/* ////////////////////////////////////////////////////////////////////////////
-- Testing cunmlq
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float Cnorm, error, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_int_t mm, m, n, k, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max;
magmaFloatComplex *C, *R, *A, *W, *tau;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
float tol = opts.tolerance * lapackf77_slamch("E");
// test all combinations of input parameters
magma_side_t side [] = { MagmaLeft, MagmaRight };
magma_trans_t trans[] = { Magma_ConjTrans, MagmaNoTrans };
printf("%% M N K side trans CPU Gflop/s (sec) GPU Gflop/s (sec) ||R||_F / ||QC||_F\n");
printf("%%==============================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
nb = magma_get_cgelqf_nb( m, n );
ldc = m;
// A is k x m (left) or k x n (right)
mm = (side[iside] == MagmaLeft ? m : n);
lda = k;
gflops = FLOPS_CUNMLQ( m, n, k, side[iside] ) / 1e9;
if ( side[iside] == MagmaLeft && m < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=left and m < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
if ( side[iside] == MagmaRight && n < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=right and n < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
// need at least 2*nb*nb for gelqf
lwork_max = max( max( m*nb, n*nb ), 2*nb*nb );
// this rounds it up slightly if needed to agree with lwork query
lwork_max = int( real( magma_cmake_lwork( lwork_max )));
TESTING_MALLOC_CPU( C, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( R, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( A, magmaFloatComplex, lda*mm );
TESTING_MALLOC_CPU( W, magmaFloatComplex, lwork_max );
TESTING_MALLOC_CPU( tau, magmaFloatComplex, k );
// C is full, m x n
size = ldc*n;
lapackf77_clarnv( &ione, ISEED, &size, C );
lapackf77_clacpy( "Full", &m, &n, C, &ldc, R, &ldc );
size = lda*mm;
lapackf77_clarnv( &ione, ISEED, &size, A );
// compute LQ factorization to get Householder vectors in A, tau
magma_cgelqf( k, mm, A, lda, tau, W, lwork_max, &info );
if (info != 0) {
printf("magma_cgelqf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_cunmlq( lapack_side_const( side[iside] ), lapack_trans_const( trans[itran] ),
&m, &n, &k,
A, &lda, tau, C, &ldc, W, &lwork_max, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_cunmlq returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for workspace size
lwork = -1;
magma_cunmlq( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
if (info != 0) {
printf("magma_cunmlq (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = (magma_int_t) MAGMA_C_REAL( W[0] );
if ( lwork < 0 || lwork > lwork_max ) {
printf("Warning: optimal lwork %d > allocated lwork_max %d\n", (int) lwork, (int) lwork_max );
lwork = lwork_max;
}
gpu_time = magma_wtime();
magma_cunmlq( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_cunmlq returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
size = ldc*n;
blasf77_caxpy( &size, &c_neg_one, C, &ione, R, &ione );
Cnorm = lapackf77_clange( "Fro", &m, &n, C, &ldc, work );
error = lapackf77_clange( "Fro", &m, &n, R, &ldc, work ) / (magma_ssqrt(m*n) * Cnorm);
printf( "%5d %5d %5d %4c %5c %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ),
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
TESTING_FREE_CPU( C );
TESTING_FREE_CPU( R );
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( W );
TESTING_FREE_CPU( tau );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}} // end iside, itran
printf( "\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/***************************************************************************//**
Purpose
-------
CUNMTR overwrites the general complex M-by-N matrix C with
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = Magma_ConjTrans: Q**H * C C * Q**H
where Q is a complex unitary matrix of order nq,
with nq = m if SIDE = MagmaLeft
and nq = n if SIDE = MagmaRight. Q is defined as the product of
nq-1 elementary reflectors, as returned by CHETRD:
if UPLO = MagmaUpper, Q = H(nq-1) . . . H(2) H(1);
if UPLO = MagmaLower, Q = H(1) H(2) . . . H(nq-1).
Arguments
---------
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangle of A contains elementary reflectors
from CHETRD;
- = MagmaLower: Lower triangle of A contains elementary reflectors
from CHETRD.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = Magma_ConjTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
A COMPLEX array, dimension
(LDA,M) if SIDE = MagmaLeft
(LDA,N) if SIDE = MagmaRight
The vectors which define the elementary reflectors, as
returned by CHETRD.
@param[in]
lda INTEGER
The leading dimension of the array A.
LDA >= max(1,M) if SIDE = MagmaLeft;
LDA >= max(1,N) if SIDE = MagmaRight.
@param[in]
tau COMPLEX array, dimension
(M-1) if SIDE = MagmaLeft
(N-1) if SIDE = MagmaRight
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CHETRD.
@param[in,out]
C COMPLEX array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H * C or C * Q**H or C*Q.
@param[in]
ldc INTEGER
The leading dimension of the array C. LDC >= max(1,M).
@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.
If SIDE = MagmaLeft, LWORK >= max(1,N);
if SIDE = MagmaRight, LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = MagmaLeft, and
LWORK >= M*NB if SIDE = MagmaRight, where NB is the optimal
blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_unmtr
*******************************************************************************/
extern "C" magma_int_t
magma_cunmtr(
magma_side_t side, magma_uplo_t uplo, magma_trans_t trans,
magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *C, magma_int_t ldc,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_,j_) (A + (i_) + (j_)*lda)
#define C(i_,j_) (C + (i_) + (j_)*ldc)
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t i__2;
magma_int_t i1, i2, nb, mi, ni, nq, nw;
magma_int_t iinfo;
magma_int_t lwkopt;
*info = 0;
bool left = (side == MagmaLeft);
bool upper = (uplo == MagmaUpper);
bool lquery = (lwork == -1);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = n;
} else {
nq = n;
nw = m;
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! upper && uplo != MagmaLower) {
*info = -2;
} else if (trans != MagmaNoTrans &&
trans != Magma_ConjTrans) {
*info = -3;
} else if (m < 0) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,nq)) {
*info = -7;
} else if (ldc < max(1,m)) {
*info = -10;
} else if (lwork < max(1,nw) && ! lquery) {
*info = -12;
}
nb = 32;
lwkopt = max(1,nw) * 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 (m == 0 || n == 0 || nq == 1) {
work[0] = c_one;
return *info;
}
if (left) {
mi = m - 1;
ni = n;
} else {
mi = m;
ni = n - 1;
}
if (upper) {
/* Q was determined by a call to CHETRD with UPLO = MagmaUpper */
i__2 = nq - 1;
//lapackf77_cunmql(side_, trans_, &mi, &ni, &i__2, A(0,1), &lda,
// tau, C, &ldc, work, &lwork, &iinfo);
magma_cunmql(side, trans, mi, ni, i__2, A(0,1), lda, tau,
C, ldc, work, lwork, &iinfo);
}
else {
/* Q was determined by a call to CHETRD with UPLO = MagmaLower */
if (left) {
i1 = 1;
i2 = 0;
} else {
i1 = 0;
i2 = 1;
}
i__2 = nq - 1;
magma_cunmqr(side, trans, mi, ni, i__2, A(1,0), lda, tau,
C(i1,i2), ldc, work, lwork, &iinfo);
}
work[0] = magma_cmake_lwork( lwkopt );
return *info;
} /* magma_cunmtr */
/**
Purpose
-------
CGEQRF_OOC computes a QR factorization of a COMPLEX M-by-N matrix A:
A = Q * R. This version does not require work space on the GPU
passed as input. GPU memory is allocated in the routine.
This is an out-of-core (ooc) version that is similar to magma_cgeqrf but
the difference is that this version can use a GPU even if the matrix
does not fit into the GPU memory at once.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau COMPLEX array, dimension (min(M,N))
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.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= N*NB,
where NB can be obtained through magma_get_cgeqrf_nb( M, N ).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_cgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgeqrf_ooc(
magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info )
{
#define A(i_,j_) ( A + (i_) + (j_)*lda )
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
/* Constants */
const magmaFloatComplex c_one = MAGMA_C_ONE;
/* Local variables */
magmaFloatComplex_ptr dA, dwork;
magma_int_t i, ib, IB, j, min_mn, lddwork, ldda, rows;
magma_int_t nb = magma_get_cgeqrf_nb( m, n );
magma_int_t lwkopt = n * nb;
work[0] = magma_cmake_lwork( lwkopt );
bool lquery = (lwork == -1);
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1,n) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Check how much memory do we have */
size_t freeMem, totalMem;
cudaMemGetInfo( &freeMem, &totalMem );
freeMem /= sizeof(magmaFloatComplex);
magma_int_t NB = magma_int_t(0.8*freeMem/m);
NB = (NB / nb) * nb;
if (NB >= n)
return magma_cgeqrf(m, n, A, lda, tau, work, lwork, info);
min_mn = min(m,n);
if (min_mn == 0) {
work[0] = c_one;
return *info;
}
lddwork = magma_roundup( NB, 32 ) + nb;
ldda = magma_roundup( m, 32 );
if (MAGMA_SUCCESS != magma_cmalloc( &dA, (NB + nb)*ldda + nb*lddwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t queues[2];
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
magmaFloatComplex_ptr ptr = dA + ldda*NB;
dwork = dA + ldda*(NB + nb);
/* start the main loop over the blocks that fit in the GPU memory */
for (i=0; i < n; i += NB) {
IB = min( n-i, NB );
//printf("Processing %5d columns -- %5d to %5d ... \n", IB, i, i+IB);
/* 1. Copy the next part of the matrix to the GPU */
magma_csetmatrix_async( m, IB,
A(0,i), lda,
dA(0,0), ldda, queues[0] );
magma_queue_sync( queues[0] );
/* 2. Update it with the previous transformations */
for (j=0; j < min(i,min_mn); j += nb) {
ib = min( min_mn-j, nb );
/* Get a panel in ptr. */
// 1. Form the triangular factor of the block reflector
// 2. Send it to the GPU.
// 3. Put 0s in the upper triangular part of V.
// 4. Send V to the GPU in ptr.
// 5. Update the matrix.
