void magmaf_dlarfb_gpu(
magma_side_t *side, magma_trans_t *trans, magma_direct_t *direct, magma_storev_t *storev, magma_int_t *m, magma_int_t *n, magma_int_t *k,
devptr_t *dv, magma_int_t *ldv,
devptr_t *dt, magma_int_t *ldt,
devptr_t *dc, magma_int_t *ldc,
devptr_t *dwork, magma_int_t *ldwork )
{
magma_dlarfb_gpu(
*side, *trans, *direct, *storev, *m, *n, *k,
magma_ddevptr(dv), *ldv,
magma_ddevptr(dt), *ldt,
magma_ddevptr(dc), *ldc,
magma_ddevptr(dwork), *ldwork );
}
extern "C" magma_int_t
magma_dorgqr2(magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DORGQR generates an M-by-N DOUBLE_PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
This version recomputes the T matrices on the CPU and sends them to the GPU.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A (input/output) DOUBLE_PRECISION array A, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
===================================================================== */
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(i,j) (dA + (i) + (j)*ldda)
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t nb = magma_get_dgeqrf_nb(min(m, n));
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, ldda;
magma_int_t i, ib, ki, kk; //, iinfo;
magma_int_t lddwork;
double *dA, *dV, *dW, *dT, *T;
double *work;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
} else {
ki = 0;
kk = 0;
}
// Allocate GPU work space
// ldda*n for matrix dA
// ldda*nb for dV
// lddwork*nb for dW larfb workspace
ldda = ((m + 31) / 32) * 32;
lddwork = ((n + 31) / 32) * 32;
if (MAGMA_SUCCESS != magma_dmalloc( &dA, ldda*n + ldda*nb + lddwork*nb + nb*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dV = dA + ldda*n;
dW = dA + ldda*n + ldda*nb;
dT = dA + ldda*n + ldda*nb + lddwork*nb;
// Allocate CPU work space
lwork = (n+m+nb) * nb;
magma_dmalloc_cpu( &work, lwork );
T = work;
if (work == NULL) {
magma_free( dA );
magma_free_cpu( work );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
double *V = work + (n+nb)*nb;
magma_queue_t stream;
magma_queue_create( &stream );
// Use unblocked code for the last or only block.
if (kk < n) {
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
/*
lapackf77_dorgqr( &m_kk, &n_kk, &k_kk,
A(kk, kk), &lda,
&tau[kk], work, &lwork, &iinfo );
*/
lapackf77_dlacpy( MagmaUpperLowerStr, &m_kk, &k_kk, A(kk,kk), &lda, V, &m_kk);
lapackf77_dlaset( MagmaUpperLowerStr, &m_kk, &n_kk, &c_zero, &c_one, A(kk, kk), &lda );
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &k_kk,
V, &m_kk, &tau[kk], work, &k_kk);
lapackf77_dlarfb( MagmaLeftStr, MagmaNoTransStr, MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &n_kk, &k_kk,
V, &m_kk, work, &k_kk, A(kk, kk), &lda, work+k_kk*k_kk, &n_kk );
if (kk > 0) {
magma_dsetmatrix( m_kk, n_kk,
A(kk, kk), lda,
dA(kk, kk), ldda );
// Set A(1:kk,kk+1:n) to zero.
magmablas_dlaset( MagmaUpperLower, kk, n - kk, dA(0, kk), ldda );
}
}
if (kk > 0) {
// Use blocked code
// stream: set Aii (V) --> laset --> laset --> larfb --> [next]
// CPU has no computation
magmablasSetKernelStream( stream );
for (i = ki; i >= 0; i -= nb) {
ib = min(nb, k - i);
// Send current panel to the GPU
mi = m - i;
lapackf77_dlaset( "Upper", &ib, &ib, &c_zero, &c_one, A(i, i), &lda );
magma_dsetmatrix_async( mi, ib,
A(i, i), lda,
dV, ldda, stream );
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&mi, &ib,
A(i,i), &lda, &tau[i], T, &nb);
magma_dsetmatrix_async( ib, ib,
T, nb,
dT , nb, stream );
// set panel to identity
magmablas_dlaset( MagmaUpperLower, i, ib, dA(0, i), ldda );
magmablas_dlaset_identity( mi, ib, dA(i, i), ldda );
magma_queue_sync( stream );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, n-i, ib,
dV, ldda, dT, nb,
dA(i, i), ldda, dW, lddwork );
}
}
// copy result back to CPU
magma_dgetmatrix( m, n,
dA(0, 0), ldda, A(0, 0), lda);
}
magmablasSetKernelStream( NULL );
magma_queue_destroy( stream );
magma_free( dA );
magma_free_cpu( work );
return *info;
} /* magma_dorgqr */
/**
Purpose
-------
DORMQR overwrites the general real M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaTrans: Q**H * C C * Q**H
@endverbatim
where Q is a real unitary matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = MagmaLeft and of order N
if SIDE = MagmaRight.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@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;
- = MagmaTrans: 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 DOUBLE_PRECISION 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
DGEQRF in the first k columns of its array argument A.
@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 DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
@param[in,out]
C DOUBLE_PRECISION 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) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK.
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 by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dormqr_m(
magma_int_t ngpu,
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
double *C, magma_int_t ldc,
double *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define C(i, j) (C + (j)*ldc + (i))
#define dC(gpui, i, j) (dw[gpui] + (j)*lddc + (i))
#define dA_c(gpui, ind, i, j) (dw[gpui] + maxnlocal*lddc + (ind)*lddar*lddac + (i) + (j)*lddac)
#define dA_r(gpui, ind, i, j) (dw[gpui] + maxnlocal*lddc + (ind)*lddar*lddac + (i) + (j)*lddar)
#define dT(gpui, ind) (dw[gpui] + maxnlocal*lddc + 2*lddac*lddar + (ind)*((nb+1)*nb))
#define dwork(gpui, ind) (dw[gpui] + maxnlocal*lddc + 2*lddac*lddar + 2*((nb+1)*nb) + (ind)*(lddwork*nb))
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
const char* side_ = lapack_side_const( side );
const char* trans_ = lapack_trans_const( trans );
// TODO fix memory leak (alloc after argument checks)
magma_int_t nb = 128;
double *T;
magma_dmalloc_pinned(&T, nb*nb);
//printf("calling dormqr_m with nb=%d\n", (int) nb);
double* dw[MagmaMaxGPUs];
magma_queue_t stream [MagmaMaxGPUs][2];
magma_event_t event [MagmaMaxGPUs][2];
magma_int_t ind_c;
magma_device_t igpu;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
*info = 0;
magma_int_t left = (side == MagmaLeft);
magma_int_t notran = (trans == MagmaNoTrans);
magma_int_t lquery = (lwork == -1);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
magma_int_t nq, nw;
if (left) {
nq = m;
nw = n;
} else {
nq = n;
nw = m;
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != MagmaTrans) {
*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;
}
magma_int_t lwkopt = max(1,nw) * nb;
if (*info == 0) {
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
}
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] = c_one;
return *info;
}
if (nb >= k) {
/* Use CPU code */
lapackf77_dormqr(side_, trans_, &m, &n, &k, A, &lda, tau,
C, &ldc, work, &lwork, info);
return *info;
}
magma_int_t lddc = (m+63)/64*64;
magma_int_t lddac = nq;
magma_int_t lddar = nb;
magma_int_t lddwork = nw;
magma_int_t nlocal[ MagmaMaxGPUs ] = { 0 };
magma_int_t nb_l=256;
magma_int_t nbl = (n-1)/nb_l+1; // number of blocks
magma_int_t maxnlocal = (nbl+ngpu-1)/ngpu*nb_l;
ngpu = min(ngpu, (n+nb_l-1)/nb_l); // Don't use GPU that will not have data.
magma_int_t ldw = maxnlocal*lddc // dC
+ 2*lddac*lddar // 2*dA
+ 2*(nb + 1 + lddwork)*nb; // 2*(dT and dwork)
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
if (MAGMA_SUCCESS != magma_dmalloc( &dw[igpu], ldw )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
magma_xerbla( __func__, -(*info) );
return *info;
}
magma_queue_create( &stream[igpu][0] );
magma_queue_create( &stream[igpu][1] );
magma_event_create( &event[igpu][0] );
magma_event_create( &event[igpu][1] );
}
/* Use hybrid CPU-MGPU code */
if (left) {
//copy C to mgpus
for (magma_int_t i = 0; i < nbl; ++i) {
magma_int_t igpu = i%ngpu;
magma_setdevice(igpu);
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_dsetmatrix_async( m, kb,
C(0, i*nb_l), ldc,
dC(igpu, 0, i/ngpu*nb_l), lddc, stream[igpu][0] );
nlocal[igpu] += kb;
}
magma_int_t i1, i2, i3;
if ( !notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
ind_c = 0;
for (magma_int_t i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3) {
// start the copy of A panel
magma_int_t kb = min(nb, k - i);
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_event_sync(event[igpu][ind_c]); // check if the new data can be copied
magma_dsetmatrix_async(nq-i, kb,
A(i, i), lda,
dA_c(igpu, ind_c, i, 0), lddac, stream[igpu][0] );
// set upper triangular part of dA to identity
magmablas_dlaset_band_q( MagmaUpper, kb, kb, kb, c_zero, c_one, dA_c(igpu, ind_c, i, 0), lddac, stream[igpu][0] );
}
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
magma_int_t nqi = nq - i;
lapackf77_dlarft("F", "C", &nqi, &kb, A(i, i), &lda,
&tau[i], T, &kb);
/* H or H' is applied to C(1:m,i:n) */
/* Apply H or H'; First copy T to the GPU */
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_dsetmatrix_async(kb, kb,
T, kb,
dT(igpu, ind_c), kb, stream[igpu][0] );
}
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_queue_sync( stream[igpu][0] ); // check if the data was copied
magmablasSetKernelStream(stream[igpu][1]);
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
m-i, nlocal[igpu], kb,
dA_c(igpu, ind_c, i, 0), lddac, dT(igpu, ind_c), kb,
dC(igpu, i, 0), lddc,
dwork(igpu, ind_c), lddwork);
magma_event_record(event[igpu][ind_c], stream[igpu][1] );
}
ind_c = (ind_c+1)%2;
}
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_queue_sync( stream[igpu][1] );
}
//copy C from mgpus
for (magma_int_t i = 0; i < nbl; ++i) {
magma_int_t igpu = i%ngpu;
magma_setdevice(igpu);
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_dgetmatrix( m, kb,
dC(igpu, 0, i/ngpu*nb_l), lddc,
C(0, i*nb_l), ldc );
// magma_dgetmatrix_async( m, kb,
// dC(igpu, 0, i/ngpu*nb_l), lddc,
// C(0, i*nb_l), ldc, stream[igpu][0] );
}
} else {
// TODO fix memory leak T, dw, event, stream
fprintf(stderr, "The case (side == right) is not implemented\n");
*info = MAGMA_ERR_NOT_IMPLEMENTED;
magma_xerbla( __func__, -(*info) );
return *info;
/*
if ( notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
mi = m;
ic = 0;
for (i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3) {
ib = min(nb, k - i);
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
i__4 = nq - i;
lapackf77_dlarft("F", "C", &i__4, &ib, A(i, i), &lda,
&tau[i], T, &ib);
// 1) copy the panel from A to the GPU, and
// 2) set upper triangular part of dA to identity
magma_dsetmatrix( i__4, ib, A(i, i), lda, dA(i, 0), ldda );
magmablas_dlaset_band( MagmaUpper, ib, ib, ib, c_zero, c_one, dA(i, 0), ldda );
// H or H' is applied to C(1:m,i:n)
ni = n - i;
jc = i;
// Apply H or H'; First copy T to the GPU
magma_dsetmatrix( ib, ib, T, ib, dT, ib );
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dA(i, 0), ldda, dT, ib,
dC(ic, jc), lddc,
dwork, lddwork);
}
*/
}
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
for (igpu = 0; igpu < ngpu; ++igpu) {
magma_setdevice(igpu);
magma_event_destroy( event[igpu][0] );
magma_event_destroy( event[igpu][1] );
magma_queue_destroy( stream[igpu][0] );
magma_queue_destroy( stream[igpu][1] );
magma_free( dw[igpu] );
}
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
return *info;
} /* magma_dormqr */
extern "C" magma_int_t
magma_dormqr_gpu_2stages(const char side, const char trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *da, magma_int_t ldda,
double *dc, magma_int_t lddc,
double *dT, magma_int_t nb,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DORMQR_GPU overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
DA (input) DOUBLE_PRECISION array on the GPU, dimension (LDDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGEQRF in the first k columns of its array argument DA.
DA is modified by the routine but restored on exit.
LDDA (input) INTEGER
The leading dimension of the array DA.
If SIDE = 'L', LDDA >= max(1,M);
if SIDE = 'R', LDDA >= max(1,N).
DC (input/output) DOUBLE_PRECISION array on the GPU, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T * C or C * Q**T or C*Q.
LDDC (input) INTEGER
The leading dimension of the array DC. LDDC >= max(1,M).
DT (input) DOUBLE_PRECISION array on the GPU that is the output
(the 9th argument) of magma_dgeqrf_gpu.
NB (input) INTEGER
This is the blocking size that was used in pre-computing DT, e.g.,
the blocking size used in magma_dgeqrf_gpu.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
char side_[2] = {side, 0};
char trans_[2] = {trans, 0};
double *dwork;
magma_int_t i1, i2, i3, ib, ic, jc, mi, ni, nq, nw, ret;
int left, notran;
//magma_int_t lwkopt;
*info = 0;
left = lapackf77_lsame(side_, "L");
notran = lapackf77_lsame(trans_, "N");
/* 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) && (!lapackf77_lsame(side_, "R")) ) {
*info = -1;
} else if ( (!notran) && (!lapackf77_lsame(trans_, MagmaTransStr)) ) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
}
if(MAGMA_SUCCESS != magma_dmalloc( &dwork, n*nb )) {
printf ("!!!! dorgqr_2stage magma_alloc failed for: dwork\n" );
exit(-1);
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
return *info;
}
if ( (left && (! notran)) || ( (!left) && notran ) ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
jc = 0;
} else {
mi = m;
ic = 0;
}
for (magma_int_t i=i1; (i3<0 ? i>=i2 : i<i2); i+=i3)
{
ib = min(nb, k - i);
if (left){
mi = m - i;
ic = i;
}
else {
ni = n - i;
jc = i;
}
ret = magma_dlarfb_gpu( MagmaLeft, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib, da+i+i*ldda, ldda, dT+i*nb, nb,
dc+ic+jc*lddc, lddc, dwork, nw);
if ( ret != MAGMA_SUCCESS ){
magma_free(dwork);
return ret;
}
}
return MAGMA_SUCCESS;
} /* End of MAGMA_DORMQR_GPU_2stages */
/**
Purpose
-------
DORGQR generates an M-by-N DOUBLE_PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF_GPU.
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. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
dA DOUBLE_PRECISION array A on the GPU device,
dimension (LDDA,N). On entry, the i-th column must contain
the vector which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the first k
columns of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
ldda INTEGER
The first dimension of the array A. LDDA >= max(1,M).
@param[in]
tau DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
@param[in]
dT DOUBLE_PRECISION work space array on the GPU device,
dimension (MIN(M, N) )*NB.
This must be the 6th argument of magma_dgeqrf_gpu
[ note that if N here is bigger than N in magma_dgeqrf_gpu,
the workspace requirement DT in magma_dgeqrf_gpu must be
as specified in this routine ].
@param[in]
nb INTEGER
This is the block size used in DGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument has an illegal value
@ingroup magma_dsyev_2stage
********************************************************************/
extern "C" magma_int_t
magma_dorgqr_2stage_gpu(magma_int_t m, magma_int_t n, magma_int_t k,
double *dA, magma_int_t ldda,
double *tau, double *dT,
magma_int_t nb, magma_int_t *info)
{
#define dA(a_1,a_2) (dA + (a_2)*(ldda) + (a_1))
#define dT(a_1) (dT + (a_1)*nb)
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t i__1, i__2, i__3;
//magma_int_t lwork;
magma_int_t i, ib, ki, kk; //, iinfo;
//magma_int_t lddwork = min(m, n);
//double *work, *panel;
double *dwork;
//magma_queue_t stream[2];
magma_int_t ldt=nb; // need to be an input parameter
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (ldda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0)
return *info;
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, n*nb )) {
printf ("!!!! dorgqr_2stage magma_alloc failed for: dwork\n" );
exit(-1);
}
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code after the last block.
The first kk columns are handled by the block method.
ki is start of 2nd-to-last block. */
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
/* Set A(1:kk,kk+1:n) to zero. */
/* and A(kk+1:m, kk+1:n) = I */
magmablas_dlaset( MagmaFull, kk, n-kk, c_zero, c_zero, dA(0, kk), ldda );
magmablas_dlaset( MagmaFull, m-kk, n-kk, c_zero, c_one, dA(kk,kk), ldda );
}
else {
ki = 0;
kk = 0;
}
/* Allocate work space on CPU in pinned memory */
//lwork = (n+m) * nb;
//if (kk < n)
// lwork = max(lwork, n * nb + (m-kk)*(n-kk));
//if (MAGMA_SUCCESS != magma_dmalloc_pinned( &work, (lwork) )) {
// *info = MAGMA_ERR_HOST_ALLOC;
// return *info;
//}
//panel = work + n * nb;
//magma_queue_create( &stream[0] );
//magma_queue_create( &stream[1] );
/* Use unblocked code for the last or only block. */
if (kk < n) {
i__1 = m - kk;
i__2 = n - kk;
i__3 = k - kk;
//magma_dgetmatrix(i__1, i__2, dA(kk, kk), ldda, panel, i__1);
//lapackf77_dorgqr(&i__1, &i__2, &i__3, panel, &i__1, &tau[kk],
// work, &lwork, &iinfo);
//
//magma_dsetmatrix(i__1, i__2, panel, i__1, dA(kk, kk), ldda);
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
i__1, i__2, i__3,
dA(kk, kk-nb), ldda, dT(kk-nb), ldt,
dA(kk, kk), ldda, dwork, i__2);
//magmablas_dlaset(MagmaFull, kk-nb, nb, c_zero, c_zero, dA(0,kk-nb), ldda);
//magmablas_dlaset(MagmaFull, m-(kk-nb), nb, c_zero, c_one, dA(kk-nb,kk-nb), ldda);
}
if (kk > 0) {
/* Use blocked code */
for (i = ki; i >= nb; i -= nb) {
ib = min(nb, k - i);
/* Send current panel to the CPU for update */
i__2 = m - i;
//magma_dgetmatrix_async( i__2, ib, dA(i,i), ldda, panel, i__2, stream[0] ); // verify
if (i + ib < n) {
/* Apply H to A(i:m,i+ib:n) from the left */
i__3 = n - i;
magmablas_dlaset( MagmaFull, i, ib, c_zero, c_zero, dA(0,i), ldda );
magmablas_dlaset( MagmaFull, m-i, ib, c_zero, c_one, dA(i,i), ldda );
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
i__2, i__3, ib,
dA(i, i-nb), ldda, dT(i-nb), ldt,
dA(i, i), ldda, dwork, i__3);
}
/* Apply H to rows i:m of current block on the CPU */
//magma_queue_sync( stream[0] );
//lapackf77_dorgqr(&i__2, &ib, &ib, panel, &i__2, &tau[i],
// work, &lwork, &iinfo);
//magma_dsetmatrix_async( i__2, ib, panel, i__2, dA(i,i), ldda, stream[1] ); // verify
/* Set rows 1:i-1 of current block to zero */
i__2 = i + ib;
//magmablas_dlaset(MagmaFull, i-ib, ib, c_zero, c_zero, dA(0,i-ib), ldda);
//magmablas_dlaset(MagmaFull, m-(i-ib), ib, c_zero, c_one, dA(i-ib,i-ib), ldda);
}
}
magmablas_dlaset( MagmaFull, m, nb, c_zero, c_one, dA(0,0), ldda );
magma_free( dwork );
//magma_free_pinned( work );
//magma_queue_destroy( stream[0] );
//magma_queue_destroy( stream[1] );
return *info;
} /* magma_dorgqr_gpu */
extern "C" magma_int_t
magma_dormqr_m(magma_int_t nrgpu, char side, char trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *a, magma_int_t lda,
double *tau,
double *c, magma_int_t ldc,
double *work, magma_int_t lwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.1) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
December 2013
Purpose
=======
DORMQR overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) DOUBLE_PRECISION 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
DGEQRF in the first k columns of its array argument A.
