extern "C" void
magma_cher2k_mgpu(
magma_int_t num_gpus, magma_uplo_t uplo, magma_trans_t trans, magma_int_t nb, magma_int_t n, magma_int_t k,
magmaFloatComplex alpha,
magmaFloatComplex **db, magma_int_t lddb, magma_int_t offset_b,
float beta,
magmaFloatComplex **dc, magma_int_t lddc, magma_int_t offset,
magma_int_t num_streams, magma_queue_t stream[][10])
{
#define dB(id, i, j) (db[(id)]+(j)*lddb + (i)+offset_b)
#define dB1(id, i, j) (db[(id)]+(j)*lddb + (i)+offset_b)+k*lddb
#define dC(id, i, j) (dc[(id)]+(j)*lddc + (i))
magma_int_t i, id, ib, ii, kk, n1;
magmaFloatComplex c_one = MAGMA_C_ONE;
/* diagonal update */
for( i=0; i < n; i += nb ) {
id = ((i+offset)/nb)%num_gpus;
kk = (i/(nb*num_gpus))%num_streams;
magma_setdevice(id);
magmablasSetKernelStream(stream[id][kk]);
ib = min(nb, n-i);
ii = nb*((i+offset)/(nb*num_gpus));
/* cher2k on diagonal block */
trace_gpu_start( id, kk, "syr2k", "syr2k" );
magma_cher2k(uplo, trans, ib, k,
alpha, dB1(id, i, 0 ), lddb,
dB(id, i, 0 ), lddb,
beta, dC(id, i+offset, ii), lddc);
trace_gpu_end( id, kk );
}
/* off-diagonal update */
if (uplo == MagmaUpper) {
for( i=nb; i < n; i += nb ) {
id = ((i+offset)/nb)%num_gpus;
kk = (i/(nb*num_gpus))%num_streams;
magma_setdevice(id);
magmablasSetKernelStream(stream[id][kk]);
ib = min(nb, n-i);
ii = nb*((i+offset)/(nb*num_gpus));
magma_cgemm(MagmaNoTrans, MagmaConjTrans, i, ib, k,
alpha, dB1(id, 0, 0 ), lddb,
dB(id, i, 0 ), lddb,
c_one, dC(id, 0, ii), lddc);
}
}
else {
for( i=0; i < n-nb; i += nb ) {
id = ((i+offset)/nb)%num_gpus;
kk = (i/(nb*num_gpus))%num_streams;
magma_setdevice(id);
magmablasSetKernelStream(stream[id][kk]);
ib = min(nb, n-i);
ii = nb*((i+offset)/(nb*num_gpus));
n1 = n-i-ib;
// cgemm on off-diagonal blocks
trace_gpu_start( id, kk, "gemm_up", "gemm_up" );
magma_cgemm(MagmaNoTrans, MagmaConjTrans, n1, ib, k,
alpha, dB1(id, i+ib, 0 ), lddb,
dB(id, i, 0 ), lddb,
c_one, dC(id, i+offset+ib, ii), lddc);
trace_gpu_end( id, kk );
}
}
if (uplo == MagmaUpper) {
for( i=nb; i < n; i += nb ) {
id = ((i+offset)/nb)%num_gpus;
kk = (i/(nb*num_gpus))%num_streams;
magma_setdevice(id);
magmablasSetKernelStream(stream[id][kk]);
ib = min(nb, n-i);
ii = nb*((i+offset)/(nb*num_gpus));
magma_cgemm(MagmaNoTrans, MagmaConjTrans, i, ib, k,
alpha, dB( id, 0, 0 ), lddb,
dB1(id, i, 0 ), lddb,
c_one, dC(id, 0, ii), lddc);
}
} else {
for( i=0; i < n-nb; i += nb ) {
id = ((i+offset)/nb)%num_gpus;
kk = (i/(nb*num_gpus))%num_streams;
magma_setdevice(id);
magmablasSetKernelStream(stream[id][kk]);
ib = min(nb, n-i);
ii = nb*((i+offset)/(nb*num_gpus));
n1 = n-i-ib;
/* cgemm on off-diagonal blocks */
trace_gpu_start( id, kk, "gemm_up", "gemm_up" );
magma_cgemm(MagmaNoTrans, MagmaConjTrans, n1, ib, k,
alpha, dB(id, i+ib, 0 ), lddb,
dB1(id, i, 0 ), lddb,
c_one, dC(id, i+offset+ib, ii), lddc);
trace_gpu_end( id, kk );
}
}
for( id=0; id < num_gpus; id++ ) {
magma_setdevice(id);
for( kk=0; kk < num_streams; kk++ ) magma_queue_sync(stream[id][kk]);
magmablasSetKernelStream(NULL);
}
}
/**
Purpose
-------
CHEGST_GPU reduces a complex Hermitian-definite generalized
eigenproblem to standard form.
If ITYPE = 1, the problem is A*x = lambda*B*x,
and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L.
B must have been previously factorized as U**H*U or L*L**H by CPOTRF.
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 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.
\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 COMPLEX array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B,
as returned by CPOTRF.