// 6. Restore the upper part of V.
rows = m-j;
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(j,j), &lda, tau+j, work, &ib);
magma_csetmatrix_async( ib, ib,
work, ib,
dwork, lddwork, queues[1] );
magma_cpanel_to_q( MagmaUpper, ib, A(j,j), lda, work+ib*ib );
magma_csetmatrix_async( rows, ib,
A(j,j), lda,
ptr, rows, queues[1] );
magma_queue_sync( queues[1] );
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, IB, ib,
ptr, rows, dwork, lddwork,
dA(j, 0), ldda, dwork+ib, lddwork, queues[1] );
magma_cq_to_panel( MagmaUpper, ib, A(j,j), lda, work+ib*ib );
}
/* 3. Do a QR on the current part */
if (i < min_mn)
magma_cgeqrf2_gpu( m-i, IB, dA(i,0), ldda, tau+i, info );
/* 4. Copy the current part back to the CPU */
magma_cgetmatrix_async( m, IB,
dA(0,0), ldda,
A(0,i), lda, queues[0] );
}
magma_queue_sync( queues[0] );
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dA );
return *info;
} /* magma_cgeqrf_ooc */
/***************************************************************************//**
Purpose
-------
CGEQRF computes a QR factorization of a COMPLEX M-by-N matrix A:
A = Q * R using multiple GPUs. This version does not require work space on the GPU
passed as input. GPU memory is allocated in the routine.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau COMPLEX array, dimension (min(M,N))
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.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= N*NB,
where NB can be obtained through magma_get_cgeqrf_nb( M, N ).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_geqrf
*******************************************************************************/
extern "C" magma_int_t
magma_cgeqrf_m(
magma_int_t ngpu,
magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info )
{
magmaFloatComplex *da[MagmaMaxGPUs];
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t i, min_mn, ldda;
*info = 0;
magma_int_t nb = magma_get_cgeqrf_nb( m, n );
magma_int_t lwkopt = n * nb;
work[0] = magma_cmake_lwork( lwkopt );
bool lquery = (lwork == -1);
if (ngpu < 0 || ngpu > MagmaMaxGPUs) {
*info = -1;
} else if (m < 0) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
} else if (lwork < max(1,n) && ! lquery) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
min_mn = min(m,n);
if (min_mn == 0) {
work[0] = c_one;
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
ldda = magma_roundup( m, 32 );
magma_int_t n_local[MagmaMaxGPUs];
for (i=0; i < ngpu; i++) {
n_local[i] = ((n/nb)/ngpu)*nb;
if (i < (n/nb)%ngpu)
n_local[i] += nb;
else if (i == (n/nb)%ngpu)
n_local[i] += n%nb;
magma_setdevice(i);
// TODO on failure, free previously allocated memory
if (MAGMA_SUCCESS != magma_cmalloc( &da[i], ldda*n_local[i] )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
}
if (m > nb && n > nb) {
magma_queue_t queues[MagmaMaxGPUs];
for( magma_int_t dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_create( dev, &queues[dev] );
}
/* Copy the matrix to the GPUs in 1D block cyclic distribution */
magma_csetmatrix_1D_col_bcyclic( ngpu, m, n, nb, A, lda, da, ldda, queues );
for( magma_int_t dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( queues[dev] );
}
/* Factor using the GPU interface */
magma_cgeqrf2_mgpu( ngpu, m, n, da, ldda, tau, info);
/* Copy the matrix back from the GPUs to the CPU */
magma_cgetmatrix_1D_col_bcyclic( ngpu, m, n, nb, da, ldda, A, lda, queues );
for( magma_int_t dev=0; dev < ngpu; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( queues[dev] );
magma_queue_destroy( queues[dev] );
}
}
else {
lapackf77_cgeqrf(&m, &n, A, &lda, tau, work, &lwork, info);
}
/* Free the allocated GPU memory */
for (i=0; i < ngpu; i++) {
magma_setdevice(i);
magma_free( da[i] );
}
magma_setdevice( orig_dev );
return *info;
} /* magma_cgeqrf4 */
/***************************************************************************//**
Purpose
-------
CGEQRS solves the least squares problem
min || A*X - C ||
using the QR factorization A = Q*R computed by CGEQRF_GPU.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. M >= N >= 0.
@param[in]
nrhs INTEGER
The number of columns of the matrix C. NRHS >= 0.
@param[in]
dA COMPLEX array on the GPU, dimension (LDDA,N)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,n, as returned by
CGEQRF_GPU in the first n columns of its array argument A.
@param[in]
ldda INTEGER
The leading dimension of the array A, LDDA >= M.
@param[in]
tau COMPLEX array, dimension (N)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by MAGMA_CGEQRF_GPU.
@param[in,out]
dB COMPLEX array on the GPU, dimension (LDDB,NRHS)
On entry, the M-by-NRHS matrix C.
On exit, the N-by-NRHS solution matrix X.
@param[in,out]
dT COMPLEX array that is the output (the 6th argument)
of magma_cgeqrf_gpu of size
2*MIN(M, N)*NB + ceil(N/32)*32 )* MAX(NB, NRHS).
The array starts with a block of size MIN(M,N)*NB that stores
the triangular T matrices used in the QR factorization,
followed by MIN(M,N)*NB block storing the diagonal block
inverses for the R matrix, followed by work space of size
(ceil(N/32)*32)* MAX(NB, NRHS).
@param[in]
lddb INTEGER
The leading dimension of the array dB. LDDB >= M.
@param[out]
hwork (workspace) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK,
LWORK >= (M - N + NB)*(NRHS + NB) + NRHS*NB,
where NB is the blocksize given by magma_get_cgeqrf_nb( M, N ).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the HWORK array, returns
this value as the first entry of the WORK array.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_geqrs
*******************************************************************************/
extern "C" magma_int_t
magma_cgeqrs_gpu(
magma_int_t m, magma_int_t n, magma_int_t nrhs,
magmaFloatComplex_const_ptr dA, magma_int_t ldda,
magmaFloatComplex const *tau,
magmaFloatComplex_ptr dT,
magmaFloatComplex_ptr dB, magma_int_t lddb,
magmaFloatComplex *hwork, magma_int_t lwork,
magma_int_t *info)
{
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dT(i_) (dT + (lddwork + (i_))*nb)
/* Constants */
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
const magma_int_t ione = 1;
/* Local variables */
magmaFloatComplex_ptr dwork;
magma_int_t i, min_mn, lddwork, rows, ib;
magma_int_t nb = magma_get_cgeqrf_nb( m, n );
magma_int_t lwkopt = (m - n + nb)*(nrhs + nb) + nrhs*nb;
bool lquery = (lwork == -1);
hwork[0] = magma_cmake_lwork( lwkopt );
*info = 0;
if (m < 0)
*info = -1;
else if (n < 0 || m < n)
*info = -2;
else if (nrhs < 0)
*info = -3;
else if (ldda < max(1,m))
*info = -5;
else if (lddb < max(1,m))
*info = -9;
else if (lwork < lwkopt && ! lquery)
*info = -11;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
min_mn = min(m,n);
if (min_mn == 0) {
hwork[0] = c_one;
return *info;
}
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
/* B := Q^H * B */
magma_cunmqr_gpu( MagmaLeft, Magma_ConjTrans,
m, nrhs, n,
dA(0,0), ldda, tau,
dB, lddb, hwork, lwork, dT, nb, info );
if ( *info != 0 ) {
magma_queue_destroy( queue );
return *info;
}
/* Solve R*X = B(1:n,:) */
lddwork= min_mn;
if (nb < min_mn)
dwork = dT+2*lddwork*nb;
else
dwork = dT;
// To do: Why did we have this line originally; seems to be a bug (Stan)?
// dwork = dT;
i = (min_mn - 1)/nb * nb;
ib = n-i;
rows = m-i;
// TODO: this assumes that, on exit from magma_cunmqr_gpu, hwork contains
// the last block of A and B (i.e., C in cunmqr). This should be fixed.
// Seems this data should already be on the GPU, so could switch to
// magma_ctrsm and drop the csetmatrix.
if ( nrhs == 1 ) {
blasf77_ctrsv( MagmaUpperStr, MagmaNoTransStr, MagmaNonUnitStr,
&ib, hwork, &rows,
hwork+rows*ib, &ione);
} else {
blasf77_ctrsm( MagmaLeftStr, MagmaUpperStr, MagmaNoTransStr, MagmaNonUnitStr,
&ib, &nrhs,
&c_one, hwork, &rows,
hwork+rows*ib, &rows);
}
// update the solution vector
magma_csetmatrix( ib, nrhs,
hwork+rows*ib, rows,
dwork+i, lddwork, queue );
// update c
if (nrhs == 1) {
magma_cgemv( MagmaNoTrans, i, ib,
c_neg_one, dA(0, i), ldda,
dwork + i, 1,
c_one, dB, 1, queue );
}
else {
magma_cgemm( MagmaNoTrans, MagmaNoTrans, i, nrhs, ib,
c_neg_one, dA(0, i), ldda,
dwork + i, lddwork,
c_one, dB, lddb, queue );
}
magma_int_t start = i-nb;
if (nb < min_mn) {
for (i = start; i >= 0; i -= nb) {
ib = min(min_mn - i, nb);
rows = m - i;
if (i + ib < n) {
if (nrhs == 1) {
magma_cgemv( MagmaNoTrans, ib, ib,
c_one, dT(i), ib,
dB+i, 1,
c_zero, dwork+i, 1, queue );
magma_cgemv( MagmaNoTrans, i, ib,
c_neg_one, dA(0, i), ldda,
dwork + i, 1,
c_one, dB, 1, queue );
}
else {
magma_cgemm( MagmaNoTrans, MagmaNoTrans, ib, nrhs, ib,
c_one, dT(i), ib,
dB+i, lddb,
c_zero, dwork+i, lddwork, queue );
magma_cgemm( MagmaNoTrans, MagmaNoTrans, i, nrhs, ib,
c_neg_one, dA(0, i), ldda,
dwork + i, lddwork,
c_one, dB, lddb, queue );
}
}
}
}
magma_ccopymatrix( n, nrhs,
dwork, lddwork,
dB, lddb, queue );
magma_queue_destroy( queue );
return *info;
}
/***************************************************************************//**
Purpose
-------
CHEEVD computes all eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix A. If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
@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. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A.
If JOBZ = MagmaNoVec, then on exit the lower triangle (if UPLO=MagmaLower)
or the upper triangle (if UPLO=MagmaUpper) of A, including the
diagonal, is destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in]
vl REAL
@param[in]
vu REAL
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@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 length of the array WORK.
- If N <= 1, LWORK >= 1.
- If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB.
- If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
NB can be obtained through magma_get_chetrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) REAL array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
- If N <= 1, LRWORK >= 1.
- If JOBZ = MagmaNoVec and N > 1, LRWORK >= N.
- If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
\n
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
@param[in]
liwork INTEGER
The dimension of the array IWORK.
- If N <= 1, LIWORK >= 1.
- If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
- If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N.
\n
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: if INFO = i and JOBZ = MagmaNoVec, then the algorithm failed
to converge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
if INFO = i and JOBZ = MagmaVec, then the algorithm failed
to compute an eigenvalue while working on the submatrix
lying in rows and columns INFO/(N+1) through
mod(INFO,N+1).
Further Details
---------------
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.
