/**
Purpose
-------
DSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric
band-diagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
This version stores the triangular matrices T used in the accumulated
Householder transformations (I - V T V').
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,out]
A DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 UPLO = MagmaUpper, the Upper band-diagonal of A is
overwritten by the corresponding elements of the
band-diagonal matrix T, and the elements above the band
diagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the the Lower band-diagonal of A is overwritten by
the corresponding elements of the band-diagonal
matrix T, and the elements below the band-diagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
tau DOUBLE_PRECISION array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
dT DOUBLE_PRECISION array on the GPU, dimension N*NB,
where NB is the optimal blocksize.
On exit dT holds the upper triangular matrices T from the
accumulated Householder transformations (I - V T V') used
in the factorization. The nb x nb matrices T are ordered
consecutively in memory one after another.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
@ingroup magma_dsyev_2stage
********************************************************************/
extern "C" magma_int_t
magma_dsytrd_sy2sb( magma_uplo_t uplo, magma_int_t n, magma_int_t nb,
double *A, magma_int_t lda,
double *tau,
double *work, magma_int_t lwork,
double *dT,
magma_int_t *info)
{
#define A(a_1,a_2) ( A + ((a_2)-1)*( lda) + (a_1)-1)
#define dA(a_1,a_2) (dA + ((a_2)-1)*(ldda) + (a_1)-1)
#define tau_ref(a_1) (tau + (a_1)-1)
#define dT(a_1) (dT + ((a_1)-1)*(lddt))
int ldda = ((n+31)/32)*32;
int lddt = nb;
double c_neg_one = MAGMA_D_NEG_ONE;
double c_neg_half = MAGMA_D_NEG_HALF;
double c_one = MAGMA_D_ONE;
double c_zero = MAGMA_D_ZERO;
double d_one = MAGMA_D_ONE;
magma_int_t pm, pn, indi, indj, pk;
magma_int_t pm_old=0, pn_old=0, indi_old=0, indj_old=0;
int i;
int lwkopt;
int lquery;
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (lwork < 1 && ! lquery) {
*info = -9;
}
/* Determine the block size. */
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
}
if (*info != 0)
return *info;
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
double *dA;
if (MAGMA_SUCCESS != magma_dmalloc( &dA, (n + 2*nb)*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
// limit to 16 threads
magma_int_t orig_threads = magma_get_lapack_numthreads();
magma_set_lapack_numthreads( min(orig_threads,16) );
/* Use the first panel of dA as work space */
double *dwork = dA + n*ldda;
double *dW = dwork + nb*ldda;
#ifdef TRACING
char buf[80];
#endif
magma_queue_t stream[3];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
stream[2] = 0; // default stream
trace_init( 1, 1, 3, stream );
double *hT = work + lwork - nb*nb;
lwork -= nb*nb;
memset( hT, 0, nb*nb*sizeof(double));
magmablasSetKernelStream( stream[0] );
magma_event_t Pupdate_event;
cudaEventCreateWithFlags(&Pupdate_event,cudaEventDisableTiming);
//magma_event_create(&Pupdate_event);
if (upper) {
printf("DSYTRD_HE2HB is not yet implemented for upper matrix storage. Exit.\n");
exit(1);
} else {
/* Copy the matrix to the GPU */
if (1 <= n-nb) {
trace_gpu_start( 0, 0, "set", "set A" );
magma_dsetmatrix_async( (n-nb), (n-nb),
A(nb+1, nb+1), lda,
dA(nb+1, nb+1), ldda, stream[0] );
trace_gpu_end( 0, 0 );
}
/* Reduce the lower triangle of A */
for (i = 1; i <= n-nb; i += nb) {
indi = i+nb;
indj = i;
pm = n - i - nb + 1;
//pn = min(i+nb-1, n-nb) -i + 1;
pn = nb;
/* Get the current panel (no need for the 1st iteration) */
if (i > 1 ) {
// dpanel_to_q copy the upper oof diagonal part of
// the matrix to work to be restored later. acctually
// the zero's and one's putted are not used this is only
// because we don't have a function that copy only the
// upper part of A to be restored after copying the
// lookahead panel that has been computted from GPU to CPU.
dpanel_to_q(MagmaUpper, pn-1, A(i, i+1), lda, work);
trace_gpu_start( 0, 1, "get", "get panel" );
//magma_queue_sync( stream[0] );
magma_queue_wait_event(stream[1], Pupdate_event); //, 0);
magma_dgetmatrix_async( (pm+pn), pn,
dA( i, i), ldda,
A ( i, i), lda, stream[1] );
trace_gpu_end( 0, 1 );
trace_gpu_start( 0, 2, "her2k", "her2k" );
magma_dsyr2k(MagmaLower, MagmaNoTrans, pm_old-pn_old, pn_old, c_neg_one,
dA(indi_old+pn_old, indj_old), ldda,
dW + pn_old, pm_old, d_one,
dA(indi_old+pn_old, indi_old+pn_old), ldda);
trace_gpu_end( 0, 2 );
trace_cpu_start( 0, "sync", "sync on 1" );
magma_queue_sync( stream[1] );
trace_cpu_end( 0 );
dq_to_panel(MagmaUpper, pn-1, A(i, i+1), lda, work);
}
/* ==========================================================
QR factorization on a panel starting nb off of the diagonal.
Prepare the V and T matrices.
========================================================== */
#ifdef TRACING
snprintf( buf, sizeof(buf), "panel %d", i );
#endif
trace_cpu_start( 0, "geqrf", buf );
lapackf77_dgeqrf(&pm, &pn, A(indi, indj), &lda,
tau_ref(i), work, &lwork, info);
/* Form the matrix T */
pk=min(pm,pn);
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&pm, &pk, A(indi, indj), &lda,
tau_ref(i), hT, &nb);
/* Prepare V - put 0s in the upper triangular part of the panel
(and 1s on the diagonal), temporaly storing the original in work */
dpanel_to_q(MagmaUpper, pk, A(indi, indj), lda, work);
trace_cpu_end( 0 );
/* Send V from the CPU to the GPU */
trace_gpu_start( 0, 0, "set", "set V and T" );
magma_dsetmatrix_async( pm, pk,
A(indi, indj), lda,
dA(indi, indj), ldda, stream[0] );
/* Send the triangular factor T to the GPU */
magma_dsetmatrix_async( pk, pk,
hT, nb,
dT(i), lddt, stream[0] );
trace_gpu_end( 0, 0 );
/* ==========================================================
Compute W:
1. X = A (V T)
2. W = X - 0.5* V * (T' * (V' * X))
========================================================== */
/* dwork = V T */
trace_cpu_start( 0, "sync", "sync on 0" );
// this sync is done here to be sure that the copy has been finished
// because below we made a restore dq_to_panel and this restore need
// to ensure that the copy has been finished. we did it here to allow
// overlapp of restore with next gemm and symm.