@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_cheev_comp
********************************************************************/
extern "C" magma_int_t
magma_chegst_gpu(magma_int_t itype, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
magmaFloatComplex *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;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_half = MAGMA_C_HALF;
magmaFloatComplex c_neg_half = MAGMA_C_NEG_HALF;
magmaFloatComplex *w;
magma_int_t lda;
magma_int_t ldb;
float 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_chegst_nb(n);
lda = nb;
ldb = nb;
if (MAGMA_SUCCESS != magma_cmalloc_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_cgetmatrix_async( kb, kb,
dB(0, 0), lddb,
B(0, 0), nb, stream[2] );
magma_cgetmatrix_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_chegst( &itype, uplo_, &kb, A(0,0), &lda, B(0,0), &ldb, info);
magma_csetmatrix_async( kb, kb,
A(0, 0), lda,
dA(k, k), ldda, stream[0] );
if (k+kb < n) {
// Start copying the new B block
magma_cgetmatrix_async( kb2, kb2,
dB(k+kb, k+kb), lddb,
B(0, 0), nb, stream[2] );
magma_ctrsm(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_chemm(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_cher2k(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_cgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(0, 0), lda, stream[1] );
magma_chemm(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_ctrsm(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_cgetmatrix_async( kb, kb,
dB(0, 0), lddb,
B(0, 0), nb, stream[2] );
magma_cgetmatrix_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_chegst( &itype, uplo_, &kb, A(0, 0), &lda, B(0, 0), &ldb, info);
magma_csetmatrix_async( kb, kb,
A(0, 0), lda,
dA(k, k), ldda, stream[0] );
if (k+kb < n) {
// Start copying the new B block
magma_cgetmatrix_async( kb2, kb2,
dB(k+kb, k+kb), lddb,
B(0, 0), nb, stream[2] );
magma_ctrsm(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_chemm(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_cher2k(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_cgetmatrix_async( kb2, kb2,
dA(k+kb, k+kb), ldda,
A(0, 0), lda, stream[1] );
magma_chemm(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_ctrsm(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_cgetmatrix_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_ctrmm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit,
k, kb,
c_one, dB(0,0), lddb,
dA(0,k), ldda);
magma_chemm(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_cgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(0, 0), lda, stream[0] );
if (k > 0) {
magma_cher2k(MagmaUpper, MagmaNoTrans,
k, kb,
c_one, dA(0,k), ldda,
dB(0,k), lddb,
d_one, dA(0,0), ldda);
magma_chemm(MagmaRight, MagmaUpper,
k, kb,
c_half, dA(k,k), ldda,
dB(0,k), lddb,
c_one, dA(0, k), ldda);
magma_ctrmm(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_chegst( &itype, uplo_, &kb, A(0, 0), &lda, B(0, 0), &ldb, info);
magma_csetmatrix_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_cgetmatrix_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_ctrmm(MagmaRight, MagmaLower, MagmaNoTrans, MagmaNonUnit,
kb, k,
c_one, dB(0,0), lddb,
dA(k,0), ldda);
magma_chemm(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_cgetmatrix_async( kb, kb,
dA(k, k), ldda,
A(0, 0), lda, stream[0] );
if (k > 0) {
magma_cher2k(MagmaLower, MagmaConjTrans,
k, kb,
c_one, dA(k,0), ldda,
dB(k,0), lddb,
d_one, dA(0,0), ldda);
magma_chemm(MagmaLeft, MagmaLower,
kb, k,
c_half, dA(k,k), ldda,
dB(k,0), lddb,
c_one, dA(k, 0), ldda);
magma_ctrmm(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_chegst( &itype, uplo_, &kb, A(0, 0), &lda, B(0, 0), &ldb, info);
magma_csetmatrix_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_chegst_gpu */
extern "C" magma_int_t
magma_chetrd_he2hb_mgpu( char uplo, magma_int_t n, magma_int_t nb,
magmaFloatComplex *a, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *dAmgpu[], magma_int_t ldda,
magmaFloatComplex *dTmgpu[], magma_int_t lddt,
magma_int_t ngpu, magma_int_t distblk,
magma_queue_t streams[][20], magma_int_t nstream,
magma_int_t threads, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CHETRD_HE2HB reduces a complex Hermitian 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
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = 'U', 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
= 'L', 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.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (output) COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
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.
dT (output) COMPLEX 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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
If UPLO = 'U', 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 = 'L', 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 = 'U': if UPLO = 'L':
( 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).