LDA (input) INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).
TAU (input) DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
C (input/output) DOUBLE_PRECISION array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(0) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R', where NB is the optimal
blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
double c_one = MAGMA_D_ONE;
char side_[2] = {side, 0};
char trans_[2] = {trans, 0};
magma_int_t nb = 128;
double *t ;
magma_dmalloc_pinned (&t, nb*nb);
//printf("calling dormqr_m with nb=%d\n", (int) nb);
double* dw[MagmaMaxGPUs];
magma_queue_t stream [MagmaMaxGPUs][2];
magma_event_t event [MagmaMaxGPUs][2];
magma_int_t ind_c;
magma_int_t igpu = 0;
int gpu_b;
magma_getdevice(&gpu_b);
*info = 0;
magma_int_t left = lapackf77_lsame(side_, "L");
magma_int_t notran = lapackf77_lsame(trans_, "N");
magma_int_t lquery = (lwork == -1);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
magma_int_t nq, nw;
if (left) {
nq = m;
nw = n;
} else {
nq = n;
nw = m;
}
if (! left && ! lapackf77_lsame(side_, "R")) {
*info = -1;
} else if (! notran && ! lapackf77_lsame(trans_, "T")) {
*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;
}
magma_int_t lwkopt = max(1,nw) * nb;
if (*info == 0)
{
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
}
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] = c_one;
return *info;
}
if (nb >= k)
{
/* Use CPU code */
lapackf77_dormqr(side_, trans_, &m, &n, &k, a, &lda, tau,
c, &ldc, work, &lwork, info);
return *info;
}
magma_int_t lddc = (m+63)/64*64;
magma_int_t lddac = nq;
magma_int_t lddar = nb;
magma_int_t lddwork = nw;
magma_int_t nlocal[ MagmaMaxGPUs ] = { 0 };
magma_int_t nb_l=256;
magma_int_t nbl = (n-1)/nb_l+1; // number of blocks
magma_int_t maxnlocal = (nbl+nrgpu-1)/nrgpu*nb_l;
nrgpu = min(nrgpu, (n+nb_l-1)/nb_l); // Don't use GPU that will not have data.
magma_int_t ldw = maxnlocal*lddc // dC
+ 2*lddac*lddar // 2*dA
+ 2*(nb + 1 + lddwork)*nb; // 2*(dT and dwork)
for (igpu = 0; igpu < nrgpu; ++igpu){
magma_setdevice(igpu);
if (MAGMA_SUCCESS != magma_dmalloc( &dw[igpu], ldw)) {
magma_xerbla( __func__, -(*info) );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_create( &stream[igpu][0] );
magma_queue_create( &stream[igpu][1] );
magma_event_create( &event[igpu][0] );
magma_event_create( &event[igpu][1] );
}
/* Use hybrid CPU-MGPU code */
if (left) {
//copy C to mgpus
for (magma_int_t i = 0; i < nbl; ++i){
magma_int_t igpu = i%nrgpu;
magma_setdevice(igpu);
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_dsetmatrix_async( m, kb,
C(0, i*nb_l), ldc,
dC(igpu, 0, i/nrgpu*nb_l), lddc, stream[igpu][0] );
nlocal[igpu] += kb;
}
magma_int_t i1, i2, i3;
if ( !notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
ind_c = 0;
for (magma_int_t i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3)
{
// start the copy of A panel
magma_int_t kb = min(nb, k - i);
for (igpu = 0; igpu < nrgpu; ++igpu){
magma_setdevice(igpu);
magma_event_sync(event[igpu][ind_c]); // check if the new data can be copied
magma_dsetmatrix_async(nq-i, kb,
A(i, i), lda,
dA_c(igpu, ind_c, i, 0), lddac, stream[igpu][0] );
// Put 0s in the upper triangular part of dA;
magmablas_dsetdiag1subdiag0_stream('L', kb, kb, dA_c(igpu, ind_c, i, 0), lddac, stream[igpu][0]);
}
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
magma_int_t nqi = nq - i;
lapackf77_dlarft("F", "C", &nqi, &kb, A(i, i), &lda,
&tau[i], t, &kb);
/* H or H' is applied to C(1:m,i:n) */
/* Apply H or H'; First copy T to the GPU */
for (igpu = 0; igpu < nrgpu; ++igpu){
magma_setdevice(igpu);
magma_dsetmatrix_async(kb, kb,
t, kb,
dt(igpu, ind_c), kb, stream[igpu][0] );
}
for (igpu = 0; igpu < nrgpu; ++igpu){
magma_setdevice(igpu);
magma_queue_sync( stream[igpu][0] ); // check if the data was copied
magmablasSetKernelStream(stream[igpu][1]);
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
m-i, nlocal[igpu], kb,
dA_c(igpu, ind_c, i, 0), lddac, dt(igpu, ind_c), kb,
dC(igpu, i, 0), lddc,
dwork(igpu, ind_c), lddwork);
magma_event_record(event[igpu][ind_c], stream[igpu][1] );
}
ind_c = (ind_c+1)%2;
}
for (igpu = 0; igpu < nrgpu; ++igpu){
magma_setdevice(igpu);
magma_queue_sync( stream[igpu][1] );
}
//copy C from mgpus
for (magma_int_t i = 0; i < nbl; ++i){
magma_int_t igpu = i%nrgpu;
magma_setdevice(igpu);
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_dgetmatrix( m, kb,
dC(igpu, 0, i/nrgpu*nb_l), lddc,
C(0, i*nb_l), ldc );
// magma_dgetmatrix_async( m, kb,
// dC(igpu, 0, i/nrgpu*nb_l), lddc,
// C(0, i*nb_l), ldc, stream[igpu][0] );
}
} else {
fprintf(stderr, "The case (side == right) is not implemented\n");
magma_xerbla( __func__, 1 );
return *info;
/*
if ( notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
mi = m;
ic = 0;
for (i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3)
{
ib = min(nb, k - i);
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
i__4 = nq - i;
lapackf77_dlarft("F", "C", &i__4, &ib, A(i, i), &lda,
&tau[i], t, &ib);
// 1) copy the panel from A to the GPU, and
// 2) Put 0s in the upper triangular part of dA;
magma_dsetmatrix( i__4, ib, A(i, i), lda, dA(i, 0), ldda );
magmablas_dsetdiag1subdiag0('L', ib, ib, dA(i, 0), ldda);
// H or H' is applied to C(1:m,i:n)
ni = n - i;
jc = i;
// Apply H or H'; First copy T to the GPU
magma_dsetmatrix( ib, ib, t, ib, dt, ib );
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dA(i, 0), ldda, dt, ib,
dC(ic, jc), lddc,
dwork, lddwork);
}
*/
}
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
for (igpu = 0; igpu < nrgpu; ++igpu){
magma_setdevice(igpu);
magmablasSetKernelStream(NULL);
magma_event_destroy( event[igpu][0] );
magma_event_destroy( event[igpu][1] );
magma_queue_destroy( stream[igpu][0] );
magma_queue_destroy( stream[igpu][1] );
magma_free( dw[igpu] );
}
magma_setdevice(gpu_b);
return *info;
} /* magma_dormqr */
extern "C" magma_err_t
magma_dgeqrf_gpu( magma_int_t m, magma_int_t n,
magmaDouble_ptr dA, size_t dA_offset, magma_int_t ldda,
double *tau, magmaDouble_ptr dT, size_t dT_offset,
magma_int_t *info, magma_queue_t queue)
{
/* -- clMAGMA (version 1.1.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2014
Purpose
=======
DGEQRF computes a QR factorization of a DOUBLE_PRECISION M-by-N matrix A:
A = Q * R. 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
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) DOUBLE_PRECISION array on the GPU, dimension (LDDA,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).
LDDA (input) INTEGER
The leading dimension of the array A. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
TAU (output) DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
dT (workspace/output) DOUBLE_PRECISION array on the GPU,
dimension (2*MIN(M, N) + (N+31)/32*32 )*NB,
where NB can be obtained through magma_get_dgeqrf_nb(M).
It starts with MIN(M,N)*NB block that store the triangular T
matrices, followed by the MIN(M,N)*NB block of the diagonal
inverses for the R matrix. The rest of the array is used as workspace.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
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 real scalar, and v is a real 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).
===================================================================== */
#define a_ref(a_1,a_2) dA, (dA_offset + (a_1) + (a_2)*(ldda))
#define t_ref(a_1) dT, (dT_offset + (a_1)*nb)
#define d_ref(a_1) dT, (dT_offset + (minmn + (a_1))*nb)
#define dd_ref(a_1) dT, (dT_offset + (2*minmn+(a_1))*nb)
#define work_ref(a_1) ( work + (a_1))
#define hwork ( work + (nb)*(m))
magma_int_t i, k, minmn, old_i, old_ib, rows, cols;
magma_int_t ib, nb;
magma_int_t ldwork, lddwork, lwork, lhwork;
double *work, *ut;
/* check arguments */
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
k = minmn = min(m,n);
if (k == 0)
return *info;
nb = magma_get_dgeqrf_nb(m);
lwork = (m + n + nb)*nb;
lhwork = lwork - m*nb;
if (MAGMA_SUCCESS != magma_dmalloc_cpu( &work, lwork )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
ut = hwork+nb*(n);
memset( ut, 0, nb*nb*sizeof(double));
magma_event_t event[2] = {NULL, NULL};
ldwork = m;
lddwork= n;
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially */
old_i = 0; old_ib = nb;
for (i = 0; i < k-nb; i += nb) {
ib = min(k-i, nb);
rows = m -i;
magma_dgetmatrix_async( rows, ib,
a_ref(i,i), ldda,
work_ref(i), 0, ldwork, queue, &event[1] );
if (i>0){
/* Apply H' to A(i:m,i+2*ib:n) from the left */
cols = n-old_i-2*old_ib;
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
m-old_i, cols, old_ib,
a_ref(old_i, old_i ), ldda, t_ref(old_i), nb,
a_ref(old_i, old_i+2*old_ib), ldda, dd_ref(0), lddwork, queue);
/* store the diagonal */
magma_dsetmatrix_async( old_ib, old_ib,
ut, 0, old_ib,
d_ref(old_i), old_ib, queue, &event[0] );
}
magma_event_sync(event[1]);
lapackf77_dgeqrf(&rows, &ib, work_ref(i), &ldwork, tau+i, hwork, &lhwork, info);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
work_ref(i), &ldwork, tau+i, hwork, &ib);
/* Put 0s in the upper triangular part of a panel (and 1s on the
diagonal); copy the upper triangular in ut and invert it */
magma_event_sync(event[0]);
dsplit_diag_block(ib, work_ref(i), ldwork, ut);
magma_dsetmatrix( rows, ib, work_ref(i), 0, ldwork, a_ref(i,i), ldda, queue);
if (i + ib < n) {
/* Send the triangular factor T to the GPU */
magma_dsetmatrix( ib, ib, hwork, 0, ib, t_ref(i), nb, queue );
if (i+nb < k-nb){
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
a_ref(i, i ), ldda, t_ref(i), nb,
a_ref(i, i+ib), ldda, dd_ref(0), lddwork, queue);
}
else {
cols = n-i-ib;
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, cols, ib,
a_ref(i, i ), ldda, t_ref(i), nb,
a_ref(i, i+ib), ldda, dd_ref(0), lddwork, queue);
/* Fix the diagonal block */
magma_dsetmatrix( ib, ib, ut, 0, ib, d_ref(i), ib , queue);
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
rows = m-i;
magma_dgetmatrix( rows, ib, a_ref(i, i), ldda, work, 0, rows, queue );
lhwork = lwork - rows*ib;
lapackf77_dgeqrf(&rows, &ib, work, &rows, tau+i, work+ib*rows, &lhwork, info);
magma_dsetmatrix( rows, ib, work, 0, rows, a_ref(i, i), ldda, queue );
}
magma_free_cpu( work );
return *info;
} /* magma_dgeqrf */
extern "C" magma_int_t
magma_dorgqr_gpu(magma_int_t m, magma_int_t n, magma_int_t k,
double *dA, magma_int_t ldda,
double *tau,
double *dT, magma_int_t nb,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DORGQR generates an M-by-N DOUBLE_PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF_GPU.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
DA (input/output) DOUBLE_PRECISION array A on the GPU, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
LDDA (input) INTEGER
The first dimension of the array A. LDDA >= max(1,M).
TAU (input) DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
DT (input/workspace) DOUBLE_PRECISION work space array on the GPU,
dimension (2*MIN(M, N) + (N+31)/32*32 )*NB.
This must be the 6th argument of magma_dgeqrf_gpu
[ note that if N here is bigger than N in magma_dgeqrf_gpu,
the workspace requirement DT in magma_dgeqrf_gpu must be
as specified in this routine ].
NB (input) INTEGER
This is the block size used in DGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
===================================================================== */
#define dA(i,j) (dA + (i) + (j)*ldda)
#define dT(j) (dT + (j)*nb)
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, lpanel;
magma_int_t i, ib, ki, kk, iinfo;
magma_int_t lddwork;
double *dV, *dW;
double *work, *panel;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (ldda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min( k, ki+nb );
} else {
ki = 0;
kk = 0;
}
// Allocate CPU work space
// n*nb for dorgqr workspace
// (m - kk)*(n - kk) for last block's panel
lwork = n*nb;
lpanel = (m - kk)*(n - kk);
magma_dmalloc_cpu( &work, lwork + lpanel );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
panel = work + lwork;
// Allocate work space on GPU
if (MAGMA_SUCCESS != magma_dmalloc( &dV, ldda*nb )) {
magma_free_cpu( work );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
// dT workspace has:
// 2*min(m,n)*nb for T and R^{-1} matrices from geqrf
// ((n+31)/32*32 )*nb for dW larfb workspace.
lddwork = min(m,n);
dW = dT + 2*lddwork*nb;
magma_queue_t stream;
magma_queue_create( &stream );
// Use unblocked code for the last or only block.
if (kk < n) {
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
magma_dgetmatrix( m_kk, k_kk,
dA(kk, kk), ldda, panel, m_kk );
lapackf77_dorgqr( &m_kk, &n_kk, &k_kk,
panel, &m_kk,
&tau[kk], work, &lwork, &iinfo );
magma_dsetmatrix( m_kk, n_kk,
panel, m_kk, dA(kk, kk), ldda );
// Set A(1:kk,kk+1:n) to zero.
magmablas_dlaset( MagmaUpperLower, kk, n - kk, dA(0, kk), ldda );
}
if (kk > 0) {
// Use blocked code
// stream: copy Aii to V --> laset --> laset --> larfb --> [next]
// CPU has no computation
magmablasSetKernelStream( stream );
for (i = ki; i >= 0; i -= nb) {
ib = min( nb, k-i );
mi = m - i;
// Copy current panel on the GPU from dA to dV
magma_dcopymatrix_async( mi, ib,
dA(i,i), ldda,
dV, ldda, stream );
// set panel to identity
magmablas_dlaset( MagmaUpperLower, i, ib, dA(0, i), ldda );
magmablas_dlaset_identity( mi, ib, dA(i, i), ldda );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, n-i, ib,
dV, ldda, dT(i), nb,
dA(i, i), ldda, dW, lddwork );
}
}
}
magma_queue_sync( stream );
magmablasSetKernelStream( NULL );
magma_free( dV );
magma_free_cpu( work );
magma_queue_destroy( stream );
return *info;
} /* magma_dorgqr_gpu */
/**
Purpose
-------
DGEQRF computes a QR factorization of a DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
\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_dgeqrf_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 real scalar, and v is a real 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_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dgeqrf(
magma_int_t m, magma_int_t n,
double *A, magma_int_t lda,
double *tau,
double *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 double c_one = MAGMA_D_ONE;
/* Local variables */
magmaDouble_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_dgeqrf_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_dmake_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_dgeqrf_m( ngpu, m, n, A, lda, tau, work, lwork, info );
}
// allocate space for dA, dwork, and dT
if (MAGMA_SUCCESS != magma_dmalloc( &dA, n*ldda + nb*lddwork + nb*nb )) {
/* alloc failed so call non-GPU-resident version */
return magma_dgeqrf_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] );
//used for timing CPU and GPU
int iter = 0;
float cpu_time = 0.0;
float gpu_time = 0.0;
int affinity = map_cpu(0);
if(affinity != 0)
{
printf("affinity failed\n");
return -1;
}
magma_set_lapack_numthreads(1);
// for initial setting, better to be automatic in the future
// SetGPUFreq(324, 324);
// system("echo 1200000 > /sys/devices/system/cpu/cpu0/cpufreq/scaling_setspeed");
SetGPUFreq(2600, 705);
system("echo 2500000 > /sys/devices/system/cpu/cpu0/cpufreq/scaling_setspeed");
double gpu_iter1_low = 2096.544434;
double gpu_iter1_high = 478.825226;
double cpu_iter1_low = 1792.011230;
double cpu_iter1_high = 1413.732788;
double gpu_pred_high = gpu_iter1_high;
double gpu_pred_low = gpu_iter1_low;
double cpu_pred_high = cpu_iter1_high;
double cpu_pred_low = cpu_iter1_low;
double ratio_split_freq = 0;
double time_until_interrupt = 0;
cudaEvent_t start_cpu, stop_cpu;
cudaEvent_t start_gpu, stop_gpu;
// switches for different modes
bool timing = false; //for initial setting only, greatly impact performance
bool dvfs = false; //turn on dvfs energy saving
bool relax = false; //turn on relax scheme
bool r2h = false; // turn on race to halt
//these parameters need to be tuned in future works.
double dvfs_converage = 0.5;
double prediction_offset_gpu = 0.65;
double prediction_offset_cpu = 0.65;
//for nvprof profiler, brings slight constant performance overhead
//cudaProfilerStart();
if ( (nb > 1) && (nb < min_mn) ) {
/* Use blocked code initially.
