extern "C" magma_int_t
magma_svtranspose(
magma_s_matrix x,
magma_s_matrix *y,
magma_queue_t queue )
{
magma_int_t info = 0;
magma_int_t m = x.num_rows;
magma_int_t n = x.num_cols;
// set queue for old dense routines
magma_queue_t orig_queue=NULL;
magmablasGetKernelStream( &orig_queue );
magma_s_matrix x_d={Magma_CSR}, y_d={Magma_CSR};
if ( x.memory_location == Magma_DEV ) {
CHECK( magma_svinit( y, Magma_DEV, x.num_rows,x.num_cols, MAGMA_S_ZERO, queue ));
y->num_rows = x.num_rows;
y->num_cols = x.num_cols;
y->storage_type = x.storage_type;
if ( x.major == MagmaColMajor) {
y->major = MagmaRowMajor;
magmablas_stranspose( m, n, x.val, m, y->val, n );
}
else {
y->major = MagmaColMajor;
magmablas_stranspose( n, m, x.val, n, y->val, m );
}
} else {
CHECK( magma_smtransfer( x, &x_d, Magma_CPU, Magma_DEV, queue ));
CHECK( magma_svtranspose( x_d, &y_d, queue ));
CHECK( magma_smtransfer( y_d, y, Magma_DEV, Magma_CPU, queue ));
}
cleanup:
if( info != 0 ){
magma_smfree( y, queue );
}
magma_smfree( &x_d, queue );
magma_smfree( &y_d, queue );
magmablasSetKernelStream( orig_queue );
return info;
}
/**
Purpose
-------
SGETRF computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges. This version does not
require work space on the GPU passed as input. GPU memory is allocated
in the routine.
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]
A REAL array, dimension (LDA,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.
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= 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_sgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_sgetrf(
magma_int_t m, magma_int_t n, float *A, magma_int_t lda,
magma_int_t *ipiv,
magma_int_t *info)
{
#define dAT(i_, j_) (dAT + (i_)*nb*ldda + (j_)*nb)
float *dAT, *dA, *da, *work;
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
magma_int_t iinfo, nb;
/* Check arguments */
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0)
*info = -2;
else if (lda < max(1,m))
*info = -4;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* Function Body */
nb = magma_get_sgetrf_nb(m);
if ( (nb <= 1) || (nb >= min(m,n)) ) {
/* Use CPU code. */
lapackf77_sgetrf(&m, &n, A, &lda, ipiv, info);
} else {
/* Use hybrid blocked code. */
magma_int_t maxm, maxn, ldda, maxdim;
magma_int_t i, j, rows, cols, s = min(m, n)/nb;
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
maxdim = max(maxm, maxn);
/* set number of GPUs */
magma_int_t ngpu = magma_num_gpus();
if ( ngpu > 1 ) {
/* call multi-GPU non-GPU-resident interface */
magma_sgetrf_m(ngpu, m, n, A, lda, ipiv, info);
return *info;
}
/* explicitly checking the memory requirement */
size_t freeMem, totalMem;
cudaMemGetInfo( &freeMem, &totalMem );
freeMem /= sizeof(float);
int h = 1+(2+ngpu), ngpu2 = ngpu;
int NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
const char* ngr_nb_char = getenv("MAGMA_NGR_NB");
if ( ngr_nb_char != NULL )
NB = max( nb, min( NB, atoi(ngr_nb_char) ) );
if ( ngpu > ceil((float)NB/nb) ) {
ngpu2 = (int)ceil((float)NB/nb);
h = 1+(2+ngpu2);
NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
}
if ( ngpu2*NB < n ) {
/* require too much memory, so call non-GPU-resident version */
magma_sgetrf_m(ngpu, m, n, A, lda, ipiv, info);
return *info;
}
ldda = maxn;
work = A;
if (maxdim*maxdim < 2*maxm*maxn) {
// if close to square, allocate square matrix and transpose in-place
if (MAGMA_SUCCESS != magma_smalloc( &dA, nb*maxm + maxdim*maxdim )) {
/* alloc failed so call non-GPU-resident version */
magma_sgetrf_m(ngpu, m, n, A, lda, ipiv, info);
return *info;
}
da = dA + nb*maxm;
ldda = maxdim;
magma_ssetmatrix( m, n, A, lda, da, ldda );
dAT = da;
magmablas_stranspose_inplace( ldda, dAT, ldda );
}
else {
// if very rectangular, allocate dA and dAT and transpose out-of-place
if (MAGMA_SUCCESS != magma_smalloc( &dA, (nb + maxn)*maxm )) {
/* alloc failed so call non-GPU-resident version */
magma_sgetrf_m(ngpu, m, n, A, lda, ipiv, info);
return *info;
}
da = dA + nb*maxm;
magma_ssetmatrix( m, n, A, lda, da, maxm );
if (MAGMA_SUCCESS != magma_smalloc( &dAT, maxm*maxn )) {
/* alloc failed so call non-GPU-resident version */
magma_free( dA );
magma_sgetrf_m(ngpu, m, n, A, lda, ipiv, info);
return *info;
}
magmablas_stranspose( m, n, da, maxm, dAT, ldda );
}
lapackf77_sgetrf( &m, &nb, work, &lda, ipiv, &iinfo);
/* Define user stream if current stream is NULL */
magma_queue_t stream[2];
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
magma_queue_create( &stream[0] );
if (orig_stream == NULL) {
magma_queue_create( &stream[1] );
magmablasSetKernelStream(stream[1]);
}
else {
stream[1] = orig_stream;
}
for( j = 0; j < s; j++ ) {
// download j-th panel
cols = maxm - j*nb;
if (j > 0) {
magmablas_stranspose( nb, cols, dAT(j,j), ldda, dA, cols );
// make sure that gpu queue is empty
magma_device_sync();
magma_sgetmatrix_async( m-j*nb, nb, dA, cols, work, lda,
stream[0]);
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (j+1)*nb, nb,
c_one, dAT(j-1,j-1), ldda,
dAT(j-1,j+1), ldda );
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
n-(j+1)*nb, m-j*nb, nb,
c_neg_one, dAT(j-1,j+1), ldda,
dAT(j, j-1), ldda,
c_one, dAT(j, j+1), ldda );
// do the cpu part
rows = m - j*nb;
magma_queue_sync( stream[0] );
lapackf77_sgetrf( &rows, &nb, work, &lda, ipiv+j*nb, &iinfo);
}
if (*info == 0 && iinfo > 0)
*info = iinfo + j*nb;
// upload j-th panel
magma_ssetmatrix_async( m-j*nb, nb, work, lda, dA, cols,
stream[0]);
for( i=j*nb; i < j*nb + nb; ++i ) {
ipiv[i] += j*nb;
}
magmablas_slaswp( n, dAT, ldda, j*nb + 1, j*nb + nb, ipiv, 1 );
magma_queue_sync( stream[0] );
magmablas_stranspose( cols, nb, dA, cols, dAT(j,j), ldda );
// do the small non-parallel computations (next panel update)
if (s > (j+1)) {
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dAT(j, j ), ldda,
dAT(j, j+1), ldda);
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
nb, m-(j+1)*nb, nb,
c_neg_one, dAT(j, j+1), ldda,
dAT(j+1, j ), ldda,
c_one, dAT(j+1, j+1), ldda );
}
else {
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, dAT(j, j ), ldda,
dAT(j, j+1), ldda);
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
n-(j+1)*nb, m-(j+1)*nb, nb,
c_neg_one, dAT(j, j+1), ldda,
dAT(j+1, j ), ldda,
c_one, dAT(j+1, j+1), ldda );
}
}
magma_int_t nb0 = min(m - s*nb, n - s*nb);
if ( nb0 > 0 ) {
rows = m - s*nb;
cols = maxm - s*nb;
magmablas_stranspose( nb0, rows, dAT(s,s), ldda, dA, cols );
magma_sgetmatrix( rows, nb0, dA, cols, work, lda );
// make sure that gpu queue is empty
magma_device_sync();
// do the cpu part
lapackf77_sgetrf( &rows, &nb0, work, &lda, ipiv+s*nb, &iinfo);
if (*info == 0 && iinfo > 0)
*info = iinfo + s*nb;
for( i=s*nb; i < s*nb + nb0; ++i ) {
ipiv[i] += s*nb;
}
magmablas_slaswp( n, dAT, ldda, s*nb + 1, s*nb + nb0, ipiv, 1 );
// upload j-th panel
magma_ssetmatrix( rows, nb0, work, lda, dA, cols );
magmablas_stranspose( rows, nb0, dA, cols, dAT(s,s), ldda );
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb-nb0, nb0,
c_one, dAT(s,s), ldda,
dAT(s,s)+nb0, ldda);
}
// undo transpose
if (maxdim*maxdim < 2*maxm*maxn) {
magmablas_stranspose_inplace( ldda, dAT, ldda );
magma_sgetmatrix( m, n, da, ldda, A, lda );
}
else {
magmablas_stranspose( n, m, dAT, ldda, da, maxm );
magma_sgetmatrix( m, n, da, maxm, A, lda );
magma_free( dAT );
}
magma_free( dA );
magma_queue_destroy( stream[0] );
if (orig_stream == NULL) {
magma_queue_destroy( stream[1] );
}
magmablasSetKernelStream( orig_stream );
}
return *info;
} /* magma_sgetrf */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing stranspose
Code is very similar to testing_ssymmetrize.cpp
*/
int main( int argc, char** argv)
{
TESTING_INIT();
real_Double_t gbytes, gpu_perf, gpu_time, gpu_perf2=0, gpu_time2=0, cpu_perf, cpu_time;
float error, error2, work[1];
float c_neg_one = MAGMA_S_NEG_ONE;
float *h_A, *h_B, *h_R;
magmaFloat_ptr d_A, d_B;
magma_int_t M, N, size, lda, ldda, ldb, lddb;
magma_int_t ione = 1;
magma_int_t status = 0;
magma_opts opts;
parse_opts( argc, argv, &opts );
printf("Inplace transpose requires M==N.\n");
printf(" M N CPU GByte/s (ms) GPU GByte/s (ms) check Inplace GB/s (ms) check\n");
printf("====================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
M = opts.msize[itest];
N = opts.nsize[itest];
lda = M;
ldda = ((M+31)/32)*32;
ldb = N;
lddb = ((N+31)/32)*32;
// load entire matrix, save entire matrix
gbytes = sizeof(float) * 2.*M*N / 1e9;
TESTING_MALLOC_CPU( h_A, float, lda*N ); // input: M x N
TESTING_MALLOC_CPU( h_B, float, ldb*M ); // output: N x M
TESTING_MALLOC_CPU( h_R, float, ldb*M ); // output: N x M
TESTING_MALLOC_DEV( d_A, float, ldda*N ); // input: M x N
TESTING_MALLOC_DEV( d_B, float, lddb*M ); // output: N x M
/* Initialize the matrix */
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < M; ++i ) {
h_A[i + j*lda] = MAGMA_S_MAKE( i + j/10000., j );
}
}
for( int j = 0; j < M; ++j ) {
for( int i = 0; i < N; ++i ) {
h_B[i + j*ldb] = MAGMA_S_MAKE( i + j/10000., j );
}
}
magma_ssetmatrix( N, M, h_B, ldb, d_B, lddb );
/* =====================================================================
Performs operation using naive out-of-place algorithm
(LAPACK doesn't implement transpose)
=================================================================== */
cpu_time = magma_wtime();
//for( int j = 1; j < N-1; ++j ) { // inset by 1 row & col
// for( int i = 1; i < M-1; ++i ) { // inset by 1 row & col
for( int j = 0; j < N; ++j ) {
for( int i = 0; i < M; ++i ) {
h_B[j + i*ldb] = h_A[i + j*lda];
}
}
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gbytes / cpu_time;
/* ====================================================================