===================================================================== */
#define a_ref(a_1,a_2) ( a + ((a_2)-1)*( lda) + (a_1)-1)
#define da_ref(a_1,a_2) (da + ((a_2)-1)*(ldda) + (a_1)-1)
#define tau_ref(a_1) (tau + (a_1)-1)
#define t_ref(a_1) (dT + ((a_1)-1)*(lddt))
#define Atest(a_1,a_2) ( Atest + ((a_2)-1)*( lda) + (a_1)-1)
#define dttest(a_0, a_1, a_2) (dTmgpu[a_0] + ((a_2)-1)*(lddt))
#define datest(a_0, a_1, a_2) (dAmgpu[a_0] + ((a_2)-1)*(ldda) + (a_1)-1)
char uplo_[2] = {uplo, 0};
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_neg_half = MAGMA_C_NEG_HALF;
magmaFloatComplex c_one = MAGMA_C_ONE ;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
float 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, flipV=-1;
magma_int_t iblock, idev, di;
int i;
int lwkopt;
int lquery;
assert (nstream>=3);
assert (nstream>=(ngpu+1));
*info = 0;
int upper = lapackf77_lsame(uplo_, "U");
lquery = lwork == -1;
if (! upper && ! lapackf77_lsame(uplo_, "L")) {
*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) {
MAGMA_C_SET2REAL( work[0], lwkopt );
}
if (*info != 0)
return *info;
else if (lquery)
return *info;
/* Quick return if possible */
if (n == 0) {
work[0] = c_one;
return *info;
}
magma_int_t mklth = min(threads,16);
magma_setlapack_numthreads(mklth);
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
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_t cstream;
magmablasGetKernelStream(&cstream);
magmaFloatComplex *dspace[MagmaMaxGPUs];
magmaFloatComplex *dwork[MagmaMaxGPUs], *dworkbis[MagmaMaxGPUs];
magmaFloatComplex *dvall[MagmaMaxGPUs], *dv[MagmaMaxGPUs], *dw[MagmaMaxGPUs];
magmaFloatComplex *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
for( magma_int_t dev = 0; dev < ngpu; ++dev ) {
magma_setdevice( dev );
magma_cmalloc( &dspace[dev], devworksiz );
magma_cmalloc_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( streams[ dev ][ 0 ] );
for( magma_int_t i = 0; i < nbevents; ++i ) {
cudaEventCreateWithFlags(&redevents[dev][i],cudaEventDisableTiming);
}
}
magma_cmalloc_pinned ( &workngpu[ngpu], worksiz);
magmaFloatComplex *worktest = NULL; //(magmaFloatComplex *) malloc(n*nb*sizeof(magmaFloatComplex)); // not used
// ======================
magmaFloatComplex *hT = work + lwork - nb*nb;
lwork -= nb*nb;
memset( hT, 0, nb*nb*sizeof(magmaFloatComplex));
if (upper) {
printf("CHETRD_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 ){
// cpanel_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.
cpanel_to_q(MagmaUpper, pn-1, a_ref(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_cgetmatrix_async( (pm+pn), pn,
datest(idev, i, di+1), ldda,
a_ref ( i, i), lda, streams[ idev ][ nstream-1 ] );
/*
magma_device_sync();
cudaMemcpy2DAsync(a_ref(i,i), lda*sizeof(magmaFloatComplex),
datest(idev,i,di+1), ldda*sizeof(magmaFloatComplex),
(pm+pn)*sizeof(magmaFloatComplex), pn,
cudaMemcpyDeviceToHost, streams[ idev ][ nstream-1 ]);
*/
//magma_setdevice( 0 );
//printf("updating cher2k 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 CHER2K_MGPU
magmablas_cher2k_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, streams, 2 );
//magma_setdevice( 0 );
magma_setdevice( idev );
magma_queue_sync( streams[idev][ nstream-1 ] );
//magma_setdevice( 0 );
cq_to_panel(MagmaUpper, pn-1, a_ref(i, i+1), lda, work);
}
/* ==========================================================
QR factorization on a panel starting nb off of the diagonal.
Prepare the V and T matrices.
========================================================== */
lapackf77_cgeqrf(&pm, &pn, a_ref(indi, indj), &lda,
tau_ref(i), work, &lwork, info);
/* Form the matrix T */
pk=min(pm,pn);
