/**
Purpose
-------
ZPOTRS solves a system of linear equations A*X = B with a Hermitian
positive definite matrix A using the Cholesky factorization
A = U**H*U or A = L*L**H computed by ZPOTRF.
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 COMPLEX_16 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 ZPOTRF.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDDA >= max(1,N).
@param[in,out]
dB COMPLEX_16 array on the GPU, dimension (LDDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
@param[in]
lddb INTEGER
The leading dimension of the array B. LDDB >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zposv_comp
********************************************************************/
extern "C" magma_int_t
magma_zpotrs_gpu(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magmaDoubleComplex_ptr dB, magma_int_t lddb,
magma_int_t *info)
{
magmaDoubleComplex c_one = MAGMA_Z_ONE;
*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;
}
if ( uplo == MagmaUpper ) {
if ( nrhs == 1) {
magma_ztrsv(MagmaUpper, MagmaConjTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
magma_ztrsv(MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
} else {
magma_ztrsm(MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb);
magma_ztrsm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb);
}
}
else {
if ( nrhs == 1) {
magma_ztrsv(MagmaLower, MagmaNoTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
magma_ztrsv(MagmaLower, MagmaConjTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
} else {
magma_ztrsm(MagmaLeft, MagmaLower, MagmaNoTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb);
magma_ztrsm(MagmaLeft, MagmaLower, MagmaConjTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb);
}
}
return *info;
}
/**
Purpose
-------
Solves a system of linear equations A*X = B with a complex
Hermitian matrix A using the factorization A = U*D*U**H or
A = L*D*L**H computed by ZHETRF_NOPIV_GPU.
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 COMPLEX_16 array on the GPU, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZHETRF_NOPIV_GPU.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
param[in,out]
dB COMPLEX_16 array on the GPU, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
@param[in]
lddb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zhesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zhetrs_nopiv_gpu(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magmaDoubleComplex_ptr dB, magma_int_t lddb,
magma_int_t *info)
{
magmaDoubleComplex c_one = MAGMA_Z_ONE;
int upper = (uplo == MagmaUpper);
*info = 0;
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (nrhs < 0) {
*info = -3;
} else if (ldda < max(1,n)) {
*info = -5;
} else 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;
}
if (upper) {
magmablas_ztrsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaUnit,
n, nrhs, c_one,
dA, ldda, dB, lddb );
magmablas_zlascl_diag(MagmaUpper, 1, n, dA, ldda, dB,1, info);
magmablas_ztrsm( MagmaLeft, MagmaUpper,
MagmaNoTrans, MagmaUnit,
n, nrhs, c_one,
dA, ldda, dB, lddb );
} else {
magma_ztrsm( MagmaLeft, MagmaLower,
MagmaNoTrans, MagmaUnit,
n, nrhs, c_one,
dA, ldda, dB, lddb );
magmablas_zlascl_diag(MagmaLower, 1, n, dA, ldda, dB,1, info);
magmablas_ztrsm( MagmaLeft, MagmaLower,
MagmaConjTrans, MagmaUnit,
n, nrhs, c_one,
dA, ldda, dB, lddb );
}
return *info;
}
/**
Purpose
-------
ZTRTRI computes the inverse of a real upper or lower triangular
matrix A.
This is the Level 3 BLAS version of the algorithm.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: A is upper triangular;
- = MagmaLower: A is lower triangular.
@param[in]
diag magma_diag_t
- = MagmaNonUnit: A is non-unit triangular;
- = MagmaUnit: A is unit triangular.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
A COMPLEX_16 array, dimension (LDA,N)
On entry, the triangular matrix A. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of the array A contains
the upper triangular matrix, and the strictly lower
triangular part of A is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of the array A contains
the lower triangular matrix, and the strictly upper
triangular part of A is not referenced. If DIAG = MagmaUnit, the
diagonal elements of A are also not referenced and are
assumed to be 1.
On exit, the (triangular) inverse of the original matrix, in
the same storage format.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse cannot be computed.
@ingroup magma_zgesv_aux
********************************************************************/
extern "C" magma_int_t
magma_ztrtri(
magma_uplo_t uplo, magma_diag_t diag, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda,
magma_int_t *info)
{
#define A(i, j) ( A + (i) + (j)*lda )
#define dA(i, j) (dA + (i) + (j)*ldda)
/* Local variables */
const char* uplo_ = lapack_uplo_const( uplo );
const char* diag_ = lapack_diag_const( diag );
magma_int_t ldda, nb, nn, j, jb;
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *dA;
int upper = (uplo == MagmaUpper);
int nounit = (diag == MagmaNonUnit);
*info = 0;
if (! upper && uplo != MagmaLower)
*info = -1;
else if (! nounit && diag != MagmaUnit)
*info = -2;
else if (n < 0)
*info = -3;
else if (lda < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return */
if ( n == 0 )
return *info;
/* Check for singularity if non-unit */
if (nounit) {
for (j=0; j < n; ++j) {
if ( MAGMA_Z_EQUAL( *A(j,j), c_zero )) {
*info = j+1; // Fortran index
return *info;
}
}
}
/* Determine the block size for this environment */
nb = magma_get_zpotrf_nb(n);
ldda = ((n+31)/32)*32;
if (MAGMA_SUCCESS != magma_zmalloc( &dA, (n)*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
if (nb <= 1 || nb >= n)
lapackf77_ztrtri(uplo_, diag_, &n, A, &lda, info);
else {
if (upper) {
/* Compute inverse of upper triangular matrix */
for (j=0; j < n; j += nb) {
jb = min(nb, (n-j));
magma_zsetmatrix( jb, (n-j),
A(j, j), lda,
dA(j, j), ldda );
/* Compute rows 1:j-1 of current block column */
magma_ztrmm( MagmaLeft, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_one, dA(0,0), ldda, dA(0, j),ldda);
magma_ztrsm( MagmaRight, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_neg_one, dA(j,j), ldda, dA(0, j),ldda);
magma_zgetmatrix_async( jb, jb,
dA(j, j), ldda,
A(j, j), lda, stream[1] );
magma_zgetmatrix_async( j, jb,
dA(0, j), ldda,
A(0, j), lda, stream[0] );
magma_queue_sync( stream[1] );
/* Compute inverse of current diagonal block */
lapackf77_ztrtri(MagmaUpperStr, diag_, &jb, A(j,j), &lda, info);
magma_zsetmatrix( jb, jb,
A(j, j), lda,
dA(j, j), ldda );
}
}
else {
/* Compute inverse of lower triangular matrix */
nn=((n-1)/nb)*nb+1;
for (j=nn-1; j >= 0; j -= nb) {
jb=min(nb,(n-j));
if ((j+jb) < n) {
magma_zsetmatrix( (n-j), jb,
A(j, j), lda,
dA(j, j), ldda );
/* Compute rows j+jb:n of current block column */
magma_ztrmm( MagmaLeft, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_one, dA(j+jb,j+jb), ldda, dA(j+jb, j), ldda );
magma_ztrsm( MagmaRight, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_neg_one, dA(j,j), ldda, dA(j+jb, j), ldda );
magma_zgetmatrix_async( n-j-jb, jb,
dA(j+jb, j), ldda,
A(j+jb, j), lda, stream[1] );
magma_zgetmatrix_async( jb, jb,
dA(j,j), ldda,
A(j,j), lda, stream[0] );
magma_queue_sync( stream[0] );
}
/* Compute inverse of current diagonal block */
lapackf77_ztrtri(MagmaLowerStr, diag_, &jb, A(j,j), &lda, info);
magma_zsetmatrix( jb, jb,
A(j, j), lda,
dA(j, j), ldda );
}
}
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free( dA );
return *info;
}
extern "C" magma_int_t
magma_zlobpcg(
magma_z_matrix A,
magma_z_solver_par *solver_par,
magma_z_preconditioner *precond_par,
magma_queue_t queue )
{
magma_int_t info = 0;
#define residualNorms(i,iter) ( residualNorms + (i) + (iter)*n )
#define SWAP(x, y) { pointer = x; x = y; y = pointer; }
#define hresidualNorms(i,iter) (hresidualNorms + (i) + (iter)*n )
#define gramA( m, n) (gramA + (m) + (n)*ldgram)
#define gramB( m, n) (gramB + (m) + (n)*ldgram)
#define gevectors(m, n) (gevectors + (m) + (n)*ldgram)
#define h_gramB( m, n) (h_gramB + (m) + (n)*ldgram)
#define magma_z_bspmv_tuned(m, n, alpha, A, X, beta, AX, queue) { \
magma_z_matrix x={Magma_CSR}, ax={Magma_CSR}; \
x.memory_location = Magma_DEV; x.num_rows = m; x.num_cols = n; x.major = MagmaColMajor; x.nnz = m*n; x.dval = X; x.storage_type = Magma_DENSE; \
ax.memory_location= Magma_DEV; ax.num_rows = m; ax.num_cols = n; ax.major = MagmaColMajor; ax.nnz = m*n; ax.dval = AX; ax.storage_type = Magma_DENSE; \
CHECK( magma_z_spmv(alpha, A, x, beta, ax, queue )); \
}
//**************************************************************
// Memory allocation for the eigenvectors, eigenvalues, and workspace
solver_par->solver = Magma_LOBPCG;
magma_int_t m = A.num_rows;
magma_int_t n = (solver_par->num_eigenvalues);
magmaDoubleComplex *blockX = solver_par->eigenvectors;
double *evalues = solver_par->eigenvalues;
solver_par->numiter = 0;
solver_par->spmv_count = 0;
magmaDoubleComplex *dwork=NULL, *hwork=NULL;
magmaDoubleComplex *blockP=NULL, *blockAP=NULL, *blockR=NULL, *blockAR=NULL, *blockAX=NULL, *blockW=NULL;
magmaDoubleComplex *gramA=NULL, *gramB=NULL, *gramM=NULL;
magmaDoubleComplex *gevectors=NULL, *h_gramB=NULL;
dwork = NULL;
hwork = NULL;
blockP = NULL;
blockR = NULL;
blockAP = NULL;
blockAR = NULL;
blockAX = NULL;
blockW = NULL;
gramA = NULL;
gramB = NULL;
gramM = NULL;
gevectors = NULL;
h_gramB = NULL;
magmaDoubleComplex *pointer, *origX = blockX;
double *eval_gpu=NULL;
magma_int_t iterationNumber, cBlockSize, restart = 1, iter;
//Chronometry
real_Double_t tempo1, tempo2, tempop1, tempop2;
magma_int_t lwork = max( 2*n+n*magma_get_dsytrd_nb(n),
1 + 6*3*n + 2* 3*n* 3*n);
magma_int_t *iwork={0}, liwork = 15*n+9;
magma_int_t gramDim, ldgram = 3*n, ikind = 3;
magmaDoubleComplex *hW={0};
// === Set solver parameters ===
double residualTolerance = solver_par->rtol;
magma_int_t maxIterations = solver_par->maxiter;
double tmp;
double r0=0; // set in 1st iteration
// === Set some constants & defaults ===
magmaDoubleComplex c_zero = MAGMA_Z_ZERO;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
double *residualNorms={0}, *condestGhistory={0}, condestG={0};
double *gevalues={0};
magma_int_t *activeMask={0};
double *hresidualNorms={0};
#ifdef COMPLEX
double *rwork={0};
magma_int_t lrwork = 1 + 5*(3*n) + 2*(3*n)*(3*n);
CHECK( magma_dmalloc_cpu(&rwork, lrwork));
#endif
CHECK( magma_zmalloc_pinned( &hwork , lwork ));
CHECK( magma_zmalloc( &blockAX , m*n ));
CHECK( magma_zmalloc( &blockAR , m*n ));
CHECK( magma_zmalloc( &blockAP , m*n ));
CHECK( magma_zmalloc( &blockR , m*n ));
CHECK( magma_zmalloc( &blockP , m*n ));
CHECK( magma_zmalloc( &blockW , m*n ));
CHECK( magma_zmalloc( &dwork , m*n ));
CHECK( magma_dmalloc( &eval_gpu , 3*n ));
//**********************************************************+
// === Check some parameters for possible quick exit ===
solver_par->info = MAGMA_SUCCESS;
if (m < 2)
info = MAGMA_DIVERGENCE;
else if (n > m)
info = MAGMA_SLOW_CONVERGENCE;
if (solver_par->info != 0) {
magma_xerbla( __func__, -(info) );
goto cleanup;
}
solver_par->info = info; // local info variable;
// === Allocate GPU memory for the residual norms' history ===
CHECK( magma_dmalloc(&residualNorms, (maxIterations+1) * n));
CHECK( magma_malloc( (void **)&activeMask, (n+1) * sizeof(magma_int_t) ));
// === Allocate CPU work space ===
CHECK( magma_dmalloc_cpu(&condestGhistory, maxIterations+1));
CHECK( magma_dmalloc_cpu(&gevalues, 3 * n));
CHECK( magma_malloc_cpu((void **)&iwork, liwork * sizeof(magma_int_t)));
CHECK( magma_zmalloc_pinned(&hW, n*n));
CHECK( magma_zmalloc_pinned(&gevectors, 9*n*n));
CHECK( magma_zmalloc_pinned(&h_gramB , 9*n*n));
// === Allocate GPU workspace ===
CHECK( magma_zmalloc(&gramM, n * n));
CHECK( magma_zmalloc(&gramA, 9 * n * n));
CHECK( magma_zmalloc(&gramB, 9 * n * n));
// === Set activemask to one ===
for(magma_int_t k =0; k<n; k++){
iwork[k]=1;
}
magma_setmatrix(n, 1, sizeof(magma_int_t), iwork, n , activeMask, n, queue);
#if defined(PRECISION_s)
ikind = 3;
#endif
// === Make the initial vectors orthonormal ===
magma_zgegqr_gpu(ikind, m, n, blockX, m, dwork, hwork, &info );
//magma_zorthomgs( m, n, blockX, queue );
magma_z_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX, queue );
solver_par->spmv_count++;
// === Compute the Gram matrix = (X, AX) & its eigenstates ===
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero, gramM, n, queue );
magma_zheevd_gpu( MagmaVec, MagmaUpper,
n, gramM, n, evalues, hW, n, hwork, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork, &info );
// === Update X = X * evectors ===
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockX, m, gramM, n, c_zero, blockW, m, queue );
SWAP(blockW, blockX);
// === Update AX = AX * evectors ===
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockAX, m, gramM, n, c_zero, blockW, m, queue );
SWAP(blockW, blockAX);
condestGhistory[1] = 7.82;
tempo1 = magma_sync_wtime( queue );
// === Main LOBPCG loop ============================================================
for(iterationNumber = 1; iterationNumber < maxIterations; iterationNumber++)
{
// === compute the residuals (R = Ax - x evalues )
magmablas_zlacpy( MagmaFull, m, n, blockAX, m, blockR, m, queue );
/*
for(magma_int_t i=0; i<n; i++) {
magma_zaxpy( m, MAGMA_Z_MAKE(-evalues[i],0), blockX+i*m, 1, blockR+i*m, 1, queue );
}
*/
magma_dsetmatrix( 3*n, 1, evalues, 3*n, eval_gpu, 3*n, queue );
CHECK( magma_zlobpcg_res( m, n, eval_gpu, blockX, blockR, eval_gpu, queue ));
magmablas_dznrm2_cols( m, n, blockR, m, residualNorms(0, iterationNumber), queue );
// === remove the residuals corresponding to already converged evectors
CHECK( magma_zcompact(m, n, blockR, m,
residualNorms(0, iterationNumber), residualTolerance,
activeMask, &cBlockSize, queue ));
if (cBlockSize == 0)
break;
// === apply a preconditioner P to the active residulas: R_new = P R_old
// === for now set P to be identity (no preconditioner => nothing to be done )
//magmablas_zlacpy( MagmaFull, m, cBlockSize, blockR, m, blockW, m, queue );
//SWAP(blockW, blockR);
// preconditioner
magma_z_matrix bWv={Magma_CSR}, bRv={Magma_CSR};
bWv.memory_location = Magma_DEV; bWv.num_rows = m; bWv.num_cols = cBlockSize; bWv.major = MagmaColMajor; bWv.nnz = m*cBlockSize; bWv.dval = blockW;
bRv.memory_location = Magma_DEV; bRv.num_rows = m; bRv.num_cols = cBlockSize; bRv.major = MagmaColMajor; bRv.nnz = m*cBlockSize; bRv.dval = blockR;
tempop1 = magma_sync_wtime( queue );
CHECK( magma_z_applyprecond_left( MagmaNoTrans, A, bRv, &bWv, precond_par, queue ));
CHECK( magma_z_applyprecond_right( MagmaNoTrans, A, bWv, &bRv, precond_par, queue ));
tempop2 = magma_sync_wtime( queue );
precond_par->runtime += tempop2-tempop1;
// === make the preconditioned residuals orthogonal to X
if( precond_par->solver != Magma_NONE){
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, cBlockSize, m,
c_one, blockX, m, blockR, m, c_zero, gramB(0,0), ldgram, queue );
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n,
c_neg_one, blockX, m, gramB(0,0), ldgram, c_one, blockR, m, queue );
}
// === make the active preconditioned residuals orthonormal
magma_zgegqr_gpu(ikind, m, cBlockSize, blockR, m, dwork, hwork, &info );
#if defined(PRECISION_s)
// re-orthogonalization
SWAP(blockX, dwork);
magma_zgegqr_gpu(ikind, m, cBlockSize, blockR, m, dwork, hwork, &info );
#endif
//magma_zorthomgs( m, cBlockSize, blockR, queue );
// === compute AR
magma_z_bspmv_tuned(m, cBlockSize, c_one, A, blockR, c_zero, blockAR, queue );
solver_par->spmv_count++;
if (!restart) {
// === compact P & AP as well
CHECK( magma_zcompactActive(m, n, blockP, m, activeMask, queue ));
CHECK( magma_zcompactActive(m, n, blockAP, m, activeMask, queue ));
/*
// === make P orthogonal to X ?
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, cBlockSize, m,
c_one, blockX, m, blockP, m, c_zero, gramB(0,0), ldgram, queue );
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, cBlockSize, n,
c_neg_one, blockX, m, gramB(0,0), ldgram, c_one, blockP, m, queue );
// === make P orthogonal to R ?
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockR, m, blockP, m, c_zero, gramB(0,0), ldgram, queue );
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, cBlockSize, cBlockSize,
c_neg_one, blockR, m, gramB(0,0), ldgram, c_one, blockP, m, queue );
*/
// === Make P orthonormal & properly change AP (without multiplication by A)
magma_zgegqr_gpu(ikind, m, cBlockSize, blockP, m, dwork, hwork, &info );
#if defined(PRECISION_s)
// re-orthogonalization
SWAP(blockX, dwork);
magma_zgegqr_gpu(ikind, m, cBlockSize, blockP, m, dwork, hwork, &info );
#endif
//magma_zorthomgs( m, cBlockSize, blockP, queue );
//magma_z_bspmv_tuned(m, cBlockSize, c_one, A, blockP, c_zero, blockAP, queue );
magma_zsetmatrix( cBlockSize, cBlockSize, hwork, cBlockSize, dwork, cBlockSize, queue );
// replacement according to Stan
#if defined(PRECISION_s) || defined(PRECISION_d)
magmablas_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m, queue );
#else
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
m, cBlockSize, c_one, dwork, cBlockSize, blockAP, m, queue );
#endif
}
iter = max( 1, iterationNumber - 10 - int(log(1.*cBlockSize)) );
double condestGmean = 0.;
for(magma_int_t i = 0; i<iterationNumber-iter+1; i++){
condestGmean += condestGhistory[i];
}
condestGmean = condestGmean / (iterationNumber-iter+1);
if (restart)
gramDim = n+cBlockSize;
else
gramDim = n+2*cBlockSize;
/* --- The Raileight-Ritz method for [X R P] -----------------------
[ X R P ]' [AX AR AP] y = evalues [ X R P ]' [ X R P ], i.e.,
GramA GramB
/ X'AX X'AR X'AP \ / X'X X'R X'P \
| R'AX R'AR R'AP | y = evalues | R'X R'R R'P |
\ P'AX P'AR P'AP / \ P'X P'R P'P /
----------------------------------------------------------------- */
// === assemble GramB; first, set it to I
magmablas_zlaset( MagmaFull, ldgram, ldgram, c_zero, c_one, gramB, ldgram, queue ); // identity
if (!restart) {
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockP, m, blockX, m, c_zero, gramB(n+cBlockSize,0), ldgram, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockR, m, c_zero, gramB(n+cBlockSize,n), ldgram, queue );
}
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockR, m, blockX, m, c_zero, gramB(n,0), ldgram, queue );
// === get GramB from the GPU to the CPU and compute its eigenvalues only
magma_zgetmatrix( gramDim, gramDim, gramB, ldgram, h_gramB, ldgram, queue );
lapackf77_zheev("N", "L", &gramDim, h_gramB, &ldgram, gevalues,
hwork, &lwork,
#ifdef COMPLEX
rwork,
#endif
&info);
// === check stability criteria if we need to restart
condestG = log10( gevalues[gramDim-1]/gevalues[0] ) + 1.;
if ((condestG/condestGmean>2 && condestG>2) || condestG>8) {
// Steepest descent restart for stability
restart=1;
printf("restart at step #%d\n", int(iterationNumber));
}
// === assemble GramA; first, set it to I
magmablas_zlaset( MagmaFull, ldgram, ldgram, c_zero, c_one, gramA, ldgram, queue ); // identity
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockR, m, blockAX, m, c_zero, gramA(n,0), ldgram, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockR, m, blockAR, m, c_zero, gramA(n,n), ldgram, queue );
if (!restart) {
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, n, m,
c_one, blockP, m, blockAX, m, c_zero,
gramA(n+cBlockSize,0), ldgram, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockAR, m, c_zero,
gramA(n+cBlockSize,n), ldgram, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, cBlockSize, cBlockSize, m,
c_one, blockP, m, blockAP, m, c_zero,
gramA(n+cBlockSize,n+cBlockSize), ldgram, queue );
}
/*
// === Compute X' AX or just use the eigenvalues below ?
