB_array, lddb, // dB
dwork_array, n, // dX //output
dinvA_array, invA_msize,
dW1_displ, dW2_displ,
dW3_displ, dW4_displ,
1, batchCount, queue );
// solve L^{T}X= dwork ==> X = L^{-T} dwork
magmablas_dtrsm_outofplace_batched( MagmaLeft, MagmaLower, MagmaConjTrans, MagmaNonUnit, 1,
n, nrhs,
c_one,
dA_array, ldda, // dA
dwork_array, n, // dB
dB_array, lddb, // dX //output
dinvA_array, invA_msize,
dW1_displ, dW2_displ,
dW3_displ, dW4_displ,
1, batchCount, queue );
}
else
{
// A = L L^T
// solve LX= B ==> dwork = L^{-1} B
magmablas_dtrsv_outofplace_batched( MagmaLower, MagmaNoTrans, MagmaNonUnit,
n,
dA_array, ldda, // dA
dB_array, 1, // dB
dwork_array, // dX //output
batchCount, queue, 0 );
// solve L^{T}X= dwork ==> X = L^{-T} dwork
magmablas_dtrsv_outofplace_batched( MagmaLower, MagmaConjTrans, MagmaNonUnit,
n,
dA_array, ldda, // dA
dwork_array, 1, // dB
dB_array, // dX //output
batchCount, queue, 0 );
}
}
magma_queue_sync(queue);
magma_free(dW1_displ);
magma_free(dW2_displ);
magma_free(dW3_displ);
magma_free(dW4_displ);
magma_free(dinvA_array);
magma_free(dwork_array);
magma_free( dinvA );
magma_free( dwork );
return info;
}
/**
Purpose
-------
DGETRF computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges.
The factorization has the form
A = P * L * U
where P is a permutation matrix, L is lower triangular with unit
diagonal elements (lower trapezoidal if m > n), and U is upper
triangular (upper trapezoidal if m < n).
This is the right-looking Level 3 BLAS version of the algorithm.
If the current stream is NULL, this version replaces it with a new
stream to overlap computation with communication.
Arguments
---------
@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]
dA DOUBLE_PRECISION array on the GPU, dimension (LDDA,N).
On entry, the M-by-N matrix to be factored.
On exit, the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDDA >= max(1,M).
@param[out]
ipiv INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).
@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.
- > 0: if INFO = i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.
@ingroup magma_dgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_dgetrf_batched(
magma_int_t m, magma_int_t n,
double **dA_array,
magma_int_t ldda,
magma_int_t **ipiv_array,
magma_int_t *info_array,
magma_int_t batchCount, magma_queue_t queue)
{
#define A(i_, j_) (A + (i_) + (j_)*ldda)
magma_int_t min_mn = min(m, n);
cudaMemset(info_array, 0, batchCount*sizeof(magma_int_t));
/* Check arguments */
magma_int_t arginfo = 0;
if (m < 0)
arginfo = -1;
else if (n < 0)
arginfo = -2;
else if (ldda < max(1,m))
arginfo = -4;
if (arginfo != 0) {
magma_xerbla( __func__, -(arginfo) );
return arginfo;
}
/* Quick return if possible */
if (m == 0 || n == 0)
if(min_mn == 0 ) return arginfo;
if( m > 2048 || n > 2048 ){
printf("=========================================================================================\n");
printf(" WARNING batched routines are designed for small sizes it might be better to use the\n Native/Hybrid classical routines if you want performance\n");
printf("=========================================================================================\n");
}
//#define ENABLE_TIMER3
#if defined(ENABLE_TIMER3)
real_Double_t tall=0.0, tloop=0., talloc=0., tdalloc=0.;
tall = magma_sync_wtime(0);
talloc = magma_sync_wtime(0);
#endif
double neg_one = MAGMA_D_NEG_ONE;
double one = MAGMA_D_ONE;
magma_int_t ib, i, k, pm;
magma_int_t nb = BATRF_NB;
magma_int_t gemm_crossover = nb > 32 ? 127 : 160;
// magma_int_t gemm_crossover = n;// use only stream gemm
#if defined(USE_CUOPT)
cublasHandle_t myhandle;
cublasCreate_v2(&myhandle);
#else
cublasHandle_t myhandle=NULL;
#endif
magma_int_t **dipiv_displ = NULL;
double **dA_displ = NULL;
double **dW0_displ = NULL;
double **dW1_displ = NULL;
double **dW2_displ = NULL;
double **dW3_displ = NULL;
double **dW4_displ = NULL;
double **dinvA_array = NULL;
double **dwork_array = NULL;
magma_malloc((void**)&dipiv_displ, batchCount * sizeof(*dipiv_displ));
