/**
Purpose
-------
CHETRD reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q\*\*H * A * Q = T.
Arguments
---------
@param[in]
num_gpus INTEGER
The number of GPUs. num_gpus > 0.
@param[in]
num_streams INTEGER
The number of GPU streams used for update. 10 >= num_streams > 0.
@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 COMPLEX array, dimension (LDA,N)
On entry, the Hermitian 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 diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, 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]
d COMPLEX array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
@param[out]
e COMPLEX array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower.
@param[out]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) 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]
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 complex scalar, and v is a complex 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 complex scalar, and v is a complex 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_cheev_comp
********************************************************************/
extern "C" magma_int_t
magma_chetrd_mgpu(
magma_int_t num_gpus, magma_int_t num_streams, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
float *d, float *e, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define dA(id, i, j) (dA[(id)] + (j)*ldda + (i))
#define dW(id, i, j) (dwork[(id)] + (j)*ldda + (i))
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t ln, ldda;
magma_int_t nb = magma_get_chetrd_nb(n), ib;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
float d_one = MAGMA_D_ONE;
float mv_time = 0.0;
#ifdef PROFILE_SY2RK
float up_time = 0.0;
#endif
magma_int_t kk, nx;
magma_int_t i = 0, ii, iii, j, did, i_n;
magma_int_t iinfo;
magma_int_t ldwork, lddwork, lwkopt, ldwork2;
magma_int_t lquery;
magma_queue_t stream[MagmaMaxGPUs][10];
magmaFloatComplex *dx[MagmaMaxGPUs], *dy[MagmaMaxGPUs], *hwork;
magmaFloatComplex *dwork2[MagmaMaxGPUs];
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
printf( " uplo = %c\n",uplo );
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,n)) {
*info = -4;
} else if (lwork < nb*n && ! lquery) {
*info = -9;
} else if ( num_streams > 2 ) {
*info = 2;
}
/* Determine the block size. */
ldwork = lddwork = n;
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return MAGMA_ERR_ILLEGAL_VALUE;
}
else if (lquery)
return 0;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return 0;
}
magmaFloatComplex *dA[MagmaMaxGPUs];
magmaFloatComplex *dwork[MagmaMaxGPUs];
float times[11];
for( did=0; did < 11; did++ )
times[did] = 0;
//#define PROFILE_SY2RK
#ifdef PROFILE_SY2RK
magma_event_t start, stop;
float etime;
magma_setdevice(0);
magma_event_create( &start );
magma_event_create( &stop );
#endif
ldda = lda;
ln = ((nb*(1+n/(nb*num_gpus))+31)/32)*32;
ldwork2 = (1+ n / nb + (n % nb != 0)) * ldda;
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
// TODO fix memory leak
if ( MAGMA_SUCCESS != magma_cmalloc(&dA[did], ln*ldda+3*lddwork*nb) ||
MAGMA_SUCCESS != magma_cmalloc(&dx[did], num_streams*n) ||
MAGMA_SUCCESS != magma_cmalloc(&dy[did], num_streams*n) ||
MAGMA_SUCCESS != magma_cmalloc(&dwork2[did], ldwork2 ) ) {
for( i=0; i < did; i++ ) {
magma_setdevice(i);
magma_free(dA[i]);
magma_free(dx[i]);
magma_free(dy[i]);
}
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dwork[did] = dA[did] + ln*ldda;
for( kk=0; kk < num_streams; kk++ )
magma_queue_create(&stream[did][kk]);
}