Performs operation using MAGMA, out-of-place
=================================================================== */
magma_ssetmatrix( M, N, h_A, lda, d_A, ldda );
magma_ssetmatrix( N, M, h_B, ldb, d_B, lddb );
gpu_time = magma_sync_wtime( 0 );
//magmablas_stranspose( M-2, N-2, d_A+1+ldda, ldda, d_B+1+lddb, lddb ); // inset by 1 row & col
magmablas_stranspose( M, N, d_A, ldda, d_B, lddb );
gpu_time = magma_sync_wtime( 0 ) - gpu_time;
gpu_perf = gbytes / gpu_time;
/* ====================================================================
Performs operation using MAGMA, in-place
=================================================================== */
if ( M == N ) {
magma_ssetmatrix( M, N, h_A, lda, d_A, ldda );
gpu_time2 = magma_sync_wtime( 0 );
//magmablas_stranspose_inplace( N-2, d_A+1+ldda, ldda ); // inset by 1 row & col
magmablas_stranspose_inplace( N, d_A, ldda );
gpu_time2 = magma_sync_wtime( 0 ) - gpu_time2;
gpu_perf2 = gbytes / gpu_time2;
}
/* =====================================================================
Check the result
=================================================================== */
// check out-of-place transpose (d_B)
size = ldb*M;
magma_sgetmatrix( N, M, d_B, lddb, h_R, ldb );
blasf77_saxpy( &size, &c_neg_one, h_B, &ione, h_R, &ione );
error = lapackf77_slange("f", &N, &M, h_R, &ldb, work );
if ( M == N ) {
// also check in-place tranpose (d_A)
magma_sgetmatrix( N, M, d_A, ldda, h_R, ldb );
blasf77_saxpy( &size, &c_neg_one, h_B, &ione, h_R, &ione );
error2 = lapackf77_slange("f", &N, &M, h_R, &ldb, work );
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %6s %7.2f (%7.2f) %s\n",
(int) M, (int) N,
cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
(error == 0. ? "ok" : "failed"),
gpu_perf2, gpu_time2,
(error2 == 0. ? "ok" : "failed") );
status += ! (error == 0. && error2 == 0.);
}
else {
printf("%5d %5d %7.2f (%7.2f) %7.2f (%7.2f) %6s --- ( --- )\n",
(int) M, (int) N,
cpu_perf, cpu_time*1000., gpu_perf, gpu_time*1000.,
(error == 0. ? "ok" : "failed") );
status += ! (error == 0.);
}
TESTING_FREE_CPU( h_A );
TESTING_FREE_CPU( h_B );
TESTING_FREE_CPU( h_R );
TESTING_FREE_DEV( d_A );
TESTING_FREE_DEV( d_B );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
SGETRF computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges. This version does not
require work space on the GPU passed as input. GPU memory is allocated
in the routine.
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.
It uses 2 queues to overlap communication and computation.
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]
A REAL array, dimension (LDA,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.
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= 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_sgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_sgetrf(
magma_int_t m, magma_int_t n,
float *A, magma_int_t lda,
magma_int_t *ipiv,
magma_int_t *info)
{
#ifdef HAVE_clBLAS
#define dA(i_, j_) dA, ((i_)*nb + (j_)*nb*ldda + dA_offset)
#define dAT(i_, j_) dAT, ((i_)*nb*lddat + (j_)*nb + dAT_offset)
#define dwork(i_) dwork, (i_)
#else
#define dA(i_, j_) ( dA + (i_)*nb + (j_)*nb*ldda)
#define dAT(i_, j_) ( dAT + (i_)*nb*lddat + (j_)*nb)
#define dwork(i_) (dwork + (i_))
#endif
// Constants
const float c_one = MAGMA_S_ONE;
const float c_neg_one = MAGMA_S_NEG_ONE;
// Local variables
float *work;
magmaFloat_ptr dA, dAT, dwork;
magma_int_t iinfo, nb;
/* Check arguments */
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0)
*info = -2;
else if (lda < max(1,m))
*info = -4;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* Function Body */
nb = magma_get_sgetrf_nb( m, n );
if ( (nb <= 1) || (nb >= min(m,n)) ) {
/* Use CPU code. */
lapackf77_sgetrf( &m, &n, A, &lda, ipiv, info );
}
else {
/* Use hybrid blocked code. */
magma_int_t maxm, maxn, ldda, lddat, maxdim;
magma_int_t i, j, rows, cols, s = min(m, n)/nb;
maxm = magma_roundup( m, 32 );
maxn = magma_roundup( n, 32 );
maxdim = max( maxm, maxn );
lddat = maxn;
ldda = maxm;
/* set number of GPUs */
magma_int_t ngpu = magma_num_gpus();
if ( ngpu > 1 ) {
/* call multi-GPU non-GPU-resident interface */
magma_sgetrf_m( ngpu, m, n, A, lda, ipiv, info );
return *info;
}
magma_queue_t queues[2] = { NULL, NULL };
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
/* check the memory requirement */
size_t mem_size = magma_queue_mem_size( queues[0] );
mem_size /= sizeof(float);
magma_int_t h = 1+(2+ngpu);
magma_int_t ngpu2 = ngpu;
magma_int_t NB = (magma_int_t)(0.8*mem_size/maxm - h*nb);
const char* ngr_nb_char = getenv("MAGMA_NGR_NB");
if ( ngr_nb_char != NULL )
NB = max( nb, min( NB, atoi(ngr_nb_char) ) );
if ( ngpu > ceil((float)NB/nb) ) {
ngpu2 = (magma_int_t)ceil((float)NB/nb);
h = 1+(2+ngpu2);
NB = (magma_int_t)(0.8*mem_size/maxm - h*nb);
}
if ( ngpu2*NB < n ) {
/* require too much memory, so call non-GPU-resident version */
magma_sgetrf_m( ngpu, m, n, A, lda, ipiv, info );
return *info;
}
work = A;
if (maxdim*maxdim < 2*maxm*maxn) {
// if close to square, allocate square matrix and transpose in-place
// dwork is nb*maxm for panel, and maxdim*maxdim for A
if (MAGMA_SUCCESS != magma_smalloc( &dwork, nb*maxm + maxdim*maxdim )) {
/* alloc failed so call non-GPU-resident version */
magma_sgetrf_m( ngpu, m, n, A, lda, ipiv, info );
return *info;
}
dA = dwork + nb*maxm;
ldda = lddat = maxdim;
magma_ssetmatrix( m, n, A, lda, dA(0,0), ldda, queues[0] );
dAT = dA;
magmablas_stranspose_inplace( maxdim, dAT(0,0), lddat, queues[0] );
}
else {
// if very rectangular, allocate dA and dAT and transpose out-of-place
// dwork is nb*maxm for panel, and maxm*maxn for A
if (MAGMA_SUCCESS != magma_smalloc( &dwork, (nb + maxn)*maxm )) {
/* alloc failed so call non-GPU-resident version */
magma_sgetrf_m( ngpu, m, n, A, lda, ipiv, info );
return *info;
}
dA = dwork + nb*maxm;
magma_ssetmatrix( m, n, A, lda, dA(0,0), ldda, queues[0] );
if (MAGMA_SUCCESS != magma_smalloc( &dAT, maxm*maxn )) {
/* alloc failed so call non-GPU-resident version */
magma_free( dwork );
magma_sgetrf_m( ngpu, m, n, A, lda, ipiv, info );
return *info;
}
magmablas_stranspose( m, n, dA(0,0), ldda, dAT(0,0), lddat, queues[0] );
}
lapackf77_sgetrf( &m, &nb, work, &lda, ipiv, &iinfo );
for( j = 0; j < s; j++ ) {
// get j-th panel from device
cols = maxm - j*nb;
if (j > 0) {
magmablas_stranspose( nb, cols, dAT(j,j), lddat, dwork(0), cols, queues[0] );
magma_queue_sync( queues[0] );
magma_sgetmatrix_async( m-j*nb, nb, dwork(0), cols, work, lda, queues[1] );
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (j+1)*nb, nb,
c_one, dAT(j-1,j-1), lddat,
dAT(j-1,j+1), lddat, queues[0] );
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
n-(j+1)*nb, m-j*nb, nb,
c_neg_one, dAT(j-1,j+1), lddat,
dAT(j, j-1), lddat,
c_one, dAT(j, j+1), lddat, queues[0] );
// do the cpu part
rows = m - j*nb;
magma_queue_sync( queues[1] );
lapackf77_sgetrf( &rows, &nb, work, &lda, ipiv+j*nb, &iinfo );
}
if (*info == 0 && iinfo > 0)
*info = iinfo + j*nb;
// put j-th panel onto device
magma_ssetmatrix_async( m-j*nb, nb, work, lda, dwork(0), cols, queues[1] );
for( i=j*nb; i < j*nb + nb; ++i ) {
ipiv[i] += j*nb;
}
magmablas_slaswp( n, dAT(0,0), lddat, j*nb + 1, j*nb + nb, ipiv, 1, queues[0] );
magma_queue_sync( queues[1] );
magmablas_stranspose( cols, nb, dwork(0), cols, dAT(j,j), lddat, queues[0] );
// do the small non-parallel computations (next panel update)
if (s > (j+1)) {
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dAT(j, j ), lddat,
dAT(j, j+1), lddat, queues[0] );
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
nb, m-(j+1)*nb, nb,
c_neg_one, dAT(j, j+1), lddat,
dAT(j+1, j ), lddat,
c_one, dAT(j+1, j+1), lddat, queues[0] );
}
else {
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, dAT(j, j ), lddat,
dAT(j, j+1), lddat, queues[0] );
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
n-(j+1)*nb, m-(j+1)*nb, nb,
c_neg_one, dAT(j, j+1), lddat,
dAT(j+1, j ), lddat,
c_one, dAT(j+1, j+1), lddat, queues[0] );
}
}
magma_int_t nb0 = min( m - s*nb, n - s*nb );
if ( nb0 > 0 ) {
rows = m - s*nb;
cols = maxm - s*nb;
magmablas_stranspose( nb0, rows, dAT(s,s), lddat, dwork(0), cols, queues[0] );
magma_sgetmatrix_async( rows, nb0, dwork(0), cols, work, lda, queues[0] );
magma_queue_sync( queues[0] );
// do the cpu part
lapackf77_sgetrf( &rows, &nb0, work, &lda, ipiv+s*nb, &iinfo );
if (*info == 0 && iinfo > 0)
*info = iinfo + s*nb;
for( i=s*nb; i < s*nb + nb0; ++i ) {
ipiv[i] += s*nb;
}
magmablas_slaswp( n, dAT(0,0), lddat, s*nb + 1, s*nb + nb0, ipiv, 1, queues[0] );
// put j-th panel onto device
magma_ssetmatrix_async( rows, nb0, work, lda, dwork(0), cols, queues[0] );
magmablas_stranspose( rows, nb0, dwork(0), cols, dAT(s,s), lddat, queues[0] );
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb-nb0, nb0,
c_one, dAT(s, s), lddat,
dAT(s, s)+nb0, lddat, queues[0] );
}
// undo transpose
if (maxdim*maxdim < 2*maxm*maxn) {
magmablas_stranspose_inplace( maxdim, dAT(0,0), lddat, queues[0] );
magma_sgetmatrix( m, n, dAT(0,0), lddat, A, lda, queues[0] );
}
else {
magmablas_stranspose( n, m, dAT(0,0), lddat, dA(0,0), ldda, queues[0] );
magma_sgetmatrix( m, n, dA(0,0), ldda, A, lda, queues[0] );
magma_free( dAT );
}
magma_free( dwork );
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
}
return *info;
} /* magma_sgetrf */
/**
Purpose
-------
SGETRF_m computes an LU factorization of a general M-by-N matrix A
using partial pivoting with row interchanges. This version does not
require work space on the GPU passed as input. GPU memory is allocated
in the routine. The matrix may exceed the GPU memory.