magma_malloc((void**)&dA_displ, batchCount * sizeof(*dA_displ));
magma_malloc((void**)&dW0_displ, batchCount * sizeof(*dW0_displ));
magma_malloc((void**)&dW1_displ, batchCount * sizeof(*dW1_displ));
magma_malloc((void**)&dW2_displ, batchCount * sizeof(*dW2_displ));
magma_malloc((void**)&dW3_displ, batchCount * sizeof(*dW3_displ));
magma_malloc((void**)&dW4_displ, batchCount * sizeof(*dW4_displ));
magma_malloc((void**)&dinvA_array, batchCount * sizeof(*dinvA_array));
magma_malloc((void**)&dwork_array, batchCount * sizeof(*dwork_array));
magma_int_t invA_msize = ((n+TRI_NB-1)/TRI_NB)*TRI_NB*TRI_NB;
magma_int_t dwork_msize = n*nb;
magma_int_t **pivinfo_array = NULL;
magma_int_t *pivinfo = NULL;
double* dinvA = NULL;
double* dwork = NULL;// dinvA and dwork are workspace in dtrsm
double **cpuAarray = NULL;
magma_dmalloc( &dinvA, invA_msize * batchCount);
magma_dmalloc( &dwork, dwork_msize * batchCount );
magma_malloc((void**)&pivinfo_array, batchCount * sizeof(*pivinfo_array));
magma_malloc((void**)&pivinfo, batchCount * m * sizeof(magma_int_t));
magma_malloc_cpu((void**) &cpuAarray, batchCount*sizeof(double*));
/* check allocation */
if ( dA_displ == NULL || dW0_displ == NULL || dW1_displ == NULL || dW2_displ == NULL ||
dW3_displ == NULL || dW4_displ == NULL || dinvA_array == NULL || dwork_array == NULL ||
dinvA == NULL || dwork == NULL || cpuAarray == NULL ||
dipiv_displ == NULL || pivinfo_array == NULL || pivinfo == NULL) {
magma_free(dA_displ);
magma_free(dW0_displ);
magma_free(dW1_displ);
magma_free(dW2_displ);
magma_free(dW3_displ);
magma_free(dW4_displ);
magma_free(dinvA_array);
magma_free(dwork_array);
magma_free( dinvA );
magma_free( dwork );
free(cpuAarray);
magma_free(dipiv_displ);
magma_free(pivinfo_array);
magma_free(pivinfo);
magma_int_t info = MAGMA_ERR_DEVICE_ALLOC;
magma_xerbla( __func__, -(info) );
return info;
}
magmablas_dlaset_q(MagmaFull, invA_msize, batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dinvA, invA_msize, queue);
magmablas_dlaset_q(MagmaFull, dwork_msize, batchCount, MAGMA_D_ZERO, MAGMA_D_ZERO, dwork, dwork_msize, queue);
dset_pointer(dwork_array, dwork, 1, 0, 0, dwork_msize, batchCount, queue);
dset_pointer(dinvA_array, dinvA, TRI_NB, 0, 0, invA_msize, batchCount, queue);
set_ipointer(pivinfo_array, pivinfo, 1, 0, 0, m, batchCount, queue);
// printf(" I am in dgetrfbatched\n");
magma_queue_t cstream;
magmablasGetKernelStream(&cstream);
magma_int_t streamid;
const magma_int_t nbstreams=32;
magma_queue_t stream[nbstreams];
for(i=0; i<nbstreams; i++){
magma_queue_create( &stream[i] );
}
magma_getvector( batchCount, sizeof(double*), dA_array, 1, cpuAarray, 1);
#if defined(ENABLE_TIMER3)
printf(" I am after malloc\n");
talloc = magma_sync_wtime(0) - talloc;
tloop = magma_sync_wtime(0);
#endif
for(i = 0; i < min_mn; i+=nb)
{
magmablasSetKernelStream(NULL);
ib = min(nb, min_mn-i);
pm = m-i;
magma_idisplace_pointers(dipiv_displ, ipiv_array, ldda, i, 0, batchCount, queue);
magma_ddisplace_pointers(dA_displ, dA_array, ldda, i, i, batchCount, queue);
//===============================================
// panel factorization
//===============================================
#if 0
arginfo = magma_dgetf2_batched(
pm, ib,
dA_displ, ldda,
dW1_displ, dW2_displ, dW3_displ,
dipiv_displ,
info_array, i, batchCount, myhandle);
#else
arginfo = magma_dgetrf_recpanel_batched(
pm, ib, 16,
dA_displ, ldda,
dipiv_displ, pivinfo_array,
dwork_array, nb,
dinvA_array, invA_msize,
dW0_displ, dW1_displ, dW2_displ,
dW3_displ, dW4_displ,
info_array, i,
batchCount, myhandle, queue);
#endif
if(arginfo != 0 ) goto fin;
//===============================================
// end of panel
//===============================================
#define RUN_ALL
#ifdef RUN_ALL
// setup pivinfo before adjusting ipiv
setup_pivinfo_batched(pivinfo_array, dipiv_displ, pm, ib, batchCount, queue);
adjust_ipiv_batched(dipiv_displ, ib, i, batchCount, queue);
// stepinit_ipiv(pivinfo_array, pm, batchCount);// for debug and check swap, it create an ipiv