magma_setdevice(0);
// TODO fix memory leak dwork2
if ( MAGMA_SUCCESS != magma_cmalloc_pinned( &hwork, num_streams*num_gpus*n ) ) {
for( i=0; i < num_gpus; i++ ) {
magma_setdevice(i);
magma_free(dA[i]);
magma_free(dx[i]);
magma_free(dy[i]);
}
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if (n < 2048)
nx = n;
else
nx = 512;
if (upper) {
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_chtodhe(num_gpus, uplo, n, nb, A, lda, dA, ldda, stream, &iinfo );
}
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
for (i = nb*((n-1)/nb); i >= nx; i -= nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
/* wait for the next panel */
if (i != nb*((n-1)/nb)) {
magma_setdevice(did);
magma_queue_sync(stream[did][0]);
}
magma_clatrd_mgpu(num_gpus, uplo, n, i+ib, ib, nb,
A(0, 0), lda, e, tau,
work, ldwork,
dA, ldda, 0,
dwork, i+ib,
dwork2, ldwork2,
1, dx, dy, hwork,
stream, times);
magma_cher2k_mgpu(num_gpus, MagmaUpper, MagmaNoTrans, nb, i, ib,
c_neg_one, dwork, i+ib, 0,
d_one, dA, ldda, 0,
num_streams, stream);
/* get the next panel */
if (i-nb >= nx ) {
ib = min(nb, n-(i-nb));
ii = nb*((i-nb)/(nb*num_gpus));
did = ((i-nb)/nb)%num_gpus;
magma_setdevice(did);
magma_cgetmatrix_async( (i-nb)+ib, ib,
dA(did, 0, ii), ldda,
A(0, i-nb), lda,
stream[did][0] );
}
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j > 0 ) {
*A(j-1,j) = MAGMA_C_MAKE( e[j - 1], 0 );
}
d[j] = MAGMA_C_REAL( *A(j, j) );
}
} /* end of for i=... */
if ( nx > 0 ) {
if (1 <= n-nx) { /* else A is already on CPU */
for (i=0; i < nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
magma_setdevice(did);
magma_cgetmatrix_async( nx, ib,
dA(did, 0, ii), ldda,
A(0, i), lda,
stream[did][0] );
}
}
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
magma_queue_sync(stream[did][0]);
}
/* Use unblocked code to reduce the last or only block */
lapackf77_chetd2(uplo_, &nx, A(0, 0), &lda, d, e, tau, &iinfo);
}
}
else {
trace_init( 1, num_gpus, num_streams, (CUstream_st**)stream );
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_chtodhe(num_gpus, uplo, n, nb, A, lda, dA, ldda, stream, &iinfo );
}
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
/* Reduce columns i:i+ib-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i != 0) {
magma_setdevice(did);
trace_gpu_start( did, 0, "comm", "get" );
magma_cgetmatrix_async( n-i, ib,
dA(did, i, ii), ldda,
A(i,i), lda,
stream[did][0] );
trace_gpu_end( did, 0 );
magma_queue_sync(stream[did][0]);
magma_setdevice(0);
}
mv_time +=
magma_clatrd_mgpu(num_gpus, uplo, n, n-i, ib, nb,
A(i, i), lda, &e[i],
&tau[i], work, ldwork,
dA, ldda, i,
dwork, (n-i),
dwork2, ldwork2,
1, dx, dy, hwork,
stream, times );
#ifdef PROFILE_SY2RK
magma_setdevice(0);
if ( i > 0 ) {
cudaEventElapsedTime(&etime, start, stop);
up_time += (etime/1000.0);
}
magma_event_record(start, 0);
#endif
magma_cher2k_mgpu(num_gpus, MagmaLower, MagmaNoTrans, nb, n-i-ib, ib,
c_neg_one, dwork, n-i, ib,
d_one, dA, ldda, i+ib, num_streams, stream);
#ifdef PROFILE_SY2RK
magma_setdevice(0);
magma_event_record(stop, 0);
#endif
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j+1 < n ) {
*A(j+1,j) = MAGMA_C_MAKE( e[j], 0 );
}
d[j] = MAGMA_C_REAL( *A(j, j) );
}
} /* for i=... */
/* Use unblocked code to reduce the last or only block */
if ( i < n ) {
iii = i;
i_n = n-i;
if ( i > 0 ) {
for (; i < n; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*num_gpus));
did = (i/nb)%num_gpus;
magma_setdevice(did);
magma_cgetmatrix_async( i_n, ib,
dA(did, iii, ii), ldda,
A(iii, i), lda,
stream[did][0] );