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&pm, &pk, a_ref(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 */
cpanel_to_q(MagmaUpper, pk, a_ref(indi, indj), lda, work);
/* Send V and T from the CPU to the GPU */
// To be able to overlap the GET with the CHER2K
// it should be done on last stream.
// TO Avoid a BUG that is overwriting the old_V
// used atthis moment by cher2k 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_csetmatrix_async( pm, pk,
a_ref(indi, indj), lda,
dv[dev], pm, streams[dev][nstream-1] );
// Send the triangular factor T to the GPU
magma_csetmatrix_async( pk, pk,
hT, nb,
dttest(dev, 1, i), lddt, streams[dev][nstream-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( streams[ dev ][ nstream-1 ] );
magma_queue_sync( streams[dev][nstream-1] );
magma_cgemm(MagmaNoTrans, MagmaNoTrans, pm, pk, pk,
c_one, dv[dev], pm,
dttest(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 < nstream; ++s )
magma_queue_sync( streams[dev][s] );
}
// compute CHEMM_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( streams[ 0 ][ 0 ] );
magma_chemm(MagmaLeft, uplo, pm, pk,
c_one, dAmgpu[0]+(indi-1)*ldda+(indi-1), ldda,
dwork[0], pm,
c_zero, dw[0], pm);
}else{
magmablas_chemm_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, streams, nstream-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 CHEMM 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( streams[ dev ][ 0 ] );
// magma_queue_sync( streams[dev][0] );
magma_cgemm(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_cgemm(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*/
cq_to_panel(MagmaUpper, pk, a_ref(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 CHER2K 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( streams[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( streams[ idev ][ nstream-1 ] );
//magma_queue_sync( streams[idev][0] ); removed because the sync has been done in the loop above
magma_cgemm(MagmaNoTrans, MagmaConjTrans, pm, pn, pn, c_neg_one,
dv[idev], pm,
dw[idev] , pm, c_one,
datest(idev, indi, di+1), ldda);
magma_cgemm(MagmaNoTrans, MagmaConjTrans, pm, pn, pn, c_neg_one,
dw[idev] , pm,
dv[idev], pm, c_one,
datest(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( streams[ idev ][ 0 ] );
//printf("LAST CHER2K idev %d on A(%d,%d) of size %d \n",idev, indi-1,di,pk);
magma_cher2k(MagmaLower, MagmaNoTrans, pk, pk, c_neg_one,
dv[idev], pm,
dw[idev] , pm, d_one,
datest(idev, indi, di+1), ldda);
/* Send the last block to the CPU */
cpanel_to_q(MagmaUpper, pk-1, a_ref(n-pk+1, n-pk+2), lda, work);
magma_cgetmatrix( pk, pk,
datest(idev, indi, di+1), ldda,
a_ref(n-pk+1, n-pk+1), lda );
cq_to_panel(MagmaUpper, pk-1, a_ref(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 ) {
cudaEventDestroy(redevents[dev][e]);
}
}
magma_free_pinned(workngpu[ngpu]);
free(worktest);
magma_setdevice( cdev );
magmablasSetKernelStream( cstream );
MAGMA_C_SET2REAL( work[0], lwkopt );
magma_setlapack_numthreads(1);
return *info;
} /* chetrd_he2hb_ */
extern "C" magma_int_t
magma_chetrd2_gpu(char uplo, magma_int_t n,
magmaFloatComplex *da, magma_int_t ldda,
float *d, float *e, magmaFloatComplex *tau,
magmaFloatComplex *wa, magma_int_t ldwa,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *dwork, magma_int_t ldwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CHETRD2_GPU reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
This version passes a workspace that is used in an optimized
GPU matrix-vector product.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
DA (device input/output) COMPLEX array, dimension (LDA,N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.