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero,
gramA(0,0), ldgram, queue );
*/
if (restart==0) {
magma_zgetmatrix( gramDim, gramDim, gramA, ldgram, gevectors, ldgram, queue );
}
else {
gramDim = n+cBlockSize;
magma_zgetmatrix( gramDim, gramDim, gramA, ldgram, gevectors, ldgram, queue );
}
for(magma_int_t k=0; k<n; k++)
*gevectors(k,k) = MAGMA_Z_MAKE(evalues[k], 0);
// === the previous eigensolver destroyed what is in h_gramB => must copy it again
magma_zgetmatrix( gramDim, gramDim, gramB, ldgram, h_gramB, ldgram, queue );
magma_int_t itype = 1;
lapackf77_zhegvd(&itype, "V", "L", &gramDim,
gevectors, &ldgram, h_gramB, &ldgram,
gevalues, hwork, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork, &info);
for(magma_int_t k =0; k<n; k++)
evalues[k] = gevalues[k];
// === copy back the result to gramA on the GPU and use it for the updates
magma_zsetmatrix( gramDim, gramDim, gevectors, ldgram, gramA, ldgram, queue );
if (restart == 0) {
// === contribution from P to the new X (in new search direction P)
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m, queue );
SWAP(dwork, blockP);
// === contribution from R to the new X (in new search direction P)
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockR, m, gramA(n,0), ldgram, c_one, blockP, m, queue );
// === corresponding contribution from AP to the new AX (in AP)
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockAP, m, gramA(n+cBlockSize,0), ldgram, c_zero, dwork, m, queue );
SWAP(dwork, blockAP);
// === corresponding contribution from AR to the new AX (in AP)
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockAR, m, gramA(n,0), ldgram, c_one, blockAP, m, queue );
}
else {
// === contribution from R (only) to the new X
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, cBlockSize,
c_one, blockR, m, gramA(n,0), ldgram, c_zero, blockP, m, queue );
// === corresponding contribution from AR (only) to the new AX
magma_zgemm( MagmaNoTrans, MagmaNoTrans,m, n, cBlockSize,
c_one, blockAR, m, gramA(n,0), ldgram, c_zero, blockAP, m, queue );
}
// === contribution from old X to the new X + the new search direction P
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockX, m, gramA, ldgram, c_zero, dwork, m, queue );
SWAP(dwork, blockX);
//magma_zaxpy( m*n, c_one, blockP, 1, blockX, 1, queue );
CHECK( magma_zlobpcg_maxpy( m, n, blockP, blockX, queue ));
// === corresponding contribution from old AX to new AX + AP
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, blockAX, m, gramA, ldgram, c_zero, dwork, m, queue );
SWAP(dwork, blockAX);
//magma_zaxpy( m*n, c_one, blockAP, 1, blockAX, 1, queue );
CHECK( magma_zlobpcg_maxpy( m, n, blockAP, blockAX, queue ));
condestGhistory[iterationNumber+1]=condestG;
magma_dgetmatrix( 1, 1, residualNorms(0, iterationNumber), 1, &tmp, 1, queue );
if ( iterationNumber == 1 ) {
solver_par->init_res = tmp;
r0 = tmp * solver_par->rtol;
if ( r0 < ATOLERANCE )
r0 = ATOLERANCE;
}
solver_par->final_res = tmp;
if ( tmp < r0 ) {
break;
}
if (cBlockSize == 0) {
break;
}
if ( solver_par->verbose!=0 ) {
if ( iterationNumber%solver_par->verbose == 0 ) {
// double res;
// magma_zgetmatrix( 1, 1,
// (magmaDoubleComplex*)residualNorms(0, iterationNumber), 1,
// (magmaDoubleComplex*)&res, 1, queue );
//
// printf("Iteration %4d, CBS %4d, Residual: %10.7f\n",
// iterationNumber, cBlockSize, res);
printf("%4d-%2d ", int(iterationNumber), int(cBlockSize));
magma_dprint_gpu(1, n, residualNorms(0, iterationNumber), 1);
}
}
restart = 0;
} // === end for iterationNumber = 1,maxIterations =======================
// fill solver info
tempo2 = magma_sync_wtime( queue );
solver_par->runtime = (real_Double_t) tempo2-tempo1;
solver_par->numiter = iterationNumber;
if ( solver_par->numiter < solver_par->maxiter) {
info = MAGMA_SUCCESS;
} else if ( solver_par->init_res > solver_par->final_res )
info = MAGMA_SLOW_CONVERGENCE;
else
info = MAGMA_DIVERGENCE;
// =============================================================================
// === postprocessing;
// =============================================================================
// === compute the real AX and corresponding eigenvalues
magma_z_bspmv_tuned(m, n, c_one, A, blockX, c_zero, blockAX, queue );
magma_zgemm( MagmaConjTrans, MagmaNoTrans, n, n, m,
c_one, blockX, m, blockAX, m, c_zero, gramM, n, queue );
magma_zheevd_gpu( MagmaVec, MagmaUpper,
n, gramM, n, gevalues, dwork, n, hwork, lwork,
#ifdef COMPLEX
rwork, lrwork,
#endif
iwork, liwork, &info );
for(magma_int_t k =0; k<n; k++)
evalues[k] = gevalues[k];
// === update X = X * evectors
SWAP(blockX, dwork);
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, dwork, m, gramM, n, c_zero, blockX, m, queue );
// === update AX = AX * evectors to compute the final residual
SWAP(blockAX, dwork);
magma_zgemm( MagmaNoTrans, MagmaNoTrans, m, n, n,
c_one, dwork, m, gramM, n, c_zero, blockAX, m, queue );
// === compute R = AX - evalues X
magmablas_zlacpy( MagmaFull, m, n, blockAX, m, blockR, m, queue );
for(magma_int_t i=0; i<n; i++)
magma_zaxpy( m, MAGMA_Z_MAKE(-evalues[i], 0), blockX+i*m, 1, blockR+i*m, 1, queue );
// === residualNorms[iterationNumber] = || R ||
magmablas_dznrm2_cols( m, n, blockR, m, residualNorms(0, iterationNumber), queue );
// === restore blockX if needed
if (blockX != origX)
magmablas_zlacpy( MagmaFull, m, n, blockX, m, origX, m, queue );
printf("Eigenvalues:\n");
for(magma_int_t i =0; i<n; i++)
printf("%e ", evalues[i]);
printf("\n\n");
printf("Final residuals:\n");
magma_dprint_gpu(1, n, residualNorms(0, iterationNumber), 1);
printf("\n\n");
//=== Prmagma_int_t residual history in a file for plotting ====
CHECK( magma_dmalloc_cpu(&hresidualNorms, (iterationNumber+1) * n));
magma_dgetmatrix( n, iterationNumber,
residualNorms, n,
hresidualNorms, n, queue );
solver_par->iter_res = *hresidualNorms(0, iterationNumber-1);
printf("Residuals are stored in file residualNorms\n");
printf("Plot the residuals using: myplot \n");
FILE *residuals_file;
residuals_file = fopen("residualNorms", "w");
for(magma_int_t i =1; i<iterationNumber; i++) {
for(magma_int_t j = 0; j<n; j++)
fprintf(residuals_file, "%f ", *hresidualNorms(j,i));
fprintf(residuals_file, "\n");
}
fclose(residuals_file);
cleanup:
magma_free_cpu(hresidualNorms);
// === free work space
magma_free( residualNorms );
magma_free_cpu( condestGhistory );
magma_free_cpu( gevalues );
magma_free_cpu( iwork );
magma_free_pinned( hW );
magma_free_pinned( gevectors );
magma_free_pinned( h_gramB );
magma_free( gramM );
magma_free( gramA );
magma_free( gramB );
magma_free( activeMask );
if (blockX != (solver_par->eigenvectors))
magma_free( blockX );
if (blockAX != (solver_par->eigenvectors))
magma_free( blockAX );
if (blockAR != (solver_par->eigenvectors))
magma_free( blockAR );
if (blockAP != (solver_par->eigenvectors))
magma_free( blockAP );
if (blockR != (solver_par->eigenvectors))
magma_free( blockR );
if (blockP != (solver_par->eigenvectors))
magma_free( blockP );
if (blockW != (solver_par->eigenvectors))
magma_free( blockW );
if (dwork != (solver_par->eigenvectors))
magma_free( dwork );
magma_free( eval_gpu );
magma_free_pinned( hwork );
#ifdef COMPLEX
magma_free_cpu( rwork );
rwork = NULL;
#endif
return info;
}
extern "C" magma_int_t
magma_zgessm_gpu( char storev, magma_int_t m, magma_int_t n, magma_int_t k, magma_int_t ib,
magma_int_t *ipiv,
magmaDoubleComplex *dL1, magma_int_t lddl1,
magmaDoubleComplex *dL, magma_int_t lddl,
magmaDoubleComplex *dA, magma_int_t ldda,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
ZGESSM applies the factors L computed by ZGETRF_INCPIV to
a complex M-by-N tile A.
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.
K (input) INTEGER
The number of columns of the matrix L. K >= 0.
IB (input) INTEGER
The inner-blocking size. IB >= 0.
IPIV (input) INTEGER array on the cpu.
The pivot indices array of size K as returned by
ZGETRF_INCPIV.
dL1 (input) DOUBLE COMPLEX array, dimension(LDDL1, N)
The IB-by-K matrix in which is stored L^(-1) as returned by GETRF_INCPIV
LDDL1 (input) INTEGER
The leading dimension of the array L1. LDDL1 >= max(1,2*IB).
dL (input) DOUBLE COMPLEX array, dimension(LDDL, N)
The M-by-K lower triangular tile on the gpu.
LDDL (input) INTEGER
The leading dimension of the array L. LDDL >= max(1,M).
dA (input/output) DOUBLE COMPLEX array, dimension (LDDA, N)
On entry, the M-by-N tile A on the gpu.
On exit, updated by the application of L on the gpu.
===================================================================== */
#define AT(i,j) (dAT + (i)*ldda + (j) )
#define L(i,j) (dL + (i) + (j)*lddl )
#define dL1(j) (dL1 + (j)*lddl1)
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
int i, s, sb;
magmaDoubleComplex *dAT;
/* 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;
if ( (storev == 'C') || (storev == 'c') ) {
magmablas_zgetmo_in( dA, dAT, ldda, m, n );
} else {
dAT = dA;
}
s = k / ib;
for(i = 0; i < k; i += ib) {
sb = min(ib, k-i);
magmablas_zlaswp( n, dAT, ldda, i+1, i+sb, ipiv, 1 );
#ifndef WITHOUTTRTRI
magma_ztrmm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n, sb,
c_one, dL1(i), lddl1,
AT(i, 0), ldda);
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n, sb,
c_one, L( i, i), lddl,
AT(i, 0), ldda);
#endif
if ( (i+sb) < m) {
magma_zgemm( MagmaNoTrans, MagmaTrans,
n, m-(i+sb), sb,
c_neg_one, AT(i, 0), ldda,
L( i+sb, i), lddl,
c_one, AT(i+sb, 0), ldda );
}
}
if ( (storev == 'C') || (storev == 'c') ) {
magmablas_zgetmo_in( dA, dAT, ldda, m, n );
}
return *info;
/* End of MAGMA_ZGETRF_GPU */
}
extern "C" magma_int_t
magma_zgetrf2_mgpu(magma_int_t num_gpus,
magma_int_t m, magma_int_t n, magma_int_t nb, magma_int_t offset,
cuDoubleComplex **d_lAT, magma_int_t lddat, magma_int_t *ipiv,
cuDoubleComplex **d_lAP, cuDoubleComplex *w, magma_int_t ldw,
cudaStream_t streaml[][2], magma_int_t *info)
#endif
{
/* -- MAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
November 2010
Purpose
=======
ZGETRF 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) COMPLEX_16 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
if INFO = -7, internal GPU 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 inAT(id,i,j) (d_lAT[(id)] + ((offset)+(i)*nb)*lddat + (j)*nb)
#define W(j) (w+((j)%num_gpus)*nb*ldw)
cuDoubleComplex c_one = MAGMA_Z_ONE;
cuDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t block_size = 32;
magma_int_t iinfo, n_local[4];
magma_int_t maxm, mindim;
magma_int_t i, ii, d, dd, rows, cols, s, ldpan[4];
magma_int_t id, i_local, i_local2, nb0, nb1;
cuDoubleComplex *d_panel[4], *panel_local[4];
//cudaStream_t streaml[4][2];
/* 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);
//nb = magma_get_zgetrf_nb(m);
if( num_gpus > ceil((double)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++){
magmaSetDevice(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][nb*maxm]); /* temporary panel storage */
/* create local streams */
//magma_queue_create(&streaml[i][0]);
//magma_queue_create(&streaml[i][1]);
}
trace_init( 1, num_gpus, 2, (CUstream_st**)streaml );
/* start sending the panel to cpu */
nb0 = min(mindim, nb);
magmaSetDevice(0);
magmablasSetKernelStream(streaml[0][1]);
trace_gpu_start( 0, 1, "comm", "get" );
if( nb0 == nb )
magmablas_ztranspose( d_lAP[0], maxm, inAT(0,0,0), lddat, nb0, maxm );
else
magmablas_ztranspose2( d_lAP[0], maxm, inAT(0,0,0), lddat, nb0, maxm );
magma_zgetmatrix_async( m, nb0,
d_lAP[0], maxm,
W(0), ldw, streaml[0][1] );
trace_gpu_end( 0, 1 );
/* ------------------------------------------------------------------------------------- */
#ifdef PROFILE
magma_timestr_t start_timer, end_timer;
start_timer = get_current_time();
#endif
s = mindim / nb;
for( i=0; i<s; i++ )
{
/* Set the GPU number that holds the current panel */
id = i%num_gpus;
magmaSetDevice(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" );
#ifdef PANEL_FACT_MC
cntxt->nb = 12;
magma_zgetrf_mc(cntxt, &rows, &nb, W(i), &ldw, ipiv+i*nb, &iinfo);
#else
lapackf77_zgetrf( &rows, &nb, W(i), &ldw, ipiv+i*nb, &iinfo);
#endif
if ( (*info == 0) && (iinfo > 0) ) {
*info = iinfo + i*nb;
//break;
}
trace_cpu_end( 0 );
/* start sending the panel to all the gpus */
d = (i+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
magmaSetDevice(d);
trace_gpu_start( 0, 1, "comm", "set" );
magma_zsetmatrix_async( rows, nb,
W(i), ldw,
d_lAP[d], 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++ ) {
magmaSetDevice(d);
magmablasSetKernelStream(streaml[d][0]);
trace_gpu_start( d, 1, "pivot", "pivot" );
if( dd == 0 )
magmablas_zpermute_long2( lddat, inAT(d,0,0), lddat, ipiv, nb, i*nb );
else
magmablas_zpermute_long3( inAT(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++ ) {
magmaSetDevice(d);
/* storage for panel */
if( d == id ) {
/* the panel belond to this gpu */
panel_local[d] = inAT(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][(i%2)*nb*maxm];
//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" );
} 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" );
}
magmablas_ztranspose(panel_local[d], ldpan[d], d_lAP[d], cols, cols, nb);
/* gpu updating the trailing matrix */
//magmablas_ztrsm(
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb, c_one,
panel_local[d], ldpan[d],
inAT(d, i, i_local2), lddat);
//cublasZgemm
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
nb1, m-(i+1)*nb, nb,
c_neg_one, inAT(d, i, i_local2), lddat,
&(panel_local[d][nb*ldpan[d]]), ldpan[d],
c_one, inAT(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" );
if( i+1 < s )
magmablas_ztranspose( d_lAP[d], ldda, inAT(d,loff,i_local), lddat, nb0, ldda );
else
magmablas_ztranspose2( d_lAP[d], ldda, inAT(d,loff,i_local), lddat, nb0, ldda );
/* send the panel to cpu */
magma_zgetmatrix_async( cols, nb0,
d_lAP[d], 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;
magmaSetDevice(d);
magmablasSetKernelStream(streaml[d][0]);
trace_gpu_start( d, 0, "gemm", "gemm" );
//magmablas_ztrsm
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n_local[d] - (i_local+1)*nb, nb,
c_one, panel_local[d], ldpan[d],
inAT(d,i,i_local+1), lddat );
//cublasZgemm
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
n_local[d]-(i_local+1)*nb, rows, nb,
c_neg_one, inAT(d,i,i_local+1), lddat,
&(panel_local[d][nb*ldpan[d]]), ldpan[d],
c_one, inAT(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 ) {
magmaSetDevice(id);
/* wait for the last panel on cpu */
magma_queue_sync( streaml[id][1] );
/* factor on cpu */
lapackf77_zgetrf( &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++ ) {
magmaSetDevice(d);
i_local2 = i_local;
if( d < id ) i_local2 ++;
if( d == id || n_local[d] > i_local2*nb ) {
magma_zsetmatrix_async( rows, nb0,
W(s), ldw,
d_lAP[d], cols, streaml[d][1] );
}
}
for( d=0; d<num_gpus; d++ ) {
magmaSetDevice(d);
magmablasSetKernelStream(streaml[d][0]);
if( d == 0 )
magmablas_zpermute_long2( lddat, inAT(d,0,0), lddat, ipiv, nb0, s*nb );
else
magmablas_zpermute_long3( inAT(d,0,0), lddat, ipiv, nb0, s*nb );
}
for( d=0; d<num_gpus; d++ ) {
magmaSetDevice(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] = inAT(d,s,i_local);
/* next column */
nb1 = n_local[d] - i_local*nb-nb0;
magmablas_ztranspose2( panel_local[d], lddat, d_lAP[d], cols, rows, nb0);
if( nb1 > 0 )
//cublasZtrsm
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb0, c_one,
panel_local[d], lddat,
inAT(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][(s%2)*nb*maxm];
//panel_local[d] = d_panel[d];
/* next column */
nb1 = n_local[d] - i_local2*nb;
magmablas_ztranspose2( panel_local[d], nb, d_lAP[d], cols, rows, nb0);
//cublasZtrsm
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb1, nb0, c_one,
panel_local[d], nb,
inAT(d,s,i_local2), lddat);
}
}
} /* if( nb0 > 0 ) */
/* clean up */
trace_finalize( "zgetrf_mgpu.svg","trace.css" );
for( d=0; d<num_gpus; d++ ) {
magmaSetDevice(d);
magma_queue_sync( streaml[d][0] );
magma_queue_sync( streaml[d][1] );
//magma_queue_destroy(streaml[d][0]);
//magma_queue_destroy(streaml[d][1]);
magmablasSetKernelStream(NULL);
}
magmaSetDevice(0);
#ifdef PROFILE
end_timer = get_current_time();
printf("\n Performance %f GFlop/s\n", (2./3.*n*n*n /1000000.) / GetTimerValue(start_timer, end_timer));
#endif
}
return *info;
/* End of MAGMA_ZGETRF2_MGPU */
}
/**
Purpose
-------
Solves a system of linear equations
A * X = B, A**T * X = B, or A**H * X = B
with a general N-by-N matrix A using the LU factorization computed by ZGETRF_GPU.
Arguments
---------
@param[in]
trans magma_trans_t
Specifies the form of the system of equations:
- = MagmaNoTrans: A * X = B (No transpose)
- = MagmaTrans: A**T * X = B (Transpose)
- = MagmaConjTrans: A**H * X = B (Conjugate transpose)
@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 COMPLEX_16 array on the GPU, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U as computed
by ZGETRF_GPU.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in]
ipiv INTEGER array, dimension (N)
The pivot indices from ZGETRF; for 1 <= i <= N, row i of the
matrix was interchanged with row IPIV(i).
@param[in,out]
dB COMPLEX_16 array on the GPU, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
@param[in]
lddb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zgetrs_gpu(
magma_trans_t trans, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *ipiv,
magmaDoubleComplex_ptr dB, magma_int_t lddb,
magma_int_t *info)
{
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex *work = NULL;
int notran = (trans == MagmaNoTrans);
magma_int_t i1, i2, inc;
*info = 0;
if ( (! notran) &&
(trans != MagmaTrans) &&
(trans != MagmaConjTrans) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (nrhs < 0) {
*info = -3;
} else if (ldda < max(1,n)) {
*info = -5;
} else if (lddb < max(1,n)) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (n == 0 || nrhs == 0) {
return *info;
}
magma_zmalloc_cpu( &work, n * nrhs );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
i1 = 1;
i2 = n;
if (notran) {
inc = 1;
/* Solve A * X = B. */
magma_zgetmatrix( n, nrhs, dB, lddb, work, n );
lapackf77_zlaswp(&nrhs, work, &n, &i1, &i2, ipiv, &inc);
magma_zsetmatrix( n, nrhs, work, n, dB, lddb );
if ( nrhs == 1) {
magma_ztrsv(MagmaLower, MagmaNoTrans, MagmaUnit, n, dA, ldda, dB, 1 );
magma_ztrsv(MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
} else {
magma_ztrsm(MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
magma_ztrsm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
}
} else {
inc = -1;
/* Solve A**T * X = B or A**H * X = B. */
if ( nrhs == 1) {
magma_ztrsv(MagmaUpper, trans, MagmaNonUnit, n, dA, ldda, dB, 1 );
magma_ztrsv(MagmaLower, trans, MagmaUnit, n, dA, ldda, dB, 1 );
} else {
magma_ztrsm(MagmaLeft, MagmaUpper, trans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
magma_ztrsm(MagmaLeft, MagmaLower, trans, MagmaUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
}
magma_zgetmatrix( n, nrhs, dB, lddb, work, n );
lapackf77_zlaswp(&nrhs, work, &n, &i1, &i2, ipiv, &inc);
magma_zsetmatrix( n, nrhs, work, n, dB, lddb );
}
magma_free_cpu(work);
return *info;
}
extern "C" magma_int_t
magma_zpotrf3_mgpu(magma_int_t num_gpus, char uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaDoubleComplex *d_lA[], magma_int_t ldda,
magmaDoubleComplex *d_lP[], magma_int_t lddp,
magmaDoubleComplex *a, magma_int_t lda, magma_int_t h,
magma_queue_t stream[][3], magma_event_t event[][5],
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
Auxiliary subroutine for zpotrf2_ooc. It is multiple gpu interface to compute
Cholesky of a "rectangular" matrix.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
magma_int_t j, jb, nb0, nb2, d, dd, id, j_local, j_local2, buf;
char uplo_[2] = {uplo, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
double d_one = 1.0;
double d_neg_one = -1.0;
int upper = lapackf77_lsame(uplo_, "U");
magmaDoubleComplex *dlpanel;
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
const magma_int_t stream1 = 0, stream2 = 1, stream3 = 2;
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
/* used by ztrsm_work */
int trsm_nb = 128;
int trsm_n = trsm_nb*((nb+trsm_nb-1)/trsm_nb);
magmaDoubleComplex *d_dinvA[MagmaMaxGPUs];
magmaDoubleComplex *d_x[MagmaMaxGPUs];
#define dinvA(d,j) &(d_dinvA[(d)][(j)*trsm_nb*trsm_n])
#define dx(d,j) &(d_x[(d)][(j)*nb*m])
/*
* Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
if ( (MAGMA_SUCCESS != magma_zmalloc( &d_dinvA[d], 2*trsm_nb*trsm_n )) ||
(MAGMA_SUCCESS != magma_zmalloc( &d_x[d], 2*nb*(upper ? n : m) )) ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
magma_setdevice(0);
#endif
*info = 0;
if ( (! upper) && (! lapackf77_lsame(uplo_, "L")) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (!upper && num_gpus*ldda < max(1,n)) {
*info = -4;
} else if (upper && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* initialization */
for( d=0; d<num_gpus; d++ ) {
/* local-n and local-ld */
if (upper) {
n_local[d] = (n/(nb*num_gpus))*nb;
if (d < (n/nb)%num_gpus)
n_local[d] += nb;
else if (d == (n/nb)%num_gpus)
n_local[d] += n%nb;
} else {
n_local[d] = (m/(nb*num_gpus))*nb;
if (d < (m/nb)%num_gpus)
n_local[d] += nb;
else if (d == (m/nb)%num_gpus)
n_local[d] += m%nb;
}
}
/* == initialize the trace */
trace_init( 1, num_gpus, 3, (CUstream_st**)stream );
if (upper)
{
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
for (j=0; j<m; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus; // right now, we have num_gpu buffers, so id and buf are the same..
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (m-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
trace_gpu_start( id, stream1, "syrk", "syrk" );
magma_zherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda);
trace_gpu_end( id, stream1 );
}
/* send the diagonal to cpu on stream1 */
trace_gpu_start( id, stream1, "comm", "D to CPU" );
magma_zgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
/* update off-diagonal blocks in the panel */
if( j > 0 ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2; // number of local columns in the panel, while jb is panel-size (number of rows)
if( n_local[d] > nb0 ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
if( d == id ) {
dlpanel = dlA(d,0,nb*j_local);
ldpanel = ldda;
// the GPU owns the row from start, and no need of synch.
//magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
} else {
dlpanel = dlP(d,nb,0,buf);
ldpanel = lddp;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
trace_gpu_start( d, stream2, "gemm", "gemm" );
magma_zgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda);
trace_gpu_end( d, stream2 );
magma_event_record( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for panel and factorize it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_zpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
magma_setdevice(d);
trace_gpu_start( d, stream1, "comm", "comm" );
magma_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
trace_gpu_end( d, stream1 );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
trace_gpu_start( id, stream1, "comm", "comm" );
magma_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
stream[id][stream1] );
trace_gpu_end( id, stream1 );
}
/* panel-factorize the off-diagonal */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d,j,nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
nb2 = n_local[d] - j_local2*nb;
magma_setdevice(d);
if( j+jb < m && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead next block on stream1 */
nb0 = min(nb, nb2);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb, trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb0,jb, dx(d,0),nb0 );
magmablas_ztrsm_work( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ztrsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
trace_gpu_end( d, stream1 );
} else if( nb2 > 0 ) {
/* update all the blocks on stream2 */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for cholesky factor
trace_gpu_start( d, stream2, "trsm", "trsm" );
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,0),nb2 );
magmablas_ztrsm_work( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ztrsm( MagmaLeft, MagmaUpper,
MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream2 );
}
d = (d+1)%num_gpus;
} /* end of for */
/* ========================================================== */
if( j+jb < m ) {
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, off-diagonals are copied to cpu (synchronize at the end). *
* so we have the Cholesky factor, but only diagonal submatrix of the big panel, *
* on cpu at the end. */
int d2, buf2;
magma_setdevice(d);
/* lookahead done */
magma_queue_wait_event( stream[d][stream3], event[d][4] );
trace_gpu_start( d, stream3, "comm", "row to CPU" );
magma_zgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
stream[d][stream3] );
trace_gpu_end( d, stream3 );
magma_event_record( event[d][3], stream[d][stream3] );
/* needed on pluto */
//magma_queue_sync( stream[d][stream3] );
/* broadcast rows to gpus on stream2 */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
trace_gpu_start( d2, stream3, "comm", "row to GPUs" );
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // rows arrived at cpu on stream3
magma_zsetmatrix_async( j+jb, nb0,
Aup(0,j+jb), lda,
dlP(d2,nb,0,buf2), lddp,
stream[d2][stream3] );
trace_gpu_end( d2, stream3 );
magma_event_record( event[d2][0], stream[d2][stream3] );
}
}
/* =========================== */
/* update the remaining blocks */
nb2 = n_local[d]-(nb*j_local2 + nb0);
if( nb2 > 0 ) {
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d,0,0,buf);
ldpanel = lddp;
}
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
trace_gpu_start( d, stream2, "trsm", "trsm" );
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( stream[d][stream2], event[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,flag),trsm_nb );
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
}
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,1),nb2 );
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
flag, dinvA(d,flag), dx(d,1) );
#else
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for cholesky factor
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda);
#endif
trace_gpu_end( d, stream2 );
}
}
} /* end of ztrsm */
} /* end of for j=1, .., n */
} else {
/* ---------------------------------------------- */
/* Lower-triangular case */
/* > Compute the Cholesky factorization A = L*L'. */
/* ---------------------------------------------- */
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (n-j));
/* Update the current diagonal block on stream1 */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
magma_zherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda);
}
/* send the diagonal to cpu on stream1 */
magma_zgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
stream[id][stream1] );
/* update off-diagonal blocks of the panel */
if( j > 0 ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( nb0 < n_local[d] ) {
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
if( d == id ) {
dlpanel = dlA(d, nb*j_local, 0);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,nb,buf);
ldpanel = nb;
magma_queue_wait_event( stream[d][stream2], event[d][0] ); // rows arrived at gpu
}
magma_zgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, ldpanel,
c_one, dlA(d, nb0, j), ldda);
magma_event_record( event[d][2], stream[d][stream2] );
}
d = (d+1)%num_gpus;
}
}
/* wait for the panel and factorized it on cpu */
magma_setdevice(id);
magma_queue_sync( stream[id][stream1] );
lapackf77_zpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus on stream1 */
if ( (j+jb) < m) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
magma_setdevice(d);
magma_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, ldpanel,
stream[d][stream1] );
magma_event_record( event[d][1], stream[d][stream1] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
magma_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
stream[id][stream1] );
}
/* panel factorize the off-diagonal */
if ( (j+jb) < m) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2);
magma_setdevice(d);
if( j+nb < n && d == (j/nb+1)%num_gpus ) { /* owns next column, look-ahead next block on stream1 */
if ( j > 0 ) magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for gemm update
magmablasSetKernelStream(stream[d][stream1]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb, trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb0,jb, dx(d,0),nb0 );
magmablas_ztrsm_work( MagmaRight, MagmaLower,
MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ztrsm( MagmaRight, MagmaLower,
MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
magma_event_record( event[d][4], stream[d][stream1] );
} else if( nb2 > 0 ) { /* other gpus updating all the blocks on stream2 */
/* update the entire column */
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // wait for the cholesky factor
magmablasSetKernelStream(stream[d][stream2]);
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,0),trsm_nb );
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,0),nb2 );
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
1, dinvA(d,0), dx(d,0) );
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
}
d = (d+1)%num_gpus;
} /* end for d */
/* ========================================================== */
if( j+jb < n ) {
d = (j/nb+1)%num_gpus;
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
nb0 = min(nb, n_local[d]-nb*j_local2 );
/* even on 1 gpu, we copy off-diagonal to cpu (but don't synchronize). */
/* so we have the Cholesky factor on cpu at the end. */
int d2, buf2;
//#define ZPOTRF_DEVICE_TO_DEVICE
#ifdef ZPOTRF_DEVICE_TO_DEVICE
// lookahead done
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
magma_setdevice(d2);
magma_queue_wait_event( stream[d2][stream3], event[d][4] );
if( d2 != d ) {
magma_zcopymatrix_async( nb0, j+jb,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
dlA(d, nb*j_local2, 0), ldda,
stream[d2][stream3] );
magma_event_record( event[d2][0], stream[d2][stream3] );
} else {
magma_zgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream3] );
}
}
#else
// lookahead done
magma_setdevice(d);
magma_queue_wait_event( stream[d][stream3], event[d][4] );
magma_zgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream3] );
magma_event_record( event[d][3], stream[d][stream3] );
/* syn on rows on CPU, seem to be needed on Pluto */
//magma_queue_sync( stream[d][stream3] );
/* broadcast the rows to gpus */
buf2 = ((j+jb)/nb)%num_gpus;
for( d2=0; d2<num_gpus; d2++ ) {
if( d2 != d )
{
magma_setdevice(d2);
magma_queue_wait_event( stream[d2][stream3], event[d][3] ); // getmatrix done
magma_zsetmatrix_async( nb0, j+jb,
Alo(j+jb,0), lda,
dlPT(d2,0,nb,buf2), nb, // first nbxnb reserved for diagonal block
stream[d2][stream3] );
magma_event_record( event[d2][0], stream[d2][stream3] );
}
}
#endif
/* =================================== */
/* updates remaining blocks on stream2 */
nb2 = n_local[d] - (j_local2*nb + nb0);
if( nb2 > 0 ) {
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d,0,0,buf);
ldpanel = nb;
}
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream2]);
/* update the remaining blocks in the column */
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
int flag = 0;
if (flag == 0) {
magma_queue_wait_event( stream[d][stream2], event[d][4] ); // lookahead -> diagonal inversion
} else {
magmablas_zlaset( MagmaUpperLower, trsm_nb,trsm_n, dinvA(d,flag),trsm_nb );
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
}
magmablas_zlaset( MagmaUpperLower, nb2,jb, dx(d,1),nb2 );
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
flag, dinvA(d,flag), dx(d,1) );
#else
magma_queue_wait_event( stream[d][stream2], event[d][1] ); // panel received
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda);
#endif
}
}
}
}
} /* end of else not upper */
/* == finalize the trace == */
trace_finalize( "zpotrf.svg","trace.css" );
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<3; j++ ) {
magma_queue_sync( stream[d][j] );
}
#if (defined(PRECISION_d) || defined(PRECISION_s)) && defined(ZTRSM_WORK)
magma_free( d_dinvA[d] );
magma_free( d_x[d] );
#endif
magmablasSetKernelStream(NULL);
}
magma_setdevice(0);
return *info;
} /* magma_zpotrf_mgpu */
magma_err_t
magma_zgetrf_gpu(magma_int_t m, magma_int_t n,
magmaDoubleComplex_ptr dA, size_t dA_offset, magma_int_t ldda,
magma_int_t *ipiv, magma_int_t *info,
magma_queue_t queue )
{
/* -- clMAGMA (version 1.1.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2014
Purpose
=======
ZGETRF 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
=========
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) COMPLEX_16 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
if INFO = -7, internal GPU 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 inAT(i,j) dAT, dAT_offset + (i)*nb*lddat + (j)*nb
magmaDoubleComplex c_one = MAGMA_Z_MAKE( 1.0, 0.0 );
magmaDoubleComplex c_neg_one = MAGMA_Z_MAKE( -1.0, 0.0 );
magma_int_t iinfo, nb;
magma_int_t maxm, maxn, mindim;
magma_int_t i, rows, cols, s, lddat, lddwork;
magmaDoubleComplex_ptr dAT, dAP;
magmaDoubleComplex *work;
magma_err_t err;
*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;
}
if (m == 0 || n == 0)
return MAGMA_SUCCESS;
mindim = min(m, n);
nb = magma_get_zgetrf_nb(m);
s = mindim / nb;
if (nb <= 1 || nb >= min(m,n))
{
// use CPU code
err = magma_zmalloc_cpu( &work, m*n );
if ( err != MAGMA_SUCCESS ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
chk( magma_zgetmatrix( m, n, dA, dA_offset, ldda, work, 0, m, queue ));
lapackf77_zgetrf(&m, &n, work, &m, ipiv, info);
chk( magma_zsetmatrix( m, n, work, 0, m, dA, dA_offset, ldda, queue ));
magma_free_cpu(work);
}
else
{
size_t dAT_offset;
// use hybrid blocked code
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
lddat = maxn;
lddwork = maxm;
if ( MAGMA_SUCCESS != magma_zmalloc( &dAP, nb*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if ((m == n) && (m % 32 == 0) && (ldda%32 == 0))
{
dAT = dA;
dAT_offset = dA_offset;
magma_ztranspose_inplace( dAT, dAT_offset, ldda, lddat, queue );
}
else
{
dAT_offset = 0;
if ( MAGMA_SUCCESS != magma_zmalloc( &dAT, maxm*maxn )) {
magma_free( dAP );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_ztranspose2( dAT, dAT_offset, lddat, dA, dA_offset, ldda, m, n, queue );
}
if ( MAGMA_SUCCESS != magma_zmalloc_cpu( &work, maxm*nb ) ) {
magma_free( dAP );
if (! ((m == n) && (m % 32 == 0) && (ldda%32 == 0)) )
magma_free( dAT );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
for( i=0; i<s; i++ )
{
// download i-th panel
cols = maxm - i*nb;
magma_ztranspose( dAP, 0, cols, inAT(i,i), lddat, nb, cols, queue );
magma_zgetmatrix(m-i*nb, nb, dAP, 0, cols, work, 0, lddwork, queue);
if ( i>0 ){
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (i+1)*nb, nb,
c_one, inAT(i-1,i-1), lddat,
inAT(i-1,i+1), lddat, queue );
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-i*nb, nb,
c_neg_one, inAT(i-1,i+1), lddat,
inAT(i, i-1), lddat,
c_one, inAT(i, i+1), lddat, queue );
}
// do the cpu part
rows = m - i*nb;
lapackf77_zgetrf( &rows, &nb, work, &lddwork, ipiv+i*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + i*nb;
magma_zpermute_long2(n, dAT, dAT_offset, lddat, ipiv, nb, i*nb, queue );
// upload i-th panel
magma_zsetmatrix(m-i*nb, nb, work, 0, lddwork, dAP, 0, maxm, queue);
magma_ztranspose(inAT(i,i), lddat, dAP, 0, maxm, cols, nb, queue );
// do the small non-parallel computations
if ( s > (i+1) ) {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, inAT(i, i ), lddat,
inAT(i, i+1), lddat, queue);
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
nb, m-(i+1)*nb, nb,
c_neg_one, inAT(i, i+1), lddat,
inAT(i+1, i ), lddat,
c_one, inAT(i+1, i+1), lddat, queue );
}
else {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, inAT(i, i ), lddat,
inAT(i, i+1), lddat, queue);
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-(i+1)*nb, nb,
c_neg_one, inAT(i, i+1), lddat,
inAT(i+1, i ), lddat,
c_one, inAT(i+1, i+1), lddat, queue );
}
}
magma_int_t nb0 = min(m - s*nb, n - s*nb);
rows = m - s*nb;
cols = maxm - s*nb;
magma_ztranspose2( dAP, 0, maxm, inAT(s,s), lddat, nb0, rows, queue);
magma_zgetmatrix(rows, nb0, dAP, 0, maxm, work, 0, lddwork, queue);
// do the cpu part
lapackf77_zgetrf( &rows, &nb0, work, &lddwork, ipiv+s*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + s*nb;
magma_zpermute_long2(n, dAT, dAT_offset, lddat, ipiv, nb0, s*nb, queue );
// upload i-th panel
magma_zsetmatrix(rows, nb0, work, 0, lddwork, dAP, 0, maxm, queue);
magma_ztranspose2( inAT(s,s), lddat, dAP, 0, maxm, rows, nb0, queue );
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb-nb0, nb0,
c_one, inAT(s,s), lddat,
inAT(s,s)+nb0, lddat, queue);
if ((m == n) && (m % 32 == 0) && (ldda%32 == 0)) {
magma_ztranspose_inplace( dAT, dAT_offset, lddat, ldda, queue );
}
else {
magma_ztranspose2( dA, dA_offset, ldda, dAT, dAT_offset, lddat, n, m, queue );
magma_free( dAT );
}
magma_free( dAP );
magma_free_cpu( work );
}
return *info;
/* End of MAGMA_ZGETRF_GPU */
}
/**
Purpose
-------
Solves the least squares problem
min || A*X - C ||
using the QR factorization A = Q*R computed by ZGEQRF3_GPU.
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. M >= N >= 0.
@param[in]
nrhs INTEGER
The number of columns of the matrix C. NRHS >= 0.
@param[in]
dA COMPLEX_16 array on the GPU, dimension (LDDA,N)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,n, as returned by
ZGEQRF3_GPU in the first n columns of its array argument A.
@param[in]
ldda INTEGER
The leading dimension of the array A, LDDA >= M.
@param[in]
tau COMPLEX_16 array, dimension (N)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by MAGMA_ZGEQRF_GPU.
@param[in,out]
dB COMPLEX_16 array on the GPU, dimension (LDDB,NRHS)
On entry, the M-by-NRHS matrix C.
On exit, the N-by-NRHS solution matrix X.
@param[in]
dT COMPLEX_16 array that is the output (the 6th argument)
of magma_zgeqrf_gpu of size
2*MIN(M, N)*NB + ((N+31)/32*32 )* MAX(NB, NRHS).
The array starts with a block of size MIN(M,N)*NB that stores
the triangular T matrices used in the QR factorization,
followed by MIN(M,N)*NB block storing the diagonal block
matrices for the R matrix, followed by work space of size
((N+31)/32*32 )* MAX(NB, NRHS).
@param[in]
lddb INTEGER
The leading dimension of the array dB. LDDB >= M.
@param[out]
hwork (workspace) COMPLEX_16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK,
LWORK >= (M - N + NB)*(NRHS + NB) + NRHS*NB,
where NB is the blocksize given by magma_get_zgeqrf_nb( M ).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the HWORK array, returns
this value as the first entry of the WORK array.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zgels_comp
********************************************************************/
extern "C" magma_int_t
magma_zgeqrs3_gpu(magma_int_t m, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex *dA, magma_int_t ldda,
magmaDoubleComplex *tau, magmaDoubleComplex *dT,
magmaDoubleComplex *dB, magma_int_t lddb,
magmaDoubleComplex *hwork, magma_int_t lwork,
magma_int_t *info)
{
#define dA(a_1,a_2) (dA + (a_2)*(ldda) + (a_1))
#define dT(a_1) (dT + (lddwork+(a_1))*nb)
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t k, lddwork;
magma_int_t nb = magma_get_zgeqrf_nb(m);
magma_int_t lwkopt = (m - n + nb)*(nrhs + nb) + nrhs*nb;
int lquery = (lwork == -1);
hwork[0] = MAGMA_Z_MAKE( (double)lwkopt, 0. );
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0 || m < n)
*info = -2;
else if (nrhs < 0)
*info = -3;
else if (ldda < max(1,m))
*info = -5;
else if (lddb < max(1,m))
*info = -8;
else if (lwork < lwkopt && ! lquery)
*info = -10;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
k = min(m,n);
if (k == 0) {
hwork[0] = c_one;
return *info;
}
lddwork= k;
/* B := Q' * B */
magma_zunmqr_gpu( MagmaLeft, MagmaConjTrans,
m, nrhs, n,
dA(0,0), ldda, tau,
dB, lddb, hwork, lwork, dT, nb, info );
if ( *info != 0 ) {
return *info;
}
/* Solve R*X = B(1:n,:)
1. Move the block diagonal submatrices from dT to R
2. Solve
3. Restore the data format moving data from R back to dT
*/
magmablas_zswapdblk(k, nb, dA(0,0), ldda, 1, dT(0), nb, 0);
if ( nrhs == 1 ) {
magma_ztrsv(MagmaUpper, MagmaNoTrans, MagmaNonUnit,
n, dA(0,0), ldda, dB, 1);
} else {
magma_ztrsm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
n, nrhs, c_one, dA(0,0), ldda, dB, lddb);
}
magmablas_zswapdblk(k, nb, dT(0), nb, 0, dA(0,0), ldda, 1);
return *info;
}
extern "C" magma_err_t
magma_zgetrs_gpu(magma_trans_t trans, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex_ptr dA, size_t dA_offset, magma_int_t ldda,
magma_int_t *ipiv,
magmaDoubleComplex_ptr dB, size_t dB_offset, magma_int_t lddb,
magma_int_t *info, magma_queue_t queue)
{
/* -- clMagma (version 0.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
April 2012
Purpose
=======
Solves a system of linear equations
A * X = B or A' * X = B
with a general N-by-N matrix A using the LU factorization computed by ZGETRF_GPU.
Arguments
=========
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A'* X = B (Transpose)
= 'C': A'* X = B (Conjugate transpose = Transpose)
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input) COMPLEX_16 array on the GPU, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U as computed
by ZGETRF_GPU.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indices from ZGETRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIV(i).
B (input/output) COMPLEX_16 array on the GPU, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
HWORK (workspace) COMPLEX_16 array, dimension N*NRHS
===================================================================== */
magmaDoubleComplex z_one = MAGMA_Z_MAKE( 1.0, 0.0 );
magmaDoubleComplex *work = NULL;
magma_trans_t trans_ = trans;
long int notran = lapackf77_lsame(lapack_const(trans_), lapack_const(MagmaNoTrans));
magma_int_t i1, i2, inc;
*info = 0;
if ( (! notran) &&
(! lapackf77_lsame(lapack_const(trans_), lapack_const(MagmaTrans))) &&
(! lapackf77_lsame(lapack_const(trans_), lapack_const(MagmaConjTrans))) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (nrhs < 0) {
*info = -3;
} else if (ldda < max(1,n)) {
*info = -5;
} else if (lddb < max(1,n)) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (n == 0 || nrhs == 0) {
return *info;
}
work=(magmaDoubleComplex*)malloc( n*nrhs*sizeof(magmaDoubleComplex) );
if ( !work ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
i1 = 1;
i2 = n;
if (notran) {
inc = 1;
/* Solve A * X = B. */
magma_zgetmatrix( n, nrhs, dB, dB_offset, lddb, work, 0, n, queue );
lapackf77_zlaswp(&nrhs, work, &n, &i1, &i2, ipiv, &inc);
magma_zsetmatrix( n, nrhs, work, 0, n, dB, dB_offset, lddb, queue );
if ( nrhs == 1) {
chk(magma_ztrsv(MagmaLower, MagmaNoTrans, MagmaUnit, n, dA, dA_offset, ldda, dB, dB_offset, 1, queue));
chk(magma_ztrsv(MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, dA, dA_offset, ldda, dB, dB_offset, 1, queue));
} else {
chk(magma_ztrsm(MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit, n, nrhs, z_one, dA, dA_offset, ldda, dB, dB_offset, lddb, queue));
chk(magma_ztrsm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, nrhs, z_one, dA, dA_offset, ldda, dB, dB_offset, lddb, queue));
}
} else {
inc = -1;
/* Solve A' * X = B. */
if ( nrhs == 1) {
chk(magma_ztrsv(MagmaUpper, trans, MagmaNonUnit, n, dA, dA_offset, ldda, dB, dB_offset, 1, queue ));
chk(magma_ztrsv(MagmaLower, trans, MagmaUnit, n, dA, dA_offset, ldda, dB, dB_offset, 1, queue ));
} else {
chk(magma_ztrsm(MagmaLeft, MagmaUpper, trans, MagmaNonUnit, n, nrhs, z_one, dA, dA_offset, ldda, dB, dB_offset, lddb, queue));
chk(magma_ztrsm(MagmaLeft, MagmaLower, trans, MagmaUnit, n, nrhs, z_one, dA, dA_offset, ldda, dB, dB_offset, lddb, queue));
}
magma_zgetmatrix( n, nrhs, dB, dB_offset, lddb, work, 0, n, queue );
lapackf77_zlaswp(&nrhs, work, &n, &i1, &i2, ipiv, &inc);
magma_zsetmatrix( n, nrhs, work, 0, n, dB, dB_offset, lddb, queue );
}
free(work);
return *info;
}
/**
Purpose
=======
ZHETRF_nopiv_gpu computes the LDLt factorization of a complex Hermitian
matrix A.
The factorization has the form
A = U^H * D * U , if UPLO = 'U', or
A = L * D * L^H, if UPLO = 'L',
where U is an upper triangular matrix, L is lower triangular, and
D is a diagonal matrix.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
---------
@param[in]
UPLO CHARACTER*1
- = 'U': Upper triangle of A is stored;
- = 'L': Lower triangle of A is stored.
@param[in]
N INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
dA COMPLEX_16 array on the GPU, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U^H D U or A = L D L^H.
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using cudaMallocHost.
@param[in]
LDA INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
INFO INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
if INFO = -6, the GPU memory allocation failed
- > 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
@ingroup magma_zhetrf_comp
******************************************************************* */
extern "C" magma_int_t
magma_zhetrf_nopiv_gpu(
magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magma_int_t *info)
{
#define A(i, j) (A)
#define dA(i, j) (dA +(j)*ldda + (i))
#define dW(i, j) (dW +(j)*ldda + (i))
#define dWt(i, j) (dW +(j)*nb + (i))
/* Local variables */
magmaDoubleComplex zone = MAGMA_Z_ONE;
magmaDoubleComplex mzone = MAGMA_Z_NEG_ONE;
int upper = (uplo == MagmaUpper);
magma_int_t j, k, jb, nb, ib, iinfo;
*info = 0;
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return MAGMA_ERR_ILLEGAL_VALUE;
}
/* Quick return */
if ( n == 0 )
return MAGMA_SUCCESS;
nb = magma_get_zhetrf_nopiv_nb(n);
ib = min(32, nb); // inner-block for diagonal factorization
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
magma_queue_t stream[2];
magma_event_t event;
magma_queue_create(&stream[0]);
magma_queue_create(&stream[1]);
magma_event_create( &event );
trace_init( 1, 1, 2, stream );
// CPU workspace
magmaDoubleComplex *A;
if (MAGMA_SUCCESS != magma_zmalloc_pinned( &A, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
// GPU workspace
magmaDoubleComplex_ptr dW;
if (MAGMA_SUCCESS != magma_zmalloc( &dW, (1+nb)*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* Use hybrid blocked code. */
if (upper) {
//=========================================================
// Compute the LDLt factorization A = U'*D*U without pivoting.
