/**
Purpose
-------
If VECT = MagmaQ, CUNMBR overwrites the general complex M-by-N matrix C with
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q*C C*Q
TRANS = Magma_ConjTrans: Q**H*C C*Q**H
If VECT = MagmaP, CUNMBR overwrites the general complex M-by-N matrix C with
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: P*C C*P
TRANS = Magma_ConjTrans: P**H*C C*P**H
Here Q and P**H are the unitary matrices determined by CGEBRD when
reducing A complex matrix A to bidiagonal form: A = Q*B * P**H. Q
and P**H are defined as products of elementary reflectors H(i) and
G(i) respectively.
Let nq = m if SIDE = MagmaLeft and nq = n if SIDE = MagmaRight. Thus nq is the
order of the unitary matrix Q or P**H that is applied.
If VECT = MagmaQ, A is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).
If VECT = MagmaP, A is assumed to have been A K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).
Arguments
---------
@param[in]
vect magma_vect_t
- = MagmaQ: apply Q or Q**H;
- = MagmaP: apply P or P**H.
@param[in]
side magma_side_t
- = MagmaLeft: apply Q, Q**H, P or P**H from the Left;
- = MagmaRight: apply Q, Q**H, P or P**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q or P;
- = Magma_ConjTrans: Conjugate transpose, apply Q**H or P**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
If VECT = MagmaQ, the number of columns in the original
matrix reduced by CGEBRD.
If VECT = MagmaP, the number of rows in the original
matrix reduced by CGEBRD.
K >= 0.
@param[in]
A COMPLEX array, dimension
(LDA,min(nq,K)) if VECT = MagmaQ
(LDA,nq) if VECT = MagmaP
The vectors which define the elementary reflectors H(i) and
G(i), whose products determine the matrices Q and P, as
returned by CGEBRD.
@param[in]
lda INTEGER
The leading dimension of the array A.
If VECT = MagmaQ, LDA >= max(1,nq);
if VECT = MagmaP, LDA >= max(1,min(nq,K)).
@param[in]
tau COMPLEX array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i) which determines Q or P, as returned
by CGEBRD in the array argument TAUQ or TAUP.
@param[in,out]
C COMPLEX array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
or P*C or P**H*C or C*P or C*P**H.
@param[in]
ldc INTEGER
The leading dimension of the array C. LDC >= max(1,M).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK.
If SIDE = MagmaLeft, LWORK >= max(1,N);
if SIDE = MagmaRight, LWORK >= max(1,M);
if N = 0 or M = 0, LWORK >= 1.
For optimum performance
if SIDE = MagmaLeft, LWORK >= max(1,N*NB);
if SIDE = MagmaRight, LWORK >= max(1,M*NB),
where NB is the optimal blocksize. (NB = 0 if M = 0 or N = 0.)
\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_cgesvd_comp
********************************************************************/
extern "C" magma_int_t
magma_cunmbr(
magma_vect_t vect, magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *C, magma_int_t ldc,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i,j) (A + (i) + (j)*lda)
#define C(i,j) (C + (i) + (j)*ldc)
magma_int_t i1, i2, nb, mi, ni, nq, nq_1, nw, iinfo, lwkopt;
magma_int_t left, notran, applyq, lquery;
magma_trans_t transt;
*info = 0;
applyq = (vect == MagmaQ);
left = (side == MagmaLeft);
notran = (trans == MagmaNoTrans);
lquery = (lwork == -1);
/* NQ is the order of Q or P and NW is the minimum dimension of WORK */
if (left) {
nq = m;
nw = n;
}
else {
nq = n;
nw = m;
}
if (m == 0 || n == 0) {
nw = 0;
}
/* check arguments */
if (! applyq && vect != MagmaP) {
*info = -1;
}
else if (! left && side != MagmaRight) {
*info = -2;
}
else if (! notran && trans != Magma_ConjTrans) {
*info = -3;
}
else if (m < 0) {
*info = -4;
}
else if (n < 0) {
*info = -5;
}
else if (k < 0) {
*info = -6;
}
else if ( ( applyq && lda < max(1,nq) ) ||
( ! applyq && lda < max(1,min(nq,k)) ) ) {
*info = -8;
}
else if (ldc < max(1,m)) {
*info = -11;
}
else if (lwork < max(1,nw) && ! lquery) {
*info = -13;
}
if (*info == 0) {
if (nw > 0) {
// TODO have get_cunmqr_nb and get_cunmlq_nb routines? see original LAPACK cunmbr.