magma_queue_sync( stream[0] );
trace_cpu_end( 0 );
trace_gpu_start( 0, 2, "gemm", "work = V*T" );
magma_dgemm(MagmaNoTrans, MagmaNoTrans, pm, pk, pk,
c_one, dA(indi, indj), ldda,
dT(i), lddt,
c_zero, dwork, pm);
trace_gpu_end( 0, 2 );
/* dW = X = A*V*T. dW = A*dwork */
trace_gpu_start( 0, 2, "hemm", "X = A*work" );
magma_dsymm(MagmaLeft, uplo, pm, pk,
c_one, dA(indi, indi), ldda,
dwork, pm,
c_zero, dW, pm);
trace_gpu_end( 0, 2 );
/* restore the panel */
dq_to_panel(MagmaUpper, pk, A(indi, indj), lda, work);
/* dwork = V*T already ==> dwork' = T'*V'
* compute T'*V'*X ==> dwork'*W ==>
* dwork + pm*nb = ((T' * V') * X) = dwork' * X = dwork' * W */
trace_gpu_start( 0, 2, "gemm", "work = T'*V'*X" );
magma_dgemm(MagmaConjTrans, MagmaNoTrans, pk, pk, pm,
c_one, dwork, pm,
dW, pm,
c_zero, dwork + pm*nb, nb);
trace_gpu_end( 0, 2 );
/* W = X - 0.5 * V * T'*V'*X
* = X - 0.5 * V * (dwork + pm*nb) = W - 0.5 * V * (dwork + pm*nb) */
trace_gpu_start( 0, 2, "gemm", "W = X - 0.5*V*(T'*V'*X)" );
magma_dgemm(MagmaNoTrans, MagmaNoTrans, pm, pk, pk,
c_neg_half, dA(indi, indj), ldda,
dwork + pm*nb, nb,
c_one, dW, pm);
trace_gpu_end( 0, 2 );
/* ==========================================================
Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V'
========================================================== */
if (i + nb <= n-nb) {
/* There would be next iteration;
do lookahead - update the next panel */
trace_gpu_start( 0, 2, "gemm", "gemm 4 next panel left" );
magma_dgemm(MagmaNoTrans, MagmaConjTrans, pm, pn, pn, c_neg_one,
dA(indi, indj), ldda,
dW, pm, c_one,
dA(indi, indi), ldda);
trace_gpu_end( 0, 2 );
trace_gpu_start( 0, 2, "gemm", "gemm 5 next panel right" );
magma_dgemm(MagmaNoTrans, MagmaConjTrans, pm, pn, pn, c_neg_one,
dW, pm,
dA(indi, indj), ldda, c_one,
dA(indi, indi), ldda);
trace_gpu_end( 0, 2 );
magma_event_record(Pupdate_event, stream[0]);
}
else {
/* no look-ahead as this is last iteration */
trace_gpu_start( 0, 2, "her2k", "her2k last iteration" );
magma_dsyr2k(MagmaLower, MagmaNoTrans, pk, pk, c_neg_one,
dA(indi, indj), ldda,
dW, pm, d_one,
dA(indi, indi), ldda);
trace_gpu_end( 0, 2 );
}
indi_old = indi;
indj_old = indj;
pm_old = pm;
pn_old = pn;
} // end loop for (i)
/* Send the last block to the CPU */
pk = min(pm,pn);
if (1 <= n-nb) {
dpanel_to_q(MagmaUpper, pk-1, A(n-pk+1, n-pk+2), lda, work);
trace_gpu_start( 0, 2, "get", "get last block" );
magma_dgetmatrix( pk, pk,
dA(n-pk+1, n-pk+1), ldda,
A(n-pk+1, n-pk+1), lda );
trace_gpu_end( 0, 2 );
dq_to_panel(MagmaUpper, pk-1, A(n-pk+1, n-pk+2), lda, work);
}
}// end of LOWER
trace_finalize( "dsytrd_sy2sb.svg", "trace.css" );
magma_event_destroy( Pupdate_event );
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free( dA );
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
magmablasSetKernelStream( orig_stream );
magma_set_lapack_numthreads( orig_threads );
return *info;
} /* magma_dsytrd_sy2sb */
/**
Purpose
-------
DSYTRD_HE2HB reduces a real symmetric matrix A to real symmetric
band-diagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
This version stores the triangular matrices T used in the accumulated
Householder transformations (I - V T V').
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,out]
A DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 UPLO = MagmaUpper, the Upper band-diagonal of A is
overwritten by the corresponding elements of the
band-diagonal matrix T, and the elements above the band
diagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the the Lower band-diagonal of A is overwritten by
the corresponding elements of the band-diagonal
matrix T, and the elements below the band-diagonal, with
the array TAU, represent the orthogonal matrix Q as a product
of elementary reflectors. See Further Details.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
tau DOUBLE_PRECISION array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
dT DOUBLE_PRECISION array on the GPU, dimension N*NB,
where NB is the optimal blocksize.
On exit dT holds the upper triangular matrices T from the
accumulated Householder transformations (I - V T V') used
in the factorization. The nb x nb matrices T are ordered
consecutively in memory one after another.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
Further Details
---------------
If UPLO = MagmaUpper, the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = MagmaLower, the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
and tau in TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = MagmaUpper: if UPLO = MagmaLower:
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
@ingroup magma_dsyev_2stage
********************************************************************/
extern "C" magma_int_t
magma_dsytrd_sy2sb_mgpu(
magma_uplo_t uplo, magma_int_t n, magma_int_t nb,
double *A, magma_int_t lda,
double *tau,
double *work, magma_int_t lwork,
magmaDouble_ptr dAmgpu[], magma_int_t ldda,
magmaDouble_ptr dTmgpu[], magma_int_t lddt,
magma_int_t ngpu, magma_int_t distblk,
magma_queue_t queues[][20], magma_int_t nqueue,
magma_int_t *info)
{
#define A(a_1,a_2) ( A + ((a_2)-1)*( lda) + (a_1)-1)
#define tau_ref(a_1) (tau + (a_1)-1)
#define dT(a_0, a_1, a_2) (dTmgpu[a_0] + ((a_2)-1)*(lddt) + (a_1)-1)
#define dA(a_0, a_1, a_2) (dAmgpu[a_0] + ((a_2)-1)*(ldda) + (a_1)-1)
double c_neg_one = MAGMA_D_NEG_ONE;
double c_neg_half = MAGMA_D_NEG_HALF;
double c_one = MAGMA_D_ONE;
double c_zero = MAGMA_D_ZERO;
double d_one = MAGMA_D_ONE;
magma_int_t pm, pn, indi, indj, pk;
magma_int_t pm_old=0, pn_old=0, indi_old=0, flipV=-1;
magma_int_t iblock, idev, di;
int i;
int lwkopt;
int lquery;
assert (nqueue >= 3);
assert (nqueue >= (ngpu+1));
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (lwork < 1 && ! lquery) {
*info = -9;
}
/* Determine the block size. */
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
}
if (*info != 0)
return *info;
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
// limit to 16 threads
magma_int_t orig_threads = magma_get_lapack_numthreads();
magma_set_lapack_numthreads( min(orig_threads,16) );
magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2];
magma_int_t nbcmplx=0;
magma_buildconnection_mgpu(gnode, &nbcmplx, ngpu);
#ifdef ENABLE_DEBUG
printf(" Initializing communication pattern.... GPU-ncmplx %d\n\n", nbcmplx);
#endif
double *dspace[MagmaMaxGPUs];
double *dwork[MagmaMaxGPUs], *dworkbis[MagmaMaxGPUs];
double *dvall[MagmaMaxGPUs], *dv[MagmaMaxGPUs], *dw[MagmaMaxGPUs];
double *workngpu[MagmaMaxGPUs+1];
magma_event_t redevents[MagmaMaxGPUs][MagmaMaxGPUs*MagmaMaxGPUs+10];
magma_int_t nbevents = MagmaMaxGPUs*MagmaMaxGPUs;
magma_int_t lddv = ldda;
magma_int_t lddw = lddv;
magma_int_t dwrk2siz = ldda*nb*(ngpu+1);
magma_int_t worksiz = n*nb;
magma_int_t devworksiz = 2*nb*lddv + nb*lddw + nb*ldda + dwrk2siz; // 2*dv(dv0+dv1) + dw + dwork +dworkbis
// local allocation and stream creation
// TODO check malloc
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
magma_dmalloc( &dspace[dev], devworksiz );
magma_dmalloc_pinned ( &workngpu[dev], worksiz);
dvall[dev] = dspace[dev];
dw[dev] = dvall[dev] + 2*nb*lddv;
dwork[dev] = dw[dev] + nb*lddw;
dworkbis[dev] = dwork[dev] + nb*ldda;
magmablasSetKernelStream( queues[ dev ][ 0 ] );
for( magma_int_t i = 0; i < nbevents; ++i ) {
cudaEventCreateWithFlags(&redevents[dev][i],cudaEventDisableTiming);
}
}
magma_dmalloc_pinned ( &workngpu[ngpu], worksiz);
double *worktest = NULL;
//magma_dmalloc_cpu( &worktest, n*nb ); // not used
// ======================
double *hT = work + lwork - nb*nb;
lwork -= nb*nb;
memset( hT, 0, nb*nb*sizeof(double));
if (upper) {
printf("DSYTRD_HE2HB is not yet implemented for upper matrix storage. Exit.\n");
exit(1);
} else {
/* Reduce the lower triangle of A */
for (i = 1; i <= n-nb; i += nb) {
indi = i+nb;
indj = i;
pm = n - i - nb + 1;
//pn = min(i+nb-1, n-nb) -i + 1;
pn = nb;
/* Get the current panel (no need for the 1st iteration) */
if (i > 1 ) {
// dpanel_to_q copy the upper oof diagonal part of
// the matrix to work to be restored later. acctually
// the zero's and one's putted are not used this is only
// because we don't have a function that copy only the
// upper part of A to be restored after copying the
// lookahead panel that has been computted from GPU to CPU.
dpanel_to_q(MagmaUpper, pn-1, A(i, i+1), lda, work);
// find the device who own the panel then send it to the CPU.