@ingroup magma_heevdx
*******************************************************************************/
extern "C" magma_int_t
magma_cheevdx_m(
magma_int_t ngpu,
magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo,
magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
float vl, float vu, magma_int_t il, magma_int_t iu,
magma_int_t *m, float *w,
magmaFloatComplex *work, magma_int_t lwork,
#ifdef COMPLEX
float *rwork, magma_int_t lrwork,
#endif
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magma_int_t ione = 1;
magma_int_t izero = 0;
float d_one = 1.;
float d__1;
float eps;
magma_int_t inde;
float anrm;
magma_int_t imax;
float rmin, rmax;
float sigma;
magma_int_t iinfo, lwmin;
magma_int_t lower;
magma_int_t llrwk;
magma_int_t wantz;
magma_int_t indwk2, llwrk2;
magma_int_t iscale;
float safmin;
float bignum;
magma_int_t indtau;
magma_int_t indrwk, indwrk, liwmin;
magma_int_t lrwmin, llwork;
float smlnum;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1 || lrwork == -1 || liwork == -1);
*info = 0;
if (! (wantz || (jobz == MagmaNoVec))) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (lda < max(1,n)) {
*info = -6;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -8;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -9;
} else if (iu < min(n,il) || iu > n) {
*info = -10;
}
}
}
magma_int_t nb = magma_get_chetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( n + n*nb, 2*n + n*n );
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = n + n*nb;
lrwmin = n;
liwmin = 1;
}
work[0] = magma_cmake_lwork( lwmin );
rwork[0] = magma_smake_lwork( lrwmin );
iwork[0] = liwmin;
if ((lwork < lwmin) && !lquery) {
*info = -14;
} else if ((lrwork < lrwmin) && ! lquery) {
*info = -16;
} else if ((liwork < liwmin) && ! lquery) {
*info = -18;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (n == 1) {
w[0] = MAGMA_C_REAL(A[0]);
if (wantz) {
A[0] = MAGMA_C_ONE;
}
return *info;
}
/* Check if matrix is very small then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
#ifdef ENABLE_DEBUG
printf("--------------------------------------------------------------\n");
printf(" warning matrix too small N=%lld NB=%lld, calling lapack on CPU\n", (long long) n, (long long) nb );
printf("--------------------------------------------------------------\n");
#endif
lapackf77_cheevd(jobz_, uplo_,
&n, A, &lda,
w, work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork, info);
return *info;
}
/* Get machine constants. */
safmin = lapackf77_slamch("Safe minimum");
eps = lapackf77_slamch("Precision");
smlnum = safmin / eps;
bignum = 1. / smlnum;
rmin = magma_ssqrt(smlnum);
rmax = magma_ssqrt(bignum);
/* Scale matrix to allowable range, if necessary. */
anrm = lapackf77_clanhe("M", uplo_, &n, A, &lda, rwork);
iscale = 0;
if (anrm > 0. && anrm < rmin) {
iscale = 1;
sigma = rmin / anrm;
} else if (anrm > rmax) {
iscale = 1;
sigma = rmax / anrm;
}
if (iscale == 1) {
lapackf77_clascl(uplo_, &izero, &izero, &d_one, &sigma, &n, &n, A,
&lda, info);
}
/* Call CHETRD to reduce Hermitian matrix to tridiagonal form. */
inde = 0;
indtau = 0;
indwrk = indtau + n;
indrwk = inde + n;
indwk2 = indwrk + n * n;
llwork = lwork - indwrk;
llwrk2 = lwork - indwk2;
llrwk = lrwork - indrwk;
magma_timer_t time=0;
timer_start( time );
magma_chetrd_mgpu(ngpu, 1, uplo, n, A, lda, w, &rwork[inde],
&work[indtau], &work[indwrk], llwork, &iinfo);
timer_stop( time );
timer_printf( "time chetrd = %6.2f\n", time );
/* For eigenvalues only, call SSTERF. For eigenvectors, first call
CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
tridiagonal matrix, then call CUNMTR to multiply it to the Householder
transformations represented as Householder vectors in A. */
if (! wantz) {
lapackf77_ssterf(&n, w, &rwork[inde], info);
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
}
else {
timer_start( time );
magma_cstedx_m(ngpu, range, n, vl, vu, il, iu, w, &rwork[inde],
&work[indwrk], n, &rwork[indrwk],
llrwk, iwork, liwork, info);
timer_stop( time );
timer_printf( "time cstedc = %6.2f\n", time );
timer_start( time );
magma_smove_eig(range, n, w, &il, &iu, vl, vu, m);
magma_cunmtr_m(ngpu, MagmaLeft, uplo, MagmaNoTrans, n, *m, A, lda, &work[indtau],
&work[indwrk + n * (il-1)], n, &work[indwk2], llwrk2, &iinfo);
lapackf77_clacpy("A", &n, m, &work[indwrk + n * (il-1)], &n, A, &lda);
timer_stop( time );
timer_printf( "time cunmtr + copy = %6.2f\n", time );
}
/* If matrix was scaled, then rescale eigenvalues appropriately. */
if (iscale == 1) {
if (*info == 0) {
imax = n;
} else {
imax = *info - 1;
}
d__1 = 1. / sigma;
blasf77_sscal(&imax, &d__1, w, &ione);
}
work[0] = magma_cmake_lwork( lwmin );
rwork[0] = magma_smake_lwork( lrwmin );
iwork[0] = liwmin;
return *info;
} /* magma_cheevd_m */
/**
Purpose
-------
CGEQRF computes a QR factorization of a COMPLEX M-by-N matrix A:
A = Q * R. This version does not require work space on the GPU
passed as input. GPU memory is allocated in the routine.
This uses 2 queues to overlap communication and computation.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if m >= n); the elements below the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of min(m,n) elementary reflectors (see Further
Details).
\n
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,M).
@param[out]
tau COMPLEX array, dimension (min(M,N))
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.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= max( N*NB, 2*NB*NB ),
where NB can be obtained through magma_get_cgeqrf_nb( M, N ).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(1) H(2) . . . H(k), where k = min(m,n).
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-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
and tau in TAU(i).
@ingroup magma_cgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgeqrf(
magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info )
{
#define A(i_,j_) (A + (i_) + (j_)*lda)
#ifdef HAVE_clBLAS
#define dA(i_,j_) dA, ((i_) + (j_)*ldda + dA_offset)
#define dT(i_,j_) dT, ((i_) + (j_)*nb + dT_offset)
#define dwork(i_) dwork, ((i_) + dwork_offset)
#else
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dT(i_,j_) (dT + (i_) + (j_)*nb)
#define dwork(i_) (dwork + (i_))
#endif
/* Constants */
const magmaFloatComplex c_one = MAGMA_C_ONE;
/* Local variables */
magmaFloatComplex_ptr dA, dT, dwork;
magma_int_t i, ib, min_mn, ldda, lddwork, old_i, old_ib;
/* Function Body */
*info = 0;
magma_int_t nb = magma_get_cgeqrf_nb( m, n );
// need 2*nb*nb to store T and upper triangle of V simultaneously
magma_int_t lwkopt = max( n*nb, 2*nb*nb );
work[0] = magma_cmake_lwork( lwkopt );
bool lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
} else if (lwork < max(1, lwkopt) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
min_mn = min( m, n );
if (min_mn == 0) {
work[0] = c_one;
return *info;
}
// largest N for larfb is n-nb (trailing matrix lacks 1st panel)
lddwork = magma_roundup( n, 32 ) - nb;
ldda = magma_roundup( m, 32 );
magma_int_t ngpu = magma_num_gpus();
if ( ngpu > 1 ) {
/* call multiple-GPU interface */
return magma_cgeqrf_m( ngpu, m, n, A, lda, tau, work, lwork, info );
}
// allocate space for dA, dwork, and dT
if (MAGMA_SUCCESS != magma_cmalloc( &dA, n*ldda + nb*lddwork + nb*nb )) {
/* alloc failed so call non-GPU-resident version */
return magma_cgeqrf_ooc( m, n, A, lda, tau, work, lwork, info );
}
dwork = dA + n*ldda;
dT = dA + n*ldda + nb*lddwork;
magma_queue_t queues[2];
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queues[0] );
magma_queue_create( cdev, &queues[1] );
if ( (nb > 1) && (nb < min_mn) ) {
/* Use blocked code initially.
Asynchronously send the matrix to the GPU except the first panel. */
magma_csetmatrix_async( m, n-nb,
A(0,nb), lda,
dA(0,nb), ldda, queues[0] );
old_i = 0;
old_ib = nb;
for (i = 0; i < min_mn-nb; i += nb) {
ib = min( min_mn-i, nb );
if (i > 0) {
/* get i-th panel from device */
magma_queue_sync( queues[1] );
magma_cgetmatrix_async( m-i, ib,
dA(i,i), ldda,
A(i,i), lda, queues[0] );
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, n-old_i-2*old_ib, old_ib,
dA(old_i, old_i), ldda, dT(0,0), nb,
dA(old_i, old_i+2*old_ib), ldda, dwork(0), lddwork, queues[1] );
magma_cgetmatrix_async( i, ib,
dA(0,i), ldda,
A(0,i), lda, queues[1] );
magma_queue_sync( queues[0] );
}
magma_int_t rows = m-i;
lapackf77_cgeqrf( &rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info );
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_clarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(i,i), &lda, tau+i, work, &ib );
magma_cpanel_to_q( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
/* put i-th V matrix onto device */
magma_csetmatrix_async( rows, ib, A(i,i), lda, dA(i,i), ldda, queues[0] );
/* put T matrix onto device */
magma_queue_sync( queues[1] );
magma_csetmatrix_async( ib, ib, work, ib, dT(0,0), nb, queues[0] );
magma_queue_sync( queues[0] );
if (i + ib < n) {
if (i+ib < min_mn-nb) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left (look-ahead) */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT(0,0), nb,
dA(i, i+ib), ldda, dwork(0), lddwork, queues[1] );
magma_cq_to_panel( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
}
else {
/* After last panel, update whole trailing matrix. */
/* Apply H' to A(i:m,i+ib:n) from the left */
magma_clarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dT(0,0), nb,
dA(i, i+ib), ldda, dwork(0), lddwork, queues[1] );
magma_cq_to_panel( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < min_mn) {
ib = n-i;
if (i != 0) {
magma_cgetmatrix( m, ib, dA(0,i), ldda, A(0,i), lda, queues[1] );
}
magma_int_t rows = m-i;
lapackf77_cgeqrf( &rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info );
}
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dA );
return *info;
} /* magma_cgeqrf */
/**
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 */
/***************************************************************************//**
Purpose
-------
CGEEV computes for an N-by-N complex nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors.
The right eigenvector v(j) of A satisfies
A * v(j) = lambda(j) * v(j)
where lambda(j) is its eigenvalue.
The left eigenvector u(j) of A satisfies
u(j)**H * A = lambda(j) * u(j)**H
where u(j)**H denotes the conjugate transpose of u(j).
The computed eigenvectors are normalized to have Euclidean norm
equal to 1 and largest component real.
Arguments
---------
@param[in]
jobvl magma_vec_t
- = MagmaNoVec: left eigenvectors of A are not computed;
- = MagmaVec: left eigenvectors of are computed.
@param[in]
jobvr magma_vec_t
- = MagmaNoVec: right eigenvectors of A are not computed;
- = MagmaVec: right eigenvectors of A are computed.
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the N-by-N matrix A.
On exit, A has been overwritten.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[out]
w COMPLEX array, dimension (N)
W contains the computed eigenvalues.
@param[out]
VL COMPLEX array, dimension (LDVL,N)
If JOBVL = MagmaVec, the left eigenvectors u(j) are stored one
after another in the columns of VL, in the same order
as their eigenvalues.
If JOBVL = MagmaNoVec, VL is not referenced.
u(j) = VL(:,j), the j-th column of VL.
@param[in]
ldvl INTEGER
The leading dimension of the array VL. LDVL >= 1; if
JOBVL = MagmaVec, LDVL >= N.
@param[out]
VR COMPLEX array, dimension (LDVR,N)
If JOBVR = MagmaVec, the right eigenvectors v(j) are stored one
after another in the columns of VR, in the same order
as their eigenvalues.
If JOBVR = MagmaNoVec, VR is not referenced.
v(j) = VR(:,j), the j-th column of VR.
@param[in]
ldvr INTEGER
The leading dimension of the array VR. LDVR >= 1; if
JOBVR = MagmaVec, LDVR >= 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 + nb + nb*ngpu)*N.
For optimal performance, LWORK >= (1 + 2*nb + nb*ngpu)*N.
\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
rwork (workspace) REAL array, dimension (2*N)
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value.
- > 0: if INFO = i, the QR algorithm failed to compute all the
eigenvalues, and no eigenvectors have been computed;
elements and i+1:N of W contain eigenvalues which have
converged.