// TODO make them dependent on m, n, and k?
nb = magma_get_cgebrd_nb( min( m, n ));
lwkopt = max(1, nw*nb);
}
else {
lwkopt = 1;
}
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0) {
return *info;
}
if (applyq) {
/* Apply Q */
if (nq >= k) {
/* Q was determined by a call to CGEBRD with nq >= k */
#if VERSION == 1
lapackf77_cunmqr( lapack_side_const(side), lapack_trans_const(trans),
&m, &n, &k, A, &lda, tau, C, &ldc, work, &lwork, &iinfo);
#else
magma_cunmqr( side, trans,
m, n, k, A, lda, tau, C, ldc, work, lwork, &iinfo);
#endif
}
else if (nq > 1) {
/* Q was determined by a call to CGEBRD with nq < k */
if (left) {
mi = m - 1;
ni = n;
i1 = 1;
i2 = 0;
}
else {
mi = m;
ni = n - 1;
i1 = 0;
i2 = 1;
}
nq_1 = nq - 1;
#if VERSION == 1
lapackf77_cunmqr( lapack_side_const(side), lapack_trans_const(trans),
&mi, &ni, &nq_1, A(1,0), &lda, tau, C(i1,i2), &ldc, work, &lwork, &iinfo);
#else
magma_cunmqr( side, trans,
mi, ni, nq-1, A(1,0), lda, tau, C(i1,i2), ldc, work, lwork, &iinfo);
#endif
}
}
else {
/* Apply P */
if (notran) {
transt = Magma_ConjTrans;
}
else {
transt = MagmaNoTrans;
}
if (nq > k) {
/* P was determined by a call to CGEBRD with nq > k */
#if VERSION == 1
lapackf77_cunmlq( lapack_side_const(side), lapack_trans_const(transt),
&m, &n, &k, A, &lda, tau, C, &ldc, work, &lwork, &iinfo);
#else
magma_cunmlq( side, transt,
m, n, k, A, lda, tau, C, ldc, work, lwork, &iinfo);
#endif
}
else if (nq > 1) {
/* P was determined by a call to CGEBRD with nq <= k */
if (left) {
mi = m - 1;
ni = n;
i1 = 1;
i2 = 0;
}
else {
mi = m;
ni = n - 1;
i1 = 0;
i2 = 1;
}
nq_1 = nq - 1;
#if VERSION == 1
lapackf77_cunmlq( lapack_side_const(side), lapack_trans_const(transt),
&mi, &ni, &nq_1, A(0,1), &lda, tau, C(i1,i2), &ldc, work, &lwork, &iinfo);
#else
magma_cunmlq( side, transt,
mi, ni, nq-1, A(0,1), lda, tau, C(i1,i2), ldc, work, lwork, &iinfo);
#endif
}
}
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
return *info;
} /* magma_cunmbr */
/* ////////////////////////////////////////////////////////////////////////////
-- Testing cunmlq
*/
int main( int argc, char** argv )
{
TESTING_INIT();
real_Double_t gflops, gpu_perf, gpu_time, cpu_perf, cpu_time;
float Cnorm, error, work[1];
magmaFloatComplex c_neg_one = MAGMA_C_NEG_ONE;
magma_int_t ione = 1;
magma_int_t mm, m, n, k, size, info;
magma_int_t ISEED[4] = {0,0,0,1};
magma_int_t nb, ldc, lda, lwork, lwork_max;
magmaFloatComplex *C, *R, *A, *W, *tau;
magma_int_t status = 0;
magma_opts opts;
opts.parse_opts( argc, argv );
// need slightly looser bound (60*eps instead of 30*eps) for some tests
opts.tolerance = max( 60., opts.tolerance );
float tol = opts.tolerance * lapackf77_slamch("E");
// test all combinations of input parameters
magma_side_t side [] = { MagmaLeft, MagmaRight };
magma_trans_t trans[] = { Magma_ConjTrans, MagmaNoTrans };
printf("%% M N K side trans CPU Gflop/s (sec) GPU Gflop/s (sec) ||R||_F / ||QC||_F\n");
printf("%%==============================================================================================\n");
for( int itest = 0; itest < opts.ntest; ++itest ) {
for( int iside = 0; iside < 2; ++iside ) {
for( int itran = 0; itran < 2; ++itran ) {
for( int iter = 0; iter < opts.niter; ++iter ) {
m = opts.msize[itest];
n = opts.nsize[itest];
k = opts.ksize[itest];
nb = magma_get_cgelqf_nb( m, n );
ldc = m;
// A is k x m (left) or k x n (right)
mm = (side[iside] == MagmaLeft ? m : n);
lda = k;
gflops = FLOPS_CUNMLQ( m, n, k, side[iside] ) / 1e9;
if ( side[iside] == MagmaLeft && m < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=left and m < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
if ( side[iside] == MagmaRight && n < k ) {