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.
Note: The factorization of big panel is done calling multiple-gpu-interface.
Pivots are applied on GPU within the big panel.
Arguments
---------
@param[in]
num_gpus INTEGER
The number of GPUs. num_gpus > 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]
A REAL array, dimension (LDA,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.
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= 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_sgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_sgetrf_m(magma_int_t num_gpus, magma_int_t m, magma_int_t n,
float *A, magma_int_t lda,
magma_int_t *ipiv, magma_int_t *info)
{
#define A(i,j) (A + (j)*lda + (i))
#define dAT(d,i,j) (dAT[d] + (i)*nb*ldn_local + (j)*nb)
#define dPT(d,i,j) (dPT[d] + (i)*nb*nb + (j)*nb*maxm)
magma_timer_t time=0, time_total=0, time_alloc=0, time_set=0, time_get=0, time_comp=0;
timer_start( time_total );
real_Double_t flops;
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
float *dAT[MagmaMaxGPUs], *dA[MagmaMaxGPUs], *dPT[MagmaMaxGPUs];
magma_int_t iinfo = 0, nb, nbi, maxm, n_local[MagmaMaxGPUs], ldn_local;
magma_int_t N, M, NB, NBk, I, d, num_gpus0 = num_gpus;
magma_int_t ii, jj, h, offset, ib, rows, s;
magma_queue_t stream[MagmaMaxGPUs][2];
magma_event_t event[MagmaMaxGPUs][2];
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0)
*info = -2;
else if (lda < max(1,m))
*info = -4;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
/* initialize nb */
nb = magma_get_sgetrf_nb(m);
maxm = ((m + 31)/32)*32;
/* figure out NB */
size_t freeMem, totalMem;
cudaMemGetInfo( &freeMem, &totalMem );
freeMem /= sizeof(float);
/* number of columns in the big panel */
h = 1+(2+num_gpus0);
NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
const char* ngr_nb_char = getenv("MAGMA_NGR_NB");
if ( ngr_nb_char != NULL )
NB = max( nb, min( NB, atoi(ngr_nb_char) ) );
//NB = 5*max(nb,32);
if ( num_gpus0 > ceil((float)NB/nb) ) {
num_gpus = (int)ceil((float)NB/nb);
h = 1+(2+num_gpus);
NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
} else {
num_gpus = num_gpus0;
}
if ( num_gpus*NB >= n ) {
#ifdef CHECK_SGETRF_OOC
printf( " * still fit in GPU memory.\n" );
#endif
NB = n;
} else {
#ifdef CHECK_SGETRF_OOC
printf( " * don't fit in GPU memory.\n" );
#endif
NB = num_gpus*NB;
NB = max( nb, (NB / nb) * nb); /* making sure it's devisable by nb (x64) */
}
#ifdef CHECK_SGETRF_OOC
if ( NB != n ) printf( " * running in out-core mode (n=%d, NB=%d, nb=%d, freeMem=%.2e).\n", n, NB, nb, (float)freeMem );
else printf( " * running in in-core mode (n=%d, NB=%d, nb=%d, freeMem=%.2e).\n", n, NB, nb, (float)freeMem );
#endif
if ( (nb <= 1) || (nb >= min(m,n)) ) {
/* Use CPU code for scalar of one tile. */
lapackf77_sgetrf(&m, &n, A, &lda, ipiv, info);
} else {
/* Use hybrid blocked code. */
/* allocate memory on GPU to store the big panel */
timer_start( time_alloc );
n_local[0] = (NB/nb)/num_gpus;
if ( NB%(nb*num_gpus) != 0 )
n_local[0]++;
n_local[0] *= nb;
ldn_local = ((n_local[0]+31)/32)*32;
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
if (MAGMA_SUCCESS != magma_smalloc( &dA[d], (ldn_local+h*nb)*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dPT[d] = dA[d] + nb*maxm; /* for storing the previous panel from CPU */
dAT[d] = dA[d] + h*nb*maxm; /* for storing the big panel */
magma_queue_create( &stream[d][0] );
magma_queue_create( &stream[d][1] );
magma_event_create( &event[d][0] );
magma_event_create( &event[d][1] );
}
//magma_setdevice(0);
timer_stop( time_alloc );
for( I=0; I < n; I += NB ) {
M = m;
N = min( NB, n-I ); /* number of columns in this big panel */
s = min( max(m-I,0), N )/nb; /* number of small block-columns in this big panel */
maxm = ((M + 31)/32)*32;
if ( num_gpus0 > ceil((float)N/nb) ) {
num_gpus = (int)ceil((float)N/nb);
} else {
num_gpus = num_gpus0;
}
for( d=0; d < num_gpus; d++ ) {
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;
}
ldn_local = ((n_local[0]+31)/32)*32;
/* upload the next big panel into GPU, transpose (A->A'), and pivot it */
timer_start( time );
magmablas_ssetmatrix_transpose_mgpu(num_gpus, stream, A(0,I), lda,
dAT, ldn_local, dA, maxm, M, N, nb);
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magmablasSetKernelStream(NULL);
}
time_set += timer_stop( time );
timer_start( time );
/* == --------------------------------------------------------------- == */
/* == loop around the previous big-panels to update the new big-panel == */
for( offset = 0; offset < min(m,I); offset += NB ) {
NBk = min( m-offset, NB );
/* start sending the first tile from the previous big-panels to gpus */
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
nbi = min( nb, NBk );
magma_ssetmatrix_async( (M-offset), nbi,
A(offset,offset), lda,
dA[d], (maxm-offset), stream[d][0] );
/* make sure the previous update finished */
magmablasSetKernelStream(stream[d][0]);
//magma_queue_sync( stream[d][1] );
magma_queue_wait_event( stream[d][0], event[d][0] );
/* transpose */
magmablas_stranspose( M-offset, nbi, dA[d], maxm-offset, dPT(d,0,0), nb );
}
/* applying the pivot from the previous big-panel */
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][1]);
magmablas_spermute_long3( dAT(d,0,0), ldn_local, ipiv, NBk, offset );
}
/* == going through each block-column of previous big-panels == */
for( jj=0, ib=offset/nb; jj < NBk; jj += nb, ib++ ) {
ii = offset+jj;
rows = maxm - ii;
nbi = min( nb, NBk-jj );
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
/* wait for a block-column on GPU */
magma_queue_sync( stream[d][0] );
/* start sending next column */
if ( jj+nb < NBk ) {
magma_ssetmatrix_async( (M-ii-nb), min(nb,NBk-jj-nb),
A(ii+nb,ii+nb), lda,
dA[d], (rows-nb), stream[d][0] );
/* make sure the previous update finished */
magmablasSetKernelStream(stream[d][0]);
//magma_queue_sync( stream[d][1] );
magma_queue_wait_event( stream[d][0], event[d][(1+jj/nb)%2] );
/* transpose next column */
magmablas_stranspose( M-ii-nb, nb, dA[d], rows-nb, dPT(d,0,(1+jj/nb)%2), nb );
}
/* update with the block column */
magmablasSetKernelStream(stream[d][1]);
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n_local[d], nbi, c_one, dPT(d,0,(jj/nb)%2), nb, dAT(d,ib,0), ldn_local );
if ( M > ii+nb ) {
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
n_local[d], M-(ii+nb), nbi, c_neg_one, dAT(d,ib,0), ldn_local,
dPT(d,1,(jj/nb)%2), nb, c_one, dAT(d,ib+1,0), ldn_local );
}
magma_event_record( event[d][(jj/nb)%2], stream[d][1] );
} /* end of for each block-columns in a big-panel */
}
} /* end of for each previous big-panels */
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magmablasSetKernelStream(NULL);
}
/* calling magma-gpu interface to panel-factorize the big panel */
if ( M > I ) {
//magma_sgetrf1_mgpu(num_gpus, M-I, N, nb, I, dAT, ldn_local, ipiv+I, dA, A(0,I), lda,
// (magma_queue_t **)stream, &iinfo);
magma_sgetrf2_mgpu(num_gpus, M-I, N, nb, I, dAT, ldn_local, ipiv+I, dA, A(0,I), lda,
stream, &iinfo);
if ( iinfo < 0 ) {
*info = iinfo;
break;
} else if ( iinfo != 0 ) {
*info = iinfo + I * NB;
//break;
}
/* adjust pivots */
for( ii=I; ii < min(I+N,m); ii++ )
ipiv[ii] += I;
}
time_comp += timer_stop( time );
/* download the current big panel to CPU */
timer_start( time );
magmablas_sgetmatrix_transpose_mgpu(num_gpus, stream, dAT, ldn_local, A(0,I), lda, dA, maxm, M, N, nb);
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magmablasSetKernelStream(NULL);
}
time_get += timer_stop( time );
} /* end of for */
timer_stop( time_total );
flops = FLOPS_SGETRF( m, n ) / 1e9;
timer_printf(" memory-allocation time: %e\n", time_alloc );
timer_printf(" NB=%d nb=%d\n", (int) NB, (int) nb );
timer_printf(" memcopy and transpose %e seconds\n", time_set );
timer_printf(" total time %e seconds\n", time_total );
timer_printf(" Performance %f GFlop/s, %f seconds without htod and dtoh\n", flops / (time_comp), time_comp );
timer_printf(" Performance %f GFlop/s, %f seconds with htod\n", flops / (time_comp + time_set), time_comp + time_set );
timer_printf(" Performance %f GFlop/s, %f seconds with dtoh\n", flops / (time_comp + time_get), time_comp + time_get );
timer_printf(" Performance %f GFlop/s, %f seconds without memory-allocation\n", flops / (time_total - time_alloc), time_total - time_alloc );
for( d=0; d < num_gpus0; d++ ) {
magma_setdevice(d);
magma_free( dA[d] );
magma_event_destroy( event[d][0] );
magma_event_destroy( event[d][1] );
magma_queue_destroy( stream[d][0] );
magma_queue_destroy( stream[d][1] );
}
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
}
if ( *info >= 0 )
magma_sgetrf_piv(m, n, NB, A, lda, ipiv, info);
return *info;
} /* magma_sgetrf_m */
/***************************************************************************//**
Purpose
-------
SGELQF computes an LQ factorization of a REAL M-by-N matrix dA:
dA = L * Q.