// main loop
for (j=0; j<n; j += nb) {
jb = min(nb, (n-j));
// copy A(j,j) back to CPU
trace_gpu_start( 0, 0, "get", "get" );
//magma_queue_wait_event( stream[1], event );
magma_event_sync(event);
magma_zgetmatrix_async(jb, jb, dA(j, j), ldda, A(j,j), nb, stream[1]);
trace_gpu_end( 0, 0 );
// factorize the diagonal block
magma_queue_sync(stream[1]);
trace_cpu_start( 0, "potrf", "potrf" );
zhetrf_nopiv_cpu(MagmaUpper, jb, ib, A(j, j), nb, info);
trace_cpu_end( 0 );
if (*info != 0){
*info = *info + j;
break;
}
// copy A(j,j) back to GPU
trace_gpu_start( 0, 0, "set", "set" );
magma_zsetmatrix_async(jb, jb, A(j, j), nb, dA(j, j), ldda, stream[0]);
trace_gpu_end( 0, 0 );
if ( (j+jb) < n) {
// compute the off-diagonal blocks of current block column
magmablasSetKernelStream( stream[0] );
trace_gpu_start( 0, 0, "trsm", "trsm" );
magma_ztrsm(MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaUnit,
jb, (n-j-jb),
zone, dA(j, j), ldda,
dA(j, j+jb), ldda);
magma_zcopymatrix( jb, n-j-jb, dA( j, j+jb ), ldda, dWt( 0, j+jb ), nb );
// update the trailing submatrix with D
magmablas_zlascl_diag(MagmaUpper, jb, n-j-jb,
dA(j, j), ldda,
dA(j, j+jb), ldda,
&iinfo);
trace_gpu_end( 0, 0 );
// update the trailing submatrix with U and W
trace_gpu_start( 0, 0, "gemm", "gemm" );
for (k=j+jb; k<n; k+=nb) {
magma_int_t kb = min(nb,n-k);
magma_zgemm(MagmaConjTrans, MagmaNoTrans, kb, n-k, jb,
mzone, dWt(0, k), nb,
dA(j, k), ldda,
zone, dA(k, k), ldda);
if (k==j+jb)
magma_event_record( event, stream[0] );
}
trace_gpu_end( 0, 0 );
}
}
} else {
//=========================================================
// Compute the LDLt factorization A = L*D*L' without pivoting.
// main loop
for (j=0; j<n; j+=nb) {
jb = min(nb, (n-j));
// copy A(j,j) back to CPU
trace_gpu_start( 0, 0, "get", "get" );
//magma_queue_wait_event( stream[0], event );
magma_event_sync(event);
magma_zgetmatrix_async(jb, jb, dA(j, j), ldda, A(j,j), nb, stream[1]);
trace_gpu_end( 0, 0 );
// factorize the diagonal block
magma_queue_sync(stream[1]);
trace_cpu_start( 0, "potrf", "potrf" );
zhetrf_nopiv_cpu(MagmaLower, jb, ib, A(j, j), nb, info);
trace_cpu_end( 0 );
if (*info != 0){
*info = *info + j;
break;
}
// copy A(j,j) back to GPU
trace_gpu_start( 0, 0, "set", "set" );
magma_zsetmatrix_async(jb, jb, A(j, j), nb, dA(j, j), ldda, stream[0]);
trace_gpu_end( 0, 0 );
if ( (j+jb) < n) {
// compute the off-diagonal blocks of current block column
magmablasSetKernelStream( stream[0] );
trace_gpu_start( 0, 0, "trsm", "trsm" );
magma_ztrsm(MagmaRight, MagmaLower, MagmaConjTrans, MagmaUnit,
(n-j-jb), jb,
zone, dA(j, j), ldda,
dA(j+jb, j), ldda);
magma_zcopymatrix( n-j-jb,jb, dA( j+jb, j ), ldda, dW( j+jb, 0 ), ldda );
// update the trailing submatrix with D
magmablas_zlascl_diag(MagmaLower, n-j-jb, jb,
dA(j, j), ldda,
dA(j+jb, j), ldda,
&iinfo);
trace_gpu_end( 0, 0 );
// update the trailing submatrix with L and W
trace_gpu_start( 0, 0, "gemm", "gemm" );
for (k=j+jb; k<n; k+=nb) {
magma_int_t kb = min(nb,n-k);
magma_zgemm(MagmaNoTrans, MagmaConjTrans, n-k, kb, jb,
mzone, dA(k, j), ldda,
dW(k, 0), ldda,
zone, dA(k, k), ldda);
if (k==j+jb)
magma_event_record( event, stream[0] );
}
trace_gpu_end( 0, 0 );
}
}
}
trace_finalize( "zhetrf.svg","trace.css" );
magma_queue_destroy(stream[0]);
magma_queue_destroy(stream[1]);
magma_event_destroy( event );
magma_free( dW );
magma_free_pinned( A );
magmablasSetKernelStream( orig_stream );
return MAGMA_SUCCESS;
} /* magma_zhetrf_nopiv */
/**
Purpose
-------
ZGETRF 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.
This version assumes the computation runs through the NULL stream
and therefore is not overlapping 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 COMPLEX_16 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_zgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zgetrf2_gpu(magma_int_t m, magma_int_t n,
magmaDoubleComplex *dA, magma_int_t ldda,
magma_int_t *ipiv, magma_int_t *info)
{
#define dAT(i,j) (dAT + (i)*nb*lddat + (j)*nb)
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t iinfo, nb;
magma_int_t maxm, maxn, mindim;
magma_int_t i, rows, cols, s, lddat, lddwork;
magmaDoubleComplex *dAT, *dAP, *work;
/* 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);
nb = magma_get_zgetrf_nb(m);
s = mindim / nb;
if (nb <= 1 || nb >= min(m,n)) {
/* Use CPU code. */
magma_zmalloc_cpu( &work, m * n );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_zgetmatrix( m, n, dA, ldda, work, m );
lapackf77_zgetrf(&m, &n, work, &m, ipiv, info);
magma_zsetmatrix( m, n, work, m, dA, ldda );
magma_free_cpu(work);
}
else {
/* Use hybrid blocked code. */
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
lddat = maxn;
lddwork = maxm;
dAT = dA;
if (MAGMA_SUCCESS != magma_zmalloc( &dAP, nb*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if ( m == n ) {
lddat = ldda;
magmablas_ztranspose_inplace( m, dAT, ldda );
}
else {
if (MAGMA_SUCCESS != magma_zmalloc( &dAT, maxm*maxn )) {
magma_free( dAP );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmablas_ztranspose( m, n, dA, ldda, dAT, lddat );
}
if (MAGMA_SUCCESS != magma_zmalloc_pinned( &work, maxm*nb )) {
magma_free( dAP );
if ( ! (m == n))
magma_free( dAT );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
for( i=0; i < s; i++ ) {
// download i-th panel
cols = maxm - i*nb;
//magmablas_ztranspose( nb, cols, dAT(i,i), lddat, dAP, cols );
magmablas_ztranspose( nb, m-i*nb, dAT(i,i), lddat, dAP, cols );
magma_zgetmatrix( m-i*nb, nb, dAP, cols, work, lddwork );
// make sure that gpu queue is empty
magma_device_sync();
if ( i > 0 ) {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (i+1)*nb, nb,
c_one, dAT(i-1,i-1), lddat,
dAT(i-1,i+1), lddat );
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-i*nb, nb,
c_neg_one, dAT(i-1,i+1), lddat,
dAT(i, i-1), lddat,
c_one, dAT(i, i+1), lddat );
}
// do the cpu part
rows = m - i*nb;
lapackf77_zgetrf( &rows, &nb, work, &lddwork, ipiv+i*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + i*nb;
magmablas_zpermute_long2( n, dAT, lddat, ipiv, nb, i*nb );
// upload i-th panel
magma_zsetmatrix( m-i*nb, nb, work, lddwork, dAP, maxm );
//magmablas_ztranspose( cols, nb, dAP, maxm, dAT(i,i), lddat );
magmablas_ztranspose( m-i*nb, nb, dAP, maxm, dAT(i,i), lddat );
// do the small non-parallel computations (next panel update)
if ( s > (i+1) ) {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dAT(i, i ), lddat,
dAT(i, i+1), lddat);
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
nb, m-(i+1)*nb, nb,
c_neg_one, dAT(i, i+1), lddat,
dAT(i+1, i ), lddat,
c_one, dAT(i+1, i+1), lddat );
}
else {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, dAT(i, i ), lddat,
dAT(i, i+1), lddat);
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
n-(i+1)*nb, m-(i+1)*nb, nb,
c_neg_one, dAT(i, i+1), lddat,
dAT(i+1, i ), lddat,
c_one, dAT(i+1, i+1), lddat );
}
}
magma_int_t nb0 = min(m - s*nb, n - s*nb);
rows = m - s*nb;
cols = maxm - s*nb;
magmablas_ztranspose( nb0, rows, dAT(s,s), lddat, dAP, maxm );
magma_zgetmatrix( rows, nb0, dAP, maxm, work, lddwork );
// make sure that gpu queue is empty
magma_device_sync();
// do the cpu part
lapackf77_zgetrf( &rows, &nb0, work, &lddwork, ipiv+s*nb, &iinfo);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + s*nb;
magmablas_zpermute_long2( n, dAT, lddat, ipiv, nb0, s*nb );
// upload i-th panel
magma_zsetmatrix( rows, nb0, work, lddwork, dAP, maxm );
magmablas_ztranspose( rows, nb0, dAP, maxm, dAT(s,s), lddat );
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb-nb0, nb0,
c_one, dAT(s,s), lddat,
dAT(s,s)+nb0, lddat);
if ( m == n ) {
magmablas_ztranspose_inplace( m, dAT, lddat );
}
else {
magmablas_ztranspose( n, m, dAT, lddat, dA, ldda );
magma_free( dAT );
}
magma_free( dAP );
magma_free_pinned( work );
}
return *info;
} /* magma_zgetrf2_gpu */
/**
Purpose
-------
ZSSSSM applies the LU factorization update from a complex
matrix formed by a lower triangular IB-by-K tile L1 on top of a
M2-by-K tile L2 to a second complex matrix formed by a M1-by-N1
tile A1 on top of a M2-by-N2 tile A2 (N1 == N2).
This is the right-looking Level 2.5 BLAS version of the algorithm.
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]
ib INTEGER
The inner-blocking size. IB >= 0.
@param[in]
NB INTEGER
The blocking size. NB >= 0.
@param[in,out]
hU COMPLEX_16 array, dimension(LDHU, N), on cpu.
On entry, the NB-by-N upper triangular tile hU.
On exit, the content is incomplete. Shouldn't be used.
@param[in]
ldhu INTEGER
The leading dimension of the array hU. LDHU >= max(1,NB).
@param[in,out]
dU COMPLEX_16 array, dimension(LDDU, N), on gpu.
On entry, the NB-by-N upper triangular tile dU identical to hU.
On exit, the new factor U from the factorization.
@param[in]
lddu INTEGER
The leading dimension of the array dU. LDDU >= max(1,NB).
@param[in,out]
hA COMPLEX_16 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.
@param[in]
ldha INTEGER
The leading dimension of the array hA. LDHA >= max(1,M).
@param[in,out]
dA COMPLEX_16 array, dimension(LDDA, N), on gpu.
On entry, the M-by-N tile to be factored.
On exit, the factor L from the factorization
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
@param[out]
hL COMPLEX_16 array, dimension(LDHL, K), on vpu.
On exit, contains in the upper part the IB-by-K lower triangular tile,
and in the lower part IB-by-K the inverse of the top part.
@param[in]
ldhl INTEGER
The leading dimension of the array hL. LDHL >= max(1,2*IB).
@param[out]
dL COMPLEX_16 array, dimension(LDDL, K), on gpu.
On exit, contains in the upper part the IB-by-K lower triangular tile,
and in the lower part IB-by-K the inverse of the top part.
@param[in]
lddl INTEGER
The leading dimension of the array dL. LDDL >= max(1,2*IB).
@param[out]
hWORK COMPLEX_16 array, dimension(LDHWORK, 2*IB), on cpu.
Workspace.
@param[in]
ldhwork INTEGER
The leading dimension of the array hWORK. LDHWORK >= max(NB, 1).
@param[out]
dWORK COMPLEX_16 array, dimension(LDDWORK, 2*IB), on gpu.
Workspace.
@param[in]
lddwork INTEGER
The leading dimension of the array dWORK. LDDWORK >= max(NB, 1).
@param[out]
ipiv INTEGER array on the cpu.
The pivot indices array of size K as returned by ZTSTRF
@param[out]
info 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.
@ingroup magma_zgesv_tile
********************************************************************/
extern "C" magma_int_t
magma_ztstrf_gpu(
magma_order_t order, magma_int_t m, magma_int_t n,
magma_int_t ib, magma_int_t nb,
magmaDoubleComplex *hU, magma_int_t ldhu,
magmaDoubleComplex_ptr dU, magma_int_t lddu,
magmaDoubleComplex *hA, magma_int_t ldha,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magmaDoubleComplex *hL, magma_int_t ldhl,
magmaDoubleComplex_ptr dL, magma_int_t lddl,
magma_int_t *ipiv,
magmaDoubleComplex *hwork, magma_int_t ldhwork,
magmaDoubleComplex_ptr dwork, magma_int_t lddwork,
magma_int_t *info)
{
#define UT(i,j) (dUT + (i)*ib*lddu + (j)*ib )
#define AT(i,j) (dAT + (i)*ib*ldda + (j)*ib )
#define L(i) (dL + (i)*ib*lddl )
#define L2(i) (dL2 + (i)*ib*lddl )
#define hU(i,j) (hU + (j)*ib*ldhu + (i)*ib )
#define hA(i,j) (hA + (j)*ib*ldha + (i)*ib )
#define hL(i) (hL + (i)*ib*ldhl )
#define hL2(i) (hL2 + (i)*ib*ldhl )
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
int iinfo = 0;
int maxm, mindim;
int i, j, im, s, ip, ii, sb, p = 1;
magmaDoubleComplex_ptr dAT, dUT;
magmaDoubleComplex_ptr dAp, dUp;
#ifndef WITHOUTTRTRI
magmaDoubleComplex_ptr dL2 = dL + ib;
magmaDoubleComplex *hL2 = hL + ib;
p = 2;
#endif
/* Check input arguments */
*info = 0;
if (m < 0) {
*info = -1;
}
else if (n < 0) {
*info = -2;
}
else if (ib < 0) {
*info = -3;
}
else if ((lddu < max(1,m)) && (m > 0)) {
*info = -6;
}
else if ((ldda < max(1,m)) && (m > 0)) {
*info = -8;
}
else if ((lddl < max(1,ib)) && (ib > 0)) {
*info = -10;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* quick return */
if ((m == 0) || (n == 0) || (ib == 0))
return *info;
ip = 0;
/* Function Body */
mindim = min(m, n);
s = mindim / ib;
if ( ib >= mindim ) {
/* Use CPU code. */
CORE_ztstrf(m, n, ib, nb,
(PLASMA_Complex64_t*)hU, ldhu,
(PLASMA_Complex64_t*)hA, ldha,
(PLASMA_Complex64_t*)hL, ldhl,
ipiv,
(PLASMA_Complex64_t*)hwork, ldhwork,
info);
#ifndef WITHOUTTRTRI
CORE_zlacpy( PlasmaUpperLower, mindim, mindim,
(PLASMA_Complex64_t*)hL, ldhl,
(PLASMA_Complex64_t*)hL2, ldhl );
CORE_ztrtri( PlasmaLower, PlasmaUnit, mindim,
(PLASMA_Complex64_t*)hL2, ldhl, info );
if (*info != 0 ) {
fprintf(stderr, "ERROR, trtri returned with info = %d\n", *info);
}
#endif
if ( order == MagmaRowMajor ) {
magma_zsetmatrix( m, n, hU, ldhu, dwork, lddwork );
magmablas_ztranspose( m, n, dwork, lddwork, dU, lddu );
magma_zsetmatrix( m, n, hA, ldha, dwork, lddwork );
magmablas_ztranspose( m, n, dwork, lddwork, dA, ldda );
} else {
magma_zsetmatrix( m, n, hU, ldhu, dU, lddu );
magma_zsetmatrix( m, n, hA, ldha, dA, ldda );
}
magma_zsetmatrix( p*ib, n, hL, ldhl, dL, lddl );
}
else {
/* Use hybrid blocked code. */
maxm = magma_roundup( m, 32 );
if ( order == MagmaColMajor ) {
magmablas_zgetmo_in( dU, dUT, lddu, m, n );
magmablas_zgetmo_in( dA, dAT, ldda, m, n );
} else {
dUT = dU; dAT = dA;
}
dAp = dwork;
dUp = dAp + ib*lddwork;
ip = 0;
for( i=0; i < s; i++ ) {
ii = i * ib;
sb = min(mindim-ii, ib);
if ( i > 0 ) {
// download i-th panel
magmablas_ztranspose( sb, ii, UT(0,i), lddu, dUp, lddu );
magmablas_ztranspose( sb, m, AT(0,i), ldda, dAp, ldda );
magma_zgetmatrix( ii, sb, dUp, lddu, hU(0, i), ldhu );
magma_zgetmatrix( m, sb, dAp, ldda, hA(0, i), ldha );
// make sure that gpu queue is empty
//magma_device_sync();
#ifndef WITHOUTTRTRI
magma_ztrmm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n-(ii+sb), ib,
c_one, L2(i-1), lddl,
UT(i-1, i+1), lddu);
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n-(ii+sb), ib,
c_one, L(i-1), lddl,
UT(i-1, i+1), lddu);
#endif
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
n-(ii+sb), m, ib,
c_neg_one, UT(i-1, i+1), lddu,
AT(0, i-1), ldda,
c_one, AT(0, i+1), ldda );
}
// do the cpu part
CORE_ztstrf(m, sb, ib, nb,
(PLASMA_Complex64_t*)hU(i, i), ldhu,
(PLASMA_Complex64_t*)hA(0, i), ldha,
(PLASMA_Complex64_t*)hL(i), ldhl,
ipiv+ii,
(PLASMA_Complex64_t*)hwork, ldhwork,
info);
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + ii;
// Need to swap betw U and A
#ifndef NOSWAPBLK
magmablas_zswapblk( MagmaRowMajor, n-(ii+sb),
UT(i, i+1), lddu,
AT(0, i+1), ldda,
1, sb, ipiv+ii, 1, nb );
for (j=0; j < ib; j++) {
im = ipiv[ip]-1;
if ( im == j ) {
ipiv[ip] += ii;
}
ip++;
}
#else
for (j=0; j < ib; j++) {
im = ipiv[ip]-1;
if ( im != (j) ) {
im = im - nb;
assert( (im >= 0) && (im < m) );
magmablas_zswap( n-(ii+sb), UT(i, i+1)+j*lddu, 1, AT(0, i+1)+im*ldda, 1 );
} else {
ipiv[ip] += ii;
}
ip++;
}
#endif
#ifndef WITHOUTTRTRI
CORE_zlacpy( PlasmaUpperLower, sb, sb,
(PLASMA_Complex64_t*)hL(i), ldhl,
(PLASMA_Complex64_t*)hL2(i), ldhl );
CORE_ztrtri( PlasmaLower, PlasmaUnit, sb,
(PLASMA_Complex64_t*)hL2(i), ldhl, info );
if (*info != 0 ) {
fprintf(stderr, "ERROR, trtri returned with info = %d\n", *info);
}
#endif
// upload i-th panel
magma_zsetmatrix( sb, sb, hU(i, i), ldhu, dUp, lddu );
magma_zsetmatrix( m, sb, hA(0, i), ldha, dAp, ldda );
magma_zsetmatrix( p*ib, sb, hL(i), ldhl, L(i), lddl );
magmablas_ztranspose( sb, sb, dUp, lddu, UT(i,i), lddu );
magmablas_ztranspose( m, sb, dAp, ldda, AT(0,i), ldda );
// make sure that gpu queue is empty
//magma_device_sync();
// do the small non-parallel computations
if ( s > (i+1) ) {
#ifndef WITHOUTTRTRI
magma_ztrmm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
sb, sb,
c_one, L2(i), lddl,
UT(i, i+1), lddu);
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
sb, sb,
c_one, L(i), lddl,
UT(i, i+1), lddu);
#endif
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
sb, m, sb,
c_neg_one, UT(i, i+1), lddu,
AT(0, i ), ldda,
c_one, AT(0, i+1), ldda );
}
else {
#ifndef WITHOUTTRTRI
magma_ztrmm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n-mindim, sb,
c_one, L2(i), lddl,
UT(i, i+1), lddu);
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n-mindim, sb,
c_one, L(i), lddl,
UT(i, i+1), lddu);
#endif
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
n-mindim, m, sb,
c_neg_one, UT(i, i+1), lddu,
AT(0, i ), ldda,
c_one, AT(0, i+1), ldda );
}
}
if ( order == MagmaColMajor ) {
magmablas_zgetmo_out( dU, dUT, lddu, m, n );
magmablas_zgetmo_out( dA, dAT, ldda, m, n );
}
}
return *info;
}
extern "C" magma_int_t
magma_zpotrs_gpu(char uplo, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex *dA, magma_int_t ldda,
magmaDoubleComplex *dB, magma_int_t lddb, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZPOTRS solves a system of linear equations A*X = B with a Hermitian
positive definite matrix A using the Cholesky factorization
A = U**H*U or A = L*L**H computed by ZPOTRF.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
dA (input) COMPLEX_16 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 ZPOTRF.
LDDA (input) INTEGER
The leading dimension of the array A. LDDA >= max(1,N).
dB (input/output) COMPLEX_16 array on the GPU, dimension (LDDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDDB (input) INTEGER
The leading dimension of the array B. LDDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
magmaDoubleComplex c_one = MAGMA_Z_ONE;
*info = 0 ;
if( (uplo != 'U') && (uplo != 'u') && (uplo != 'L') && (uplo != 'l') )
*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;
}
if( (uplo=='U') || (uplo=='u') ){
if ( nrhs == 1) {
magma_ztrsv(MagmaUpper, MagmaConjTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
magma_ztrsv(MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
} else {
magma_ztrsm(MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb);
magma_ztrsm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb);
}
}
else{
if ( nrhs == 1) {
magma_ztrsv(MagmaLower, MagmaNoTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
magma_ztrsv(MagmaLower, MagmaConjTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
} else {
magma_ztrsm(MagmaLeft, MagmaLower, MagmaNoTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb);
magma_ztrsm(MagmaLeft, MagmaLower, MagmaConjTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb);
}
}
return *info;
}
/**
Purpose
-------
ZGETRF_NOPIV_GPU computes an LU factorization of a general M-by-N
matrix A without any pivoting.
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]
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 COMPLEX_16 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]
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_zgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zgetrf_nopiv_gpu(magma_int_t m, magma_int_t n,
magmaDoubleComplex *dA, magma_int_t ldda,
magma_int_t *info)
{
#define dA(i,j) (dA + (i)*nb + (j)*nb*ldda)
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t iinfo, nb;
magma_int_t maxm, maxn, mindim;
magma_int_t i, rows, cols, s, lddwork;
magmaDoubleComplex *work;
/* 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);
nb = magma_get_zgetrf_nb(m);
s = mindim / nb;
if (nb <= 1 || nb >= min(m,n)) {
/* Use CPU code. */
magma_zmalloc_cpu( &work, m * n );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_zgetmatrix( m, n, dA, ldda, work, m );
magma_zgetrf_nopiv( m, n, work, m, info);
magma_zsetmatrix( m, n, work, m, dA, ldda );
magma_free_cpu(work);
}
else {
/* Use hybrid blocked code. */
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
lddwork = maxm;
if (MAGMA_SUCCESS != magma_zmalloc_pinned( &work, maxm*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
/* 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( i=0; i < s; i++ ) {
// download i-th panel
cols = maxm - i*nb;
magma_queue_sync( stream[1] );
magma_zgetmatrix_async( m-i*nb, nb, dA(i,i), ldda, work, lddwork, stream[0] );
if ( i > 0 ) {
magma_ztrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit,
nb, n - (i+1)*nb,
c_one, dA(i-1,i-1), ldda,
dA(i-1,i+1), ldda );
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
m-i*nb, n-(i+1)*nb, nb,
c_neg_one, dA(i, i-1), ldda, dA(i-1,i+1), ldda,
c_one, dA(i, i+1), ldda );
}
// do the cpu part
rows = m - i*nb;
magma_queue_sync( stream[0] );
magma_zgetrf_nopiv( rows, nb, work, lddwork, &iinfo );
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + i*nb;
// upload i-th panel
magma_zsetmatrix_async( m-i*nb, nb, work, lddwork, dA(i, i), ldda, stream[0] );
magma_queue_sync( stream[0] );
// do the small non-parallel computations
if ( s > (i+1) ) {
magma_ztrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dA(i, i ), ldda,
dA(i, i+1), ldda);
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
m-(i+1)*nb, nb, nb,
c_neg_one, dA(i+1, i ), ldda, dA(i, i+1), ldda,
c_one, dA(i+1, i+1), ldda );
}
else {
magma_ztrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit,
nb, n-s*nb,
c_one, dA(i, i ), ldda,
dA(i, i+1), ldda);
magma_zgemm( MagmaNoTrans, MagmaNoTrans,
m-(i+1)*nb, n-(i+1)*nb, nb,
c_neg_one, dA(i+1, i ), ldda, dA(i, i+1), ldda,
c_one, dA(i+1, i+1), ldda );
}
}
magma_int_t nb0 = min(m - s*nb, n - s*nb);
rows = m - s*nb;
cols = maxm - s*nb;
magma_zgetmatrix( rows, nb0, dA(s,s), ldda, work, lddwork );
// make sure that gpu queue is empty
magma_device_sync();
// do the cpu part
magma_zgetrf_nopiv( rows, nb0, work, lddwork, &iinfo );
if ( (*info == 0) && (iinfo > 0) )
*info = iinfo + s*nb;
// upload i-th panel
magma_zsetmatrix( rows, nb0, work, lddwork, dA(s,s), ldda );
magma_ztrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit,
nb0, n-s*nb-nb0,
c_one, dA(s,s), ldda,
dA(s,s)+nb0, ldda);
magma_free_pinned( work );
magma_queue_destroy( stream[0] );
if (orig_stream == NULL) {
magma_queue_destroy( stream[1] );
}
magmablasSetKernelStream( orig_stream );
}
return *info;
} /* magma_zgetrf_nopiv_gpu */
/**
Purpose
-------
ZSSSSM applies the LU factorization update from a complex
matrix formed by a lower triangular IB-by-K tile L1 on top of a
M2-by-K tile L2 to a second complex matrix formed by a M1-by-N1
tile A1 on top of a M2-by-N2 tile A2 (N1 == N2).