On exit, if UPLO = 'U', 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
= 'L', 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.
LDDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
D (output) COMPLEX array, dimension (N)
The diagonal elements of the tridiagonal matrix T:
D(i) = A(i,i).
E (output) COMPLEX array, dimension (N-1)
The off-diagonal elements of the tridiagonal matrix T:
E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
TAU (output) COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details).
WA (workspace/output) COMPLEX array, dimension (LDA,N)
On exit the diagonal, the upper part (UPLO='U')
or the lower part (UPLO='L') are copies of DA
LDWA (input) INTEGER
The leading dimension of the array WA. LDWA >= max(1,N).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= 1.
For optimum performance LWORK >= N*NB, where NB is the
optimal blocksize.
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.
DWORK (workspace/output) COMPLEX array on the GPU, dim (MAX(1,LDWORK))
LDWORK (input) INTEGER
The dimension of the array DWORK.
LDWORK >= (n*n+64-1)/64 + 2*n*nb, where nb = magma_get_chetrd_nb(n)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Further Details
===============
If UPLO = 'U', 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 = 'L', 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 = 'U': if UPLO = 'L':
( 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).
===================================================================== */
char uplo_[2] = {uplo, 0};
magma_int_t nb = magma_get_chetrd_nb(n);
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
float d_one = MAGMA_D_ONE;
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldw, lddw, lwkopt;
magma_int_t lquery;
*info = 0;
int upper = lapackf77_lsame(uplo_, "U");
lquery = lwork == -1;
if (! upper && ! lapackf77_lsame(uplo_, "L")) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
} else if (ldwa < max(1,n)) {
*info = -9;
} else if (lwork < 1 && ! lquery) {
*info = -11;
}
/* Determine the block size. */
ldw = lddw = n;
lwkopt = n * nb;
if (*info == 0) {
MAGMA_C_SET2REAL( work[0], 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;
}
if (n < 1024)
nx = n;
else
nx = 300;
if (ldwork<(ldw*n+64-1)/64 + 2*ldw*nb) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (upper) {
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - (n - nx + nb - 1) / nb * nb;
for (i = n - nb; i >= kk; i -= nb)
{
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), ldwa );
magma_clatrd2(uplo, i+nb, nb, A(0, 0), ldwa, e, tau,
work, ldw, dA(0, 0), ldda, dwork, lddw, dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( i + nb, nb, work, ldw, dwork, lddw );
magma_cher2k(uplo, MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork,
lddw, d_one, dA(0, 0), ldda);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
MAGMA_C_SET2REAL( *A(j-1, j), e[j - 1] );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
magma_cgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), ldwa );
/* Use CPU code to reduce the last or only block */
lapackf77_chetrd(uplo_, &kk, A(0, 0), &ldwa, d, e, tau, work, &lwork, &iinfo);
magma_csetmatrix( kk, kk, A(0, 0), ldwa, dA(0, 0), ldda );
}
else
{
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb)
{
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), ldwa );
magma_clatrd2(uplo, n-i, nb, A(i, i), ldwa, &e[i],
&tau[i], work, ldw,
dA(i, i), ldda,
dwork, lddw,
dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( n-i, nb, work, ldw, dwork, lddw );
magma_cher2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda,
&dwork[nb], lddw, d_one,
dA(i+nb, i+nb), ldda);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
MAGMA_C_SET2REAL( *A(j+1, j), e[j] );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
/* Use unblocked code to reduce the last or only block */
magma_cgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), ldwa );
i_n = n-i;
lapackf77_chetrd(uplo_, &i_n, A(i, i), &ldwa, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo);
magma_csetmatrix( n-i, n-i, A(i, i), ldwa, dA(i, i), ldda );
}
MAGMA_C_SET2REAL( work[0], lwkopt );
return *info;
} /* chetrd2_gpu */
// ----------------------------------------------------------------------
extern "C" void
magma_cher2k_mgpu(
magma_int_t ngpu,
magma_uplo_t uplo, magma_trans_t trans, magma_int_t nb, magma_int_t n, magma_int_t k,
magmaFloatComplex alpha,
magmaFloatComplex_ptr dB[], magma_int_t lddb, magma_int_t b_offset,
float beta,
magmaFloatComplex_ptr dC[], magma_int_t lddc, magma_int_t c_offset,
magma_int_t nqueue, magma_queue_t queues[][10])
{
#define dB(id, i, j) (dB[(id)] + (j)*lddb + (i)+b_offset)
#define dB1(id, i, j) (dB[(id)] + (j)*lddb + (i)+b_offset) + k*lddb
#define dC(id, i, j) (dC[(id)] + (j)*lddc + (i))
magma_int_t i, id, ib, ii, kk, n1;
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
/* diagonal update */
for( i=0; i < n; i += nb ) {
id = ((i+c_offset)/nb)%ngpu;
kk = (i/(nb*ngpu))%nqueue;
magma_setdevice( id );
ib = min(nb, n-i);
ii = nb*((i+c_offset)/(nb*ngpu));
/* cher2k on diagonal block */
trace_gpu_start( id, kk, "syr2k", "syr2k" );
magma_cher2k( uplo, trans, ib, k,
alpha, dB1(id, i, 0 ), lddb,
dB(id, i, 0 ), lddb,
beta, dC(id, i+c_offset, ii), lddc, queues[id][kk] );
trace_gpu_end( id, kk );
}
/* off-diagonal update */
if (uplo == MagmaUpper) {
for( i=nb; i < n; i += nb ) {
id = ((i+c_offset)/nb)%ngpu;
kk = (i/(nb*ngpu))%nqueue;
magma_setdevice( id );
ib = min(nb, n-i);
ii = nb*((i+c_offset)/(nb*ngpu));
magma_cgemm( MagmaNoTrans, MagmaConjTrans, i, ib, k,
alpha, dB1(id, 0, 0 ), lddb,
dB(id, i, 0 ), lddb,
c_one, dC(id, 0, ii), lddc, queues[id][kk] );
}
}
else {
for( i=0; i < n-nb; i += nb ) {
id = ((i+c_offset)/nb)%ngpu;
kk = (i/(nb*ngpu))%nqueue;
magma_setdevice( id );
ib = min(nb, n-i);
ii = nb*((i+c_offset)/(nb*ngpu));
n1 = n-i-ib;