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 REAL array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix dA.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors (see Further Details).
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
@param[out]
tau REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is the
optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued.
@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(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).
@ingroup magma_gelqf
*******************************************************************************/
extern "C" magma_int_t
magma_sgelqf_gpu(
magma_int_t m, magma_int_t n,
magmaFloat_ptr dA, magma_int_t ldda,
float *tau,
float *work, magma_int_t lwork,
magma_int_t *info)
{
/* Constants */
const float c_one = MAGMA_S_ONE;
const magma_int_t ione = 1;
MAGMA_UNUSED( ione ); // used only for real
/* Local variables */
magmaFloat_ptr dAT=NULL;
magma_int_t min_mn, maxm, maxn, nb;
magma_int_t iinfo;
*info = 0;
nb = magma_get_sgelqf_nb( m, n );
min_mn = min( m, n );
work[0] = magma_smake_lwork( m*nb );
bool lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
} else if (lwork < max(1,m) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (min_mn == 0) {
work[0] = c_one;
return *info;
}
maxm = magma_roundup( m, 32 );
maxn = magma_roundup( n, 32 );
magma_int_t lddat = maxn;
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
if ( m == n ) {
dAT = dA;
lddat = ldda;
magmablas_stranspose_inplace( m, dAT, ldda, queue );
}
else {
if (MAGMA_SUCCESS != magma_smalloc( &dAT, maxm*maxn ) ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
magmablas_stranspose( m, n, dA, ldda, dAT, lddat, queue );
}
magma_sgeqrf2_gpu( n, m, dAT, lddat, tau, &iinfo );
assert( iinfo >= 0 );
if ( iinfo > 0 ) {
*info = iinfo;
}
// conjugate tau
#ifdef COMPLEX
lapackf77_slacgv( &min_mn, tau, &ione );
#endif
if ( m == n ) {
magmablas_stranspose_inplace( m, dAT, lddat, queue );
}
else {
magmablas_stranspose( n, m, dAT, lddat, dA, ldda, queue );
magma_free( dAT );
}
cleanup:
magma_queue_destroy( queue );
return *info;
} /* magma_sgelqf_gpu */
/**
Purpose
-------
SGETRF 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.
Use two buffer to send panels.
Arguments
---------
@param[in]
num_gpus INTEGER
The number of GPUs to be used for the factorization.
@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]
A REAL 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_sgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_sgetrf2_mgpu(magma_int_t num_gpus,
magma_int_t m, magma_int_t n, magma_int_t nb, magma_int_t offset,
float *d_lAT[], magma_int_t lddat, magma_int_t *ipiv,
float *d_lAP[], float *w, magma_int_t ldw,
magma_queue_t streaml[][2], magma_int_t *info)
{
#define dAT(id,i,j) (d_lAT[(id)] + ((offset)+(i)*nb)*lddat + (j)*nb)
#define W(j) (w+((j)%num_gpus)*nb*ldw)
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
magma_int_t block_size = 32;
magma_int_t iinfo, n_local[MagmaMaxGPUs];
magma_int_t maxm, mindim;
magma_int_t i, d, dd, rows, cols, s, ldpan[MagmaMaxGPUs];
magma_int_t id, i_local, i_local2, nb0, nb1, h = 2+num_gpus;
float *d_panel[MagmaMaxGPUs], *panel_local[MagmaMaxGPUs];
/* Check arguments */
*info = 0;
if (m < 0)
*info = -2;
else if (n < 0)
*info = -3;
else if (num_gpus*lddat < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* Function Body */
mindim = min(m, n);
if ( num_gpus > ceil((float)n/nb) ) {
*info = -1;
return *info;
}
/* Use hybrid blocked code. */
maxm = ((m + block_size-1)/block_size)*block_size;
/* some initializations */
for (i=0; i < num_gpus; i++) {
magma_setdevice(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;
/* workspaces */
d_panel[i] = &(d_lAP[i][h*nb*maxm]); /* temporary panel storage */
}
trace_init( 1, num_gpus, 2, (CUstream_st**)streaml );
/* start sending the panel to cpu */
nb0 = min(mindim, nb);
magma_setdevice(0);
magmablasSetKernelStream(streaml[0][1]);
trace_gpu_start( 0, 1, "comm", "get" );
magmablas_stranspose( nb0, m, dAT(0,0,0), lddat, d_lAP[0], maxm );
magma_sgetmatrix_async( m, nb0,
d_lAP[0], maxm,
W(0), ldw, streaml[0][1] );
trace_gpu_end( 0, 1 );
/* ------------------------------------------------------------------------------------- */
magma_timer_t time=0;
timer_start( time );
s = mindim / nb;
for( i=0; i < s; i++ ) {
/* Set the GPU number that holds the current panel */
id = i%num_gpus;
magma_setdevice(id);
/* Set the local index where the current panel is */
i_local = i/num_gpus;
cols = maxm - i*nb;
rows = m - i*nb;
/* synchrnoize i-th panel from id-th gpu into work */
magma_queue_sync( streaml[id][1] );
/* i-th panel factorization */
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_sgetrf( &rows, &nb, W(i), &ldw, ipiv+i*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) ) {
*info = iinfo + i*nb;
}
trace_cpu_end( 0 );
/* start sending the panel to all the gpus */
d = (i+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
magma_setdevice(d);
trace_gpu_start( 0, 1, "comm", "set" );
magma_ssetmatrix_async( rows, nb,
W(i), ldw,
&d_lAP[d][(i%h)*nb*maxm], cols,
streaml[d][1] );
trace_gpu_end( 0, 1 );
d = (d+1)%num_gpus;
}
/* apply the pivoting */
d = (i+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
magma_setdevice(d);
magmablasSetKernelStream(streaml[d][0]);
trace_gpu_start( d, 1, "pivot", "pivot" );
if ( dd == 0 )
magmablas_spermute_long2( lddat, dAT(d,0,0), lddat, ipiv, nb, i*nb );
else
magmablas_spermute_long3( dAT(d,0,0), lddat, ipiv, nb, i*nb );
trace_gpu_end( d, 1 );
d = (d+1)%num_gpus;
}
/* update the trailing-matrix/look-ahead */
d = (i+1)%num_gpus;
for( dd=0; dd < num_gpus; dd++ ) {
magma_setdevice(d);
/* storage for panel */
if ( d == id ) {
/* the panel belond to this gpu */
panel_local[d] = dAT(d,i,i_local);
ldpan[d] = lddat;
/* next column */
i_local2 = i_local+1;
} else {
/* the panel belong to another gpu */
panel_local[d] = d_panel[d];
ldpan[d] = nb;
/* next column */
i_local2 = i_local;
if ( d < id ) i_local2 ++;
}
/* the size of the next column */
if ( s > (i+1) ) {
nb0 = nb;
} else {
nb0 = n_local[d]-nb*(s/num_gpus);
if ( d < s%num_gpus ) nb0 -= nb;
}
if ( d == (i+1)%num_gpus) {
/* owns the next column, look-ahead the column */
nb1 = nb0;
magmablasSetKernelStream(streaml[d][1]);
/* make sure all the pivoting has been applied */
magma_queue_sync(streaml[d][0]);
trace_gpu_start( d, 1, "gemm", "gemm" );
/* transpose panel on GPU */
magmablas_stranspose( rows, nb, &d_lAP[d][(i%h)*nb*maxm], cols, panel_local[d], ldpan[d] );
/* synch for remaining update */
magma_queue_sync(streaml[d][1]);
} else {
/* update the entire trailing matrix */
nb1 = n_local[d] - i_local2*nb;
magmablasSetKernelStream(streaml[d][0]);
/* synchronization to make sure panel arrived on gpu */
magma_queue_sync(streaml[d][1]);
trace_gpu_start( d, 0, "gemm", "gemm" );
/* transpose panel on GPU */
magmablas_stranspose( rows, nb, &d_lAP[d][(i%h)*nb*maxm], cols, panel_local[d], ldpan[d] );
}
/* gpu updating the trailing matrix */
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb, c_one,
panel_local[d], ldpan[d],
dAT(d, i, i_local2), lddat);
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
nb1, m-(i+1)*nb, nb,
c_neg_one, dAT(d, i, i_local2), lddat,
&(panel_local[d][nb*ldpan[d]]), ldpan[d],
c_one, dAT(d, i+1, i_local2), lddat );
if ( d == (i+1)%num_gpus ) {
/* Set the local index where the current panel is */
int loff = i+1;
int i_local = (i+1)/num_gpus;
int ldda = maxm - (i+1)*nb;
int cols = m - (i+1)*nb;
nb0 = min(nb, mindim - (i+1)*nb); /* size of the diagonal block */
trace_gpu_end( d, 1 );
if ( nb0 > 0 ) {
/* transpose the panel for sending it to cpu */
trace_gpu_start( d, 1, "comm", "get" );
magmablas_stranspose( nb0, m-(i+1)*nb, dAT(d,loff,i_local), lddat, &d_lAP[d][((i+1)%h)*nb*maxm], ldda );
/* send the panel to cpu */
magma_sgetmatrix_async( cols, nb0,
&d_lAP[d][((i+1)%h)*nb*maxm], ldda,
W(i+1), ldw, streaml[d][1] );
trace_gpu_end( d, 1 );
}
} else {
trace_gpu_end( d, 0 );
}
d = (d+1)%num_gpus;
}
/* update the remaining matrix by gpu owning the next panel */
if ( (i+1) < s ) {
int i_local = (i+1)/num_gpus;
int rows = m - (i+1)*nb;
d = (i+1)%num_gpus;
magma_setdevice(d);
magmablasSetKernelStream(streaml[d][0]);
trace_gpu_start( d, 0, "gemm", "gemm" );
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n_local[d] - (i_local+1)*nb, nb,
c_one, panel_local[d], ldpan[d],
dAT(d,i,i_local+1), lddat );
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
n_local[d]-(i_local+1)*nb, rows, nb,
c_neg_one, dAT(d,i,i_local+1), lddat,
&(panel_local[d][nb*ldpan[d]]), ldpan[d],