printf( "%5d %5d %5d %4c %5c skipping because side=right and n < k\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ) );
continue;
}
// need at least 2*nb*nb for gelqf
lwork_max = max( max( m*nb, n*nb ), 2*nb*nb );
// this rounds it up slightly if needed to agree with lwork query
lwork_max = int( real( magma_cmake_lwork( lwork_max )));
TESTING_MALLOC_CPU( C, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( R, magmaFloatComplex, ldc*n );
TESTING_MALLOC_CPU( A, magmaFloatComplex, lda*mm );
TESTING_MALLOC_CPU( W, magmaFloatComplex, lwork_max );
TESTING_MALLOC_CPU( tau, magmaFloatComplex, k );
// C is full, m x n
size = ldc*n;
lapackf77_clarnv( &ione, ISEED, &size, C );
lapackf77_clacpy( "Full", &m, &n, C, &ldc, R, &ldc );
size = lda*mm;
lapackf77_clarnv( &ione, ISEED, &size, A );
// compute LQ factorization to get Householder vectors in A, tau
magma_cgelqf( k, mm, A, lda, tau, W, lwork_max, &info );
if (info != 0) {
printf("magma_cgelqf returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
Performs operation using LAPACK
=================================================================== */
cpu_time = magma_wtime();
lapackf77_cunmlq( lapack_side_const( side[iside] ), lapack_trans_const( trans[itran] ),
&m, &n, &k,
A, &lda, tau, C, &ldc, W, &lwork_max, &info );
cpu_time = magma_wtime() - cpu_time;
cpu_perf = gflops / cpu_time;
if (info != 0) {
printf("lapackf77_cunmlq returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* ====================================================================
Performs operation using MAGMA
=================================================================== */
// query for workspace size
lwork = -1;
magma_cunmlq( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
if (info != 0) {
printf("magma_cunmlq (lwork query) returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
lwork = (magma_int_t) MAGMA_C_REAL( W[0] );
if ( lwork < 0 || lwork > lwork_max ) {
printf("Warning: optimal lwork %d > allocated lwork_max %d\n", (int) lwork, (int) lwork_max );
lwork = lwork_max;
}
gpu_time = magma_wtime();
magma_cunmlq( side[iside], trans[itran],
m, n, k,
A, lda, tau, R, ldc, W, lwork, &info );
gpu_time = magma_wtime() - gpu_time;
gpu_perf = gflops / gpu_time;
if (info != 0) {
printf("magma_cunmlq returned error %d: %s.\n",
(int) info, magma_strerror( info ));
}
/* =====================================================================
compute relative error |QC_magma - QC_lapack| / |QC_lapack|
=================================================================== */
size = ldc*n;
blasf77_caxpy( &size, &c_neg_one, C, &ione, R, &ione );
Cnorm = lapackf77_clange( "Fro", &m, &n, C, &ldc, work );
error = lapackf77_clange( "Fro", &m, &n, R, &ldc, work ) / (magma_ssqrt(m*n) * Cnorm);
printf( "%5d %5d %5d %4c %5c %7.2f (%7.2f) %7.2f (%7.2f) %8.2e %s\n",
(int) m, (int) n, (int) k,
lapacke_side_const( side[iside] ),
lapacke_trans_const( trans[itran] ),
cpu_perf, cpu_time, gpu_perf, gpu_time,
error, (error < tol ? "ok" : "failed") );
status += ! (error < tol);
TESTING_FREE_CPU( C );
TESTING_FREE_CPU( R );
TESTING_FREE_CPU( A );
TESTING_FREE_CPU( W );
TESTING_FREE_CPU( tau );
fflush( stdout );
}
if ( opts.niter > 1 ) {
printf( "\n" );
}
}} // end iside, itran
printf( "\n" );
}
opts.cleanup();
TESTING_FINALIZE();
return status;
}
/**
Purpose
-------
CUNMLQ overwrites the general complex M-by-N matrix C with
@verbatim
SIDE = MagmaLeft SIDE = MagmaRight
TRANS = MagmaNoTrans: Q * C C * Q
TRANS = Magma_ConjTrans: Q**H * C C * Q**H
@endverbatim
where Q is a complexunitary matrix defined as the product of k
elementary reflectors
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by CGELQF. Q is of order M if SIDE = MagmaLeft and of order N
if SIDE = MagmaRight.