This is the right-looking Level 2.5 BLAS version of the algorithm.
Arguments
---------
@param[in]
m1 INTEGER
The number of rows of the matrix A1. M1 >= 0.
@param[in]
n1 INTEGER
The number of columns of the matrix A1. N1 >= 0.
@param[in]
m2 INTEGER
The number of rows of the matrix A2. M2 >= 0.
@param[in]
n2 INTEGER
The number of columns of the matrix A2. N2 >= 0.
@param[in]
k INTEGER
The number of columns of the matrix L1 and L2. K >= 0.
@param[in]
ib INTEGER
The inner-blocking size. IB >= 0.
@param[in,out]
dA1 COMPLEX_16 array, dimension(LDDA1, N), on gpu.
On entry, the M1-by-N1 tile dA1.
On exit, dA1 is updated by the application of dL (dL1 dL2).
@param[in]
ldda1 INTEGER
The leading dimension of the array dA1. LDDA1 >= max(1,M1).
@param[in,out]
dA2 COMPLEX_16 array, dimension(LDDA2, N), on gpu.
On entry, the M2-by-N2 tile dA2.
On exit, dA2 is updated by the application of dL (dL1 dL2).
@param[in]
ldda2 INTEGER
The leading dimension of the array dA2. LDDA2 >= max(1,M2).
@param[in]
dL1 COMPLEX_16 array, dimension(LDDL1, K), on gpu.
The inverse of the IB-by-K lower triangular tile as returned by
ZTSTRF.
@param[in]
lddl1 INTEGER
The leading dimension of the array L1. LDDL1 >= max(1,2*IB).
@param[in]
dL2 COMPLEX_16 array, dimension(LDDL2, K)
The M2-by-K tile as returned by ZTSTRF.
@param[in]
lddl2 INTEGER
The leading dimension of the array L2. LDDL2 >= max(1,M2).
@param[in]
ipiv INTEGER array on the cpu.
The pivot indices array of size K as returned by ZTSTRF
@ingroup magma_zgesv_tile
********************************************************************/
extern "C" magma_int_t
magma_zssssm_gpu(
magma_order_t order, magma_int_t m1, magma_int_t n1,
magma_int_t m2, magma_int_t n2, magma_int_t k, magma_int_t ib,
magmaDoubleComplex_ptr dA1, magma_int_t ldda1,
magmaDoubleComplex_ptr dA2, magma_int_t ldda2,
magmaDoubleComplex_ptr dL1, magma_int_t lddl1,
magmaDoubleComplex_ptr dL2, magma_int_t lddl2,
magma_int_t *ipiv,
magma_int_t *info)
{
#define A1T(i,j) (dA1T + (i)*ldda1 + (j))
#define A2T(i,j) (dA2T + (i)*ldda2 + (j))
#define L1(i) (dL1 + (i)*lddl1 )
#define L2(i,j) (dL2 + (i)*lddl2i + (j)*lddl2j)
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
int ip, ii, sb;
magmaDoubleComplex_ptr dA1T, dA2T;
magma_trans_t transL;
int lddl2i, lddl2j;
MAGMA_UNUSED( ip ); // used only if NOSWAPBLK
/* Check input arguments */
*info = 0;
if (m1 < 0) {
*info = -1;
}
else if (n1 < 0) {
*info = -2;
}
else if (m2 < 0) {
*info = -3;
}
else if (n2 < 0) {
*info = -4;
}
else if (k < 0) {
*info = -5;
}
else if (ib < 0) {
*info = -6;
}
else if (ldda1 < max(1,m1)) {
*info = -8;
}
else if (ldda2 < max(1,m2)) {
*info = -10;
}
else if (lddl1 < max(1,ib)) {
*info = -12;
}
else if (lddl2 < max(1,m2)) {
*info = -14;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return */
if ((m1 == 0) || (n1 == 0) || (m2 == 0) || (n2 == 0) || (k == 0) || (ib == 0))
return *info;
if ( order == MagmaColMajor ) {
magmablas_zgetmo_in( dA1, dA1T, ldda1, m1, n1 );
magmablas_zgetmo_in( dA2, dA2T, ldda2, m2, n2 );
transL = MagmaTrans;
lddl2i = 1; lddl2j = lddl2;
} else {
dA1T = dA1;
dA2T = dA2;
transL = MagmaNoTrans;
lddl2i = lddl2; lddl2j = 1;
}
ip = 0;
for( ii=0; ii < k; ii += ib ) {
sb = min( k-ii, ib);
#ifndef NOSWAPBLK
magmablas_zswapblk( MagmaRowMajor, n1,
A1T(0, 0), ldda1,
A2T(0, 0), ldda2,
ii+1, ii+ib, ipiv, 1, m1 );
#else
{
int im;
for (i=0; i < ib; i++) {
im = ipiv[ip]-1;
if (im != (ii+i)) {
im = im - m1;
assert( (im >= 0) && (im < m1) && (im < m2) );
magmablas_zswap( n1, A1T(ii+i, 0), 1, A2T(im, 0), 1 );
}
ip++;
}
}
#endif
#ifndef WITHOUTTRTRI
/* Lower, Trans, because L1 is not transposed */
magma_ztrmm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n1, sb,
c_one, L1( ii), lddl1,
A1T(ii, 0), ldda1);
#else
/* Lower, Trans, because L1 is not transposed */
magma_ztrsm( MagmaRight, MagmaLower, MagmaTrans, MagmaUnit,
n1, sb,
c_one, L1( ii), lddl1,
A1T(ii, 0), ldda1);
#endif
/* Second parameter is trans because L2 is not transposed */
magma_zgemm( MagmaNoTrans, transL,
n2, m2, sb,
c_neg_one, A1T(ii, 0), ldda1,
L2( 0, ii), lddl2,
c_one, A2T(0, 0 ), ldda2 );
}
if ( order == MagmaColMajor ) {
magmablas_zgetmo_out( dA1, dA1T, ldda1, m1, n1 );
magmablas_zgetmo_out( dA2, dA2T, ldda2, m2, n2 );
}
return *info;
}
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, t1, t2;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t ione = 1;
magma_trans_t trans[] = { MagmaNoTrans, MagmaConjTrans, MagmaTrans };
magma_uplo_t uplo [] = { MagmaLower, MagmaUpper };
magma_diag_t diag [] = { MagmaUnit, MagmaNonUnit };
magma_side_t side [] = { MagmaLeft, MagmaRight };
magmaDoubleComplex *A, *B, *C, *C2, *LU;
magmaDoubleComplex *dA, *dB, *dC1, *dC2;
magmaDoubleComplex alpha = MAGMA_Z_MAKE( 0.5, 0.1 );
magmaDoubleComplex beta = MAGMA_Z_MAKE( 0.7, 0.2 );
double dalpha = 0.6;
double dbeta = 0.8;
double work[1], error, total_error;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t m, n, k, size, maxn, ld, info;
magma_int_t *piv;
magma_int_t err;
magma_opts opts;
parse_opts( argc, argv, &opts );
printf( "Compares magma wrapper function to cublas function; all diffs should be exactly 0.\n\n" );
total_error = 0.;
for( int itest = 0; itest < opts.ntest; ++itest ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
printf("=========================================================================\n");
printf( "m=%d, n=%d, k=%d\n", (int) m, (int) n, (int) k );
// allocate matrices
// over-allocate so they can be any combination of {m,n,k} x {m,n,k}.
maxn = max( max( m, n ), k );
ld = max( 1, maxn );
size = ld*maxn;
err = magma_malloc_cpu( (void**) &piv, maxn*sizeof(magma_int_t) ); assert( err == 0 );
err = magma_zmalloc_pinned( &A, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &B, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &C, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &C2, size ); assert( err == 0 );
err = magma_zmalloc_pinned( &LU, size ); assert( err == 0 );
err = magma_zmalloc( &dA, size ); assert( err == 0 );
err = magma_zmalloc( &dB, size ); assert( err == 0 );
err = magma_zmalloc( &dC1, size ); assert( err == 0 );
err = magma_zmalloc( &dC2, size ); assert( err == 0 );
// initialize matrices
size = maxn*maxn;
lapackf77_zlarnv( &ione, ISEED, &size, A );
lapackf77_zlarnv( &ione, ISEED, &size, B );
lapackf77_zlarnv( &ione, ISEED, &size, C );
printf( "========== Level 1 BLAS ==========\n" );
// ----- test ZSWAP
// swap columns 2 and 3 of dA, then copy to C2 and compare with A
if ( n >= 3 ) {
magma_zsetmatrix( m, n, A, ld, dA, ld );
magma_zsetmatrix( m, n, A, ld, dB, ld );
magma_zswap( m, dA(0,1), 1, dA(0,2), 1 );
magma_zswap( m, dB(0,1), 1, dB(0,2), 1 );
// check results, storing diff between magma and cuda calls in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dA, 1, dB, 1 );
magma_zgetmatrix( m, n, dB, ld, C2, ld );
error = lapackf77_zlange( "F", &m, &k, C2, &ld, work );
total_error += error;
printf( "zswap diff %.2g\n", error );
}
else {
printf( "zswap skipped for n < 3\n" );
}
// ----- test IZAMAX
// get argmax of column of A
magma_zsetmatrix( m, k, A, ld, dA, ld );
error = 0;
for( int j = 0; j < k; ++j ) {
magma_int_t i1 = magma_izamax( m, dA(0,j), 1 );
int i2; // NOT magma_int_t, for cublas
cublasIzamax( handle, m, dA(0,j), 1, &i2 );
// todo need sync here?
assert( i1 == i2 );
error += abs( i1 - i2 );
}
total_error += error;
gflops = (double)m * k / 1e9;
printf( "izamax diff %.2g\n", error );
printf( "\n" );
printf( "========== Level 2 BLAS ==========\n" );
// ----- test ZGEMV
// c = alpha*A*b + beta*c, with A m*n; b,c m or n-vectors
// try no-trans/trans
for( int ia = 0; ia < 3; ++ia ) {
magma_zsetmatrix( m, n, A, ld, dA, ld );
magma_zsetvector( maxn, B, 1, dB, 1 );
magma_zsetvector( maxn, C, 1, dC1, 1 );
magma_zsetvector( maxn, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_zgemv( trans[ia], m, n, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZgemv( handle, cublas_trans_const(trans[ia]),
m, n, &alpha, dA, ld, dB, 1, &beta, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
size = (trans[ia] == MagmaNoTrans ? m : n);
cublasZaxpy( handle, size, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetvector( size, dC2, 1, C2, 1 );
error = lapackf77_zlange( "F", &size, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZGEMV( m, n ) / 1e9;
printf( "zgemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test ZHEMV
// c = alpha*A*b + beta*c, with A m*m symmetric; b,c m-vectors
// try upper/lower
for( int iu = 0; iu < 2; ++iu ) {
magma_zsetmatrix( m, m, A, ld, dA, ld );
magma_zsetvector( m, B, 1, dB, 1 );
magma_zsetvector( m, C, 1, dC1, 1 );
magma_zsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_zhemv( uplo[iu], m, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZhemv( handle, cublas_uplo_const(uplo[iu]),
m, &alpha, dA, ld, dB, 1, &beta, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_zlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHEMV( m ) / 1e9;
printf( "zhemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test ZTRSV
// solve A*c = c, with A m*m triangular; c m-vector
// try upper/lower, no-trans/trans, unit/non-unit diag
// Factor A into LU to get well-conditioned triangles, else solve yields garbage.
// Still can give garbage if solves aren't consistent with LU factors,
// e.g., using unit diag for U, so copy lower triangle to upper triangle.
// Also used for trsm later.
lapackf77_zlacpy( "Full", &maxn, &maxn, A, &ld, LU, &ld );
lapackf77_zgetrf( &maxn, &maxn, LU, &ld, piv, &info );
for( int j = 0; j < maxn; ++j ) {
for( int i = 0; i < j; ++i ) {
*LU(i,j) = *LU(j,i);
}
}
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
magma_zsetmatrix( m, m, LU, ld, dA, ld );
magma_zsetvector( m, C, 1, dC1, 1 );
magma_zsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_ztrsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZtrsv( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
cublas_diag_const(diag[id]), m, dA, ld, dC2, 1 );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_zlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZTRSM( MagmaLeft, m, 1 ) / 1e9;
printf( "ztrsv( %c, %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]), lapacke_diag_const(diag[id]),
error, gflops/t1, gflops/t2 );
}}}
printf( "\n" );
printf( "========== Level 3 BLAS ==========\n" );
// ----- test ZGEMM
// C = alpha*A*B + beta*C, with A m*k or k*m; B k*n or n*k; C m*n
// try combinations of no-trans/trans
for( int ia = 0; ia < 3; ++ia ) {
for( int ib = 0; ib < 3; ++ib ) {
bool nta = (trans[ia] == MagmaNoTrans);
bool ntb = (trans[ib] == MagmaNoTrans);
magma_zsetmatrix( (nta ? m : k), (nta ? m : k), A, ld, dA, ld );
magma_zsetmatrix( (ntb ? k : n), (ntb ? n : k), B, ld, dB, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zgemm( trans[ia], trans[ib], m, n, k, alpha, dA, ld, dB, ld, beta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZgemm( handle, cublas_trans_const(trans[ia]), cublas_trans_const(trans[ib]),
m, n, k, &alpha, dA, ld, dB, ld, &beta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZGEMM( m, n, k ) / 1e9;
printf( "zgemm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), lapacke_trans_const(trans[ib]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZHEMM
// C = alpha*A*B + beta*C (left) with A m*m symmetric; B,C m*n; or
// C = alpha*B*A + beta*C (right) with A n*n symmetric; B,C m*n
// try left/right, upper/lower
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
magma_zsetmatrix( m, m, A, ld, dA, ld );
magma_zsetmatrix( m, n, B, ld, dB, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zhemm( side[is], uplo[iu], m, n, alpha, dA, ld, dB, ld, beta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZhemm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
m, n, &alpha, dA, ld, dB, ld, &beta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHEMM( side[is], m, n ) / 1e9;
printf( "zhemm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_side_const(side[is]), lapacke_uplo_const(uplo[iu]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZHERK
// C = alpha*A*A^H + beta*C (no-trans) with A m*k and C m*m symmetric; or
// C = alpha*A^H*A + beta*C (trans) with A k*m and C m*m symmetric
// try upper/lower, no-trans/trans
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
magma_zsetmatrix( n, k, A, ld, dA, ld );
magma_zsetmatrix( n, n, C, ld, dC1, ld );
magma_zsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zherk( uplo[iu], trans[it], n, k, dalpha, dA, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZherk( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
n, k, &dalpha, dA, ld, &dbeta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHERK( k, n ) / 1e9;
printf( "zherk( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZHER2K
// C = alpha*A*B^H + ^alpha*B*A^H + beta*C (no-trans) with A,B n*k; C n*n symmetric; or
// C = alpha*A^H*B + ^alpha*B^H*A + beta*C (trans) with A,B k*n; C n*n symmetric
// try upper/lower, no-trans/trans
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
bool nt = (trans[it] == MagmaNoTrans);
magma_zsetmatrix( (nt ? n : k), (nt ? n : k), A, ld, dA, ld );
magma_zsetmatrix( n, n, C, ld, dC1, ld );
magma_zsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_zher2k( uplo[iu], trans[it], n, k, alpha, dA, ld, dB, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZher2k( handle, cublas_uplo_const(uplo[iu]), cublas_trans_const(trans[it]),
n, k, &alpha, dA, ld, dB, ld, &dbeta, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZHER2K( k, n ) / 1e9;
printf( "zher2k( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}
printf( "\n" );
// ----- test ZTRMM
// C = alpha*A*C (left) with A m*m triangular; C m*n; or
// C = alpha*C*A (right) with A n*n triangular; C m*n
// try left/right, upper/lower, no-trans/trans, unit/non-unit
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
bool left = (side[is] == MagmaLeft);
magma_zsetmatrix( (left ? m : n), (left ? m : n), A, ld, dA, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ztrmm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
// note cublas does trmm out-of-place (i.e., adds output matrix C),
// but allows C=B to do in-place.