// cgemm on off-diagonal blocks
trace_gpu_start( id, kk, "gemm_up", "gemm_up" );
magma_cgemm( MagmaNoTrans, MagmaConjTrans, n1, ib, k,
alpha, dB1(id, i+ib, 0 ), lddb,
dB(id, i, 0 ), lddb,
c_one, dC(id, i+c_offset+ib, ii), lddc, queues[id][kk] );
trace_gpu_end( id, kk );
}
}
if (uplo == MagmaUpper) {
for( i=nb; i < n; i += nb ) {
id = ((i+c_offset)/nb)%ngpu;
kk = (i/(nb*ngpu))%nqueue;
magma_setdevice( id );
ib = min(nb, n-i);
ii = nb*((i+c_offset)/(nb*ngpu));
magma_cgemm( MagmaNoTrans, MagmaConjTrans, i, ib, k,
alpha, dB( id, 0, 0 ), lddb,
dB1(id, i, 0 ), lddb,
c_one, dC(id, 0, ii), lddc, queues[id][kk] );
}
} else {
for( i=0; i < n-nb; i += nb ) {
id = ((i+c_offset)/nb)%ngpu;
kk = (i/(nb*ngpu))%nqueue;
magma_setdevice( id );
ib = min(nb, n-i);
ii = nb*((i+c_offset)/(nb*ngpu));
n1 = n-i-ib;
/* cgemm on off-diagonal blocks */
trace_gpu_start( id, kk, "gemm_up", "gemm_up" );
magma_cgemm( MagmaNoTrans, MagmaConjTrans, n1, ib, k,
alpha, dB(id, i+ib, 0 ), lddb,
dB1(id, i, 0 ), lddb,
c_one, dC(id, i+c_offset+ib, ii), lddc, queues[id][kk] );
trace_gpu_end( id, kk );
}
}
for( id=0; id < ngpu; id++ ) {
magma_setdevice( id );
for( kk=0; kk < nqueue; kk++ ) {
magma_queue_sync( queues[id][kk] );
}
}
magma_setdevice( orig_dev );
}
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, t1, t2;
magmaFloatComplex c_neg_one = MAGMA_C_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 };
magmaFloatComplex *A, *B, *C, *C2, *LU;
magmaFloatComplex_ptr dA, dB, dC1, dC2;
magmaFloatComplex alpha = MAGMA_C_MAKE( 0.5, 0.1 );
magmaFloatComplex beta = MAGMA_C_MAKE( 0.7, 0.2 );
float dalpha = 0.6;
float dbeta = 0.8;
float 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_cmalloc_pinned( &A, size ); assert( err == 0 );
err = magma_cmalloc_pinned( &B, size ); assert( err == 0 );
err = magma_cmalloc_pinned( &C, size ); assert( err == 0 );
err = magma_cmalloc_pinned( &C2, size ); assert( err == 0 );
err = magma_cmalloc_pinned( &LU, size ); assert( err == 0 );
err = magma_cmalloc( &dA, size ); assert( err == 0 );
err = magma_cmalloc( &dB, size ); assert( err == 0 );
err = magma_cmalloc( &dC1, size ); assert( err == 0 );
err = magma_cmalloc( &dC2, size ); assert( err == 0 );
// initialize matrices
size = maxn*maxn;
lapackf77_clarnv( &ione, ISEED, &size, A );
lapackf77_clarnv( &ione, ISEED, &size, B );
lapackf77_clarnv( &ione, ISEED, &size, C );
printf( "========== Level 1 BLAS ==========\n" );
// ----- test CSWAP
// swap columns 2 and 3 of dA, then copy to C2 and compare with A
if ( n >= 3 ) {
magma_csetmatrix( m, n, A, ld, dA, ld );
magma_csetmatrix( m, n, A, ld, dB, ld );
magma_cswap( m, dA(0,1), 1, dA(0,2), 1 );
magma_cswap( m, dB(0,1), 1, dB(0,2), 1 );
// check results, storing diff between magma and cuda calls in C2
cublasCaxpy( opts.handle, ld*n, &c_neg_one, dA, 1, dB, 1 );
magma_cgetmatrix( m, n, dB, ld, C2, ld );
error = lapackf77_clange( "F", &m, &k, C2, &ld, work );
total_error += error;
printf( "cswap diff %.2g\n", error );
}
else {
printf( "cswap skipped for n < 3\n" );
}
// ----- test ICAMAX
// get argmax of column of A
magma_csetmatrix( m, k, A, ld, dA, ld );
error = 0;
for( int j = 0; j < k; ++j ) {
magma_int_t i1 = magma_icamax( m, dA(0,j), 1 );
int i2; // NOT magma_int_t, for cublas
cublasIcamax( opts.handle, m, dA(0,j), 1, &i2 );
// todo need sync here?
assert( i1 == i2 );
error += abs( i1 - i2 );
}
total_error += error;
gflops = (float)m * k / 1e9;
printf( "icamax diff %.2g\n", error );
printf( "\n" );
printf( "========== Level 2 BLAS ==========\n" );
// ----- test CGEMV
// 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_csetmatrix( m, n, A, ld, dA, ld );
magma_csetvector( maxn, B, 1, dB, 1 );
magma_csetvector( maxn, C, 1, dC1, 1 );
magma_csetvector( maxn, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_cgemv( trans[ia], m, n, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasCgemv( opts.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);
cublasCaxpy( opts.handle, size, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetvector( size, dC2, 1, C2, 1 );
error = lapackf77_clange( "F", &size, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_CGEMV( m, n ) / 1e9;
printf( "cgemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_trans_const(trans[ia]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test CHEMV
// 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_csetmatrix( m, m, A, ld, dA, ld );
magma_csetvector( m, B, 1, dB, 1 );
magma_csetvector( m, C, 1, dC1, 1 );
magma_csetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_chemv( uplo[iu], m, alpha, dA, ld, dB, 1, beta, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasChemv( opts.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
cublasCaxpy( opts.handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_clange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_CHEMV( m ) / 1e9;
printf( "chemv( %c ) diff %.2g, Gflop/s %7.2f, %7.2f\n",
lapacke_uplo_const(uplo[iu]), error, gflops/t1, gflops/t2 );
}
printf( "\n" );
// ----- test CTRSV
// 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_clacpy( "Full", &maxn, &maxn, A, &ld, LU, &ld );
lapackf77_cgetrf( &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_csetmatrix( m, m, LU, ld, dA, ld );
magma_csetvector( m, C, 1, dC1, 1 );
magma_csetvector( m, C, 1, dC2, 1 );
t1 = magma_sync_wtime( 0 );
magma_ctrsv( uplo[iu], trans[it], diag[id], m, dA, ld, dC1, 1 );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasCtrsv( opts.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
cublasCaxpy( opts.handle, m, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetvector( m, dC2, 1, C2, 1 );
error = lapackf77_clange( "F", &m, &ione, C2, &ld, work );
total_error += error;
gflops = FLOPS_CTRSM( MagmaLeft, m, 1 ) / 1e9;
printf( "ctrsv( %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 CGEMM