Asynchronously send the matrix to the GPU except the first panel. */
magma_dsetmatrix_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_dgetmatrix_async( m-i, ib,
dA(i,i), ldda,
A(i,i), lda, queues[0] );
if (timing) {
//start gpu timing
cudaEventCreate(&start_gpu);
cudaEventCreate(&stop_gpu);
cudaEventRecord(start_gpu, 0);
}
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_dlarfb_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] );
double ratio_slack_pred = 1.0 - (double)nb/(m-iter*nb);
cpu_pred_high = cpu_pred_high * ratio_slack_pred;
cpu_pred_low = cpu_pred_low * ratio_slack_pred;
gpu_pred_high = gpu_pred_high * ratio_slack_pred * ratio_slack_pred;
gpu_pred_low = gpu_pred_low * ratio_slack_pred * ratio_slack_pred;
if (timing) {
printf("iter:%d GPU time pred:%f\n", iter, gpu_pred_high);
printf("iter:%d CPU time pred:%f\n", iter, cpu_pred_high);
}
if (iter < dvfs_converage*(min_mn-nb)/nb) {
if (cpu_pred_high > gpu_pred_high) { //slack on GPU
ratio_split_freq = (cpu_pred_high - gpu_pred_high) / (gpu_pred_high * ((gpu_iter1_low / gpu_iter1_high) - 1));
time_until_interrupt = gpu_pred_low * ratio_split_freq;
//printf("iter:%d time_until_interrupt:%f\n", iter, time_until_interrupt);
// printf("iter:%d ratio_split_freq:%f\n", iter, ratio_split_freq);
if (dvfs) {
if ((!relax) || (relax && ratio_split_freq > 0.05)) {
if (ratio_split_freq < 1)
dvfs_adjust(time_until_interrupt*prediction_offset_gpu, 'g');
else
dvfs_adjust(cpu_pred_high, 'g');
}
} else if (r2h) {
r2h_adjust(gpu_pred_high, cpu_pred_high - gpu_pred_high, 'g');
}
} else { //slack on CPU
ratio_split_freq = (gpu_pred_high - cpu_pred_high) / (cpu_pred_high * ((cpu_iter1_low / cpu_iter1_high) - 1));
time_until_interrupt = cpu_pred_low * ratio_split_freq;
if (dvfs) {
if ((!relax) || (relax && ratio_split_freq > 0.05)) {
if (ratio_split_freq < 1)
dvfs_adjust(time_until_interrupt*prediction_offset_cpu, 'c');
else
dvfs_adjust(gpu_pred_high, 'c');
}
} else if (r2h) {
r2h_adjust(cpu_pred_high, gpu_pred_high - cpu_pred_high, 'c');
}
}
}
if (timing) {
//end gpu timing
cudaEventRecord(stop_gpu, 0);
cudaEventSynchronize(stop_gpu);
cudaEventElapsedTime(&gpu_time, start_gpu, stop_gpu);
cudaEventDestroy(start_gpu);
cudaEventDestroy(stop_gpu);
printf("iter:%d GPU time:%f\n", iter, gpu_time);
}
magma_dgetmatrix_async( i, ib,
dA(0,i), ldda,
A(0,i), lda, queues[1] );
magma_queue_sync( queues[0] );
}
magma_int_t rows = m-i;
if (timing) {
//start cpu timing
cudaEventCreate(&start_cpu);
cudaEventCreate(&stop_cpu);
cudaEventRecord(start_cpu, 0);
}
lapackf77_dgeqrf( &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_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(i,i), &lda, tau+i, work, &ib );
if (timing) {
//end cpu timing
cudaEventRecord(stop_cpu, 0);
cudaEventSynchronize(stop_cpu);
cudaEventElapsedTime(&cpu_time, start_cpu, stop_cpu);
cudaEventDestroy(start_cpu);
cudaEventDestroy(stop_cpu);
printf("iter:%d CPU time:%f\n", iter, cpu_time);
if (gpu_time < cpu_time) {
printf("slack: +\n");
} else {
printf("slack: -\n");
}
}
magma_dpanel_to_q( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
/* put i-th V matrix onto device */
magma_dsetmatrix_async( rows, ib, A(i,i), lda, dA(i,i), ldda, queues[0] );
/* put T matrix onto device */
magma_queue_sync( queues[1] );
magma_dsetmatrix_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_dlarfb_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_dq_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_dlarfb_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_dq_to_panel( MagmaUpper, ib, A(i,i), lda, work+ib*ib );
}
old_i = i;
old_ib = ib;
}
iter ++;
}
//for nvprof profiler.
//cudaProfilerStop();
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < min_mn) {
ib = n-i;
if (i != 0) {
magma_dgetmatrix( m, ib, dA(0,i), ldda, A(0,i), lda, queues[1] );
}
magma_int_t rows = m-i;
lapackf77_dgeqrf( &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_dgeqrf */
/**
Purpose
-------
DORGQR generates an M-by-N DOUBLE_PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF_GPU.
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. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
dA DOUBLE_PRECISION array A on the GPU, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
ldda INTEGER
The first dimension of the array A. LDDA >= max(1,M).
@param[in]
tau DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
@param[in]
dT (workspace) DOUBLE_PRECISION work space array on the GPU,
dimension (2*MIN(M, N) + (N+31)/32*32 )*NB.
This must be the 6th argument of magma_dgeqrf_gpu
[ note that if N here is bigger than N in magma_dgeqrf_gpu,
the workspace requirement DT in magma_dgeqrf_gpu must be
as specified in this routine ].
@param[in]
nb INTEGER
This is the block size used in DGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument has an illegal value
@ingroup magma_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dorgqr_gpu(
magma_int_t m, magma_int_t n, magma_int_t k,
magmaDouble_ptr dA, magma_int_t ldda,
double *tau,
magmaDouble_ptr dT, magma_int_t nb,
magma_int_t *info)
{
#define dA(i,j) (dA + (i) + (j)*ldda)
#define dT(j) (dT + (j)*nb)
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, lpanel;
magma_int_t i, ib, ki, kk, iinfo;
magma_int_t lddwork;
magmaDouble_ptr dV, dW;
double *work, *panel;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (ldda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min( k, ki+nb );
} else {
ki = 0;
kk = 0;
}
// Allocate CPU work space
// n*nb for dorgqr workspace
// (m - kk)*(n - kk) for last block's panel
lwork = n*nb;
lpanel = (m - kk)*(n - kk);
magma_dmalloc_cpu( &work, lwork + lpanel );
if ( work == NULL ) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
panel = work + lwork;
// Allocate work space on GPU
if (MAGMA_SUCCESS != magma_dmalloc( &dV, ldda*nb )) {
magma_free_cpu( work );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
// dT workspace has:
// 2*min(m,n)*nb for T and R^{-1} matrices from geqrf
// ((n+31)/32*32 )*nb for dW larfb workspace.
lddwork = min(m,n);
dW = dT + 2*lddwork*nb;
magma_queue_t stream;
magma_queue_create( &stream );
// Use unblocked code for the last or only block.
if (kk < n) {
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
magma_dgetmatrix( m_kk, k_kk,
dA(kk, kk), ldda, panel, m_kk );
lapackf77_dorgqr( &m_kk, &n_kk, &k_kk,
panel, &m_kk,
&tau[kk], work, &lwork, &iinfo );
magma_dsetmatrix( m_kk, n_kk,
panel, m_kk, dA(kk, kk), ldda );
// Set A(1:kk,kk+1:n) to zero.
magmablas_dlaset( MagmaFull, kk, n - kk, c_zero, c_zero, dA(0, kk), ldda );
}
if (kk > 0) {
// Use blocked code
// stream: copy Aii to V --> laset --> laset --> larfb --> [next]
// CPU has no computation
magmablasSetKernelStream( stream );
for (i = ki; i >= 0; i -= nb) {
ib = min( nb, k-i );
mi = m - i;
// Copy current panel on the GPU from dA to dV
magma_dcopymatrix_async( mi, ib,
dA(i,i), ldda,
dV, ldda, stream );
// set panel to identity
magmablas_dlaset( MagmaFull, i, ib, c_zero, c_zero, dA(0, i), ldda );
magmablas_dlaset( MagmaFull, mi, ib, c_zero, c_one, dA(i, i), ldda );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, n-i, ib,
dV, ldda, dT(i), nb,
dA(i, i), ldda, dW, lddwork );
}
}
}
magma_queue_sync( stream );
magma_free( dV );
magma_free_cpu( work );
magma_queue_destroy( stream );
magmablasSetKernelStream( orig_stream );
return *info;
} /* magma_dorgqr_gpu */
extern "C" void magma_dbulge_applyQ(
magma_int_t WANTZ, magma_side_t SIDE, magma_int_t NE, magma_int_t N, magma_int_t NB,
magma_int_t Vblksiz, double *E, magma_int_t LDE,
double *V, double *TAU, double *T,
magma_int_t *INFO, double *dV, double *dT,
double *dE, magma_int_t copytype )
{
//%===========================
//% local variables
//%===========================
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t LDT, LDV, blklen, firstcolj;
magma_int_t bg, nbGblk, rownbm, k, m, n;
magma_int_t st, ed, fst, vlen, vnb, colj, len;
magma_int_t blkid, vpos, taupos, tpos;
//double *WORK;
magma_int_t LWORK;
magma_int_t cur_blksiz, avai_blksiz, ncolinvolvd;
magma_int_t nbgr, colst, coled, versionL, versionR;
magma_int_t blkcnt=-1;
*INFO=0;
versionL = 113;
versionR = 92;
LDT = Vblksiz;
LDV = NB+Vblksiz-1;
blklen = LDV*Vblksiz;
nbGblk = plasma_ceildiv((N-1), Vblksiz);
//magma_dmalloc_cpu( &WORK, LWORK );
/* find the size of the matrix T V*/
findVTsiz(N, NB, Vblksiz, &blkcnt, &LDV);
/* Copy E & V & T to the GPU in dE and dV and dT
* depending on copytype:
* 1: mean copy only V
* 2: mean copy V and T
* 3: mean copy V, T and E
* */
if (copytype > 0) magma_dsetmatrix( LDV, blkcnt*Vblksiz, V, LDV, dV, LDV );
if (copytype > 1) magma_dsetmatrix( LDT, blkcnt*Vblksiz, T, LDT, dT, LDT );
if (copytype > 2) magma_dsetmatrix( N, NE, E, N, dE, N );
double *dwork;
magma_int_t ldwork;
ldwork = NE;
LWORK = 2*N*max(Vblksiz, 64);
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, LWORK )) {
printf ("!!!! magma_dbulge_applyQ magma_alloc failed for: dwork\n" );
exit(-1);
}
/* SIDE LEFT meaning apply E = Q*E = (q_1*q_2*.....*q_n) * E ==> so traverse Vs in reverse order (forward) from q_n to q_1
* Also E is splitten by row meaning each apply consist in a block of row (horizontal block) */
/* SIDE RIGHT meaning apply E = E*Q = E * (q_1*q_2*.....*q_n) ==> so tarverse Vs in normal order (forward) from q_1 to q_n
* Also E is splitten by col meaning each apply consist in a block of col (vertical block) */
/* WANTZ = 1 meaning E is IDENTITY so form Q using optimized update.
* So we use the reverse order from small q to large one,
* so from q_n to q_1 so Left update to Identity.
* Use versionL 113 because in 114 we need to update the whole matrix and not in icreasing order.
* WANTZ = 2 meaning E is a full matrix and need to be updated from Left or Right so use normal update
* */
if (WANTZ == 1) {
versionL=113;
SIDE = MagmaLeft;
//set the matrix to Identity here to avoid copying it from the CPU
magmablas_dlaset( MagmaFull, N, N, c_zero, c_one, dE, N );
}
printf(" APPLY Q_v115 GPU with N %d NB %d Vblksiz %d SIDE %c versionL %d versionR %d WANTZ %d \n",
(int) N, (int) NB, (int) Vblksiz, SIDE, (int) versionL, (int) versionR, (int) WANTZ);
#if defined(USESTREAM)
magma_int_t N2=N/2;
magma_int_t N1=N-N2;
printf("using stream\n");
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
#endif
if (SIDE == MagmaLeft) {
if (versionL == 113) {
for (bg = nbGblk; bg > 0; bg--) {
firstcolj = (bg-1)*Vblksiz + 1;
if (bg == nbGblk)
rownbm = plasma_ceildiv((N-(firstcolj)), NB); // last blk has size=1 used for real to handle A(N,N-1)
else
rownbm = plasma_ceildiv((N-(firstcolj+1)), NB);
for (m = rownbm; m > 0; m--) {
vlen = 0;
vnb = 0;
colj = (bg-1)*Vblksiz; // for k=0; I compute the fst and then can remove it from the loop
fst = (rownbm -m)*NB+colj +1;
for (k=0; k < Vblksiz; k++) {
colj = (bg-1)*Vblksiz + k;
st = (rownbm -m)*NB+colj +1;
ed = min(st+NB-1, N-1);
if (st > ed) break;
if ((st == ed) && (colj != N-2)) break;
vlen=ed-fst+1;
vnb=k+1;
}
colst = (bg-1)*Vblksiz;
findVTpos(N, NB, Vblksiz, colst, fst, &vpos, &taupos, &tpos, &blkid);
printf("voici bg %d m %d vlen %d vnb %d fcolj %d vpos %d taupos %d \n", (int) bg, (int) m, (int) vlen, (int) vnb, (int) colst+1, (int) vpos+1, (int) taupos+1);
if ((vlen > 0) && (vnb > 0)) {
if (WANTZ == 1) {
len = N-colst;
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, len, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,colst), LDE, dwork, len);
} else {
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, NE, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,0), LDE, dwork, NE);
}
}
}
}
} else if (versionL == 114) {
rownbm = plasma_ceildiv((N-1), NB);
for (m = rownbm; m > 0; m--) {
ncolinvolvd = min(N-1, m*NB);
avai_blksiz=min(Vblksiz, ncolinvolvd);
nbgr = plasma_ceildiv(ncolinvolvd, avai_blksiz);
for (n = nbgr; n > 0; n--) {
vlen = 0;
vnb = 0;
cur_blksiz = min(ncolinvolvd-(n-1)*avai_blksiz, avai_blksiz);
colst = (n-1)*avai_blksiz;
coled = colst + cur_blksiz -1;
fst = (rownbm -m)*NB+colst +1;
for (colj=colst; colj <= coled; colj++) {
st = (rownbm -m)*NB+colj +1;
ed = min(st+NB-1, N-1);
if (st > ed) break;
if ((st == ed) && (colj != N-2)) break;
vlen=ed-fst+1;
vnb=vnb+1;
}
findVTpos(N, NB, Vblksiz, colst, fst, &vpos, &taupos, &tpos, &blkid);
//printf("voici bg %d m %d vlen %d vnb %d fcolj %d vpos %d taupos %d \n", bg, m, vlen, vnb, colst+1, vpos+1, taupos+1);
if ((vlen > 0) && (vnb > 0)) {
#if defined(USESTREAM)
magmablasSetKernelStream(stream[0]);
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, N1, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,0), LDE, dwork, N1);
magmablasSetKernelStream(stream[1]);
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, N2, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,N1), LDE, &dwork[N1*Vblksiz], N2);
#else
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise, vlen, NE, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(fst,0), LDE, dwork, NE);
#endif
}
}
}
}
} else if (SIDE == MagmaRight) {
if (versionR == 91) {
for (bg =1; bg <= nbGblk; bg++) {
firstcolj = (bg-1)*Vblksiz + 1;
rownbm = plasma_ceildiv((N-(firstcolj+1)), NB);
if (bg == nbGblk) rownbm = plasma_ceildiv((N-(firstcolj)), NB); // last blk has size=1 used for real to handle A(N,N-1)
for (m = 1; m <= rownbm; m++) {
vlen = 0;
vnb = 0;
// for k=0; I compute the fst and then can remove it from the loop
colj = (bg-1)*Vblksiz;
fst = (rownbm -m)*NB+colj +1;
for (k=0; k < Vblksiz; k++) {
colj = (bg-1)*Vblksiz + k;
st = (rownbm -m)*NB+colj +1;
ed = min(st+NB-1, N-1);
if (st > ed) break;
if ((st == ed) && (colj != N-2)) break;
vlen=ed-fst+1;
vnb=k+1;
}
colj = (bg-1)*Vblksiz;
findVTpos(N, NB, Vblksiz, colj, fst, &vpos, &taupos, &tpos, &blkid);
//printf("voici bg %d m %d vlen %d vnb %d fcolj %d vpos %d taupos %d \n", bg, m, vlen, vnb, colj, vpos, taupos);
if ((vlen > 0) && (vnb > 0)) {
#if defined(USESTREAM)
magmablasSetKernelStream(stream[0]);
magma_dlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, N1, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(0, fst), LDE, dwork, N1);
magmablasSetKernelStream(stream[1]);
magma_dlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, N2, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(N1, fst), LDE, &dwork[N1*Vblksiz], N2);
#else
magma_dlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, NE, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(0, fst), LDE, dwork, NE);
#endif
}
}
}
} else if (versionR == 92) {
rownbm = plasma_ceildiv((N-1), NB);
for (m = 1; m <= rownbm; m++) {
ncolinvolvd = min(N-1, m*NB);
avai_blksiz=min(Vblksiz, ncolinvolvd);
nbgr = plasma_ceildiv(ncolinvolvd, avai_blksiz);
for (n = 1; n <= nbgr; n++) {
vlen = 0;
vnb = 0;
cur_blksiz = min(ncolinvolvd-(n-1)*avai_blksiz, avai_blksiz);
colst = (n-1)*avai_blksiz;
coled = colst + cur_blksiz -1;
fst = (rownbm -m)*NB+colst +1;
for (colj=colst; colj <= coled; colj++) {
st = (rownbm -m)*NB+colj +1;
ed = min(st+NB-1, N-1);
if (st > ed) break;
if ((st == ed) && (colj != N-2)) break;
vlen=ed-fst+1;
vnb=vnb+1;
}
findVTpos(N, NB, Vblksiz, colst, fst, &vpos, &taupos, &tpos, &blkid);
if ((vlen > 0) && (vnb > 0)) {
#if defined(USESTREAM)
magmablasSetKernelStream(stream[0]);
magma_dlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, N1, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(0, fst), LDE, dwork, N1);
magmablasSetKernelStream(stream[1]);
magma_dlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, N2, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(N1, fst), LDE, &dwork[N1*Vblksiz], N2);
#else
magma_dlarfb_gpu( MagmaRight, MagmaNoTrans, MagmaForward, MagmaColumnwise, NE, vlen, vnb, dV(vpos), LDV, dT(tpos), LDT, dE(0, fst), LDE, dwork, NE);
#endif
}
}
}
}
} else {
printf("ERROR SIDE %d\n", SIDE);
}
#if defined(USESTREAM)
magmablasSetKernelStream(NULL);
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
#endif
}
/**
Purpose
-------
DORMQR overwrites the general real M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaTrans: Q**H * C C * Q**H
@endverbatim
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = MagmaLeft and of order N
if SIDE = MagmaRight.
Arguments
---------
@param[in]
ngpu INTEGER
Number of GPUs to use. ngpu > 0.
@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;
- = MagmaTrans: 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 DOUBLE PRECISION 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
DGEQRF in the first k columns of its array argument A.
@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 DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
@param[in,out]
C DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK.