@ingroup magma_geev
*******************************************************************************/
extern "C" magma_int_t
magma_cgeev_m(
magma_vec_t jobvl, magma_vec_t jobvr, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
#ifdef COMPLEX
magmaFloatComplex *w,
#else
float *wr, float *wi,
#endif
magmaFloatComplex *VL, magma_int_t ldvl,
magmaFloatComplex *VR, magma_int_t ldvr,
magmaFloatComplex *work, magma_int_t lwork,
#ifdef COMPLEX
float *rwork,
#endif
magma_int_t *info )
{
#define VL(i,j) (VL + (i) + (j)*ldvl)
#define VR(i,j) (VR + (i) + (j)*ldvr)
const magma_int_t ione = 1;
const magma_int_t izero = 0;
float d__1, d__2;
magmaFloatComplex tmp;
float scl;
float dum[1], eps;
float anrm, cscale, bignum, smlnum;
magma_int_t i, k, ilo, ihi;
magma_int_t ibal, ierr, itau, iwrk, nout, liwrk, nb;
magma_int_t scalea, minwrk, optwrk, irwork, lquery, wantvl, wantvr, select[1];
magma_side_t side = MagmaRight;
magma_int_t ngpu = magma_num_gpus();
irwork = 0;
*info = 0;
lquery = (lwork == -1);
wantvl = (jobvl == MagmaVec);
wantvr = (jobvr == MagmaVec);
if (! wantvl && jobvl != MagmaNoVec) {
*info = -1;
} else if (! wantvr && jobvr != MagmaNoVec) {
*info = -2;
} else if (n < 0) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if ( (ldvl < 1) || (wantvl && (ldvl < n))) {
*info = -8;
} else if ( (ldvr < 1) || (wantvr && (ldvr < n))) {
*info = -10;
}
/* Compute workspace */
nb = magma_get_cgehrd_nb( n );
if (*info == 0) {
minwrk = (1 + nb + nb*ngpu)*n;
optwrk = (1 + 2*nb + nb*ngpu)*n;
work[0] = magma_cmake_lwork( optwrk );
if (lwork < minwrk && ! lquery) {
*info = -12;
}
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
#if defined(Version3)
magmaFloatComplex *dT;
if (MAGMA_SUCCESS != magma_cmalloc( &dT, nb*n )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
#endif
#if defined(Version5)
magmaFloatComplex *T;
if (MAGMA_SUCCESS != magma_cmalloc_cpu( &T, nb*n )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
#endif
/* Get machine constants */
eps = lapackf77_slamch( "P" );
smlnum = lapackf77_slamch( "S" );
bignum = 1. / smlnum;
lapackf77_slabad( &smlnum, &bignum );
smlnum = magma_ssqrt( smlnum ) / eps;
bignum = 1. / smlnum;
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
anrm = lapackf77_clange( "M", &n, &n, A, &lda, dum );
scalea = 0;
if (anrm > 0. && anrm < smlnum) {
scalea = 1;
cscale = smlnum;
} else if (anrm > bignum) {
scalea = 1;
cscale = bignum;
}
if (scalea) {
lapackf77_clascl( "G", &izero, &izero, &anrm, &cscale, &n, &n, A, &lda, &ierr );
}
/* Balance the matrix
* (CWorkspace: none)
* (RWorkspace: need N)
* - this space is reserved until after gebak */
ibal = 0;
lapackf77_cgebal( "B", &n, A, &lda, &ilo, &ihi, &rwork[ibal], &ierr );
/* Reduce to upper Hessenberg form
* (CWorkspace: need 2*N, prefer N + N*NB + NB*NGPU)
* (RWorkspace: N)
* - added NB*NGPU needed for multi-GPU magma_cgehrd_m
* - including N reserved for gebal/gebak, unused by cgehrd */
itau = 0;
iwrk = itau + n;
liwrk = lwork - iwrk;
#if defined(Version1)
// Version 1 - LAPACK
lapackf77_cgehrd( &n, &ilo, &ihi, A, &lda,
&work[itau], &work[iwrk], &liwrk, &ierr );
#elif defined(Version2)
// Version 2 - LAPACK consistent HRD
magma_cgehrd2( n, ilo, ihi, A, lda,
&work[itau], &work[iwrk], liwrk, &ierr );
#elif defined(Version3)
// Version 3 - LAPACK consistent MAGMA HRD + T matrices stored,
magma_cgehrd( n, ilo, ihi, A, lda,
&work[itau], &work[iwrk], liwrk, dT, &ierr );
#elif defined(Version5)
// Version 4 - Multi-GPU, T on host
magma_cgehrd_m( n, ilo, ihi, A, lda,
&work[itau], &work[iwrk], liwrk, T, &ierr );
#endif
if (wantvl) {
/* Want left eigenvectors
* Copy Householder vectors to VL */
side = MagmaLeft;
lapackf77_clacpy( MagmaLowerStr, &n, &n, A, &lda, VL, &ldvl );
/* Generate unitary matrix in VL
* (CWorkspace: need 2*N-1, prefer N + (N-1)*NB)
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by cunghr */
#if defined(Version1) || defined(Version2)
// Version 1 & 2 - LAPACK
lapackf77_cunghr( &n, &ilo, &ihi, VL, &ldvl, &work[itau],
&work[iwrk], &liwrk, &ierr );
#elif defined(Version3)
// Version 3 - LAPACK consistent MAGMA HRD + T matrices stored
magma_cunghr( n, ilo, ihi, VL, ldvl, &work[itau], dT, nb, &ierr );
#elif defined(Version5)
// Version 5 - Multi-GPU, T on host
magma_cunghr_m( n, ilo, ihi, VL, ldvl, &work[itau], T, nb, &ierr );
#endif
/* Perform QR iteration, accumulating Schur vectors in VL
* (CWorkspace: need 1, prefer HSWORK (see comments) )
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by chseqr */
iwrk = itau;
liwrk = lwork - iwrk;
lapackf77_chseqr( "S", "V", &n, &ilo, &ihi, A, &lda, w,
VL, &ldvl, &work[iwrk], &liwrk, info );
if (wantvr) {
/* Want left and right eigenvectors
* Copy Schur vectors to VR */
side = MagmaBothSides;
lapackf77_clacpy( "F", &n, &n, VL, &ldvl, VR, &ldvr );
}
}
else if (wantvr) {
/* Want right eigenvectors
* Copy Householder vectors to VR */
side = MagmaRight;
lapackf77_clacpy( "L", &n, &n, A, &lda, VR, &ldvr );
/* Generate unitary matrix in VR
* (CWorkspace: need 2*N-1, prefer N + (N-1)*NB)
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by cunghr */
#if defined(Version1) || defined(Version2)
// Version 1 & 2 - LAPACK
lapackf77_cunghr( &n, &ilo, &ihi, VR, &ldvr, &work[itau],
&work[iwrk], &liwrk, &ierr );
#elif defined(Version3)
// Version 3 - LAPACK consistent MAGMA HRD + T matrices stored
magma_cunghr( n, ilo, ihi, VR, ldvr, &work[itau], dT, nb, &ierr );
#elif defined(Version5)
// Version 5 - Multi-GPU, T on host
magma_cunghr_m( n, ilo, ihi, VR, ldvr, &work[itau], T, nb, &ierr );
#endif
/* Perform QR iteration, accumulating Schur vectors in VR
* (CWorkspace: need 1, prefer HSWORK (see comments) )
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by chseqr */
iwrk = itau;
liwrk = lwork - iwrk;
lapackf77_chseqr( "S", "V", &n, &ilo, &ihi, A, &lda, w,
VR, &ldvr, &work[iwrk], &liwrk, info );
}
else {
/* Compute eigenvalues only
* (CWorkspace: need 1, prefer HSWORK (see comments) )
* (RWorkspace: N)
* - including N reserved for gebal/gebak, unused by chseqr */
iwrk = itau;
liwrk = lwork - iwrk;
lapackf77_chseqr( "E", "N", &n, &ilo, &ihi, A, &lda, w,
VR, &ldvr, &work[iwrk], &liwrk, info );
}
/* If INFO > 0 from CHSEQR, then quit */
if (*info > 0) {
goto CLEANUP;
}
if (wantvl || wantvr) {
/* Compute left and/or right eigenvectors
* (CWorkspace: need 2*N)
* (RWorkspace: need 2*N)
* - including N reserved for gebal/gebak, unused by ctrevc */
irwork = ibal + n;
#if TREVC_VERSION == 1
lapackf77_ctrevc( lapack_side_const(side), "B", select, &n, A, &lda, VL, &ldvl,
VR, &ldvr, &n, &nout, &work[iwrk], &rwork[irwork], &ierr );
#elif TREVC_VERSION == 2
liwrk = lwork - iwrk;
lapackf77_ctrevc3( lapack_side_const(side), "B", select, &n, A, &lda, VL, &ldvl,
VR, &ldvr, &n, &nout, &work[iwrk], &liwrk, &rwork[irwork], &ierr );
#elif TREVC_VERSION == 3
magma_ctrevc3( side, MagmaBacktransVec, select, n, A, lda, VL, ldvl,
VR, ldvr, n, &nout, &work[iwrk], liwrk, &rwork[irwork], &ierr );
#elif TREVC_VERSION == 4
magma_ctrevc3_mt( side, MagmaBacktransVec, select, n, A, lda, VL, ldvl,
VR, ldvr, n, &nout, &work[iwrk], liwrk, &rwork[irwork], &ierr );
#elif TREVC_VERSION == 5
magma_ctrevc3_mt_gpu( side, MagmaBacktransVec, select, n, A, lda, VL, ldvl,
VR, ldvr, n, &nout, &work[iwrk], liwrk, &rwork[irwork], &ierr );
#else
#error Unknown TREVC_VERSION
#endif
}
if (wantvl) {
/* Undo balancing of left eigenvectors
* (CWorkspace: none)
* (RWorkspace: need N) */
lapackf77_cgebak( "B", "L", &n, &ilo, &ihi, &rwork[ibal], &n,
VL, &ldvl, &ierr );
/* Normalize left eigenvectors and make largest component real */
for (i = 0; i < n; ++i) {
scl = 1. / magma_cblas_scnrm2( n, VL(0,i), 1 );
blasf77_csscal( &n, &scl, VL(0,i), &ione );
for (k = 0; k < n; ++k) {
/* Computing 2nd power */
d__1 = MAGMA_C_REAL( *VL(k,i) );
d__2 = MAGMA_C_IMAG( *VL(k,i) );
rwork[irwork + k] = d__1*d__1 + d__2*d__2;
}
k = blasf77_isamax( &n, &rwork[irwork], &ione ) - 1; // subtract 1; k is 0-based
tmp = MAGMA_C_CONJ( *VL(k,i) ) / magma_ssqrt( rwork[irwork + k] );
blasf77_cscal( &n, &tmp, VL(0,i), &ione );
*VL(k,i) = MAGMA_C_MAKE( MAGMA_C_REAL( *VL(k,i) ), 0 );
}
}
if (wantvr) {
/* Undo balancing of right eigenvectors
* (CWorkspace: none)
* (RWorkspace: need N) */
lapackf77_cgebak( "B", "R", &n, &ilo, &ihi, &rwork[ibal], &n,
VR, &ldvr, &ierr );
/* Normalize right eigenvectors and make largest component real */
for (i = 0; i < n; ++i) {
scl = 1. / magma_cblas_scnrm2( n, VR(0,i), 1 );
blasf77_csscal( &n, &scl, VR(0,i), &ione );
for (k = 0; k < n; ++k) {
/* Computing 2nd power */
d__1 = MAGMA_C_REAL( *VR(k,i) );
d__2 = MAGMA_C_IMAG( *VR(k,i) );
rwork[irwork + k] = d__1*d__1 + d__2*d__2;
}
k = blasf77_isamax( &n, &rwork[irwork], &ione ) - 1; // subtract 1; k is 0-based
tmp = MAGMA_C_CONJ( *VR(k,i) ) / magma_ssqrt( rwork[irwork + k] );
blasf77_cscal( &n, &tmp, VR(0,i), &ione );
*VR(k,i) = MAGMA_C_MAKE( MAGMA_C_REAL( *VR(k,i) ), 0 );
}
}
CLEANUP:
/* Undo scaling if necessary */
if (scalea) {
// converged eigenvalues, stored in WR[i+1:n] and WI[i+1:n] for i = INFO
magma_int_t nval = n - (*info);
magma_int_t ld = max( nval, 1 );
lapackf77_clascl( "G", &izero, &izero, &cscale, &anrm, &nval, &ione, w + (*info), &ld, &ierr );
if (*info > 0) {
// first ilo columns were already upper triangular,
// so the corresponding eigenvalues are also valid.