// 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_csetmatrix( (nta ? m : k), (nta ? m : k), A, ld, dA, ld );
magma_csetmatrix( (ntb ? k : n), (ntb ? n : k), B, ld, dB, ld );
magma_csetmatrix( m, n, C, ld, dC1, ld );
magma_csetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_cgemm( 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 );
cublasCgemm( opts.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
cublasCaxpy( opts.handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CGEMM( m, n, k ) / 1e9;
printf( "cgemm( %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 CHEMM
// 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_csetmatrix( m, m, A, ld, dA, ld );
magma_csetmatrix( m, n, B, ld, dB, ld );
magma_csetmatrix( m, n, C, ld, dC1, ld );
magma_csetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_chemm( 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 );
cublasChemm( opts.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
cublasCaxpy( opts.handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &m, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CHEMM( side[is], m, n ) / 1e9;
printf( "chemm( %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 CHERK
// 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_csetmatrix( n, k, A, ld, dA, ld );
magma_csetmatrix( n, n, C, ld, dC1, ld );
magma_csetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_cherk( uplo[iu], trans[it], n, k, dalpha, dA, ld, dbeta, dC1, ld );
t1 = magma_sync_wtime( 0 ) - t1;
t2 = magma_sync_wtime( 0 );
cublasCherk( opts.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
cublasCaxpy( opts.handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CHERK( k, n ) / 1e9;
printf( "cherk( %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 CHER2K
// 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_csetmatrix( (nt ? n : k), (nt ? n : k), A, ld, dA, ld );
magma_csetmatrix( n, n, C, ld, dC1, ld );
magma_csetmatrix( n, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_cher2k( 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 );
cublasCher2k( opts.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
cublasCaxpy( opts.handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( n, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CHER2K( k, n ) / 1e9;
printf( "cher2k( %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 CTRMM
// 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_csetmatrix( (left ? m : n), (left ? m : n), A, ld, dA, ld );
magma_csetmatrix( m, n, C, ld, dC1, ld );
magma_csetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ctrmm( 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 );
cublasCtrmm( opts.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
cublasCaxpy( opts.handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CTRMM( side[is], m, n ) / 1e9;
printf( "ctrmm( %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 CTRSM
// 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_csetmatrix( (left ? m : n), (left ? m : n), LU, ld, dA, ld );
magma_csetmatrix( m, n, C, ld, dC1, ld );
magma_csetmatrix( m, n, C, ld, dC2, ld );
t1 = magma_sync_wtime( 0 );
magma_ctrsm( 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 );
cublasCtrsm( opts.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
cublasCaxpy( opts.handle, ld*n, &c_neg_one, dC1, 1, dC2, 1 );
magma_cgetmatrix( m, n, dC2, ld, C2, ld );
error = lapackf77_clange( "F", &n, &n, C2, &ld, work );
total_error += error;
gflops = FLOPS_CTRSM( side[is], m, n ) / 1e9;
printf( "ctrsm( %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
-------
CHETRD2_GPU reduces a complex Hermitian matrix A to real symmetric
tridiagonal form T by an orthogonal similarity transformation:
Q**H * A * Q = T.
This version passes a workspace that is used in an optimized
GPU matrix-vector product.
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]
dA 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]
ldda 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]
wA (workspace) COMPLEX array, dimension (LDA,N)
On exit the diagonal, the upper part (UPLO=MagmaUpper)
or the lower part (UPLO=MagmaLower) are copies of DA
@param[in]
ldwa INTEGER
The leading dimension of the array wA. LDWA >= max(1,N).
@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 >= 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]
dwork (workspace) COMPLEX array on the GPU, dim (MAX(1,LDWORK))
@param[in]
ldwork INTEGER
The dimension of the array DWORK.
LDWORK >= (n*n+64-1)/64 + 2*n*nb, where nb = magma_get_chetrd_nb(n)
@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_chetrd2_gpu(magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *dA, magma_int_t ldda,
float *d, float *e, magmaFloatComplex *tau,
magmaFloatComplex *wA, magma_int_t ldwa,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *dwork, magma_int_t ldwork,
magma_int_t *info)
{
#define A(i, j) (wA + (j)*ldwa + (i))
#define dA(i, j) (dA + (j)*ldda + (i))
const char* uplo_ = lapack_uplo_const( uplo );
magma_int_t nb = magma_get_chetrd_nb(n);
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_one = MAGMA_C_ONE;
float d_one = MAGMA_D_ONE;
magma_int_t kk, nx;
magma_int_t i, j, i_n;
magma_int_t iinfo;
magma_int_t ldw, lddw, lwkopt;
magma_int_t lquery;
*info = 0;
int upper = (uplo == MagmaUpper);
lquery = (lwork == -1);
if (! upper && uplo != MagmaLower) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,n)) {
*info = -4;
} else if (ldwa < max(1,n)) {
*info = -9;
} else if (lwork < 1 && ! lquery) {
*info = -11;
}
/* Determine the block size. */
ldw = lddw = n;
lwkopt = n * nb;
if (*info == 0) {
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
}
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;
}
if (n < 1024)
nx = n;
else
nx = 300;
if (ldwork < (ldw*n+64-1)/64 + 2*ldw*nb) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (upper) {
/* Reduce the upper triangle of A.