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 by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dormqr_m(
magma_int_t ngpu,
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
double *C, magma_int_t ldc,
double *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i, j) (A + (j)*lda + (i))
#define C(i, j) (C + (j)*ldc + (i))
#define dC(gpui, i, j) (dw[gpui] + (j)*lddc + (i))
#define dA_c(gpui, ind, i, j) (dw[gpui] + maxnlocal*lddc + (ind)*lddar*lddac + (i) + (j)*lddac)
#define dA_r(gpui, ind, i, j) (dw[gpui] + maxnlocal*lddc + (ind)*lddar*lddac + (i) + (j)*lddar)
#define dT(gpui, ind) (dw[gpui] + maxnlocal*lddc + 2*lddac*lddar + (ind)*((nb+1)*nb))
#define dwork(gpui, ind) (dw[gpui] + maxnlocal*lddc + 2*lddac*lddar + 2*((nb+1)*nb) + (ind)*(lddwork*nb))
/* Constants */
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
/* Local variables */
const char* side_ = lapack_side_const( side );
const char* trans_ = lapack_trans_const( trans );
magma_int_t nb = 128;
double *T = NULL;
magmaDouble_ptr dw[MagmaMaxGPUs] = { NULL };
magma_queue_t queues[MagmaMaxGPUs][2] = {{ NULL }};
magma_event_t events[MagmaMaxGPUs][2] = {{ NULL }};
magma_int_t ind_c;
magma_device_t dev;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
*info = 0;
magma_int_t left = (side == MagmaLeft);
magma_int_t notran = (trans == MagmaNoTrans);
magma_int_t lquery = (lwork == -1);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
magma_int_t nq, nw;
if (left) {
nq = m;
nw = n;
} else {
nq = n;
nw = m;
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != MagmaTrans) {
*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;
}
magma_int_t lwkopt = max(1,nw) * nb;
if (*info == 0) {
work[0] = magma_dmake_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] = c_one;
return *info;
}
if (nb >= k) {
/* Use CPU code */
lapackf77_dormqr(side_, trans_, &m, &n, &k, A, &lda, tau,
C, &ldc, work, &lwork, info);
return *info;
}
magma_int_t lddc = magma_roundup( m, 64 ); // TODO why 64 instead of 32 ?
magma_int_t lddac = nq;
magma_int_t lddar = nb;
magma_int_t lddwork = nw;
magma_int_t nlocal[ MagmaMaxGPUs ] = { 0 };
magma_int_t nb_l=256;
magma_int_t nbl = magma_ceildiv( n, nb_l ); // number of blocks
magma_int_t maxnlocal = magma_ceildiv( nbl, ngpu )*nb_l;
ngpu = min( ngpu, magma_ceildiv( n, nb_l )); // Don't use GPU that will not have data.
magma_int_t ldw = maxnlocal*lddc // dC
+ 2*lddac*lddar // 2*dA
+ 2*(nb + 1 + lddwork)*nb; // 2*(dT and dwork)
if (MAGMA_SUCCESS != magma_dmalloc_pinned( &T, nb*nb )) {
*info = MAGMA_ERR_HOST_ALLOC;
goto cleanup;
}
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
if (MAGMA_SUCCESS != magma_dmalloc( &dw[dev], ldw )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
magma_queue_create( dev, &queues[dev][0] );
magma_queue_create( dev, &queues[dev][1] );
magma_event_create( &events[dev][0] );
magma_event_create( &events[dev][1] );
}
/* Use hybrid CPU-MGPU code */
if (left) {
//copy C to mgpus
for (magma_int_t i = 0; i < nbl; ++i) {
dev = i % ngpu;
magma_setdevice( dev );
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_dsetmatrix_async( m, kb,
C(0, i*nb_l), ldc,
dC(dev, 0, i/ngpu*nb_l), lddc, queues[dev][0] );
nlocal[dev] += kb;
}
magma_int_t i1, i2, i3;
if ( !notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
ind_c = 0;
for (magma_int_t i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3) {
// start the copy of A panel
magma_int_t kb = min(nb, k - i);
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_event_sync( events[dev][ind_c] ); // check if the new data can be copied
magma_dsetmatrix_async(nq-i, kb,
A(i, i), lda,
dA_c(dev, ind_c, i, 0), lddac, queues[dev][0] );
// set upper triangular part of dA to identity
magmablas_dlaset_band( MagmaUpper, kb, kb, kb, c_zero, c_one, dA_c(dev, ind_c, i, 0), lddac, queues[dev][0] );
}
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
magma_int_t nqi = nq - i;
lapackf77_dlarft("F", "C", &nqi, &kb, A(i, i), &lda,
&tau[i], T, &kb);
/* H or H' is applied to C(1:m,i:n) */
/* Apply H or H'; First copy T to the GPU */
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_dsetmatrix_async(kb, kb,
T, kb,
dT(dev, ind_c), kb, queues[dev][0] );
}
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][0] ); // check if the data was copied
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
m-i, nlocal[dev], kb,
dA_c(dev, ind_c, i, 0), lddac, dT(dev, ind_c), kb,
dC(dev, i, 0), lddc,
dwork(dev, ind_c), lddwork, queues[dev][1] );
magma_event_record(events[dev][ind_c], queues[dev][1] );
}
ind_c = (ind_c+1)%2;
}
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_queue_sync( queues[dev][1] );
}
//copy C from mgpus
for (magma_int_t i = 0; i < nbl; ++i) {
dev = i % ngpu;
magma_setdevice( dev );
magma_int_t kb = min(nb_l, n-i*nb_l);
magma_dgetmatrix( m, kb,
dC(dev, 0, i/ngpu*nb_l), lddc,
C(0, i*nb_l), ldc, queues[dev][1] );
// magma_dgetmatrix_async( m, kb,
// dC(dev, 0, i/ngpu*nb_l), lddc,
// C(0, i*nb_l), ldc, queues[dev][0] );
}
} else {
*info = MAGMA_ERR_NOT_IMPLEMENTED;
magma_xerbla( __func__, -(*info) );
goto cleanup;
/*
if ( notran ) {
i1 = 0;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb;
i2 = 0;
i3 = -nb;
}
mi = m;
ic = 0;
for (i = i1; (i3 < 0 ? i >= i2 : i < i2); i += i3) {
ib = min(nb, k - i);
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
i__4 = nq - i;
lapackf77_dlarft("F", "C", &i__4, &ib, A(i, i), &lda,
&tau[i], T, &ib);
// 1) copy the panel from A to the GPU, and
// 2) set upper triangular part of dA to identity
magma_dsetmatrix( i__4, ib, A(i, i), lda, dA(i, 0), ldda, queues[dev][1] );
magmablas_dlaset_band( MagmaUpper, ib, ib, ib, c_zero, c_one, dA(i, 0), ldda, queues[dev][1] );
// H or H' is applied to C(1:m,i:n)
ni = n - i;
jc = i;
// Apply H or H'; First copy T to the GPU
magma_dsetmatrix( ib, ib, T, ib, dT, ib, queues[dev][1] );
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dA(i, 0), ldda, dT, ib,
dC(ic, jc), lddc,
dwork, lddwork, queues[dev][1] );
}
*/
}
cleanup:
work[0] = magma_dmake_lwork( lwkopt );
for (dev = 0; dev < ngpu; ++dev) {
magma_setdevice( dev );
magma_event_destroy( events[dev][0] );
magma_event_destroy( events[dev][1] );
magma_queue_destroy( queues[dev][0] );
magma_queue_destroy( queues[dev][1] );
magma_free( dw[dev] );
}
magma_setdevice( orig_dev );
magma_free_pinned( T );
return *info;
} /* magma_dormqr */
/**
Purpose
-------
DGEQRF2_MGPU computes a QR factorization of a real M-by-N matrix A:
A = Q * R. This is a GPU interface of the routine.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
dA DOUBLE_PRECISION array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix dA.
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).
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
tau DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@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 real scalar, and v is a real 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_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dgeqrf2_mgpu( magma_int_t num_gpus, magma_int_t m, magma_int_t n,
double **dlA, magma_int_t ldda,
double *tau,
magma_int_t *info )
{
#define dlA(dev, i, j) (dlA[dev] + (i) + (j)*(ldda))
#define hpanel(i) (hpanel + (i))
// set to NULL to make cleanup easy: free(NULL) does nothing.
double *dwork[MagmaMaxGPUs]={NULL}, *dpanel[MagmaMaxGPUs]={NULL};
double *hwork=NULL, *hpanel=NULL;
magma_queue_t stream[MagmaMaxGPUs][2]={{NULL}};
magma_event_t panel_event[MagmaMaxGPUs]={NULL};
magma_int_t i, j, min_mn, dev, ldhpanel, lddwork, rows;
magma_int_t ib, nb;
magma_int_t lhwork, lwork;
magma_int_t panel_dev, i_local, i_nb_local, n_local[MagmaMaxGPUs], la_dev, dpanel_offset;
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
min_mn = min(m,n);
if (min_mn == 0)
return *info;
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
nb = magma_get_dgeqrf_nb( m );
/* dwork is (n*nb) --- for T (nb*nb) and dlarfb work ((n-nb)*nb) ---
* + dpanel (ldda*nb), on each GPU.
* I think dlarfb work could be smaller, max(n_local[:]).
* Oddly, T and dlarfb work get stacked on top of each other, both with lddwork=n.
* on GPU that owns panel, set dpanel = dlA(dev,i,i_local).
* on other GPUs, set dpanel = dwork[dev] + dpanel_offset. */
lddwork = n;
dpanel_offset = lddwork*nb;
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
if ( MAGMA_SUCCESS != magma_dmalloc( &(dwork[dev]), (lddwork + ldda)*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto CLEANUP;
}
}
/* hwork is MAX( workspace for dgeqrf (n*nb), two copies of T (2*nb*nb) )
* + hpanel (m*nb).
* for last block, need 2*n*nb total. */
ldhpanel = m;
lhwork = max( n*nb, 2*nb*nb );
lwork = max( lhwork + ldhpanel*nb, 2*n*nb );
if ( MAGMA_SUCCESS != magma_dmalloc_pinned( &hwork, lwork )) {
*info = MAGMA_ERR_HOST_ALLOC;
goto CLEANUP;
}
hpanel = hwork + lhwork;
/* Set the number of local n for each GPU */
for( dev=0; dev < num_gpus; dev++ ) {
n_local[dev] = ((n/nb)/num_gpus)*nb;
if (dev < (n/nb) % num_gpus)
n_local[dev] += nb;
else if (dev == (n/nb) % num_gpus)
n_local[dev] += n % nb;
}
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_queue_create( &stream[dev][0] );
magma_queue_create( &stream[dev][1] );
magma_event_create( &panel_event[dev] );
}
if ( nb < min_mn ) {
/* Use blocked code initially */
// Note: as written, ib cannot be < nb.
for( i = 0; i < min_mn-nb; i += nb ) {
/* Set the GPU number that holds the current panel */
panel_dev = (i/nb) % num_gpus;
/* Set the local index where the current panel is (j == i) */
i_local = i/(nb*num_gpus)*nb;
ib = min(min_mn-i, nb);
rows = m-i;
/* Send current panel to the CPU, after panel_event indicates it has been updated */
magma_setdevice( panel_dev );
magma_queue_wait_event( stream[panel_dev][1], panel_event[panel_dev] );
magma_dgetmatrix_async( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hpanel(i), ldhpanel, stream[panel_dev][1] );
magma_queue_sync( stream[panel_dev][1] );
// Factor panel
lapackf77_dgeqrf( &rows, &ib, hpanel(i), &ldhpanel, tau+i,
hwork, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %d\n", (int) *info );
}
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
hpanel(i), &ldhpanel, tau+i, hwork, &ib );
dpanel_to_q( MagmaUpper, ib, hpanel(i), ldhpanel, hwork + ib*ib );
// Send the current panel back to the GPUs
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
if (dev == panel_dev)
dpanel[dev] = dlA(dev, i, i_local);
else
dpanel[dev] = dwork[dev] + dpanel_offset;
magma_dsetmatrix_async( rows, ib,
hpanel(i), ldhpanel,
dpanel[dev], ldda, stream[dev][0] );
}
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_queue_sync( stream[dev][0] );
}
// TODO: if dpanel_to_q copied whole block, wouldn't need to restore
// -- just send the copy to the GPUs.
// TODO: also, could zero out the lower triangle and use Azzam's larfb w/ gemm.
/* Restore the panel */
dq_to_panel( MagmaUpper, ib, hpanel(i), ldhpanel, hwork + ib*ib );
if (i + ib < n) {
/* Send the T matrix to the GPU. */
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_dsetmatrix_async( ib, ib,
hwork, ib,
dwork[dev], lddwork, stream[dev][0] );
}
la_dev = (panel_dev+1) % num_gpus;
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magmablasSetKernelStream( stream[dev][0] );
if (dev == la_dev && i+nb < min_mn-nb) {
// If not last panel,
// for look-ahead panel, apply H' to A(i:m,i+ib:i+2*ib)
i_nb_local = (i+nb)/(nb*num_gpus)*nb;
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local), ldda, // C
dwork[dev]+ib, lddwork ); // work
magma_event_record( panel_event[dev], stream[dev][0] );
// for trailing matrix, apply H' to A(i:m,i+2*ib:n)
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[dev]-(i_nb_local+ib), ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local+ib), ldda, // C
dwork[dev]+ib, lddwork ); // work
}
else {
// for trailing matrix, apply H' to A(i:m,i+ib:n)
i_nb_local = i_local;
if (dev <= panel_dev) {
i_nb_local += ib;
}
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n_local[dev]-i_nb_local, ib,
dpanel[dev], ldda, // V
dwork[dev], lddwork, // T
dlA(dev, i, i_nb_local), ldda, // C
dwork[dev]+ib, lddwork ); // work
}
}
// Restore top of panel (after larfb is done)
magma_setdevice( panel_dev );
magma_dsetmatrix_async( ib, ib,
hpanel(i), ldhpanel,
dlA(panel_dev, i, i_local), ldda, stream[panel_dev][0] );
}
}
}
else {
i = 0;
}
/* Use unblocked code to factor the last or only block row. */
if (i < min_mn) {
rows = m-i;
for( j=i; j < n; j += nb ) {
panel_dev = (j/nb) % num_gpus;
i_local = j/(nb*num_gpus)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_dgetmatrix( rows, ib,
dlA(panel_dev, i, i_local), ldda,
hwork + (j-i)*rows, rows );
}
// needs lwork >= 2*n*nb:
// needs (m-i)*(n-i) for last block row, bounded by nb*n.
// needs (n-i)*nb for dgeqrf work, bounded by n*nb.
ib = n-i; // total columns in block row
lhwork = lwork - ib*rows;
lapackf77_dgeqrf( &rows, &ib, hwork, &rows, tau+i, hwork + ib*rows, &lhwork, info );
if ( *info != 0 ) {
fprintf( stderr, "error %d\n", (int) *info );
}
for( j=i; j < n; j += nb ) {
panel_dev = (j/nb) % num_gpus;
i_local = j/(nb*num_gpus)*nb;
ib = min( n-j, nb );
magma_setdevice( panel_dev );
magma_dsetmatrix( rows, ib,
hwork + (j-i)*rows, rows,
dlA(panel_dev, i, i_local), ldda );
}
}
CLEANUP:
// free(NULL) does nothing.
for( dev=0; dev < num_gpus; dev++ ) {
magma_setdevice( dev );
magma_queue_destroy( stream[dev][0] );
magma_queue_destroy( stream[dev][1] );
magma_event_destroy( panel_event[dev] );
magma_free( dwork[dev] );
}
magma_free_pinned( hwork );
magma_setdevice( orig_dev );
magmablasSetKernelStream( orig_stream );
return *info;
} /* magma_dgeqrf2_mgpu */
extern "C" magma_int_t
magma_dgeqrf_ooc(magma_int_t m, magma_int_t n,
double *a, magma_int_t lda, double *tau,
double *work, magma_int_t lwork,
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DGEQRF_OOC computes a QR factorization of a DOUBLE_PRECISION 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_dgeqrf 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
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) DOUBLE_PRECISION 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).
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= N*NB,
where NB can be obtained through magma_get_dgeqrf_nb(M).
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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
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 real scalar, and v is a real 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).
===================================================================== */
#define a_ref(a_1,a_2) ( a+(a_2)*(lda) + (a_1))
#define da_ref(a_1,a_2) (da+(a_2)*ldda + (a_1))
double *da, *dwork;
double c_one = MAGMA_D_ONE;
int k, lddwork, ldda;
*info = 0;
int nb = magma_get_dgeqrf_nb(min(m, n));
int lwkopt = n * nb;
work[0] = MAGMA_D_MAKE( (double)lwkopt, 0 );
int 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,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(double);
magma_int_t IB, NB = (magma_int_t)(0.8*freeMem/m);
NB = (NB / nb) * nb;
if (NB >= n)
return magma_dgeqrf(m, n, a, lda, tau, work, lwork, info);
k = min(m,n);
if (k == 0) {
work[0] = c_one;
return *info;
}
lddwork = ((NB+31)/32)*32+nb;
ldda = ((m+31)/32)*32;
if (MAGMA_SUCCESS != magma_dmalloc( &da, (NB + nb)*ldda + nb*lddwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
// magmablasSetKernelStream(stream[1]);
double *ptr = da + ldda * NB;
dwork = da + ldda*(NB + nb);
/* start the main loop over the blocks that fit in the GPU memory */
for(int 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_dsetmatrix_async( (m), IB,
a_ref(0,i), lda,
da_ref(0,0), ldda, stream[0] );
magma_queue_sync( stream[0] );
/* 2. Update it with the previous transformations */
for(int j=0; j<min(i,k); j+=nb) {
magma_int_t ib = min(k-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.
magma_int_t rows = m-j;
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, a_ref(j,j), &lda, tau+j, work, &ib);
magma_dsetmatrix_async( ib, ib,
work, ib,
dwork, lddwork, stream[1] );
dpanel_to_q(MagmaUpper, ib, a_ref(j,j), lda, work+ib*ib);
magma_dsetmatrix_async( rows, ib,
a_ref(j,j), lda,
ptr, rows, stream[1] );
magma_queue_sync( stream[1] );
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, IB, ib,
ptr, rows, dwork, lddwork,
da_ref(j, 0), ldda, dwork+ib, lddwork);
dq_to_panel(MagmaUpper, ib, a_ref(j,j), lda, work+ib*ib);
}
/* 3. Do a QR on the current part */
if (i<k)
magma_dgeqrf2_gpu(m-i, IB, da_ref(i,0), ldda, tau+i, info);
/* 4. Copy the current part back to the CPU */
magma_dgetmatrix_async( (m), IB,
da_ref(0,0), ldda,
a_ref(0,i), lda, stream[0] );
}
magma_queue_sync( stream[0] );
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free( da );
return *info;
} /* magma_dgeqrf_ooc */
/**
Purpose
-------
DGEQRF3 computes a QR factorization of a real M-by-N matrix A:
A = Q * R.
This version stores the triangular dT matrices used in
the block QR factorization so that they can be applied directly (i.e.,
without being recomputed) later. As a result, the application
of Q is much faster. Also, the upper triangular matrices for V have 0s
in them and the corresponding parts of the upper triangular R are
stored separately in dT.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
dA DOUBLE_PRECISION array on the GPU, dimension (LDDA,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).
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
tau DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
dT (workspace) DOUBLE_PRECISION array on the GPU,
dimension (2*MIN(M, N) + (N+31)/32*32 )*NB,
where NB can be obtained through magma_get_dgeqrf_nb(M).
It starts with MIN(M,N)*NB block that store the triangular T
matrices, followed by the MIN(M,N)*NB block of the diagonal
matrices for the R matrix. The rest of the array is used as workspace.