c_one, dAT(d,i+1, i_local+1), lddat );
trace_gpu_end( d, 0 );
}
} /* end of for i=1..s */
/* ------------------------------------------------------------------------------ */
/* Set the GPU number that holds the last panel */
id = s%num_gpus;
/* Set the local index where the last panel is */
i_local = s/num_gpus;
/* size of the last diagonal-block */
nb0 = min(m - s*nb, n - s*nb);
rows = m - s*nb;
cols = maxm - s*nb;
if ( nb0 > 0 ) {
magma_setdevice(id);
/* wait for the last panel on cpu */
magma_queue_sync( streaml[id][1] );
/* factor on cpu */
lapackf77_sgetrf( &rows, &nb0, W(s), &ldw, ipiv+s*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + s*nb;
/* send the factor to gpus */
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
i_local2 = i_local;
if ( d < id ) i_local2 ++;
if ( d == id || n_local[d] > i_local2*nb ) {
magma_ssetmatrix_async( rows, nb0,
W(s), ldw,
&d_lAP[d][(s%h)*nb*maxm],
cols, streaml[d][1] );
}
}
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
magmablasSetKernelStream(streaml[d][0]);
if ( d == 0 )
magmablas_spermute_long2( lddat, dAT(d,0,0), lddat, ipiv, nb0, s*nb );
else
magmablas_spermute_long3( dAT(d,0,0), lddat, ipiv, nb0, s*nb );
}
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
magmablasSetKernelStream(streaml[d][1]);
/* wait for the pivoting to be done */
magma_queue_sync( streaml[d][0] );
i_local2 = i_local;
if ( d < id ) i_local2++;
if ( d == id ) {
/* the panel belond to this gpu */
panel_local[d] = dAT(d,s,i_local);
/* next column */
nb1 = n_local[d] - i_local*nb-nb0;
magmablas_stranspose( rows, nb0, &d_lAP[d][(s%h)*nb*maxm], cols, panel_local[d], lddat );
if ( nb1 > 0 ) {
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb0, c_one,
panel_local[d], lddat,
dAT(d,s,i_local)+nb0, lddat);
}
} else if ( n_local[d] > i_local2*nb ) {
/* the panel belong to another gpu */
panel_local[d] = d_panel[d];
/* next column */
nb1 = n_local[d] - i_local2*nb;
magmablas_stranspose( rows, nb0, &d_lAP[d][(s%h)*nb*maxm], cols, panel_local[d], nb );
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb0, c_one,
panel_local[d], nb,
dAT(d,s,i_local2), lddat);
}
}
} /* if ( nb0 > 0 ) */
/* clean up */
trace_finalize( "sgetrf_mgpu.svg","trace.css" );
for( d=0; d < num_gpus; d++ ) {
magma_setdevice(d);
magma_queue_sync( streaml[d][0] );
magma_queue_sync( streaml[d][1] );
magmablasSetKernelStream(NULL);
}
magma_setdevice(0);
timer_start( time );
timer_printf("\n Performance %f GFlop/s\n", FLOPS_SGETRF(m,n) / 1e9 / time );
return *info;
} /* magma_sgetrf2_mgpu */
extern "C" magma_int_t
magma_sgetrf_msub(
magma_trans_t trans, magma_int_t num_subs, magma_int_t num_gpus,
magma_int_t m, magma_int_t n,
magmaFloat_ptr *d_lA, size_t dlA_offset, magma_int_t ldda,
magma_int_t *ipiv,
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
=======
SGETRF 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.
Arguments
=========
NUM_GPUS
(input) INTEGER
The number of GPUS to be used for the factorization.
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.
A (input/output) REAL 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.
LDDA (input) INTEGER
The leading dimension of the array A. LDDA >= max(1,M).
IPIV (output) 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).
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.
> 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.
===================================================================== */
#define d_lAT(id,i,j) d_lAT[(id)], (((i)*nb)*lddat + (j)*nb)
#define d_lA( id,i,j) d_lA[(id)], (((i)*nb)+ldda * (j)*nb)
magma_int_t maxm, tot_subs = num_subs*num_gpus;
magma_int_t i, j, d, lddat;
/* submatrix info */
magma_int_t nb, n_local[ MagmaMaxSubs * MagmaMaxGPUs ];
magmaFloat_ptr d_lAT[ MagmaMaxSubs * MagmaMaxGPUs ];
/* local workspace per GPU */
magmaFloat_ptr d_panel[ MagmaMaxGPUs ];
magmaFloat_ptr d_lAP[ MagmaMaxGPUs ];
float *work;
/* Check arguments */
*info = 0;
if (m < 0)
*info = -2;
else if (n < 0)
*info = -3;
else if (trans == MagmaTrans && ldda < max(1,m))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* Function Body */
nb = magma_get_sgetrf_nb(m);
if (nb <= 1 || nb >= n) {
/* Use CPU code. */
magma_smalloc_cpu( &work, m * n );
if (work == NULL) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
printf( "trans %c, m %d, n %d\n", lapacke_trans_const(trans), m, n );
magma_sgetmatrix( m, n, d_lA[0], 0, ldda, work, m, queues[0] );
lapackf77_sgetrf( &m, &n, work, &m, ipiv, info );
magma_ssetmatrix( m, n, work, m, d_lA[0], 0, ldda, queues[0] );
magma_free_cpu( work );
} else {
/* Use hybrid blocked code. */
maxm = ((m + 31)/32)*32;
if (tot_subs > ceil((float)n/nb)) {
printf( " * too many GPUs for the matrix size, using %d GPUs\n", (int) tot_subs );
*info = -1;
return *info;
}
/* allocate workspace for each GPU */
lddat = n/nb; /* number of block columns */
lddat = lddat/tot_subs; /* number of block columns per GPU */
lddat = nb*lddat; /* number of columns per GPU */
if (lddat * tot_subs < n) {
/* left over */
if (n-lddat*tot_subs >= nb) {
lddat += nb;
} else {
lddat += (n-lddat*tot_subs)%nb;
}
}
lddat = ((lddat+31)/32)*32; /* make it a multiple of 32 */
/* allocating workspace */
for (d=0; d < num_gpus; d++) {
//#define SINGLE_GPU_PER_CONTEXT
#ifdef SINGLE_GPU_PER_CONTEXT
if ((MAGMA_SUCCESS != magma_smalloc_mgpu( d, &d_panel[d], (2+num_gpus)*nb*maxm )) ||
(MAGMA_SUCCESS != magma_smalloc_mgpu( d, &d_lAP[d], (2+num_gpus)*nb*maxm )) ) {
#else
if ((MAGMA_SUCCESS != magma_smalloc( &d_panel[d], (2+num_gpus)*nb*maxm )) ||
(MAGMA_SUCCESS != magma_smalloc( &d_lAP[d], (2+num_gpus)*nb*maxm )) ) {
#endif
for( i=0; i < d; i++ ) {
magma_free( d_panel[i] );
magma_free( d_lAP[i] );
}
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
/* transposing the local matrix */
for (i=0; i < tot_subs; i++) {
/* local-n and local-ld */
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;
/* local-matrix storage */
if (trans == MagmaNoTrans) {
d_lAT[i] = d_lA[i];
} else {
if ( m == n_local[i] ) {
d_lAT[i] = d_lA[i];
magmablas_stranspose_inplace( m, d_lA[i], 0, ldda, queues[2*(i%num_gpus)+1] );
} else {
#ifdef SINGLE_GPU_PER_CONTEXT
if (MAGMA_SUCCESS != magma_smalloc_mgpu( i%num_gpus, &d_lAT[i], lddat*maxm )) {
#else
if (MAGMA_SUCCESS != magma_smalloc( &d_lAT[i], lddat*maxm )) {
#endif
for (j=0; j <= i; j++) {
magma_free( d_panel[j] );
magma_free( d_lAP[j] );
}
for (j=0; j < i; j++) {
if (d_lAT[j] != d_lA[j]) magma_free( d_lAT[j] );
}
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmablas_stranspose( m, n_local[i], d_lA[i], 0, ldda, d_lAT[i], 0, lddat, queues[2*(i%num_gpus)+1]);
}
}
}
if (trans == MagmaNoTrans) {
for (d=0; d < num_gpus; d++){
magma_queue_sync(queues[2*d+1]);
}
}
/* cpu workspace */
#ifdef USE_PINNED_CLMEMORY
cl_mem buffer = clCreateBuffer(gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, sizeof(float)*maxm*nb*(1+num_gpus), NULL, NULL);
for (d=0; d < num_gpus; d++) {
work = (float*)clEnqueueMapBuffer(queues[2*d], buffer, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0,
sizeof(float)*maxm*nb*(1+num_gpus), 0, NULL, NULL, NULL);
}
#else
if (MAGMA_SUCCESS != magma_smalloc_cpu( &work, maxm*nb*(1+num_gpus) )) {
for(d=0; d < num_gpus; d++ ) magma_free( d_panel[d] );
for(d=0; d < tot_subs; d++ ) {
if( d_lAT[d] != d_lA[d] ) magma_free( d_lAT[d] );
}
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
#endif
/* calling multi-gpu interface with allocated workspaces and streams */
magma_sgetrf2_msub(num_subs, num_gpus, m, n, nb, 0, d_lAT, 0, lddat, ipiv, d_lAP, d_panel, 0, work, maxm,
queues, info);
/* save on output */
for (d=0; d < tot_subs; d++) {
if (trans == MagmaNoTrans) {
//magma_scopymatrix( n_local[d], m, d_lAT[d], 0, lddat, d_lA[d], 0, ldda, queues[2*d+1] );
} else {
if (d_lAT[d] == d_lA[d]) {
magmablas_stranspose_inplace( m, d_lA[d], 0, ldda, queues[2*(d%num_gpus)+1] );
} else {
magmablas_stranspose( n_local[d], m, d_lAT[d], 0, lddat, d_lA[d], 0, ldda, queues[2*(d%num_gpus)+1] );
}
}
}
/* clean up */
for (d=0; d < num_gpus; d++) {
magma_queue_sync(queues[2*d+1]);
magma_free( d_panel[d] );
magma_free( d_lAP[d] );
d_panel[d] = d_lAP[d] = NULL;
}
for (d=0; d < tot_subs; d++) {
if (d_lAT[d] != d_lA[d]) {
magma_free( d_lAT[d] );
d_lAT[d] = NULL;
}
}
#ifdef USE_PINNED_CLMEMORY
for (d=0; d < num_gpus; d++) {
clEnqueueUnmapMemObject(queues[2*d], buffer, work, 0, NULL, NULL);
}
clReleaseMemObject( buffer );
#else
magma_free_cpu( work );
#endif
work = NULL;
}
return *info;
/* End of MAGMA_SGETRF_MSUB */
}
/**
Purpose
-------
SGETRF 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.