#if 0
dlaswp_batched( i, dA_displ, ldda,
i, i+ib,
dipiv_displ, pivinfo_array, batchCount);
#else
magma_ddisplace_pointers(dA_displ, dA_array, ldda, i, 0, batchCount, queue);
magma_ddisplace_pointers(dW0_displ, dA_array, ldda, i, 0, batchCount, queue);
magma_dlaswp_rowparallel_batched( i, dA_displ, ldda,
dW0_displ, ldda,
i, i+ib,
pivinfo_array, batchCount, queue);
#endif
if( (i + ib) < n)
{
// swap right side and trsm
magma_ddisplace_pointers(dA_displ, dA_array, ldda, i, i+ib, batchCount, queue);
dset_pointer(dwork_array, dwork, nb, 0, 0, dwork_msize, batchCount, queue); // I don't think it is needed Azzam
magma_dlaswp_rowparallel_batched( n-(i+ib), dA_displ, ldda,
dwork_array, nb,
i, i+ib,
pivinfo_array, batchCount, queue);
magma_ddisplace_pointers(dA_displ, dA_array, ldda, i, i, batchCount, queue);
magma_ddisplace_pointers(dW0_displ, dA_array, ldda, i, i+ib, batchCount, queue);
magmablas_dtrsm_outofplace_batched(MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit, 1,
ib, n-i-ib,
MAGMA_D_ONE,
dA_displ, ldda, // dA
dwork_array, nb, // dB
dW0_displ, ldda, // dX
dinvA_array, invA_msize,
dW1_displ, dW2_displ,
dW3_displ, dW4_displ,
0, batchCount, queue);
if( (i + ib) < m)
{
// if gemm size is >160 use a streamed classical cublas gemm since it is faster
// the batched is faster only when M=N<=160 for K40c
//-------------------------------------------
// USE STREAM GEMM
//-------------------------------------------
if( (m-i-ib) > gemm_crossover && (n-i-ib) > gemm_crossover)
{
//printf("caling streamed dgemm %d %d %d \n", m-i-ib, n-i-ib, ib);
// since it use different stream I need to wait the TRSM and swap.
// But since the code use the NULL stream everywhere,
// so I don't need it, because the NULL stream do the sync by itself
//magma_queue_sync(NULL);
//
for(k=0; k<batchCount; k++)
{
streamid = k%nbstreams;
magmablasSetKernelStream(stream[streamid]);
magma_dgemm(MagmaNoTrans, MagmaNoTrans,
m-i-ib, n-i-ib, ib,
neg_one, cpuAarray[k] + (i+ib)+i*ldda, ldda,
cpuAarray[k] + i+(i+ib)*ldda, ldda,
one, cpuAarray[k] + (i+ib)+(i+ib)*ldda, ldda);
}
// need to synchronise to be sure that dgetf2 do not start before
// finishing the update at least of the next panel
// BUT no need for it as soon as the other portion of the code
// use the NULL stream which do the sync by itself
//magma_device_sync();
}
//-------------------------------------------
// USE BATCHED GEMM
//-------------------------------------------
else
{
magma_ddisplace_pointers(dA_displ, dA_array, ldda, i+ib, i, batchCount, queue);
magma_ddisplace_pointers(dW1_displ, dA_array, ldda, i, i+ib, batchCount, queue);
magma_ddisplace_pointers(dW2_displ, dA_array, ldda, i+ib, i+ib, batchCount, queue);
//printf("caling batched dgemm %d %d %d \n", m-i-ib, n-i-ib, ib);
magmablas_dgemm_batched( MagmaNoTrans, MagmaNoTrans, m-i-ib, n-i-ib, ib,
neg_one, dA_displ, ldda,
dW1_displ, ldda,
one, dW2_displ, ldda,
batchCount, queue);
} // end of batched/stream gemm
} // end of if( (i + ib) < m)
} // end of if( (i + ib) < n)
#endif
}// end of for
fin:
magma_queue_sync(NULL);
#if defined(ENABLE_TIMER3)
tloop = magma_sync_wtime(0) - tloop;
tdalloc = magma_sync_wtime(0);
#endif
for(i=0; i<nbstreams; i++){
magma_queue_destroy( stream[i] );
}
magmablasSetKernelStream(cstream);
#if defined(USE_CUOPT)
cublasDestroy_v2(myhandle);
#endif
magma_free(dA_displ);
magma_free(dW0_displ);
magma_free(dW1_displ);
magma_free(dW2_displ);
magma_free(dW3_displ);
magma_free(dW4_displ);
magma_free(dinvA_array);
magma_free(dwork_array);
magma_free( dinvA );
magma_free( dwork );
free(cpuAarray);
magma_free(dipiv_displ);
magma_free(pivinfo_array);
magma_free(pivinfo);
#if defined(ENABLE_TIMER3)
tdalloc = magma_sync_wtime(0) - tdalloc;
tall = magma_sync_wtime(0) - tall;
printf("here is the timing from inside dgetrf_batched talloc: %10.5f tloop: %10.5f tdalloc: %10.5f tall: %10.5f sum: %10.5f\n", talloc, tloop, tdalloc, tall, talloc+tloop+tdalloc );
#endif
return arginfo;
}