Arguments
---------
@param[in]
side magma_side_t
- = MagmaLeft: apply Q or Q**H from the Left;
- = MagmaRight: apply Q or Q**H from the Right.
@param[in]
trans magma_trans_t
- = MagmaNoTrans: No transpose, apply Q;
- = Magma_ConjTrans: Conjugate transpose, apply Q**H.
@param[in]
m INTEGER
The number of rows of the matrix C. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix C. N >= 0.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines
the matrix Q.
If SIDE = MagmaLeft, M >= K >= 0;
if SIDE = MagmaRight, N >= K >= 0.
@param[in]
A COMPLEX array, dimension
(LDA,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
CGELQF 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 COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGELQF.
@param[in,out]
C COMPLEX array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
@param[in]
ldc INTEGER
The leading dimension of the array C. LDC >= max(1,M).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK.
If SIDE = MagmaLeft, LWORK >= max(1,N);
if SIDE = MagmaRight, LWORK >= max(1,M).
For optimum performance
if SIDE = MagmaLeft, LWORK >= N*NB;
if SIDE = MagmaRight, LWORK >= M*NB,
where NB is the optimal blocksize.
\n
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_cgelqf_comp
********************************************************************/
extern "C" magma_int_t
magma_cunmlq(
magma_side_t side, magma_trans_t trans,
magma_int_t m, magma_int_t n, magma_int_t k,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *C, magma_int_t ldc,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dC(i_,j_) (dC + (i_) + (j_)*lddc)
#define dV(i_,j_) (dV + (i_) + (j_)*ib)
#define dT(i_,j_) (dT + (i_) + (j_)*ib)
#define dwork(i_) (dwork + (i_))
magmaFloatComplex *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 != Magma_ConjTrans) {
*info = -2;
} else if (m < 0) {
*info = -3;
} else if (n < 0) {
*info = -4;
} else if (k < 0 || k > nq) {
*info = -5;
} else if (lda < max(1,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_cgelqf_nb( min( m, n ));
lwkopt = max(1,nw)*nb;
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (m == 0 || n == 0 || k == 0) {
work[0] = MAGMA_C_ONE;
return *info;
}
ldwork = nw;
if (nb >= k) {
/* Use CPU code */
lapackf77_cunmlq( 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;
magmaFloatComplex_ptr dwork, dV, dT, dC;
magma_cmalloc( &dwork, (nw + nq + nb)*nb + lddc*n );
if ( dwork == NULL ) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
dV = dwork + nw*nb;
dT = dV + nq*nb;
dC = dT + nb*nb;
/* work space on CPU.
* nb*nb for T
* nb*nb for T2, used to save and restore diagonal block of panel */
magma_cmalloc_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_csetmatrix( m, n, C, ldc, dC(0,0), 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 = Magma_ConjTrans;
} 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_clarft("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 */
cpanel_to_q( MagmaLower, ib, A(i,i), lda, T2 );
magma_csetmatrix( ib, nq_i, A(i,i), lda, dV(0,0), ib );
cq_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_csetmatrix( ib, ib, T, ib, dT(0,0), ib );
magma_clarfb_gpu( side, transt, MagmaForward, MagmaRowwise,
mi, ni, ib,
dV(0,0), ib,
dT(0,0), ib,
dC(ic,jc), lddc,
dwork(0), ldwork );
}
magma_cgetmatrix( m, n, dC(0,0), lddc, C, ldc );
magma_free( dwork );
magma_free_cpu( T );
}
work[0] = MAGMA_C_MAKE( lwkopt, 0 );
return *info;
} /* magma_cunmlq */