nval = ilo - 1;
lapackf77_clascl( "G", &izero, &izero, &cscale, &anrm, &nval, &ione, w, &n, &ierr );
}
}
#if defined(Version3)
magma_free( dT );
#endif
#if defined(Version5)
magma_free_cpu( T );
#endif
work[0] = magma_cmake_lwork( minwrk ); // TODO use optwrk as in dgeev
return *info;
} /* magma_cgeev */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cunmqr_gpu
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float Cnorm, error, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_int_t mm, m, n, k, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max, dt_size;
magmaFloatComplex *C, *R, *A, *hwork, *tau;
magmaFloatComplex_ptr dC, dA, dT;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
float tol = opts.tolerance * lapackf77_slamch("E");
// test all combinations of input parameters
magma_side_t side [] = { MagmaLeft, MagmaRight };
magma_trans_t trans[] = { Magma_ConjTrans, MagmaNoTrans };
printf("%% M N K side trans CPU Gflop/s (sec) GPU Gflop/s (sec) ||R||_F / ||QC||_F\n");
printf("%%==============================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
ldc = magma_roundup( m, opts.align ); // multiple of 32 by default
// A is m x k (left) or n x k (right)
mm = (side[iside] == MagmaLeft ? m : n);
nb = magma_get_cgeqrf_nb( mm, k );
lda = magma_roundup( mm, opts.align ); // multiple of 32 by default
gflops = FLOPS_CUNMQR( m, n, k, side[iside] ) / 1e9;
if ( side[iside] == MagmaLeft && m < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=left and m < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
if ( side[iside] == MagmaRight && n < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=right and n < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
if ( side[iside] == MagmaLeft ) {
// side = left
lwork_max = (m - k + nb)*(n + nb) + n*nb;
dt_size = ( 2*min(m,k) + magma_roundup( max(m,n), 32) )*nb;
}
else {
// side = right
lwork_max = (n - k + nb)*(m + nb) + m*nb;
dt_size = ( 2*min(n,k) + magma_roundup( max(m,n), 32 ) )*nb;
}
// this rounds it up slightly if needed to agree with lwork query below
lwork_max = int( real( magma_cmake_lwork( lwork_max )));
TESTING_MALLOC_CPU( C, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( R, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( A, magmaFloatComplex, lda*k );
TESTING_MALLOC_CPU( hwork, magmaFloatComplex, lwork_max );
TESTING_MALLOC_CPU( tau, magmaFloatComplex, k );
TESTING_MALLOC_DEV( dC, magmaFloatComplex, ldc*n );
TESTING_MALLOC_DEV( dA, magmaFloatComplex, lda*k );
TESTING_MALLOC_DEV( dT, magmaFloatComplex, dt_size );
// C is full, m x n
size = ldc*n;
lapackf77_clarnv( &ione, ISEED, &size, C );
magma_csetmatrix( m, n, C, ldc, dC, ldc );
// A is m x k (left) or n x k (right)
size = lda*k;
lapackf77_clarnv( &ione, ISEED, &size, A );
// compute QR factorization to get Householder vectors in dA, tau, dT
magma_csetmatrix( mm, k, A, lda, dA, lda );
magma_cgeqrf_gpu( mm, k, dA, lda, tau, dT, &info );
magma_cgetmatrix( mm, k, dA, lda, A, lda );
if (info != 0) {
printf("magma_cgeqrf_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_cunmqr( lapack_side_const( side[iside] ), lapack_trans_const( trans[itran] ),
&m, &n, &k,
A, &lda, tau, C, &ldc, hwork, &lwork_max, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_cunmqr returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for workspace size
lwork = -1;
magma_cunmqr_gpu( side[iside], trans[itran],
m, n, k,
dA, lda, tau, dC, ldc, hwork, lwork, dT, nb, &info );
if (info != 0) {
printf("magma_cunmqr_gpu (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = (magma_int_t) MAGMA_C_REAL( hwork[0] );
if ( lwork < 0 || lwork > lwork_max ) {
printf("Warning: optimal lwork %d > allocated lwork_max %d\n", (int) lwork, (int) lwork_max );
lwork = lwork_max;
}
// cunmqr2 takes a copy of dA in CPU memory
if ( opts.version == 2 ) {
magma_cgetmatrix( mm, k, dA, lda, A, lda );
}
magmablasSetKernelStream( opts.queue );
gpu_time = magma_sync_wtime( opts.queue ); // sync needed for L,N and R,T cases
if ( opts.version == 1 ) {
magma_cunmqr_gpu( side[iside], trans[itran],
m, n, k,
dA, lda, tau, dC, ldc, hwork, lwork, dT, nb, &info );
}
else if ( opts.version == 2 ) {
magma_cunmqr2_gpu( side[iside], trans[itran],
m, n, k,
dA, lda, tau, dC, ldc, A, lda, &info );
}
gpu_time = magma_sync_wtime( opts.queue ) - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_cunmqr_gpu returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
magma_cgetmatrix( m, n, dC, ldc, R, ldc );
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
size = ldc*n;
blasf77_caxpy( &size, &c_neg_one, C, &ione, R, &ione );
Cnorm = lapackf77_clange( "Fro", &m, &n, C, &ldc, work );
error = lapackf77_clange( "Fro", &m, &n, R, &ldc, work ) / (magma_ssqrt(m*n) * Cnorm);
printf( "%5d %5d %5d %4c %5c %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ),
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
TESTING_FREE_CPU( C );
TESTING_FREE_CPU( R );
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( hwork );
TESTING_FREE_CPU( tau );
TESTING_FREE_DEV( dC );
TESTING_FREE_DEV( dA );
TESTING_FREE_DEV( dT );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}} // end iside, itran
printf( "\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
CHEGVX computes selected eigenvalues, and optionally, eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
Eigenvalues and eigenvectors can be selected by specifying either a
range of values or a range of indices for the desired eigenvalues.
Arguments
---------
@param[in]
itype INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
range magma_range_t
- = MagmaRangeAll: all eigenvalues will be found.
- = MagmaRangeV: all eigenvalues in the half-open interval (VL,VU]
will be found.
- = MagmaRangeI: the IL-th through IU-th eigenvalues will be found.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangles of A and B are stored;
- = MagmaLower: Lower triangles of A and B are stored.
@param[in]
n INTEGER
The order of the matrices A and B. 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. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
\n
On exit, the lower triangle (if UPLO=MagmaLower) or the upper
triangle (if UPLO=MagmaUpper) of A, including the diagonal, is
destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
B COMPLEX array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
\n
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
@param[in]
ldb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[in]
vl REAL
@param[in]
vu REAL
If RANGE=MagmaRangeV, the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeI.
@param[in]
il INTEGER
@param[in]
iu INTEGER
If RANGE=MagmaRangeI, the indices (in ascending order) of the
smallest and largest eigenvalues to be returned.
1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
Not referenced if RANGE = MagmaRangeAll or MagmaRangeV.
@param[in]
abstol REAL
The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
\n
ABSTOL + EPS * max( |a|,|b| ),
\n
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained
by reducing A to tridiagonal form.
\n
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*SLAMCH('S'), not zero.
If this routine returns with INFO > 0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*SLAMCH('S').
@param[out]
m INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = MagmaRangeAll, M = N, and if RANGE = MagmaRangeI, M = IU-IL+1.
@param[out]
w REAL array, dimension (N)
The first M elements contain the selected
eigenvalues in ascending order.
@param[out]
Z COMPLEX array, dimension (LDZ, max(1,M))
If JOBZ = MagmaNoVec, then Z is not referenced.
If JOBZ = MagmaVec, then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the i-th
column of Z holding the eigenvector associated with W(i).
The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**T*B*Z = I;
if ITYPE = 3, Z**T*inv(B)*Z = I.
\n
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = MagmaRangeV, the exact value of M
is not known in advance and an upper bound must be used.
@param[in]
ldz INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = MagmaVec, LDZ >= 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 length of the array WORK. LWORK >= max(1,2*N).
For optimal efficiency, LWORK >= (NB+1)*N,
where NB is the blocksize for CHETRD returned by ILAENV.
\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
rwork (workspace) REAL array, dimension (7*N)
@param
iwork (workspace) INTEGER array, dimension (5*N)
@param[out]
ifail INTEGER array, dimension (N)
If JOBZ = MagmaVec, then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the
indices of the eigenvectors that failed to converge.
If JOBZ = MagmaNoVec, then IFAIL is not referenced.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: CPOTRF or CHEEVX returned an error code:
<= N: if INFO = i, CHEEVX failed to converge;
i eigenvectors failed to converge. Their indices
are stored in array IFAIL.