// below a -1 was added and then a -1 was done on di because of the fortran indexing
iblock = ((i-1) / distblk) / ngpu; // local block id
di = iblock*distblk + (i-1)%distblk; // local index in parent matrix
idev = ((i-1) / distblk) % ngpu; // device with this block
//printf("Receiving panel ofsize %d %d from idev %d A(%d,%d) \n",(pm+pn), pn,idev,i-1,di);
magma_setdevice( idev );
//magma_device_sync();
magma_dgetmatrix_async( (pm+pn), pn,
dA(idev, i, di+1), ldda,
A( i, i), lda, queues[ idev ][ nqueue-1 ] );
//magma_setdevice( 0 );
//printf("updating dsyr2k on A(%d,%d) of size %d %d \n",indi_old+pn_old-1,indi_old+pn_old-1,pm_old-pn_old,pn_old);
// compute DSYR2K_MGPU
magmablas_dsyr2k_mgpu2(
MagmaLower, MagmaNoTrans, pm_old-pn_old, pn_old,
c_neg_one, dv, pm_old, pn_old,
dw, pm_old, pn_old,
d_one, dAmgpu, ldda, indi_old+pn_old-1,
ngpu, distblk, queues, 2 );
//magma_setdevice( 0 );
magma_setdevice( idev );
magma_queue_sync( queues[idev][ nqueue-1 ] );
//magma_setdevice( 0 );
dq_to_panel(MagmaUpper, pn-1, A(i, i+1), lda, work);
}
/* ==========================================================
QR factorization on a panel starting nb off of the diagonal.
Prepare the V and T matrices.
========================================================== */
lapackf77_dgeqrf(&pm, &pn, A(indi, indj), &lda,
tau_ref(i), work, &lwork, info);
/* Form the matrix T */
pk=min(pm,pn);
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&pm, &pk, A(indi, indj), &lda,
tau_ref(i), hT, &nb);
/* Prepare V - put 0s in the upper triangular part of the panel
(and 1s on the diagonal), temporaly storing the original in work */
dpanel_to_q(MagmaUpper, pk, A(indi, indj), lda, work);
/* Send V and T from the CPU to the GPU */
// To be able to overlap the GET with the DSYR2K
// it should be done on last stream.
// TO Avoid a BUG that is overwriting the old_V
// used atthis moment by dsyr2k with the new_V
// send it now, we decide to have a flipflop
// vector of Vs. if step%2=0 use V[0] else use V[nb*n]
flipV = ((i-1)/nb)%2;
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
dv[dev] = dvall[dev] + flipV*nb*lddv;
}
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
// send V
magma_dsetmatrix_async( pm, pk,
A(indi, indj), lda,
dv[dev], pm, queues[dev][nqueue-1] );
// Send the triangular factor T to the GPU
magma_dsetmatrix_async( pk, pk,
hT, nb,
dT(dev, 1, i), lddt, queues[dev][nqueue-1] );
}
/* ==========================================================
Compute W:
1. X = A (V T)
2. W = X - 0.5* V * (T' * (V' * X))
========================================================== */
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
// dwork = V T
magma_setdevice( dev );
magmablasSetKernelStream( queues[ dev ][ nqueue-1 ] );
magma_queue_sync( queues[dev][nqueue-1] );
magma_dgemm(MagmaNoTrans, MagmaNoTrans, pm, pk, pk,
c_one, dv[dev], pm,
dT(dev, 1, i), lddt,
c_zero, dwork[dev], pm);
}
// ===============================================
// SYNC TO BE SURE THAT BOTH V AND T WERE
// RECEIVED AND VT IS COMPUTED and SYR2K is done
// ===============================================
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
for( magma_int_t s = 0; s < nqueue; ++s )
magma_queue_sync( queues[dev][s] );
}
// compute DSYMM_MGPU
// The broadcast of the result done inside this function
// should be done in stream [0] because i am assuming this
// for the GEMMs below otherwise I have to SYNC over the
// Broadcasting stream.
if (ngpu == 1) {
magmablasSetKernelStream( queues[ 0 ][ 0 ] );
magma_dsymm(MagmaLeft, uplo, pm, pk,
c_one, dAmgpu[0]+(indi-1)*ldda+(indi-1), ldda,
dwork[0], pm,
c_zero, dw[0], pm);
} else {
magmablas_dsymm_mgpu_com(
MagmaLeft, uplo, pm, pk,
c_one, dAmgpu, ldda, indi-1,
dwork, pm,
c_zero, dw, pm, dworkbis, dwrk2siz, worktest, pm, workngpu, worksiz,
ngpu, distblk, queues, nqueue-1, redevents, nbevents, gnode, nbcmplx);
}
/* dwork = V*T already ==> dwork' = T'*V'
* compute T'*V'*X ==> dwork'*W ==>
* dwork + pm*nb = ((T' * V') * X) = dwork' * X = dwork' * W */
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
// Here we have to wait until the broadcast of DSYMM has been done.
// Note that the broadcast should be done on stream[0] so in a way
// we can continue here on the same stream and avoid a sync
magma_setdevice( dev );
magmablasSetKernelStream( queues[ dev ][ 0 ] );
// magma_queue_sync( queues[dev][0] );
magma_dgemm(MagmaConjTrans, MagmaNoTrans, pk, pk, pm,
c_one, dwork[dev], pm,
dw[dev], pm,
c_zero, dworkbis[dev], nb);
/* W = X - 0.5 * V * T'*V'*X
* = X - 0.5 * V * (dwork + pm*nb) = W - 0.5 * V * (dwork + pm*nb) */
magma_dgemm(MagmaNoTrans, MagmaNoTrans, pm, pk, pk,
c_neg_half, dv[dev], pm,
dworkbis[dev], nb,
c_one, dw[dev], pm);
}
/* restore the panel it is put here to overlap with the previous GEMM*/
dq_to_panel(MagmaUpper, pk, A(indi, indj), lda, work);
// ===============================================
// SYNC TO BE SURE THAT BOTH V AND W ARE DONE
// ===============================================
// Synchronise to be sure that W has been computed
// because next DSYR2K use streaming and may happen
// that lunch a gemm on stream 2 while stream 0
// which compute those 2 GEMM above has not been
// computed and also used for the same reason in
// the panel update below and also for the last HER2K
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] );
}
/* ==========================================================
Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V'
========================================================== */
if (i + nb <= n-nb) {
/* There would be next iteration;
do lookahead - update the next panel */
// below a -1 was added and then a -1 was done on di because of the fortran indexing
iblock = ((indi-1) / distblk) / ngpu; // local block id
di = iblock*distblk + (indi-1)%distblk; // local index in parent matrix
idev = ((indi-1) / distblk) % ngpu; // device with this block
magma_setdevice( idev );
magmablasSetKernelStream( queues[ idev ][ nqueue-1 ] );
//magma_queue_sync( queues[idev][0] ); removed because the sync has been done in the loop above
magma_dgemm(MagmaNoTrans, MagmaConjTrans, pm, pn, pn, c_neg_one,
dv[idev], pm,
dw[idev], pm, c_one,
dA(idev, indi, di+1), ldda);
magma_dgemm(MagmaNoTrans, MagmaConjTrans, pm, pn, pn, c_neg_one,
dw[idev], pm,
dv[idev], pm, c_one,
dA(idev, indi, di+1), ldda);
//printf("updating next panel distblk %d idev %d on A(%d,%d) of size %d %d %d \n",distblk,idev,indi-1,di,pm,pn,pn);
}
else {
/* no look-ahead as this is last iteration */
// below a -1 was added and then a -1 was done on di because of the fortran indexing
iblock = ((indi-1) / distblk) / ngpu; // local block id
di = iblock*distblk + (indi-1)%distblk; // local index in parent matrix
idev = ((indi-1) / distblk) % ngpu; // device with this block
magma_setdevice( idev );
magmablasSetKernelStream( queues[ idev ][ 0 ] );
//printf("LAST DSYR2K idev %d on A(%d,%d) of size %d \n",idev, indi-1,di,pk);
magma_dsyr2k(MagmaLower, MagmaNoTrans, pk, pk, c_neg_one,
dv[idev], pm,
dw[idev], pm, d_one,
dA(idev, indi, di+1), ldda);
/* Send the last block to the CPU */
dpanel_to_q(MagmaUpper, pk-1, A(n-pk+1, n-pk+2), lda, work);
magma_dgetmatrix( pk, pk,
dA(idev, indi, di+1), ldda,
A(n-pk+1, n-pk+1), lda );
dq_to_panel(MagmaUpper, pk-1, A(n-pk+1, n-pk+2), lda, work);
}
indi_old = indi;
//indj_old = indj;
pm_old = pm;
pn_old = pn;
} // end loop for (i)
}// end of LOWER
//magma_setdevice( 0 );
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
magma_free( dspace[dev]);
magma_free_pinned(workngpu[dev]);
for( magma_int_t e = 0; e < nbevents; ++e ) {
magma_event_destroy( redevents[dev][e] );
}
}
magma_free_pinned(workngpu[ngpu]);
magma_free_cpu(worktest);
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
magma_set_lapack_numthreads( orig_threads );
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
return *info;
} /* magma_dsytrd_sy2sb_mgpu */
/**
Purpose
-------
DSYGST reduces a real symmetric-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 DPOTRF.