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]
d_lA REAL 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 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 d_lA. 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_sgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_sgetrf_mgpu(
magma_int_t ngpu,
magma_int_t m, magma_int_t n,
magmaFloat_ptr d_lA[], magma_int_t ldda, magma_int_t *ipiv,
magma_int_t *info)
{
magma_int_t nb, n_local[MagmaMaxGPUs];
magma_int_t maxm;
magma_int_t i, j, d, lddat, lddwork;
float *d_lAT[MagmaMaxGPUs];
float *d_panel[MagmaMaxGPUs], *work;
magma_queue_t queues[MagmaMaxGPUs][2];
/* Check arguments */
*info = 0;
if (m < 0)
*info = -2;
else if (n < 0)
*info = -3;
else if (ldda < max(1,m))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* create the queues */
for( d=0; d < ngpu; d++ ) {
magma_queue_create( d, &queues[d][0] );
magma_queue_create( d, &queues[d][1] );
}
/* Function Body */
nb = magma_get_sgetrf_nb( m, n );
if (nb <= 1 || nb >= n) {
/* Use CPU code. */
magma_smalloc_cpu( &work, m * n );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_sgetmatrix( m, n, d_lA[0], ldda, work, m, queues[0][0] );
lapackf77_sgetrf(&m, &n, work, &m, ipiv, info);
magma_ssetmatrix( m, n, work, m, d_lA[0], ldda, queues[0][0] );
magma_free_cpu(work);
} else {
/* Use hybrid blocked code. */
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
maxm = magma_roundup( m, 32 );
if ( ngpu > ceil((float)n/nb) ) {
printf( " * too many GPUs for the matrix size, using %d GPUs\n", (int) ngpu );
*info = -1;
return *info;
}
/* allocate workspace for each GPU */
lddat = magma_roundup( ((magma_ceildiv( n, nb )/ngpu)*nb), 32 );
lddat = magma_ceildiv( n, nb ); /* number of block columns */
lddat = magma_ceildiv( lddat, ngpu ); /* number of block columns per GPU */
lddat = nb*lddat; /* number of columns per GPU */
lddat = magma_roundup( lddat, 32 ); /* make it a multiple of 32 */
for (i=0; i < ngpu; i++) {
magma_setdevice(i);
/* local-n and local-ld */
n_local[i] = ((n/nb)/ngpu)*nb;
if (i < (n/nb)%ngpu)
n_local[i] += nb;
else if (i == (n/nb)%ngpu)
n_local[i] += n%nb;
/* workspaces */
if (MAGMA_SUCCESS != magma_smalloc( &d_panel[i], (3+ngpu)*nb*maxm )) {
for( j=0; j <= i; j++ ) {
magma_setdevice(j);
}
for( j=0; j < i; j++ ) {
magma_setdevice(j);
magma_free( d_panel[j] );
magma_free( d_lAT[j] );
}
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* local-matrix storage */
if (MAGMA_SUCCESS != magma_smalloc( &d_lAT[i], lddat*maxm )) {
for( j=0; j <= i; j++ ) {
magma_setdevice(j);
magma_free( d_panel[j] );
}
for( j=0; j < i; j++ ) {
magma_setdevice(j);
magma_free( d_lAT[j] );
}
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmablas_stranspose( m, n_local[i], d_lA[i], ldda, d_lAT[i], lddat, queues[i][1] );
}
for (i=0; i < ngpu; i++) {
magma_setdevice(i);
magma_queue_sync(queues[i][0]);
}
magma_setdevice(0);
/* cpu workspace */
lddwork = maxm;
if (MAGMA_SUCCESS != magma_smalloc_pinned( &work, lddwork*nb*ngpu )) {
for (i=0; i < ngpu; i++ ) {
magma_setdevice(i);
magma_free( d_panel[i] );
magma_free( d_lAT[i] );
}
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
/* calling multi-gpu interface with allocated workspaces and queues */
magma_sgetrf2_mgpu(ngpu, m, n, nb, 0, d_lAT, lddat, ipiv, d_panel, work, maxm,
queues, info);
/* clean up */
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
/* save on output */
magmablas_stranspose( n_local[d], m, d_lAT[d], lddat, d_lA[d], ldda, queues[d][0] );
magma_queue_sync(queues[d][0]);
magma_queue_sync(queues[d][1]);
magma_free( d_lAT[d] );
magma_free( d_panel[d] );
} /* end of for d=1,..,ngpu */
magma_setdevice( orig_dev );
magma_free_pinned( work );
}
/* clean up */
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magma_queue_destroy( queues[d][0] );
magma_queue_destroy( queues[d][1] );
}
return *info;
}
extern "C" magma_int_t
magma_sgetrf2_msub(
magma_int_t num_subs, magma_int_t ngpu,
magma_int_t m, magma_int_t n, magma_int_t nb, magma_int_t offset,
magmaFloat_ptr *d_lAT, size_t dlAT_offset, magma_int_t lddat,
magma_int_t *ipiv,
magmaFloat_ptr *d_panel,
magmaFloat_ptr *d_lAP, size_t dlAP_offset,
float *w, magma_int_t ldw,
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
=======
SGETRF 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.
Use two buffer to send panels..
Arguments
=========
NUM_GPUS
(input) INTEGER
The number of GPUS to be used for the factorization.
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.
A (input/output) REAL 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.
LDDA (input) INTEGER
The leading dimension of the array A. LDDA >= max(1,M).
IPIV (output) 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).
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.
> 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.