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Further Details
---------------
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
@ingroup magma_chegv_driver
********************************************************************/
extern "C" magma_int_t
magma_chegvx(
magma_int_t itype, magma_vec_t jobz, magma_range_t range, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *B, magma_int_t ldb,
float vl, float vu, magma_int_t il, magma_int_t iu, float abstol,
magma_int_t *m, float *w, magmaFloatComplex *Z, magma_int_t ldz,
magmaFloatComplex *work, magma_int_t lwork, float *rwork,
magma_int_t *iwork, magma_int_t *ifail,
magma_int_t *info)
{
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex *dA;
magmaFloatComplex *dB;
magmaFloatComplex *dZ;
magma_int_t ldda = n;
magma_int_t lddb = n;
magma_int_t lddz = n;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz;
magma_int_t lquery;
magma_int_t alleig, valeig, indeig;
magma_int_t lwmin;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
alleig = (range == MagmaRangeAll);
valeig = (range == MagmaRangeV);
indeig = (range == MagmaRangeI);
lquery = (lwork == -1);
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (alleig || valeig || indeig)) {
*info = -2;
} else if (! (wantz || (jobz == MagmaNoVec))) {
*info = -3;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -4;
} else if (n < 0) {
*info = -5;
} else if (lda < max(1,n)) {
*info = -7;
} else if (ldb < max(1,n)) {
*info = -9;
} else if (ldz < 1 || (wantz && ldz < n)) {
*info = -18;
} else {
if (valeig) {
if (n > 0 && vu <= vl) {
*info = -11;
}
} else if (indeig) {
if (il < 1 || il > max(1,n)) {
*info = -12;
} else if (iu < min(n,il) || iu > n) {
*info = -13;
}
}
}
magma_int_t nb = magma_get_chetrd_nb(n);
lwmin = n * (nb + 1);
work[0] = magma_cmake_lwork( lwmin );
if (lwork < lwmin && ! lquery) {
*info = -20;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info));
return *info;
} else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
if (MAGMA_SUCCESS != magma_cmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_cmalloc( &dB, n*lddb ) ||
MAGMA_SUCCESS != magma_cmalloc( &dZ, n*lddz )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
/* Form a Cholesky factorization of B. */
magma_csetmatrix( n, n, B, ldb, dB, lddb, queue );
magma_csetmatrix_async( n, n,
A, lda,
dA, ldda, queue );
magma_cpotrf_gpu(uplo, n, dB, lddb, info);
if (*info != 0) {
*info = n + *info;
return *info;
}
magma_queue_sync( queue );
magma_cgetmatrix_async( n, n,
dB, lddb,
B, ldb, queue );
/* Transform problem to standard eigenvalue problem and solve. */
magma_chegst_gpu(itype, uplo, n, dA, ldda, dB, lddb, info);
magma_cheevx_gpu(jobz, range, uplo, n, dA, ldda, vl, vu, il, iu, abstol, m, w, dZ, lddz, A, lda, Z, ldz, work, lwork, rwork, iwork, ifail, info);
if (wantz && *info == 0) {
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
trans = MagmaConjTrans;
} else {
trans = MagmaNoTrans;
}
magma_ctrsm( MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dZ, lddz, queue );
}
else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
trans = MagmaNoTrans;
} else {
trans = MagmaConjTrans;
}
magma_ctrmm( MagmaLeft, uplo, trans, MagmaNonUnit, n, *m, c_one, dB, lddb, dZ, lddz, queue );
}
magma_cgetmatrix( n, *m, dZ, lddz, Z, ldz, queue );
}
magma_queue_sync( queue );
magma_queue_destroy( queue );
magma_free( dA );
magma_free( dB );
magma_free( dZ );
return *info;
} /* magma_chegvx */
/**
Purpose
-------
CUNMQL overwrites the general complex M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = Magma_ConjTrans: Q**H * C C * Q**H
@endverbatim
where Q is a complex unitary matrix defined as the product of k
elementary reflectors
Q = H(k) . . . H(2) H(1)
as returned by CGEQLF.
Q is of order M if SIDE = MagmaLeft
and of order N if SIDE = MagmaRight.
Arguments
---------
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = Magma_ConjTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = MagmaLeft, M >= K >= 0;
if SIDE = MagmaRight, N >= K >= 0.
@param[in]
A COMPLEX array, dimension (LDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
CGEQLF in the last k columns of its array argument A.
A is modified by the routine but restored on exit.
@param[in]
lda INTEGER
The leading dimension of the array A.
If SIDE = MagmaLeft, LDA >= max(1,M);
if SIDE = MagmaRight, LDA >= max(1,N).
@param[in]
tau COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGEQLF.
@param[in,out]
C COMPLEX array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
@param[in]
ldc INTEGER
The leading dimension of the array C. LDC >= max(1,M).
@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.
If SIDE = MagmaLeft, LWORK >= max(1,N);
if SIDE = MagmaRight, LWORK >= max(1,M).
For optimum performance
if SIDE = MagmaLeft, LWORK >= N*NB;
if SIDE = MagmaRight, LWORK >= M*NB,
where NB is the optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_cgeqlf_comp
********************************************************************/
extern "C" magma_int_t
magma_cunmql(
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *C, magma_int_t ldc,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dC(i_,j_) (dC + (i_) + (j_)*lddc)
magmaFloatComplex *T, *T2;
magma_int_t i, i1, i2, ib, nb, mi, ni, nq, nq_i, nw, step;
magma_int_t iinfo, ldwork, lwkopt;
*info = 0;
bool left = (side == MagmaLeft);
bool notran = (trans == MagmaNoTrans);
bool lquery = (lwork == -1);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = n;
} else {
nq = n;
nw = m;
}
/* Test the input arguments */
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != Magma_ConjTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (lda < max(1,nq)) {
*info = -7;
} else if (ldc < max(1,m)) {
*info = -10;
} else if (lwork < max(1,nw) && ! lquery) {
*info = -12;
}
if (*info == 0) {
nb = magma_get_cgelqf_nb( m, n );
lwkopt = max(1,nw)*nb;
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 (m == 0 || n == 0 || k == 0) {
work[0] = MAGMA_C_ONE;
return *info;
}
ldwork = nw;
if ( nb >= k ) {
/* Use CPU code */
lapackf77_cunmql( lapack_side_const(side), lapack_trans_const(trans),
&m, &n, &k, A, &lda, tau, C, &ldc, work, &lwork, &iinfo );
}
else {
/* Use hybrid CPU-GPU code */
/* Allocate work space on the GPU.
* nw*nb for dwork (m or n) by nb
* nq*nb for dV (n or m) by nb
* nb*nb for dT
* lddc*n for dC.
*/
magma_int_t lddc = magma_roundup( m, 32 );
magmaFloatComplex *dwork, *dV, *dT, *dC;
magma_cmalloc( &dwork, (nw + nq + nb)*nb + lddc*n );
if ( dwork == NULL ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dV = dwork + nw*nb;
dT = dV + nq*nb;
dC = dT + nb*nb;
/* work space on CPU.
* nb*nb for T
* nb*nb for T2, used to save and restore diagonal block of panel */
magma_cmalloc_pinned( &T, 2*nb*nb );
if ( T == NULL ) {
magma_free( dwork );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
T2 = T + nb*nb;
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
/* Copy matrix C from the CPU to the GPU */
magma_csetmatrix( m, n, C, ldc, dC, lddc, queue );
if ( (left && notran) || (! left && ! notran) ) {
i1 = 0;
i2 = k;
step = nb;
} else {
i1 = ((k - 1) / nb) * nb;
i2 = 0;
step = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
} else {
mi = m;
}
for (i = i1; (step < 0 ? i >= i2 : i < i2); i += step) {
ib = min(nb, k - i);
/* Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i) */
nq_i = nq - k + i + ib;
lapackf77_clarft("Backward", "Columnwise", &nq_i, &ib,
A(0,i), &lda, &tau[i], T, &ib);
/* 1) set lower triangle of panel in A to identity,
2) copy the panel from A to the GPU, and
3) restore A */
magma_cpanel_to_q( MagmaLower, ib, A(nq_i-ib,i), lda, T2 );
magma_csetmatrix( nq_i, ib, A(0,i), lda, dV, nq_i, queue );
magma_cq_to_panel( MagmaLower, ib, A(nq_i-ib,i), lda, T2 );
if (left) {
/* H or H**H is applied to C(1:m-k+i+ib-1,1:n) */
mi = m - k + i + ib;
}
else {
/* H or H**H is applied to C(1:m,1:n-k+i+ib-1) */
ni = n - k + i + ib;
}
/* Apply H or H**H; First copy T to the GPU */
magma_csetmatrix( ib, ib, T, ib, dT, ib, queue );
magma_clarfb_gpu( side, trans, MagmaBackward, MagmaColumnwise,
mi, ni, ib,
dV, nq_i,
dT, ib,
dC, lddc,
dwork, ldwork, queue );
}
magma_cgetmatrix( m, n, dC, lddc, C, ldc, queue );
magma_queue_destroy( queue );
magma_free( dwork );
magma_free_pinned( T );
}
work[0] = magma_cmake_lwork( lwkopt );
return *info;
} /* magma_cunmql */
/**
Purpose
-------
CGEHRD reduces a COMPLEX general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation: Q' * A * Q = H . This version
stores the triangular matrices used in the factorization so that they can
be applied directly (i.e., without being recomputed) later. As a result,
the application of Q is much faster.
Arguments
---------
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
ilo INTEGER
@param[in]
ihi INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to CGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, 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]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
zero.
@param[out]
work (workspace) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. 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 NB*N,
where NB is the optimal blocksize. It stores the NB*NB blocks
of the triangular T matrices used in the reduction.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
---------------
The matrix Q is represented as a product of (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-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, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
@verbatim
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
@endverbatim
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
This implementation follows the hybrid algorithm and notations described in
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
This version stores the T matrices in dT, for later use in magma_cunghr.
@ingroup magma_cgeev_comp
********************************************************************/
extern "C" magma_int_t
magma_cgehrd(
magma_int_t n, magma_int_t ilo, magma_int_t ihi,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex_ptr dT,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#ifdef HAVE_clBLAS
#define dA(i_,j_) dwork, ((i_) + (j_)*ldda + nb*ldda*2)
#define dT(i_,j_) dT, ((i_) + (j_)*nb + dT_offset)
#define dV(i_,j_) dwork, ((i_) + (j_)*ldda + nb*ldda)
#define dwork(i_) dwork, ((i_))
#else
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dT(i_,j_) (dT + (i_) + (j_)*nb)
#define dV(i_,j_) (dV + (i_) + (j_)*ldda)
#define dwork(i_) (dwork + (i_))
#endif
// Constants
const magmaFloatComplex c_one = MAGMA_C_ONE;
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
// Local variables
magma_int_t nb = magma_get_cgehrd_nb( n );
magma_int_t ldda = magma_roundup( n, 32 );
magma_int_t i, nh, iws;
magma_int_t iinfo;
magma_int_t lquery;
*info = 0;
iws = n*nb;
work[0] = magma_cmake_lwork( iws );
lquery = (lwork == -1);
if (n < 0) {
*info = -1;
} else if (ilo < 1 || ilo > max(1,n)) {
*info = -2;
} else if (ihi < min(ilo,n) || ihi > n) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (lwork < iws && ! lquery) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
// Adjust from 1-based indexing
ilo -= 1;
// Quick return if possible
nh = ihi - ilo;
if (nh <= 1) {
work[0] = c_one;
return *info;
}
// Now requires lwork >= iws; else dT won't be computed in unblocked code.
