/* ////////////////////////////////////////////////////////////////////////////
-- 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
-------
CGELQF computes an LQ factorization of a COMPLEX M-by-N matrix A:
A = L * Q.
Arguments
---------
@param[in]
m INTEGER
The number of rows of the matrix A. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix A. N >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
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 COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
@param[out]
work (workspace) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK[0] returns the optimal LWORK.
\n
Higher performance is achieved if WORK is in pinned memory, e.g.
allocated using magma_malloc_pinned.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= max(1,M).
For optimum performance 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.
@param[out]
info INTEGER
- = 0: successful exit
- < 0: if INFO = -i, the i-th argument had an illegal value
if INFO = -10 internal GPU 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 complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).
@ingroup magma_cgelqf_comp
********************************************************************/
extern "C" magma_int_t
magma_cgelqf( magma_int_t m, magma_int_t n,
magmaFloatComplex *A, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info)
{
magmaFloatComplex *dA, *dAT;
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t maxm, maxn, maxdim, nb;
magma_int_t iinfo, ldda;
int lquery;
/* Function Body */
*info = 0;
nb = magma_get_cgelqf_nb(m);
work[0] = MAGMA_C_MAKE( (float)(m*nb), 0 );
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,m) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (min(m, n) == 0) {
work[0] = c_one;
return *info;
}
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
maxdim = max(maxm, maxn);
if (maxdim*maxdim < 2*maxm*maxn) {
ldda = maxdim;
if (MAGMA_SUCCESS != magma_cmalloc( &dA, maxdim*maxdim )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_csetmatrix( m, n, A, lda, dA, ldda );
dAT = dA;
magmablas_ctranspose_inplace( ldda, dAT, ldda );
}
else {
ldda = maxn;
if (MAGMA_SUCCESS != magma_cmalloc( &dA, 2*maxn*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_csetmatrix( m, n, A, lda, dA, maxm );
dAT = dA + maxn * maxm;
magmablas_ctranspose( m, n, dA, maxm, dAT, ldda );
}
magma_cgeqrf2_gpu(n, m, dAT, ldda, tau, &iinfo);
if (maxdim*maxdim < 2*maxm*maxn) {
magmablas_ctranspose_inplace( ldda, dAT, ldda );
magma_cgetmatrix( m, n, dA, ldda, A, lda );
} else {
magmablas_ctranspose( n, m, dAT, ldda, dA, maxm );
magma_cgetmatrix( m, n, dA, maxm, A, lda );
}
magma_free( dA );
return *info;
} /* magma_cgelqf */
/**
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 */
extern "C" magma_int_t
magma_cgelqf( magma_int_t m, magma_int_t n,
magmaFloatComplex *a, magma_int_t lda, magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork, magma_int_t *info)
{
/* -- MAGMA (version 1.4.0) --
Univ. of Tennessee, Knoxville
Univ. of California, Berkeley
Univ. of Colorado, Denver
August 2013
Purpose
=======
CGELQF computes an LQ factorization of a COMPLEX M-by-N matrix A:
A = L * Q.
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) COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and below the diagonal of the array
contain the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
with the array TAU, represent the orthogonal matrix Q as a
product of 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) COMPLEX array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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(1,M).
For optimum performance LWORK >= M*NB, where NB is the
optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
if INFO = -10 internal GPU 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 complex scalar, and v is a complex vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).
===================================================================== */
#define a_ref(a_1,a_2) ( a+(a_2)*(lda) + (a_1))
magmaFloatComplex *dA, *dAT;
magmaFloatComplex c_one = MAGMA_C_ONE;
magma_int_t maxm, maxn, maxdim, nb;
magma_int_t iinfo, ldda;
int lquery;
/* Function Body */
*info = 0;
nb = magma_get_cgelqf_nb(m);
work[0] = MAGMA_C_MAKE( (float)(m*nb), 0 );
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,m) && ! lquery) {
*info = -7;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
/* Quick return if possible */
if (min(m, n) == 0) {
work[0] = c_one;
return *info;
}
maxm = ((m + 31)/32)*32;
maxn = ((n + 31)/32)*32;
maxdim = max(maxm, maxn);
if (maxdim*maxdim < 2*maxm*maxn)
{
ldda = maxdim;
if (MAGMA_SUCCESS != magma_cmalloc( &dA, maxdim*maxdim )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_csetmatrix( m, n, a, lda, dA, ldda );
dAT = dA;
magmablas_ctranspose_inplace( ldda, dAT, ldda );
}
else
{
ldda = maxn;
if (MAGMA_SUCCESS != magma_cmalloc( &dA, 2*maxn*maxm )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
return *info;
}
magma_csetmatrix( m, n, a, lda, dA, maxm );
dAT = dA + maxn * maxm;
magmablas_ctranspose2( dAT, ldda, dA, maxm, m, n );
}
magma_cgeqrf2_gpu(n, m, dAT, ldda, tau, &iinfo);
if (maxdim*maxdim < 2*maxm*maxn) {
magmablas_ctranspose_inplace( ldda, dAT, ldda );
magma_cgetmatrix( m, n, dA, ldda, a, lda );
} else {
magmablas_ctranspose2( dA, maxm, dAT, ldda, n, m );
magma_cgetmatrix( m, n, dA, maxm, a, lda );
}
magma_free( dA );
return *info;
} /* magma_cgelqf */
/**
Purpose:
---------
CUNGLQ generates an M-by-N complex matrix Q with orthonormal rows,
which is defined as the first M rows of a product of K elementary
reflectors of order N
Q = H(k)**H . . . H(2)**H H(1)**H
as returned by CGELQF.
Arguments:
---------
@param[in]
m INTEGER
The number of rows of the matrix Q. M >= 0.