}
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
magma_queue_sync(stream[did][0]);
}
}
lapackf77_chetrd(uplo_, &i_n, A(iii, iii), &lda, &d[iii], &e[iii],
&tau[iii], work, &lwork, &iinfo);
}
}
#ifdef PROFILE_SY2RK
magma_setdevice(0);
if ( n > nx ) {
cudaEventElapsedTime(&etime, start, stop);
up_time += (etime/1000.0);
}
magma_event_destroy( start );
magma_event_destroy( stop );
#endif
trace_finalize( "chetrd.svg", "trace.css" );
for( did=0; did < num_gpus; did++ ) {
magma_setdevice(did);
for( kk=0; kk < num_streams; kk++ )
magma_queue_sync(stream[did][kk]);
for( kk=0; kk < num_streams; kk++ )
magma_queue_destroy(stream[did][kk]);
magma_free(dA[did]);
magma_free(dx[did]);
magma_free(dy[did]);
magma_free(dwork2[did]);
}
magma_setdevice(0);
magma_free_pinned(hwork);
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
#ifdef PROFILE_SY2RK
printf( " n=%d nb=%d\n",n,nb );
printf( " Time in CLARFG: %.2e seconds\n",times[0] );
printf( " Time in CHEMV : %.2e seconds\n",mv_time );
printf( " Time in CHER2K: %.2e seconds\n",up_time );
#endif
return MAGMA_SUCCESS;
} /* magma_chetrd */
/**
Purpose
-------
CHETRD reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
nqueue INTEGER
The number of GPU queues used for update. 10 >= nqueue > 0.
@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 COMPLEX array, dimension (LDA,N)
On entry, the Hermitian 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 diagonal and first superdiagonal
of A are overwritten by the corresponding elements of the
tridiagonal matrix T, and the elements above the first
superdiagonal, with the array TAU, represent the orthogonal
matrix Q as a product of elementary reflectors; if UPLO
= MagmaLower, the diagonal and first subdiagonal of A are over-
written by the corresponding elements of the tridiagonal
matrix T, and the elements below the first subdiagonal, 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]
d COMPLEX array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
@param[out]
e COMPLEX array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = MagmaUpper, E(i) = A(i+1,i) if UPLO = MagmaLower.
@param[out]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) COMPLEX 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 >= N*NB, where NB is the
optimal blocksize given by magma_get_chetrd_nb().
\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]
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 complex scalar, and v is a complex 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 complex scalar, and v is a complex 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_cheev_comp
********************************************************************/
extern "C" magma_int_t
magma_chetrd_mgpu(
magma_int_t ngpu,
magma_int_t nqueue, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
float *d, float *e, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define dA(id, i, j) (dA[(id)] + (j)*ldda + (i))
#define dW(id, i, j) (dW[(id)] + (j)*ldda + (i))
/* Constants */
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const float d_one = MAGMA_D_ONE;
/* Local variables */
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t nlocal, ldda;
magma_int_t nb = magma_get_chetrd_nb(n), ib, ib2;
#ifdef PROFILE_SY2RK
float mv_time = 0.0;
float up_time = 0.0;
#endif
magma_int_t kk, nx;
magma_int_t i, ii, iii, j, dev, i_n;
magma_int_t iinfo;
magma_int_t ldwork, lddw, lwkopt, ldwork2, lhwork;
// set pointers to NULL so it is safe to goto CLEANUP if any malloc fails.