// If not enough workspace, use unblocked code
//if ( lwork < iws ) {
// nb = 1;
//}
if (nb == 1 || nb > nh) {
// Use unblocked code below
i = ilo;
}
else {
// Use blocked code
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
// GPU workspace is:
// nb*ldda for dwork for clahru
// nb*ldda for dV
// n*ldda for dA
magmaFloatComplex_ptr dwork;
if (MAGMA_SUCCESS != magma_cmalloc( &dwork, 2*nb*ldda + n*ldda )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magmaFloatComplex *dV = dwork + nb*ldda;
magmaFloatComplex *dA = dwork + nb*ldda*2;
magmaFloatComplex *T;
magma_cmalloc_cpu( &T, nb*nb );
if ( T == NULL ) {
magma_free( dwork );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
// zero first block of V, which is lower triangular
magmablas_claset( MagmaFull, nb, nb, c_zero, c_zero, dV(0,0), ldda, queue );
// Set elements 0:ILO-1 and IHI-1:N-2 of TAU to zero
for (i = 0; i < ilo; ++i)
tau[i] = c_zero;
for (i = max(0,ihi-1); i < n-1; ++i)
tau[i] = c_zero;
assert( nb % 4 == 0 );
for (i=0; i < nb*nb; i += 4)
T[i] = T[i+1] = T[i+2] = T[i+3] = c_zero;
magmablas_claset( MagmaFull, nb, n, c_zero, c_zero, dT(0,0), nb, queue );
// Copy the matrix to the GPU
magma_csetmatrix( n, n-ilo, A(0,ilo), lda, dA(0,0), ldda, queue );
for (i = ilo; i < ihi-1 - nb; i += nb) {
// Reduce columns i:i+nb-1 to Hessenberg form, returning the
// matrices V and T of the block reflector H = I - V*T*V'
// which performs the reduction, and also the matrix Y = A*V*T
// Get the current panel (no need for the 1st iteration)
magma_cgetmatrix( ihi-i, nb,
dA(i,i-ilo), ldda,
A(i,i), lda, queue );
// add 1 to i for 1-based index
magma_clahr2( ihi, i+1, nb,
dA(0,i-ilo), ldda,
dV(0,0), ldda,
A(0,i), lda,
&tau[i], T, nb, work, n, queue );
// Copy T from the CPU to dT on the GPU
magma_csetmatrix( nb, nb, T, nb, dT(0,i-ilo), nb, queue );
magma_clahru( n, ihi, i, nb,
A(0,i), lda,
dA(0,i-ilo), ldda, // dA
dA(i,i-ilo), ldda, // dY, stored over current panel
dV(0,0), ldda,
dT(0,i-ilo), dwork(0), queue );
}
// Copy remainder to host
magma_cgetmatrix( n, n-i,
dA(0,i-ilo), ldda,
A(0,i), lda, queue );
magma_free( dwork );
magma_free_cpu( T );
magma_queue_destroy( queue );
}
// Use unblocked code to reduce the rest of the matrix
// add 1 to i for 1-based index
i += 1;
lapackf77_cgehd2(&n, &i, &ihi, A, &lda, tau, work, &iinfo);
work[0] = magma_cmake_lwork( iws );
return *info;
} /* magma_cgehrd */
/**
Purpose
-------
CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian and B is also positive definite.
If eigenvectors are desired, it uses a divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@param[in]
itype INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
@param[in]
jobz magma_vec_t
- = MagmaNoVec: Compute eigenvalues only;
- = MagmaVec: Compute eigenvalues and eigenvectors.
@param[in]
uplo magma_uplo_t
- = MagmaUpper: Upper triangles of A and B are stored;
- = MagmaLower: Lower triangles of A and B are stored.
@param[in]
n INTEGER
The order of the matrices A and B. 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. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of A contains
the lower triangular part of the matrix A.
\n
On exit, if JOBZ = MagmaVec, then if INFO = 0, A contains the
matrix Z of eigenvectors. The eigenvectors are normalized
as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = MagmaNoVec, then on exit the upper triangle (if UPLO=MagmaUpper)
or the lower triangle (if UPLO=MagmaLower) of A, including the
diagonal, is destroyed.
@param[in]
lda INTEGER
The leading dimension of the array A. LDA >= max(1,N).
@param[in,out]
B COMPLEX array, dimension (LDB, N)
On entry, the Hermitian matrix B. If UPLO = MagmaUpper, the
leading N-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = MagmaLower,
the leading N-by-N lower triangular part of B contains
the lower triangular part of the matrix B.
\n
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
@param[in]
ldb INTEGER
The leading dimension of the array B. LDB >= max(1,N).
@param[out]
w REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
@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 length of the array WORK.
If N <= 1, LWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LWORK >= N + N*NB.
If JOBZ = MagmaVec and N > 1, LWORK >= max( N + N*NB, 2*N + N**2 ).
NB can be obtained through magma_get_chetrd_nb(N).
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
rwork (workspace) REAL array, dimension (MAX(1,LRWORK))
On exit, if INFO = 0, RWORK[0] returns the optimal LRWORK.
@param[in]
lrwork INTEGER
The dimension of the array RWORK.
If N <= 1, LRWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LRWORK >= N.
If JOBZ = MagmaVec and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
\n
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
iwork (workspace) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK[0] returns the optimal LIWORK.
@param[in]
liwork INTEGER
The dimension of the array IWORK.
If N <= 1, LIWORK >= 1.
If JOBZ = MagmaNoVec and N > 1, LIWORK >= 1.
If JOBZ = MagmaVec and N > 1, LIWORK >= 3 + 5*N.
\n
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
- > 0: CPOTRF or CHEEVD returned an error code:
<= N: if INFO = i and JOBZ = MagmaNoVec, then the algorithm
failed to converge; i off-diagonal elements of an
intermediate tridiagonal form did not converge to
zero;
if INFO = i and JOBZ = MagmaVec, then the algorithm
failed to compute an eigenvalue while working on
the submatrix lying in rows and columns INFO/(N+1)
through mod(INFO,N+1);
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite.
The factorization of B could not be completed and
no eigenvalues or eigenvectors were computed.
Further Details
---------------
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
Modified so that no backsubstitution is performed if CHEEVD fails to
converge (NEIG in old code could be greater than N causing out of
bounds reference to A - reported by Ralf Meyer). Also corrected the
description of INFO and the test on ITYPE. Sven, 16 Feb 05.
@ingroup magma_chegv_driver
********************************************************************/
extern "C" magma_int_t
magma_chegvd_m(
magma_int_t ngpu,
magma_int_t itype, magma_vec_t jobz, magma_uplo_t uplo, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *B, magma_int_t ldb,
float *w, magmaFloatComplex *work, magma_int_t lwork,
#ifdef COMPLEX
float *rwork, magma_int_t lrwork,
#endif
magma_int_t *iwork, magma_int_t liwork,
magma_int_t *info)
{
const char* uplo_ = lapack_uplo_const( uplo );
const char* jobz_ = lapack_vec_const( jobz );
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t lower;
magma_trans_t trans;
magma_int_t wantz;
magma_int_t lquery;
magma_int_t lwmin;
magma_int_t liwmin;
magma_int_t lrwmin;
wantz = (jobz == MagmaVec);
lower = (uplo == MagmaLower);
lquery = (lwork == -1 || lrwork == -1 || liwork == -1);
*info = 0;
if (itype < 1 || itype > 3) {
*info = -1;
} else if (! (wantz || (jobz == MagmaNoVec))) {
*info = -2;
} else if (! (lower || (uplo == MagmaUpper))) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (lda < max(1,n)) {
*info = -6;
} else if (ldb < max(1,n)) {
*info = -8;
}
magma_int_t nb = magma_get_chetrd_nb( n );
if ( n <= 1 ) {
lwmin = 1;
lrwmin = 1;
liwmin = 1;
}
else if ( wantz ) {
lwmin = max( n + n*nb, 2*n + n*n );
lrwmin = 1 + 5*n + 2*n*n;
liwmin = 3 + 5*n;
}
else {
lwmin = n + n*nb;
lrwmin = n;
liwmin = 1;
}
work[0] = magma_cmake_lwork( lwmin );
rwork[0] = magma_smake_lwork( lrwmin );
iwork[0] = liwmin;
if (lwork < lwmin && ! lquery) {
*info = -11;
} else if (lrwork < lrwmin && ! lquery) {
*info = -13;
} else if (liwork < liwmin && ! lquery) {
*info = -15;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (n == 0) {
return *info;
}
/* If matrix is very small, then just call LAPACK on CPU, no need for GPU */
if (n <= 128) {
lapackf77_chegvd( &itype, jobz_, uplo_,
&n, A, &lda, B, &ldb,
w, work, &lwork,
#ifdef COMPLEX
rwork, &lrwork,
#endif
iwork, &liwork, info);
return *info;
}
magma_timer_t time=0;
timer_start( time );
magma_cpotrf_m( ngpu, uplo, n, B, ldb, info );
if (*info != 0) {
*info = n + *info;
return *info;
}
timer_stop( time );
timer_printf( "time cpotrf = %6.2f\n", time );
timer_start( time );
/* Transform problem to standard eigenvalue problem and solve. */
magma_chegst_m( ngpu, itype, uplo, n, A, lda, B, ldb, info );
timer_stop( time );
timer_printf( "time chegst = %6.2f\n", time );
timer_start( time );
magma_cheevd_m( ngpu, jobz, uplo, n, A, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info );
timer_stop( time );
timer_printf( "time cheevd = %6.2f\n", time );
if (wantz && *info == 0) {
timer_start( time );
/* Backtransform eigenvectors to the original problem. */
if (itype == 1 || itype == 2) {
/* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
backtransform eigenvectors: x = inv(L)'*y or inv(U)*y */
if (lower) {
trans = MagmaConjTrans;
} else {
trans = MagmaNoTrans;
}
magma_ctrsm_m( ngpu, MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, c_one, B, ldb, A, lda );
}
else if (itype == 3) {
/* For B*A*x=(lambda)*x;
backtransform eigenvectors: x = L*y or U'*y */
if (lower) {
trans = MagmaNoTrans;
} else {
trans = MagmaConjTrans;
}
#ifdef ENABLE_DEBUG
printf("--- the multi GPU version is falling back to 1 GPU to perform the last TRMM since there is no TRMM_mgpu --- \n");
#endif
magmaFloatComplex *dA=NULL, *dB=NULL;
magma_int_t ldda = magma_roundup( n, 32 );
magma_int_t lddb = ldda;
if (MAGMA_SUCCESS != magma_cmalloc( &dA, n*ldda ) ||
MAGMA_SUCCESS != magma_cmalloc( &dB, n*lddb )) {
magma_free( dA );
magma_free( dB );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t queue;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
magma_csetmatrix( n, n, B, ldb, dB, lddb, queue );
magma_csetmatrix( n, n, A, lda, dA, ldda, queue );
magma_ctrmm( MagmaLeft, uplo, trans, MagmaNonUnit,
n, n, c_one, dB, lddb, dA, ldda, queue );
magma_cgetmatrix( n, n, dA, ldda, A, lda, queue );
magma_queue_destroy( queue );
magma_free( dA );
magma_free( dB );
}
timer_stop( time );
timer_printf( "time setmatrices trsm/mm + getmatrices = %6.2f\n", time );
}
work[0] = magma_cmake_lwork( lwmin );
rwork[0] = magma_smake_lwork( lrwmin );
iwork[0] = liwmin;
return *info;
} /* magma_chegvd_m */
/**
Purpose:
---------
CUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
which is defined as the first M rows of a product of K elementary
reflectors of order N
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by CGELQF.
Arguments:
---------
@param[in]
m INTEGER
The number of rows of the matrix Q. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix Q. N >= M.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by CGELQF in the first k rows of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
lda INTEGER
The first dimension of the array A. LDA >= max(1,M).
@param[in]
tau COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGELQF.
@param[out]
work 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 >= NB*NB, where NB is
the optimal blocksize.