Arguments
---------
@param[in]
itype 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.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored and B is factored as U^H*U;
- = MagmaLower: Lower triangle of A is stored and B is factored as L*L^H.
@param[in]
n INTEGER
The order of the matrices A and B. N >= 0.
@param[in,out]
A DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 transformed matrix, stored in the
same format as A.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
B DOUBLE PRECISION array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B,
as returned by DPOTRF.
B is modified by the routine but restored on exit (in lapack dsygst/dsygs2).
@param[in]
ldb 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_dsyev_comp
********************************************************************/
extern "C" magma_int_t
magma_dsygst(
magma_int_t itype, magma_uplo_t uplo, magma_int_t n,
double *A, magma_int_t lda,
double *B, magma_int_t ldb,
magma_int_t *info)
{
#define A(i_, j_) (A + (i_) + (j_)*lda)
#define B(i_, j_) (B + (i_) + (j_)*ldb)
#define dA(i_, j_) (dwork + (i_) + (j_)*ldda )
#define dB(i_, j_) (dwork + (i_) + (j_)*lddb + n*ldda)
/* Constants */
const double c_one = MAGMA_D_ONE;
const double c_neg_one = MAGMA_D_NEG_ONE;
const double c_half = MAGMA_D_HALF;
const double c_neg_half = MAGMA_D_NEG_HALF;
const double d_one = 1.0;
/* Local variables */
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t k, kb, kb2, nb;
magma_int_t ldda = n;
magma_int_t lddb = n;
magmaDouble_ptr dwork;
bool upper = (uplo == MagmaUpper);
/* Test the input parameters. */
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! upper && uplo != MagmaLower) {
*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_dmalloc( &dwork, 2*n*n )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
nb = magma_get_dsygst_nb( n );
magma_queue_t queues[2];
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
magma_dsetmatrix( n, n, A(0, 0), lda, dA(0, 0), ldda, queues[1] );
magma_dsetmatrix( n, n, B(0, 0), ldb, dB(0, 0), lddb, queues[1] );
/* Use hybrid blocked code */
if (itype == 1) {
if (upper) {
/* Compute inv(U^H)*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_dsygst( &itype, uplo_, &kb, A(k,k), &lda, B(k,k), &ldb, info );
magma_dsetmatrix_async( kb, kb,
A(k, k), lda,
dA(k, k), ldda, queues[0] );
if (k+kb < n) {
magma_dtrsm( MagmaLeft, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
kb, n-k-kb,
c_one, dB(k,k), lddb,
dA(k,k+kb), ldda, queues[1] );
magma_queue_sync( queues[0] ); // finish set dA(k,k)
magma_dsymm( 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, queues[1] );
magma_dsyr2k( 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, queues[1] );
// Start copying next A block
magma_queue_sync( queues[1] );
magma_dgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(k+kb, k+kb), lda, queues[0] );
magma_dsymm( 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, queues[1] );
magma_dtrsm( MagmaRight, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
kb, n-k-kb,
c_one, dB(k+kb,k+kb), lddb,
dA(k,k+kb), ldda, queues[1] );
magma_queue_sync( queues[0] ); // finish get A(k+kb,k+kb)
}
}
}
else {
/* Compute inv(L)*A*inv(L^H) */
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_dsygst( &itype, uplo_, &kb, A(k,k), &lda, B(k,k), &ldb, info );
magma_dsetmatrix_async( kb, kb,
A(k, k), lda,
dA(k, k), ldda, queues[0] );
if (k+kb < n) {
magma_dtrsm( MagmaRight, MagmaLower, MagmaConjTrans, MagmaNonUnit,
n-k-kb, kb,
c_one, dB(k,k), lddb,
dA(k+kb,k), ldda, queues[1] );
magma_queue_sync( queues[0] ); // finish set dA(k,k)
magma_dsymm( 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, queues[1] );
magma_dsyr2k( 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, queues[1] );
// Start copying next A block
magma_queue_sync( queues[1] );
magma_dgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(k+kb, k+kb), lda, queues[0] );
magma_dsymm( 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, queues[1] );
magma_dtrsm( MagmaLeft, MagmaLower, MagmaNoTrans, MagmaNonUnit,
n-k-kb, kb,
c_one, dB(k+kb,k+kb), lddb,
dA(k+kb,k), ldda, queues[1] );
magma_queue_sync( queues[0] ); // finish get A(k+kb,k+kb)
}
}
}
}
else { // itype == 2 or 3
if (upper) {
/* Compute U*A*U^H */
for (k = 0; k < n; k += nb) {
kb = min( n-k, nb );
magma_dgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(k, k), lda, queues[0] );
/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */
if (k > 0) {
magma_dtrmm( MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
k, kb,
c_one, dB(0,0), lddb,
dA(0,k), ldda, queues[1] );
magma_dsymm( MagmaRight, MagmaUpper,
k, kb,
c_half, dA(k,k), ldda,
dB(0,k), lddb,
c_one, dA(0,k), ldda, queues[1] );
magma_dsyr2k( MagmaUpper, MagmaNoTrans,
k, kb,
c_one, dA(0,k), ldda,
dB(0,k), lddb,
d_one, dA(0,0), ldda, queues[1] );
magma_dsymm( MagmaRight, MagmaUpper,
k, kb,
c_half, dA(k,k), ldda,
dB(0,k), lddb,
c_one, dA(0,k), ldda, queues[1] );
magma_dtrmm( MagmaRight, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
k, kb,
c_one, dB(k,k), lddb,
dA(0,k), ldda, queues[1] );
}
magma_queue_sync( queues[0] ); // finish get A(k,k)
lapackf77_dsygst( &itype, uplo_, &kb, A(k, k), &lda, B(k, k), &ldb, info );
// this could be done on a 3rd queue
magma_dsetmatrix_async( kb, kb,
A(k, k), lda,
dA(k, k), ldda, queues[1] );
}
}
else {
/* Compute L^H*A*L */
for (k = 0; k < n; k += nb) {
kb = min( n-k, nb );
magma_dgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(k, k), lda, queues[0] );
/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */
if (k > 0) {
magma_dtrmm( MagmaRight, MagmaLower, MagmaNoTrans, MagmaNonUnit,
kb, k,
c_one, dB(0,0), lddb,
dA(k,0), ldda, queues[1] );
magma_dsymm( MagmaLeft, MagmaLower,
kb, k,
c_half, dA(k,k), ldda,
dB(k,0), lddb,
c_one, dA(k, 0), ldda, queues[1] );
magma_dsyr2k( MagmaLower, MagmaConjTrans,
k, kb,
c_one, dA(k,0), ldda,
dB(k,0), lddb,
d_one, dA(0,0), ldda, queues[1] );
magma_dsymm( MagmaLeft, MagmaLower,
kb, k,
c_half, dA(k,k), ldda,
dB(k,0), lddb,
c_one, dA(k, 0), ldda, queues[1] );
magma_dtrmm( MagmaLeft, MagmaLower, MagmaConjTrans, MagmaNonUnit,
kb, k,
c_one, dB(k,k), lddb,
dA(k,0), ldda, queues[1] );
}
magma_queue_sync( queues[0] ); // finish get A(k,k)
lapackf77_dsygst( &itype, uplo_, &kb, A(k,k), &lda, B(k,k), &ldb, info );
// this could be done on a 3rd queue
magma_dsetmatrix_async( kb, kb,
A(k, k), lda,
dA(k, k), ldda, queues[1] );
}
}
}
magma_queue_sync( queues[0] ); // finish set dA(k,k) for itype 1
magma_dgetmatrix( n, n, dA(0, 0), ldda, A(0, 0), lda, queues[1] );
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dwork );
return *info;
} /* magma_dsygst_gpu */
/**
Purpose
-------
DSPOSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix and X and B
are N-by-NRHS matrices.