t2 = magma_sync_wtime( 0 );
cublasZtrmm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
cublas_trans_const(trans[it]), cublas_diag_const(diag[id]),
m, n, &alpha, dA, ld, dC2, ld, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZTRMM( side[is], m, n ) / 1e9;
printf( "ztrmm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}}}
printf( "\n" );
// ----- test ZTRSM
// solve A*X = alpha*B (left) with A m*m triangular; B m*n; or
// solve X*A = alpha*B (right) with A n*n triangular; B m*n
// try left/right, upper/lower, no-trans/trans, unit/non-unit
for( int is = 0; is < 2; ++is ) {
for( int iu = 0; iu < 2; ++iu ) {
for( int it = 0; it < 3; ++it ) {
for( int id = 0; id < 2; ++id ) {
bool left = (side[is] == MagmaLeft);
magma_zsetmatrix( (left ? m : n), (left ? m : n), LU, ld, dA, ld );
magma_zsetmatrix( m, n, C, ld, dC1, ld );
magma_zsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ztrsm( side[is], uplo[iu], trans[it], diag[id], m, n, alpha, dA, ld, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasZtrsm( handle, cublas_side_const(side[is]), cublas_uplo_const(uplo[iu]),
cublas_trans_const(trans[it]), cublas_diag_const(diag[id]),
m, n, &alpha, dA, ld, dC2, ld );
t2 = magma_sync_wtime( 0 ) - t2;
// check results, storing diff between magma and cuda call in C2
cublasZaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_zgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_zlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_ZTRSM( side[is], m, n ) / 1e9;
printf( "ztrsm( %c, %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), lapacke_trans_const(trans[it]),
error, gflops/t1, gflops/t2 );
}}}}
printf( "\n" );
// cleanup
magma_free_cpu( piv );
magma_free_pinned( A );
magma_free_pinned( B );
magma_free_pinned( C );
magma_free_pinned( C2 );
magma_free_pinned( LU );
magma_free( dA );
magma_free( dB );
magma_free( dC1 );
magma_free( dC2 );
fflush( stdout );
}
if ( total_error != 0. ) {
printf( "total error %.2g -- ought to be 0 -- some test failed (see above).\n",
total_error );
}
else {
printf( "all tests passed\n" );
}
TESTING_FINALIZE();
int status = (total_error != 0.);
return status;
}
extern "C" magma_int_t
magma_zpotrf2_mgpu(int num_gpus, char uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaDoubleComplex **d_lA, magma_int_t ldda,
magmaDoubleComplex **d_lP, magma_int_t lddp,
magmaDoubleComplex *a, magma_int_t lda, magma_int_t h,
magma_queue_t stream[][3], magma_event_t event[][5],
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
magma_int_t j, jb, nb0, nb2, dd, d, id, j_local, j_local2, buf;
char uplo_[2] = {uplo, 0};
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
double d_one = 1.0;
double d_neg_one = -1.0;
int upper = lapackf77_lsame(uplo_, "U");
magmaDoubleComplex *dlpanel;
//magma_event_t event0[MagmaMaxGPUs], // syrk
// event1[MagmaMaxGPUs], // send off-diagonal
// event2[MagmaMaxGPUs], // send diagonal
// event3[MagmaMaxGPUs]; // trsm
magma_int_t n_local[MagmaMaxGPUs], ldpanel;
int stream0 = 0, stream1 = 1;
#ifdef ZTRSM_WORK
magmaDoubleComplex *d_dinvA[MagmaMaxGPUs][2], *d_x[MagmaMaxGPUs][2]; /* used by ztrsm_work */
#endif
*info = 0;
if ( (! upper) && (! lapackf77_lsame(uplo_, "L")) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (!upper && num_gpus*ldda < max(1,n)) {
*info = -4;
} else if (upper && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
for( d=0; d<num_gpus; d++ ) {
/* local-n and local-ld */
if (upper) {
n_local[d] = ((n/nb)/num_gpus)*nb;
if (d < (n/nb)%num_gpus)
n_local[d] += nb;
else if (d == (n/nb)%num_gpus)
n_local[d] += n%nb;
} else {
n_local[d] = ((m/nb)/num_gpus)*nb;
if (d < (m/nb)%num_gpus)
n_local[d] += nb;
else if (d == (m/nb)%num_gpus)
n_local[d] += m%nb;
}
//magma_setdevice(d);
//magma_event_create( &event0[d] );
//magma_event_create( &event1[d] );
//magma_event_create( &event2[d] );
//magma_event_create( &event3[d] );
}
magma_setdevice(0);
/* == initialize the trace */
trace_init( 1, num_gpus, 3, stream );
/* Use blocked code. */
if (upper) {
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
/* invert the diagonals
* Allocate device memory for the inversed diagonal blocks, size=m*NB
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<2; j++ ) {
magma_zmalloc( &d_dinvA[d][j], nb*nb );
magma_zmalloc( &d_x[d][j], n*nb );
cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(magmaDoubleComplex));
cudaMemset(d_x[d][j], 0, n*nb*sizeof(magmaDoubleComplex));
}
}
magma_setdevice(0);
#endif
for (j=0; j<m; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (m-j));
if( j > 0 ) {
/* needed on pluto... */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] ); // wait for the column on CPU
/* broadcast off-diagonal column to all gpus */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d != id ) {
magma_setdevice(d);
/* wait for it on CPU */
magma_queue_wait_event( stream[d][stream0], event[id][1] );
/* send it to GPU */
trace_gpu_start( d, stream0, "comm", "rows to GPUs" );
magma_zsetmatrix_async( j, jb,
Aup(0,j), lda,
dlP(d,jb,0,buf), lddp,
stream[d][stream0] );
trace_gpu_end( d, stream0 );
magma_event_record( event[d][1], stream[d][stream0] );
}
d = (d+1)%num_gpus;
}
}
/* Update the current diagonal block */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
trace_gpu_start( id, stream1, "syrk", "syrk" );
magma_zherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda);
trace_gpu_end( id, stream1 );
magma_event_record( event[id][0], stream[id][stream1] );
}
/* send the diagonal to cpu */
magma_queue_wait_event( stream[id][stream0], event[id][0] ); // wait for syrk
trace_gpu_start( id, stream0, "comm", "D to CPU" );
magma_zgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup(j,j), lda,
stream[id][stream0] );
trace_gpu_end( id, stream0 );
if ( j > 0 ) {
/* Compute the local block column of the panel. */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( n_local[d] > nb0 ) {
/* wait for the off-diagonal */
if( d != id ) {
//magma_queue_sync( stream[id][3] );
dlpanel = dlP(d, jb, 0, buf);
ldpanel = lddp;
/* wait for the offdiagonal column */
magma_queue_wait_event( stream[d][stream1], event[d][1] );
} else {
dlpanel = dlA(d, 0, nb*j_local);
ldpanel = ldda;
}
/* update the panel */
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
trace_gpu_start( d, stream1, "gemm", "gemm" );
magma_zgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda);
trace_gpu_end( d, stream1 );
}
d = (d+1)%num_gpus;
}
}
/* factor the diagonal */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] ); // wait for the diagonal
trace_cpu_start( 0, "getrf", "getrf" );
lapackf77_zpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end( 0 );
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
magma_setdevice(d);
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, 0, 0, buf);
ldpanel = lddp;
}
trace_gpu_start( d, stream0, "comm", "D to GPUs" );
magma_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlpanel, ldpanel,
stream[d][stream0] );
trace_gpu_end( d, stream0 );
magma_event_record( event[d][2], stream[d][stream0] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
trace_gpu_start( id, stream0, "comm", "D to GPUs" );
magma_zsetmatrix_async( jb, jb,
Aup(j,j), lda,
dlA(id, j, nb*j_local), ldda,
stream[id][stream0] );
trace_gpu_end( id, stream0 );
}
/* panel-factorize the off-diagonal */
if ( (j+jb) < n) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = dlP(d, 0, 0, buf);
ldpanel = lddp;
}
nb2 = n_local[d]-nb*j_local2;
nb0 = min(nb, nb2 );
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for the diagonal
if( j+jb < m && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead the column */
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d][0], d_x[d][0] );
/*nb2 = n_local[d] - j_local2*nb;
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d], d_x[d] );*/
#else
/*nb2 = n_local[d] - j_local2*nb;
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldda,
dlA(d, j, nb*j_local2), ldda);
*/
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream1 );
magma_event_record( event[d][3], stream[d][stream1] );
/* send the column to cpu */
if( j+jb < m ) {
trace_gpu_start( d, stream0, "comm", "rows to CPU" );
magma_queue_wait_event( stream[d][stream0], event[d][3] ); // wait for lookahead
magma_zgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup(0,j+jb), lda,
stream[d][stream0] );
trace_gpu_end( d, stream0 );
magma_event_record( event[d][1], stream[d][stream0] );
}
/* update the remaining blocks */
nb2 = nb2 - nb0;
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda);
#endif
} else if( nb2 > 0 ) {
/* update the entire trailing matrix */
trace_gpu_start( d, stream1, "trsm", "trsm" );
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, ldpanel,
dlA(d, j, nb*j_local2), ldda);
#endif
trace_gpu_end( d, stream1 );
}
d = (d+1)%num_gpus;
}
} /* end of ztrsm */
} /* end of for j=1, .., n */
} else {
/* -------------------------------------------- */
/* Lower-triangular case */
/* Compute the Cholesky factorization A = L*L'. */
/* -------------------------------------------- */
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
/*
* Allocate device memory for the inversed diagonal blocks, size=N*BLOCK_SIZE
*/
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
for( j=0; j<2; j++ ) {
magma_zmalloc( &d_dinvA[d][j], nb*nb );
magma_zmalloc( &d_x[d][j], nb*m );
cudaMemset(d_dinvA[d][j], 0, nb*nb*sizeof(magmaDoubleComplex));
cudaMemset(d_x[d][j], 0, nb* m*sizeof(magmaDoubleComplex));
}
}
magma_setdevice(0);
#endif
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%num_gpus;
buf = (j/nb)%num_gpus;
/* Set the local index where the current panel is */
j_local = j/(nb*num_gpus);
jb = min(nb, (n-j));
if( j > 0 ) {
/* needed on pluto... */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] ); // wait for the column on CPU
/* broadcast offdiagonal row to all gpus */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
if( d != id ) {
magma_setdevice(d);
/* wait for it on CPU */
magma_queue_wait_event( stream[d][stream0], event[id][1] );
/* send it to GPU */
magma_zsetmatrix_async( jb, j,
Alo(j,0), lda,
dlPT(d,0,jb,buf), nb,
stream[d][stream0] );
magma_event_record( event[d][1], stream[d][stream0] );
}
d = (d+1)%num_gpus;
}
}
/* Update the current diagonal block */
magma_setdevice(id);
if( j > 0 ) {
magmablasSetKernelStream(stream[id][stream1]);
magma_zherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda);
magma_event_record( event[id][0], stream[id][stream1] );
}
/* send the diagonal to cpu */
magma_queue_wait_event( stream[id][stream0], event[id][0] ); // wait for syrk
magma_zgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo(j,j), lda,
stream[id][stream0] );
/* update the offdiagonal blocks */
if ( j > 0 ) {
/* compute the block-rows of the panel */
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
j_local2 = j_local+1;
if( d > id ) j_local2 --;
nb0 = nb*j_local2;
if( nb0 < n_local[d] ) {
if( d != id ) {
dlpanel = dlPT(d, 0, jb, buf);
ldpanel = nb;
/* wait for offdiagonal row */
magma_queue_wait_event( stream[d][stream1], event[d][1] );
} else {
dlpanel = dlA(d, nb*j_local, 0);
ldpanel = ldda;
}
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
magma_zgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, ldpanel,
c_one, dlA(d, nb0, j), ldda);
}
d = (d+1)%num_gpus;
}
}
/* factor the diagonal */
magma_setdevice(id);
magma_queue_sync( stream[id][stream0] );
lapackf77_zpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ( (j+jb) < m ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
magma_setdevice(d);
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
magma_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlpanel, ldpanel,
stream[d][stream0] );
magma_event_record( event[d][2], stream[d][stream0] );
d = (d+1)%num_gpus;
}
} else {
magma_setdevice(id);
magma_zsetmatrix_async( jb, jb,
Alo(j,j), lda,
dlA(id, nb*j_local, j), ldda,
stream[id][stream0] );
}
/* factorize off-diagonal blocks */
if ( (j+jb) < m ) {
d = (j/nb+1)%num_gpus;
for( dd=0; dd<num_gpus; dd++ ) {
/* next column */
j_local2 = j_local+1;
if( d > id ) j_local2--;
if( d == id ) {
dlpanel = dlA(d, nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = dlPT(d, 0, 0, buf);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2 );
magma_setdevice(d);
magmablasSetKernelStream(stream[d][stream1]);
magma_queue_wait_event( stream[d][stream1], event[d][2] ); // wait for the diagonal
if( j+jb < n && d == (j/nb+1)%num_gpus ) {
/* owns the next column, look-ahead the column */
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
d_dinvA[d][0], d_x[d][0]);
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
magma_event_record( event[d][3], stream[d][stream1] );
/* send the column to cpu */
if( j+jb < n ) {
magma_queue_wait_event( stream[d][stream0], event[d][3] ); // wait for lookahead
magma_zgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo(j+jb,0), lda,
stream[d][stream0] );
magma_event_record( event[d][1], stream[d][stream0] );
}
/* update the remaining blocks */
nb2 = nb2 - nb0;
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda);
#endif
} else if( nb2 > 0 ) {
/* update the entire trailing matrix */
#if defined(PRECISION_d) && defined(ZTRSM_WORK)
magmablas_ztrsm_work( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda,
d_dinvA[d][1], d_x[d][1] );
#else
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, ldpanel,
dlA(d, nb*j_local2, j), ldda);
#endif
}
d = (d+1)%num_gpus;
}
}
}
} /* end of else not upper */
/* == finalize the trace == */
trace_finalize( "zpotrf.svg","trace.css" );
/* clean up */
for( d=0; d<num_gpus; d++ ) {
magma_setdevice(d);
magma_queue_sync( stream[d][0] );
magma_queue_sync( stream[d][1] );
magmablasSetKernelStream(NULL);
//magma_event_destroy( event0[d] );
//magma_event_destroy( event1[d] );
//magma_event_destroy( event2[d] );
//magma_event_destroy( event3[d] );
}
magma_setdevice(0);
return *info;
} /* magma_zpotrf_mgpu */
/**
Purpose
-------
ZGETRF 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 COMPLEX_16 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_zgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zgetrf_gpu(
magma_int_t m, magma_int_t n,
magmaDoubleComplex_ptr dA, magma_int_t ldda, magma_int_t *ipiv,
magma_int_t *info)
{
#define dAT(i_, j_) (dAT + (i_)*nb*lddat + (j_)*nb)
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t iinfo, nb;
magma_int_t maxm, maxn, mindim;
magma_int_t i, j, rows, cols, s, lddat, ldwork;
magmaDoubleComplex *dAT, *dAP, *work;
/* 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);
nb = magma_get_zgetrf_nb(m);
s = mindim / nb;
if (nb <= 1 || nb >= min(m,n)) {
/* Use CPU code. */
magma_zmalloc_cpu( &work, m * n );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_zgetmatrix( m, n, dA, ldda, work, m );
lapackf77_zgetrf(&m, &n, work, &m, ipiv, info);
magma_zsetmatrix( m, n, work, m, dA, ldda );
magma_free_cpu(work);
}
else {
/* Use hybrid blocked code. */
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
if (MAGMA_SUCCESS != magma_zmalloc( &dAP, nb*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
// square matrices can be done in place;
// rectangular requires copy to transpose
if ( m == n ) {
dAT = dA;
lddat = ldda;
magmablas_ztranspose_inplace( m, dAT, ldda );
}
else {
lddat = maxn; // N-by-M
if (MAGMA_SUCCESS != magma_zmalloc( &dAT, lddat*maxm )) {
magma_free( dAP );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmablas_ztranspose( m, n, dA, ldda, dAT, lddat );
}
ldwork = maxm;
if (MAGMA_SUCCESS != magma_zmalloc_pinned( &work, ldwork*nb )) {
magma_free( dAP );
if ( ! (m == n))
magma_free( dAT );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
/* 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;
magmablas_ztranspose( nb, m-j*nb, dAT(j,j), lddat, dAP, cols );
// make sure that the transpose has completed
magma_queue_sync( stream[1] );
magma_zgetmatrix_async( m-j*nb, nb, dAP, cols, work, ldwork,
stream[0]);
if ( j > 0 ) {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (j+1)*nb, nb,
c_one, dAT(j-1,j-1), lddat,
dAT(j-1,j+1), lddat );
magma_zgemm( 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 );
}
// do the cpu part
rows = m - j*nb;
magma_queue_sync( stream[0] );
lapackf77_zgetrf( &rows, &nb, work, &ldwork, ipiv+j*nb, &iinfo);
if ( *info == 0 && iinfo > 0 )
*info = iinfo + j*nb;
// upload j-th panel
magma_zsetmatrix_async( m-j*nb, nb, work, ldwork, dAP, maxm,
stream[0]);
for( i=j*nb; i < j*nb + nb; ++i ) {
ipiv[i] += j*nb;
}
magmablas_zlaswp( n, dAT, lddat, j*nb + 1, j*nb + nb, ipiv, 1 );
magma_queue_sync( stream[0] );
magmablas_ztranspose( m-j*nb, nb, dAP, maxm, dAT(j,j), lddat );
// do the small non-parallel computations (next panel update)
if ( s > (j+1) ) {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dAT(j, j ), lddat,
dAT(j, j+1), lddat);
magma_zgemm( 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 );
}
else {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, dAT(j, j ), lddat,
dAT(j, j+1), lddat);
magma_zgemm( 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 );
}
}
magma_int_t nb0 = min(m - s*nb, n - s*nb);
if ( nb0 > 0 ) {
rows = m - s*nb;
cols = maxm - s*nb;
magmablas_ztranspose( nb0, rows, dAT(s,s), lddat, dAP, maxm );
magma_zgetmatrix( rows, nb0, dAP, maxm, work, ldwork );
// do the cpu part
lapackf77_zgetrf( &rows, &nb0, work, &ldwork, 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_zlaswp( n, dAT, lddat, s*nb + 1, s*nb + nb0, ipiv, 1 );
// upload j-th panel
magma_zsetmatrix( rows, nb0, work, ldwork, dAP, maxm );
magmablas_ztranspose( rows, nb0, dAP, maxm, dAT(s,s), lddat );
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb-nb0, nb0,
c_one, dAT(s,s), lddat,
dAT(s,s)+nb0, lddat);
}
// undo transpose
if ( m == n ) {
magmablas_ztranspose_inplace( m, dAT, lddat );
}
else {
magmablas_ztranspose( n, m, dAT, lddat, dA, ldda );
magma_free( dAT );
}
magma_free( dAP );
magma_free_pinned( work );
magma_queue_destroy( stream[0] );
if (orig_stream == NULL) {
magma_queue_destroy( stream[1] );
}
magmablasSetKernelStream( orig_stream );
}
return *info;
} /* magma_zgetrf_gpu */
extern "C" magma_int_t
magma_ztrtri_gpu(magma_uplo_t uplo, magma_diag_t diag, magma_int_t n,
magmaDoubleComplex_ptr dA, size_t dA_offset, magma_int_t ldda, magma_int_t *info)
{
/* -- clMAGMA (version 1.0.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2012
Purpose
=======
ZTRTRI computes the inverse of a real upper or lower triangular
matrix dA.
This is the Level 3 BLAS version of the algorithm.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
dA (input/output) DOUBLE PRECISION array ON THE GPU, dimension (LDDA,N)
On entry, the triangular matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of the array dA contains
the upper triangular matrix, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of the array dA contains
the lower triangular matrix, and the strictly upper
triangular part of A is not referenced. If DIAG = 'U', the
diagonal elements of A are also not referenced and are
assumed to be 1.
On exit, the (triangular) inverse of the original matrix, in
the same storage format.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, dA(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.
===================================================================== */
/* Local variables */
magma_uplo_t uplo_ = uplo;
magma_diag_t diag_ = diag;
magma_int_t nb, nn, j, jb;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *work;
int upper = lapackf77_lsame(lapack_const(uplo_), lapack_const(MagmaUpper));
int nounit = lapackf77_lsame(lapack_const(diag_), lapack_const(MagmaNonUnit));
*info = 0;
if ((! upper) && (! lapackf77_lsame(lapack_const(uplo_), lapack_const(MagmaLower))))
*info = -1;
else if ((! nounit) && (! lapackf77_lsame(lapack_const(diag_), lapack_const(MagmaUnit))))
*info = -2;
else if (n < 0)
*info = -3;
else if (ldda < max(1,n))
*info = -5;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
nb = magma_get_zpotrf_nb(n);
/* Create Queues */
magma_queue_t queues[2];
magma_device_t device;
int num = 0;
magma_err_t err;
err = magma_get_devices( &device, 1, &num );
if ( err != 0 || num < 1 ) {
fprintf( stderr, "magma_get_devices failed: %d\n", err );
exit(-1);
}
err = magma_queue_create( device, &queues[0] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create 0 failed: %d\n", err );
exit(-1);
}
err = magma_queue_create( device, &queues[1] );
if ( err != 0 ) {
fprintf( stderr, "magma_queue_create 1 failed: %d\n", err );
exit(-1);
}
if (MAGMA_SUCCESS != magma_malloc_host( (void**)&work, nb*nb*sizeof(magmaDoubleComplex) )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if (nb <= 1 || nb >= n)
{
magma_zgetmatrix( n, n, dA, dA_offset, ldda, work, 0, n, queues[0] );
lapackf77_ztrtri(lapack_const(uplo_), lapack_const(diag_), &n, work, &n, info);
magma_zsetmatrix( n, n, work, 0, n, dA, dA_offset, ldda, queues[0] );
}
else
{
if (upper){
/* Compute inverse of upper triangular matrix */
for (j=0; j<n; j =j+ nb){
jb = min(nb, (n-j));
/* Compute rows 1:j-1 of current block column */
magma_ztrmm(MagmaLeft, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_one, dA(0,0), ldda, dA(0, j), ldda,
queues[0]);
magma_ztrsm(MagmaRight, MagmaUpper,
MagmaNoTrans, MagmaNonUnit, j, jb,
c_neg_one, dA(j,j), ldda, dA(0, j), ldda,
queues[0]);
magma_zgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, 0, jb, queues[1], NULL );
magma_queue_sync( queues[1] );
/* Compute inverse of current diagonal block */
lapackf77_ztrtri(MagmaUpperStr, lapack_const(diag_), &jb, work, &jb, info);
/*
magma_zsetmatrix_async( jb, jb,
work, 0, jb,
dA(j, j), ldda, queues[0], NULL );
*/
magma_zsetmatrix( jb, jb,
work, 0, jb,
dA(j, j), ldda, queues[0]);
}
}
else{
/* Compute inverse of lower triangular matrix */
nn=((n-1)/nb)*nb+1;
for(j=nn-1; j>=0; j=j-nb){
jb=min(nb,(n-j));
if((j+jb) < n){
/* Compute rows j+jb:n of current block column */
magma_ztrmm(MagmaLeft, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_one, dA(j+jb,j+jb), ldda, dA(j+jb, j), ldda,
queues[0]);
magma_ztrsm(MagmaRight, MagmaLower,
MagmaNoTrans, MagmaNonUnit, (n-j-jb), jb,
c_neg_one, dA(j,j), ldda, dA(j+jb, j), ldda,
queues[0]);
}
magma_zgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, 0, jb, queues[1], NULL );
magma_queue_sync( queues[1] );
/* Compute inverse of current diagonal block */
lapackf77_ztrtri(MagmaLowerStr, lapack_const(diag_), &jb, work, &jb, info);
/*
magma_zsetmatrix_async( jb, jb,
work, 0, jb,
dA(j, j), ldda, queues[0], NULL );
*/
magma_zsetmatrix( jb, jb,
work, 0, jb,
dA(j, j), ldda, queues[0] );
}
}
}
magma_free_host( work );
magma_queue_destroy(queues[0]);
magma_queue_destroy(queues[1]);
return *info;
}
extern "C" magma_int_t
magma_zgetrf(
magma_int_t m, magma_int_t n,
magmaDoubleComplex *A, magma_int_t lda, magma_int_t *ipiv,
magma_queue_t queue[2],
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
=======
ZGETRF 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 user defined
stream to overlap computation with communication.
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.
A (input/output) COMPLEX_16 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.
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= 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 dAT(i,j) dAT, dAT_offset + ((i)*nb*lddat + (j)*nb)
magmaDoubleComplex *work;
magmaDoubleComplex_ptr dAT, dA, dwork, dAP;
size_t dA_offset, dAT_offset;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t iinfo, nb;
*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;
nb = magma_get_zgetrf_nb(m);
if ( (nb <= 1) || (nb >= min(m,n)) ) {
/* Use CPU code. */
lapackf77_zgetrf(&m, &n, A, &lda, ipiv, info);
} else {
/* Use hybrid blocked code. */
magma_int_t maxm, maxn, ldda, maxdim, lddat;
magma_int_t i, j, rows, cols, s = min(m, n)/nb;
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
lddat = maxn;
ldda = maxm;
maxdim = max(maxm, maxn);
/* set number of GPUs */
magma_int_t num_gpus = magma_num_gpus();
if ( num_gpus > 1 ) {
/* call multi-GPU non-GPU-resident interface */
printf("multiple-GPU verison not implemented\n");
return MAGMA_ERR_NOT_IMPLEMENTED;
// magma_zgetrf_m(num_gpus, m, n, A, lda, ipiv, info);
// return *info;
}
/* explicitly checking the memory requirement */
magma_int_t totalMem = magma_queue_meminfo( queue[0] );
totalMem /= sizeof(magmaDoubleComplex);
int h = 1+(2+num_gpus), num_gpus2 = num_gpus;
int NB = (magma_int_t)(0.8*totalMem/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( num_gpus > ceil((double)NB/nb) ) {
num_gpus2 = (int)ceil((double)NB/nb);
h = 1+(2+num_gpus2);
NB = (magma_int_t)(0.8*totalMem/maxm-h*nb);
}
if( num_gpus2*NB < n ) {
/* require too much memory, so call non-GPU-resident version */
printf("non-GPU-resident version not implemented\n");
return MAGMA_ERR_NOT_IMPLEMENTED;
//magma_zgetrf_m(num_gpus, 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
if (MAGMA_SUCCESS !=
magma_zmalloc( &dwork, (nb*maxm + maxdim*maxdim) ) ) {
/* alloc failed so call non-GPU-resident version */
printf("non-GPU-resident version not implemented\n");
return MAGMA_ERR_NOT_IMPLEMENTED;
//magma_zgetrf_m(num_gpus, m, n, A, lda, ipiv, info);
//return *info;
}
dAP = dwork;
dA = dwork;
dA_offset = nb*maxm;
ldda = lddat = maxdim;
magma_zsetmatrix( m, n, A, lda, dA, dA_offset, ldda, queue[0] );
dAT = dA;
dAT_offset = dA_offset;
magmablas_ztranspose_inplace( m, dAT, dAT_offset, ldda, queue[0] );
}
else {
// if very rectangular, allocate dA and dAT and transpose out-of-place
if (MAGMA_SUCCESS !=
magma_zmalloc( &dwork, (nb + maxn)*maxm )) {
/* alloc failed so call non-GPU-resident version */
printf("non-GPU-resident version not implemented\n");
return MAGMA_ERR_NOT_IMPLEMENTED;
//magma_zgetrf_m(num_gpus, m, n, A, lda, ipiv, info);
//return *info;
}
dAP = dwork;
dA = dwork;
dA_offset = nb*maxm;
magma_zsetmatrix( m, n, A, lda, dA, dA_offset, ldda, queue[0] );
if (MAGMA_SUCCESS != magma_zmalloc( &dAT, maxm*maxn )) {
/* alloc failed so call non-GPU-resident version */
magma_free( dwork );
printf("non-GPU-resident version not implemented\n");
return MAGMA_ERR_NOT_IMPLEMENTED;
//magma_zgetrf_m(num_gpus, m, n, A, lda, ipiv, info);
//return *info;
}
dAT_offset = 0;
magmablas_ztranspose( m, n, dA, dA_offset, ldda, dAT, dAT_offset, lddat, queue[0] );
}
lapackf77_zgetrf( &m, &nb, work, &lda, ipiv, &iinfo);
for( j = 0; j < s; j++ )
{
// download j-th panel
cols = maxm - j*nb;
if (j>0){
// download j-th panel
magmablas_ztranspose( nb, cols, dAT(j,j), lddat, dAP, 0, cols, queue[0] );
magma_queue_sync(queue[0]);
magma_zgetmatrix_async( m-j*nb, nb, dAP, 0, cols, work, lda,
queue[1], NULL);
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n - (j+1)*nb, nb,
c_one, dAT(j-1,j-1), lddat,
dAT(j-1,j+1), lddat, queue[0] );
magma_zgemm( 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, queue[0] );
// do the cpu part
rows = m - j*nb;
magma_queue_sync( queue[1] );
lapackf77_zgetrf( &rows, &nb, work, &lda, ipiv+j*nb, &iinfo);
}
if (*info == 0 && iinfo > 0)
*info = iinfo + j*nb;
for( i=j*nb; i < j*nb + nb; ++i ) {
ipiv[i] += j*nb;
}
magmablas_zlaswp( n, dAT, dAT_offset, lddat, j*nb + 1, j*nb + nb, ipiv, 1, queue[0] );
// upload j-th panel
magma_zsetmatrix_async( m-j*nb, nb, work, lda, dAP, 0, maxm,
queue[1], NULL);
magma_queue_sync( queue[1] );
magmablas_ztranspose( cols, nb, dAP, 0, maxm, dAT(j,j), lddat, queue[0] );
// do the small non-parallel computations
if (s > (j+1)){
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dAT(j, j ), lddat,
dAT(j, j+1), lddat, queue[0]);
magma_zgemm( 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, queue[0] );
}
else{
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, dAT(j, j ), lddat,
dAT(j, j+1), lddat, queue[0] );
magma_zgemm( 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, queue[0] );
}
}
magma_int_t nb0 = min(m - s*nb, n - s*nb);
if ( nb0 > 0 ) {
rows = m - s*nb;
cols = maxm - s*nb;
magmablas_ztranspose( nb0, rows, dAT(s,s), lddat, dAP, 0, maxm, queue[0]);
magma_queue_sync(queue[0]);
magma_zgetmatrix_async( rows, nb0, dAP, 0, maxm, work, lda, queue[1], NULL );
magma_queue_sync(queue[1]);
// do the cpu part
lapackf77_zgetrf( &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_zlaswp( n, dAT, dAT_offset, lddat, s*nb + 1, s*nb + nb0, ipiv, 1, queue[0] );
magma_zsetmatrix_async( rows, nb0, work, lda, dAP, 0, maxm, queue[1], NULL );
magma_queue_sync(queue[1]);
magmablas_ztranspose( rows, nb0, dAP, 0, maxm, dAT(s,s), lddat, queue[0]);
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb-nb0, nb0,
c_one, dAT(s, s), lddat,
dAT(s, s)+nb0, lddat, queue[0] );
}
if (maxdim*maxdim < 2*maxm*maxn) {
magmablas_ztranspose_inplace( m, dAT, dAT_offset, lddat, queue[0] );
magma_zgetmatrix( m, n, dA, dA_offset, ldda, A, lda, queue[0] );
} else {
magmablas_ztranspose( n, m, dAT, dAT_offset, lddat, dA, dA_offset, ldda, queue[0] );
magma_zgetmatrix( m, n, dA, dA_offset, ldda, A, lda, queue[0] );
magma_queue_sync(queue[0]);
magma_free( dAT );
}
magma_queue_sync(queue[0]);
magma_free( dwork );
}
return *info;
} /* magma_zgetrf */
extern "C" magma_int_t
magma_zhegst(magma_int_t itype, char uplo, magma_int_t n,
magmaDoubleComplex *a, magma_int_t lda,
magmaDoubleComplex *b, magma_int_t ldb, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
ZHEGST reduces a complex Hermitian-definite generalized
eigenproblem to standard form.