If LWORK = -1, 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
@ingroup magma_cgelqf_comp
********************************************************************/
extern "C" magma_int_t
magma_cunglq(
magma_int_t m, magma_int_t n, magma_int_t k,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define tau(i_) (tau + (i_))
// Constants
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
const magmaFloatComplex c_one = MAGMA_C_ONE;
// Local variables
bool lquery;
magma_int_t i, ib, ki, ldda, lddwork, lwkopt, mib, nb, n_i;
magma_queue_t queue = NULL;
magmaFloatComplex_ptr dA = NULL;
magmaFloatComplex* work2 = NULL;
// Test the input arguments
*info = 0;
nb = magma_get_cgelqf_nb( m, n );
lwkopt = nb*nb;
work[0] = magma_cmake_lwork( lwkopt );
lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0 || n < m) {
*info = -2;
} else if (k < 0 || k > m) {
*info = -3;
} else if (lda < max( 1, m )) {
*info = -5;
} else if (lwork < max( 1, lwkopt ) && ! lquery) {
*info = -8;
//printf( "m %d, n %d, nb %d: lwork %d, required %d\n", m, n, nb, lwork, lwkopt );
//*info = 0;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
// Quick return if possible
if (m <= 0) {
work[0] = c_one;
return *info;
}
//if (lwork < lwkopt) {
// magma_cmalloc_cpu( &work2, lwkopt );
//}
//else {
// work2 = work;
//}
work2 = work;
// Allocate GPU work space
// ldda*n for matrix dA
// nb*n for dV
// lddwork*nb for dW larfb workspace
ldda = magma_roundup( m, 32 );
lddwork = magma_roundup( m, 32 );
if (MAGMA_SUCCESS != magma_cmalloc( &dA, ldda*n + n*nb + lddwork*nb + nb*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
magmaFloatComplex_ptr dV; dV = dA + ldda*n;
magmaFloatComplex_ptr dW; dW = dA + ldda*n + n*nb;
magmaFloatComplex_ptr dT; dT = dA + ldda*n + n*nb + lddwork*nb;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
magmablas_claset( MagmaFull, m, n, MAGMA_C_NAN, MAGMA_C_NAN, dA, ldda, queue );
// all columns are handled by blocked method.
// ki is start of last (partial) block
ki = ((k - 1) / nb) * nb;
// Use blocked code
for( i=ki; i >= 0; i -= nb ) {
ib = min( nb, k-i );
// first block has extra rows to update
mib = ib;
if ( i == ki ) {
mib = m - i;
}
// Send current panel of V (block row) to the GPU
lapackf77_claset( "Lower", &ib, &ib, &c_zero, &c_one, A(i,i), &lda );
// TODO: having this _async was causing numerical errors. Why?
magma_csetmatrix( ib, n-i,
A(i,i), lda,
dV, nb, queue );
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
n_i = n - i;
lapackf77_clarft( MagmaForwardStr, MagmaRowwiseStr, &n_i, &ib,
A(i,i), &lda, &tau[i], work2, &nb );
magma_csetmatrix_async( ib, ib,
work2, nb,
dT, nb, queue );
// set panel of A (block row) to identity
magmablas_claset( MagmaFull, mib, i, c_zero, c_zero, dA(i,0), ldda, queue );
magmablas_claset( MagmaFull, mib, n-i, c_zero, c_one, dA(i,i), ldda, queue );
if (i < m) {
// Apply H**H to A(i:m,i:n) from the right
magma_clarfb_gpu( MagmaRight, MagmaConjTrans, MagmaForward, MagmaRowwise,
m-i, n-i, ib,
dV, nb, dT, nb,
dA(i,i), ldda, dW, lddwork, queue );
}
}
// copy result back to CPU
magma_cgetmatrix( m, n,
dA(0,0), ldda, A(0,0), lda, queue );
cleanup:
magma_queue_destroy( queue );
magma_free( dA );
//if (work2 != work) {
// magma_free_cpu( work2 );
//}
work[0] = magma_cmake_lwork( lwkopt );
return *info;
}
/**
Purpose
-------
CGEHRD reduces a COMPLEX general matrix A to upper Hessenberg form H by
an orthogonal similarity transformation: Q' * A * Q = H . This version
stores the triangular matrices used in the factorization so that they can
be applied directly (i.e., without being recomputed) later. As a result,
the application of Q is much faster.
Arguments
---------
@param[in]
n INTEGER
The order of the matrix A. N >= 0.
@param[in]
ilo INTEGER
@param[in]
ihi INTEGER
It is assumed that A is already upper triangular in rows
and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
set by a previous call to CGEBAL; otherwise they should be
set to 1 and N respectively. See Further Details.
1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the N-by-N general matrix to be reduced.
On exit, the upper triangle and the first subdiagonal of A
are overwritten with the upper Hessenberg matrix H, 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]
tau COMPLEX array, dimension (N-1)
The scalar factors of the elementary reflectors (see Further
Details). Elements 1:ILO-1 and IHI:N-1 of TAU are set to
zero.
@param[out]
work (workspace) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The length of the array WORK. 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]
T COMPLEX array, dimension NB*N,
where NB is the optimal blocksize. It stores the NB*NB blocks
of the triangular T matrices used in the reduction.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value.
Further Details
---------------
The matrix Q is represented as a product of (ihi-ilo) elementary
reflectors
Q = H(ilo) H(ilo+1) . . . H(ihi-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, v(i+1) = 1 and v(ihi+1:n) = 0; v(i+2:ihi) is stored on
exit in A(i+2:ihi,i), and tau in TAU(i).
The contents of A are illustrated by the following example, with
n = 7, ilo = 2 and ihi = 6:
@verbatim
on entry, on exit,
( a a a a a a a ) ( a a h h h h a )
( a a a a a a ) ( a h h h h a )
( a a a a a a ) ( h h h h h h )
( a a a a a a ) ( v2 h h h h h )
( a a a a a a ) ( v2 v3 h h h h )
( a a a a a a ) ( v2 v3 v4 h h h )
( a ) ( a )
@endverbatim
where a denotes an element of the original matrix A, h denotes a
modified element of the upper Hessenberg matrix H, and vi denotes an
element of the vector defining H(i).
This implementation follows the hybrid algorithm and notations described in
S. Tomov and J. Dongarra, "Accelerating the reduction to upper Hessenberg
form through hybrid GPU-based computing," University of Tennessee Computer
Science Technical Report, UT-CS-09-642 (also LAPACK Working Note 219),
May 24, 2009.
This version stores the T matrices, for later use in magma_cunghr.
@ingroup magma_cgeev_comp
********************************************************************/
extern "C" magma_int_t
magma_cgehrd_m(
magma_int_t n, magma_int_t ilo, magma_int_t ihi,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magmaFloatComplex *T,
magma_int_t *info)
{
#define A( i, j ) (A + (i) + (j)*lda)
#define dA( d, i, j ) (data.A[d] + (i) + (j)*ldda)
magmaFloatComplex c_one = MAGMA_C_ONE;
magmaFloatComplex c_zero = MAGMA_C_ZERO;
magma_int_t nb = magma_get_cgehrd_nb(n);
magma_int_t nh, iws, ldda, min_lblocks, max_lblocks, last_dev, d;
magma_int_t dpanel, di, nlocal, i, i2, ib, ldwork;
magma_int_t iinfo;
magma_int_t lquery;
struct cgehrd_data data;
magma_int_t ngpu = magma_num_gpus();
*info = 0;
iws = n*(nb + nb*ngpu);
work[0] = magma_cmake_lwork( iws );
lquery = (lwork == -1);
if (n < 0) {
*info = -1;
} else if (ilo < 1 || ilo > max(1,n)) {
*info = -2;
} else if (ihi < min(ilo,n) || ihi > n) {
*info = -3;
} else if (lda < max(1,n)) {
*info = -5;
} else if (lwork < iws && ! lquery) {
*info = -8;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
// Adjust from 1-based indexing
ilo -= 1;
// Quick return if possible
nh = ihi - ilo;
if (nh <= 1) {
work[0] = c_one;
return *info;
}
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
// Set elements 0:ILO-1 and IHI-1:N-2 of TAU to zero
for (i = 0; i < ilo; ++i)
tau[i] = c_zero;
for (i = max(0,ihi-1); i < n-1; ++i)
tau[i] = c_zero;
// set T to zero
lapackf77_claset( "Full", &nb, &n, &c_zero, &c_zero, T, &nb );
// set to null, to simplify cleanup code
for( d = 0; d < ngpu; ++d ) {
data.A[d] = NULL;
data.queues[d] = NULL;
}
// Now requires lwork >= iws; else dT won't be computed in unblocked code.
// If not enough workspace, use unblocked code
//if ( lwork < iws ) {
// nb = 1;
//}
if (nb == 1 || nb >= nh) {
// Use unblocked code below
i = ilo;
}
else {
// Use blocked code
// allocate memory on GPUs for A and workspaces
ldda = magma_roundup( n, 32 );
min_lblocks = (n / nb) / ngpu;
max_lblocks = ((n-1) / nb) / ngpu + 1;
last_dev = (n / nb) % ngpu;
// V and Vd need to be padded for copying in mclahr2
data.ngpu = ngpu;
data.ldda = ldda;
data.ldv = nb*max_lblocks*ngpu;
data.ldvd = nb*max_lblocks;
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
nlocal = min_lblocks*nb;
if ( d < last_dev ) {
nlocal += nb;
}
else if ( d == last_dev ) {
nlocal += (n % nb);
}
ldwork = nlocal*ldda // A
+ nb*data.ldv // V
+ nb*data.ldvd // Vd
+ nb*ldda // Y
+ nb*ldda // W
+ nb*nb; // Ti
if ( MAGMA_SUCCESS != magma_cmalloc( &data.A[d], ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
data.V [d] = data.A [d] + nlocal*ldda;
data.Vd[d] = data.V [d] + nb*data.ldv;
data.Y [d] = data.Vd[d] + nb*data.ldvd;
data.W [d] = data.Y [d] + nb*ldda;
data.Ti[d] = data.W [d] + nb*ldda;
magma_queue_create( d, &data.queues[d] );
}
// Copy the matrix to GPUs
magma_csetmatrix_1D_col_bcyclic( n, n, A, lda, data.A, ldda, ngpu, nb, data.queues );
// round ilo down to block boundary
ilo = (ilo/nb)*nb;
for (i = ilo; i < ihi - 1 - nb; i += nb) {
// Reduce columns i:i+nb-1 to Hessenberg form, returning the
// matrices V and T of the block reflector H = I - V*T*V'
// which performs the reduction, and also the matrix Y = A*V*T
// Get the current panel (no need for the 1st iteration)
dpanel = (i / nb) % ngpu;
di = ((i / nb) / ngpu) * nb;
if ( i > ilo ) {
magma_setdevice( dpanel );
magma_cgetmatrix( ihi-i, nb,
dA(dpanel, i, di), ldda,
A(i,i), lda, data.queues[dpanel] );
}
// add 1 to i for 1-based index
magma_clahr2_m( ihi, i+1, nb, A(0,i), lda,
&tau[i], &T[i*nb], nb, work, n, &data );
magma_clahru_m( n, ihi, i, nb, A, lda, &data );
// copy first i rows above panel to host
magma_setdevice( dpanel );
magma_cgetmatrix_async( i, nb,
dA(dpanel, 0, di), ldda,
A(0,i), lda, data.queues[dpanel] );
}
// Copy remainder to host, block-by-block
for( i2 = i; i2 < n; i2 += nb ) {
ib = min( nb, n-i2 );
d = (i2 / nb) % ngpu;
di = (i2 / nb) / ngpu * nb;
magma_setdevice( d );
magma_cgetmatrix( n, ib,
dA(d, 0, di), ldda,
A(0,i2), lda, data.queues[d] );
}
}
// Use unblocked code to reduce the rest of the matrix
// add 1 to i for 1-based index
i += 1;
lapackf77_cgehd2(&n, &i, &ihi, A, &lda, tau, work, &iinfo);
work[0] = magma_cmake_lwork( iws );
CLEANUP:
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_free( data.A[d] );
magma_queue_destroy( data.queues[d] );
}
magma_setdevice( orig_dev );
return *info;
} /* magma_cgehrd */