DSPOSV first attempts to factorize the matrix in real SINGLE PRECISION
and use this factorization within an iterative refinement procedure
to produce a solution with real DOUBLE PRECISION norm-wise backward error
quality (see below). If the approach fails the method switches to a
real DOUBLE PRECISION factorization and solve.
The iterative refinement is not going to be a winning strategy if
the ratio real SINGLE PRECISION performance over real DOUBLE PRECISION
performance is too small. A reasonable strategy should take the
number of right-hand sides and the size of the matrix into account.
This might be done with a call to ILAENV in the future. Up to now, we
always try iterative refinement.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively.
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 number of linear equations, i.e., 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,out]
dA DOUBLE PRECISION array on the GPU, dimension (LDDA,N)
On entry, the symmetric matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 iterative refinement has been successfully used
(INFO.EQ.0 and ITER.GE.0, see description below), then A is
unchanged, if double factorization has been used
(INFO.EQ.0 and ITER.LT.0, see description below), then the
array dA contains the factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T.
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,N).
@param[in]
dB DOUBLE PRECISION array on the GPU, dimension (LDDB,NRHS)
The N-by-NRHS right hand side matrix B.
@param[in]
lddb INTEGER
The leading dimension of the array dB. LDDB >= max(1,N).
@param[out]
dX DOUBLE PRECISION array on the GPU, dimension (LDDX,NRHS)
If INFO = 0, the N-by-NRHS solution matrix X.
@param[in]
lddx INTEGER
The leading dimension of the array dX. LDDX >= max(1,N).
@param
dworkd (workspace) DOUBLE PRECISION array on the GPU, dimension (N*NRHS)
This array is used to hold the residual vectors.
@param
dworks (workspace) SINGLE PRECISION array on the GPU, dimension (N*(N+NRHS))
This array is used to store the real single precision matrix
and the right-hand sides or solutions in single precision.
@param[out]
iter INTEGER
- < 0: iterative refinement has failed, double precision
factorization has been performed
+ -1 : the routine fell back to full precision for
implementation- or machine-specific reasons
+ -2 : narrowing the precision induced an overflow,
the routine fell back to full precision
+ -3 : failure of SPOTRF
+ -31: stop the iterative refinement after the 30th iteration
- > 0: iterative refinement has been successfully used.
Returns the number of iterations
@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 of (DOUBLE
PRECISION) A is not positive definite, so the
factorization could not be completed, and the solution
has not been computed.
@ingroup magma_dposv_driver
********************************************************************/
extern "C" magma_int_t
magma_dsposv_gpu(
magma_uplo_t uplo, magma_int_t n, magma_int_t nrhs,
magmaDouble_ptr dA, magma_int_t ldda,
magmaDouble_ptr dB, magma_int_t lddb,
magmaDouble_ptr dX, magma_int_t lddx,
magmaDouble_ptr dworkd, magmaFloat_ptr dworks,
magma_int_t *iter,
magma_int_t *info)
{
#define dB(i,j) (dB + (i) + (j)*lddb)
#define dX(i,j) (dX + (i) + (j)*lddx)
#define dR(i,j) (dR + (i) + (j)*lddr)
#define dSX(i,j) (dSX + (i) + (j)*lddsx)
// Constants
const double BWDMAX = 1.0;
const magma_int_t ITERMAX = 30;
const double c_neg_one = MAGMA_D_NEG_ONE;
const double c_one = MAGMA_D_ONE;
const magma_int_t ione = 1;
// Local variables
magmaDouble_ptr dR;
magmaFloat_ptr dSA, dSX;
double Xnrmv, Rnrmv;
double Anrm, Xnrm, Rnrm, cte, eps;
magma_int_t i, j, iiter, lddsa, lddsx, lddr;
/* Check arguments */
*iter = 0;
*info = 0;
if ( n < 0 )
*info = -1;
else if ( nrhs < 0 )
*info = -2;
else if ( ldda < max(1,n))
*info = -4;
else if ( lddb < max(1,n))
*info = -7;
else if ( lddx < max(1,n))
*info = -9;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if ( n == 0 || nrhs == 0 )
return *info;
lddsa = n;
lddsx = n;
lddr = n;
dSA = dworks;
dSX = dSA + lddsa*n;
dR = dworkd;
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
eps = lapackf77_dlamch("Epsilon");
Anrm = magmablas_dlansy( MagmaInfNorm, uplo, n, dA, ldda, (double*)dworkd, n*nrhs, queue );
cte = Anrm * eps * magma_dsqrt( n ) * BWDMAX;
/*
* Convert to single precision
*/
magmablas_dlag2s( n, nrhs, dB, lddb, dSX, lddsx, queue, info );
if (*info != 0) {
*iter = -2;
goto fallback;
}
magmablas_dlat2s( uplo, n, dA, ldda, dSA, lddsa, queue, info );
if (*info != 0) {
*iter = -2;
goto fallback;
}
// factor dSA in single precision
magma_spotrf_gpu( uplo, n, dSA, lddsa, info );
if (*info != 0) {
*iter = -3;
goto fallback;
}
// solve dSA*dSX = dB in single precision
magma_spotrs_gpu( uplo, n, nrhs, dSA, lddsa, dSX, lddsx, info );
// residual dR = dB - dA*dX in double precision
magmablas_slag2d( n, nrhs, dSX, lddsx, dX, lddx, queue, info );
magmablas_dlacpy( MagmaFull, n, nrhs, dB, lddb, dR, lddr, queue );
if ( nrhs == 1 ) {
magma_dsymv( uplo, n,
c_neg_one, dA, ldda,
dX, 1,
c_one, dR, 1, queue );
}
else {
magma_dsymm( MagmaLeft, uplo, n, nrhs,
c_neg_one, dA, ldda,
dX, lddx,
c_one, dR, lddr, queue );
}
// TODO: use MAGMA_D_ABS( dX(i,j) ) instead of dlange?
for( j=0; j < nrhs; j++ ) {
i = magma_idamax( n, dX(0,j), 1, queue ) - 1;
magma_dgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1, queue );
Xnrm = lapackf77_dlange( "F", &ione, &ione, &Xnrmv, &ione, NULL );
i = magma_idamax( n, dR(0,j), 1, queue ) - 1;
magma_dgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1, queue );
Rnrm = lapackf77_dlange( "F", &ione, &ione, &Rnrmv, &ione, NULL );
if ( Rnrm > Xnrm*cte ) {
goto refinement;
}
}
*iter = 0;
goto cleanup;
//return *info;
refinement:
for( iiter=1; iiter < ITERMAX; ) {
*info = 0;
// convert residual dR to single precision dSX
magmablas_dlag2s( n, nrhs, dR, lddr, dSX, lddsx, queue, info );
if (*info != 0) {
*iter = -2;
goto fallback;
}
// solve dSA*dSX = R in single precision
magma_spotrs_gpu( uplo, n, nrhs, dSA, lddsa, dSX, lddsx, info );
// Add correction and setup residual
// dX += dSX [including conversion] --and--
// dR = dB
for( j=0; j < nrhs; j++ ) {
magmablas_dsaxpycp( n, dSX(0,j), dX(0,j), dB(0,j), dR(0,j), queue );
}
// residual dR = dB - dA*dX in double precision
if ( nrhs == 1 ) {
magma_dsymv( uplo, n,
c_neg_one, dA, ldda,
dX, 1,
c_one, dR, 1, queue );
}
else {
magma_dsymm( MagmaLeft, uplo, n, nrhs,
c_neg_one, dA, ldda,
dX, lddx,
c_one, dR, lddr, queue );
}
// TODO: use MAGMA_D_ABS( dX(i,j) ) instead of dlange?