If ITYPE = 1, the problem is A*x = lambda*B*x,
and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
B must have been previously factorized as U**H*U or L*L**H by ZPOTRF.
Arguments
=========
ITYPE (input) INTEGER
= 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H);
= 2 or 3: compute U*A*U**H or L**H*A*L.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored and B is factored as
U**H*U;
= 'L': Lower triangle of A is stored and B is factored as
L*L**H.
N (input) INTEGER
The order of the matrices A and B. N >= 0.
A (input/output) COMPLEX_16 array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if INFO = 0, the transformed matrix, stored in the
same format as A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input) COMPLEX_16 array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B,
as returned by ZPOTRF.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================*/
char uplo_[2] = {uplo, 0};
magma_int_t nb;
magma_int_t k, kb, kb2;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex c_half = MAGMA_Z_HALF;
magmaDoubleComplex c_neg_half = MAGMA_Z_NEG_HALF;
magmaDoubleComplex *dw;
magma_int_t ldda = n;
magma_int_t lddb = n;
double d_one = 1.0;
int upper = lapackf77_lsame(uplo_, "U");
/* Test the input parameters. */
*info = 0;
if (itype<1 || itype>3){
*info = -1;
}else if ((! upper) && (! lapackf77_lsame(uplo_, "L"))) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
}else if (ldb < max(1,n)) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return */
if ( n == 0 )
return *info;
if (MAGMA_SUCCESS != magma_zmalloc( &dw, 2*n*n )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
nb = magma_get_zhegst_nb(n);
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
magma_zsetmatrix( n, n, A(0, 0), lda, dA(0, 0), ldda );
magma_zsetmatrix( n, n, B(0, 0), ldb, dB(0, 0), lddb );
/* Use hybrid blocked code */
if (itype==1) {
if (upper) {
/* Compute inv(U')*A*inv(U) */
for(k = 0; k<n; k+=nb){
kb = min(n-k,nb);
kb2= min(n-k-nb,nb);
/* Update the upper triangle of A(k:n,k:n) */
lapackf77_zhegst( &itype, uplo_, &kb, A(k,k), &lda, B(k,k), &ldb, info);
magma_zsetmatrix_async( kb, kb,
A(k, k), lda,
dA(k, k), ldda, stream[0] );
if(k+kb<n){
magma_ztrsm(MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
kb, n-k-kb,
c_one, dB(k,k), lddb,
dA(k,k+kb), ldda);
magma_queue_sync( stream[0] );
magma_zhemm(MagmaLeft, MagmaUpper,
kb, n-k-kb,
c_neg_half, dA(k,k), ldda,
dB(k,k+kb), lddb,
c_one, dA(k, k+kb), ldda);
magma_zher2k(MagmaUpper, MagmaConjTrans,
n-k-kb, kb,
c_neg_one, dA(k,k+kb), ldda,
dB(k,k+kb), lddb,
d_one, dA(k+kb,k+kb), ldda);
magma_zgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(k+kb, k+kb), lda, stream[1] );
magma_zhemm(MagmaLeft, MagmaUpper,
kb, n-k-kb,
c_neg_half, dA(k,k), ldda,
dB(k,k+kb), lddb,
c_one, dA(k, k+kb), ldda);
magma_ztrsm(MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
kb, n-k-kb,
c_one ,dB(k+kb,k+kb), lddb,
dA(k,k+kb), ldda);
magma_queue_sync( stream[1] );
}
}
magma_queue_sync( stream[0] );
}
else {
/* Compute inv(L)*A*inv(L') */
for(k = 0; k<n; k+=nb){
kb= min(n-k,nb);
kb2= min(n-k-nb,nb);
/* Update the lower triangle of A(k:n,k:n) */
lapackf77_zhegst( &itype, uplo_, &kb, A(k,k), &lda, B(k,k), &ldb, info);
magma_zsetmatrix_async( kb, kb,
A(k, k), lda,
dA(k, k), ldda, stream[0] );
if(k+kb<n){
magma_ztrsm(MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
n-k-kb, kb,
c_one, dB(k,k), lddb,
dA(k+kb,k), ldda);
magma_queue_sync( stream[0] );
magma_zhemm(MagmaRight, MagmaLower,
n-k-kb, kb,
c_neg_half, dA(k,k), ldda,
dB(k+kb,k), lddb,
c_one, dA(k+kb, k), ldda);
magma_zher2k(MagmaLower, MagmaNoTrans,
n-k-kb, kb,
c_neg_one, dA(k+kb,k), ldda,
dB(k+kb,k), lddb,
d_one, dA(k+kb,k+kb), ldda);
magma_zgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(k+kb, k+kb), lda, stream[1] );
magma_zhemm(MagmaRight, MagmaLower,
n-k-kb, kb,
c_neg_half, dA(k,k), ldda,
dB(k+kb,k), lddb,
c_one, dA(k+kb, k), ldda);
magma_ztrsm(MagmaLeft, MagmaLower, MagmaNoTrans, MagmaNonUnit,
n-k-kb, kb,
c_one, dB(k+kb,k+kb), lddb,
dA(k+kb,k), ldda);
}
magma_queue_sync( stream[1] );
}
}
magma_queue_sync( stream[0] );
}
else {
if (upper) {
/* Compute U*A*U' */
for(k = 0; k<n; k+=nb){
kb= min(n-k,nb);
magma_zgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(k, k), lda, stream[0] );
/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */
if(k>0){
magma_ztrmm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
k, kb,
c_one ,dB(0,0), lddb,
dA(0,k), ldda);
magma_zhemm(MagmaRight, MagmaUpper,
k, kb,
c_half, dA(k,k), ldda,
dB(0,k), lddb,
c_one, dA(0, k), ldda);
magma_queue_sync( stream[1] );
magma_zher2k(MagmaUpper, MagmaNoTrans,
k, kb,
c_one, dA(0,k), ldda,
dB(0,k), lddb,
d_one, dA(0,0), ldda);
magma_zhemm(MagmaRight, MagmaUpper,
k, kb,
c_half, dA(k,k), ldda,
dB(0,k), lddb,
c_one, dA(0, k), ldda);
magma_ztrmm(MagmaRight, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
k, kb,
c_one, dB(k,k), lddb,
dA(0,k), ldda);
}
magma_queue_sync( stream[0] );
lapackf77_zhegst( &itype, uplo_, &kb, A(k, k), &lda, B(k, k), &ldb, info);
magma_zsetmatrix_async( kb, kb,
A(k, k), lda,
dA(k, k), ldda, stream[1] );
}
magma_queue_sync( stream[1] );
}
else {
/* Compute L'*A*L */
for(k = 0; k<n; k+=nb){
kb= min(n-k,nb);
magma_zgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(k, k), lda, stream[0] );
/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */
if(k>0){
magma_ztrmm(MagmaRight, MagmaLower, MagmaNoTrans, MagmaNonUnit,
kb, k,
c_one ,dB(0,0), lddb,
dA(k,0), ldda);
magma_zhemm(MagmaLeft, MagmaLower,
kb, k,
c_half, dA(k,k), ldda,
dB(k,0), lddb,
c_one, dA(k, 0), ldda);
magma_queue_sync( stream[1] );
magma_zher2k(MagmaLower, MagmaConjTrans,
k, kb,
c_one, dA(k,0), ldda,
dB(k,0), lddb,
d_one, dA(0,0), ldda);
magma_zhemm(MagmaLeft, MagmaLower,
kb, k,
c_half, dA(k,k), ldda,
dB(k,0), lddb,
c_one, dA(k, 0), ldda);
magma_ztrmm(MagmaLeft, MagmaLower, MagmaConjTrans, MagmaNonUnit,
kb, k,
c_one, dB(k,k), lddb,
dA(k,0), ldda);
}
magma_queue_sync( stream[0] );
lapackf77_zhegst( &itype, uplo_, &kb, A(k,k), &lda, B(k,k), &ldb, info);
magma_zsetmatrix_async( kb, kb,
A(k, k), lda,
dA(k, k), ldda, stream[1] );
}
magma_queue_sync( stream[1] );
}
}
magma_zgetmatrix( n, n, dA(0, 0), ldda, A(0, 0), lda );
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free( dw );
return *info;
} /* magma_zhegst_gpu */
extern "C" magma_err_t
magma_zpotrf2_msub(int num_subs, int num_gpus, magma_uplo_t uplo, magma_int_t m, magma_int_t n,
magma_int_t off_i, magma_int_t off_j, magma_int_t nb,
magmaDoubleComplex_ptr *d_lA, size_t d_lA_offset, magma_int_t ldda,
magmaDoubleComplex_ptr *d_lP, magma_int_t lddp,
magmaDoubleComplex *a, magma_int_t lda, magma_int_t h,
magma_int_t *info, magma_queue_t *queues )
{
/* -- clMAGMA (version 1.1.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2014
Purpose
=======
ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = 'U', or
dA = L * L**H, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of dA is stored;
= 'L': Lower triangle of dA is stored.
N (input) INTEGER
The order of the matrix dA. N >= 0.
dA (input/output) COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = 'U', the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
===================================================================== */
int tot_subs = num_subs*num_gpus;
magma_int_t j, jb, nb0, nb2, dd, d, id, j_local, j_local2;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
double d_one = 1.0;
double d_neg_one = -1.0;
magmaDoubleComplex_ptr dlpanel;
size_t dlpanel_offset;
magma_int_t n_local[MagmaMaxSubs * MagmaMaxGPUs], ldpanel;
// initialize trace
trace_init(1, num_gpus, 2, queues);
*info = 0;
if ( (uplo != MagmaUpper) && (uplo != MagmaLower) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if ((uplo != MagmaUpper) && tot_subs*ldda < max(1,n)) {
*info = -4;
} else if ((uplo == MagmaUpper) && ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
for (d=0; d<tot_subs; d++) {
/* local-n and local-ld */
if (uplo == MagmaUpper) {
n_local[d] = ((n/nb)/tot_subs)*nb;
if (d < (n/nb)%tot_subs)
n_local[d] += nb;
else if (d == (n/nb)%tot_subs)
n_local[d] += n%nb;
} else {
n_local[d] = ((m/nb)/tot_subs)*nb;
if (d < (m/nb)%tot_subs)
n_local[d] += nb;
else if (d == (m/nb)%tot_subs)
n_local[d] += m%nb;
}
}
/* Use blocked code. */
if (uplo == MagmaUpper) {
/* ---------------------------------------------- */
/* Upper-triangular case */
/* > Compute the Cholesky factorization A = U'*U. */
/* ---------------------------------------------- */
for (j=0; j<m; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%tot_subs;
/* Set the local index where the current panel is */
j_local = j/(nb*tot_subs);
jb = min(nb, (m-j));
if (j > 0) {
// Wait for the column on CPU
magma_queue_sync(queues[2*(id%num_gpus)]);
/* broadcast off-diagonal column to all gpus */
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d != id%num_gpus) {
magma_zsetmatrix_async( j, jb,
Aup_off(0,j), lda,
dlP(d,jb,0,id%num_gpus), lddp,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-col") );
}
d = (d+1)%num_gpus;
}
/* Update the current diagonal block */
trace_gpu_start(id%num_gpus, 1, "herk", "herk");
magma_zherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dlA(id, 0, nb*j_local), ldda,
d_one, dlA(id, j, nb*j_local), ldda,
queues[2*(id%num_gpus)+1]);
magma_queue_sync(queues[2*(id%num_gpus)+1]); // Wait for syrk
}
/* Send the diagonal to cpu */
magma_zgetmatrix_async( jb, jb,
dlA(id, j, nb*j_local), ldda,
Aup_off(j,j), lda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "get", "get-diag") );
if (j > 0) {
/* Compute the local block column of the panel. */
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
j_local2 = j_local+1;
if (d > id) j_local2 --;
nb0 = nb*j_local2;
if (n_local[d] > nb0) {
if (d%num_gpus != id%num_gpus) {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlP_offset(jb, 0, id%num_gpus);
ldpanel = lddp;
/* Wait for the offdiagonal column */
if (dd < num_gpus) magma_queue_sync(queues[2*(d%num_gpus)]);
} else {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(0, nb*j_local);
ldpanel = ldda;
}
/* update the panel */
trace_gpu_start(d%num_gpus, 1, "gemm", "gemm");
magma_zgemm(MagmaConjTrans, MagmaNoTrans,
jb, n_local[d]-nb0, j,
c_neg_one, dlpanel, dlpanel_offset, ldpanel,
dlA(d, 0, nb0), ldda,
c_one, dlA(d, j, nb0), ldda,
queues[2*(d%num_gpus)+1]);
}
d = (d+1)%tot_subs;
}
}
/* factor the diagonal */
magma_queue_sync( queues[2*(id%num_gpus)] ); // wait for the diagonal
trace_cpu_start(0, "potrf", "potrf");
lapackf77_zpotrf(MagmaUpperStr, &jb, Aup(j,j), &lda, info);
trace_cpu_end(0);
if (*info != 0) {
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ((j+jb) < n) {
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = d_lP[d];
dlpanel_offset = dlP_offset(0, 0, id%num_gpus);
ldpanel = lddp;
}
magma_zsetmatrix_async( jb, jb,
Aup_off(j,j), lda,
dlpanel, dlpanel_offset, ldpanel,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-diag"));
d = (d+1)%num_gpus;
}
} else {
magma_zsetmatrix_async( jb, jb,
Aup_off(j,j), lda,
dlA(id, j, nb*j_local), ldda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "set", "set-diag") );
}
/* panel-factorize the off-diagonal */
if ((j+jb) < n) {
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
/* next column */
j_local2 = j_local+1;
if (d > id) j_local2--;
if (d%num_gpus == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(j, nb*j_local);
ldpanel = ldda;
} else {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlP_offset(0, 0, id%num_gpus);
ldpanel = lddp;
}
nb2 = n_local[d]-nb*j_local2;
nb0 = min(nb, nb2);
if (dd < num_gpus) magma_queue_sync( queues[2*(d%num_gpus)] ); // wait for the diagonal
if (j+jb < m && d == (j/nb+1)%tot_subs) {
/* owns the next column, look-ahead the column */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb0, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2), ldda,
queues[2*(d%num_gpus)+1] );
/* send the column to cpu */
magma_queue_sync(queues[2*(d%num_gpus)+1]); // wait for lookahead
magma_zgetmatrix_async( (j+jb), nb0,
dlA(d, 0, nb*j_local2), ldda,
Aup_off(0,j+jb), lda,
queues[2*(d%num_gpus)],
trace_gpu_event(d%num_gpus, 0, "get", "get-col") );
/* update the remaining blocks */
nb2 = nb2 - nb0;
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2+nb0), ldda,
queues[2*(d%num_gpus)+1] );
} else if (nb2 > 0) {
/* update the entire trailing matrix */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, nb2, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, j, nb*j_local2), ldda,
queues[2*(d%num_gpus)+1] );
}
d = (d+1)%tot_subs;
}
}
}
} else {
/* -------------------------------------------- */
/* Lower-triangular case */
/* Compute the Cholesky factorization A = L*L'. */
/* -------------------------------------------- */
for (j=0; j<n; j+=nb) {
/* Set the GPU number that holds the current panel */
id = (j/nb)%tot_subs;
/* Set the local index where the current panel is */
j_local = j/(nb*tot_subs);
jb = min(nb, (n-j));
if (j > 0) {
if (num_gpus > 1) {
// Wait for the row on CPU to broadcast
magma_queue_sync(queues[2*(id%num_gpus)]);
}
/* broadcast off-diagonal row to all the GPUs */
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d != id%num_gpus) {
/* send it to GPU-d */
magma_zsetmatrix_async( jb, j,
Alo_off(j,0), lda,
dlPT(d,0,jb,id%num_gpus), nb,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-row") );
}
d = (d+1)%num_gpus;
}
/* Update the current diagonal block */
trace_gpu_start(id%num_gpus, 1, "herk", "herk");
magma_zherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dlA(id, nb*j_local, 0), ldda,
d_one, dlA(id, nb*j_local, j), ldda,
queues[2*(id%num_gpus)+1]);
magma_queue_sync(queues[2*(id%num_gpus)+1]); // wait for syrk
}
/* send the diagonal to cpu */
magma_zgetmatrix_async( jb, jb,
dlA(id, nb*j_local, j), ldda,
Alo_off(j,j), lda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "get", "get") );
/* update the offdiagonal blocks */
if (j > 0) {
/* compute the block-rows of the panel */
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
j_local2 = j_local+1;
if (d > id) j_local2 --;
nb0 = nb*j_local2;
if (nb0 < n_local[d]) {
if (d%num_gpus != id%num_gpus) {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlPT_offset(0, jb, id%num_gpus);
ldpanel = nb;
/* Wait for offdiagonal row */
if (dd < num_gpus) magma_queue_sync(queues[2*(d%num_gpus)]);
} else {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(nb*j_local, 0);
ldpanel = ldda;
}
/* Update the panel */
trace_gpu_start(d%num_gpus, 1, "gemm", "gemm");
magma_zgemm( MagmaNoTrans, MagmaConjTrans,
n_local[d]-nb0, jb, j,
c_neg_one, dlA(d, nb0, 0), ldda,
dlpanel, dlpanel_offset, ldpanel,
c_one, dlA(d, nb0, j), ldda,
queues[2*(d%num_gpus)+1]);
}
d = (d+1)%tot_subs;
}
}
/* factor the diagonal */
magma_queue_sync( queues[2*(id%num_gpus)] );
trace_cpu_start(0, "potrf", "potrf");
lapackf77_zpotrf(MagmaLowerStr, &jb, Alo(j,j), &lda, info);
trace_cpu_end(0);
if (*info != 0) {
printf( " zpotrf returned %d (id=%d,j=%d,j_local=%d,jb=%d)\n",*info,id,j,j_local,jb );
*info = *info + j;
break;
}
/* send the diagonal to gpus */
if ((j+jb) < m) {
d = (j/nb+1)%num_gpus;
for (dd=0; dd<num_gpus; dd++) {
if (d == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = d_lP[d];
dlpanel_offset = dlPT_offset(0, 0, id%num_gpus);
ldpanel = nb;
}
magma_zsetmatrix_async( jb, jb,
Alo_off(j,j), lda,
dlpanel, dlpanel_offset, ldpanel,
queues[2*d],
trace_gpu_event(d, 0, "set", "set-diag") );
d = (d+1)%num_gpus;
}
} else {
magma_zsetmatrix_async( jb, jb,
Alo_off(j,j), lda,
dlA(id, nb*j_local, j), ldda,
queues[2*(id%num_gpus)],
trace_gpu_event(id%num_gpus, 0, "set", "set-diag") );
}
/* factorize off-diagonal blocks */
if ((j+jb) < m) {
d = (j/nb+1)%tot_subs;
for (dd=0; dd<tot_subs; dd++) {
/* next column */
j_local2 = j_local+1;
if (d > id) j_local2--;
if (d%num_gpus == id%num_gpus) {
dlpanel = d_lA[id];
dlpanel_offset = dlA_offset(nb*j_local, j);
ldpanel = ldda;
} else {
dlpanel = d_lP[d%num_gpus];
dlpanel_offset = dlPT_offset(0, 0, id%num_gpus);
ldpanel = nb;
}
nb2 = n_local[d] - j_local2*nb;
nb0 = min(nb, nb2 );
// wait for the diagonal
if (dd < num_gpus) magma_queue_sync(queues[2*(d%num_gpus)]);
if (j+jb < n && d == (j/nb+1)%tot_subs) {
/* owns the next column, look-ahead the column */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb0, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2, j), ldda,
queues[2*(d%num_gpus)+1]);
/* send the column to cpu */
magma_queue_sync( queues[2*(d%num_gpus)+1] ); // wait for lookahead
magma_zgetmatrix_async( nb0, j+jb,
dlA(d, nb*j_local2, 0), ldda,
Alo_off(j+jb,0), lda,
queues[2*(d%num_gpus)],
trace_gpu_event(d%num_gpus, 0, "get", "get") );
/* update the remaining blocks */
nb2 = nb2 - nb0;
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2+nb0, j), ldda,
queues[2*(d%num_gpus)+1]);
} else if (nb2 > 0) {
/* update the entire trailing matrix */
trace_gpu_start(d%num_gpus, 1, "trsm", "trsm");
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
nb2, jb, c_one,
dlpanel, dlpanel_offset, ldpanel,
dlA(d, nb*j_local2, j), ldda,
queues[2*(d%num_gpus)+1]);
}
d = (d+1)%tot_subs;
}
}
}
} /* end of else not upper */
/* clean up */
for( d=0; d<num_gpus; d++ ) {
magma_queue_sync( queues[2*d] );
magma_queue_sync( queues[2*d+1] );
}
trace_finalize("zpotrf_msub.svg", "trace.css");
return *info;
} /* magma_zpotrf2_msub */
/**
Purpose
-------
ZGETRS solves a system of linear equations
A * X = B,
A**T * X = B, or
A**H * X = B
with a general N-by-N matrix A using the LU factorization computed by ZGETRF_NOPIV_GPU.
Arguments
---------
@param[in]
trans magma_trans_t
Specifies the form of the system of equations:
- = MagmaNoTrans: A * X = B (No transpose)
- = MagmaTrans: A**T * X = B (Transpose)
- = MagmaConjTrans: A**H * X = B (Conjugate transpose)
@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 COMPLEX_16 array on the GPU, dimension (LDDA,N)
The factors L and U from the factorization A = P*L*U as computed
by ZGETRF_GPU.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDDA >= max(1,N).
@param[in,out]
dB COMPLEX_16 array on the GPU, dimension (LDDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
@param[in]
lddb INTEGER
The leading dimension of the array B. LDDB >= max(1,N).