@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 real scalar, and v is a real 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_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dgeqrf3_gpu(
magma_int_t m, magma_int_t n,
magmaDouble_ptr dA, magma_int_t ldda,
double *tau,
magmaDouble_ptr dT,
magma_int_t *info )
{
#define dA(a_1,a_2) (dA + (a_2)*(ldda) + (a_1))
#define dT(a_1) (dT + (a_1)*nb)
#define d_ref(a_1) (dT + ( minmn+(a_1))*nb)
#define dd_ref(a_1) (dT + (2*minmn+(a_1))*nb)
#define work(a_1) (work + (a_1))
#define hwork (work + (nb)*(m))
magma_int_t i, k, minmn, old_i, old_ib, rows, cols;
magma_int_t ib, nb;
magma_int_t ldwork, lddwork, lwork, lhwork;
double *work, *ut;
/* check arguments */
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
k = minmn = min(m,n);
if (k == 0)
return *info;
nb = magma_get_dgeqrf_nb(m);
lwork = (m + n + nb)*nb;
lhwork = lwork - m*nb;
if (MAGMA_SUCCESS != magma_dmalloc_pinned( &work, lwork )) {
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
ut = hwork+nb*(n);
memset( ut, 0, nb*nb*sizeof(double));
magma_queue_t stream[2];
magma_queue_create( &stream[0] );
magma_queue_create( &stream[1] );
ldwork = m;
lddwork= n;
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially */
old_i = 0; old_ib = nb;
for (i = 0; i < k-nb; i += nb) {
ib = min(k-i, nb);
rows = m -i;
magma_dgetmatrix_async( rows, ib,
dA(i,i), ldda,
work(i), ldwork, stream[1] );
if (i > 0) {
/* Apply H' to A(i:m,i+2*ib:n) from the left */
cols = n-old_i-2*old_ib;
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, cols, old_ib,
dA(old_i, old_i ), ldda, dT(old_i), nb,
dA(old_i, old_i+2*old_ib), ldda, dd_ref(0), lddwork);
/* store the diagonal */
magma_dsetmatrix_async( old_ib, old_ib,
ut, old_ib,
d_ref(old_i), old_ib, stream[0] );
}
magma_queue_sync( stream[1] );
lapackf77_dgeqrf(&rows, &ib, work(i), &ldwork, tau+i, hwork, &lhwork, info);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
work(i), &ldwork, tau+i, hwork, &ib);
/* Put 0s in the upper triangular part of a panel (and 1s on the
diagonal); copy the upper triangular in ut. */
magma_queue_sync( stream[0] );
dsplit_diag_block3(ib, work(i), ldwork, ut);
magma_dsetmatrix( rows, ib, work(i), ldwork, dA(i,i), ldda );
if (i + ib < n) {
/* Send the triangular factor T to the GPU */
magma_dsetmatrix( ib, ib, hwork, ib, dT(i), nb );
if (i+nb < k-nb) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT(i), nb,
dA(i, i+ib), ldda, dd_ref(0), lddwork);
}
else {
cols = n-i-ib;
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, cols, ib,
dA(i, i ), ldda, dT(i), nb,
dA(i, i+ib), ldda, dd_ref(0), lddwork);
/* Fix the diagonal block */
magma_dsetmatrix( ib, ib, ut, ib, d_ref(i), ib );
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
rows = m-i;
magma_dgetmatrix( rows, ib, dA(i, i), ldda, work, rows );
lhwork = lwork - rows*ib;
lapackf77_dgeqrf(&rows, &ib, work, &rows, tau+i, work+ib*rows, &lhwork, info);
magma_dsetmatrix( rows, ib, work, rows, dA(i, i), ldda );
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[1] );
magma_free_pinned( work );
return *info;
} /* magma_dgeqrf_gpu */
extern "C" magma_int_t
magma_dormqr(const char side, const char trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
double *C, magma_int_t ldc,
double *work, magma_int_t lwork,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DORMQR overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) DOUBLE_PRECISION 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
DGEQRF in the first k columns of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).
TAU (input) DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
C (input/output) DOUBLE_PRECISION array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T * C or C * Q**T or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(0) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance
LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R',
where NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
#define A(a_1,a_2) ( A + (a_1) + (a_2)*lda)
#define dC(a_1,a_2) (dC + (a_1) + (a_2)*lddc)
magma_int_t nb = magma_get_dgeqrf_nb( min( m, n ));
double c_one = MAGMA_D_ONE;
char side_[2] = {side, 0};
char trans_[2] = {trans, 0};
magma_int_t nq_i, lddwork;
magma_int_t i;
double *T;
magma_int_t i1, i2, step, ib, ic, jc, mi, ni, nq, nw;
int left, notran, lquery;
magma_int_t iinfo, lwkopt;
*info = 0;
left = lapackf77_lsame(side_, "L");
notran = lapackf77_lsame(trans_, "N");
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;
}
lwkopt = max(1,nw) * nb;
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
if (! left && ! lapackf77_lsame(side_, "R")) {
*info = -1;
} else if (! notran && ! lapackf77_lsame(trans_, MagmaTransStr)) {
*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) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
work[0] = c_one;
return *info;
}
/* Allocate work space on the GPU */
magma_int_t lddc = m;
double *dwork, *dC;
magma_dmalloc( &dC, lddc*n );
magma_dmalloc( &dwork, (m + n + nb)*nb );
if ( dC == NULL || dwork == NULL ) {
magma_free( dC );
magma_free( dwork );
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/* work space on CPU */
T = (double*) malloc( 2*nb*nb * sizeof(double) );
if ( T == NULL ) {
magma_free( dC );
magma_free( dwork );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
/* Copy matrix C from the CPU to the GPU */
magma_dsetmatrix( m, n, C, ldc, dC, lddc );
if (nb >= k) {
/* Use CPU code */
lapackf77_dormqr(side_, trans_, &m, &n, &k, A, &lda, &tau[1],
C, &ldc, work, &lwork, &iinfo);
}
else {
/* Use hybrid CPU-GPU code */
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;
jc = 0;
} else {
mi = m;
ic = 0;
}
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) H(i+1) . . . H(i+ib-1) */
nq_i = nq - i;
lapackf77_dlarft("F", "C", &nq_i, &ib, A(i,i), &lda,
&tau[i], T, &ib);
/* 1) Put 0s in the upper triangular part of A;
2) copy the panel from A to the GPU, and
3) restore A */
dpanel_to_q('U', ib, A(i,i), lda, T+ib*ib);
magma_dsetmatrix( nq_i, ib, A(i,i), lda, dwork, nq_i );
dq_to_panel('U', ib, A(i,i), lda, T+ib*ib);
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = m - i;
ic = i;
}
else {
/* H or H' is applied to C(1:m,i:n) */
ni = n - i;
jc = i;
}
if (left)
lddwork = ni;
else
lddwork = mi;
/* Apply H or H'; First copy T to the GPU */
magma_dsetmatrix( ib, ib, T, ib, dwork+nq_i*ib, ib );
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dwork, nq_i, dwork+nq_i*ib, ib,
dC(ic,jc), lddc,
dwork+nq_i*ib + ib*ib, lddwork);
}
magma_dgetmatrix( m, n, dC, lddc, C, ldc );
}
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
magma_free( dC );
magma_free( dwork );
free( T );
return *info;
} /* magma_dormqr */
extern "C" magma_int_t
magma_dormqr2_gpu(const char side, const char trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *da, magma_int_t ldda,
double *tau,
double *dc, magma_int_t lddc,
double *wa, magma_int_t ldwa,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DORMQR overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
DA (input) DOUBLE_PRECISION 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
DGEQRF in the first k columns of its array argument A.
The diagonal and the upper part
are destroyed, the reflectors are not modified.
LDDA (input) INTEGER
The leading dimension of the array DA.
LDDA >= max(1,M) if SIDE = 'L'; LDDA >= max(1,N) if SIDE = 'R'.
TAU (input) DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
DC (device input/output) DOUBLE_PRECISION array, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by (Q*C) or (Q**T * C) or (C * Q**T) or (C*Q).
LDDC (input) INTEGER
The leading dimension of the array C. LDDC >= max(1,M).
WA (input/workspace) DOUBLE_PRECISION array, dimension
(LDWA,M) if SIDE = 'L'
(LDWA,N) if SIDE = 'R'
The vectors which define the elementary reflectors, as
returned by DSYTRD_GPU.
LDWA (input) INTEGER
The leading dimension of the array A.
LDWA >= max(1,M) if SIDE = 'L'; LDWA >= max(1,N) if SIDE = 'R'.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
char side_[2] = {side, 0};
char trans_[2] = {trans, 0};
/* Allocate work space on the GPU */
double *dwork;
magma_int_t wa_offset, dc_offset, i__4, lddwork;
magma_int_t i;
double t[2*4160] /* was [65][64] */;
magma_int_t i1, i2, step, ib, ic, jc, nb, mi, ni, nq, nw;
int left, notran;
wa_offset = 1 + ldwa;
wa -= wa_offset;
--tau;
dc_offset = 1 + lddc;
dc -= dc_offset;
*info = 0;
left = lapackf77_lsame(side_, "L");
notran = lapackf77_lsame(trans_, "N");
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = n;
magma_dmalloc( &dwork, (n + 64)*64 );
} else {
nq = n;
nw = m;
magma_dmalloc( &dwork, (m + 64)*64 );
}
if (! left && ! lapackf77_lsame(side_, "R")) {
*info = -1;
} else if (! notran && ! lapackf77_lsame(trans_, "T")) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
} else if (ldwa < max(1,nq)) {
*info = -12;
}
// size of the block
nb = 64;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
return *info;
}
/* Use hybrid CPU-GPU code */
if ( ( left && (! notran) ) || ( (! left) && notran ) ) {
i1 = 1;
i2 = k;
step = nb;
} else {
i1 = ((k - 1)/nb)*nb + 1;
i2 = 1;
step = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
jc = 1;
} else {
mi = m;
ic = 1;
}
magmablas_dsetdiag1subdiag0('L', k, nb, da, ldda);
// for i=i1 to i2 by step
for (i = i1; (step < 0 ? i >= i2 : i <= i2); i += step) {
ib = min(nb, k - i + 1);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__4 = nq - i + 1;
lapackf77_dlarft("F", "C", &i__4, &ib, &wa[i + i*ldwa], &ldwa,
&tau[i], t, &ib);
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = m - i + 1;
ic = i;
}
else {
/* H or H' is applied to C(1:m,i:n) */
ni = n - i + 1;
jc = i;
}
if (left)
lddwork = ni;
else
lddwork = mi;
/* Apply H or H'; First copy T to the GPU */
magma_dsetmatrix( ib, ib, t, ib, dwork, ib );
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
da + (i - 1) + (i - 1)*ldda , ldda, dwork, ib,
&dc[ic + jc*lddc], lddc,
dwork + ib*ib, lddwork);
}
magma_free( dwork );
return *info;
} /* magma_dormqr */
/**
Purpose
-------
DORMQR overwrites the general real M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaTrans: Q**H * C C * Q**H
@endverbatim
where Q is a real unitary matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. 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;
- = MagmaTrans: 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]
dA DOUBLE_PRECISION 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
DGEQRF in the first k columns of its array argument A.
The diagonal and the upper part
are destroyed, the reflectors are not modified.
@param[in]
ldda INTEGER
The leading dimension of the array DA.
LDDA >= max(1,M) if SIDE = MagmaLeft; LDDA >= max(1,N) if SIDE = MagmaRight.
@param[in]
tau DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
@param[in,out]
dC DOUBLE_PRECISION array, dimension (LDDC,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]
lddc INTEGER
The leading dimension of the array C. LDDC >= max(1,M).
@param[in]
wA (workspace) DOUBLE_PRECISION array, dimension
(LDWA,M) if SIDE = MagmaLeft
(LDWA,N) if SIDE = MagmaRight
The vectors which define the elementary reflectors, as
returned by DSYTRD_GPU.
@param[in]
ldwa INTEGER
The leading dimension of the array wA.
LDWA >= max(1,M) if SIDE = MagmaLeft; LDWA >= max(1,N) if SIDE = MagmaRight.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dormqr2_gpu(magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *dA, magma_int_t ldda,
double *tau,
double *dC, magma_int_t lddc,
double *wA, magma_int_t ldwa,
magma_int_t *info)
{
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define dC(i_,j_) (dC + (i_) + (j_)*lddc)
#define wA(i_,j_) (wA + (i_) + (j_)*ldwa)
/* Allocate work space on the GPU */
double *dwork;
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t i, i__4, lddwork;
double T[2*4160] /* was [65][64] */;
magma_int_t i1, i2, step, ib, ic, jc, nb, mi, ni, nq, nw;
int left, notran;
wA -= 1 + ldwa;
dC -= 1 + lddc;
--tau;
*info = 0;
left = (side == MagmaLeft);
notran = (trans == MagmaNoTrans);
/* NQ is the order of Q and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = n;
magma_dmalloc( &dwork, (n + 64)*64 ); // TODO after checking args, else memory leak!
} else {
nq = n;
nw = m;
magma_dmalloc( &dwork, (m + 64)*64 ); // TODO after checking args, else memory leak!
}
if (! left && side != MagmaRight) {
*info = -1;
} else if (! notran && trans != MagmaTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
} else if (ldwa < max(1,nq)) {
*info = -12;
}
// size of the block
nb = 64;
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
return *info;
}
/* Use hybrid CPU-GPU code */
if ( ( left && (! notran) ) || ( (! left) && notran ) ) {
i1 = 1;
i2 = k;
step = nb;
} else {
i1 = ((k - 1)/nb)*nb + 1;
i2 = 1;
step = -nb;
}
// silence "uninitialized" warnings
mi = 0;
ni = 0;
if (left) {
ni = n;
jc = 1;
} else {
mi = m;
ic = 1;
}
// set nb-1 super-diagonals to 0, and diagonal to 1.
// This way we can copy V directly to the GPU,
// with the upper triangle parts already set to identity.
magmablas_dlaset_band( MagmaUpper, k, k, nb, c_zero, c_one, dA, ldda );
// for i=i1 to i2 by step
for (i = i1; (step < 0 ? i >= i2 : i <= i2); i += step) {
ib = min(nb, k - i + 1);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__4 = nq - i + 1;
lapackf77_dlarft("Forward", "Columnwise", &i__4, &ib,
wA(i,i), &ldwa, &tau[i], T, &ib);
if (left) {
/* H or H' is applied to C(i:m,1:n) */
mi = m - i + 1;
ic = i;
}
else {
/* H or H' is applied to C(1:m,i:n) */
ni = n - i + 1;
jc = i;
}
if (left)
lddwork = ni;
else
lddwork = mi;
/* Apply H or H'; First copy T to the GPU */
magma_dsetmatrix( ib, ib, T, ib, dwork, ib );
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dA(i-1,i-1), ldda, dwork, ib, // dA using 0-based indices here
dC(ic,jc), lddc,
dwork + ib*ib, lddwork);
}
magma_free( dwork );
return *info;
} /* magma_dormqr */
/**
Purpose
-------
DORMLQ overwrites the general real M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = MagmaTrans: Q**H * C C * Q**H
@endverbatim
where Q is a realunitary matrix defined as the product of k
elementary reflectors
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by DGELQF. 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;
- = MagmaTrans: 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 DOUBLE_PRECISION array, dimension
(LDA,M) if SIDE = MagmaLeft,
(LDA,N) if SIDE = MagmaRight.
The i-th row must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGELQF in the first k rows 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. LDA >= max(1,K).
@param[in]
tau DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGELQF.
@param[in,out]
C DOUBLE_PRECISION 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) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK.
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_dgelqf_comp
********************************************************************/
extern "C" magma_int_t
magma_dormlq(
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
double *C, magma_int_t ldc,
double *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)
double *T, *T2;
magma_int_t i, i1, i2, ib, ic, jc, nb, mi, ni, nq, nq_i, nw, step;
magma_int_t iinfo, ldwork, lwkopt;
magma_int_t left, notran, lquery;
magma_trans_t transt;
*info = 0;
left = (side == MagmaLeft);
notran = (trans == MagmaNoTrans);
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 != MagmaTrans) {
*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,k)) {
*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_dgelqf_nb( min( m, n ));
lwkopt = max(1,nw)*nb;
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
}
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_D_ONE;
return *info;
}
ldwork = nw;
if (nb >= k) {
/* Use CPU code */
lapackf77_dormlq( 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 = ((m+31)/32)*32;
double *dwork, *dV, *dT, *dC;
magma_dmalloc( &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_dmalloc_cpu( &T, 2*nb*nb );
if ( T == NULL ) {
magma_free( dwork );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
T2 = T + nb*nb;
/* Copy matrix C from the CPU to the GPU */
magma_dsetmatrix( m, n, C, ldc, dC, lddc );
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;
jc = 0;
} else {
mi = m;
ic = 0;
}
if (notran) {
transt = MagmaTrans;
} else {
transt = MagmaNoTrans;
}
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) H(i + 1) . . . H(i + ib-1) */
nq_i = nq - i;
lapackf77_dlarft("Forward", "Rowwise", &nq_i, &ib,
A(i,i), &lda, &tau[i], T, &ib);
/* 1) set upper triangle of panel in A to identity,
2) copy the panel from A to the GPU, and
3) restore A */
dpanel_to_q( MagmaLower, ib, A(i,i), lda, T2 );
magma_dsetmatrix( ib, nq_i, A(i,i), lda, dV, ib );
dq_to_panel( MagmaLower, ib, A(i,i), lda, T2 );
if (left) {
/* H or H**H is applied to C(i:m,1:n) */
mi = m - i;
ic = i;
}
else {
/* H or H**H is applied to C(1:m,i:n) */
ni = n - i;
jc = i;
}
/* Apply H or H**H; First copy T to the GPU */
magma_dsetmatrix( ib, ib, T, ib, dT, ib );
magma_dlarfb_gpu( side, transt, MagmaForward, MagmaRowwise,
mi, ni, ib,
dV, ib,
dT, ib,
dC(ic,jc), lddc,
dwork, ldwork );
}
magma_dgetmatrix( m, n, dC, lddc, C, ldc );
magma_free( dwork );
magma_free_cpu( T );
}
work[0] = MAGMA_D_MAKE( lwkopt, 0 );
return *info;
} /* magma_dormlq */
magma_err_t
magma_dgeqrf2_2q_gpu( magma_int_t m, magma_int_t n,
magmaDouble_ptr dA, size_t dA_offset, magma_int_t ldda,
double *tau, magma_err_t *info,
magma_queue_t* queues)
{
/* -- clMAGMA (version 1.1.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date January 2014
Purpose
=======
DGEQRF computes a QR factorization of a real M-by-N matrix A:
A = Q * R.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
dA (input/output) DOUBLE_PRECISION array on the GPU, dimension (LDDA,N)
On entry, the M-by-N matrix dA.
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).
LDDA (input) INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
dividable by 16.
TAU (output) DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
if INFO = -9, internal GPU 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 real scalar, and v is a real 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).