magma_queue_t queues[MagmaMaxGPUs][10] = { { NULL, NULL } };
magma_queue_t queues0[MagmaMaxGPUs] = { NULL };
magmaFloatComplex *hwork = NULL;
magmaFloatComplex_ptr dwork2[MagmaMaxGPUs] = { NULL };
magmaFloatComplex_ptr dA[MagmaMaxGPUs] = { NULL };
magmaFloatComplex_ptr dW[MagmaMaxGPUs] = { NULL };
*info = 0;
bool upper = (uplo == MagmaUpper);
bool 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 < nb*n && ! lquery) {
*info = -9;
} else if ( nqueue > 2 ) {
*info = 2; // TODO fix
}
/* Determine the block size. */
ldwork = n;
lwkopt = n * nb;
if (*info == 0) {
work[0] = magma_cmake_lwork( lwkopt );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
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 );
//#define PROFILE_SY2RK
#ifdef PROFILE_SY2RK
float times[11] = { 0 };
magma_event_t start, stop;
float etime;
magma_setdevice( 0 );
magma_event_create( &start );
magma_event_create( &stop );
#endif
ldda = magma_roundup( lda, 32 );
lddw = ldda;
nlocal = nb*(1 + n/(nb*ngpu));
ldwork2 = ldda*( magma_ceildiv( n, nb ) + 1); // i.e., ldda*(blocks + 1)
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
// TODO fix memory leak
if ( MAGMA_SUCCESS != magma_cmalloc( &dA[dev], nlocal*ldda + 3*lddw*nb ) ||
MAGMA_SUCCESS != magma_cmalloc( &dwork2[dev], ldwork2 ) ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
dW[dev] = dA[dev] + nlocal*ldda;
for( kk=0; kk < nqueue; kk++ ) {
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[dev][kk] );
}
queues0[dev] = queues[dev][0];
}
lhwork = nqueue*ngpu*n;
if ( MAGMA_SUCCESS != magma_cmalloc_pinned( &hwork, lhwork ) ) {
*info = MAGMA_ERR_HOST_ALLOC;
goto CLEANUP;
}
// nx <= n is required
// use LAPACK for n < 3000, otherwise switch at 512
if (n < 3000)
nx = n;
else
nx = 512;
if (upper) {
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_chtodhe( ngpu, uplo, n, nb, A, lda, dA, ldda, queues, &iinfo );
}
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
for (i = nb*((n-1)/nb); i >= nx; i -= nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*ngpu));
dev = (i/nb)%ngpu;
/* wait for the next panel */
if (i != nb*((n-1)/nb)) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] );
}
magma_clatrd_mgpu( ngpu, uplo, i+ib, ib, nb,
A(0, 0), lda, e, tau,
work, ldwork,
dA, ldda, 0,
dW, i+ib,
hwork, lhwork,
dwork2, ldwork2,
queues0 );
magma_cher2k_mgpu( ngpu, MagmaUpper, MagmaNoTrans, nb, i, ib,
c_neg_one, dW, i+ib, 0,
d_one, dA, ldda, 0,
nqueue, queues );
/* get the next panel */
if (i-nb >= nx ) {
ib2 = min(nb, n-(i-nb));
ii = nb*((i-nb)/(nb*ngpu));
dev = ((i-nb)/nb)%ngpu;
magma_setdevice( dev );
magma_cgetmatrix_async( (i-nb)+ib2, ib2,
dA(dev, 0, ii), ldda,
A(0, i-nb), lda,
queues[dev][0] );
}
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j > 0 ) {
*A(j-1,j) = MAGMA_C_MAKE( e[j - 1], 0 );
}
d[j] = MAGMA_C_REAL( *A(j, j) );
}
} /* end of for i=... */
if ( nx > 0 ) {
if (1 <= n-nx) { /* else A is already on CPU */
for (i=0; i < nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*ngpu));
dev = (i/nb)%ngpu;
magma_setdevice( dev );