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_zgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zgetrs_nopiv_gpu(
magma_trans_t trans, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magmaDoubleComplex_ptr dB, magma_int_t lddb,
magma_int_t *info)
{
// Constants
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
// Local variables
bool notran = (trans == MagmaNoTrans);
*info = 0;
if ( (! notran) &&
(trans != MagmaTrans) &&
(trans != MagmaConjTrans) ) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (nrhs < 0) {
*info = -3;
} else if (ldda < max(1,n)) {
*info = -5;
} else 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;
}
magma_queue_t queue = NULL;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
if (notran) {
/* Solve A * X = B. */
if ( nrhs == 1) {
magma_ztrsv( MagmaLower, MagmaNoTrans, MagmaUnit, n, dA, ldda, dB, 1, queue );
magma_ztrsv( MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, dA, ldda, dB, 1, queue );
} else {
magma_ztrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit, n, nrhs, c_one, dA, ldda, dB, lddb, queue );
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb, queue );
}
} else {
/* Solve A**T * X = B or A**H * X = B. */
if ( nrhs == 1) {
magma_ztrsv( MagmaUpper, trans, MagmaNonUnit, n, dA, ldda, dB, 1, queue );
magma_ztrsv( MagmaLower, trans, MagmaUnit, n, dA, ldda, dB, 1, queue );
} else {
magma_ztrsm( MagmaLeft, MagmaUpper, trans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb, queue );
magma_ztrsm( MagmaLeft, MagmaLower, trans, MagmaUnit, n, nrhs, c_one, dA, ldda, dB, lddb, queue );
}
}
magma_queue_destroy( queue );
return *info;
}
extern "C" magma_int_t
magma_zgeqrs3_gpu(magma_int_t m, magma_int_t n, magma_int_t nrhs,
magmaDoubleComplex *dA, magma_int_t ldda,
magmaDoubleComplex *tau, magmaDoubleComplex *dT,
magmaDoubleComplex *dB, magma_int_t lddb,
magmaDoubleComplex *hwork, magma_int_t lwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
Solves the least squares problem
min || A*X - C ||
using the QR factorization A = Q*R computed by ZGEQRF3_GPU.
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. M >= N >= 0.
NRHS (input) INTEGER
The number of columns of the matrix C. NRHS >= 0.
A (input) COMPLEX_16 array on the GPU, dimension (LDDA,N)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,n, as returned by
ZGEQRF3_GPU in the first n columns of its array argument A.
LDDA (input) INTEGER
The leading dimension of the array A, LDDA >= M.
TAU (input) COMPLEX_16 array, dimension (N)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by MAGMA_ZGEQRF_GPU.
DB (input/output) COMPLEX_16 array on the GPU, dimension (LDDB,NRHS)
On entry, the M-by-NRHS matrix C.
On exit, the N-by-NRHS solution matrix X.
DT (input) COMPLEX_16 array that is the output (the 6th argument)
of magma_zgeqrf_gpu of size
2*MIN(M, N)*NB + ((N+31)/32*32 )* MAX(NB, NRHS).
The array starts with a block of size MIN(M,N)*NB that stores
the triangular T matrices used in the QR factorization,
followed by MIN(M,N)*NB block storing the diagonal block
matrices for the R matrix, followed by work space of size
((N+31)/32*32 )* MAX(NB, NRHS).
LDDB (input) INTEGER
The leading dimension of the array DB. LDDB >= M.
HWORK (workspace/output) COMPLEX_16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK,
LWORK >= (M - N + NB)*(NRHS + NB) + NRHS*NB,
where NB is the blocksize given by magma_get_zgeqrf_nb( M ).
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the HWORK array, returns
this value as the first entry of the WORK array.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
#define a_ref(a_1,a_2) (dA+(a_2)*(ldda) + (a_1))
#define d_ref(a_1) (dT+(lddwork+(a_1))*nb)
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magma_int_t k, lddwork;
magma_int_t nb = magma_get_zgeqrf_nb(m);
magma_int_t lwkopt = (m - n + nb)*(nrhs + nb) + nrhs*nb;
int lquery = (lwork == -1);
hwork[0] = MAGMA_Z_MAKE( (double)lwkopt, 0. );
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0 || m < n)
*info = -2;
else if (nrhs < 0)
*info = -3;
else if (ldda < max(1,m))
*info = -5;
else if (lddb < max(1,m))
*info = -8;
else if (lwork < lwkopt && ! lquery)
*info = -10;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
k = min(m,n);
if (k == 0) {
hwork[0] = c_one;
return *info;
}
lddwork= k;
/* B := Q' * B */
magma_zunmqr_gpu( MagmaLeft, MagmaConjTrans,
m, nrhs, n,
a_ref(0,0), ldda, tau,
dB, lddb, hwork, lwork, dT, nb, info );
if ( *info != 0 ) {
return *info;
}
/* Solve R*X = B(1:n,:)
1. Move the block diagonal submatrices from d_ref to R
2. Solve
3. Restore the data format moving data from R back to d_ref
*/
magmablas_zswapdblk(k, nb, a_ref(0,0), ldda, 1, d_ref(0), nb, 0);
if ( nrhs == 1 ) {
magma_ztrsv(MagmaUpper, MagmaNoTrans, MagmaNonUnit,
n, a_ref(0,0), ldda, dB, 1);
} else {
magma_ztrsm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
n, nrhs, c_one, a_ref(0,0), ldda, dB, lddb);
}
magmablas_zswapdblk(k, nb, d_ref(0), nb, 0, a_ref(0,0), ldda, 1);
return *info;
}
/**
Purpose
-------
ZGETRF_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]
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]
A COMPLEX_16 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_zgesv_comp
********************************************************************/
extern "C" magma_int_t
magma_zgetrf_m(
magma_int_t ngpu,
magma_int_t m, magma_int_t n,
magmaDoubleComplex *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;
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *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, ngpu0 = ngpu;
magma_int_t ii, jj, h, offset, ib, rows;
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_zgetrf_nb(m);
maxm = ((m + 31)/32)*32;
/* figure out NB */
size_t freeMem, totalMem;
cudaMemGetInfo( &freeMem, &totalMem );
freeMem /= sizeof(magmaDoubleComplex);
/* number of columns in the big panel */
h = 1+(2+ngpu0);
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 ( ngpu0 > ceil((double)NB/nb) ) {
ngpu = (int)ceil((double)NB/nb);
h = 1+(2+ngpu);
NB = (magma_int_t)(0.8*freeMem/maxm-h*nb);
} else {
ngpu = ngpu0;
}
if ( ngpu*NB >= n ) {
#ifdef CHECK_ZGETRF_OOC
printf( " * still fit in GPU memory.\n" );
#endif
NB = n;
} else {
#ifdef CHECK_ZGETRF_OOC
printf( " * don't fit in GPU memory.\n" );
#endif
NB = ngpu*NB;
NB = max( nb, (NB / nb) * nb); /* making sure it's devisable by nb (x64) */
}
#ifdef CHECK_ZGETRF_OOC
if ( NB != n ) printf( " * running in out-core mode (n=%d, NB=%d, nb=%d, freeMem=%.2e).\n", n, NB, nb, (double)freeMem );
else printf( " * running in in-core mode (n=%d, NB=%d, nb=%d, freeMem=%.2e).\n", n, NB, nb, (double)freeMem );
#endif
if ( (nb <= 1) || (nb >= min(m,n)) ) {
/* Use CPU code for scalar of one tile. */
lapackf77_zgetrf(&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)/ngpu;
if ( NB%(nb*ngpu) != 0 )
n_local[0]++;
n_local[0] *= nb;
ldn_local = ((n_local[0]+31)/32)*32;
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
if (MAGMA_SUCCESS != magma_zmalloc( &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 ( ngpu0 > ceil((double)N/nb) ) {
ngpu = (int)ceil((double)N/nb);
} else {
ngpu = ngpu0;
}
for( d=0; d < ngpu; d++ ) {
n_local[d] = ((N/nb)/ngpu)*nb;
if (d < (N/nb)%ngpu)
n_local[d] += nb;
else if (d == (N/nb)%ngpu)
n_local[d] += N%nb;
}
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_zsetmatrix_transpose_mgpu(ngpu, stream, A(0,I), lda,
dAT, ldn_local, dA, maxm, M, N, nb);
for( d=0; d < ngpu; 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 < ngpu; d++ ) {
magma_setdevice(d);
nbi = min( nb, NBk );
magma_zsetmatrix_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_ztranspose( M-offset, nbi, dA[d], maxm-offset, dPT(d,0,0), nb );
}
/* applying the pivot from the previous big-panel */
for( d=0; d < ngpu; d++ ) {
magma_setdevice(d);
magmablas_zlaswp_q( ldn_local, dAT(d,0,0), ldn_local, offset+1, offset+NBk, ipiv, 1, stream[d][1] );
}
/* == 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 < ngpu; 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_zsetmatrix_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_ztranspose( 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_ztrsm( 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_zgemm( 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 < ngpu; 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_zgetrf2_mgpu(ngpu, 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_zgetmatrix_transpose_mgpu(ngpu, stream, dAT, ldn_local, A(0,I), lda, dA, maxm, M, N, nb);
for( d=0; d < ngpu; 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_ZGETRF( 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 < ngpu0; 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_zgetrf_piv(m, n, NB, A, lda, ipiv, info);
return *info;
} /* magma_zgetrf_m */
extern "C" magma_int_t
magma_zgetrf2_gpu(
magma_int_t m, magma_int_t n,
magmaDoubleComplex_ptr dA, size_t dA_offset, magma_int_t ldda,
magma_int_t *ipiv,
magma_queue_t queues[2],
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
=======
ZGETRF 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
=========
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) COMPLEX_16 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 dA(i_, j_) dA, dA_offset + (i_)*nb + (j_)*nb*ldda
#define dAT(i_, j_) dAT, dAT_offset + (i_)*nb*lddat + (j_)*nb
#define dAP(i_, j_) dAP, (i_) + (j_)*maxm
#define work(i_) (work + (i_))
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magma_int_t iinfo, nb;
magma_int_t maxm, maxn, mindim;
magma_int_t i, j, rows, s, lddat, ldwork;
magmaDoubleComplex_ptr dAT, dAP;
magmaDoubleComplex *work;
size_t dAT_offset;
/* 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);
nb = magma_get_zgetrf_nb(m);
s = mindim / nb;
if (nb <= 1 || nb >= min(m,n)) {
/* Use CPU code. */
if ( MAGMA_SUCCESS != magma_zmalloc_cpu( &work, m*n )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_zgetmatrix( m, n, dA(0,0), ldda, work(0), m, queues[0] );
lapackf77_zgetrf( &m, &n, work, &m, ipiv, info );
magma_zsetmatrix( m, n, work(0), m, dA(0,0), ldda, queues[0] );
magma_free_cpu( work );
}
else {
/* Use hybrid blocked code. */
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
if ( MAGMA_SUCCESS != magma_zmalloc( &dAP, nb*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
// square matrices can be done in place;
// rectangular requires copy to transpose
if ( m == n ) {
dAT = dA;
dAT_offset = dA_offset;
lddat = ldda;
magmablas_ztranspose_inplace( m, dAT(0,0), lddat, queues[0] );
}
else {
lddat = maxn; // N-by-M
dAT_offset = 0;
if ( MAGMA_SUCCESS != magma_zmalloc( &dAT, lddat*maxm )) {
magma_free( dAP );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmablas_ztranspose( m, n, dA(0,0), ldda, dAT(0,0), lddat, queues[0] );
}
ldwork = maxm;
/*
if ( MAGMA_SUCCESS != magma_zmalloc_cpu( &work, ldwork*nb ) ) {
magma_free( dAP );
if ( dA != dAT )
magma_free( dAT );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
*/
cl_mem work_mapped = clCreateBuffer( gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, ldwork*nb * sizeof(magmaDoubleComplex), NULL, NULL );
work = (magmaDoubleComplex*) clEnqueueMapBuffer( queues[0], work_mapped, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0, ldwork*nb * sizeof(magmaDoubleComplex), 0, NULL, NULL, NULL );
for( j=0; j < s; j++ ) {
// download j-th panel
magmablas_ztranspose( nb, m-j*nb, dAT(j,j), lddat, dAP(0,0), maxm, queues[0] );
clFlush( queues[0] );
magma_queue_sync( queues[0] );
magma_zgetmatrix_async( m-j*nb, nb, dAP(0,0), maxm, work(0), ldwork, queues[1], NULL );
clFlush( queues[1] );
if ( j > 0 ) {
magma_ztrsm( 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_zgemm( 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] );
}
magma_queue_sync( queues[1] );
// do the cpu part
rows = m - j*nb;
lapackf77_zgetrf( &rows, &nb, work, &ldwork, ipiv+j*nb, &iinfo );
if ( *info == 0 && iinfo > 0 )
*info = iinfo + j*nb;
for( i=j*nb; i < j*nb + nb; ++i ) {
ipiv[i] += j*nb;
}
magmablas_zlaswp( n, dAT(0,0), lddat, j*nb + 1, j*nb + nb, ipiv, 1, queues[0] );
clFlush( queues[0] );
// upload j-th panel
magma_zsetmatrix_async( m-j*nb, nb, work(0), ldwork, dAP(0,0), maxm, queues[1], NULL );
magma_queue_sync( queues[1] );
magmablas_ztranspose( m-j*nb, nb, dAP(0,0), maxm, dAT(j,j), lddat, queues[0] );
clFlush( queues[0] );
// do the small non-parallel computations (next panel update)
if ( s > (j+1) ) {
magma_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
nb, nb,
c_one, dAT(j, j ), lddat,
dAT(j, j+1), lddat, queues[0] );
magma_zgemm( 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_ztrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaUnit,
n-s*nb, nb,
c_one, dAT(j, j ), lddat,
dAT(j, j+1), lddat, queues[0] );
magma_zgemm( 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;
magmablas_ztranspose( nb0, rows, dAT(s,s), lddat, dAP(0,0), maxm, queues[0] );
clFlush( queues[0] );
magma_queue_sync( queues[0] );
magma_zgetmatrix_async( rows, nb0, dAP(0,0), maxm, work(0), ldwork, queues[1], NULL );
magma_queue_sync( queues[1] );
// do the cpu part
lapackf77_zgetrf( &rows, &nb0, work, &ldwork, 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_zlaswp( n, dAT(0,0), lddat, s*nb + 1, s*nb + nb0, ipiv, 1, queues[0] );
clFlush( queues[0] );
// upload j-th panel
magma_zsetmatrix_async( rows, nb0, work(0), ldwork, dAP(0,0), maxm, queues[1], NULL );
magma_queue_sync( queues[1] );
magmablas_ztranspose( rows, nb0, dAP(0,0), maxm, dAT(s,s), lddat, queues[0] );
clFlush( queues[0] );
magma_ztrsm( 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 ( dA == dAT ) {
magmablas_ztranspose_inplace( m, dAT(0,0), lddat, queues[0] );
}
else {
magmablas_ztranspose( n, m, dAT(0,0), lddat, dA(0,0), ldda, queues[0] );
magma_free( dAT );
}
magma_queue_sync( queues[0] );
magma_queue_sync( queues[1] );
magma_free( dAP );
// magma_free_cpu( work );
clEnqueueUnmapMemObject( queues[0], work_mapped, work, 0, NULL, NULL );
clReleaseMemObject( work_mapped );
}
return *info;
} /* magma_zgetrf_gpu */
/**
Purpose
-------
ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = MagmaUpper, or
dA = L * L**H, if UPLO = MagmaLower,
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of dA is stored;
- = MagmaLower: Lower triangle of dA is stored.
@param[in]
n INTEGER
The order of the matrix dA. N >= 0.
@param[in,out]
dA COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = MagmaUpper, the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
@ingroup magma_zposv_comp
********************************************************************/
extern "C" magma_int_t
magma_zpotrf_gpu(
magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex_ptr dA, magma_int_t ldda,
magma_int_t *info )
{
#ifdef HAVE_clBLAS
#define dA(i_, j_) dA, ((i_) + (j_)*ldda + dA_offset)
#else
#define dA(i_, j_) (dA + (i_) + (j_)*ldda)
#endif
/* Constants */
const magmaDoubleComplex c_one = MAGMA_Z_ONE;
const magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
const double d_one = 1.0;
const double d_neg_one = -1.0;
/* Local variables */
const char* uplo_ = lapack_uplo_const( uplo );
bool upper = (uplo == MagmaUpper);
magma_int_t j, jb, nb;
magmaDoubleComplex *work;
*info = 0;
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
nb = magma_get_zpotrf_nb( n );
if (MAGMA_SUCCESS != magma_zmalloc_pinned( &work, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_queue_t queues[2];
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
if (nb <= 1 || nb >= n) {
/* Use unblocked code. */
magma_zgetmatrix( n, n, dA(0,0), ldda, work, n, queues[0] );
lapackf77_zpotrf( uplo_, &n, work, &n, info );
magma_zsetmatrix( n, n, work, n, dA(0,0), ldda, queues[0] );
}
else {
/* Use blocked code. */
if (upper) {
//=========================================================
/* Compute the Cholesky factorization A = U'*U. */
for (j=0; j < n; j += nb) {
// apply all previous updates to diagonal block,
// then transfer it to CPU
jb = min( nb, n-j );
magma_zherk( MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dA(0, j), ldda,
d_one, dA(j, j), ldda, queues[1] );
magma_queue_sync( queues[1] );
magma_zgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, queues[0] );
// apply all previous updates to block row right of diagonal block
if (j+jb < n) {
magma_zgemm( MagmaConjTrans, MagmaNoTrans,
jb, n-j-jb, j,
c_neg_one, dA(0, j ), ldda,
dA(0, j+jb), ldda,
c_one, dA(j, j+jb), ldda, queues[1] );
}
// simultaneous with above zgemm, transfer diagonal block,
// factor it on CPU, and test for positive definiteness
magma_queue_sync( queues[0] );
lapackf77_zpotrf( MagmaUpperStr, &jb, work, &jb, info );
magma_zsetmatrix_async( jb, jb,
work, jb,
dA(j, j), ldda, queues[1] );
if (*info != 0) {
*info = *info + j;
break;
}
// apply diagonal block to block row right of diagonal block
if (j+jb < n) {
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, n-j-jb,
c_one, dA(j, j), ldda,
dA(j, j+jb), ldda, queues[1] );
}
}
}
else {
//=========================================================
// Compute the Cholesky factorization A = L*L'.
for (j=0; j < n; j += nb) {
// apply all previous updates to diagonal block,
// then transfer it to CPU
jb = min( nb, n-j );
magma_zherk( MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dA(j, 0), ldda,
d_one, dA(j, j), ldda, queues[1] );
magma_queue_sync( queues[1] );
magma_zgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, queues[0] );
// apply all previous updates to block column below diagonal block
if (j+jb < n) {
magma_zgemm( MagmaNoTrans, MagmaConjTrans,
n-j-jb, jb, j,
c_neg_one, dA(j+jb, 0), ldda,
dA(j, 0), ldda,
c_one, dA(j+jb, j), ldda, queues[1] );
}
// simultaneous with above zgemm, transfer diagonal block,
// factor it on CPU, and test for positive definiteness
magma_queue_sync( queues[0] );
lapackf77_zpotrf( MagmaLowerStr, &jb, work, &jb, info );
magma_zsetmatrix_async( jb, jb,
work, jb,
dA(j, j), ldda, queues[1] );
if (*info != 0) {
*info = *info + j;
break;
}
// apply diagonal block to block column below diagonal
if (j+jb < n) {
magma_ztrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
n-j-jb, jb,
c_one, dA(j, j), ldda,
dA(j+jb, j), ldda, queues[1] );
}
}
}
}
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free_pinned( work );
return *info;
} /* magma_zpotrf_gpu */
/**
Purpose
-------
ZPOTRF computes the Cholesky factorization of a complex Hermitian
positive definite matrix dA.
The factorization has the form
dA = U**H * U, if UPLO = MagmaUpper, or
dA = L * L**H, if UPLO = MagmaLower,
where U is an upper triangular matrix and L is lower triangular.
This is the block version of the algorithm, calling Level 3 BLAS.
This version assumes the computation runs through the NULL stream
and therefore is not overlapping some computation with communication.
Arguments
---------
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of dA is stored;
- = MagmaLower: Lower triangle of dA is stored.
@param[in]
n INTEGER
The order of the matrix dA. N >= 0.
@param[in,out]
dA COMPLEX_16 array on the GPU, dimension (LDDA,N)
On entry, the Hermitian matrix dA. If UPLO = MagmaUpper, the leading
N-by-N upper triangular part of dA contains the upper
triangular part of the matrix dA, and the strictly lower
triangular part of dA is not referenced. If UPLO = MagmaLower, the
leading N-by-N lower triangular part of dA contains the lower
triangular part of the matrix dA, and the strictly upper
triangular part of dA is not referenced.
\n
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization dA = U**H * U or dA = L * L**H.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i, the leading minor of order i is not
positive definite, and the factorization could not be
completed.
@ingroup magma_zposv_comp
********************************************************************/
extern "C" magma_int_t
magma_zpotrf_gpu(magma_uplo_t uplo, magma_int_t n,
magmaDoubleComplex *dA, magma_int_t ldda, magma_int_t *info)
{
#define dA(i, j) (dA + (j)*ldda + (i))
magma_int_t j, jb, nb;
const char* uplo_ = lapack_uplo_const( uplo );
magmaDoubleComplex c_one = MAGMA_Z_ONE;
magmaDoubleComplex c_neg_one = MAGMA_Z_NEG_ONE;
magmaDoubleComplex *work;
double d_one = 1.0;
double d_neg_one = -1.0;
int upper = (uplo == MagmaUpper);
*info = 0;
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
nb = magma_get_zpotrf_nb(n);
if (MAGMA_SUCCESS != magma_zmalloc_pinned( &work, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
if ((nb <= 1) || (nb >= n)) {
/* Use unblocked code. */
magma_zgetmatrix( n, n, dA, ldda, work, n );
lapackf77_zpotrf(uplo_, &n, work, &n, info);
magma_zsetmatrix( n, n, work, n, dA, ldda );
}
else {
/* Use blocked code. */
if (upper) {
/* Compute the Cholesky factorization A = U'*U. */
for (j=0; j < n; j += nb) {
/* Update and factorize the current diagonal block and test
for non-positive-definiteness. Computing MIN */
jb = min(nb, (n-j));
magma_zherk(MagmaUpper, MagmaConjTrans, jb, j,
d_neg_one, dA(0, j), ldda,
d_one, dA(j, j), ldda);
magma_zgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, stream[1] );
if ( (j+jb) < n) {
/* Compute the current block row. */
magma_zgemm(MagmaConjTrans, MagmaNoTrans,
jb, (n-j-jb), j,
c_neg_one, dA(0, j ), ldda,
dA(0, j+jb), ldda,
c_one, dA(j, j+jb), ldda);
}
magma_queue_sync( stream[1] );
lapackf77_zpotrf(MagmaUpperStr, &jb, work, &jb, info);
magma_zsetmatrix_async( jb, jb,
work, jb,
dA(j, j), ldda, stream[0] );
if (*info != 0) {
*info = *info + j;
break;
}
if ( (j+jb) < n) {
magma_ztrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
jb, (n-j-jb),
c_one, dA(j, j ), ldda,
dA(j, j+jb), ldda);
}
}
}
else {
//=========================================================
// Compute the Cholesky factorization A = L*L'.
for (j=0; j < n; j += nb) {
// Update and factorize the current diagonal block and test
// for non-positive-definiteness. Computing MIN
jb = min(nb, (n-j));
magma_zherk(MagmaLower, MagmaNoTrans, jb, j,
d_neg_one, dA(j, 0), ldda,
d_one, dA(j, j), ldda);
magma_zgetmatrix_async( jb, jb,
dA(j, j), ldda,
work, jb, stream[1] );
if ( (j+jb) < n) {
magma_zgemm( MagmaNoTrans, MagmaConjTrans,
(n-j-jb), jb, j,
c_neg_one, dA(j+jb, 0), ldda,
dA(j, 0), ldda,
c_one, dA(j+jb, j), ldda);
}
magma_queue_sync( stream[1] );
lapackf77_zpotrf(MagmaLowerStr, &jb, work, &jb, info);
magma_zsetmatrix_async( jb, jb,
work, jb,
dA(j, j), ldda, stream[0] );
if (*info != 0) {
*info = *info + j;
break;
}
if ( (j+jb) < n) {
magma_ztrsm(MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
(n-j-jb), jb,
c_one, dA(j, j), ldda,
dA(j+jb, j), ldda);
}
}
}
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free_pinned( work );
return *info;
} /* magma_zpotrf_gpu */