/* Check whether the nrhs normwise backward errors satisfy the
* stopping criterion. If yes, set ITER=IITER > 0 and return. */
for( j=0; j < nrhs; j++ ) {
i = magma_idamax( n, dX(0,j), 1, queue ) - 1;
magma_dgetmatrix( 1, 1, dX(i,j), 1, &Xnrmv, 1, queue );
Xnrm = lapackf77_dlange( "F", &ione, &ione, &Xnrmv, &ione, NULL );
i = magma_idamax( n, dR(0,j), 1, queue ) - 1;
magma_dgetmatrix( 1, 1, dR(i,j), 1, &Rnrmv, 1, queue );
Rnrm = lapackf77_dlange( "F", &ione, &ione, &Rnrmv, &ione, NULL );
if ( Rnrm > Xnrm*cte ) {
goto L20;
}
}
/* If we are here, the nrhs normwise backward errors satisfy
* the stopping criterion, we are good to exit. */
*iter = iiter;
goto cleanup;
//return *info;
L20:
iiter++;
}
/* If we are at this place of the code, this is because we have
* performed ITER=ITERMAX iterations and never satisified the
* stopping criterion. Set up the ITER flag accordingly and follow
* up on double precision routine. */
*iter = -ITERMAX - 1;
fallback:
/* Single-precision iterative refinement failed to converge to a
* satisfactory solution, so we resort to double precision. */
magma_dpotrf_gpu( uplo, n, dA, ldda, info );
if (*info == 0) {
magmablas_dlacpy( MagmaFull, n, nrhs, dB, lddb, dX, lddx, queue );
magma_dpotrs_gpu( uplo, n, nrhs, dA, ldda, dX, lddx, info );
}
cleanup:
magma_queue_destroy( queue );
return *info;
}
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, t1, t2;
double c_neg_one = MAGMA_D_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 };
double *A, *B, *C, *C2, *LU;
double *dA, *dB, *dC1, *dC2;
double alpha = MAGMA_D_MAKE( 0.5, 0.1 );
double beta = MAGMA_D_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_dmalloc_pinned( &A, size ); assert( err == 0 );
err = magma_dmalloc_pinned( &B, size ); assert( err == 0 );
err = magma_dmalloc_pinned( &C, size ); assert( err == 0 );
err = magma_dmalloc_pinned( &C2, size ); assert( err == 0 );
err = magma_dmalloc_pinned( &LU, size ); assert( err == 0 );
err = magma_dmalloc( &dA, size ); assert( err == 0 );
err = magma_dmalloc( &dB, size ); assert( err == 0 );
err = magma_dmalloc( &dC1, size ); assert( err == 0 );
err = magma_dmalloc( &dC2, size ); assert( err == 0 );
// initialize matrices
size = maxn*maxn;
lapackf77_dlarnv( &ione, ISEED, &size, A );
lapackf77_dlarnv( &ione, ISEED, &size, B );
lapackf77_dlarnv( &ione, ISEED, &size, C );
printf( "========== Level 1 BLAS ==========\n" );
// ----- test DSWAP
// swap columns 2 and 3 of dA, then copy to C2 and compare with A
if ( n >= 3 ) {
magma_dsetmatrix( m, n, A, ld, dA, ld );
magma_dsetmatrix( m, n, A, ld, dB, ld );
magma_dswap( m, dA(0,1), 1, dA(0,2), 1 );
magma_dswap( m, dB(0,1), 1, dB(0,2), 1 );
// check results, storing diff between magma and cuda calls in C2
cublasDaxpy( handle, ld*n, &c_neg_one, dA, 1, dB, 1 );
magma_dgetmatrix( m, n, dB, ld, C2, ld );
error = lapackf77_dlange( "F", &m, &k, C2, &ld, work );
total_error += error;
printf( "dswap diff %.2g\n", error );
}
else {
printf( "dswap skipped for n < 3\n" );
}
// ----- test IDAMAX
// get argmax of column of A
magma_dsetmatrix( m, k, A, ld, dA, ld );
error = 0;
for( int j = 0; j < k; ++j ) {
magma_int_t i1 = magma_idamax( m, dA(0,j), 1 );
int i2; // NOT magma_int_t, for cublas
cublasIdamax( 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( "idamax diff %.2g\n", error );
printf( "\n" );
printf( "========== Level 2 BLAS ==========\n" );
// ----- test DGEMV
// 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_dsetmatrix( m, n, A, ld, dA, ld );
magma_dsetvector( maxn, B, 1, dB, 1 );
magma_dsetvector( maxn, C, 1, dC1, 1 );
magma_dsetvector( maxn, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_dgemv( trans[ia], m, n, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasDgemv( 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);
cublasDaxpy( handle, size, &c_neg_one, dC1, 1, dC2, 1 );
magma_dgetvector( size, dC2, 1, C2, 1 );
error = lapackf77_dlange( "F", &size, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_DGEMV( m, n ) / 1e9;
printf( "dgemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test DSYMV
// 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_dsetmatrix( m, m, A, ld, dA, ld );
magma_dsetvector( m, B, 1, dB, 1 );
magma_dsetvector( m, C, 1, dC1, 1 );
magma_dsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_dsymv( uplo[iu], m, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasDsymv( 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
cublasDaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_dgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_dlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_DSYMV( m ) / 1e9;
printf( "dsymv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test DTRSV
// 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_dlacpy( "Full", &maxn, &maxn, A, &ld, LU, &ld );
lapackf77_dgetrf( &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_dsetmatrix( m, m, LU, ld, dA, ld );
magma_dsetvector( m, C, 1, dC1, 1 );
magma_dsetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_dtrsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasDtrsv( 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
cublasDaxpy( handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_dgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_dlange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_DTRSM( MagmaLeft, m, 1 ) / 1e9;
printf( "dtrsv( %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 DGEMM
// 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_dsetmatrix( (nta ? m : k), (nta ? m : k), A, ld, dA, ld );
magma_dsetmatrix( (ntb ? k : n), (ntb ? n : k), B, ld, dB, ld );
magma_dsetmatrix( m, n, C, ld, dC1, ld );
magma_dsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dgemm( 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 );
cublasDgemm( 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
cublasDaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DGEMM( m, n, k ) / 1e9;
printf( "dgemm( %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 DSYMM
// 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_dsetmatrix( m, m, A, ld, dA, ld );
magma_dsetmatrix( m, n, B, ld, dB, ld );
magma_dsetmatrix( m, n, C, ld, dC1, ld );
magma_dsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dsymm( 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 );
cublasDsymm( 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
cublasDaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DSYMM( side[is], m, n ) / 1e9;
printf( "dsymm( %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 DSYRK
// 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_dsetmatrix( n, k, A, ld, dA, ld );
magma_dsetmatrix( n, n, C, ld, dC1, ld );
magma_dsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dsyrk( uplo[iu], trans[it], n, k, dalpha, dA, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasDsyrk( 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
cublasDaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DSYRK( k, n ) / 1e9;
printf( "dsyrk( %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 DSYR2K
// 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_dsetmatrix( (nt ? n : k), (nt ? n : k), A, ld, dA, ld );
magma_dsetmatrix( n, n, C, ld, dC1, ld );
magma_dsetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dsyr2k( 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 );
cublasDsyr2k( 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
cublasDaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DSYR2K( k, n ) / 1e9;
printf( "dsyr2k( %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 DTRMM
// 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_dsetmatrix( (left ? m : n), (left ? m : n), A, ld, dA, ld );
magma_dsetmatrix( m, n, C, ld, dC1, ld );
magma_dsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dtrmm( 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 );
cublasDtrmm( 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
cublasDaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DTRMM( side[is], m, n ) / 1e9;
printf( "dtrmm( %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 DTRSM
// 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_dsetmatrix( (left ? m : n), (left ? m : n), LU, ld, dA, ld );
magma_dsetmatrix( m, n, C, ld, dC1, ld );
magma_dsetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_dtrsm( 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 );
cublasDtrsm( 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
cublasDaxpy( handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_dgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_dlange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_DTRSM( side[is], m, n ) / 1e9;
printf( "dtrsm( %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;
}
/**
Purpose
-------
DSYGST_GPU reduces a real symmetric-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 DPOTRF.
Arguments
---------
@param[in]
itype 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.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A is stored and B is factored as
U**H*U;
- = MagmaLower: Lower triangle of A is stored and B is factored as
L*L**H.