magma_cgetmatrix_async( nx, ib,
dA(dev, 0, ii), ldda,
A(0, i), lda,
queues[dev][0] );
}
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] );
}
/* Use CPU code to reduce the last or only block */
lapackf77_chetrd( uplo_, &nx, A(0, 0), &lda, d, e, tau,
work, &lwork, &iinfo );
}
}
else {
trace_init( 1, ngpu, nqueue, queues );
/* Copy the matrix to the GPU */
if (1 <= n-nx) {
magma_chtodhe( ngpu, uplo, n, nb, A, lda, dA, ldda, queues, &iinfo );
}
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*ngpu));
dev = (i/nb)%ngpu;
/* Reduce columns i:i+ib-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel (no need for the 1st iteration) */
if (i != 0) {
magma_setdevice( dev );
trace_gpu_start( dev, 0, "comm", "get" );
magma_cgetmatrix_async( n-i, ib,
dA(dev, i, ii), ldda,
A(i,i), lda,
queues[dev][0] );
trace_gpu_end( dev, 0 );
magma_queue_sync( queues[dev][0] );
magma_setdevice( 0 );
}
magma_clatrd_mgpu( ngpu, uplo, n-i, ib, nb,
A(i, i), lda, &e[i], &tau[i],
work, ldwork,
dA, ldda, i,
dW, n-i,
hwork, lhwork,
dwork2, ldwork2,
queues0 );
#ifdef PROFILE_SY2RK
magma_setdevice( 0 );
if ( i > 0 ) {
cudaEventElapsedTime( &etime, start, stop );
up_time += (etime/1000.0);
}
magma_event_record( start, 0 );
#endif
magma_cher2k_mgpu( ngpu, MagmaLower, MagmaNoTrans, nb, n-i-ib, ib,
c_neg_one, dW, n-i, ib,
d_one, dA, ldda, i+ib, nqueue, queues );
#ifdef PROFILE_SY2RK
magma_setdevice( 0 );
magma_event_record( stop, 0 );
#endif
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+ib; ++j) {
if ( j+1 < n ) {
*A(j+1,j) = MAGMA_C_MAKE( e[j], 0 );
}
d[j] = MAGMA_C_REAL( *A(j, j) );
}
} /* for i=... */
/* Use CPU code to reduce the last or only block */
if ( i < n ) {
iii = i;
i_n = n-i;
if ( i > 0 ) {
for (; i < n; i += nb) {
ib = min(nb, n-i);
ii = nb*(i/(nb*ngpu));
dev = (i/nb)%ngpu;
magma_setdevice( dev );
magma_cgetmatrix_async( i_n, ib,
dA(dev, iii, ii), ldda,
A(iii, i), lda,
queues[dev][0] );
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] );
}
}
lapackf77_chetrd( uplo_, &i_n, A(iii, iii), &lda, &d[iii], &e[iii],
&tau[iii], work, &lwork, &iinfo );
}
}
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
for( kk=0; kk < nqueue; kk++ ) {
magma_queue_sync( queues[dev][kk] );
}
}
#ifdef PROFILE_SY2RK
magma_setdevice( 0 );
if ( n > nx ) {
cudaEventElapsedTime( &etime, start, stop );
up_time += (etime/1000.0);
}
magma_event_destroy( start );
magma_event_destroy( stop );
#endif
trace_finalize( "chetrd.svg", "trace.css" );
#ifdef PROFILE_SY2RK
printf( " n=%d nb=%d\n", n, nb );
printf( " Time in CLARFG: %.2e seconds\n", times[0] );
//printf( " Time in CHEMV : %.2e seconds\n", mv_time );
printf( " Time in CHER2K: %.2e seconds\n", up_time );
#endif
CLEANUP:
for( dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
for( kk=0; kk < nqueue; kk++ ) {
magma_queue_destroy( queues[dev][kk] );
}
magma_free( dA[dev] );
magma_free( dwork2[dev] );
}
magma_free_pinned( hwork );
magma_setdevice( orig_dev );
work[0] = magma_cmake_lwork( lwkopt );
return *info;
} /* magma_chetrd */