===================================================================== */
#define d_lAT(id,i,j) d_lAT[(id)], (((offset)+(i)*nb)*lddat + (j)*nb)
#define d_lAT_offset(i, j) (((offset)+(i)*nb)*lddat + (j)*nb)
#define W(j) (w +((j)%(1+ngpu))*nb*ldw)
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
magma_int_t tot_subs = num_subs * ngpu;
magma_int_t block_size = 32;
magma_int_t iinfo, maxm, mindim;
magma_int_t i, j, d, dd, rows, cols, s;
magma_int_t id, j_local, j_local2, nb0, nb1;
/* local submatrix info */
magma_int_t ldpan[MagmaMaxSubs * MagmaMaxGPUs],
n_local[MagmaMaxSubs * MagmaMaxGPUs];
size_t dpanel_local_offset[MagmaMaxSubs * MagmaMaxGPUs];
magmaFloat_ptr dpanel_local[MagmaMaxSubs * MagmaMaxGPUs];
/* Check arguments */
*info = 0;
if (m < 0)
*info = -2;
else if (n < 0)
*info = -3;
else if (tot_subs*lddat < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* Function Body */
mindim = min(m, n);
if (tot_subs > ceil((float)n/nb)) {
*info = -1;
return *info;
}
else {
/* Use hybrid blocked code. */
maxm = ((m + block_size-1)/block_size)*block_size;
/* some initializations */
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;
}
/* start sending the first panel to cpu */
nb0 = min(mindim, nb);
magmablas_stranspose( nb0, maxm, d_lAT(0,0,0), lddat, d_lAP[0], dlAP_offset, maxm, queues[2*0+1] );
magma_sgetmatrix_async( m, nb0,
d_lAP[0], dlAP_offset, maxm,
W(0), ldw, queues[2*0+1], NULL );
clFlush(queues[2*0+1]);
/* ------------------------------------------------------------------------------------- */
s = mindim / nb;
for (j=0; j < s; j++) {
/* Set the submatrix ID that holds the current panel */
id = j%tot_subs;
/* Set the local index where the current panel is */
j_local = j/tot_subs;
// cols for gpu panel
cols = maxm - j*nb;
// rows for cpu panel
rows = m - j*nb;
/* synchrnoize j-th panel from id-th gpu into work */
magma_queue_sync( queues[2*(id%ngpu)+1] );
/* j-th panel factorization */
lapackf77_sgetrf( &rows, &nb, W(j), &ldw, ipiv+j*nb, &iinfo);
if ((*info == 0) && (iinfo > 0)) {
*info = iinfo + j*nb;
//break;
}
/* start sending the panel to all the gpus */
d = (j+1)%ngpu;
for (dd=0; dd < ngpu; dd++) {
magma_ssetmatrix_async( rows, nb,
W(j), ldw,
d_lAP[d], dlAP_offset+(j%(2+ngpu))*nb*maxm, maxm,
queues[2*d+1], NULL );
d = (d+1)%ngpu;
}
/* apply the pivoting */
for( i=j*nb; i < j*nb + nb; ++i ) {
ipiv[i] += j*nb;
}
d = (j+1)%tot_subs;
for (dd=0; dd < tot_subs; dd++) {
magmablas_slaswp( lddat, d_lAT(d,0,0), lddat, j*nb + 1, j*nb + nb, ipiv, 1, queues[2*(d%ngpu)] );
d = (d+1)%tot_subs;
}
/* update the trailing-matrix/look-ahead */
d = (j+1)%tot_subs;
for (dd=0; dd < tot_subs; dd++) {
/* storage for panel */
if (d%ngpu == id%ngpu) {
/* the panel belond to this gpu */
dpanel_local[d] = d_lAT[id];
dpanel_local_offset[d] = d_lAT_offset(j, j_local);
ldpan[d] = lddat;
/* next column */
j_local2 = j_local;
if ( d <= id )
j_local2++;
} else {
/* the panel belong to another gpu */
dpanel_local[d] = d_panel[d%ngpu];
dpanel_local_offset[d] = (j%(2+ngpu))*nb*maxm;
ldpan[d] = nb;
/* next column */
j_local2 = j_local;
if ( d < id )
j_local2++;
}
/* the size of the next column */
if (s > (j+1)) {
nb0 = nb;
} else {
nb0 = n_local[d]-nb*(s/tot_subs);
if (d < s%tot_subs)
nb0 -= nb;
}
if (d == (j+1)%tot_subs) {
/* owns the next column, look-ahead the column */
nb1 = nb0;
} else {
/* update the entire trailing matrix */
nb1 = n_local[d] - j_local2*nb;
}
/* gpu updating the trailing matrix */
if (d == (j+1)%tot_subs) { /* look-ahead, this is executed first (j.e., dd=0) */
magma_queue_sync(queues[2*(d%ngpu)]); /* pivoting done? (overwrite with panel) */
magmablas_stranspose( cols, nb,
d_lAP[d%ngpu], dlAP_offset+(j%(2+ngpu))*nb*maxm, maxm,
dpanel_local[d], dpanel_local_offset[d], ldpan[d],
queues[2*(d%ngpu)+1] );
magma_queue_sync(queues[2*(d%ngpu)+1]); /* panel arrived and transposed for remaining update ? */
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb, c_one,
dpanel_local[d], dpanel_local_offset[d], ldpan[d],
d_lAT(d, j, j_local2), lddat, queues[2*(d%ngpu)+1]);
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
nb1, m-(j+1)*nb, nb,
c_neg_one, d_lAT(d, j, j_local2), lddat,
dpanel_local[d], dpanel_local_offset[d]+nb*ldpan[d], ldpan[d],
c_one, d_lAT(d, j+1, j_local2), lddat,
queues[2*(d%ngpu)+1]);
} else { /* no look-ahead */
if (dd < ngpu) {
/* synch and transpose only the first time */
magma_queue_sync(queues[2*(d%ngpu)+1]); /* panel arrived? */
magmablas_stranspose( cols, nb,
d_lAP[d%ngpu], dlAP_offset+(j%(2+ngpu))*nb*maxm, maxm,
dpanel_local[d], dpanel_local_offset[d], ldpan[d],
queues[2*(d%ngpu)] );
}
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb, c_one,
dpanel_local[d], dpanel_local_offset[d], ldpan[d],
d_lAT(d, j, j_local2), lddat, queues[2*(d%ngpu)]);
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
nb1, m-(j+1)*nb, nb,
c_neg_one, d_lAT(d, j, j_local2), lddat,
dpanel_local[d], dpanel_local_offset[d]+nb*ldpan[d], ldpan[d],
c_one, d_lAT(d, j+1, j_local2), lddat,
queues[2*(d%ngpu)]);
}
if (d == (j+1)%tot_subs) {
/* Set the local index where the current panel is */
int loff = j+1;
int j_local = (j+1)/tot_subs;
int ldda = maxm - (j+1)*nb;
int cols = m - (j+1)*nb;
nb0 = min(nb, mindim - (j+1)*nb); /* size of the diagonal block */
if (nb0 > 0) {
/* transpose the panel for sending it to cpu */
magmablas_stranspose( nb0, ldda,
d_lAT(d,loff,j_local), lddat,
d_lAP[d%ngpu], dlAP_offset + ((j+1)%(2+ngpu))*nb*maxm, ldda,
queues[2*(d%ngpu)+1] );
/* send the panel to cpu */
magma_sgetmatrix_async( cols, nb0,
d_lAP[d%ngpu], dlAP_offset + ((j+1)%(2+ngpu))*nb*maxm, ldda,
W(j+1), ldw, queues[2*(d%ngpu)+1], NULL );
}
} else {
//trace_gpu_end( d, 0 );
}
d = (d+1)%tot_subs;
}
/* update the remaining matrix by gpu owning the next panel */
if ((j+1) < s) {
d = (j+1)%tot_subs;
int j_local = (j+1)/tot_subs;
int rows = m - (j+1)*nb;
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n_local[d] - (j_local+1)*nb, nb,
c_one, dpanel_local[d], dpanel_local_offset[d], ldpan[d],
d_lAT(d,j,j_local+1), lddat, queues[2*(d%ngpu)] );
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
n_local[d]-(j_local+1)*nb, rows, nb,
c_neg_one, d_lAT(d,j,j_local+1), lddat,
dpanel_local[d], dpanel_local_offset[d]+nb*ldpan[d], ldpan[d],
c_one, d_lAT(d,j+1, j_local+1), lddat, queues[2*(d%ngpu)] );
}
} /* end of for j=1..s */
/* ------------------------------------------------------------------------------ */
/* Set the GPU number that holds the last panel */
id = s%tot_subs;
/* Set the local index where the last panel is */
j_local = s/tot_subs;
/* size of the last diagonal-block */
nb0 = min(m - s*nb, n - s*nb);
rows = m - s*nb;
cols = maxm - s*nb;
if (nb0 > 0) {
/* wait for the last panel on cpu */
magma_queue_sync( queues[2*(id%ngpu)+1] );
/* factor on cpu */
lapackf77_sgetrf( &rows, &nb0, W(s), &ldw, ipiv+s*nb, &iinfo );
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + s*nb;
/* send the factor to gpus */
for (d=0; d < ngpu; d++) {
magma_ssetmatrix_async( rows, nb0, W(s), ldw,
d_lAP[d], dlAP_offset+(s%(2+ngpu))*nb*maxm, cols,
queues[2*d+1], NULL );
}
for( i=s*nb; i < s*nb + nb0; ++i ) {
ipiv[i] += s*nb;
}
for (d=0; d < tot_subs; d++) {
magmablas_slaswp( lddat, d_lAT(d,0,0), lddat, s*nb + 1, s*nb + nb0, ipiv, 1, queues[2*(d%ngpu)] );
}
d = id;
for (dd=0; dd < tot_subs; dd++) {
/* wait for the pivoting to be done */
if (dd < ngpu) {
/* synch only the first time */
magma_queue_sync( queues[2*(d%ngpu)] );
}
j_local2 = j_local;
if (d%ngpu == id%ngpu) {
/* the panel belond to this gpu */
dpanel_local[d] = d_lAT[id];
dpanel_local_offset[d] = d_lAT_offset(s, j_local);
if (dd < ngpu) {
magmablas_stranspose( rows, nb0,
d_lAP[d%ngpu], dlAP_offset+(s%(2+ngpu))*nb*maxm, cols,
dpanel_local[d], dpanel_local_offset[d], lddat,
queues[2*(d%ngpu)+1] );
}
/* size of the "extra" block */
if (d == id) { /* the last diagonal block belongs to this submatrix */
nb1 = nb0;
} else if (d < id) {
nb1 = nb;
} else {
nb1 = 0;
}
if (n_local[d] > j_local*nb+nb1) {
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n_local[d] - (j_local*nb+nb1), nb0, c_one,
dpanel_local[d], dpanel_local_offset[d], lddat,
d_lAT(d, s, j_local)+nb1, lddat, queues[2*(d%ngpu)+1]);
}
} else if (n_local[d] > j_local2*nb) {
/* the panel belong to another gpu */
dpanel_local[d] = d_panel[d%ngpu];
dpanel_local_offset[d] = (s%(2+ngpu))*nb*maxm;
/* next column */
if (d < ngpu) {
/* transpose only the first time */
magmablas_stranspose( rows, nb0,
d_lAP[d%ngpu], dlAP_offset+(s%(2+ngpu))*nb*maxm, cols,
dpanel_local[d], dpanel_local_offset[d], nb,
queues[2*(d%ngpu)+1] );
}
if (d < id)
j_local2++;
nb1 = n_local[d] - j_local2*nb;
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb0, c_one,
dpanel_local[d], dpanel_local_offset[d], nb,
d_lAT(d,s,j_local2), lddat, queues[2*(d%ngpu)+1]);
}
d = (d+1)%tot_subs;
}
} /* if( nb0 > 0 ) */
/* clean up */
for (d=0; d < ngpu; d++) {
magma_queue_sync( queues[2*d] );
magma_queue_sync( queues[2*d+1] );
}
}
return *info;
/* End of MAGMA_SGETRF2_MSUB */
}
/***************************************************************************//**
Purpose
-------
SGELQF computes an LQ factorization of a REAL M-by-N matrix A:
A = L * Q.
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]
A REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors (see Further Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) REAL array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is the
optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued.
\n
TODO: work is currently unused. sgeqrf2 allocates its own work of (m + n)*nb.
@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(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).