Columns 1:kk are handled by the unblocked method. */
kk = n - (n - nx + nb - 1) / nb * nb;
for (i = n - nb; i >= kk; i -= nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( i+nb, nb, dA(0, i), ldda, A(0, i), ldwa );
magma_clatrd2(uplo, i+nb, nb, A(0, 0), ldwa, e, tau,
work, ldw, dA(0, 0), ldda, dwork, lddw, dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(0:i-2,0:i-2), using an
update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( i + nb, nb, work, ldw, dwork, lddw );
magma_cher2k(uplo, MagmaNoTrans, i, nb, c_neg_one,
dA(0, i), ldda, dwork,
lddw, d_one, dA(0, 0), ldda);
/* Copy superdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j-1,j) = MAGMA_C_MAKE( e[j - 1], 0 );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
magma_cgetmatrix( kk, kk, dA(0, 0), ldda, A(0, 0), ldwa );
/* Use CPU code to reduce the last or only block */
lapackf77_chetrd(uplo_, &kk, A(0, 0), &ldwa, d, e, tau, work, &lwork, &iinfo);
magma_csetmatrix( kk, kk, A(0, 0), ldwa, dA(0, 0), ldda );
}
else {
/* Reduce the lower triangle of A */
for (i = 0; i < n-nx; i += nb) {
/* Reduce columns i:i+nb-1 to tridiagonal form and form the
matrix W which is needed to update the unreduced part of
the matrix */
/* Get the current panel */
magma_cgetmatrix( n-i, nb, dA(i, i), ldda, A(i, i), ldwa );
magma_clatrd2(uplo, n-i, nb, A(i, i), ldwa, &e[i],
&tau[i], work, ldw,
dA(i, i), ldda,
dwork, lddw,
dwork + 2*ldw*nb, ldwork - 2*ldw*nb);
/* Update the unreduced submatrix A(i+ib:n,i+ib:n), using
an update of the form: A := A - V*W' - W*V' */
magma_csetmatrix( n-i, nb, work, ldw, dwork, lddw );
magma_cher2k(MagmaLower, MagmaNoTrans, n-i-nb, nb, c_neg_one,
dA(i+nb, i), ldda,
&dwork[nb], lddw, d_one,
dA(i+nb, i+nb), ldda);
/* Copy subdiagonal elements back into A, and diagonal
elements into D */
for (j = i; j < i+nb; ++j) {
*A(j+1,j) = MAGMA_C_MAKE( e[j], 0 );
d[j] = MAGMA_C_REAL( *A(j, j) );
}
}
/* Use unblocked code to reduce the last or only block */
magma_cgetmatrix( n-i, n-i, dA(i, i), ldda, A(i, i), ldwa );
i_n = n-i;
lapackf77_chetrd(uplo_, &i_n, A(i, i), &ldwa, &d[i], &e[i],
&tau[i], work, &lwork, &iinfo);
magma_csetmatrix( n-i, n-i, A(i, i), ldwa, dA(i, i), ldda );
}
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
return *info;
} /* magma_chetrd2_gpu */
/**
Purpose
-------
CHETRD_HE2HB reduces a complex Hermitian 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 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 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 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]
dT COMPLEX 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 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_2stage
********************************************************************/
extern "C" magma_int_t
magma_chetrd_he2hb( magma_uplo_t uplo, magma_int_t n, magma_int_t nb,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *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;
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magmaFloatComplex c_neg_half = MAGMA_C_NEG_HALF;
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
float 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_C_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;
}
magmaFloatComplex *dA;
if (MAGMA_SUCCESS != magma_cmalloc( &dA, (n + 2*nb)*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_int_t threads = magma_get_lapack_numthreads();
magma_int_t mklth = min(threads,16);
magma_set_lapack_numthreads(mklth);
/* Use the first panel of dA as work space */
magmaFloatComplex *dwork = dA + n*ldda;
magmaFloatComplex *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 );
magmaFloatComplex *hT = work + lwork - nb*nb;
lwork -= nb*nb;
memset( hT, 0, nb*nb*sizeof(magmaFloatComplex));
magmablasSetKernelStream( stream[0] );
magma_event_t Pupdate_event;
cudaEventCreateWithFlags(&Pupdate_event,cudaEventDisableTiming);
//cudaEventCreate(&Pupdate_event);
if (upper) {
printf("CHETRD_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_csetmatrix_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 ) {
// cpanel_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.
cpanel_to_q(MagmaUpper, pn-1, A(i, i+1), lda, work);
trace_gpu_start( 0, 1, "get", "get panel" );
//magma_queue_sync( stream[0] );
cudaStreamWaitEvent(stream[1], Pupdate_event, 0);
magma_cgetmatrix_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_cher2k(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 );
cq_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_cgeqrf(&pm, &pn, A(indi, indj), &lda,
tau_ref(i), work, &lwork, info);
/* Form the matrix T */
pk=min(pm,pn);
lapackf77_clarft( 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 */
cpanel_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_csetmatrix_async( pm, pk,
A(indi, indj), lda,
dA(indi, indj), ldda, stream[0] );
/* Send the triangular factor T to the GPU */
magma_csetmatrix_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 cq_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_cgemm(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_chemm(MagmaLeft, uplo, pm, pk,
c_one, dA(indi, indi), ldda,
dwork, pm,
c_zero, dW, pm);
trace_gpu_end( 0, 2 );
/* restore the panel */
cq_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_cgemm(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_cgemm(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_cgemm(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_cgemm(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 );
cudaEventRecord(Pupdate_event, stream[0]);
}
else {
/* no look-ahead as this is last iteration */
trace_gpu_start( 0, 2, "her2k", "her2k last iteration" );
magma_cher2k(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) {
cpanel_to_q(MagmaUpper, pk-1, A(n-pk+1, n-pk+2), lda, work);
trace_gpu_start( 0, 2, "get", "get last block" );
magma_cgetmatrix( pk, pk,
dA(n-pk+1, n-pk+1), ldda,
A(n-pk+1, n-pk+1), lda );
trace_gpu_end( 0, 2 );
cq_to_panel(MagmaUpper, pk-1, A(n-pk+1, n-pk+2), lda, work);
}
}// end of LOWER
trace_finalize( "chetrd_he2hb.svg", "trace.css" );
cudaEventDestroy(Pupdate_event);
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free( dA );
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
magmablasSetKernelStream( 0 );
magma_set_lapack_numthreads(threads);
return *info;
} /* magma_chetrd_he2hb */