@param[in]
n INTEGER
The order of the matrices A and B. N >= 0.
@param[in,out]
dA DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A. If UPLO = MagmaUpper, 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 = MagmaLower, 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 transformed matrix, stored in the
same format as A.
@param[in]
ldda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in]
dB DOUBLE_PRECISION array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B,
as returned by DPOTRF.
@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_dsyev_comp
********************************************************************/
extern "C" magma_int_t
magma_dsygst_gpu(magma_int_t itype, magma_uplo_t uplo, magma_int_t n,
double *dA, magma_int_t ldda,
double *dB, magma_int_t lddb, magma_int_t *info)
{
#define A(i, j) (w + (j)*lda + (i))
#define B(i, j) (w + nb*lda + (j)*ldb + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
#define dB(i, j) (dB + (j)*lddb + (i))
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t nb;
magma_int_t k, kb, kb2;
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
double c_half = MAGMA_D_HALF;
double c_neg_half = MAGMA_D_NEG_HALF;
double *w;
magma_int_t lda;
magma_int_t ldb;
double d_one = 1.0;
int upper = (uplo == MagmaUpper);
/* Test the input parameters. */
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! upper && uplo != MagmaLower) {
*info = -2;
} else if (n < 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 ( n == 0 )
return *info;
nb = magma_get_dsygst_nb(n);
lda = nb;
ldb = nb;
if (MAGMA_SUCCESS != magma_dmalloc_pinned( &w, 2*nb*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t stream[3];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
magma_queue_create( &stream[2] );
/* Use hybrid blocked code */
if (itype == 1) {
if (upper) {
kb = min(n,nb);
/* Compute inv(U')*A*inv(U) */
magma_dgetmatrix_async( kb, kb,
dB(0, 0), lddb,
B(0, 0), nb, stream[2] );
magma_dgetmatrix_async( kb, kb,
dA(0, 0), ldda,
A(0, 0), nb, stream[1] );
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) */
magma_queue_sync( stream[2] );
magma_queue_sync( stream[1] );
lapackf77_dsygst( &itype, uplo_, &kb, A(0,0), &lda, B(0,0), &ldb, info);
magma_dsetmatrix_async( kb, kb,
A(0, 0), lda,
dA(k, k), ldda, stream[0] );
if (k+kb < n) {
// Start copying the new B block
magma_dgetmatrix_async( kb2, kb2,
dB(k+kb, k+kb), lddb,
B(0, 0), nb, stream[2] );
magma_dtrsm(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_dsymm(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_dsyr2k(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_dgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(0, 0), lda, stream[1] );
magma_dsymm(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_dtrsm(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[0] );
}
else {
kb = min(n,nb);
/* Compute inv(L)*A*inv(L') */
magma_dgetmatrix_async( kb, kb,
dB(0, 0), lddb,
B(0, 0), nb, stream[2] );
magma_dgetmatrix_async( kb, kb,
dA(0, 0), ldda,
A(0, 0), nb, stream[1] );
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) */
magma_queue_sync( stream[2] );
magma_queue_sync( stream[1] );
lapackf77_dsygst( &itype, uplo_, &kb, A(0, 0), &lda, B(0, 0), &ldb, info);
magma_dsetmatrix_async( kb, kb,
A(0, 0), lda,
dA(k, k), ldda, stream[0] );
if (k+kb < n) {
// Start copying the new B block
magma_dgetmatrix_async( kb2, kb2,
dB(k+kb, k+kb), lddb,
B(0, 0), nb, stream[2] );
magma_dtrsm(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_dsymm(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_dsyr2k(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_dgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(0, 0), lda, stream[1] );
magma_dsymm(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_dtrsm(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[0] );
}
else {
if (upper) {
/* Compute U*A*U' */
for (k = 0; k < n; k += nb) {
kb= min(n-k,nb);
magma_dgetmatrix_async( kb, kb,
dB(k, k), lddb,
B(0, 0), nb, stream[2] );
/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */
if (k > 0) {
magma_dtrmm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
k, kb,
c_one, dB(0,0), lddb,
dA(0,k), ldda);
magma_dsymm(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_dgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(0, 0), lda, stream[0] );
if (k > 0) {
magma_dsyr2k(MagmaUpper, MagmaNoTrans,
k, kb,
c_one, dA(0,k), ldda,
dB(0,k), lddb,
d_one, dA(0,0), ldda);
magma_dsymm(MagmaRight, MagmaUpper,
k, kb,
c_half, dA(k,k), ldda,
dB(0,k), lddb,
c_one, dA(0, k), ldda);
magma_dtrmm(MagmaRight, MagmaUpper, MagmaConjTrans, MagmaNonUnit,
k, kb,
c_one, dB(k,k), lddb,
dA(0,k), ldda);
}
magma_queue_sync( stream[2] );
magma_queue_sync( stream[0] );
lapackf77_dsygst( &itype, uplo_, &kb, A(0, 0), &lda, B(0, 0), &ldb, info);
magma_dsetmatrix_async( kb, kb,
A(0, 0), 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_dgetmatrix_async( kb, kb,
dB(k, k), lddb,
B(0, 0), nb, stream[2] );
/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */
if (k > 0) {
magma_dtrmm(MagmaRight, MagmaLower, MagmaNoTrans, MagmaNonUnit,
kb, k,
c_one, dB(0,0), lddb,
dA(k,0), ldda);
magma_dsymm(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_dgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(0, 0), lda, stream[0] );
if (k > 0) {
magma_dsyr2k(MagmaLower, MagmaConjTrans,
k, kb,
c_one, dA(k,0), ldda,
dB(k,0), lddb,
d_one, dA(0,0), ldda);
magma_dsymm(MagmaLeft, MagmaLower,
kb, k,
c_half, dA(k,k), ldda,
dB(k,0), lddb,
c_one, dA(k, 0), ldda);
magma_dtrmm(MagmaLeft, MagmaLower, MagmaConjTrans, MagmaNonUnit,
kb, k,
c_one, dB(k,k), lddb,
dA(k,0), ldda);
}
magma_queue_sync( stream[2] );
magma_queue_sync( stream[0] );
lapackf77_dsygst( &itype, uplo_, &kb, A(0, 0), &lda, B(0, 0), &ldb, info);
magma_dsetmatrix_async( kb, kb,
A(0, 0), lda,
dA(k, k), ldda, stream[1] );
}
magma_queue_sync( stream[1] );
}
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_queue_destroy( stream[2] );
magma_free_pinned( w );
return *info;
} /* magma_dsygst_gpu */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing magma_dsymm_mgpu
*/
int main( int argc, char** argv)
{
TESTING_INIT();
double c_neg_one = MAGMA_D_NEG_ONE;
double alpha = MAGMA_D_MAKE( 3.456, 5.678 );
double beta = MAGMA_D_MAKE( 1.234, 2.456 );
real_Double_t gflops, gpu_perf=0., cpu_perf=0., gpu_time=0., cpu_time=0.;
real_Double_t gpu_perf2=0., gpu_time2=0.;
double Anorm, error, work[1];
double *hA, *hB, *hC, *hR;
magmaDouble_ptr dA[MagmaMaxGPUs], dB[MagmaMaxGPUs], dC[MagmaMaxGPUs], dwork[MagmaMaxGPUs];
magmaDouble_ptr dA2;
magma_int_t i, j, dev, M, N, size, lda, ldb, ldc, ldda, lddb, lddc, msize, nb;
magma_int_t ione = 1;
magma_int_t iseed[4] = {0,0,0,1};
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
opts.ngpu = abs( opts.ngpu ); // always uses multi-GPU code
double tol = opts.tolerance * lapackf77_dlamch("E");
// default values
nb = (opts.nb > 0 ? opts.nb : 64);
magma_int_t gnode[MagmaMaxGPUs][MagmaMaxGPUs+2];
magma_int_t ncmplx = 0;
magma_buildconnection_mgpu( gnode, &ncmplx, opts.ngpu );
printf("%% Initializing communication pattern... GPU-ncmplx %d\n", (int) ncmplx);
for (i=0; i < ncmplx; ++i) {
magma_int_t myngpu = gnode[i][MagmaMaxGPUs];
printf("%% cmplx %d has %d GPUs:", i, myngpu);
for (j=0; j < myngpu; ++j) {
printf(" %d", (int) gnode[i][j]);
if (j < myngpu-1) {
printf(",");
}
}
printf("\n");
}
// number of queues per GPU. Requires ngpu.