@ingroup magma_gelqf
*******************************************************************************/
extern "C" magma_int_t
magma_sgelqf(
magma_int_t m, magma_int_t n,
float *A, magma_int_t lda, float *tau,
float *work, magma_int_t lwork,
magma_int_t *info)
{
#define dA(i_, j_) (dA + (i_) + (j_)*ldda)
#define dAT(i_, j_) (dAT + (i_) + (j_)*ldda)
/* Constants */
const float c_one = MAGMA_S_ONE;
const magma_int_t ione = 1;
MAGMA_UNUSED( ione ); // used only for real
/* Local variables */
magmaFloat_ptr dA=NULL, dAT=NULL;
magma_int_t min_mn, maxm, maxn, maxdim, nb;
magma_int_t iinfo, ldda, lddat;
/* Function Body */
*info = 0;
nb = magma_get_sgelqf_nb( m, n );
min_mn = min( m, n );
work[0] = magma_smake_lwork( m*nb );
bool lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1,m) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (min_mn == 0) {
work[0] = c_one;
return *info;
}
maxm = magma_roundup( m, 32 );
maxn = magma_roundup( n, 32 );
maxdim = max( maxm, maxn );
magma_queue_t queue = NULL;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
// copy to GPU and transpose
if (maxdim*maxdim < 2*maxm*maxn) {
// close to square, do everything in-place
ldda = maxdim;
lddat = maxdim;
if (MAGMA_SUCCESS != magma_smalloc( &dA, maxdim*maxdim )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
magma_ssetmatrix( m, n, A, lda, dA(0,0), ldda, queue );
dAT = dA;
magmablas_stranspose_inplace( lddat, dAT(0,0), lddat, queue );
}
else {
// rectangular, do everything out-of-place
ldda = maxm;
lddat = maxn;
if (MAGMA_SUCCESS != magma_smalloc( &dA, 2*maxn*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
magma_ssetmatrix( m, n, A, lda, dA(0,0), ldda, queue );
dAT = dA + maxn * maxm;
magmablas_stranspose( m, n, dA(0,0), ldda, dAT(0,0), lddat, queue );
}
// factor QR
magma_sgeqrf2_gpu( n, m, dAT(0,0), lddat, tau, &iinfo );
assert( iinfo >= 0 );
if ( iinfo > 0 ) {
*info = iinfo;
}
// conjugate tau
#ifdef COMPLEX
lapackf77_slacgv( &min_mn, tau, &ione );
#endif
// undo transpose
if (maxdim*maxdim < 2*maxm*maxn) {
magmablas_stranspose_inplace( lddat, dAT(0,0), lddat, queue );
magma_sgetmatrix( m, n, dA(0,0), ldda, A, lda, queue );
} else {
magmablas_stranspose( n, m, dAT(0,0), lddat, dA(0,0), ldda, queue );
magma_sgetmatrix( m, n, dA(0,0), ldda, A, lda, queue );
}
cleanup:
magma_queue_destroy( queue );
magma_free( dA );
return *info;
} /* magma_sgelqf */
extern "C" magma_int_t
magma_sgetrf_incpiv_gpu( char storev, magma_int_t m, magma_int_t n, magma_int_t ib,
float *hA, magma_int_t ldha, float *dA, magma_int_t ldda,
float *hL, magma_int_t ldhl, float *dL, magma_int_t lddl,
magma_int_t *ipiv,
float *dwork, magma_int_t lddwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2012
Purpose
=======
SGETRF_INCPIV computes an LU factorization of a general M-by-N tile 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 2.5 BLAS version of the algorithm.
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.
IB (input) INTEGER
The inner-blocking size. IB >= 0.
hA (input,output) DOUBLE COMPLEX array, dimension(LDHA, N), on cpu.
On entry, only the M-by-IB first panel needs to be identical to dA(1..M, 1..IB).
On exit, the content is incomplete. Shouldn't be used.
LDHA (input) INTEGER
The leading dimension of the array hA. LDHA >= max(1,M).
dA (input,output) DOUBLE COMPLEX array, dimension(LDDA, N) , on gpu.
On entry, the M-by-N tile 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.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
hL (output) DOUBLE COMPLEX array, dimension(LDHL, min(M,N)), on vpu.
On exit, contains in the upper part the IB-by-K lower triangular tile,
and in the lower part IB-by-min(M,N) the inverse of the top part.
LDHL (input) INTEGER
The leading dimension of the array hL. LDHL >= max(1,2*IB).
dL (output) DOUBLE COMPLEX array, dimension(LDDL, K), on gpu.
On exit, contains in the upper part the IB-by-min(M,N) lower triangular tile,
and in the lower part IB-by-min(M,N) the inverse of the top part.
LDDL (input) INTEGER
The leading dimension of the array dL. LDDL >= max(1,2*IB).
IPIV (output) INTEGER array, dimension min(M,N), on the cpu.
The pivot indices array.
dWORK (output) DOUBLE COMPLEX array, dimension(LDDWORK, 2*IB), on gpu.
Workspace.
LDDWORK (input) INTEGER
The leading dimension of the array dWORK. LDDWORK >= max(NB, 1).
INFO (output) INTEGER
- PLASMA_SUCCESS successful exit
- < 0 if INFO = -k, the k-th argument had an illegal value
- > 0 if INFO = k, U(k,k) 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.
===================================================================== */
#define AT(i,j) (dAT + (i)*ib*ldda + (j)*ib)
#define hA(i,j) (hA + (i)*ib + (j)*ib*ldha)
#define hL(j) (hL + (j)*ib*ldhl )
#define hL2(j) (hL2 + (j)*ib*ldhl )
#define dL(j) (dL + (j)*ib*lddl )
#define dL2(j) (dL2 + (j)*ib*lddl )
float c_one = MAGMA_S_ONE;
float c_neg_one = MAGMA_S_NEG_ONE;
magma_int_t iinfo;
magma_int_t maxm, mindim;
magma_int_t i, rows, cols, s, ii, sb;
float *dAT;
#ifndef WITHOUTTRTRI
float *dL2 = dL + ib;
float *hL2 = hL + ib;
#endif
/* Check arguments */
*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;
}
/* Quick return if possible */
if (m == 0 || n == 0)
return *info;
/* Function Body */
mindim = min(m, n);
s = mindim / ib;
if ( ib >= mindim ) {
/* Use CPU code. */
lapackf77_sgetrf(&m, &n, hA, &ldha, ipiv, info);
#ifndef WITHOUTTRTRI
CORE_slacpy(PlasmaUpperLower, mindim, mindim,
(float*)hA, ldha,
(float*)hL2, ldhl );
CORE_strtri( PlasmaLower, PlasmaUnit, mindim,
(float*)hL2, ldhl, info );
if (*info != 0 ) {
fprintf(stderr, "ERROR, trtri returned with info = %d\n", *info);
}
magma_ssetmatrix( mindim, mindim, hL2, ldhl, dL2, lddl );
#endif
if ( (storev == 'R') || (storev == 'r') ) {
magma_ssetmatrix( m, n, hA, ldha, dwork, lddwork );
magmablas_stranspose( dA, ldda, dwork, lddwork, m, n );
} else {
magma_ssetmatrix( m, n, hA, ldha, dA, ldda );
}
}
else {
/* Use hybrid blocked code. */
maxm = ((m + 31)/32)*32;
if ( (storev == 'C') || (storev == 'c') ) {
magmablas_sgetmo_in( dA, dAT, ldda, m, n );
} else {
dAT = dA;
}
for( i=0; i<s; i++ )
{
ii = i * ib;
sb = min(ib, mindim-ii);
cols = maxm - ii;
if ( i>0 ){
// download i-th panel
magmablas_stranspose( dwork, maxm, AT(0, i), ldda, sb, m );
magma_sgetmatrix( m, sb, dwork, maxm, hA(0, i), ldha );
// make sure that gpu queue is empty
//magma_device_sync();
#ifndef WITHOUTTRTRI
magma_strmm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n - (ii+sb), ib,
c_one, dL2(i-1), lddl,
AT(i-1,i+1), ldda );
#else
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (ii+sb), ib,
c_one, AT(i-1,i-1), ldda,
AT(i-1,i+1), ldda );
#endif
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
n-(ii+sb), m-ii, ib,
c_neg_one, AT(i-1,i+1), ldda,
AT(i, i-1), ldda,
c_one, AT(i, i+1), ldda );
}
// do the cpu part
rows = m - ii;
lapackf77_sgetrf( &rows, &sb, hA(i, i), &ldha, ipiv+ii, &iinfo);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + ii;
{
int j;
int fin = ii + sb;
for(j=ii ; j <fin; j++) {
ipiv[j] = ii + ipiv[j];
}
}
magmablas_slaswp( n-ii, AT(0, i), ldda, ii+1, ii+sb, ipiv, 1 );
#ifndef WITHOUTTRTRI
CORE_slacpy(PlasmaLower, sb, sb,
(float*)hA(i, i), ldha,
(float*)hL2(i), ldhl );
CORE_strtri( PlasmaLower, PlasmaUnit, sb,
(float*)hL2(i), ldhl, info );
if (*info != 0 ) {
fprintf(stderr, "ERROR, trtri returned with info = %d\n", *info);
}
magma_ssetmatrix( sb, sb, hL2(i), ldhl, dL2(i), lddl );
#endif
// upload i-th panel
magma_ssetmatrix( rows, sb, hA(i, i), ldha, dwork, cols );
magmablas_stranspose( AT(i,i), ldda, dwork, cols, rows, sb);
// do the small non-parallel computations
if ( s > (i+1) ) {
#ifndef WITHOUTTRTRI
magma_strmm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
sb, sb,
c_one, dL2(i), lddl,
AT(i, i+1), ldda);
#else
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
sb, sb,
c_one, AT(i, i ), ldda,
AT(i, i+1), ldda);
#endif
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
sb, m-(ii+sb), sb,
c_neg_one, AT(i, i+1), ldda,
AT(i+1, i ), ldda,
c_one, AT(i+1, i+1), ldda );
}
else {
/* Update of the last panel */
#ifndef WITHOUTTRTRI
magma_strmm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n-mindim, sb,
c_one, dL2(i), lddl,
AT(i, i+1), ldda);
#else
magma_strsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-mindim, sb,
c_one, AT(i, i ), ldda,
AT(i, i+1), ldda);
#endif
/* m-(ii+sb) should be always 0 */
magma_sgemm( MagmaNoTrans, MagmaNoTrans,
n-mindim, m-(ii+sb), sb,
c_neg_one, AT(i, i+1), ldda,
AT(i+1, i ), ldda,
c_one, AT(i+1, i+1), ldda );
}
}
if ( (storev == 'C') || (storev == 'c') ) {
magmablas_sgetmo_out( dA, dAT, ldda, m, n );
}
}
return *info;
}