===================================================================== */
#define dA(a_1,a_2) dA, (dA_offset + (a_1) + (a_2)*(ldda))
#define work_ref(a_1) ( work + (a_1))
#define hwork ( work + (nb)*(m))
magmaDouble_ptr dwork;
double *work;
magma_int_t i, k, ldwork, lddwork, old_i, old_ib, rows;
magma_int_t nbmin, nx, ib, nb;
magma_int_t lhwork, lwork;
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
k = min(m,n);
if (k == 0)
return MAGMA_SUCCESS;
nb = magma_get_dgeqrf_nb(m);
lwork = (m+n) * nb;
lhwork = lwork - (m)*nb;
if ( MAGMA_SUCCESS != magma_dmalloc( &dwork, n*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
/*
if ( MAGMA_SUCCESS != magma_dmalloc_cpu( &work, lwork ) ) {
*info = MAGMA_ERR_HOST_ALLOC;
magma_free( dwork );
return *info;
}
*/
cl_mem buffer = clCreateBuffer(gContext, CL_MEM_READ_WRITE | CL_MEM_ALLOC_HOST_PTR, sizeof(double)*lwork, NULL, NULL);
work = (double*)clEnqueueMapBuffer(queues[0], buffer, CL_TRUE, CL_MAP_READ | CL_MAP_WRITE, 0, lwork*sizeof(double), 0, NULL, NULL, NULL);
nbmin = 2;
nx = 2*nb;
ldwork = m;
lddwork= n;
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
old_i = 0; old_ib = nb;
for (i = 0; i < k-nx; i += nb) {
ib = min(k-i, nb);
rows = m -i;
magma_dgetmatrix_async(rows, ib, dA(i, i), ldda, work_ref(i), 0, ldwork, queues[0], NULL);
clFlush(queues[0]);
if (i>0){
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
m-old_i, n-old_i-2*old_ib, old_ib,
dA(old_i, old_i ), ldda, dwork,0, lddwork,
dA(old_i, old_i+2*old_ib), ldda, dwork,old_ib, lddwork, queues[1]);
magma_dsetmatrix_async( old_ib, old_ib, work_ref(old_i), 0, ldwork,
dA(old_i, old_i), ldda, queues[1], NULL);
clFlush(queues[1]);
}
magma_queue_sync(queues[0]);
lapackf77_dgeqrf(&rows, &ib, work_ref(i), &ldwork, tau+i, hwork, &lhwork, info);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
work_ref(i), &ldwork, tau+i, hwork, &ib);
dpanel_to_q( MagmaUpper, ib, work_ref(i), ldwork, hwork+ib*ib );
magma_dsetmatrix(rows, ib, work_ref(i), 0, ldwork, dA(i,i), ldda, queues[0]);
dq_to_panel( MagmaUpper, ib, work_ref(i), ldwork, hwork+ib*ib );
if (i + ib < n)
{
magma_dsetmatrix(ib, ib, hwork, 0, ib, dwork, 0, lddwork, queues[1]);
if (i+nb < k-nx){
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dwork,0, lddwork,
dA(i, i+ib), ldda, dwork,ib, lddwork, queues[1]);
magma_queue_sync(queues[1]);
}else {
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dwork,0, lddwork,
dA(i, i+ib), ldda, dwork,ib, lddwork, queues[1]);
magma_dsetmatrix(ib, ib, work_ref(i), 0, ldwork, dA(i,i), ldda, queues[1]);
clFlush(queues[1]);
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
magma_free(dwork);
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
rows = m-i;
magma_dgetmatrix(rows, ib, dA(i, i), ldda, work, 0, rows, queues[0]);
lhwork = lwork - rows*ib;
lapackf77_dgeqrf(&rows, &ib, work, &rows, tau+i, work+ib*rows, &lhwork, info);
magma_dsetmatrix(rows, ib, work, 0, rows, dA(i, i), ldda, queues[0]);
}
clEnqueueUnmapMemObject(queues[0], buffer, work, 0, NULL, NULL);
clReleaseMemObject(buffer);
// magma_free_cpu(work);
return *info;
} /* magma_dgeqrf2_gpu */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing dlarfb_gpu
*/
int main( int argc, char** argv )
{
TESTING_CUDA_INIT();
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
double c_neg_one = MAGMA_D_NEG_ONE;
magma_int_t ione = 1;
printf( "\nUsage: %s -M m -N n -K k\n\n", argv[0] );
magma_int_t m = 500;
magma_int_t n = 300;
magma_int_t k = 32;
for( int i = 1; i < argc; i++ ) {
if (strcmp("-M", argv[i]) == 0 && i+1 < argc) {
m = atoi( argv[++i] );
}
else if (strcmp("-N", argv[i]) == 0 && i+1 < argc) {
n = atoi( argv[++i] );
}
else if (strcmp("-K", argv[i]) == 0 && i+1 < argc) {
k = atoi( argv[++i] );
}
else {
printf( "invalid argument: %s\n", argv[i] );
exit(1);
}
}
if ( k <= 0 || k > m || k > n ) {
printf( "requires 0 < k <= min(m,n)\n" );
exit(1);
}
magma_int_t ldc = m;
magma_int_t ldv = max(m,n);
magma_int_t ldt = k;
magma_int_t ldw = max(m,n);
magma_int_t nv;
ldc = ((ldc+31)/32)*32;
ldv = ((ldv+31)/32)*32;
ldt = ((ldt+31)/32)*32;
ldw = ((ldw+31)/32)*32;
// Allocate memory for matrices
double *C, *R, *V, *T, *W;
TESTING_MALLOC( C, double, ldc*n );
TESTING_MALLOC( R, double, ldc*n );
TESTING_MALLOC( V, double, ldv*k );
TESTING_MALLOC( T, double, ldt*k );
TESTING_MALLOC( W, double, ldw*k );
double *dC, *dV, *dT, *dW;
TESTING_DEVALLOC( dC, double, ldc*n );
TESTING_DEVALLOC( dV, double, ldv*k );
TESTING_DEVALLOC( dT, double, ldt*k );
TESTING_DEVALLOC( dW, double, ldw*k );
magma_int_t size;
magma_int_t iseed[4] = { 1, 2, 3, 4 };
double error, work[1];
// test all combinations of input parameters
const char* side[] = { MagmaLeftStr, MagmaRightStr };
const char* trans[] = { MagmaTransStr, MagmaNoTransStr };
const char* direct[] = { MagmaForwardStr, MagmaBackwardStr };
const char* storev[] = { MagmaColumnwiseStr, MagmaRowwiseStr };
printf(" M N K storev side direct trans ||R||_F / ||HC||_F\n");
printf("==================================================================================\n");
for( int istor = 0; istor < 2; ++istor ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int idir = 0; idir < 2; ++idir ) {
for( int itran = 0; itran < 2; ++itran ) {
//printf( "# ----------\n" );
//printf( "# %-10s %-10s %-10s %-10s\n", storev[istor], side[iside], direct[idir], trans[itran] );
// C is full
size = ldc*n;
lapackf77_dlarnv( &ione, iseed, &size, C );
//printf( "C=" ); magma_dprint( m, n, C, ldc );
// V is ldv x nv. See larfb docs for description.
ldv = (*side[iside] == 'L' ? m : n);
nv = k;
size = ldv*nv;
lapackf77_dlarnv( &ione, iseed, &size, V );
if ( *storev[istor] == MagmaColumnwise ) {
if ( *direct[idir] == MagmaForward ) {
lapackf77_dlaset( MagmaUpperStr, &k, &k, &c_zero, &c_one, V, &ldv );
}
else {
lapackf77_dlaset( MagmaLowerStr, &k, &k, &c_zero, &c_one, &V[(ldv-k)], &ldv );
}
}
else {
// rowwise, swap V's dimensions
std::swap( ldv, nv );
if ( *direct[idir] == MagmaForward ) {
lapackf77_dlaset( MagmaLowerStr, &k, &k, &c_zero, &c_one, V, &ldv );
}
else {
lapackf77_dlaset( MagmaUpperStr, &k, &k, &c_zero, &c_one, &V[(nv-k)*ldv], &ldv );
}
}
//printf( "# ldv %d, nv %d\n", ldv, nv );
//printf( "V=" ); magma_dprint( ldv, nv, V, ldv );
// T is upper triangular for forward, and lower triangular for backward
magma_int_t k1 = k-1;
size = ldt*k;
lapackf77_dlarnv( &ione, iseed, &size, T );
if ( *direct[idir] == MagmaForward ) {
lapackf77_dlaset( MagmaLowerStr, &k1, &k1, &c_zero, &c_zero, &T[1], &ldt );
}
else {
lapackf77_dlaset( MagmaUpperStr, &k1, &k1, &c_zero, &c_zero, &T[1*ldt], &ldt );
}
//printf( "T=" ); magma_dprint( k, k, T, ldt );
magma_dsetmatrix( m, n, C, ldc, dC, ldc );
magma_dsetmatrix( ldv, nv, V, ldv, dV, ldv );
magma_dsetmatrix( k, k, T, ldt, dT, ldt );
lapackf77_dlarfb( side[iside], trans[itran], direct[idir], storev[istor],
&m, &n, &k,
V, &ldv, T, &ldt, C, &ldc, W, &ldw );
//printf( "HC=" ); magma_dprint( m, n, C, ldc );
magma_dlarfb_gpu( *side[iside], *trans[itran], *direct[idir], *storev[istor],
m, n, k,
dV, ldv, dT, ldt, dC, ldc, dW, ldw );
magma_dgetmatrix( m, n, dC, ldc, R, ldc );
//printf( "dHC=" ); magma_dprint( m, n, R, ldc );
// compute relative error |HC_magma - HC_lapack| / |HC_lapack|
error = lapackf77_dlange( "Fro", &m, &n, C, &ldc, work );
size = ldc*n;
blasf77_daxpy( &size, &c_neg_one, C, &ione, R, &ione );
error = lapackf77_dlange( "Fro", &m, &n, R, &ldc, work ) / error;
printf( "%5d %5d %5d %-10s %-10s %-10s %-10s %8.2e\n",
(int) m, (int) n, (int) k,
storev[istor], side[iside], direct[idir], trans[itran], error );
}}}}
// Memory clean up
TESTING_FREE( C );
TESTING_FREE( R );
TESTING_FREE( V );
TESTING_FREE( T );
TESTING_FREE( W );
TESTING_DEVFREE( dC );
TESTING_DEVFREE( dV );
TESTING_DEVFREE( dT );
TESTING_DEVFREE( dW );
// Shutdown
TESTING_CUDA_FINALIZE();
return 0;
}
extern "C" magma_int_t
magma_dormqr(magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *a, magma_int_t lda,
double *tau,
double *c, magma_int_t ldc,
double *work, magma_int_t lwork,
magma_int_t *info, magma_queue_t queue)
{
/* -- MAGMA (version 1.0.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
September 2012
Purpose
=======
DORMQR overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
A (input) DOUBLE_PRECISION 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
DGEQRF in the first k columns of its array argument A.
A is modified by the routine but restored on exit.
LDA (input) INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).
TAU (input) DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
C (input/output) DOUBLE_PRECISION array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T * C or C * Q**T or C*Q.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace/output) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(0) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M).
For optimum performance LWORK >= N*NB if SIDE = 'L', and
LWORK >= M*NB if SIDE = 'R', where NB is the optimal
blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
double c_one = MAGMA_D_ONE;
magma_side_t side_ = side;
magma_trans_t trans_ = trans;
/* Allocate work space on the GPU */
magmaDouble_ptr dwork, dc;
magma_malloc( &dc, (m)*(n)*sizeof(double) );
magma_malloc( &dwork, (m + n + 64)*64*sizeof(double) );
/* Copy matrix C from the CPU to the GPU */
magma_dsetmatrix( m, n, c, 0, ldc, dc, 0, m, queue );
//dc -= (1 + m);
size_t dc_offset = -(1+m);
magma_int_t a_offset, c_offset, i__4, lddwork;
magma_int_t i__;
double t[2*4160] /* was [65][64] */;
magma_int_t i1, i2, i3, ib, ic, jc, nb, mi, ni, nq, nw;
int left, notran, lquery;
magma_int_t iinfo, lwkopt;
a_offset = 1 + lda;
a -= a_offset;
--tau;
c_offset = 1 + ldc;
c -= c_offset;
*info = 0;
left = lapackf77_lsame(lapack_const(side_), "L");
notran = lapackf77_lsame(lapack_const(trans_), "N");
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 && ! lapackf77_lsame(lapack_const(side_), "R")) {
*info = -1;
} else if (! notran && ! lapackf77_lsame(lapack_const(trans_), "T")) {
*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)
{
/* Determine the block size. NB may be at most NBMAX, where NBMAX
is used to define the local array T. */
nb = 64;
lwkopt = max(1,nw) * nb;
MAGMA_D_SET2REAL( work[0], 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] = c_one;
return *info;
}
if (nb >= k)
{
/* Use CPU code */
lapackf77_dormqr(lapack_const(side_), lapack_const(trans_), &m, &n, &k, &a[a_offset], &lda, &tau[1],
&c[c_offset], &ldc, work, &lwork, &iinfo);
}
else
{
/* Use hybrid CPU-GPU code */
if ( ( left && (! notran) ) || ( (! left) && notran ) ) {
i1 = 1;
i2 = k;
i3 = nb;
} else {
i1 = (k - 1) / nb * nb + 1;
i2 = 1;
i3 = -nb;
}
if (left) {
ni = n;
jc = 1;
} else {
mi = m;
ic = 1;
}
for (i__ = i1; i3 < 0 ? i__ >= i2 : i__ <= i2; i__ += i3)
{
ib = min(nb, k - i__ + 1);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
i__4 = nq - i__ + 1;
lapackf77_dlarft("F", "C", &i__4, &ib, &a[i__ + i__ * lda], &lda,
&tau[i__], t, &ib);
/* 1) Put 0s in the upper triangular part of A;
2) copy the panel from A to the GPU, and
3) restore A */
dpanel_to_q(MagmaUpper, ib, &a[i__ + i__ * lda], lda, t+ib*ib);
magma_dsetmatrix( i__4, ib, &a[i__ + i__ * lda], 0, lda, dwork, 0, i__4, queue );
dq_to_panel(MagmaUpper, ib, &a[i__ + i__ * lda], lda, t+ib*ib);
if (left)
{
/* H or H' is applied to C(i:m,1:n) */
mi = m - i__ + 1;
ic = i__;
}
else
{
/* H or H' is applied to C(1:m,i:n) */
ni = n - i__ + 1;
jc = i__;
}
if (left)
lddwork = ni;
else
lddwork = mi;
/* Apply H or H'; First copy T to the GPU */
magma_dsetmatrix( ib, ib, t, 0, ib, dwork, i__4*ib, ib, queue );
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dwork, 0, i__4, dwork, i__4*ib, ib,
dc, dc_offset+(ic + jc * m), m,
dwork, (i__4*ib + ib*ib), lddwork, queue);
}
magma_dgetmatrix( m, n, dc, dc_offset+(1+m), m, &c[c_offset], 0, ldc, queue );
}
MAGMA_D_SET2REAL( work[0], lwkopt );
//dc += (1 + m);
magma_free( dc );
magma_free( dwork );
return *info;
} /* magma_dormqr */
/***************************************************************************//**
Purpose
-------
DORGQR generates an M-by-N DOUBLE PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
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. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
A DOUBLE PRECISION array A, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the
first k columns 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 DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
@param[in]
T DOUBLE PRECISION array, dimension (NB, min(M,N)).
T contains the T matrices used in blocking the elementary
reflectors H(i), e.g., this can be the 6th argument of
magma_dgeqrf_gpu (except stored on the CPU, not the GPU).
@param[in]
nb INTEGER
This is the block size used in DGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in T.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_ungqr
*******************************************************************************/
extern "C" magma_int_t
magma_dorgqr_m(
magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
double *T, magma_int_t nb,
magma_int_t *info)
{
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(d,i,j) (dA[d] + (i) + (j)*ldda)
#define dT(d,i,j) (dT[d] + (i) + (j)*nb)
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, ldwork;
magma_int_t d, i, ib, j, jb, ki, kk;
double *work=NULL;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
magma_int_t di, dn;
magma_int_t dpanel;
magma_int_t ngpu = magma_num_gpus();
magma_device_t orig_dev;
magma_getdevice( &orig_dev );
// Allocate memory on GPUs for A and workspaces
magma_int_t ldda = magma_roundup( m, 32 );
magma_int_t lddwork = magma_roundup( n, 32 );
magma_int_t min_lblocks = (n / nb) / ngpu; // min. blocks per gpu
magma_int_t last_dev = (n / nb) % ngpu; // device with last block
magma_int_t nlocal[ MagmaMaxGPUs ] = { 0 };
double *dA[ MagmaMaxGPUs ] = { NULL };
double *dT[ MagmaMaxGPUs ] = { NULL };
double *dV[ MagmaMaxGPUs ] = { NULL };
double *dW[ MagmaMaxGPUs ] = { NULL };
magma_queue_t queues[ MagmaMaxGPUs ] = { NULL };
for( d = 0; d < ngpu; ++d ) {
// example with n = 75, nb = 10, ngpu = 3
// min_lblocks = 2
// last_dev = 1
// gpu 0: 2 blocks, cols: 0- 9, 30-39, 60-69
// gpu 1: 1+ blocks, cols: 10-19, 40-49, 70-74 (partial)
// gpu 2: 1 block, cols: 20-29, 50-59
magma_setdevice( d );
nlocal[d] = min_lblocks*nb;
if ( d < last_dev ) {
nlocal[d] += nb;
}
else if ( d == last_dev ) {
nlocal[d] += (n % nb);
}
ldwork = nlocal[d]*ldda // dA
+ nb*m // dT
+ nb*ldda // dV
+ nb*lddwork; // dW
if ( MAGMA_SUCCESS != magma_dmalloc( &dA[d], ldwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
dT[d] = dA[d] + nlocal[d]*ldda;
dV[d] = dT[d] + nb*m;
dW[d] = dV[d] + nb*ldda;
magma_queue_create( d, &queues[d] );
}
trace_init( 1, ngpu, 1, queues );
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
} else {
ki = 0;
kk = 0;
}
// Allocate CPU work space
// n*nb for larfb work
// m*nb for V
// nb*nb for T
lwork = (n + m + nb) * nb;
magma_dmalloc_cpu( &work, lwork );
if (work == NULL) {
*info = MAGMA_ERR_HOST_ALLOC;
goto cleanup;
}
double *work_T, *work_V;
work_T = work + n*nb;
work_V = work + n*nb + nb*nb;
// Use unblocked code for the last or only block.
if (kk < n) {
trace_cpu_start( 0, "ungqr", "ungqr last block" );
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
// dorgqr requires less workspace (n*nb), but is slow if k < dorgqr's block size.
// replacing it with the 4 routines below is much faster (e.g., 60x).
//magma_int_t iinfo;
//lapackf77_dorgqr( &m_kk, &n_kk, &k_kk,
// A(kk, kk), &lda,
// &tau[kk], work, &lwork, &iinfo );
lapackf77_dlacpy( MagmaFullStr, &m_kk, &k_kk, A(kk,kk), &lda, work_V, &m_kk);
lapackf77_dlaset( MagmaFullStr, &m_kk, &n_kk, &c_zero, &c_one, A(kk, kk), &lda );
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &k_kk,
work_V, &m_kk, &tau[kk], work_T, &k_kk);
lapackf77_dlarfb( MagmaLeftStr, MagmaNoTransStr, MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &n_kk, &k_kk,
work_V, &m_kk, work_T, &k_kk, A(kk, kk), &lda, work, &n_kk );
if (kk > 0) {
for( j=kk; j < n; j += nb ) {
jb = min( n-j, nb );
d = (j / nb) % ngpu;
di = ((j / nb) / ngpu) * nb;
magma_setdevice( d );
magma_dsetmatrix( m_kk, jb,
A(kk, j), lda,
dA(d, kk, di), ldda, queues[d] );
// Set A(1:kk,kk+1:n) to zero.
magmablas_dlaset( MagmaFull, kk, jb, c_zero, c_zero, dA(d, 0, di), ldda, queues[d] );
}
}
trace_cpu_end( 0 );
}
if (kk > 0) {
// Use blocked code
// send T to all GPUs
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
trace_gpu_start( d, 0, "set", "set T" );
magma_dsetmatrix_async( nb, min(m,n), T, nb, dT[d], nb, queues[d] );
trace_gpu_end( d, 0 );
}
// queue: set Aii (V) --> laset --> laset --> larfb --> [next]
// CPU has no computation
for( i = ki; i >= 0; i -= nb ) {
ib = min(nb, k - i);
mi = m - i;
dpanel = (i / nb) % ngpu;
di = ((i / nb) / ngpu) * nb;
// Send current panel to dV on the GPUs
lapackf77_dlaset( "Upper", &ib, &ib, &c_zero, &c_one, A(i, i), &lda );
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
trace_gpu_start( d, 0, "set", "set V" );
magma_dsetmatrix_async( mi, ib,
A(i, i), lda,
dV[d], ldda, queues[d] );
trace_gpu_end( d, 0 );
}
// set panel to identity
magma_setdevice( dpanel );
trace_gpu_start( dpanel, 0, "laset", "laset" );
magmablas_dlaset( MagmaFull, i, ib, c_zero, c_zero, dA(dpanel, 0, di), ldda, queues[dpanel] );
magmablas_dlaset( MagmaFull, mi, ib, c_zero, c_one, dA(dpanel, i, di), ldda, queues[dpanel] );
trace_gpu_end( dpanel, 0 );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_indices_1D_bcyclic( nb, ngpu, d, i, n, &di, &dn );
trace_gpu_start( d, 0, "larfb", "larfb" );
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, dn-di, ib,
dV[d], ldda, dT(d,0,i), nb,
dA(d, i, di), ldda, dW[d], lddwork, queues[d] );
trace_gpu_end( d, 0 );
}
}
}
// copy result back to CPU
trace_cpu_start( 0, "get", "get A" );
magma_dgetmatrix_1D_col_bcyclic( ngpu, m, n, nb, dA, ldda, A, lda, queues );
trace_cpu_end( 0 );
}
#ifdef TRACING
char name[80];
snprintf( name, sizeof(name), "dorgqr-n%lld-ngpu%lld.svg", (long long) m, (long long) ngpu );
trace_finalize( name, "trace.css" );
#endif
cleanup:
for( d = 0; d < ngpu; ++d ) {
magma_setdevice( d );
magma_free( dA[d] );
magma_queue_destroy( queues[d] );
}
magma_free_cpu( work );
magma_setdevice( orig_dev );
return *info;
} /* magma_dorgqr */
extern "C" magma_int_t
magma_dgeqrf(magma_int_t m, magma_int_t n,
double *A, magma_int_t lda, double *tau,
double *work, magma_int_t lwork,
magma_int_t *info )
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DGEQRF computes a QR factorization of a DOUBLE_PRECISION 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.