@param[in]
n INTEGER
The number of columns of the matrix Q. N >= M.
@param[in]
k INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
@param[in,out]
A COMPLEX array, dimension (LDA,N)
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), for i = 1,2,...,k, as returned
by CGELQF in the first k rows of its array argument A.
On exit, the M-by-N matrix Q.
@param[in]
lda INTEGER
The first dimension of the array A. LDA >= max(1,M).
@param[in]
tau COMPLEX array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CGELQF.
@param[out]
work COMPLEX array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
@param[in]
lwork INTEGER
The dimension of the array WORK. LWORK >= NB*NB, where NB is
the optimal blocksize.
If LWORK = -1, a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
@param[out]
info INTEGER
- = 0: successful exit;
- < 0: if INFO = -i, the i-th argument had an illegal value
@ingroup magma_cgelqf_comp
********************************************************************/
extern "C" magma_int_t
magma_cunglq(
magma_int_t m, magma_int_t n, magma_int_t k,
magmaFloatComplex *A, magma_int_t lda,
magmaFloatComplex *tau,
magmaFloatComplex *work, magma_int_t lwork,
magma_int_t *info)
{
#define A(i_,j_) ( A + (i_) + (j_)*lda)
#define dA(i_,j_) (dA + (i_) + (j_)*ldda)
#define tau(i_) (tau + (i_))
// Constants
const magmaFloatComplex c_zero = MAGMA_C_ZERO;
const magmaFloatComplex c_one = MAGMA_C_ONE;
// Local variables
bool lquery;
magma_int_t i, ib, ki, ldda, lddwork, lwkopt, mib, nb, n_i;
magma_queue_t queue = NULL;
magmaFloatComplex_ptr dA = NULL;
magmaFloatComplex* work2 = NULL;
// Test the input arguments
*info = 0;
nb = magma_get_cgelqf_nb( m, n );
lwkopt = nb*nb;
work[0] = magma_cmake_lwork( lwkopt );
lquery = (lwork == -1);
if (m < 0) {
*info = -1;
} else if (n < 0 || n < m) {
*info = -2;
} else if (k < 0 || k > m) {
*info = -3;
} else if (lda < max( 1, m )) {
*info = -5;
} else if (lwork < max( 1, lwkopt ) && ! lquery) {
*info = -8;
//printf( "m %d, n %d, nb %d: lwork %d, required %d\n", m, n, nb, lwork, lwkopt );
//*info = 0;
}
if (*info != 0) {
magma_xerbla( __func__, -(*info) );
return *info;
}
else if (lquery) {
return *info;
}
// Quick return if possible
if (m <= 0) {
work[0] = c_one;
return *info;
}
//if (lwork < lwkopt) {
// magma_cmalloc_cpu( &work2, lwkopt );
//}
//else {
// work2 = work;
//}
work2 = work;
// Allocate GPU work space
// ldda*n for matrix dA
// nb*n for dV
// lddwork*nb for dW larfb workspace
ldda = magma_roundup( m, 32 );
lddwork = magma_roundup( m, 32 );
if (MAGMA_SUCCESS != magma_cmalloc( &dA, ldda*n + n*nb + lddwork*nb + nb*nb )) {
*info = MAGMA_ERR_DEVICE_ALLOC;
goto cleanup;
}
magmaFloatComplex_ptr dV; dV = dA + ldda*n;
magmaFloatComplex_ptr dW; dW = dA + ldda*n + n*nb;
magmaFloatComplex_ptr dT; dT = dA + ldda*n + n*nb + lddwork*nb;
magma_device_t cdev;
magma_getdevice( &cdev );
magma_queue_create( cdev, &queue );
magmablas_claset( MagmaFull, m, n, MAGMA_C_NAN, MAGMA_C_NAN, dA, ldda, queue );
// all columns are handled by blocked method.
// ki is start of last (partial) block
ki = ((k - 1) / nb) * nb;
// Use blocked code
for( i=ki; i >= 0; i -= nb ) {
ib = min( nb, k-i );
// first block has extra rows to update
mib = ib;
if ( i == ki ) {
mib = m - i;
}
// Send current panel of V (block row) to the GPU
lapackf77_claset( "Lower", &ib, &ib, &c_zero, &c_one, A(i,i), &lda );
// TODO: having this _async was causing numerical errors. Why?
magma_csetmatrix( ib, n-i,
A(i,i), lda,
dV, nb, queue );
// Form the triangular factor of the block reflector
// H = H(i) H(i+1) . . . H(i+ib-1)
n_i = n - i;
lapackf77_clarft( MagmaForwardStr, MagmaRowwiseStr, &n_i, &ib,
A(i,i), &lda, &tau[i], work2, &nb );
magma_csetmatrix_async( ib, ib,
work2, nb,
dT, nb, queue );
// set panel of A (block row) to identity
magmablas_claset( MagmaFull, mib, i, c_zero, c_zero, dA(i,0), ldda, queue );
magmablas_claset( MagmaFull, mib, n-i, c_zero, c_one, dA(i,i), ldda, queue );
if (i < m) {
// Apply H**H to A(i:m,i:n) from the right
magma_clarfb_gpu( MagmaRight, MagmaConjTrans, MagmaForward, MagmaRowwise,
m-i, n-i, ib,
dV, nb, dT, nb,
dA(i,i), ldda, dW, lddwork, queue );
}
}
// copy result back to CPU
magma_cgetmatrix( m, n,
dA(0,0), ldda, A(0,0), lda, queue );
cleanup:
magma_queue_destroy( queue );
magma_free( dA );
//if (work2 != work) {
// magma_free_cpu( work2 );
//}
work[0] = magma_cmake_lwork( lwkopt );
return *info;
}