magma_int_t nqueue = opts.ngpu;
// number of events per GPU. Require ngpu*ngpu.
magma_int_t nevents = opts.ngpu*opts.ngpu;
magma_queue_t queues[MagmaMaxGPUs][20], queues0[MagmaMaxGPUs];
magma_event_t events[MagmaMaxGPUs][MagmaMaxGPUs*MagmaMaxGPUs + 10];
for( dev = 0; dev < opts.ngpu; ++dev ) {
magma_setdevice( dev );
for( i = 0; i < nqueue; ++i ) {
magma_queue_create( dev, &queues[dev][i] );
}
queues0[dev] = queues[dev][0];
for( i = 0; i < nevents; ++i ) {
cudaEventCreateWithFlags( &events[dev][i], cudaEventDisableTiming );
}
}
printf("%% nb %d, ngpu %d, version %d\n", (int) nb, (int) opts.ngpu, (int) opts.version );
printf("%% M N nb offset CPU Gflop/s (sec) GPU Gflop/s (sec) CUBLAS hemm (sec) ||R|| / ||A||*||B||\n");
printf("%%========================================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
M = opts.msize[itest];
N = opts.nsize[itest];
for( int offset = 0; offset < N; offset += min(N,nb) ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
msize = M - offset;
lda = M; // TODO depends on side
ldb = M;
ldc = M;
ldda = magma_roundup( lda, opts.align ); // multiple of 32 by default
lddb = magma_roundup( ldb, opts.align ); // multiple of 32 by default
lddc = magma_roundup( ldc, opts.align ); // multiple of 32 by default
gflops = FLOPS_DSYMM( MagmaLeft, (double)msize, (double)N ) / 1e9;
magma_int_t dworksiz = lddc*N + (M*N)*opts.ngpu;
TESTING_MALLOC_CPU( hA, double, lda*M );
TESTING_MALLOC_CPU( hB, double, ldb*N );
TESTING_MALLOC_CPU( hC, double, ldc*N );
TESTING_MALLOC_PIN( hR, double, ldc*N );
for( dev = 0; dev < opts.ngpu; ++dev ) {
magma_int_t mlocal = ((M / nb) / opts.ngpu + 1) * nb;
magma_setdevice( dev );
TESTING_MALLOC_DEV( dA[dev], double, ldda*mlocal );
TESTING_MALLOC_DEV( dB[dev], double, lddb*N );
TESTING_MALLOC_DEV( dC[dev], double, lddc*N );
TESTING_MALLOC_DEV( dwork[dev], double, dworksiz );
}
if ( opts.check ) {
magma_setdevice( 0 );
TESTING_MALLOC_DEV( dA2, double, ldda*M );
}
size = lda*M;
lapackf77_dlarnv( &ione, iseed, &size, hA );
magma_dmake_symmetric( M, hA, lda );
size = ldb*N;
lapackf77_dlarnv( &ione, iseed, &size, hB );
size = ldc*N;
lapackf77_dlarnv( &ione, iseed, &size, hC );
lapackf77_dlacpy( "Full", &M, &N, hC, &ldc, hR, &lda );
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
magma_dsetmatrix_1D_col_bcyclic( M, M, hA, lda, dA, ldda, opts.ngpu, nb, queues0 );
for( dev = 0; dev < opts.ngpu; ++dev ) {
magma_setdevice( dev );
magma_dsetmatrix( M, N, hB, lda, dB[dev], ldda, opts.queue );
// since when offset != 0, the GPU that does beta*C may not be 0,
// send initial hC to all GPUs.
magma_dsetmatrix( M, N, hC, lda, dC[dev], ldda, opts.queue );
}
trace_init( 1, opts.ngpu, nqueue, (magma_queue_t*) queues );
gpu_time = magma_sync_wtime(0);
magmablas_dsymm_mgpu(
MagmaLeft, MagmaLower, msize, N,
alpha, dA, ldda, offset,
dB, ldda,
beta, dC, ldda, dwork, dworksiz,
opts.ngpu, nb, queues, nqueue, events, nevents, gnode, ncmplx);
gpu_time = magma_sync_wtime(0) - gpu_time;
gpu_perf = gflops / gpu_time;
#ifdef TRACING
char buf[80];
snprintf( buf, sizeof(buf), "dsymm-m%d-n%d-nb%d-ngpu%d-run%d.svg",
(int) M, (int) N, (int) nb, (int) opts.ngpu, (int) iter );
trace_finalize( buf, "trace.css" );
#endif
/* ====================================================================
Performs operation using CUBLAS
=================================================================== */
if ( opts.check && iter == 0 ) {
magma_setdevice( 0 );
magma_dsetmatrix( M, M, hA, lda, dA2, ldda, opts.queue );
magma_dsetmatrix( M, N, hB, lda, dB[0], ldda, opts.queue );
magma_dsetmatrix( M, N, hC, lda, dwork[0], ldda, opts.queue );
gpu_time2 = magma_sync_wtime(0);
magma_dsymm(
MagmaLeft, MagmaLower, msize, N,
alpha, dA2 + offset + offset*ldda, ldda,
dB[0], ldda,
beta, dwork[0], ldda, opts.queue );
gpu_time2 = magma_sync_wtime(0) - gpu_time2;
gpu_perf2 = gflops / gpu_time2;
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
if ( opts.check ) {
// store ||A||*||B||
Anorm = lapackf77_dlange("fro", &msize, &msize, hA + offset + offset*lda, &lda, work );
Anorm *= lapackf77_dlange("fro", &msize, &N, hB, &lda, work );
//printf( "A =" ); magma_dprint( M, M, hA, lda );
//printf( "B =" ); magma_dprint( M, N, hB, lda );
//printf( "C =" ); magma_dprint( M, N, hC, lda );
cpu_time = magma_wtime();
blasf77_dsymm( "Left", "Lower", &msize, &N,
&alpha, hA + offset + offset*lda, &lda,
hB, &lda,
&beta, hC, &lda );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
for (dev=0; dev < opts.ngpu; ++dev) {
magma_setdevice( dev );
magma_dgetmatrix( M, N, dC[dev], ldda, hR, lda, opts.queue );
// compute relative error ||R||/||A||*||B||, where R := C_magma - C_lapack = R - C
size = ldc*N;
blasf77_daxpy( &size, &c_neg_one, hC, &ione, hR, &ione );
error = lapackf77_dlange("fro", &msize, &N, hR, &lda, work) / Anorm;
//printf( "R =" ); magma_dprint( M, N, hR, lda );
bool okay = (error < tol);
status += ! okay;
if (dev == 0) {
printf( "%5d %5d %5d %5d %7.1f (%7.4f) %7.1f (%7.4f) %7.1f (%7.4f) %8.2e %s\n",
(int) M, (int) N, (int) nb, (int) offset,
cpu_perf, cpu_time,
gpu_perf, gpu_time,
gpu_perf2, gpu_time2,
error, (okay ? "ok" : "failed") );
}
else {
printf( " dev %d %74s %8.2e %s\n", dev, "",
error, (okay ? "ok" : "failed") );
}
}
} else {
printf( "%5d %5d %5d %5d --- ( --- ) %7.1f (%7.4f) --- ( --- ) ---\n",
(int) M, (int) N, (int) nb, (int) offset,
gpu_perf, gpu_time );
}
TESTING_FREE_CPU( hA );
TESTING_FREE_CPU( hB );
TESTING_FREE_CPU( hC );
TESTING_FREE_PIN( hR );
for( dev = 0; dev < opts.ngpu; ++dev ) {
magma_setdevice( dev );
TESTING_FREE_DEV( dA[dev] );
TESTING_FREE_DEV( dB[dev] );
TESTING_FREE_DEV( dC[dev] );
TESTING_FREE_DEV( dwork[dev] );
}
if ( opts.check ) {
magma_setdevice( 0 );
TESTING_FREE_DEV( dA2 );
}
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
} // offset
printf( "\n" );
}
for( dev = 0; dev < opts.ngpu; ++dev ) {
magma_setdevice( dev );
for( i = 0; i < nqueue; ++i ) {
magma_queue_destroy( queues[dev][i] );
}
for( i = 0; i < nevents; ++i ) {
magma_event_destroy( events[dev][i] );
}
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