If the current stream is NULL, this version replaces it with user defined
stream to overlap computation with communication.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
A (input/output) DOUBLE_PRECISION 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).
Higher performance is achieved if A is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max( N*NB, 2*NB*NB ),
where NB can be obtained through magma_get_dgeqrf_nb(M).
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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
or another error occured, such as memory allocation failed.
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 real scalar, and v is a real 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).
===================================================================== */
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(i,j) (dA + (i) + (j)*ldda)
double *dA, *dwork, *dT;
double c_one = MAGMA_D_ONE;
magma_int_t i, k, lddwork, old_i, old_ib;
magma_int_t ib, ldda;
/* Function Body */
*info = 0;
magma_int_t nb = magma_get_dgeqrf_nb(min(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_D_MAKE( (double)lwkopt, 0 );
int 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;
k = min(m,n);
if (k == 0) {
work[0] = c_one;
return *info;
}
// largest N for larfb is n-nb (trailing matrix lacks 1st panel)
lddwork = ((n+31)/32)*32 - nb;
ldda = ((m+31)/32)*32;
magma_int_t num_gpus = magma_num_gpus();
if( num_gpus > 1 ) {
/* call multiple-GPU interface */
return magma_dgeqrf4(num_gpus, m, n, A, lda, tau, work, lwork, info);
}
// allocate space for dA, dwork, and dT
if (MAGMA_SUCCESS != magma_dmalloc( &dA, n*ldda + nb*lddwork + nb*nb )) {
/* Switch to the "out-of-core" (out of GPU-memory) version */
return magma_dgeqrf_ooc(m, n, A, lda, tau, work, lwork, info);
}
/* Define user stream if current stream is NULL */
magma_queue_t stream[3], current_stream;
magmablasGetKernelStream(¤t_stream);
magma_queue_create( &stream[0] );
magma_queue_create( &stream[2] );
if (current_stream == NULL) {
magma_queue_create( &stream[1] );
magmablasSetKernelStream(stream[1]);
}
else
stream[1] = current_stream;
dwork = dA + n*ldda;
dT = dA + n*ldda + nb*lddwork;
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially.
Asynchronously send the matrix to the GPU except the first panel. */
magma_dsetmatrix_async( m, n-nb,
A(0,nb), lda,
dA(0,nb), ldda, stream[2] );
old_i = 0;
old_ib = nb;
for (i = 0; i < k-nb; i += nb) {
ib = min(k-i, nb);
if (i>0) {
/* download i-th panel */
magma_queue_sync( stream[1] );
magma_dgetmatrix_async( m-i, ib,
dA(i,i), ldda,
A(i,i), lda, stream[0] );
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
m-old_i, n-old_i-2*old_ib, old_ib,
dA(old_i, old_i), ldda, dT, nb,
dA(old_i, old_i+2*old_ib), ldda, dwork, lddwork);
magma_dgetmatrix_async( i, ib,
dA(0,i), ldda,
A(0,i), lda, stream[2] );
magma_queue_sync( stream[0] );
}
magma_int_t rows = m-i;
lapackf77_dgeqrf(&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_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(i,i), &lda, tau+i, work, &ib);
dpanel_to_q(MagmaUpper, ib, A(i,i), lda, work+ib*ib);
/* download the i-th V matrix */
magma_dsetmatrix_async( rows, ib, A(i,i), lda, dA(i,i), ldda, stream[0] );
/* download the T matrix */
magma_dsetmatrix_async( ib, ib, work, ib, dT, nb, stream[0] );
magma_queue_sync( stream[0] );
if (i + ib < n) {
if (i+ib < k-nb) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left (look-ahead) */
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT, nb,
dA(i, i+ib), ldda, dwork, lddwork);
dq_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_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dT, nb,
dA(i, i+ib), ldda, dwork, lddwork);
dq_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 < k) {
ib = n-i;
if (i != 0) {
magma_dgetmatrix( m, ib, dA(0,i), ldda, A(0,i), lda );
}
magma_int_t rows = m-i;
lapackf77_dgeqrf(&rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info);
}
magma_queue_destroy( stream[0] );
magma_queue_destroy( stream[2] );
if (current_stream == NULL) {
magma_queue_destroy( stream[1] );
magmablasSetKernelStream(NULL);
}
magma_free( dA );
return *info;
} /* magma_dgeqrf */
extern "C" magma_int_t
magma_dorgqr(
magma_int_t m, magma_int_t n, magma_int_t k,
double *a, magma_int_t lda,
double *tau, magmaDouble_ptr dT, size_t dT_offset,
magma_int_t nb,
magma_queue_t queue,
magma_int_t *info )
{
/* -- clMAGMA (version 1.3.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
@date November 2014
Purpose
=======
DORGQR generates an M-by-N DOUBLE_PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. M >= N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
A (input/output) DOUBLE_PRECISION array A, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the
first k columns of its array argument A.
On exit, the M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >= max(1,M).
TAU (input) DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
DT (input) DOUBLE_PRECISION array on the GPU device.
DT contains the T matrices used in blocking the elementary
reflectors H(i), e.g., this can be the 6th argument of
magma_dgeqrf_gpu.
NB (input) INTEGER
This is the block size used in DGEQRF_GPU, and correspondingly
the size of the T matrices, used in the factorization, and
stored in DT.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an illegal value
===================================================================== */
#define a_ref(i,j) ( a + (j)*lda + (i))
#define da_ref(i,j) da, (da_offset + (j)*ldda + (i))
#define t_ref(a_1) dT, (dT_offset + (a_1)*nb)
double c_zero = MAGMA_D_ZERO;
magma_int_t i__1, i__2, i__3;
magma_int_t lwork, ldda;
magma_int_t i, ib, ki, kk, iinfo;
magma_int_t lddwork = min(m, n);
double *work;
magmaDouble_ptr da, dwork;
size_t da_offset, dwork_offset;
magma_event_t event = NULL;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0)
return *info;
/* Allocate GPU work space */
ldda = ((m+31)/32)*32;
lddwork = ((lddwork+31)/32)*32;
if (MAGMA_SUCCESS != magma_dmalloc( &da, ((n)*ldda + nb*lddwork ) )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
da_offset = 0;
dwork = da;
dwork_offset = da_offset + (n)*ldda;
/* Allocate CPU work space */
lwork = n * nb;
magma_dmalloc_cpu( &work, lwork );
if( work == NULL ) {
magma_free( da );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
if ( (nb > 1) && (nb < k) )
{
/* Use blocked code after the last block.
The first kk columns are handled by the block method. */
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
/* Set A(1:kk,kk+1:n) to zero. */
magmablas_dlaset(MagmaFull, kk, n-kk, c_zero, c_zero, da_ref(0,kk), ldda, queue);
}
else
kk = 0;
/* Use unblocked code for the last or only block. */
if (kk < n)
{
i__1 = m - kk;
i__2 = n - kk;
i__3 = k - kk;
lapackf77_dorgqr(&i__1, &i__2, &i__3,
a_ref(kk, kk), &lda,
&tau[kk], work, &lwork, &iinfo);
magma_dsetmatrix(i__1, i__2, a_ref(kk, kk), lda, da_ref(kk, kk), ldda, queue);
}
if (kk > 0)
{
/* Use blocked code */
for (i = ki; i >= 0; i-=nb)
{
ib = min(nb, k - i);
/* Send the current panel to the GPU */
i__2 = m - i;
dpanel_to_q(MagmaUpper, ib, a_ref(i,i), lda, work);
magma_dsetmatrix(i__2, ib, a_ref(i, i), lda, da_ref(i, i), ldda, queue);
if (i + ib < n)
{
/* Apply H to A(i:m,i+ib:n) from the left */
i__3 = n - i - ib;
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
i__2, i__3, ib,
da_ref(i, i ), ldda, t_ref(i), nb,
da_ref(i, i+ib), ldda, dwork, dwork_offset, lddwork, queue);
}
/* Apply H to rows i:m of current block on the CPU */
lapackf77_dorgqr(&i__2, &ib, &ib,
a_ref(i, i), &lda,
&tau[i], work, &lwork, &iinfo);
magma_dsetmatrix_async( i__2, ib,
a_ref(i,i), lda,
da_ref(i,i), ldda, queue, &event );
/* Set rows 1:i-1 of current block to zero */
i__2 = i + ib;
magmablas_dlaset(MagmaFull, i, i__2 - i, c_zero, c_zero, da_ref(0,i), ldda, queue);
}
}
magma_dgetmatrix(m, n, da_ref(0, 0), ldda, a_ref(0, 0), lda, queue);
//cudaStreamDestroy(stream);
magma_free( da );
magma_free_cpu(work);
return *info;
} /* magma_dorgqr */
extern "C" magma_int_t
magma_dormqr_gpu(char side, char trans,
magma_int_t m, magma_int_t n, magma_int_t k,
double *dA, magma_int_t ldda,
double *tau,
double *dC, magma_int_t lddc,
double *hwork, magma_int_t lwork,
double *dT, magma_int_t nb,
magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
DORMQR_GPU overwrites the general real M-by-N matrix C with
SIDE = 'L' SIDE = 'R'
TRANS = 'N': Q * C C * Q
TRANS = 'T': Q**T * C C * Q**T
where Q is a real orthogonal matrix defined as the product of k
elementary reflectors
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF. Q is of order M if SIDE = 'L' and of order N
if SIDE = 'R'.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS (input) CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M (input) INTEGER
The number of rows of the matrix C. M >= 0.
N (input) INTEGER
The number of columns of the matrix C. N >= 0.
K (input) INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = 'L', M >= K >= 0;
if SIDE = 'R', N >= K >= 0.
DA (input) DOUBLE_PRECISION array on the GPU, dimension (LDDA,K)
The i-th column must contain the vector which defines the
elementary reflector H(i), for i = 1,2,...,k, as returned by
DGEQRF in the first k columns of its array argument DA.
DA is modified by the routine but restored on exit.
LDDA (input) INTEGER
The leading dimension of the array DA.
If SIDE = 'L', LDDA >= max(1,M);
if SIDE = 'R', LDDA >= max(1,N).
TAU (input) DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF.
DC (input/output) DOUBLE_PRECISION array on the GPU, dimension (LDDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**T * C or C * Q**T or C*Q.
LDDC (input) INTEGER
The leading dimension of the array DC. LDDC >= max(1,M).
HWORK (workspace/output) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
Currently, dgetrs_gpu assumes that on exit, hwork contains the last
block of A and C. This will change and *should not be relied on*!
LWORK (input) INTEGER
The dimension of the array HWORK.
LWORK >= (M-K+NB)*(N+NB) + N*NB if SIDE = 'L', and
LWORK >= (N-K+NB)*(M+NB) + M*NB if SIDE = 'R',
where NB is the given blocksize.
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 HWORK array, and no error
message related to LWORK is issued by XERBLA.
DT (input) DOUBLE_PRECISION array on the GPU that is the output
(the 9th argument) of magma_dgeqrf_gpu.
NB (input) INTEGER
This is the blocking size that was used in pre-computing DT, e.g.,
the blocking size used in magma_dgeqrf_gpu.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
===================================================================== */
#define dA(a_1,a_2) (dA + (a_1) + (a_2)*ldda)
#define dC(a_1,a_2) (dC + (a_1) + (a_2)*lddc)
#define dT(a_1) (dT + (a_1)*nb)
double c_one = MAGMA_D_ONE;
char side_[2] = {side, 0};
char trans_[2] = {trans, 0};
double *dwork;
magma_int_t i, lddwork;
magma_int_t i1, i2, step, ib, ic, jc, ma, mi, ni, nq, nw;
int left, notran, lquery;
magma_int_t lwkopt;
*info = 0;
left = lapackf77_lsame(side_, "L");
notran = lapackf77_lsame(trans_, "N");
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;
}
lwkopt = (nq - k + nb)*(nw + nb) + nw*nb;
hwork[0] = MAGMA_D_MAKE( lwkopt, 0 );
if ( (!left) && (!lapackf77_lsame(side_, "R")) ) {
*info = -1;
} else if ( (!notran) && (!lapackf77_lsame(trans_, MagmaTransStr)) ) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (ldda < max(1,nq)) {
*info = -7;
} else if (lddc < max(1,m)) {
*info = -10;
} else if (lwork < lwkopt && ! lquery) {
*info = -12;
}
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) {
hwork[0] = c_one;
return *info;
}
lddwork = k;
dwork = dT(2*lddwork);
if ( (left && (! notran)) || ((! left) && notran) ) {
// left trans: Q^T C
// right notrans: C Q
// multiply from first block, i = 0, to next-to-last block, i < k-nb
i1 = 0;
i2 = k-nb;
step = nb;
} else {
// left notrans: Q C
// right trans: C Q^T
// multiply from next-to-last block, i = floor((k-1-nb)/nb)*nb, to first block, i = 0
i1 = ((k - 1 - nb) / nb) * nb;
i2 = 0;
step = -nb;
}
if (left) {
ni = n;
jc = 0;
} else {
mi = m;
ic = 0;
}
/* Use unblocked code to multiply last or only block (cases Q*C or C*Q^T). */
// workspace left: A(mi*nb) + C(mi*ni) + work(ni*nb_la) = (m-k-nb)*nb + (m-k-nb)*n + n*nb
// workspace right: A(ni*nb) + C(mi*ni) + work(mi*nb_la) = (n-k-nb)*nb + m*(n-k-nb) + m*nb
if ( step < 0 ) {
// i is beginning of last block
i = i1 - step;
if ( i >= k ) {
i = i1;
}
ib = k - i;
if (left) {
// ni=n, jc=0, H or H^T is applied to C(i:m-1,0:n-1)
mi = m - i;
ma = mi;
ic = i;
}
else {
// mi=m, ic=0, H or H^T is applied to C(0:m-1,i:n-1)
ni = n - i;
ma = ni;
jc = i;
}
double* hA = hwork;
double* hC = hwork + ma*ib;
double* hW = hwork + ma*ib + mi*ni;
magma_int_t lhwork = lwork - (ma*ib + mi*ni);
magma_dgetmatrix( ma, ib, dA(i, i ), ldda, hA, ma );
magma_dgetmatrix( mi, ni, dC(ic, jc), lddc, hC, mi );
lapackf77_dormqr( side_, trans_,
&mi, &ni, &ib,
hA, &ma, tau+i,
hC, &mi,
hW, &lhwork, info );
// send the updated part of C back to the GPU
magma_dsetmatrix( mi, ni, hC, mi, dC(ic, jc), lddc );
}
/* Use blocked code to multiply blocks */
if (nb < k) {
for( i=i1; (step<0 ? i>=i2 : i<i2); i+=step ) {
ib = min(nb, k - i);
if (left) {
// ni=n, jc=0, H or H^T is applied to C(i:m-1,0:n-1)
mi = m - i;
ic = i;
}
else {
// mi=m, ic=0, H or H^T is applied to C(0:m-1,i:n-1)
ni = n - i;
jc = i;
}
magma_dlarfb_gpu( side, trans, MagmaForward, MagmaColumnwise,
mi, ni, ib,
dA(i, i ), ldda, dT(i), nb,
dC(ic, jc), lddc, dwork, nw );
}
}
else {
i = i1;
}
/* Use unblocked code to multiply the last or only block (cases Q^T*C or C*Q). */
if ( step > 0 ) {
ib = k-i;
if (left) {
// ni=n, jc=0, H or H^T is applied to C(i:m-1,0:n-1)
mi = m - i;
ma = mi;
ic = i;
}
else {
// mi=m, ic=0, H or H^T is applied to C(0:m-1,i:n-1)
ni = n - i;
ma = ni;
jc = i;
}
double* hA = hwork;
double* hC = hwork + ma*ib;
double* hW = hwork + ma*ib + mi*ni;
magma_int_t lhwork = lwork - (ma*ib + mi*ni);
magma_dgetmatrix( ma, ib, dA(i, i ), ldda, hA, ma );
magma_dgetmatrix( mi, ni, dC(ic, jc), lddc, hC, mi );
lapackf77_dormqr( side_, trans_,
&mi, &ni, &ib,
hA, &ma, tau+i,
hC, &mi,
hW, &lhwork, info );
// send the updated part of C back to the GPU
magma_dsetmatrix( mi, ni, hC, mi, dC(ic, jc), lddc );
}
// TODO sync. For cases Q*C and C*Q^T, last call is magma_dlarfb_gpu,
// which is async magma_gemm calls, so dormqr can be unfinished.
// TODO: dgeqrs_gpu ASSUMES that hwork contains the last block of A and C.
// That needs to be fixed, but until then, don't modify hwork[0] here.
// In LAPACK: On exit, if INFO = 0, HWORK(1) returns the optimal LWORK.
//hwork[0] = MAGMA_D_MAKE( lwkopt, 0 );
return *info;
} /* end of magma_dormqr_gpu */
/**
Purpose
-------
DORGQR generates an M-by-N DOUBLE_PRECISION matrix Q with orthonormal columns,
which is defined as the first N columns of a product of K elementary
reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
This version recomputes the T matrices on the CPU and sends them to the GPU.
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. M >= N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. N >= K >= 0.
@param[in,out]
A DOUBLE_PRECISION array A, dimension (LDDA,N).
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for
i = 1,2,...,k, as returned by DGEQRF_GPU in the
first k columns 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 DOUBLE_PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DGEQRF_GPU.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument has an illegal value
@ingroup magma_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dorgqr2(magma_int_t m, magma_int_t n, magma_int_t k,
double *A, magma_int_t lda,
double *tau,
magma_int_t *info)
{
#define A(i,j) ( A + (i) + (j)*lda )
#define dA(i,j) (dA + (i) + (j)*ldda)
double c_zero = MAGMA_D_ZERO;
double c_one = MAGMA_D_ONE;
magma_int_t nb = magma_get_dgeqrf_nb(min(m, n));
magma_int_t m_kk, n_kk, k_kk, mi;
magma_int_t lwork, ldda;
magma_int_t i, ib, ki, kk; //, iinfo;
magma_int_t lddwork;
double *dA, *dV, *dW, *dT, *T;
double *work;
*info = 0;
if (m < 0) {
*info = -1;
} else if ((n < 0) || (n > m)) {
*info = -2;
} else if ((k < 0) || (k > n)) {
*info = -3;
} else if (lda < max(1,m)) {
*info = -5;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
if (n <= 0) {
return *info;
}
// first kk columns are handled by blocked method.
// ki is start of 2nd-to-last block
if ((nb > 1) && (nb < k)) {
ki = (k - nb - 1) / nb * nb;
kk = min(k, ki + nb);
} else {
ki = 0;
kk = 0;
}
// Allocate GPU work space
// ldda*n for matrix dA
// ldda*nb for dV
// lddwork*nb for dW larfb workspace
ldda = ((m + 31) / 32) * 32;
lddwork = ((n + 31) / 32) * 32;
if (MAGMA_SUCCESS != magma_dmalloc( &dA, ldda*n + ldda*nb + lddwork*nb + nb*nb)) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dV = dA + ldda*n;
dW = dA + ldda*n + ldda*nb;
dT = dA + ldda*n + ldda*nb + lddwork*nb;
// Allocate CPU work space
lwork = (n+m+nb) * nb;
magma_dmalloc_cpu( &work, lwork );
T = work;
if (work == NULL) {
magma_free( dA );
magma_free_cpu( work );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
double *V = work + (n+nb)*nb;
magma_queue_t stream;
magma_queue_create( &stream );
// Use unblocked code for the last or only block.
if (kk < n) {
m_kk = m - kk;
n_kk = n - kk;
k_kk = k - kk;
/*
lapackf77_dorgqr( &m_kk, &n_kk, &k_kk,
A(kk, kk), &lda,
&tau[kk], work, &lwork, &iinfo );
*/
lapackf77_dlacpy( MagmaUpperLowerStr, &m_kk, &k_kk, A(kk,kk), &lda, V, &m_kk);
lapackf77_dlaset( MagmaUpperLowerStr, &m_kk, &n_kk, &c_zero, &c_one, A(kk, kk), &lda );
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &k_kk,
V, &m_kk, &tau[kk], work, &k_kk);
lapackf77_dlarfb( MagmaLeftStr, MagmaNoTransStr, MagmaForwardStr, MagmaColumnwiseStr,
&m_kk, &n_kk, &k_kk,
V, &m_kk, work, &k_kk, A(kk, kk), &lda, work+k_kk*k_kk, &n_kk );
if (kk > 0) {
magma_dsetmatrix( m_kk, n_kk,
A(kk, kk), lda,
dA(kk, kk), ldda );
// Set A(1:kk,kk+1:n) to zero.
magmablas_dlaset( MagmaFull, kk, n - kk, c_zero, c_zero, dA(0, kk), ldda );
}
}
if (kk > 0) {
// Use blocked code
// stream: set Aii (V) --> laset --> laset --> larfb --> [next]
// CPU has no computation
magmablasSetKernelStream( stream );
for (i = ki; i >= 0; i -= nb) {
ib = min(nb, k - i);
// Send current panel to the GPU
mi = m - i;
lapackf77_dlaset( "Upper", &ib, &ib, &c_zero, &c_one, A(i, i), &lda );
magma_dsetmatrix_async( mi, ib,
A(i, i), lda,
dV, ldda, stream );
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&mi, &ib,
A(i,i), &lda, &tau[i], T, &nb);
magma_dsetmatrix_async( ib, ib,
T, nb,
dT, nb, stream );
// set panel to identity
magmablas_dlaset( MagmaFull, i, ib, c_zero, c_zero, dA(0, i), ldda );
magmablas_dlaset( MagmaFull, mi, ib, c_zero, c_one, dA(i, i), ldda );
magma_queue_sync( stream );
if (i < n) {
// Apply H to A(i:m,i:n) from the left
magma_dlarfb_gpu( MagmaLeft, MagmaNoTrans, MagmaForward, MagmaColumnwise,
mi, n-i, ib,
dV, ldda, dT, nb,
dA(i, i), ldda, dW, lddwork );
}
}
// copy result back to CPU
magma_dgetmatrix( m, n,
dA(0, 0), ldda, A(0, 0), lda);
}
magmablasSetKernelStream( NULL );
magma_queue_destroy( stream );
magma_free( dA );
magma_free_cpu( work );
return *info;
} /* magma_dorgqr */
/**
Purpose
-------
DGEQRF computes a QR factorization of a real M-by-N matrix A:
A = Q * R.
This version has LAPACK-complaint arguments.
If the current stream is NULL, this version replaces it with a new
stream to overlap computation with communication.
Other versions (magma_dgeqrf_gpu and magma_dgeqrf3_gpu) store the
intermediate T matrices.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
dA DOUBLE_PRECISION array on the GPU, dimension (LDDA,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).
@param[in]
ldda INTEGER
The leading dimension of the array dA. LDDA >= max(1,M).
To benefit from coalescent memory accesses LDDA must be
divisible by 16.
@param[out]
tau DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@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 real scalar, and v is a real 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_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dgeqrf2_gpu( magma_int_t m, magma_int_t n,
double *dA, magma_int_t ldda,
double *tau,
magma_int_t *info )
{
#define dA(a_1,a_2) ( dA+(a_2)*(ldda) + (a_1))
#define work_ref(a_1) ( work + (a_1))
#define hwork ( work + (nb)*(m))
double *dwork;
double *work;
magma_int_t i, k, ldwork, lddwork, old_i, old_ib, rows;
magma_int_t nbmin, nx, ib, nb;
magma_int_t lhwork, lwork;
/* Function Body */
*info = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (ldda < max(1,m)) {
*info = -4;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
k = min(m,n);
if (k == 0)
return *info;
nb = magma_get_dgeqrf_nb(m);
lwork = (m+n) * nb;
lhwork = lwork - (m)*nb;
if (MAGMA_SUCCESS != magma_dmalloc( &dwork, n*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
if (MAGMA_SUCCESS != magma_dmalloc_pinned( &work, lwork )) {
magma_free( dwork );
*info = MAGMA_ERR_HOST_ALLOC;
return *info;
}
/* Define user stream if current stream is NULL */
magma_queue_t stream[2];
magma_queue_t orig_stream;
magmablasGetKernelStream( &orig_stream );
magma_queue_create( &stream[0] );
if (orig_stream == NULL) {
magma_queue_create( &stream[1] );
magmablasSetKernelStream(stream[1]);
}
else {
stream[1] = orig_stream;
}
nbmin = 2;
nx = nb;
ldwork = m;
lddwork= n;
if (nb >= nbmin && nb < k && nx < k) {
/* Use blocked code initially */
old_i = 0; old_ib = nb;
for (i = 0; i < k-nx; i += nb) {
ib = min(k-i, nb);
rows = m -i;
/* download i-th panel */
magma_queue_sync( stream[1] );
magma_dgetmatrix_async( rows, ib,
dA(i,i), ldda,
work_ref(i), ldwork, stream[0] );
if (i > 0) {
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
m-old_i, n-old_i-2*old_ib, old_ib,
dA(old_i, old_i ), ldda, dwork, lddwork,
dA(old_i, old_i+2*old_ib), ldda, dwork+old_ib, lddwork);
magma_dsetmatrix_async( old_ib, old_ib,
work_ref(old_i), ldwork,
dA(old_i, old_i), ldda, stream[1] );
}
magma_queue_sync( stream[0] );
lapackf77_dgeqrf(&rows, &ib, work_ref(i), &ldwork, tau+i, hwork, &lhwork, info);
/* Form the triangular factor of the block reflector
H = H(i) H(i+1) . . . H(i+ib-1) */
lapackf77_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib,
work_ref(i), &ldwork, tau+i, hwork, &ib);
dpanel_to_q( MagmaUpper, ib, work_ref(i), ldwork, hwork+ib*ib );
/* download the i-th V matrix */
magma_dsetmatrix_async( rows, ib, work_ref(i), ldwork, dA(i,i), ldda, stream[0] );
/* download the T matrix */
magma_queue_sync( stream[1] );
magma_dsetmatrix_async( ib, ib, hwork, ib, dwork, lddwork, stream[0] );
magma_queue_sync( stream[0] );
if (i + ib < n) {
if (i+nb < k-nx) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dwork, lddwork,
dA(i, i+ib), ldda, dwork+ib, lddwork);
dq_to_panel( MagmaUpper, ib, work_ref(i), ldwork, hwork+ib*ib );
}
else {
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dwork, lddwork,
dA(i, i+ib), ldda, dwork+ib, lddwork);
dq_to_panel( MagmaUpper, ib, work_ref(i), ldwork, hwork+ib*ib );
magma_dsetmatrix_async( ib, ib,
work_ref(i), ldwork,
dA(i,i), ldda, stream[1] );
}
old_i = i;
old_ib = ib;
}
}
} else {
i = 0;
}
magma_free( dwork );
/* Use unblocked code to factor the last or only block. */
if (i < k) {
ib = n-i;
rows = m-i;
magma_dgetmatrix_async( rows, ib, dA(i, i), ldda, work, rows, stream[1] );
magma_queue_sync( stream[1] );
lhwork = lwork - rows*ib;
lapackf77_dgeqrf(&rows, &ib, work, &rows, tau+i, work+ib*rows, &lhwork, info);
magma_dsetmatrix_async( rows, ib, work, rows, dA(i, i), ldda, stream[1] );
}
magma_free_pinned( work );
magma_queue_destroy( stream[0] );
if (orig_stream == NULL) {
magma_queue_destroy( stream[1] );
}
magmablasSetKernelStream( orig_stream );
return *info;
} /* magma_dgeqrf2_gpu */
/**
Purpose
-------
DGEQLF computes a QL factorization of a DOUBLE_PRECISION M-by-N matrix A:
A = Q * L.
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 DOUBLE_PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, if m >= n, the lower triangle of the subarray
A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
if m <= n, the elements on and below the (n-m)-th
superdiagonal contain the M-by-N lower trapezoidal matrix L;
the remaining elements, with the array TAU, represent the
orthogonal matrix Q as a product of 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 DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
\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(1,N,2*NB^2).
For optimum performance LWORK >= max(N*NB, 2*NB^2) where NB can be obtained
through magma_get_dgeqlf_nb(M).
\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
or another error occured, such as memory allocation failed.
Further Details
---------------
The matrix Q is represented as a product of elementary reflectors
Q = H(k) . . . H(2) H(1), where k = min(m,n).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
A(1:m-k+i-1,n-k+i), and tau in TAU(i).
@ingroup magma_dgeqlf_comp
********************************************************************/
extern "C" magma_int_t
magma_dgeqlf(
magma_int_t m, magma_int_t n,
double *A, magma_int_t lda, double *tau,
double *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 dwork(i_) (dwork + (i_))
magmaDouble_ptr dA, dwork;
double c_one = MAGMA_D_ONE;
magma_int_t i, k, lddwork, old_i, old_ib, nb;
magma_int_t rows, cols;
magma_int_t ib, ki, kk, mu, nu, iinfo, ldda;
int lquery;
nb = magma_get_dgeqlf_nb(m);
*info = 0;
lquery = (lwork == -1);
// silence "uninitialized" warnings
old_ib = nb;
old_i = 0;
if (m < 0) {
*info = -1;
} else if (n < 0) {
*info = -2;
} else if (lda < max(1,m)) {
*info = -4;
}
k = min(m,n);
if (*info == 0) {
if (k == 0)
work[0] = c_one;
else {
work[0] = MAGMA_D_MAKE( max(n*nb, 2*nb*nb), 0 );
}
if (lwork < max(max(1,n), 2*nb*nb) && ! lquery)
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery)
return *info;
/* Quick return if possible */
if (k == 0)
return *info;
lddwork = ((n+31)/32)*32;
ldda = ((m+31)/32)*32;
if (MAGMA_SUCCESS != magma_dmalloc( &dA, (n)*ldda + nb*lddwork )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dwork = dA + ldda*n;
magma_queue_t queues[2];
magma_queue_create( &queues[0] );
magma_queue_create( &queues[1] );
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially.
The last kk columns are handled by the block method.
First, copy the matrix on the GPU except the last kk columns */
magma_dsetmatrix_async( m, n-nb,
A(0, 0), lda,
dA(0, 0), ldda, queues[0] );
ki = ((k - nb - 1) / nb) * nb;
kk = min(k, ki + nb);
for (i = k - kk + ki; i >= k -kk; i -= nb) {
ib = min(k-i,nb);
if (i < k - kk + ki) {
/* 1. Copy asynchronously the current panel to the CPU.
2. Copy asynchronously the submatrix below the panel
to the CPU) */
rows = m - k + i + ib;
magma_dgetmatrix_async( rows, ib,
dA(0, n-k+i), ldda,
A(0, n-k+i), lda, queues[1] );
magma_dgetmatrix_async( m-rows, ib,
dA(rows, n-k+i), ldda,
A(rows, n-k+i), lda, queues[0] );
/* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left in
two steps - implementing the lookahead techniques.
This is the main update from the lookahead techniques. */
rows = m - k + old_i + old_ib;
cols = n - k + old_i - old_ib;
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaBackward, MagmaColumnwise,
rows, cols, old_ib,
dA(0, cols+old_ib), ldda, dwork(0), lddwork,
dA(0, 0 ), ldda, dwork(old_ib), lddwork);
}
magma_queue_sync( queues[1] );
/* Compute the QL factorization of the current block
A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1) */
rows = m - k + i + ib;
cols = n - k + i;
lapackf77_dgeqlf( &rows, &ib, A(0,cols), &lda, tau+i, work, &lwork, &iinfo );
if (cols > 0) {
/* Form the triangular factor of the block reflector
H = H(i+ib-1) . . . H(i+1) H(i) */
lapackf77_dlarft( MagmaBackwardStr, MagmaColumnwiseStr,
&rows, &ib,
A(0, cols), &lda, tau + i, work, &ib);
dpanel_to_q( MagmaLower, ib, A(rows-ib,cols), lda, work+ib*ib);
magma_dsetmatrix( rows, ib,
A(0,cols), lda,
dA(0,cols), ldda );
dq_to_panel( MagmaLower, ib, A(rows-ib,cols), lda, work+ib*ib);
// Send the triangular part on the GPU
magma_dsetmatrix( ib, ib, work, ib, dwork(0), lddwork );
/* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left in
two steps - implementing the lookahead techniques.
This is the update of first ib columns. */
if (i-ib >= k -kk)
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaBackward, MagmaColumnwise,
rows, ib, ib,
dA(0, cols), ldda, dwork(0), lddwork,
dA(0,cols-ib), ldda, dwork(ib), lddwork);
else {
magma_dlarfb_gpu( MagmaLeft, MagmaConjTrans, MagmaBackward, MagmaColumnwise,
rows, cols, ib,
dA(0, cols), ldda, dwork(0), lddwork,
dA(0, 0 ), ldda, dwork(ib), lddwork);
}
old_i = i;
old_ib = ib;
}
}
mu = m - k + i + nb;
nu = n - k + i + nb;
magma_dgetmatrix( m, nu, dA(0,0), ldda, A(0,0), lda );
} else {
mu = m;
nu = n;
}
/* Use unblocked code to factor the last or only block */
if (mu > 0 && nu > 0)
lapackf77_dgeqlf(&mu, &nu, A(0,0), &lda, tau, work, &lwork, &iinfo);
magma_queue_destroy( queues[0] );
magma_queue_destroy( queues[1] );
magma_free( dA );
return *info;
} /* magma_dgeqlf */
/**
Purpose
-------
DGEQRF computes a QR factorization of a DOUBLE_PRECISION 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.
If the current stream is NULL, this version replaces it with user defined
stream to overlap computation with communication.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A DOUBLE_PRECISION 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 DOUBLE_PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) DOUBLE_PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) 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_dgeqrf_nb(M).
\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 real scalar, and v is a real 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_dgeqrf_comp
********************************************************************/
extern "C" magma_int_t
magma_dgeqrf(magma_int_t m, magma_int_t n,
double *A, magma_int_t lda, double *tau,
double *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)
double *dA, *dwork, *dT;
double c_one = MAGMA_D_ONE;
magma_int_t i, k, lddwork, old_i, old_ib;
magma_int_t ib, ldda;
/* Function Body */
*info = 0;
magma_int_t nb = magma_get_dgeqrf_nb(min(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_D_MAKE( (double)lwkopt, 0 );
int 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;
k = min(m,n);
if (k == 0) {
work[0] = c_one;
return *info;
}
// largest N for larfb is n-nb (trailing matrix lacks 1st panel)
lddwork = ((n+31)/32)*32 - nb;
ldda = ((m+31)/32)*32;
magma_int_t num_gpus = magma_num_gpus();
if ( num_gpus > 1 ) {
/* call multiple-GPU interface */
return magma_dgeqrf4(num_gpus, m, n, A, lda, tau, work, lwork, info);
}
// allocate space for dA, dwork, and dT
if (MAGMA_SUCCESS != magma_dmalloc( &dA, n*ldda + nb*lddwork + nb*nb )) {
/* Switch to the "out-of-core" (out of GPU-memory) version */
return magma_dgeqrf_ooc(m, n, A, lda, tau, work, lwork, info);
}
/* Define user stream if current stream is NULL */
magma_queue_t stream[2], current_stream;
magmablasGetKernelStream(¤t_stream);
magma_queue_create( &stream[0] );
if (current_stream == NULL) {
magma_queue_create( &stream[1] );
magmablasSetKernelStream(stream[1]);
}
else {
stream[1] = current_stream;
}
dwork = dA + n*ldda;
dT = dA + n*ldda + nb*lddwork;
if ( (nb > 1) && (nb < k) ) {
/* Use blocked code initially.
Asynchronously send the matrix to the GPU except the first panel. */
magma_dsetmatrix_async( m, n-nb,
A(0,nb), lda,
dA(0,nb), ldda, stream[0] );
old_i = 0;
old_ib = nb;
for (i = 0; i < k-nb; i += nb) {
ib = min(k-i, nb);
if (i > 0) {
/* download i-th panel */
magma_queue_sync( stream[1] );
magma_dgetmatrix_async( m-i, ib,
dA(i,i), ldda,
A(i,i), lda, stream[0] );
/* Apply H' to A(i:m,i+2*ib:n) from the left */
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
m-old_i, n-old_i-2*old_ib, old_ib,
dA(old_i, old_i), ldda, dT, nb,
dA(old_i, old_i+2*old_ib), ldda, dwork, lddwork);
magma_dgetmatrix_async( i, ib,
dA(0,i), ldda,
A(0,i), lda, stream[1] );
magma_queue_sync( stream[0] );
}
magma_int_t rows = m-i;
lapackf77_dgeqrf(&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_dlarft( MagmaForwardStr, MagmaColumnwiseStr,
&rows, &ib, A(i,i), &lda, tau+i, work, &ib);
dpanel_to_q(MagmaUpper, ib, A(i,i), lda, work+ib*ib);
/* download the i-th V matrix */
magma_dsetmatrix_async( rows, ib, A(i,i), lda, dA(i,i), ldda, stream[0] );
/* download the T matrix */
magma_queue_sync( stream[1] );
magma_dsetmatrix_async( ib, ib, work, ib, dT, nb, stream[0] );
magma_queue_sync( stream[0] );
if (i + ib < n) {
if (i+ib < k-nb) {
/* Apply H' to A(i:m,i+ib:i+2*ib) from the left (look-ahead) */
magma_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, ib, ib,
dA(i, i ), ldda, dT, nb,
dA(i, i+ib), ldda, dwork, lddwork);
dq_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_dlarfb_gpu( MagmaLeft, MagmaTrans, MagmaForward, MagmaColumnwise,
rows, n-i-ib, ib,
dA(i, i ), ldda, dT, nb,
dA(i, i+ib), ldda, dwork, lddwork);
dq_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 < k) {
ib = n-i;
if (i != 0) {
magma_dgetmatrix_async( m, ib, dA(0,i), ldda, A(0,i), lda, stream[1] );
magma_queue_sync( stream[1] );
}
magma_int_t rows = m-i;
lapackf77_dgeqrf(&rows, &ib, A(i,i), &lda, tau+i, work, &lwork, info);
}
magma_queue_destroy( stream[0] );
if (current_stream == NULL) {
magma_queue_destroy( stream[1] );
magmablasSetKernelStream(NULL);
}
magma_free( dA );
return *info;
} /* magma_dgeqrf */